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Diffstat (limited to 'circuitpython/extmod/ulab')
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diff --git a/circuitpython/extmod/ulab/.readthedocs.yaml b/circuitpython/extmod/ulab/.readthedocs.yaml new file mode 100644 index 0000000..80bd461 --- /dev/null +++ b/circuitpython/extmod/ulab/.readthedocs.yaml @@ -0,0 +1,25 @@ +# .readthedocs.yaml +# Read the Docs configuration file +# See https://docs.readthedocs.io/en/stable/config-file/v2.html for details + +# Required +version: 2 + +# Set the version of Python and other tools you might need +build: + os: ubuntu-20.04 + tools: + python: "3.9" + +# Build documentation in the docs/ directory with Sphinx +sphinx: + configuration: docs/manual/source/conf.py + +# If using Sphinx, optionally build your docs in additional formats such as PDF +# formats: +# - pdf + +# Optionally declare the Python requirements required to build your docs +python: + install: + - requirements: requirements.txt diff --git a/circuitpython/extmod/ulab/CONTRIBUTING.md b/circuitpython/extmod/ulab/CONTRIBUTING.md new file mode 100644 index 0000000..edfdc7a --- /dev/null +++ b/circuitpython/extmod/ulab/CONTRIBUTING.md @@ -0,0 +1,17 @@ +Contributions of any kind are always welcome. + +# Contributing to the code base + +If you feel like adding to the code, you can simply issue a pull request. If you do so, please, try to adhere to `micropython`'s [coding conventions](https://github.com/micropython/micropython/blob/master/CODECONVENTIONS.md#c-code-conventions). + +# Documentation + +However, you can also contribute to the documentation (preferably via the [jupyter notebooks](https://github.com/v923z/micropython-ulab/tree/master/docs). + +## Testing + +If you decide to lend a hand with testing, here are the steps: + +1. Write a test script that checks a particular function, or a set of related functions! +1. Drop this script in one of the folders in [ulab tests](https://github.com/v923z/micropython-ulab/tree/master/tests)! +1. Run the [./build.sh](https://github.com/v923z/micropython-ulab/blob/master/build.sh) script in the root directory of `ulab`! This will clone the latest `micropython`, compile the firmware for `unix`, execute all scripts in the `ulab/tests`, and compare the results to those in the expected results files, which are also in `ulab/tests`, and have an extension `.exp`. In case you have a new snippet, i.e., you have no expected results file, or if the results differ from those in the expected file, a new expected file will be generated in the root directory. You should inspect the contents of this file, and if they are satisfactory, then the file can be moved to the `ulab/tests` folder, alongside your snippet. diff --git a/circuitpython/extmod/ulab/LICENSE b/circuitpython/extmod/ulab/LICENSE new file mode 100644 index 0000000..1d4df66 --- /dev/null +++ b/circuitpython/extmod/ulab/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2019 Zoltán Vörös + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/circuitpython/extmod/ulab/README.md b/circuitpython/extmod/ulab/README.md new file mode 100644 index 0000000..7112cad --- /dev/null +++ b/circuitpython/extmod/ulab/README.md @@ -0,0 +1,450 @@ +# ulab + +[](https://micropython-ulab-robert.readthedocs.io/en/latest/?badge=latest) + +`ulab` is a `numpy`-like array manipulation library for [micropython](http://micropython.org/) and [CircuitPython](https://circuitpython.org/). +The module is written in C, defines compact containers (`ndarray`s) for numerical data of one to four +dimensions, and is fast. The library is a software-only standard `micropython` user module, +i.e., it has no hardware dependencies, and can be compiled for any platform. 8-, and 16-bit signed +and unsigned integer `dtypes`, as well as `float`, and, optionally, ` complex` are supported. +The `float` implementation of `micropython` (32-bit `float`, or 64-bit `double`) is automatically +detected and handled. + +1. [Supported functions and methods](#supported-functions-and-methods) + 1. [ndarray methods](#ndarray-methods) + 2. [numpy and scipy functions](#numpy-and-scipy-functions) + 3. [ulab utilities](#ulab-utilities) + 4. [user module](#user-module) +3. [Customising the firmware](#customising-the-firmware) +4. [Usage](#usage) +5. [Finding help](#finding-help) +6. [Benchmarks](#benchmarks) +7. [Firmware](#firmware) + 1. [UNIX](#unix-port) + 1. [STM-based boards](#stm-based-boards) + 1. [ESP32-based boards](#esp32-based-boards) + 1. [RP2-based boards](#rp2-based-boards) + 1. [Compiling for CircuitPython](#compiling-for-circuitpython) +8. [Issues, contributing, and testing](#issues-contributing-and-testing) + 1. [Testing](#testing) + +# Supported functions and methods + + +## ndarray methods + +`ulab` implements `numpy`'s `ndarray` with the `==`, `!=`, `<`, `<=`, `>`, `>=`, `+`, `-`, `/`, `*`, `**`, +`+=`, `-=`, `*=`, `/=`, `**=` binary operators, and the `len`, `~`, `-`, `+`, `abs` unary operators that +operate element-wise. Type-aware `ndarray`s can be initialised from any `micropython` iterable, lists of +iterables via the `array` constructor, or by means of the `arange`, `concatenate`, `diag`, `eye`, +`frombuffer`, `full`, `linspace`, `logspace`, `ones`, or `zeros` functions. + +`ndarray`s can be sliced, and iterated on, and have a number of their own methods, and properties, such as `flatten()`, `itemsize`, `reshape()`, +`shape`, `size`, `strides`, `tobytes()`, `tolist()`, and `transpose()` and `T`. If the firmware is compiled with `complex` support, +the `imag`, and `real` properties are automatically included. + +## `numpy` and `scipy` functions + +In addition, `ulab` includes [universal functions](https://micropython-ulab.readthedocs.io/en/latest/numpy-universal.html), [many `numpy` functions](https://micropython-ulab.readthedocs.io/en/latest/numpy-functions.html), and functions from the [`numpy.fft`](https://micropython-ulab.readthedocs.io/en/latest/numpy-fft.html), [`numpy.linalg`](https://micropython-ulab.readthedocs.io/en/latest/numpy-linalg.html), [`scipy.linalg`](https://micropython-ulab.readthedocs.io/en/latest/scipy-linalg.html), [`scipy.optimize`](https://micropython-ulab.readthedocs.io/en/latest/scipy-optimize.html), [`scipy.signal`](https://micropython-ulab.readthedocs.io/en/latest/scipy-signal.html), and [`scipy.special`](https://micropython-ulab.readthedocs.io/en/latest/scipy-special.html) modules. A complete list of available routines can be found under [micropython-ulab](https://micropython-ulab.readthedocs.io/en/latest). + +## `ulab` utilities + +The [`utils`](https://micropython-ulab.readthedocs.io/en/latest/ulab-utils.html) module contains functions for +interfacing with peripheral devices supporting the buffer protocol. These functions do not have an obvious +`numpy` equivalent, but share a similar programming interface, and allow direct data input-output between +numerical arrays and hardware components. + +## `user` module + +User-defined functions operating on numerical data can easily be added via the `user` module. This allows for transparent extensions, without having to change anything in the core. Hints as to how to work with `ndarray`s at the C level can be found in the [programming manual](https://micropython-ulab.readthedocs.io/en/latest/ulab-programming.html). + +# Customising the firmware + +If flash space is a concern, unnecessary functions can be excluded from the compiled firmware with +pre-processor switches. In addition, `ulab` also has options for trading execution speed for firmware size. +A thorough discussion on how the firmware can be customised can be found in the +[corresponding section](https://micropython-ulab.readthedocs.io/en/latest/ulab-intro.html#customising-the-firmware) +of the user manual. + +# Usage + +`ulab` sports a `numpy/scipy`-compatible interface, which makes porting of `CPython` code straightforward. The following +snippet should run equally well in `micropython`, or on a PC. + +```python +try: + from ulab import numpy + from ulab import scipy +except ImportError: + import numpy + import scipy.special + +x = numpy.array([1, 2, 3]) +scipy.special.erf(x) +``` + +# Finding help + +Documentation can be found on [readthedocs](https://readthedocs.org/) under +[micropython-ulab](https://micropython-ulab.readthedocs.io/en/latest), +as well as at [circuitpython-ulab](https://circuitpython.readthedocs.io/en/latest/shared-bindings/ulab/__init__.html). +A number of practical examples are listed in Jeff Epler's excellent +[circuitpython-ulab](https://learn.adafruit.com/ulab-crunch-numbers-fast-with-circuitpython/overview) overview. +The [tricks](https://micropython-ulab.readthedocs.io/en/latest/ulab-tricks.html) chapter of the user manual discusses +methods by which RAM and speed can be leveraged in particular numerical problems. + +# Benchmarks + +Representative numbers on performance can be found under [ulab samples](https://github.com/thiagofe/ulab_samples). + +# Firmware + +## Compiled + +Compiled firmware for many hardware platforms can be downloaded from Roberto Colistete's +gitlab repository: for the [pyboard](https://gitlab.com/rcolistete/micropython-samples/-/tree/master/Pyboard/Firmware/), and +for [ESP8266](https://gitlab.com/rcolistete/micropython-samples/-/tree/master/ESP8266/Firmware). +Since a number of features can be set in the firmware (threading, support for SD card, LEDs, user switch etc.), and it is +impossible to create something that suits everyone, these releases should only be used for +quick testing of `ulab`. Otherwise, compilation from the source is required with +the appropriate settings, which are usually defined in the `mpconfigboard.h` file of the port +in question. + +`ulab` is also included in the following compiled `micropython` variants and derivatives: + +1. `CircuitPython` for SAMD51 and nRF microcontrollers https://github.com/adafruit/circuitpython +1. `MicroPython for K210` https://github.com/loboris/MicroPython_K210_LoBo +1. `MaixPy` https://github.com/sipeed/MaixPy +1. `OpenMV` https://github.com/openmv/openmv +1. `pimoroni-pico` https://github.com/pimoroni/pimoroni-pico +3. `pycom` https://pycom.io/ + +## Compiling + +If you want to try the latest version of `ulab` on `micropython` or one of its forks, the firmware can be compiled +from the source by following these steps: + +### UNIX port + +Simply clone the `ulab` repository with + +```bash +git clone https://github.com/v923z/micropython-ulab.git ulab +``` +and then run + +```bash +./build.sh +``` +This command will clone `micropython`, and build the `unix` port automatically, as well as run the test scripts. If you want an interactive `unix` session, you can launch it in + +```bash +ulab/micropython/ports/unix +``` + +### STM-based boards + +First, you have to clone the `micropython` repository by running + +```bash +git clone https://github.com/micropython/micropython.git +``` +on the command line. This will create a new repository with the name `micropython`. Staying there, clone the `ulab` repository with + +```bash +git clone https://github.com/v923z/micropython-ulab.git ulab +``` +If you don't have the cross-compiler installed, your might want to do that now, for instance on Linux by executing + +```bash +sudo apt-get install gcc-arm-none-eabi +``` + +If this step was successful, you can try to run the `make` command in the port's directory as + +```bash +make BOARD=PYBV11 USER_C_MODULES=../../../ulab all +``` +which will prepare the firmware for pyboard.v.11. Similarly, + +```bash +make BOARD=PYBD_SF6 USER_C_MODULES=../../../ulab all +``` +will compile for the SF6 member of the PYBD series. If your target is `unix`, you don't need to specify the `BOARD` parameter. + +Provided that you managed to compile the firmware, you would upload that by running either + +```bash +dfu-util --alt 0 -D firmware.dfu +``` +or + +```bash +python pydfu.py -u firmware.dfu +``` + +In case you got stuck somewhere in the process, a bit more detailed instructions can be found under https://github.com/micropython/micropython/wiki/Getting-Started, and https://github.com/micropython/micropython/wiki/Pyboard-Firmware-Update. + + +### ESP32-based boards + +Firmware for `Espressif` boards can be built in two different ways. These are discussed in the next two paragraphs. A solution for issues with the firmware size is outlined in the [last paragraph](#what-to-do-if-the-firmware-is-too-large) in this section. + +#### Compiling with cmake + +Beginning with version 1.15, `micropython` switched to `cmake` on the ESP32 port. If your operating system supports `CMake > 3.12`, you can either simply download, and run the single [build script](https://github.com/v923z/micropython-ulab/blob/master/build/esp32-cmake.sh), or follow the step in this section. Otherwise, you should skip to the [next one](#compiling-with-make), where the old, `make`-based approach is discussed. + +In case you encounter difficulties during the build process, you can consult the (general instructions for the ESP32)[https://github.com/micropython/micropython/tree/master/ports/esp32#micropython-port-to-the-esp32]. + +First, clone the `ulab`, the `micropython`, as well as the `espressif` repositories: + +```bash +export BUILD_DIR=$(pwd) + +git clone https://github.com/v923z/micropython-ulab.git ulab +git clone https://github.com/micropython/micropython.git + +cd $BUILD_DIR/micropython/ + +git clone -b v4.0.2 --recursive https://github.com/espressif/esp-idf.git + +``` +Also later releases of `esp-idf` are possible (e.g. `v4.2.1`). + +Then install the `ESP-IDF` tools: + +```bash +cd esp-idf +./install.sh +. ./export.sh +``` + +Next, build the `micropython` cross-compiler, and the `ESP` sub-modules: + +```bash +cd $BUILD_DIR/micropython/mpy-cross +make +cd $BUILD_DIR/micropython/ports/esp32 +make submodules +``` +At this point, all requirements are installed and built. We can now compile the firmware with `ulab`. In `$BUILD_DIR/micropython/ports/esp32` create a `makefile` with the following content: + +```bash +BOARD = GENERIC +USER_C_MODULES = $(BUILD_DIR)/ulab/code/micropython.cmake + +include Makefile +``` +You specify with the `BOARD` variable, what you want to compile for, a generic board, or `TINYPICO` (for `micropython` version >1.1.5, use `UM_TINYPICO`), etc. Still in `$BUILD_DIR/micropython/ports/esp32`, you can now run `make`. + +#### Compiling with make + +If your operating system does not support a recent enough version of `CMake`, you have to stay with `micropython` version 1.14. The firmware can be compiled either by downloading and running the [build script](https://github.com/v923z/micropython-ulab/blob/master/build/esp32.sh), or following the steps below: + +First, clone `ulab` with + +```bash +git clone https://github.com/v923z/micropython-ulab.git ulab +``` + +and then, in the same directory, `micropython` + +```bash +git clone https://github.com/micropython/micropython.git +``` + +At this point, you should have `ulab`, and `micropython` side by side. + +With version 1.14, `micropython` switched to `cmake` on the `ESP32` port, thus breaking compatibility with user modules. `ulab` can, however, still be compiled with version 1.14. You can check out a particular version by pinning the release tag as + +```bash + +cd ./micropython/ +git checkout tags/v1.14 + +``` +Next, update the submodules, + +```bash +git submodule update --init +cd ./mpy-cross && make # build cross-compiler (required) +``` +and find the ESP commit hash + +```bash +cd ./micropython/ports/esp32 +make ESPIDF= # will display supported ESP-IDF commit hashes +# output should look like: """ +# ... +# Supported git hash (v3.3): 9e70825d1e1cbf7988cf36981774300066580ea7 +# Supported git hash (v4.0) (experimental): 4c81978a3e2220674a432a588292a4c860eef27b +``` + +Choose an ESPIDF version from one of the options printed by the previous command: + +```bash +ESPIDF_VER=9e70825d1e1cbf7988cf36981774300066580ea7 +``` + +In the `micropython` directory, create a new directory with +```bash +mkdir esp32 +``` +Your `micropython` directory should now look like + +```bash +ls +ACKNOWLEDGEMENTS CONTRIBUTING.md esp32 lib mpy-cross README.md +CODECONVENTIONS.md docs examples LICENSE ports tests +CODEOFCONDUCT.md drivers extmod logo py tools +``` + +In `./micropython/esp32`, download the software development kit with + +```bash +git clone https://github.com/espressif/esp-idf.git esp-idf +cd ./esp-idf +git checkout $ESPIDF_VER +git submodule update --init --recursive # get idf submodules +pip install -r ./requirements.txt # install python reqs +``` + +Next, still staying in `./micropython/eps32/esd-idf/`, install the ESP32 compiler. If using an ESP-IDF version >= 4.x (chosen by `$ESPIDF_VER` above), this can be done by running `. $BUILD_DIR/esp-idf/install.sh`. Otherwise, for version 3.x, run the following commands in in `.micropython/esp32/esp-idf`: + +```bash +# for 64 bit linux +curl https://dl.espressif.com/dl/xtensa-esp32-elf-linux64-1.22.0-80-g6c4433a-5.2.0.tar.gz | tar xvz + +# for 32 bit +# curl https://dl.espressif.com/dl/xtensa-esp32-elf-linux32-1.22.0-80-g6c4433a-5.2.0.tar.gz | tar xvz + +# don't worry about adding to path; we'll specify that later + +# also, see https://docs.espressif.com/projects/esp-idf/en/v3.3.2/get-started for more info +``` + +Finally, build the firmware: + +```bash +cd ./micropython/ports/esp32 +# temporarily add esp32 compiler to path +export PATH=../../esp32/esp-idf/xtensa-esp32-elf/bin:$PATH +export ESPIDF=../../esp32/esp-idf # req'd by Makefile +export BOARD=GENERIC # options are dirs in ./boards +export USER_C_MODULES=../../../ulab # include ulab in firmware + +make submodules & make all +``` + +If it compiles without error, you can plug in your ESP32 via USB and then flash it with: + +```bash +make erase && make deploy +``` + +#### What to do, if the firmware is too large? + +When selecting `BOARD=TINYPICO`, the firmware is built but fails to deploy, because it is too large for the standard partitions. We can rectify the problem by creating a new partition table. In order to do so, in `$BUILD_DIR/micropython/ports/esp32/`, copy the following 8 lines to a file named `partitions_ulab.cvs`: + +``` +# Notes: the offset of the partition table itself is set in +# $ESPIDF/components/partition_table/Kconfig.projbuild and the +# offset of the factory/ota_0 partition is set in makeimg.py +# Name, Type, SubType, Offset, Size, Flags +nvs, data, nvs, 0x9000, 0x6000, +phy_init, data, phy, 0xf000, 0x1000, +factory, app, factory, 0x10000, 0x200000, +vfs, data, fat, 0x220000, 0x180000, +``` +This expands the `factory` partition by 128 kB, and reduces the size of `vfs` by the same amount. Having defined the new partition table, we should extend `sdkconfig.board` by adding the following two lines: + +``` +CONFIG_PARTITION_TABLE_CUSTOM=y +CONFIG_PARTITION_TABLE_CUSTOM_FILENAME="partitions_ulab.csv" +``` +This file can be found in `$BUILD_DIR/micropython/ports/esp32/boards/TINYPICO/`. Finally, run `make clean`, and `make`. The new firmware contains the modified partition table, and should fit on the microcontroller. + +### RP2-based boards + +RP2 firmware can be compiled either by downloading and running the single [build script](https://github.com/v923z/micropython-ulab/blob/master/build/rp2.sh), or executing the commands below. + +First, clone `micropython`: + +```bash +git clone https://github.com/micropython/micropython.git +``` + +Then, setup the required submodules: + +```bash +cd micropython +git submodule update --init lib/tinyusb +git submodule update --init lib/pico-sdk +cd lib/pico-sdk +git submodule update --init lib/tinyusb +``` + +You'll also need to compile `mpy-cross`: + +```bash +cd ../../mpy-cross +make +``` + +That's all you need to do for the `micropython` repository. Now, let us clone `ulab` (in a directory outside the micropython repository): + +```bash +cd ../../ +git clone https://github.com/v923z/micropython-ulab ulab +``` + +With this setup, we can now build the firmware. Back in the `micropython` repository, use these commands: + +```bash +cd ports/rp2 +make USER_C_MODULES=/path/to/ulab/code/micropython.cmake +``` + +If `micropython` and `ulab` were in the same folder on the computer, you can set `USER_C_MODULES=../../../ulab/code/micropython.cmake`. The compiled firmware will be placed in `micropython/ports/rp2/build`. + +# Compiling for CircuitPython + +[Adafruit Industries](www.adafruit.com) always include a relatively recent version of `ulab` in their nightly builds. However, if you really need the bleeding edge, you can easily compile the firmware from the source. Simply clone `circuitpython`, and move the commit pointer to the latest version of `ulab` (`ulab` will automatically be cloned with `circuitpython`): + +```bash +git clone https://github.com/adafruit/circuitpython.git + +cd circuitpyton/extmod/ulab + +# update ulab here +git checkout master +git pull +``` +You might have to check, whether the `CIRCUITPY_ULAB` variable is set to `1` for the port that you want to compile for. You find this piece of information in the `make` fragment: + +```bash +circuitpython/ports/port_of_your_choice/mpconfigport.mk +``` +After this, you would run `make` with the single `BOARD` argument, e.g.: + +```bash +make BOARD=mini_sam_m4 +``` + +# Issues, contributing, and testing + +If you find a problem with the code, please, raise an [issue](https://github.com/v923z/micropython-ulab/issues)! An issue should address a single problem, and should contain a minimal code snippet that demonstrates the difference from the expected behaviour. Reducing a problem to the bare minimum significantly increases the chances of a quick fix. + +Feature requests (porting a particular function from `numpy` or `scipy`) should also be posted at [ulab issue](https://github.com/v923z/micropython-ulab/issues). + +Contributions of any kind are always welcome. If you feel like adding to the code, you can simply issue a pull request. If you do so, please, try to adhere to `micropython`'s [coding conventions](https://github.com/micropython/micropython/blob/master/CODECONVENTIONS.md#c-code-conventions). + +However, you can also contribute to the documentation (preferably via the [jupyter notebooks](https://github.com/v923z/micropython-ulab/tree/master/docs), or improve the [tests](https://github.com/v923z/micropython-ulab/tree/master/tests). + +## Testing + +If you decide to lend a hand with testing, here are the steps: + +1. Write a test script that checks a particular function, or a set of related functions! +1. Drop this script in one of the folders in [ulab tests](https://github.com/v923z/micropython-ulab/tree/master/tests)! +1. Run the [./build.sh](https://github.com/v923z/micropython-ulab/blob/master/build.sh) script in the root directory of `ulab`! This will clone the latest `micropython`, compile the firmware for `unix`, execute all scripts in the `ulab/tests`, and compare the results to those in the expected results files, which are also in `ulab/tests`, and have an extension `.exp`. In case you have a new snippet, i.e., you have no expected results file, or if the results differ from those in the expected file, a new expected file will be generated in the root directory. You should inspect the contents of this file, and if they are satisfactory, then the file can be moved to the `ulab/tests` folder, alongside your snippet. diff --git a/circuitpython/extmod/ulab/build-cp.sh b/circuitpython/extmod/ulab/build-cp.sh new file mode 100755 index 0000000..bd66f59 --- /dev/null +++ b/circuitpython/extmod/ulab/build-cp.sh @@ -0,0 +1,53 @@ +#!/bin/sh +set -e +# POSIX compliant version +readlinkf_posix() { + [ "${1:-}" ] || return 1 + max_symlinks=40 + CDPATH='' # to avoid changing to an unexpected directory + + target=$1 + [ -e "${target%/}" ] || target=${1%"${1##*[!/]}"} # trim trailing slashes + [ -d "${target:-/}" ] && target="$target/" + + cd -P . 2>/dev/null || return 1 + while [ "$max_symlinks" -ge 0 ] && max_symlinks=$((max_symlinks - 1)); do + if [ ! "$target" = "${target%/*}" ]; then + case $target in + /*) cd -P "${target%/*}/" 2>/dev/null || break ;; + *) cd -P "./${target%/*}" 2>/dev/null || break ;; + esac + target=${target##*/} + fi + + if [ ! -L "$target" ]; then + target="${PWD%/}${target:+/}${target}" + printf '%s\n' "${target:-/}" + return 0 + fi + + # `ls -dl` format: "%s %u %s %s %u %s %s -> %s\n", + # <file mode>, <number of links>, <owner name>, <group name>, + # <size>, <date and time>, <pathname of link>, <contents of link> + # https://pubs.opengroup.org/onlinepubs/9699919799/utilities/ls.html + link=$(ls -dl -- "$target" 2>/dev/null) || break + target=${link#*" $target -> "} + done + return 1 +} +NPROC=$(python3 -c 'import multiprocessing; print(multiprocessing.cpu_count())') +HERE="$(dirname -- "$(readlinkf_posix -- "${0}")" )" +[ -e circuitpython/py/py.mk ] || (git clone --no-recurse-submodules --depth 100 --branch main https://github.com/adafruit/circuitpython && cd circuitpython && git submodule update --init lib/uzlib tools) +rm -rf circuitpython/extmod/ulab; ln -s "$HERE" circuitpython/extmod/ulab +dims=${1-2} +make -C circuitpython/mpy-cross -j$NPROC +sed -e '/MICROPY_PY_UHASHLIB/s/1/0/' < circuitpython/ports/unix/mpconfigport.h > circuitpython/ports/unix/mpconfigport_ulab.h +make -k -C circuitpython/ports/unix -j$NPROC DEBUG=1 MICROPY_PY_FFI=0 MICROPY_PY_BTREE=0 MICROPY_SSL_AXTLS=0 MICROPY_PY_USSL=0 CFLAGS_EXTRA="-DMP_CONFIGFILE=\"<mpconfigport_ulab.h>\" -Wno-tautological-constant-out-of-range-compare -Wno-unknown-pragmas -DULAB_MAX_DIMS=$dims" BUILD=build-$dims PROG=micropython-$dims + +bash test-common.sh "${dims}" "circuitpython/ports/unix/micropython-$dims" + +# Docs don't depend on the dimensionality, so only do it once +if [ "$dims" -eq 2 ]; then + (cd circuitpython && sphinx-build -E -W -b html . _build/html) + (cd circuitpython && make check-stubs) +fi diff --git a/circuitpython/extmod/ulab/build.sh b/circuitpython/extmod/ulab/build.sh new file mode 100755 index 0000000..0c422a3 --- /dev/null +++ b/circuitpython/extmod/ulab/build.sh @@ -0,0 +1,47 @@ +#!/bin/sh +# POSIX compliant version +readlinkf_posix() { + [ "${1:-}" ] || return 1 + max_symlinks=40 + CDPATH='' # to avoid changing to an unexpected directory + + target=$1 + [ -e "${target%/}" ] || target=${1%"${1##*[!/]}"} # trim trailing slashes + [ -d "${target:-/}" ] && target="$target/" + + cd -P . 2>/dev/null || return 1 + while [ "$max_symlinks" -ge 0 ] && max_symlinks=$((max_symlinks - 1)); do + if [ ! "$target" = "${target%/*}" ]; then + case $target in + /*) cd -P "${target%/*}/" 2>/dev/null || break ;; + *) cd -P "./${target%/*}" 2>/dev/null || break ;; + esac + target=${target##*/} + fi + + if [ ! -L "$target" ]; then + target="${PWD%/}${target:+/}${target}" + printf '%s\n' "${target:-/}" + return 0 + fi + + # `ls -dl` format: "%s %u %s %s %u %s %s -> %s\n", + # <file mode>, <number of links>, <owner name>, <group name>, + # <size>, <date and time>, <pathname of link>, <contents of link> + # https://pubs.opengroup.org/onlinepubs/9699919799/utilities/ls.html + link=$(ls -dl -- "$target" 2>/dev/null) || break + target=${link#*" $target -> "} + done + return 1 +} +NPROC=`python3 -c 'import multiprocessing; print(multiprocessing.cpu_count())'` +set -e +HERE="$(dirname -- "$(readlinkf_posix -- "${0}")" )" +[ -e micropython/py/py.mk ] || git clone --no-recurse-submodules https://github.com/micropython/micropython +[ -e micropython/lib/axtls/README ] || (cd micropython && git submodule update --init lib/axtls ) +dims=${1-2} +make -C micropython/mpy-cross -j${NPROC} +make -C micropython/ports/unix -j${NPROC} axtls +make -C micropython/ports/unix -j${NPROC} USER_C_MODULES="${HERE}" DEBUG=1 STRIP=: MICROPY_PY_FFI=0 MICROPY_PY_BTREE=0 CFLAGS_EXTRA=-DULAB_MAX_DIMS=$dims BUILD=build-$dims PROG=micropython-$dims + +bash test-common.sh "${dims}" "micropython/ports/unix/micropython-$dims" diff --git a/circuitpython/extmod/ulab/build/esp32-cmake.sh b/circuitpython/extmod/ulab/build/esp32-cmake.sh new file mode 100644 index 0000000..0093c5b --- /dev/null +++ b/circuitpython/extmod/ulab/build/esp32-cmake.sh @@ -0,0 +1,35 @@ +#!/bin/bash + +export BUILD_DIR=$(pwd) + +echo "--- CLONING ULAB ---" +git clone --depth 1 https://github.com/v923z/micropython-ulab.git ulab + +echo "--- CLONING MICROPYTHON ---" +git clone --depth 1 https://github.com/micropython/micropython.git + +echo "--- CLONING ESP-IDF ---" +cd $BUILD_DIR/micropython/ +git clone --depth 1 -b v4.0.2 --recursive https://github.com/espressif/esp-idf.git + +echo "--- INSTALL ESP-IDF ---" +cd $BUILD_DIR/micropython/esp-idf +./install.sh +. ./export.sh + +echo "--- MPY-CROSS ---" +cd $BUILD_DIR/micropython/mpy-cross +make + +echo "--- ESP32 SUBMODULES ---" +cd $BUILD_DIR/micropython/ports/esp32 +make submodules + +echo "--- PATCH MAKEFILE ---" +cp $BUILD_DIR/micropython/ports/esp32/Makefile $BUILD_DIR/micropython/ports/esp32/MakefileOld +echo "BOARD = GENERIC" > $BUILD_DIR/micropython/ports/esp32/Makefile +echo "USER_C_MODULES = \$(BUILD_DIR)/ulab/code/micropython.cmake" >> $BUILD_DIR/micropython/ports/esp32/Makefile +cat $BUILD_DIR/micropython/ports/esp32/MakefileOld >> $BUILD_DIR/micropython/ports/esp32/Makefile + +echo "--- MAKE ---" +make diff --git a/circuitpython/extmod/ulab/build/esp32.sh b/circuitpython/extmod/ulab/build/esp32.sh new file mode 100644 index 0000000..d5571cd --- /dev/null +++ b/circuitpython/extmod/ulab/build/esp32.sh @@ -0,0 +1,41 @@ +#!/bin/bash + +export BUILD_DIR=$(pwd) + +git clone https://github.com/v923z/micropython-ulab.git ulab +git clone https://github.com/micropython/micropython.git + +cd $BUILD_DIR/micropython/ +git checkout tags/v1.14 + +git submodule update --init +cd ./mpy-cross && make # build cross-compiler (required) + +cd $BUILD_DIR/micropython/ports/esp32 +make ESPIDF= # will display supported ESP-IDF commit hashes +# output should look like: """ +# ... +# Supported git hash (v3.3): 9e70825d1e1cbf7988cf36981774300066580ea7 +# Supported git hash (v4.0) (experimental): 4c81978a3e2220674a432a588292a4c860eef27b + +ESPIDF_VER=9e70825d1e1cbf7988cf36981774300066580ea7 + +mkdir $BUILD_DIR/micropython/esp32 + +cd $BUILD_DIR/micropython/esp32 +git clone https://github.com/espressif/esp-idf.git esp-idf +cd $BUILD_DIR/micropython/esp32/esp-idf +git checkout $ESPIDF_VER +git submodule update --init --recursive # get idf submodules +pip install -r ./requirements.txt # install python reqs + +curl https://dl.espressif.com/dl/xtensa-esp32-elf-linux64-1.22.0-80-g6c4433a-5.2.0.tar.gz | tar xvz + +cd $BUILD_DIR/micropython/ports/esp32 +# temporarily add esp32 compiler to path +export PATH=$BUILD_DIR/micropython/esp32/esp-idf/xtensa-esp32-elf/bine:$PATH +export ESPIDF=$BUILD_DIR/micropython/esp32/esp-idf +export BOARD=GENERIC # board options are in ./board +export USER_C_MODULES=$BUILD_DIR/ulab # include ulab in firmware + +make submodules & make all diff --git a/circuitpython/extmod/ulab/build/rp2.sh b/circuitpython/extmod/ulab/build/rp2.sh new file mode 100644 index 0000000..e89ab13 --- /dev/null +++ b/circuitpython/extmod/ulab/build/rp2.sh @@ -0,0 +1,24 @@ +#!/bin/bash + +export BUILD_DIR=$(pwd) +export MPY_DIR=$BUILD_DIR/micropython +export ULAB_DIR=$BUILD_DIR/../code + +if [ ! -d $ULAB_DIR ]; then + printf "Cloning ulab\n" + ULAB_DIR=$BUILD_DIR/ulab/code + git clone https://github.com/v923z/micropython-ulab.git ulab +fi + +if [ ! -d $MPY_DIR ]; then + printf "Cloning MicroPython\n" + git clone https://github.com/micropython/micropython.git micropython +fi + +cd $MPY_DIR +git submodule update --init +cd ./mpy-cross && make # build cross-compiler (required) + +cd $MPY_DIR/ports/rp2 +rm -r build +make USER_C_MODULES=$ULAB_DIR/micropython.cmake diff --git a/circuitpython/extmod/ulab/code/micropython.cmake b/circuitpython/extmod/ulab/code/micropython.cmake new file mode 100644 index 0000000..66890c0 --- /dev/null +++ b/circuitpython/extmod/ulab/code/micropython.cmake @@ -0,0 +1,18 @@ +add_library(usermod_ulab INTERFACE) + +file(GLOB_RECURSE ULAB_SOURCES ${CMAKE_CURRENT_LIST_DIR}/*.c) + +target_sources(usermod_ulab INTERFACE + ${ULAB_SOURCES} +) + +target_include_directories(usermod_ulab INTERFACE + ${CMAKE_CURRENT_LIST_DIR} +) + +target_compile_definitions(usermod_ulab INTERFACE + MODULE_ULAB_ENABLED=1 +) + +target_link_libraries(usermod INTERFACE usermod_ulab) + diff --git a/circuitpython/extmod/ulab/code/micropython.mk b/circuitpython/extmod/ulab/code/micropython.mk new file mode 100644 index 0000000..d16b177 --- /dev/null +++ b/circuitpython/extmod/ulab/code/micropython.mk @@ -0,0 +1,38 @@ + +USERMODULES_DIR := $(USERMOD_DIR) + +# Add all C files to SRC_USERMOD. +SRC_USERMOD += $(USERMODULES_DIR)/scipy/linalg/linalg.c +SRC_USERMOD += $(USERMODULES_DIR)/scipy/optimize/optimize.c +SRC_USERMOD += $(USERMODULES_DIR)/scipy/signal/signal.c +SRC_USERMOD += $(USERMODULES_DIR)/scipy/special/special.c +SRC_USERMOD += $(USERMODULES_DIR)/ndarray_operators.c +SRC_USERMOD += $(USERMODULES_DIR)/ulab_tools.c +SRC_USERMOD += $(USERMODULES_DIR)/ndarray.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/ndarray/ndarray_iter.c +SRC_USERMOD += $(USERMODULES_DIR)/ndarray_properties.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/approx.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/compare.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/carray/carray.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/carray/carray_tools.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/create.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/fft/fft.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/fft/fft_tools.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/filter.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/linalg/linalg.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/linalg/linalg_tools.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/numerical.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/poly.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/stats.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/transform.c +SRC_USERMOD += $(USERMODULES_DIR)/numpy/vector.c + +SRC_USERMOD += $(USERMODULES_DIR)/numpy/numpy.c +SRC_USERMOD += $(USERMODULES_DIR)/scipy/scipy.c +SRC_USERMOD += $(USERMODULES_DIR)/user/user.c +SRC_USERMOD += $(USERMODULES_DIR)/utils/utils.c +SRC_USERMOD += $(USERMODULES_DIR)/ulab.c + +CFLAGS_USERMOD += -I$(USERMODULES_DIR) + +override CFLAGS_EXTRA += -DMODULE_ULAB_ENABLED=1 diff --git a/circuitpython/extmod/ulab/code/ndarray.c b/circuitpython/extmod/ulab/code/ndarray.c new file mode 100644 index 0000000..f8caa67 --- /dev/null +++ b/circuitpython/extmod/ulab/code/ndarray.c @@ -0,0 +1,2255 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2022 Zoltán Vörös + * 2020 Jeff Epler for Adafruit Industries + * 2020 Taku Fukada +*/ + +#include <unistd.h> +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include "py/runtime.h" +#include "py/binary.h" +#include "py/obj.h" +#include "py/objtuple.h" +#include "py/objint.h" + +#include "ulab_tools.h" +#include "ndarray.h" +#include "ndarray_operators.h" +#include "numpy/carray/carray.h" +#include "numpy/carray/carray_tools.h" + +mp_uint_t ndarray_print_threshold = NDARRAY_PRINT_THRESHOLD; +mp_uint_t ndarray_print_edgeitems = NDARRAY_PRINT_EDGEITEMS; + +//| """Manipulate numeric data similar to numpy +//| +//| `ulab` is a numpy-like module for micropython, meant to simplify and +//| speed up common mathematical operations on arrays. The primary goal was to +//| implement a small subset of numpy that might be useful in the context of a +//| microcontroller. This means low-level data processing of linear (array) and +//| two-dimensional (matrix) data. +//| +//| `ulab` is adapted from micropython-ulab, and the original project's +//| documentation can be found at +//| https://micropython-ulab.readthedocs.io/en/latest/ +//| +//| `ulab` is modeled after numpy, and aims to be a compatible subset where +//| possible. Numpy's documentation can be found at +//| https://docs.scipy.org/doc/numpy/index.html""" +//| + +void ndarray_set_complex_value(void *p, size_t index, mp_obj_t value) { + mp_float_t real, imag; + if(mp_obj_is_type(value, &mp_type_complex)) { + mp_obj_get_complex(value, &real, &imag); + ((mp_float_t *)p)[2 * index] = real; + ((mp_float_t *)p)[2 * index + 1] = imag; + } else { + real = mp_obj_get_float(value); + ((mp_float_t *)p)[2 * index] = real; + ((mp_float_t *)p)[2 * index + 1] = MICROPY_FLOAT_CONST(0.0); + } +} + +#ifdef CIRCUITPY +void ndarray_set_value(char typecode, void *p, size_t index, mp_obj_t val_in) { + switch (typecode) { + case NDARRAY_INT8: + ((signed char *)p)[index] = mp_obj_get_int(val_in); + break; + case NDARRAY_UINT8: + ((unsigned char *)p)[index] = mp_obj_get_int(val_in); + break; + case NDARRAY_INT16: + ((short *)p)[index] = mp_obj_get_int(val_in); + break; + case NDARRAY_UINT16: + ((unsigned short *)p)[index] = mp_obj_get_int(val_in); + break; + case NDARRAY_FLOAT: + ((mp_float_t *)p)[index] = mp_obj_get_float(val_in); + break; + #if ULAB_SUPPORTS_COMPLEX + case NDARRAY_COMPLEX: + ndarray_set_complex_value(p, index, val_in); + break; + #endif + } +} +#endif + +#if defined(MICROPY_VERSION_MAJOR) && MICROPY_VERSION_MAJOR == 1 && MICROPY_VERSION_MINOR == 11 + +void mp_obj_slice_indices(mp_obj_t self_in, mp_int_t length, mp_bound_slice_t *result) { + mp_obj_slice_t *self = MP_OBJ_TO_PTR(self_in); + mp_int_t start, stop, step; + + if (self->step == mp_const_none) { + step = 1; + } else { + step = mp_obj_get_int(self->step); + if (step == 0) { + mp_raise_ValueError(translate("slice step can't be zero")); + } + } + + if (step > 0) { + // Positive step + if (self->start == mp_const_none) { + start = 0; + } else { + start = mp_obj_get_int(self->start); + if (start < 0) { + start += length; + } + start = MIN(length, MAX(start, 0)); + } + + if (self->stop == mp_const_none) { + stop = length; + } else { + stop = mp_obj_get_int(self->stop); + if (stop < 0) { + stop += length; + } + stop = MIN(length, MAX(stop, 0)); + } + } else { + // Negative step + if (self->start == mp_const_none) { + start = length - 1; + } else { + start = mp_obj_get_int(self->start); + if (start < 0) { + start += length; + } + start = MIN(length - 1, MAX(start, -1)); + } + + if (self->stop == mp_const_none) { + stop = -1; + } else { + stop = mp_obj_get_int(self->stop); + if (stop < 0) { + stop += length; + } + stop = MIN(length - 1, MAX(stop, -1)); + } + } + + result->start = start; + result->stop = stop; + result->step = step; +} +#endif /* MICROPY_VERSION v1.11 */ + +void ndarray_fill_array_iterable(mp_float_t *array, mp_obj_t iterable) { + mp_obj_iter_buf_t x_buf; + mp_obj_t x_item, x_iterable = mp_getiter(iterable, &x_buf); + while ((x_item = mp_iternext(x_iterable)) != MP_OBJ_STOP_ITERATION) { + *array++ = (mp_float_t)mp_obj_get_float(x_item); + } +} + +#if ULAB_HAS_FUNCTION_ITERATOR +size_t *ndarray_new_coords(uint8_t ndim) { + size_t *coords = m_new(size_t, ndim); + memset(coords, 0, ndim*sizeof(size_t)); + return coords; +} + +void ndarray_rewind_array(uint8_t ndim, uint8_t *array, size_t *shape, int32_t *strides, size_t *coords) { + // resets the data pointer of a single array, whenever an axis is full + // since we always iterate over the very last axis, we have to keep track of + // the last ndim-2 axes only + array -= shape[ULAB_MAX_DIMS - 1] * strides[ULAB_MAX_DIMS - 1]; + array += strides[ULAB_MAX_DIMS - 2]; + for(uint8_t i=1; i < ndim-1; i++) { + coords[ULAB_MAX_DIMS - 1 - i] += 1; + if(coords[ULAB_MAX_DIMS - 1 - i] == shape[ULAB_MAX_DIMS - 1 - i]) { // we are at a dimension boundary + array -= shape[ULAB_MAX_DIMS - 1 - i] * strides[ULAB_MAX_DIMS - 1 - i]; + array += strides[ULAB_MAX_DIMS - 2 - i]; + coords[ULAB_MAX_DIMS - 1 - i] = 0; + coords[ULAB_MAX_DIMS - 2 - i] += 1; + } else { // coordinates can change only, if the last coordinate changes + return; + } + } +} +#endif + +static int32_t *strides_from_shape(size_t *shape, uint8_t dtype) { + // returns a strides array that corresponds to a dense array with the prescribed shape + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + strides[ULAB_MAX_DIMS-1] = (int32_t)ulab_binary_get_size(dtype); + for(uint8_t i=ULAB_MAX_DIMS; i > 1; i--) { + strides[i-2] = strides[i-1] * shape[i-1]; + } + return strides; +} + +size_t *ndarray_shape_vector(size_t a, size_t b, size_t c, size_t d) { + // returns a ULAB_MAX_DIMS-aware array of shapes + // WARNING: this assumes that the maximum possible dimension is 4! + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + shape[ULAB_MAX_DIMS - 1] = d; + #if ULAB_MAX_DIMS > 1 + shape[ULAB_MAX_DIMS - 2] = c; + #endif + #if ULAB_MAX_DIMS > 2 + shape[ULAB_MAX_DIMS - 3] = b; + #endif + #if ULAB_MAX_DIMS > 3 + shape[ULAB_MAX_DIMS - 4] = a; + #endif + return shape; +} + +bool ndarray_object_is_array_like(mp_obj_t o_in) { + if(mp_obj_is_type(o_in, &ulab_ndarray_type) || + mp_obj_is_type(o_in, &mp_type_tuple) || + mp_obj_is_type(o_in, &mp_type_list) || + mp_obj_is_type(o_in, &mp_type_range)) { + return true; + } + return false; +} + +void fill_array_iterable(mp_float_t *array, mp_obj_t iterable) { + mp_obj_iter_buf_t x_buf; + mp_obj_t x_item, x_iterable = mp_getiter(iterable, &x_buf); + size_t i=0; + while ((x_item = mp_iternext(x_iterable)) != MP_OBJ_STOP_ITERATION) { + array[i] = (mp_float_t)mp_obj_get_float(x_item); + i++; + } +} + +#if NDARRAY_HAS_DTYPE +#if ULAB_HAS_DTYPE_OBJECT +void ndarray_dtype_print(const mp_print_t *print, mp_obj_t self_in, mp_print_kind_t kind) { + (void)kind; + dtype_obj_t *self = MP_OBJ_TO_PTR(self_in); + mp_print_str(print, "dtype('"); + if(self->dtype == NDARRAY_BOOLEAN) { + mp_print_str(print, "bool')"); + } else if(self->dtype == NDARRAY_UINT8) { + mp_print_str(print, "uint8')"); + } else if(self->dtype == NDARRAY_INT8) { + mp_print_str(print, "int8')"); + } else if(self->dtype == NDARRAY_UINT16) { + mp_print_str(print, "uint16')"); + } else if(self->dtype == NDARRAY_INT16) { + mp_print_str(print, "int16')"); + } + #if ULAB_SUPPORTS_COMPLEX + else if(self->dtype == NDARRAY_COMPLEX) { + mp_print_str(print, "complex')"); + } + #endif + else { + #if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT + mp_print_str(print, "float32')"); + #else + mp_print_str(print, "float64')"); + #endif + } +} + +mp_obj_t ndarray_dtype_make_new(const mp_obj_type_t *type, size_t n_args, size_t n_kw, const mp_obj_t *args) { + (void) type; + mp_arg_check_num(n_args, n_kw, 0, 1, true); + mp_map_t kw_args; + mp_map_init_fixed_table(&kw_args, n_kw, args + n_args); + + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_OBJ, { .u_obj = mp_const_none } }, + }; + mp_arg_val_t _args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, args, &kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, _args); + + dtype_obj_t *dtype = m_new_obj(dtype_obj_t); + dtype->base.type = &ulab_dtype_type; + + if(mp_obj_is_type(args[0], &ulab_ndarray_type)) { + // return the dtype of the array + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0]); + dtype->dtype = ndarray->dtype; + } else { + uint8_t _dtype; + if(mp_obj_is_int(_args[0].u_obj)) { + _dtype = mp_obj_get_int(_args[0].u_obj); + if((_dtype != NDARRAY_BOOL) && (_dtype != NDARRAY_UINT8) + && (_dtype != NDARRAY_INT8) && (_dtype != NDARRAY_UINT16) + && (_dtype != NDARRAY_INT16) && (_dtype != NDARRAY_FLOAT)) { + mp_raise_TypeError(translate("data type not understood")); + } + } else { + GET_STR_DATA_LEN(_args[0].u_obj, _dtype_, len); + if(memcmp(_dtype_, "uint8", 5) == 0) { + _dtype = NDARRAY_UINT8; + } else if(memcmp(_dtype_, "int8", 4) == 0) { + _dtype = NDARRAY_INT8; + } else if(memcmp(_dtype_, "uint16", 6) == 0) { + _dtype = NDARRAY_UINT16; + } else if(memcmp(_dtype_, "int16", 5) == 0) { + _dtype = NDARRAY_INT16; + } else if(memcmp(_dtype_, "float", 5) == 0) { + _dtype = NDARRAY_FLOAT; + } + #if ULAB_SUPPORTS_COMPLEX + else if(memcmp(_dtype_, "complex", 7) == 0) { + _dtype = NDARRAY_COMPLEX; + } + #endif + else { + mp_raise_TypeError(translate("data type not understood")); + } + } + dtype->dtype = _dtype; + } + return dtype; +} + +mp_obj_t ndarray_dtype(mp_obj_t self_in) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + dtype_obj_t *dtype = m_new_obj(dtype_obj_t); + dtype->base.type = &ulab_dtype_type; + dtype->dtype = self->dtype; + return dtype; +} + +#else +// this is the cheap implementation of tbe dtype +mp_obj_t ndarray_dtype(mp_obj_t self_in) { + uint8_t dtype; + if(mp_obj_is_type(self_in, &ulab_ndarray_type)) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + dtype = self->dtype; + } else { // we assume here that the input is a single character + GET_STR_DATA_LEN(self_in, _dtype, len); + if((len != 1) || ((*_dtype != NDARRAY_BOOL) && (*_dtype != NDARRAY_UINT8) + && (*_dtype != NDARRAY_INT8) && (*_dtype != NDARRAY_UINT16) + && (*_dtype != NDARRAY_INT16) && (*_dtype != NDARRAY_FLOAT) + #if ULAB_SUPPORTS_COMPLEX + && (*_dtype != NDARRAY_COMPLEX) + #endif + )) { + mp_raise_TypeError(translate("data type not understood")); + } + dtype = *_dtype; + } + return mp_obj_new_int(dtype); +} +#endif /* ULAB_HAS_DTYPE_OBJECT */ +#endif /* NDARRAY_HAS_DTYPE */ + +#if ULAB_HAS_PRINTOPTIONS +mp_obj_t ndarray_set_printoptions(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_threshold, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} }, + { MP_QSTR_edgeitems, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + if(args[0].u_rom_obj != mp_const_none) { + ndarray_print_threshold = mp_obj_get_int(args[0].u_rom_obj); + } + if(args[1].u_rom_obj != mp_const_none) { + ndarray_print_edgeitems = mp_obj_get_int(args[1].u_rom_obj); + } + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(ndarray_set_printoptions_obj, 0, ndarray_set_printoptions); + +mp_obj_t ndarray_get_printoptions(void) { + mp_obj_t dict = mp_obj_new_dict(2); + mp_obj_dict_store(MP_OBJ_FROM_PTR(dict), MP_OBJ_NEW_QSTR(MP_QSTR_threshold), mp_obj_new_int(ndarray_print_threshold)); + mp_obj_dict_store(MP_OBJ_FROM_PTR(dict), MP_OBJ_NEW_QSTR(MP_QSTR_edgeitems), mp_obj_new_int(ndarray_print_edgeitems)); + return dict; +} + +MP_DEFINE_CONST_FUN_OBJ_0(ndarray_get_printoptions_obj, ndarray_get_printoptions); +#endif + +mp_obj_t ndarray_get_item(ndarray_obj_t *ndarray, void *array) { + // returns a proper micropython object from an array + if(!ndarray->boolean) { + #if ULAB_SUPPORTS_COMPLEX + if(ndarray->dtype == NDARRAY_COMPLEX) { + mp_float_t *c = (mp_float_t *)array; + mp_float_t real = *c++; + mp_float_t imag = *c; + return mp_obj_new_complex(real, imag); + } + #endif + return mp_binary_get_val_array(ndarray->dtype, array, 0); + } else { + if(*(uint8_t *)array) { + return mp_const_true; + } else { + return mp_const_false; + } + } +} + +static void ndarray_print_element(const mp_print_t *print, ndarray_obj_t *ndarray, uint8_t *array) { + #if ULAB_SUPPORTS_COMPLEX + if(ndarray->dtype == NDARRAY_COMPLEX) { + // real part first + mp_float_t fvalue = *(mp_float_t *)array; + mp_obj_print_helper(print, mp_obj_new_float(fvalue), PRINT_REPR); + // imaginary part + array += ndarray->itemsize / 2; + fvalue = *(mp_float_t *)array; + if(fvalue >= MICROPY_FLOAT_CONST(0.0) || isnan(fvalue)) { + mp_print_str(print, "+"); + } + array += ndarray->itemsize / 2; + mp_obj_print_helper(print, mp_obj_new_float(fvalue), PRINT_REPR); + mp_print_str(print, "j"); + } else { + mp_obj_print_helper(print, ndarray_get_item(ndarray, array), PRINT_REPR); + } + #else + mp_obj_print_helper(print, ndarray_get_item(ndarray, array), PRINT_REPR); + #endif +} + +static void ndarray_print_row(const mp_print_t *print, ndarray_obj_t * ndarray, uint8_t *array, size_t stride, size_t n) { + if(n == 0) { + return; + } + mp_print_str(print, "["); + if((n <= ndarray_print_threshold) || (n <= 2*ndarray_print_edgeitems)) { // if the array is short, print everything + ndarray_print_element(print, ndarray, array); + array += stride; + for(size_t i=1; i < n; i++, array += stride) { + mp_print_str(print, ", "); + ndarray_print_element(print, ndarray, array); + } + } else { + mp_obj_print_helper(print, ndarray_get_item(ndarray, array), PRINT_REPR); + array += stride; + for(size_t i=1; i < ndarray_print_edgeitems; i++, array += stride) { + mp_print_str(print, ", "); + ndarray_print_element(print, ndarray, array); + } + mp_printf(print, ", ..., "); + array += stride * (n - 2 * ndarray_print_edgeitems); + ndarray_print_element(print, ndarray, array); + array += stride; + for(size_t i=1; i < ndarray_print_edgeitems; i++, array += stride) { + mp_print_str(print, ", "); + ndarray_print_element(print, ndarray, array); + } + } + mp_print_str(print, "]"); +} + +#if ULAB_MAX_DIMS > 1 +static void ndarray_print_bracket(const mp_print_t *print, const size_t condition, const size_t shape, const char *string) { + if(condition < shape) { + mp_print_str(print, string); + } +} +#endif + +void ndarray_print(const mp_print_t *print, mp_obj_t self_in, mp_print_kind_t kind) { + (void)kind; + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + uint8_t *array = (uint8_t *)self->array; + mp_print_str(print, "array("); + if(self->len == 0) { + mp_print_str(print, "[]"); + if(self->ndim > 1) { + mp_print_str(print, ", shape=("); + #if ULAB_MAX_DIMS > 1 + for(uint8_t ndim = self->ndim; ndim > 1; ndim--) { + mp_printf(MP_PYTHON_PRINTER, "%d,", self->shape[ULAB_MAX_DIMS - ndim]); + } + #else + mp_printf(MP_PYTHON_PRINTER, "%d,", self->shape[0]); + #endif + mp_printf(MP_PYTHON_PRINTER, "%d)", self->shape[ULAB_MAX_DIMS - 1]); + } + } else { + #if ULAB_MAX_DIMS > 3 + size_t i=0; + ndarray_print_bracket(print, 0, self->shape[ULAB_MAX_DIMS-4], "["); + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + ndarray_print_bracket(print, 0, self->shape[ULAB_MAX_DIMS-3], "["); + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + ndarray_print_bracket(print, 0, self->shape[ULAB_MAX_DIMS-2], "["); + do { + #endif + ndarray_print_row(print, self, array, self->strides[ULAB_MAX_DIMS-1], self->shape[ULAB_MAX_DIMS-1]); + #if ULAB_MAX_DIMS > 1 + array += self->strides[ULAB_MAX_DIMS-2]; + k++; + ndarray_print_bracket(print, k, self->shape[ULAB_MAX_DIMS-2], ",\n "); + } while(k < self->shape[ULAB_MAX_DIMS-2]); + ndarray_print_bracket(print, 0, self->shape[ULAB_MAX_DIMS-2], "]"); + #endif + #if ULAB_MAX_DIMS > 2 + j++; + ndarray_print_bracket(print, j, self->shape[ULAB_MAX_DIMS-3], ",\n\n "); + array -= self->strides[ULAB_MAX_DIMS-2] * self->shape[ULAB_MAX_DIMS-2]; + array += self->strides[ULAB_MAX_DIMS-3]; + } while(j < self->shape[ULAB_MAX_DIMS-3]); + ndarray_print_bracket(print, 0, self->shape[ULAB_MAX_DIMS-3], "]"); + #endif + #if ULAB_MAX_DIMS > 3 + array -= self->strides[ULAB_MAX_DIMS-3] * self->shape[ULAB_MAX_DIMS-3]; + array += self->strides[ULAB_MAX_DIMS-4]; + i++; + ndarray_print_bracket(print, i, self->shape[ULAB_MAX_DIMS-4], ",\n\n "); + } while(i < self->shape[ULAB_MAX_DIMS-4]); + ndarray_print_bracket(print, 0, self->shape[ULAB_MAX_DIMS-4], "]"); + #endif + } + mp_print_str(print, ", dtype="); + if(self->boolean) { + mp_print_str(print, "bool)"); + } else if(self->dtype == NDARRAY_UINT8) { + mp_print_str(print, "uint8)"); + } else if(self->dtype == NDARRAY_INT8) { + mp_print_str(print, "int8)"); + } else if(self->dtype == NDARRAY_UINT16) { + mp_print_str(print, "uint16)"); + } else if(self->dtype == NDARRAY_INT16) { + mp_print_str(print, "int16)"); + } + #if ULAB_SUPPORTS_COMPLEX + else if(self->dtype == NDARRAY_COMPLEX) { + mp_print_str(print, "complex)"); + } + #endif /* ULAB_SUPPORTS_COMPLEX */ + else { + #if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT + mp_print_str(print, "float32)"); + #else + mp_print_str(print, "float64)"); + #endif + } +} + +void ndarray_assign_elements(ndarray_obj_t *ndarray, mp_obj_t iterable, uint8_t dtype, size_t *idx) { + // assigns a single row in the tensor + mp_obj_t item; + if(ndarray->boolean) { + uint8_t *array = (uint8_t *)ndarray->array; + array += *idx; + while ((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + if(mp_obj_is_true(item)) { + *array = 1; + } + array++; + (*idx)++; + } + } else { + while ((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + #if ULAB_SUPPORTS_COMPLEX + mp_float_t real; + mp_float_t imag; + if(dtype == NDARRAY_COMPLEX) { + mp_obj_get_complex(item, &real, &imag); + ndarray_set_value(NDARRAY_FLOAT, ndarray->array, (*idx)++, mp_obj_new_float(real)); + ndarray_set_value(NDARRAY_FLOAT, ndarray->array, (*idx)++, mp_obj_new_float(imag)); + } else { + ndarray_set_value(dtype, ndarray->array, (*idx)++, item); + } + #else + ndarray_set_value(dtype, ndarray->array, (*idx)++, item); + #endif + } + } +} + +bool ndarray_is_dense(ndarray_obj_t *ndarray) { + // returns true, if the array is dense, false otherwise + // the array should be dense, if the very first stride can be calculated from shape + int32_t stride = ndarray->itemsize; + for(uint8_t i = ULAB_MAX_DIMS - 1; i > ULAB_MAX_DIMS-ndarray->ndim; i--) { + stride *= ndarray->shape[i]; + } + return stride == ndarray->strides[ULAB_MAX_DIMS-ndarray->ndim] ? true : false; +} + + +ndarray_obj_t *ndarray_new_ndarray(uint8_t ndim, size_t *shape, int32_t *strides, uint8_t dtype) { + // Creates the base ndarray with shape, and initialises the values to straight 0s + ndarray_obj_t *ndarray = m_new_obj(ndarray_obj_t); + ndarray->base.type = &ulab_ndarray_type; + ndarray->dtype = dtype == NDARRAY_BOOL ? NDARRAY_UINT8 : dtype; + ndarray->boolean = dtype == NDARRAY_BOOL ? NDARRAY_BOOLEAN : NDARRAY_NUMERIC; + ndarray->ndim = ndim; + ndarray->len = ndim == 0 ? 0 : 1; + ndarray->itemsize = ulab_binary_get_size(dtype); + int32_t *_strides; + if(strides == NULL) { + _strides = strides_from_shape(shape, ndarray->dtype); + } else { + _strides = strides; + } + for(uint8_t i=ULAB_MAX_DIMS; i > ULAB_MAX_DIMS-ndim; i--) { + ndarray->shape[i-1] = shape[i-1]; + ndarray->strides[i-1] = _strides[i-1]; + ndarray->len *= shape[i-1]; + } + + // if the length is 0, still allocate a single item, so that contractions can be handled + size_t len = ndarray->itemsize * MAX(1, ndarray->len); + uint8_t *array = m_new(byte, len); + // this should set all elements to 0, irrespective of the of the dtype (all bits are zero) + // we could, perhaps, leave this step out, and initialise the array only, when needed + memset(array, 0, len); + ndarray->array = array; + ndarray->origin = array; + return ndarray; +} + +ndarray_obj_t *ndarray_new_dense_ndarray(uint8_t ndim, size_t *shape, uint8_t dtype) { + // creates a dense array, i.e., one, where the strides are derived directly from the shapes + // the function should work in the general n-dimensional case + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + strides[ULAB_MAX_DIMS-1] = (int32_t)ulab_binary_get_size(dtype); + for(size_t i=ULAB_MAX_DIMS; i > 1; i--) { + strides[i-2] = strides[i-1] * MAX(1, shape[i-1]); + } + return ndarray_new_ndarray(ndim, shape, strides, dtype); +} + +ndarray_obj_t *ndarray_new_ndarray_from_tuple(mp_obj_tuple_t *_shape, uint8_t dtype) { + // creates a dense array from a tuple + // the function should work in the general n-dimensional case + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + for(size_t i=0; i < ULAB_MAX_DIMS; i++) { + if(i < ULAB_MAX_DIMS - _shape->len) { + shape[i] = 0; + } else { + shape[i] = mp_obj_get_int(_shape->items[i]); + } + } + return ndarray_new_dense_ndarray(_shape->len, shape, dtype); +} + +void ndarray_copy_array(ndarray_obj_t *source, ndarray_obj_t *target, uint8_t shift) { + // TODO: if the array is dense, the content could be copied in a single pass + // copies the content of source->array into a new dense void pointer + // it is assumed that the dtypes in source and target are the same + // Since the target is a new array, it is supposed to be dense + uint8_t *sarray = (uint8_t *)source->array; + uint8_t *tarray = (uint8_t *)target->array; + #if ULAB_SUPPORTS_COMPLEX + if(source->dtype == NDARRAY_COMPLEX) { + sarray += shift; + } + #endif + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + memcpy(tarray, sarray, target->itemsize); + tarray += target->itemsize; + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif +} + +ndarray_obj_t *ndarray_new_view(ndarray_obj_t *source, uint8_t ndim, size_t *shape, int32_t *strides, int32_t offset) { + // creates a new view from the input arguments + ndarray_obj_t *ndarray = m_new_obj(ndarray_obj_t); + ndarray->base.type = &ulab_ndarray_type; + ndarray->boolean = source->boolean; + ndarray->dtype = source->dtype; + ndarray->ndim = ndim; + ndarray->itemsize = source->itemsize; + ndarray->len = ndim == 0 ? 0 : 1; + for(uint8_t i=ULAB_MAX_DIMS; i > ULAB_MAX_DIMS-ndim; i--) { + ndarray->shape[i-1] = shape[i-1]; + ndarray->strides[i-1] = strides[i-1]; + ndarray->len *= shape[i-1]; + } + uint8_t *pointer = (uint8_t *)source->array; + pointer += offset; + ndarray->array = pointer; + ndarray->origin = source->origin; + return ndarray; +} + +ndarray_obj_t *ndarray_copy_view(ndarray_obj_t *source) { + // creates a one-to-one deep copy of the input ndarray or its view + // the function should work in the general n-dimensional case + // In order to make it dtype-agnostic, we copy the memory content + // instead of reading out the values + + int32_t *strides = strides_from_shape(source->shape, source->dtype); + + uint8_t dtype = source->dtype; + if(source->boolean) { + dtype = NDARRAY_BOOLEAN; + } + ndarray_obj_t *ndarray = ndarray_new_ndarray(source->ndim, source->shape, strides, dtype); + ndarray_copy_array(source, ndarray, 0); + return ndarray; +} + +ndarray_obj_t *ndarray_copy_view_convert_type(ndarray_obj_t *source, uint8_t dtype) { + // creates a copy, similar to ndarray_copy_view, but it also converts the dtype, if necessary + if(dtype == source->dtype) { + return ndarray_copy_view(source); + } + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, dtype); + uint8_t *sarray = (uint8_t *)source->array; + uint8_t *array = (uint8_t *)ndarray->array; + + #if ULAB_SUPPORTS_COMPLEX + uint8_t complex_size = 2 * sizeof(mp_float_t); + #endif + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_obj_t item; + #if ULAB_SUPPORTS_COMPLEX + if(source->dtype == NDARRAY_COMPLEX) { + if(dtype != NDARRAY_COMPLEX) { + mp_raise_TypeError(translate("cannot convert complex type")); + } else { + memcpy(array, sarray, complex_size); + } + } else { + #endif + if((source->dtype == NDARRAY_FLOAT) && (dtype != NDARRAY_FLOAT)) { + // floats must be treated separately, because they can't directly be converted to integer types + mp_float_t f = ndarray_get_float_value(sarray, source->dtype); + item = mp_obj_new_int((int32_t)MICROPY_FLOAT_C_FUN(floor)(f)); + } else { + item = mp_binary_get_val_array(source->dtype, sarray, 0); + } + #if ULAB_SUPPORTS_COMPLEX + if(dtype == NDARRAY_COMPLEX) { + ndarray_set_value(NDARRAY_FLOAT, array, 0, item); + } else { + ndarray_set_value(dtype, array, 0, item); + } + } + #else + ndarray_set_value(dtype, array, 0, item); + #endif + array += ndarray->itemsize; + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif + return MP_OBJ_FROM_PTR(ndarray); +} + +#if NDARRAY_HAS_BYTESWAP +mp_obj_t ndarray_byteswap(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + // changes the endiannes of an array + // if the dtype of the input uint8/int8/bool, simply return a copy or view + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_inplace, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_false } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + ndarray_obj_t *self = MP_OBJ_TO_PTR(args[0].u_obj); + ndarray_obj_t *ndarray = NULL; + if(args[1].u_obj == mp_const_false) { + ndarray = ndarray_copy_view(self); + } else { + ndarray = ndarray_new_view(self, self->ndim, self->shape, self->strides, 0); + } + if((self->dtype == NDARRAY_BOOL) || (self->dtype == NDARRAY_UINT8) || (self->dtype == NDARRAY_INT8)) { + return MP_OBJ_FROM_PTR(ndarray); + } else { + uint8_t *array = (uint8_t *)ndarray->array; + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + if(self->dtype == NDARRAY_FLOAT) { + #if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT + SWAP(uint8_t, array[0], array[3]); + SWAP(uint8_t, array[1], array[2]); + #else + SWAP(uint8_t, array[0], array[7]); + SWAP(uint8_t, array[1], array[6]); + SWAP(uint8_t, array[2], array[5]); + SWAP(uint8_t, array[3], array[4]); + #endif + } else { + SWAP(uint8_t, array[0], array[1]); + } + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < ndarray->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + array -= ndarray->strides[ULAB_MAX_DIMS - 1] * ndarray->shape[ULAB_MAX_DIMS-1]; + array += ndarray->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < ndarray->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + array -= ndarray->strides[ULAB_MAX_DIMS - 2] * ndarray->shape[ULAB_MAX_DIMS-2]; + array += ndarray->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < ndarray->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + array -= ndarray->strides[ULAB_MAX_DIMS - 3] * ndarray->shape[ULAB_MAX_DIMS-3]; + array += ndarray->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < ndarray->shape[ULAB_MAX_DIMS - 4]); + #endif + } + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(ndarray_byteswap_obj, 1, ndarray_byteswap); +#endif + +#if NDARRAY_HAS_COPY +mp_obj_t ndarray_copy(mp_obj_t self_in) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + return MP_OBJ_FROM_PTR(ndarray_copy_view(self)); +} + +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_copy_obj, ndarray_copy); +#endif + +ndarray_obj_t *ndarray_new_linear_array(size_t len, uint8_t dtype) { + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + if(len == 0) { + return ndarray_new_dense_ndarray(0, shape, dtype); + } + shape[ULAB_MAX_DIMS-1] = len; + return ndarray_new_dense_ndarray(1, shape, dtype); +} + +ndarray_obj_t *ndarray_from_iterable(mp_obj_t obj, uint8_t dtype) { + // returns an ndarray from an iterable micropython object + // if the input is an ndarray, returns the input... + if(mp_obj_is_type(obj, &ulab_ndarray_type)) { + return MP_OBJ_TO_PTR(obj); + } + // ... otherwise, takes the values from the iterable, and creates the corresponding ndarray + + // First, we have to figure out, whether the elements of the iterable are iterables themself + uint8_t ndim = 0; + size_t shape[ULAB_MAX_DIMS]; + mp_obj_iter_buf_t iter_buf[ULAB_MAX_DIMS]; + mp_obj_t iterable[ULAB_MAX_DIMS]; + // inspect only the very first element in each dimension; this is fast, + // but not completely safe, e.g., length compatibility is not checked + mp_obj_t item = obj; + + while(1) { + if(mp_obj_len_maybe(item) == MP_OBJ_NULL) { + break; + } + if(ndim == ULAB_MAX_DIMS) { + mp_raise_ValueError(translate("too many dimensions")); + } + shape[ndim] = MP_OBJ_SMALL_INT_VALUE(mp_obj_len_maybe(item)); + if(shape[ndim] == 0) { + ndim++; + break; + } + iterable[ndim] = mp_getiter(item, &iter_buf[ndim]); + item = mp_iternext(iterable[ndim]); + ndim++; + } + for(uint8_t i = 0; i < ndim; i++) { + // align all values to the right + shape[ULAB_MAX_DIMS - i - 1] = shape[ndim - 1 - i]; + } + + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(ndim, shape, dtype); + item = obj; + for(uint8_t i = 0; i < ndim - 1; i++) { + // if ndim > 1, descend into the hierarchy + iterable[ULAB_MAX_DIMS - ndim + i] = mp_getiter(item, &iter_buf[ULAB_MAX_DIMS - ndim + i]); + item = mp_iternext(iterable[ULAB_MAX_DIMS - ndim + i]); + } + + size_t idx = 0; + // TODO: this could surely be done in a more elegant way... + #if ULAB_MAX_DIMS > 3 + do { + #endif + #if ULAB_MAX_DIMS > 2 + do { + #endif + #if ULAB_MAX_DIMS > 1 + do { + #endif + iterable[ULAB_MAX_DIMS - 1] = mp_getiter(item, &iter_buf[ULAB_MAX_DIMS - 1]); + ndarray_assign_elements(ndarray, iterable[ULAB_MAX_DIMS - 1], ndarray->dtype, &idx); + #if ULAB_MAX_DIMS > 1 + item = ndim > 1 ? mp_iternext(iterable[ULAB_MAX_DIMS - 2]) : MP_OBJ_STOP_ITERATION; + } while(item != MP_OBJ_STOP_ITERATION); + #endif + #if ULAB_MAX_DIMS > 2 + item = ndim > 2 ? mp_iternext(iterable[ULAB_MAX_DIMS - 3]) : MP_OBJ_STOP_ITERATION; + if(item != MP_OBJ_STOP_ITERATION) { + iterable[ULAB_MAX_DIMS - 2] = mp_getiter(item, &iter_buf[ULAB_MAX_DIMS - 2]); + item = mp_iternext(iterable[ULAB_MAX_DIMS - 2]); + } else { + iterable[ULAB_MAX_DIMS - 2] = MP_OBJ_STOP_ITERATION; + } + } while(iterable[ULAB_MAX_DIMS - 2] != MP_OBJ_STOP_ITERATION); + #endif + #if ULAB_MAX_DIMS > 3 + item = ndim > 3 ? mp_iternext(iterable[ULAB_MAX_DIMS - 4]) : MP_OBJ_STOP_ITERATION; + if(item != MP_OBJ_STOP_ITERATION) { + iterable[ULAB_MAX_DIMS - 3] = mp_getiter(item, &iter_buf[ULAB_MAX_DIMS - 3]); + item = mp_iternext(iterable[ULAB_MAX_DIMS - 3]); + } else { + iterable[ULAB_MAX_DIMS - 3] = MP_OBJ_STOP_ITERATION; + } + } while(iterable[ULAB_MAX_DIMS - 3] != MP_OBJ_STOP_ITERATION); + #endif + + return ndarray; +} + +STATIC uint8_t ndarray_init_helper(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_obj = MP_ROM_INT(NDARRAY_FLOAT) } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + uint8_t _dtype; + #if ULAB_HAS_DTYPE_OBJECT + if(mp_obj_is_type(args[1].u_obj, &ulab_dtype_type)) { + dtype_obj_t *dtype = MP_OBJ_TO_PTR(args[1].u_obj); + _dtype = dtype->dtype; + } else { // this must be an integer defined as a class constant (ulba.uint8 etc.) + _dtype = mp_obj_get_int(args[1].u_obj); + } + #else + _dtype = mp_obj_get_int(args[1].u_obj); + #endif + return _dtype; +} + +STATIC mp_obj_t ndarray_make_new_core(const mp_obj_type_t *type, size_t n_args, size_t n_kw, const mp_obj_t *args, mp_map_t *kw_args) { + uint8_t dtype = ndarray_init_helper(n_args, args, kw_args); + + if(mp_obj_is_type(args[0], &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(args[0]); + return MP_OBJ_FROM_PTR(ndarray_copy_view_convert_type(source, dtype)); + } else { + // assume that the input is an iterable + return MP_OBJ_FROM_PTR(ndarray_from_iterable(args[0], dtype)); + } +} + +mp_obj_t ndarray_array_constructor(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + // array constructor for ndarray, equivalent to numpy.array(...) + return ndarray_make_new_core(&ulab_ndarray_type, n_args, kw_args->used, pos_args, kw_args); +} +MP_DEFINE_CONST_FUN_OBJ_KW(ndarray_array_constructor_obj, 1, ndarray_array_constructor); + +mp_obj_t ndarray_make_new(const mp_obj_type_t *type, size_t n_args, size_t n_kw, const mp_obj_t *args) { + (void) type; + mp_arg_check_num(n_args, n_kw, 1, 2, true); + mp_map_t kw_args; + mp_map_init_fixed_table(&kw_args, n_kw, args + n_args); + return ndarray_make_new_core(type, n_args, n_kw, args, &kw_args); +} + +// broadcasting is used at a number of places, always include +bool ndarray_can_broadcast(ndarray_obj_t *lhs, ndarray_obj_t *rhs, uint8_t *ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + // Returns true or false, depending on, whether the two arrays can be broadcast together + // with numpy's broadcasting rules. These are as follows: + // + // 1. the two shapes are either equal + // 2. one of the shapes is 1 + memset(lstrides, 0, sizeof(size_t)*ULAB_MAX_DIMS); + memset(rstrides, 0, sizeof(size_t)*ULAB_MAX_DIMS); + lstrides[ULAB_MAX_DIMS - 1] = lhs->strides[ULAB_MAX_DIMS - 1]; + rstrides[ULAB_MAX_DIMS - 1] = rhs->strides[ULAB_MAX_DIMS - 1]; + for(uint8_t i=ULAB_MAX_DIMS; i > 0; i--) { + if((lhs->shape[i-1] == rhs->shape[i-1]) || (lhs->shape[i-1] == 0) || (lhs->shape[i-1] == 1) || + (rhs->shape[i-1] == 0) || (rhs->shape[i-1] == 1)) { + shape[i-1] = MAX(lhs->shape[i-1], rhs->shape[i-1]); + if(shape[i-1] > 0) (*ndim)++; + if(lhs->shape[i-1] < 2) { + lstrides[i-1] = 0; + } else { + lstrides[i-1] = lhs->strides[i-1]; + } + if(rhs->shape[i-1] < 2) { + rstrides[i-1] = 0; + } else { + rstrides[i-1] = rhs->strides[i-1]; + } + } else { + return false; + } + } + return true; +} + +#if NDARRAY_HAS_INPLACE_OPS +bool ndarray_can_broadcast_inplace(ndarray_obj_t *lhs, ndarray_obj_t *rhs, int32_t *rstrides) { + // returns true or false, depending on, whether the two arrays can be broadcast together inplace + // this means that the right hand side always must be "smaller" than the left hand side, i.e. + // the broadcasting rules are as follows: + // + // 1. the two shapes are either equal + // 2. the shapes on the right hand side is 1 + memset(rstrides, 0, sizeof(size_t)*ULAB_MAX_DIMS); + rstrides[ULAB_MAX_DIMS - 1] = rhs->strides[ULAB_MAX_DIMS - 1]; + for(uint8_t i=ULAB_MAX_DIMS; i > 0; i--) { + if((lhs->shape[i-1] == rhs->shape[i-1]) || (rhs->shape[i-1] == 0) || (rhs->shape[i-1] == 1)) { + if(rhs->shape[i-1] < 2) { + rstrides[i-1] = 0; + } else { + rstrides[i-1] = rhs->strides[i-1]; + } + } else { + return false; + } + } + return true; +} +#endif + +#if NDARRAY_IS_SLICEABLE +static size_t slice_length(mp_bound_slice_t slice) { + ssize_t len, correction = 1; + if(slice.step > 0) correction = -1; + len = (ssize_t)(slice.stop - slice.start + (slice.step + correction)) / slice.step; + if(len < 0) return 0; + return (size_t)len; +} + +static mp_bound_slice_t generate_slice(mp_int_t n, mp_obj_t index) { + mp_bound_slice_t slice; + if(mp_obj_is_type(index, &mp_type_slice)) { + mp_obj_slice_indices(index, n, &slice); + } else if(mp_obj_is_int(index)) { + mp_int_t _index = mp_obj_get_int(index); + if(_index < 0) { + _index += n; + } + if((_index >= n) || (_index < 0)) { + mp_raise_msg(&mp_type_IndexError, translate("index is out of bounds")); + } + slice.start = _index; + slice.stop = _index + 1; + slice.step = 1; + } else { + mp_raise_msg(&mp_type_IndexError, translate("indices must be integers, slices, or Boolean lists")); + } + return slice; +} + +static ndarray_obj_t *ndarray_view_from_slices(ndarray_obj_t *ndarray, mp_obj_tuple_t *tuple) { + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memset(strides, 0, sizeof(size_t)*ULAB_MAX_DIMS); + + uint8_t ndim = ndarray->ndim; + + for(uint8_t i=0; i < ndim; i++) { + // copy from the end + shape[ULAB_MAX_DIMS - 1 - i] = ndarray->shape[ULAB_MAX_DIMS - 1 - i]; + strides[ULAB_MAX_DIMS - 1 - i] = ndarray->strides[ULAB_MAX_DIMS - 1 - i]; + } + int32_t offset = 0; + for(uint8_t i=0; i < tuple->len; i++) { + if(mp_obj_is_int(tuple->items[i])) { + // if item is an int, the dimension will first be reduced ... + ndim--; + int32_t k = mp_obj_get_int(tuple->items[i]); + if(k < 0) { + k += ndarray->shape[ULAB_MAX_DIMS - ndarray->ndim + i]; + } + if((k >= (int32_t)ndarray->shape[ULAB_MAX_DIMS - ndarray->ndim + i]) || (k < 0)) { + mp_raise_msg(&mp_type_IndexError, translate("index is out of bounds")); + } + offset += ndarray->strides[ULAB_MAX_DIMS - ndarray->ndim + i] * k; + // ... and then we have to shift the shapes to the right + for(uint8_t j=0; j < i; j++) { + shape[ULAB_MAX_DIMS - ndarray->ndim + i - j] = shape[ULAB_MAX_DIMS - ndarray->ndim + i - j - 1]; + strides[ULAB_MAX_DIMS - ndarray->ndim + i - j] = strides[ULAB_MAX_DIMS - ndarray->ndim + i - j - 1]; + } + } else { + mp_bound_slice_t slice = generate_slice(shape[ULAB_MAX_DIMS - ndarray->ndim + i], tuple->items[i]); + shape[ULAB_MAX_DIMS - ndarray->ndim + i] = slice_length(slice); + offset += ndarray->strides[ULAB_MAX_DIMS - ndarray->ndim + i] * (int32_t)slice.start; + strides[ULAB_MAX_DIMS - ndarray->ndim + i] = (int32_t)slice.step * ndarray->strides[ULAB_MAX_DIMS - ndarray->ndim + i]; + } + } + return ndarray_new_view(ndarray, ndim, shape, strides, offset); +} + +void ndarray_assign_view(ndarray_obj_t *view, ndarray_obj_t *values) { + if(values->len == 0) { + return; + } + uint8_t ndim = 0; + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + int32_t *lstrides = m_new(int32_t, ULAB_MAX_DIMS); + int32_t *rstrides = m_new(int32_t, ULAB_MAX_DIMS); + if(!ndarray_can_broadcast(view, values, &ndim, shape, lstrides, rstrides)) { + mp_raise_ValueError(translate("operands could not be broadcast together")); + m_del(size_t, shape, ULAB_MAX_DIMS); + m_del(int32_t, lstrides, ULAB_MAX_DIMS); + m_del(int32_t, rstrides, ULAB_MAX_DIMS); + } + + uint8_t *rarray = (uint8_t *)values->array; + + #if ULAB_SUPPORTS_COMPLEX + if(values->dtype == NDARRAY_COMPLEX) { + if(view->dtype != NDARRAY_COMPLEX) { + mp_raise_TypeError(translate("cannot convert complex to dtype")); + } else { + uint8_t *larray = (uint8_t *)view->array; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + memcpy(larray, rarray, view->itemsize); + larray += lstrides[ULAB_MAX_DIMS - 1]; + rarray += rstrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < view->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + larray -= lstrides[ULAB_MAX_DIMS - 1] * view->shape[ULAB_MAX_DIMS-1]; + larray += lstrides[ULAB_MAX_DIMS - 2]; + rarray -= rstrides[ULAB_MAX_DIMS - 1] * view->shape[ULAB_MAX_DIMS-1]; + rarray += rstrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < view->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + larray -= lstrides[ULAB_MAX_DIMS - 2] * view->shape[ULAB_MAX_DIMS-2]; + larray += lstrides[ULAB_MAX_DIMS - 3]; + rarray -= rstrides[ULAB_MAX_DIMS - 2] * view->shape[ULAB_MAX_DIMS-2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < view->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + larray -= lstrides[ULAB_MAX_DIMS - 3] * view->shape[ULAB_MAX_DIMS-3]; + larray += lstrides[ULAB_MAX_DIMS - 4]; + rarray -= rstrides[ULAB_MAX_DIMS - 3] * view->shape[ULAB_MAX_DIMS-3]; + rarray += rstrides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < view->shape[ULAB_MAX_DIMS - 4]); + #endif + } + return; + } + #endif + + // since in ASSIGNMENT_LOOP the array has a type, we have to divide the strides by the itemsize + for(uint8_t i=0; i < ULAB_MAX_DIMS; i++) { + lstrides[i] /= view->itemsize; + #if ULAB_SUPPORTS_COMPLEX + if(view->dtype == NDARRAY_COMPLEX) { + lstrides[i] *= 2; + } + #endif + } + + if(view->dtype == NDARRAY_UINT8) { + if(values->dtype == NDARRAY_UINT8) { + ASSIGNMENT_LOOP(view, uint8_t, uint8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT8) { + ASSIGNMENT_LOOP(view, uint8_t, int8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_UINT16) { + ASSIGNMENT_LOOP(view, uint8_t, uint16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT16) { + ASSIGNMENT_LOOP(view, uint8_t, int16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_FLOAT) { + ASSIGNMENT_LOOP(view, uint8_t, mp_float_t, lstrides, rarray, rstrides); + } + } else if(view->dtype == NDARRAY_INT8) { + if(values->dtype == NDARRAY_UINT8) { + ASSIGNMENT_LOOP(view, int8_t, uint8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT8) { + ASSIGNMENT_LOOP(view, int8_t, int8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_UINT16) { + ASSIGNMENT_LOOP(view, int8_t, uint16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT16) { + ASSIGNMENT_LOOP(view, int8_t, int16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_FLOAT) { + ASSIGNMENT_LOOP(view, int8_t, mp_float_t, lstrides, rarray, rstrides); + } + } else if(view->dtype == NDARRAY_UINT16) { + if(values->dtype == NDARRAY_UINT8) { + ASSIGNMENT_LOOP(view, uint16_t, uint8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT8) { + ASSIGNMENT_LOOP(view, uint16_t, int8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_UINT16) { + ASSIGNMENT_LOOP(view, uint16_t, uint16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT16) { + ASSIGNMENT_LOOP(view, uint16_t, int16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_FLOAT) { + ASSIGNMENT_LOOP(view, uint16_t, mp_float_t, lstrides, rarray, rstrides); + } + } else if(view->dtype == NDARRAY_INT16) { + if(values->dtype == NDARRAY_UINT8) { + ASSIGNMENT_LOOP(view, int16_t, uint8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT8) { + ASSIGNMENT_LOOP(view, int16_t, int8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_UINT16) { + ASSIGNMENT_LOOP(view, int16_t, uint16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT16) { + ASSIGNMENT_LOOP(view, int16_t, int16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_FLOAT) { + ASSIGNMENT_LOOP(view, int16_t, mp_float_t, lstrides, rarray, rstrides); + } + } else { // the dtype must be an mp_float_t or complex now + if(values->dtype == NDARRAY_UINT8) { + ASSIGNMENT_LOOP(view, mp_float_t, uint8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT8) { + ASSIGNMENT_LOOP(view, mp_float_t, int8_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_UINT16) { + ASSIGNMENT_LOOP(view, mp_float_t, uint16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_INT16) { + ASSIGNMENT_LOOP(view, mp_float_t, int16_t, lstrides, rarray, rstrides); + } else if(values->dtype == NDARRAY_FLOAT) { + ASSIGNMENT_LOOP(view, mp_float_t, mp_float_t, lstrides, rarray, rstrides); + } + } +} + +static mp_obj_t ndarray_from_boolean_index(ndarray_obj_t *ndarray, ndarray_obj_t *index) { + // returns a 1D array, indexed by a Boolean array + if(ndarray->len != index->len) { + mp_raise_ValueError(translate("array and index length must be equal")); + } + uint8_t *iarray = (uint8_t *)index->array; + // first we have to find out how many trues there are + size_t count = 0; + for(size_t i=0; i < index->len; i++) { + count += *iarray; + iarray += index->strides[ULAB_MAX_DIMS - 1]; + } + ndarray_obj_t *results = ndarray_new_linear_array(count, ndarray->dtype); + uint8_t *rarray = (uint8_t *)results->array; + uint8_t *array = (uint8_t *)ndarray->array; + // re-wind the index array + iarray = index->array; + for(size_t i=0; i < index->len; i++) { + if(*iarray) { + memcpy(rarray, array, results->itemsize); + rarray += results->itemsize; + count++; + } + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + iarray += index->strides[ULAB_MAX_DIMS - 1]; + } + return MP_OBJ_FROM_PTR(results); +} + +static mp_obj_t ndarray_assign_from_boolean_index(ndarray_obj_t *ndarray, ndarray_obj_t *index, ndarray_obj_t *values) { + // assigns values to a Boolean-indexed array + // first we have to find out how many trues there are + uint8_t *iarray = (uint8_t *)index->array; + size_t istride = index->strides[ULAB_MAX_DIMS - 1]; + size_t count = 0; + for(size_t i=0; i < index->len; i++) { + count += *iarray; + iarray += istride; + } + // re-wind the index array + iarray = index->array; + uint8_t *varray = (uint8_t *)values->array; + size_t vstride; + + if(count == values->len) { + // there are as many values as true indices + vstride = values->strides[ULAB_MAX_DIMS - 1]; + } else { + // there is a single value + vstride = 0; + } + + #if ULAB_SUPPORTS_COMPLEX + if(values->dtype == NDARRAY_COMPLEX) { + if(ndarray->dtype != NDARRAY_COMPLEX) { + mp_raise_TypeError(translate("cannot convert complex to dtype")); + } else { + uint8_t *array = (uint8_t *)ndarray->array; + for(size_t i = 0; i < ndarray->len; i++) { + if(*iarray) { + memcpy(array, varray, ndarray->itemsize); + varray += vstride; + } + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + iarray += istride; + } while(0); + return MP_OBJ_FROM_PTR(ndarray); + } + } + #endif + + int32_t lstrides = ndarray->strides[ULAB_MAX_DIMS - 1] / ndarray->itemsize; + + if(ndarray->dtype == NDARRAY_UINT8) { + if(values->dtype == NDARRAY_UINT8) { + BOOLEAN_ASSIGNMENT_LOOP(uint8_t, uint8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT8) { + BOOLEAN_ASSIGNMENT_LOOP(uint8_t, int8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_UINT16) { + BOOLEAN_ASSIGNMENT_LOOP(uint8_t, uint16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT16) { + BOOLEAN_ASSIGNMENT_LOOP(uint8_t, int16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_FLOAT) { + BOOLEAN_ASSIGNMENT_LOOP(uint8_t, mp_float_t, ndarray, lstrides, iarray, istride, varray, vstride); + } + } else if(ndarray->dtype == NDARRAY_INT8) { + if(values->dtype == NDARRAY_UINT8) { + BOOLEAN_ASSIGNMENT_LOOP(int8_t, uint8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT8) { + BOOLEAN_ASSIGNMENT_LOOP(int8_t, int8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_UINT16) { + BOOLEAN_ASSIGNMENT_LOOP(int8_t, uint16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT16) { + BOOLEAN_ASSIGNMENT_LOOP(int8_t, int16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_FLOAT) { + BOOLEAN_ASSIGNMENT_LOOP(int8_t, mp_float_t, ndarray, lstrides, iarray, istride, varray, vstride); + } + } else if(ndarray->dtype == NDARRAY_UINT16) { + if(values->dtype == NDARRAY_UINT8) { + BOOLEAN_ASSIGNMENT_LOOP(uint16_t, uint8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT8) { + BOOLEAN_ASSIGNMENT_LOOP(uint16_t, int8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_UINT16) { + BOOLEAN_ASSIGNMENT_LOOP(uint16_t, uint16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT16) { + BOOLEAN_ASSIGNMENT_LOOP(uint16_t, int16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_FLOAT) { + BOOLEAN_ASSIGNMENT_LOOP(uint16_t, mp_float_t, ndarray, lstrides, iarray, istride, varray, vstride); + } + } else if(ndarray->dtype == NDARRAY_INT16) { + if(values->dtype == NDARRAY_UINT8) { + BOOLEAN_ASSIGNMENT_LOOP(int16_t, uint8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT8) { + BOOLEAN_ASSIGNMENT_LOOP(int16_t, int8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_UINT16) { + BOOLEAN_ASSIGNMENT_LOOP(int16_t, uint16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT16) { + BOOLEAN_ASSIGNMENT_LOOP(int16_t, int16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_FLOAT) { + BOOLEAN_ASSIGNMENT_LOOP(int16_t, mp_float_t, ndarray, lstrides, iarray, istride, varray, vstride); + } + } else { + #if ULAB_SUPPORTS_COMPLEX + if(ndarray->dtype == NDARRAY_COMPLEX) { + lstrides *= 2; + } + #endif + if(values->dtype == NDARRAY_UINT8) { + BOOLEAN_ASSIGNMENT_LOOP(mp_float_t, uint8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT8) { + BOOLEAN_ASSIGNMENT_LOOP(mp_float_t, int8_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_UINT16) { + BOOLEAN_ASSIGNMENT_LOOP(mp_float_t, uint16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_INT16) { + BOOLEAN_ASSIGNMENT_LOOP(mp_float_t, int16_t, ndarray, lstrides, iarray, istride, varray, vstride); + } else if(values->dtype == NDARRAY_FLOAT) { + BOOLEAN_ASSIGNMENT_LOOP(mp_float_t, mp_float_t, ndarray, lstrides, iarray, istride, varray, vstride); + } + } + return MP_OBJ_FROM_PTR(ndarray); +} + +static mp_obj_t ndarray_get_slice(ndarray_obj_t *ndarray, mp_obj_t index, ndarray_obj_t *values) { + if(mp_obj_is_type(index, &ulab_ndarray_type)) { + ndarray_obj_t *nindex = MP_OBJ_TO_PTR(index); + if((nindex->ndim > 1) || (nindex->boolean == false)) { + mp_raise_NotImplementedError(translate("operation is implemented for 1D Boolean arrays only")); + } + if(values == NULL) { // return value(s) + return ndarray_from_boolean_index(ndarray, nindex); + } else { // assign value(s) + ndarray_assign_from_boolean_index(ndarray, nindex, values); + } + } + if(mp_obj_is_type(index, &mp_type_tuple) || mp_obj_is_int(index) || mp_obj_is_type(index, &mp_type_slice)) { + mp_obj_tuple_t *tuple; + if(mp_obj_is_type(index, &mp_type_tuple)) { + tuple = MP_OBJ_TO_PTR(index); + if(tuple->len > ndarray->ndim) { + mp_raise_msg(&mp_type_IndexError, translate("too many indices")); + } + } else { + mp_obj_t *items = m_new(mp_obj_t, 1); + items[0] = index; + tuple = mp_obj_new_tuple(1, items); + } + ndarray_obj_t *view = ndarray_view_from_slices(ndarray, tuple); + if(values == NULL) { // return value(s) + // if the view has been reduced to nothing, return a single value + if(view->ndim == 0) { + return ndarray_get_item(view, view->array); + } else { + return MP_OBJ_FROM_PTR(view); + } + } else { // assign value(s) + ndarray_assign_view(view, values); + } + } + return mp_const_none; +} + +mp_obj_t ndarray_subscr(mp_obj_t self_in, mp_obj_t index, mp_obj_t value) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + + if (value == MP_OBJ_SENTINEL) { // return value(s) + return ndarray_get_slice(self, index, NULL); + } else { // assignment to slices; the value must be an ndarray, or a scalar + ndarray_obj_t *values = ndarray_from_mp_obj(value, 0); + return ndarray_get_slice(self, index, values); + } + return mp_const_none; +} +#endif /* NDARRAY_IS_SLICEABLE */ + +#if NDARRAY_IS_ITERABLE + +// itarray iterator +mp_obj_t ndarray_getiter(mp_obj_t o_in, mp_obj_iter_buf_t *iter_buf) { + return ndarray_new_ndarray_iterator(o_in, iter_buf); +} + +typedef struct _mp_obj_ndarray_it_t { + mp_obj_base_t base; + mp_fun_1_t iternext; + mp_obj_t ndarray; + size_t cur; +} mp_obj_ndarray_it_t; + +mp_obj_t ndarray_iternext(mp_obj_t self_in) { + mp_obj_ndarray_it_t *self = MP_OBJ_TO_PTR(self_in); + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(self->ndarray); + uint8_t *array = (uint8_t *)ndarray->array; + + size_t iter_end = ndarray->shape[ULAB_MAX_DIMS-ndarray->ndim]; + if(self->cur < iter_end) { + // separating this case out saves 50 bytes for 1D arrays + #if ULAB_MAX_DIMS == 1 + array += self->cur * ndarray->strides[0]; + self->cur++; + return ndarray_get_item(ndarray, array); + #else + if(ndarray->ndim == 1) { // we have a linear array + array += self->cur * ndarray->strides[ULAB_MAX_DIMS - 1]; + self->cur++; + return ndarray_get_item(ndarray, array); + } else { // we have a tensor, return the reduced view + size_t offset = self->cur * ndarray->strides[ULAB_MAX_DIMS - ndarray->ndim]; + self->cur++; + return MP_OBJ_FROM_PTR(ndarray_new_view(ndarray, ndarray->ndim-1, ndarray->shape, ndarray->strides, offset)); + } + #endif + } else { + return MP_OBJ_STOP_ITERATION; + } +} + +mp_obj_t ndarray_new_ndarray_iterator(mp_obj_t ndarray, mp_obj_iter_buf_t *iter_buf) { + assert(sizeof(mp_obj_ndarray_it_t) <= sizeof(mp_obj_iter_buf_t)); + mp_obj_ndarray_it_t *iter = (mp_obj_ndarray_it_t *)iter_buf; + iter->base.type = &mp_type_polymorph_iter; + iter->iternext = ndarray_iternext; + iter->ndarray = ndarray; + iter->cur = 0; + return MP_OBJ_FROM_PTR(iter); +} +#endif /* NDARRAY_IS_ITERABLE */ + +#if NDARRAY_HAS_FLATTEN +mp_obj_t ndarray_flatten(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_order, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_QSTR(MP_QSTR_C)} }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args - 1, pos_args + 1, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + ndarray_obj_t *self = MP_OBJ_TO_PTR(pos_args[0]); + GET_STR_DATA_LEN(args[0].u_obj, order, len); + if((len != 1) || ((memcmp(order, "C", 1) != 0) && (memcmp(order, "F", 1) != 0))) { + mp_raise_ValueError(translate("flattening order must be either 'C', or 'F'")); + } + + uint8_t *sarray = (uint8_t *)self->array; + ndarray_obj_t *ndarray = ndarray_new_linear_array(self->len, self->dtype); + uint8_t *array = (uint8_t *)ndarray->array; + + if(memcmp(order, "C", 1) == 0) { // C-type ordering + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + memcpy(array, sarray, self->itemsize); + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + sarray += self->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < self->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= self->strides[ULAB_MAX_DIMS - 1] * self->shape[ULAB_MAX_DIMS-1]; + sarray += self->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < self->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + sarray -= self->strides[ULAB_MAX_DIMS - 2] * self->shape[ULAB_MAX_DIMS-2]; + sarray += self->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < self->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + sarray -= self->strides[ULAB_MAX_DIMS - 3] * self->shape[ULAB_MAX_DIMS-3]; + sarray += self->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < self->shape[ULAB_MAX_DIMS - 4]); + #endif + } else { // 'F', Fortran-type ordering + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + memcpy(array, sarray, self->itemsize); + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + sarray += self->strides[0]; + l++; + } while(l < self->shape[0]); + #if ULAB_MAX_DIMS > 1 + sarray -= self->strides[0] * self->shape[0]; + sarray += self->strides[1]; + k++; + } while(k < self->shape[1]); + #endif + #if ULAB_MAX_DIMS > 2 + sarray -= self->strides[1] * self->shape[1]; + sarray += self->strides[2]; + j++; + } while(j < self->shape[2]); + #endif + #if ULAB_MAX_DIMS > 3 + sarray -= self->strides[2] * self->shape[2]; + sarray += self->strides[3]; + i++; + } while(i < self->shape[3]); + #endif + } + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(ndarray_flatten_obj, 1, ndarray_flatten); +#endif + +#if NDARRAY_HAS_ITEMSIZE +mp_obj_t ndarray_itemsize(mp_obj_t self_in) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + return MP_OBJ_NEW_SMALL_INT(self->itemsize); +} +#endif + +#if NDARRAY_HAS_SHAPE +mp_obj_t ndarray_shape(mp_obj_t self_in) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + uint8_t nitems = MAX(1, self->ndim); + mp_obj_t *items = m_new(mp_obj_t, nitems); + for(uint8_t i = 0; i < nitems; i++) { + items[nitems - i - 1] = mp_obj_new_int(self->shape[ULAB_MAX_DIMS - i - 1]); + } + mp_obj_t tuple = mp_obj_new_tuple(nitems, items); + m_del(mp_obj_t, items, nitems); + return tuple; +} +#endif + +#if NDARRAY_HAS_SIZE +mp_obj_t ndarray_size(mp_obj_t self_in) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + return mp_obj_new_int(self->len); +} +#endif + +#if NDARRAY_HAS_STRIDES +mp_obj_t ndarray_strides(mp_obj_t self_in) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + mp_obj_t *items = m_new(mp_obj_t, self->ndim); + for(int8_t i=0; i < self->ndim; i++) { + items[i] = mp_obj_new_int(self->strides[ULAB_MAX_DIMS - self->ndim + i]); + } + mp_obj_t tuple = mp_obj_new_tuple(self->ndim, items); + m_del(mp_obj_t, items, self->ndim); + return tuple; +} +#endif + +#if NDARRAY_HAS_TOBYTES +mp_obj_t ndarray_tobytes(mp_obj_t self_in) { + // As opposed to numpy, this function returns a bytearray object with the data pointer (i.e., not a copy) + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + // Piping into a bytearray makes sense for dense arrays only, + // so bail out, if that is not the case + if(!ndarray_is_dense(self)) { + mp_raise_ValueError(translate("tobytes can be invoked for dense arrays only")); + } + return mp_obj_new_bytearray_by_ref(self->itemsize * self->len, self->array); +} + +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_tobytes_obj, ndarray_tobytes); +#endif + +#if NDARRAY_HAS_TOLIST +static mp_obj_t ndarray_recursive_list(ndarray_obj_t *self, uint8_t *array, uint8_t dim) { + int32_t stride = self->strides[ULAB_MAX_DIMS - dim]; + size_t len = self->shape[ULAB_MAX_DIMS - dim]; + + mp_obj_list_t *list = MP_OBJ_TO_PTR(mp_obj_new_list(len, NULL)); + for(size_t i = 0; i < len; i++) { + if(dim == 1) { + list->items[i] = ndarray_get_item(self, array); + } else { + list->items[i] = ndarray_recursive_list(self, array, dim-1); + } + array += stride; + } + return MP_OBJ_FROM_PTR(list); +} + +mp_obj_t ndarray_tolist(mp_obj_t self_in) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + uint8_t *array = (uint8_t *)self->array; + return ndarray_recursive_list(self, array, self->ndim); +} + +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_tolist_obj, ndarray_tolist); +#endif + +// Binary operations +ndarray_obj_t *ndarray_from_mp_obj(mp_obj_t obj, uint8_t other_type) { + // creates an ndarray from a micropython int or float + // if the input is an ndarray, it is returned + // if other_type is 0, return the smallest type that can accommodate the object + ndarray_obj_t *ndarray; + + if(mp_obj_is_int(obj)) { + int32_t ivalue = mp_obj_get_int(obj); + if((ivalue < -32767) || (ivalue > 32767)) { + // the integer value clearly does not fit the ulab integer types, so move on to float + ndarray = ndarray_new_linear_array(1, NDARRAY_FLOAT); + mp_float_t *array = (mp_float_t *)ndarray->array; + array[0] = (mp_float_t)ivalue; + } else { + uint8_t dtype; + if(ivalue < 0) { + if(ivalue > -128) { + dtype = NDARRAY_INT8; + } else { + dtype = NDARRAY_INT16; + } + } else { // ivalue >= 0 + if((other_type == NDARRAY_INT8) || (other_type == NDARRAY_INT16)) { + if(ivalue < 128) { + dtype = NDARRAY_INT8; + } else { + dtype = NDARRAY_INT16; + } + } else { // other_type = 0 is also included here + if(ivalue < 256) { + dtype = NDARRAY_UINT8; + } else { + dtype = NDARRAY_UINT16; + } + } + } + ndarray = ndarray_new_linear_array(1, dtype); + ndarray_set_value(dtype, ndarray->array, 0, obj); + } + } else if(mp_obj_is_float(obj)) { + ndarray = ndarray_new_linear_array(1, NDARRAY_FLOAT); + mp_float_t *array = (mp_float_t *)ndarray->array; + array[0] = mp_obj_get_float(obj); + } else if(mp_obj_is_type(obj, &ulab_ndarray_type)){ + return obj; + } + #if ULAB_SUPPORTS_COMPLEX + else if(mp_obj_is_type(obj, &mp_type_complex)) { + ndarray = ndarray_new_linear_array(1, NDARRAY_COMPLEX); + mp_float_t *array = (mp_float_t *)ndarray->array; + mp_obj_get_complex(obj, &array[0], &array[1]); + } + #endif + else { + // assume that the input is an iterable (raises an exception, if it is not the case) + ndarray = ndarray_from_iterable(obj, NDARRAY_FLOAT); + } + return ndarray; +} + +#if NDARRAY_HAS_BINARY_OPS || NDARRAY_HAS_INPLACE_OPS +mp_obj_t ndarray_binary_op(mp_binary_op_t _op, mp_obj_t lobj, mp_obj_t robj) { + // TODO: implement in-place operators + // if the ndarray stands on the right hand side of the expression, simply swap the operands + ndarray_obj_t *lhs, *rhs; + mp_binary_op_t op = _op; + if((op == MP_BINARY_OP_REVERSE_ADD) || (op == MP_BINARY_OP_REVERSE_MULTIPLY) || + (op == MP_BINARY_OP_REVERSE_POWER) || (op == MP_BINARY_OP_REVERSE_SUBTRACT) || + (op == MP_BINARY_OP_REVERSE_TRUE_DIVIDE)) { + lhs = ndarray_from_mp_obj(robj, 0); + rhs = ndarray_from_mp_obj(lobj, lhs->dtype); + } else { + lhs = ndarray_from_mp_obj(lobj, 0); + rhs = ndarray_from_mp_obj(robj, lhs->dtype); + } + if(op == MP_BINARY_OP_REVERSE_ADD) { + op = MP_BINARY_OP_ADD; + } else if(op == MP_BINARY_OP_REVERSE_MULTIPLY) { + op = MP_BINARY_OP_MULTIPLY; + } else if(op == MP_BINARY_OP_REVERSE_POWER) { + op = MP_BINARY_OP_POWER; + } else if(op == MP_BINARY_OP_REVERSE_SUBTRACT) { + op = MP_BINARY_OP_SUBTRACT; + } else if(op == MP_BINARY_OP_REVERSE_TRUE_DIVIDE) { + op = MP_BINARY_OP_TRUE_DIVIDE; + } + + uint8_t ndim = 0; + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + int32_t *lstrides = m_new(int32_t, ULAB_MAX_DIMS); + int32_t *rstrides = m_new(int32_t, ULAB_MAX_DIMS); + uint8_t broadcastable; + if((op == MP_BINARY_OP_INPLACE_ADD) || (op == MP_BINARY_OP_INPLACE_MULTIPLY) || (op == MP_BINARY_OP_INPLACE_POWER) || + (op == MP_BINARY_OP_INPLACE_SUBTRACT) || (op == MP_BINARY_OP_INPLACE_TRUE_DIVIDE)) { + broadcastable = ndarray_can_broadcast_inplace(lhs, rhs, rstrides); + } else { + broadcastable = ndarray_can_broadcast(lhs, rhs, &ndim, shape, lstrides, rstrides); + } + if(!broadcastable) { + mp_raise_ValueError(translate("operands could not be broadcast together")); + m_del(size_t, shape, ULAB_MAX_DIMS); + m_del(int32_t, lstrides, ULAB_MAX_DIMS); + m_del(int32_t, rstrides, ULAB_MAX_DIMS); + } + // the empty arrays have to be treated separately + uint8_t dtype = NDARRAY_INT16; + ndarray_obj_t *nd; + if((lhs->ndim == 0) || (rhs->ndim == 0)) { + switch(op) { + case MP_BINARY_OP_INPLACE_ADD: + case MP_BINARY_OP_INPLACE_MULTIPLY: + case MP_BINARY_OP_INPLACE_SUBTRACT: + case MP_BINARY_OP_ADD: + case MP_BINARY_OP_MULTIPLY: + case MP_BINARY_OP_SUBTRACT: + // here we don't have to list those cases that result in an int16, + // because dtype is initialised with that NDARRAY_INT16 + if(lhs->dtype == rhs->dtype) { + dtype = rhs->dtype; + } else if((lhs->dtype == NDARRAY_FLOAT) || (rhs->dtype == NDARRAY_FLOAT)) { + dtype = NDARRAY_FLOAT; + } else if(((lhs->dtype == NDARRAY_UINT8) && (rhs->dtype == NDARRAY_UINT16)) || + ((lhs->dtype == NDARRAY_INT8) && (rhs->dtype == NDARRAY_UINT16)) || + ((rhs->dtype == NDARRAY_UINT8) && (lhs->dtype == NDARRAY_UINT16)) || + ((rhs->dtype == NDARRAY_INT8) && (lhs->dtype == NDARRAY_UINT16))) { + dtype = NDARRAY_UINT16; + } + return MP_OBJ_FROM_PTR(ndarray_new_linear_array(0, dtype)); + break; + + case MP_BINARY_OP_INPLACE_POWER: + case MP_BINARY_OP_INPLACE_TRUE_DIVIDE: + case MP_BINARY_OP_POWER: + case MP_BINARY_OP_TRUE_DIVIDE: + return MP_OBJ_FROM_PTR(ndarray_new_linear_array(0, NDARRAY_FLOAT)); + break; + + case MP_BINARY_OP_LESS: + case MP_BINARY_OP_LESS_EQUAL: + case MP_BINARY_OP_MORE: + case MP_BINARY_OP_MORE_EQUAL: + case MP_BINARY_OP_EQUAL: + case MP_BINARY_OP_NOT_EQUAL: + nd = ndarray_new_linear_array(0, NDARRAY_UINT8); + nd->boolean = 1; + return MP_OBJ_FROM_PTR(nd); + + default: + return mp_const_none; + break; + } + } + + switch(op) { + // first the in-place operators + #if NDARRAY_HAS_INPLACE_ADD + case MP_BINARY_OP_INPLACE_ADD: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + return ndarray_inplace_ams(lhs, rhs, rstrides, op); + break; + #endif + #if NDARRAY_HAS_INPLACE_MULTIPLY + case MP_BINARY_OP_INPLACE_MULTIPLY: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + return ndarray_inplace_ams(lhs, rhs, rstrides, op); + break; + #endif + #if NDARRAY_HAS_INPLACE_POWER + case MP_BINARY_OP_INPLACE_POWER: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + return ndarray_inplace_power(lhs, rhs, rstrides); + break; + #endif + #if NDARRAY_HAS_INPLACE_SUBTRACT + case MP_BINARY_OP_INPLACE_SUBTRACT: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + return ndarray_inplace_ams(lhs, rhs, rstrides, op); + break; + #endif + #if NDARRAY_HAS_INPLACE_TRUE_DIVIDE + case MP_BINARY_OP_INPLACE_TRUE_DIVIDE: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + return ndarray_inplace_divide(lhs, rhs, rstrides); + break; + #endif + // end if in-place operators + + #if NDARRAY_HAS_BINARY_OP_LESS + case MP_BINARY_OP_LESS: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + // here we simply swap the operands + return ndarray_binary_more(rhs, lhs, ndim, shape, rstrides, lstrides, MP_BINARY_OP_MORE); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_LESS_EQUAL + case MP_BINARY_OP_LESS_EQUAL: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + // here we simply swap the operands + return ndarray_binary_more(rhs, lhs, ndim, shape, rstrides, lstrides, MP_BINARY_OP_MORE_EQUAL); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_EQUAL + case MP_BINARY_OP_EQUAL: + return ndarray_binary_equality(lhs, rhs, ndim, shape, lstrides, rstrides, MP_BINARY_OP_EQUAL); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_NOT_EQUAL + case MP_BINARY_OP_NOT_EQUAL: + return ndarray_binary_equality(lhs, rhs, ndim, shape, lstrides, rstrides, MP_BINARY_OP_NOT_EQUAL); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_ADD + case MP_BINARY_OP_ADD: + return ndarray_binary_add(lhs, rhs, ndim, shape, lstrides, rstrides); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_MULTIPLY + case MP_BINARY_OP_MULTIPLY: + return ndarray_binary_multiply(lhs, rhs, ndim, shape, lstrides, rstrides); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_MORE + case MP_BINARY_OP_MORE: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + return ndarray_binary_more(lhs, rhs, ndim, shape, lstrides, rstrides, MP_BINARY_OP_MORE); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_MORE_EQUAL + case MP_BINARY_OP_MORE_EQUAL: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + return ndarray_binary_more(lhs, rhs, ndim, shape, lstrides, rstrides, MP_BINARY_OP_MORE_EQUAL); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_SUBTRACT + case MP_BINARY_OP_SUBTRACT: + return ndarray_binary_subtract(lhs, rhs, ndim, shape, lstrides, rstrides); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_TRUE_DIVIDE + case MP_BINARY_OP_TRUE_DIVIDE: + return ndarray_binary_true_divide(lhs, rhs, ndim, shape, lstrides, rstrides); + break; + #endif + #if NDARRAY_HAS_BINARY_OP_POWER + case MP_BINARY_OP_POWER: + COMPLEX_DTYPE_NOT_IMPLEMENTED(lhs->dtype); + return ndarray_binary_power(lhs, rhs, ndim, shape, lstrides, rstrides); + break; + #endif + default: + return MP_OBJ_NULL; // op not supported + break; + } + return MP_OBJ_NULL; +} +#endif /* NDARRAY_HAS_BINARY_OPS || NDARRAY_HAS_INPLACE_OPS */ + +#if NDARRAY_HAS_UNARY_OPS +mp_obj_t ndarray_unary_op(mp_unary_op_t op, mp_obj_t self_in) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + ndarray_obj_t *ndarray = NULL; + + switch (op) { + #if NDARRAY_HAS_UNARY_OP_ABS + case MP_UNARY_OP_ABS: + #if ULAB_SUPPORTS_COMPLEX + if(self->dtype == NDARRAY_COMPLEX) { + int32_t *strides = strides_from_shape(self->shape, NDARRAY_FLOAT); + ndarray_obj_t *target = ndarray_new_ndarray(self->ndim, self->shape, strides, NDARRAY_FLOAT); + ndarray = carray_abs(self, target); + } else { + #endif + ndarray = ndarray_copy_view(self); + // if Boolean, NDARRAY_UINT8, or NDARRAY_UINT16, there is nothing to do + if(self->dtype == NDARRAY_INT8) { + int8_t *array = (int8_t *)ndarray->array; + for(size_t i=0; i < self->len; i++, array++) { + if(*array < 0) *array = -(*array); + } + } else if(self->dtype == NDARRAY_INT16) { + int16_t *array = (int16_t *)ndarray->array; + for(size_t i=0; i < self->len; i++, array++) { + if(*array < 0) *array = -(*array); + } + } else { + mp_float_t *array = (mp_float_t *)ndarray->array; + for(size_t i=0; i < self->len; i++, array++) { + if(*array < 0) *array = -(*array); + } + } + #if ULAB_SUPPORTS_COMPLEX + } + #endif + return MP_OBJ_FROM_PTR(ndarray); + break; + #endif + #if NDARRAY_HAS_UNARY_OP_INVERT + case MP_UNARY_OP_INVERT: + #if ULAB_SUPPORTS_COMPLEX + if(self->dtype == NDARRAY_FLOAT || self->dtype == NDARRAY_COMPLEX) { + #else + if(self->dtype == NDARRAY_FLOAT) { + #endif + mp_raise_ValueError(translate("operation is not supported for given type")); + } + // we can invert the content byte by byte, no need to distinguish between different dtypes + ndarray = ndarray_copy_view(self); // from this point, this is a dense copy + uint8_t *array = (uint8_t *)ndarray->array; + if(ndarray->boolean) { + for(size_t i=0; i < ndarray->len; i++, array++) *array = *array ^ 0x01; + } else { + uint8_t itemsize = ulab_binary_get_size(self->dtype); + for(size_t i=0; i < ndarray->len*itemsize; i++, array++) *array ^= 0xFF; + } + return MP_OBJ_FROM_PTR(ndarray); + break; + #endif + #if NDARRAY_HAS_UNARY_OP_LEN + case MP_UNARY_OP_LEN: + return mp_obj_new_int(self->shape[ULAB_MAX_DIMS - self->ndim]); + break; + #endif + #if NDARRAY_HAS_UNARY_OP_NEGATIVE + case MP_UNARY_OP_NEGATIVE: + ndarray = ndarray_copy_view(self); // from this point, this is a dense copy + if(self->dtype == NDARRAY_UINT8) { + uint8_t *array = (uint8_t *)ndarray->array; + for(size_t i=0; i < self->len; i++, array++) *array = -(*array); + } else if(self->dtype == NDARRAY_INT8) { + int8_t *array = (int8_t *)ndarray->array; + for(size_t i=0; i < self->len; i++, array++) *array = -(*array); + } else if(self->dtype == NDARRAY_UINT16) { + uint16_t *array = (uint16_t *)ndarray->array; + for(size_t i=0; i < self->len; i++, array++) *array = -(*array); + } else if(self->dtype == NDARRAY_INT16) { + int16_t *array = (int16_t *)ndarray->array; + for(size_t i=0; i < self->len; i++, array++) *array = -(*array); + } else { + mp_float_t *array = (mp_float_t *)ndarray->array; + size_t len = self->len; + #if ULAB_SUPPORTS_COMPLEX + if(self->dtype == NDARRAY_COMPLEX) { + len *= 2; + } + #endif + for(size_t i=0; i < len; i++, array++) *array = -(*array); + } + return MP_OBJ_FROM_PTR(ndarray); + break; + #endif + #if NDARRAY_HAS_UNARY_OP_POSITIVE + case MP_UNARY_OP_POSITIVE: + return MP_OBJ_FROM_PTR(ndarray_copy_view(self)); + #endif + + default: + return MP_OBJ_NULL; // operator not supported + break; + } +} +#endif /* NDARRAY_HAS_UNARY_OPS */ + +#if NDARRAY_HAS_TRANSPOSE +mp_obj_t ndarray_transpose(mp_obj_t self_in) { + #if ULAB_MAX_DIMS == 1 + return self_in; + #endif + // TODO: check, what happens to the offset here, if we have a view + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + if(self->ndim == 1) { + return self_in; + } + size_t *shape = m_new(size_t, self->ndim); + int32_t *strides = m_new(int32_t, self->ndim); + for(uint8_t i=0; i < self->ndim; i++) { + shape[ULAB_MAX_DIMS - 1 - i] = self->shape[ULAB_MAX_DIMS - self->ndim + i]; + strides[ULAB_MAX_DIMS - 1 - i] = self->strides[ULAB_MAX_DIMS - self->ndim + i]; + } + // TODO: I am not sure ndarray_new_view is OK here... + // should be deep copy... + ndarray_obj_t *ndarray = ndarray_new_view(self, self->ndim, shape, strides, 0); + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_transpose_obj, ndarray_transpose); +#endif /* NDARRAY_HAS_TRANSPOSE */ + +#if ULAB_MAX_DIMS > 1 +#if NDARRAY_HAS_RESHAPE +mp_obj_t ndarray_reshape_core(mp_obj_t oin, mp_obj_t _shape, bool inplace) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(oin); + if(!mp_obj_is_type(_shape, &mp_type_tuple)) { + mp_raise_TypeError(translate("shape must be a tuple")); + } + + mp_obj_tuple_t *shape = MP_OBJ_TO_PTR(_shape); + if(shape->len > ULAB_MAX_DIMS) { + mp_raise_ValueError(translate("maximum number of dimensions is 4")); + } + size_t *new_shape = m_new(size_t, ULAB_MAX_DIMS); + memset(new_shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + size_t new_length = 1; + for(uint8_t i=0; i < shape->len; i++) { + new_shape[ULAB_MAX_DIMS - i - 1] = mp_obj_get_int(shape->items[shape->len - i - 1]); + new_length *= new_shape[ULAB_MAX_DIMS - i - 1]; + } + if(source->len != new_length) { + mp_raise_ValueError(translate("input and output shapes are not compatible")); + } + ndarray_obj_t *ndarray; + if(ndarray_is_dense(source)) { + int32_t *new_strides = strides_from_shape(new_shape, source->dtype); + if(inplace) { + for(uint8_t i = 0; i < ULAB_MAX_DIMS; i++) { + source->shape[i] = new_shape[i]; + source->strides[i] = new_strides[i]; + } + return MP_OBJ_FROM_PTR(oin); + } else { + ndarray = ndarray_new_view(source, shape->len, new_shape, new_strides, 0); + } + } else { + if(inplace) { + mp_raise_ValueError(translate("cannot assign new shape")); + } + ndarray = ndarray_new_ndarray_from_tuple(shape, source->dtype); + ndarray_copy_array(source, ndarray, 0); + } + return MP_OBJ_FROM_PTR(ndarray); +} + +mp_obj_t ndarray_reshape(mp_obj_t oin, mp_obj_t _shape) { + return ndarray_reshape_core(oin, _shape, 0); +} + +MP_DEFINE_CONST_FUN_OBJ_2(ndarray_reshape_obj, ndarray_reshape); +#endif /* NDARRAY_HAS_RESHAPE */ +#endif /* ULAB_MAX_DIMS > 1 */ + +#if ULAB_NUMPY_HAS_NDINFO +mp_obj_t ndarray_info(mp_obj_t obj_in) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(obj_in); + if(!mp_obj_is_type(ndarray, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("function is defined for ndarrays only")); + } + mp_printf(MP_PYTHON_PRINTER, "class: ndarray\n"); + mp_printf(MP_PYTHON_PRINTER, "shape: ("); + if(ndarray->ndim == 1) { + mp_printf(MP_PYTHON_PRINTER, "%d,", ndarray->shape[ULAB_MAX_DIMS-1]); + } else { + for(uint8_t i=0; i < ndarray->ndim-1; i++) mp_printf(MP_PYTHON_PRINTER, "%d, ", ndarray->shape[i]); + mp_printf(MP_PYTHON_PRINTER, "%d", ndarray->shape[ULAB_MAX_DIMS-1]); + } + mp_printf(MP_PYTHON_PRINTER, ")\n"); + mp_printf(MP_PYTHON_PRINTER, "strides: ("); + if(ndarray->ndim == 1) { + mp_printf(MP_PYTHON_PRINTER, "%d,", ndarray->strides[ULAB_MAX_DIMS-1]); + } else { + for(uint8_t i=0; i < ndarray->ndim-1; i++) mp_printf(MP_PYTHON_PRINTER, "%d, ", ndarray->strides[i]); + mp_printf(MP_PYTHON_PRINTER, "%d", ndarray->strides[ULAB_MAX_DIMS-1]); + } + mp_printf(MP_PYTHON_PRINTER, ")\n"); + mp_printf(MP_PYTHON_PRINTER, "itemsize: %d\n", ndarray->itemsize); + mp_printf(MP_PYTHON_PRINTER, "data pointer: 0x%p\n", ndarray->array); + mp_printf(MP_PYTHON_PRINTER, "type: "); + if(ndarray->boolean) { + mp_printf(MP_PYTHON_PRINTER, "bool\n"); + } else if(ndarray->dtype == NDARRAY_UINT8) { + mp_printf(MP_PYTHON_PRINTER, "uint8\n"); + } else if(ndarray->dtype == NDARRAY_INT8) { + mp_printf(MP_PYTHON_PRINTER, "int8\n"); + } else if(ndarray->dtype == NDARRAY_UINT16) { + mp_printf(MP_PYTHON_PRINTER, "uint16\n"); + } else if(ndarray->dtype == NDARRAY_INT16) { + mp_printf(MP_PYTHON_PRINTER, "int16\n"); + } else if(ndarray->dtype == NDARRAY_FLOAT) { + mp_printf(MP_PYTHON_PRINTER, "float\n"); + } + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_info_obj, ndarray_info); +#endif + +// (the get_buffer protocol returns 0 for success, 1 for failure) +mp_int_t ndarray_get_buffer(mp_obj_t self_in, mp_buffer_info_t *bufinfo, mp_uint_t flags) { + ndarray_obj_t *self = MP_OBJ_TO_PTR(self_in); + if(!ndarray_is_dense(self)) { + return 1; + } + bufinfo->len = self->itemsize * self->len; + bufinfo->buf = self->array; + bufinfo->typecode = self->dtype; + return 0; +} diff --git a/circuitpython/extmod/ulab/code/ndarray.h b/circuitpython/extmod/ulab/code/ndarray.h new file mode 100644 index 0000000..4478f94 --- /dev/null +++ b/circuitpython/extmod/ulab/code/ndarray.h @@ -0,0 +1,749 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * 2020 Jeff Epler for Adafruit Industries +*/ + +#ifndef _NDARRAY_ +#define _NDARRAY_ + +#include "py/objarray.h" +#include "py/binary.h" +#include "py/objstr.h" +#include "py/objlist.h" + +#include "ulab.h" + +#ifndef MP_PI +#define MP_PI MICROPY_FLOAT_CONST(3.14159265358979323846) +#endif +#ifndef MP_E +#define MP_E MICROPY_FLOAT_CONST(2.71828182845904523536) +#endif + +#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT +#define FLOAT_TYPECODE 'f' +#elif MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE +#define FLOAT_TYPECODE 'd' +#endif + +// this typedef is lifted from objfloat.c, because mp_obj_float_t is not exposed +typedef struct _mp_obj_float_t { + mp_obj_base_t base; + mp_float_t value; +} mp_obj_float_t; + +#if defined(MICROPY_VERSION_MAJOR) && MICROPY_VERSION_MAJOR == 1 && MICROPY_VERSION_MINOR == 11 +typedef struct _mp_obj_slice_t { + mp_obj_base_t base; + mp_obj_t start; + mp_obj_t stop; + mp_obj_t step; +} mp_obj_slice_t; +#define MP_ERROR_TEXT(x) x +#endif + +#if !defined(MP_TYPE_FLAG_EXTENDED) +#define MP_TYPE_CALL call +#define mp_type_get_call_slot(t) t->call +#define MP_TYPE_FLAG_EXTENDED (0) +#define MP_TYPE_EXTENDED_FIELDS(...) __VA_ARGS__ +#endif + +#if !CIRCUITPY +#define translate(x) MP_ERROR_TEXT(x) +#define ndarray_set_value(a, b, c, d) mp_binary_set_val_array(a, b, c, d) +#else +void ndarray_set_value(char , void *, size_t , mp_obj_t ); +#endif + +void ndarray_set_complex_value(void *, size_t , mp_obj_t ); + +#define NDARRAY_NUMERIC 0 +#define NDARRAY_BOOLEAN 1 + +#define NDARRAY_NDARRAY_TYPE 1 +#define NDARRAY_ITERABLE_TYPE 2 + +extern const mp_obj_type_t ulab_ndarray_type; + +enum NDARRAY_TYPE { + NDARRAY_BOOL = '?', // this must never be assigned to the dtype! + NDARRAY_UINT8 = 'B', + NDARRAY_INT8 = 'b', + NDARRAY_UINT16 = 'H', + NDARRAY_INT16 = 'h', + #if ULAB_SUPPORTS_COMPLEX + NDARRAY_COMPLEX = 'c', + #endif + NDARRAY_FLOAT = FLOAT_TYPECODE, +}; + +typedef struct _ndarray_obj_t { + mp_obj_base_t base; + uint8_t dtype; + uint8_t itemsize; + uint8_t boolean; + uint8_t ndim; + size_t len; + size_t shape[ULAB_MAX_DIMS]; + int32_t strides[ULAB_MAX_DIMS]; + void *array; + void *origin; +} ndarray_obj_t; + +#if ULAB_HAS_DTYPE_OBJECT +extern const mp_obj_type_t ulab_dtype_type; + +typedef struct _dtype_obj_t { + mp_obj_base_t base; + uint8_t dtype; +} dtype_obj_t; + +void ndarray_dtype_print(const mp_print_t *, mp_obj_t , mp_print_kind_t ); + +mp_obj_t ndarray_dtype_make_new(const mp_obj_type_t *, size_t , size_t , const mp_obj_t *); +#endif /* ULAB_HAS_DTYPE_OBJECT */ + +extern const mp_obj_type_t ndarray_flatiter_type; + +mp_obj_t ndarray_new_ndarray_iterator(mp_obj_t , mp_obj_iter_buf_t *); + +mp_obj_t ndarray_get_item(ndarray_obj_t *, void *); +mp_float_t ndarray_get_float_value(void *, uint8_t ); +mp_float_t ndarray_get_float_index(void *, uint8_t , size_t ); +bool ndarray_object_is_array_like(mp_obj_t ); +void fill_array_iterable(mp_float_t *, mp_obj_t ); +size_t *ndarray_shape_vector(size_t , size_t , size_t , size_t ); + +void ndarray_print(const mp_print_t *, mp_obj_t , mp_print_kind_t ); + +#if ULAB_HAS_PRINTOPTIONS +mp_obj_t ndarray_set_printoptions(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(ndarray_set_printoptions_obj); + +mp_obj_t ndarray_get_printoptions(void); +MP_DECLARE_CONST_FUN_OBJ_0(ndarray_get_printoptions_obj); +#endif + +void ndarray_assign_elements(ndarray_obj_t *, mp_obj_t , uint8_t , size_t *); +size_t *ndarray_contract_shape(ndarray_obj_t *, uint8_t ); +int32_t *ndarray_contract_strides(ndarray_obj_t *, uint8_t ); + +ndarray_obj_t *ndarray_new_dense_ndarray(uint8_t , size_t *, uint8_t ); +ndarray_obj_t *ndarray_new_ndarray_from_tuple(mp_obj_tuple_t *, uint8_t ); +ndarray_obj_t *ndarray_new_ndarray(uint8_t , size_t *, int32_t *, uint8_t ); +ndarray_obj_t *ndarray_new_linear_array(size_t , uint8_t ); +ndarray_obj_t *ndarray_new_view(ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t ); +bool ndarray_is_dense(ndarray_obj_t *); +ndarray_obj_t *ndarray_copy_view(ndarray_obj_t *); +ndarray_obj_t *ndarray_copy_view_convert_type(ndarray_obj_t *, uint8_t ); +void ndarray_copy_array(ndarray_obj_t *, ndarray_obj_t *, uint8_t ); + +MP_DECLARE_CONST_FUN_OBJ_KW(ndarray_array_constructor_obj); +mp_obj_t ndarray_make_new(const mp_obj_type_t *, size_t , size_t , const mp_obj_t *); +mp_obj_t ndarray_subscr(mp_obj_t , mp_obj_t , mp_obj_t ); +mp_obj_t ndarray_getiter(mp_obj_t , mp_obj_iter_buf_t *); +bool ndarray_can_broadcast(ndarray_obj_t *, ndarray_obj_t *, uint8_t *, size_t *, int32_t *, int32_t *); +bool ndarray_can_broadcast_inplace(ndarray_obj_t *, ndarray_obj_t *, int32_t *); +mp_obj_t ndarray_binary_op(mp_binary_op_t , mp_obj_t , mp_obj_t ); +mp_obj_t ndarray_unary_op(mp_unary_op_t , mp_obj_t ); + +size_t *ndarray_new_coords(uint8_t ); +void ndarray_rewind_array(uint8_t , uint8_t *, size_t *, int32_t *, size_t *); + +// various ndarray methods +#if NDARRAY_HAS_BYTESWAP +mp_obj_t ndarray_byteswap(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(ndarray_byteswap_obj); +#endif + +#if NDARRAY_HAS_COPY +mp_obj_t ndarray_copy(mp_obj_t ); +MP_DECLARE_CONST_FUN_OBJ_1(ndarray_copy_obj); +#endif + +#if NDARRAY_HAS_FLATTEN +mp_obj_t ndarray_flatten(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(ndarray_flatten_obj); +#endif + +mp_obj_t ndarray_dtype(mp_obj_t ); +mp_obj_t ndarray_itemsize(mp_obj_t ); +mp_obj_t ndarray_size(mp_obj_t ); +mp_obj_t ndarray_shape(mp_obj_t ); +mp_obj_t ndarray_strides(mp_obj_t ); + +#if NDARRAY_HAS_RESHAPE +mp_obj_t ndarray_reshape_core(mp_obj_t , mp_obj_t , bool ); +mp_obj_t ndarray_reshape(mp_obj_t , mp_obj_t ); +MP_DECLARE_CONST_FUN_OBJ_2(ndarray_reshape_obj); +#endif + +#if NDARRAY_HAS_TOBYTES +mp_obj_t ndarray_tobytes(mp_obj_t ); +MP_DECLARE_CONST_FUN_OBJ_1(ndarray_tobytes_obj); +#endif + +#if NDARRAY_HAS_TOBYTES +mp_obj_t ndarray_tolist(mp_obj_t ); +MP_DECLARE_CONST_FUN_OBJ_1(ndarray_tolist_obj); +#endif + +#if NDARRAY_HAS_TRANSPOSE +mp_obj_t ndarray_transpose(mp_obj_t ); +MP_DECLARE_CONST_FUN_OBJ_1(ndarray_transpose_obj); +#endif + +#if ULAB_NUMPY_HAS_NDINFO +mp_obj_t ndarray_info(mp_obj_t ); +MP_DECLARE_CONST_FUN_OBJ_1(ndarray_info_obj); +#endif + +mp_int_t ndarray_get_buffer(mp_obj_t , mp_buffer_info_t *, mp_uint_t ); +//void ndarray_attributes(mp_obj_t , qstr , mp_obj_t *); + +ndarray_obj_t *ndarray_from_mp_obj(mp_obj_t , uint8_t ); + + +#define BOOLEAN_ASSIGNMENT_LOOP(type_left, type_right, ndarray, lstrides, iarray, istride, varray, vstride)\ + type_left *array = (type_left *)(ndarray)->array;\ + for(size_t i=0; i < (ndarray)->len; i++) {\ + if(*(iarray)) {\ + *array = (type_left)(*((type_right *)(varray)));\ + (varray) += (vstride);\ + }\ + array += (lstrides);\ + (iarray) += (istride);\ + } while(0) + +#if ULAB_HAS_FUNCTION_ITERATOR +#define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + type_out *array = (type_out *)(results)->array;\ + size_t *lcoords = ndarray_new_coords((results)->ndim);\ + size_t *rcoords = ndarray_new_coords((results)->ndim);\ + for(size_t i=0; i < (results)->len/(results)->shape[ULAB_MAX_DIMS -1]; i++) {\ + size_t l = 0;\ + do {\ + *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + ndarray_rewind_array((results)->ndim, (larray), (results)->shape, (lstrides), lcoords);\ + ndarray_rewind_array((results)->ndim, (rarray), (results)->shape, (rstrides), rcoords);\ + } while(0) + +#define INPLACE_LOOP(results, type_left, type_right, larray, rarray, rstrides, OPERATOR)\ + size_t *lcoords = ndarray_new_coords((results)->ndim);\ + size_t *rcoords = ndarray_new_coords((results)->ndim);\ + for(size_t i=0; i < (results)->len/(results)->shape[ULAB_MAX_DIMS -1]; i++) {\ + size_t l = 0;\ + do {\ + *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + ndarray_rewind_array((results)->ndim, (larray), (results)->shape, (results)->strides, lcoords);\ + ndarray_rewind_array((results)->ndim, (rarray), (results)->shape, (rstrides), rcoords);\ + } while(0) + +#define EQUALITY_LOOP(results, array, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t *lcoords = ndarray_new_coords((results)->ndim);\ + size_t *rcoords = ndarray_new_coords((results)->ndim);\ + for(size_t i=0; i < (results)->len/(results)->shape[ULAB_MAX_DIMS -1]; i++) {\ + size_t l = 0;\ + do {\ + *(array)++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? 1 : 0;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + ndarray_rewind_array((results)->ndim, (larray), (results)->shape, (lstrides), lcoords);\ + ndarray_rewind_array((results)->ndim, (rarray), (results)->shape, (rstrides), rcoords);\ + } while(0) + +#define POWER_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides)\ + type_out *array = (type_out *)(results)->array;\ + size_t *lcoords = ndarray_new_coords((results)->ndim);\ + size_t *rcoords = ndarray_new_coords((results)->ndim);\ + for(size_t i=0; i < (results)->len/(results)->shape[ULAB_MAX_DIMS -1]; i++) {\ + size_t l = 0;\ + do {\ + *array++ = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + ndarray_rewind_array((results)->ndim, (larray), (results)->shape, (lstrides), lcoords);\ + ndarray_rewind_array((results)->ndim, (rarray), (results)->shape, (rstrides), rcoords);\ + } while(0) + +#else + +#if ULAB_MAX_DIMS == 1 +#define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + type_out *array = (type_out *)results->array;\ + size_t l = 0;\ + do {\ + *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#define INPLACE_LOOP(results, type_left, type_right, larray, rarray, rstrides, OPERATOR)\ + size_t l = 0;\ + do {\ + *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#define EQUALITY_LOOP(results, array, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t l = 0;\ + do {\ + *(array)++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? 1 : 0;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#define POWER_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides)\ + type_out *array = (type_out *)results->array;\ + size_t l = 0;\ + do {\ + *array++ = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#endif /* ULAB_MAX_DIMS == 1 */ + +#if ULAB_MAX_DIMS == 2 +#define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + type_out *array = (type_out *)(results)->array;\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#define INPLACE_LOOP(results, type_left, type_right, larray, rarray, rstrides, OPERATOR)\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#define EQUALITY_LOOP(results, array, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *(array)++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? 1 : 0;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#define POWER_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides)\ + type_out *array = (type_out *)(results)->array;\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *array++ = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#endif /* ULAB_MAX_DIMS == 2 */ + +#if ULAB_MAX_DIMS == 3 +#define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + type_out *array = (type_out *)results->array;\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#define INPLACE_LOOP(results, type_left, type_right, larray, rarray, rstrides, OPERATOR)\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#define EQUALITY_LOOP(results, array, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *(array)++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? 1 : 0;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#define POWER_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides)\ + type_out *array = (type_out *)results->array;\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *array++ = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#endif /* ULAB_MAX_DIMS == 3 */ + +#if ULAB_MAX_DIMS == 4 +#define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + type_out *array = (type_out *)results->array;\ + size_t i = 0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + +#define INPLACE_LOOP(results, type_left, type_right, larray, rarray, rstrides, OPERATOR)\ + size_t i = 0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + +#define EQUALITY_LOOP(results, array, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t i = 0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *(array)++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? 1 : 0;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + +#define POWER_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides)\ + type_out *array = (type_out *)results->array;\ + size_t i = 0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *array++ = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + +#endif /* ULAB_MAX_DIMS == 4 */ +#endif /* ULAB_HAS_FUNCTION_ITERATOR */ + + +#if ULAB_MAX_DIMS == 1 +#define ASSIGNMENT_LOOP(results, type_left, type_right, lstrides, rarray, rstrides)\ + type_left *larray = (type_left *)(results)->array;\ + size_t l = 0;\ + do {\ + *larray = (type_left)(*((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#endif /* ULAB_MAX_DIMS == 1 */ + +#if ULAB_MAX_DIMS == 2 +#define ASSIGNMENT_LOOP(results, type_left, type_right, lstrides, rarray, rstrides)\ + type_left *larray = (type_left *)(results)->array;\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *larray = (type_left)(*((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#endif /* ULAB_MAX_DIMS == 2 */ + +#if ULAB_MAX_DIMS == 3 +#define ASSIGNMENT_LOOP(results, type_left, type_right, lstrides, rarray, rstrides)\ + type_left *larray = (type_left *)(results)->array;\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *larray = (type_left)(*((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#endif /* ULAB_MAX_DIMS == 3 */ + +#if ULAB_MAX_DIMS == 4 +#define ASSIGNMENT_LOOP(results, type_left, type_right, lstrides, rarray, rstrides)\ + type_left *larray = (type_left *)(results)->array;\ + size_t i = 0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *larray = (type_left)(*((type_right *)(rarray)));\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + +#endif /* ULAB_MAX_DIMS == 4 */ + +#endif diff --git a/circuitpython/extmod/ulab/code/ndarray_operators.c b/circuitpython/extmod/ulab/code/ndarray_operators.c new file mode 100644 index 0000000..de1042c --- /dev/null +++ b/circuitpython/extmod/ulab/code/ndarray_operators.c @@ -0,0 +1,839 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös +*/ + + +#include <math.h> + +#include "py/runtime.h" +#include "py/objtuple.h" +#include "ndarray.h" +#include "ndarray_operators.h" +#include "ulab.h" +#include "ulab_tools.h" +#include "numpy/carray/carray.h" + +/* + This file contains the actual implementations of the various + ndarray operators. + + These are the upcasting rules of the binary operators + + - if complex is supported, and if one of the operarands is a complex, the result is always complex + - if both operarands are real one of them is a float, then the result is also a float + - operation on identical types preserves type + + uint8 + int8 => int16 + uint8 + int16 => int16 + uint8 + uint16 => uint16 + int8 + int16 => int16 + int8 + uint16 => uint16 + uint16 + int16 => float +*/ + +#if NDARRAY_HAS_BINARY_OP_EQUAL | NDARRAY_HAS_BINARY_OP_NOT_EQUAL +mp_obj_t ndarray_binary_equality(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides, mp_binary_op_t op) { + + #if ULAB_SUPPORTS_COMPLEX + if((lhs->dtype == NDARRAY_COMPLEX) || (rhs->dtype == NDARRAY_COMPLEX)) { + return carray_binary_equal_not_equal(lhs, rhs, ndim, shape, lstrides, rstrides, op); + } + #endif + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT8); + results->boolean = 1; + uint8_t *array = (uint8_t *)results->array; + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + #if NDARRAY_HAS_BINARY_OP_EQUAL + if(op == MP_BINARY_OP_EQUAL) { + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, uint8_t, int8_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, uint8_t, int16_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, ==); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, int8_t, int8_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, int8_t, uint16_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, int8_t, int16_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, ==); + } else { + return ndarray_binary_op(op, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, uint16_t, int16_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, ==); + } else { + return ndarray_binary_op(op, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, int16_t, int16_t, larray, lstrides, rarray, rstrides, ==); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, int16_t, mp_float_t, larray, lstrides, rarray, rstrides, ==); + } else { + return ndarray_binary_op(op, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, ==); + } else { + return ndarray_binary_op(op, rhs, lhs); + } + } + } + #endif /* NDARRAY_HAS_BINARY_OP_EQUAL */ + + #if NDARRAY_HAS_BINARY_OP_NOT_EQUAL + if(op == MP_BINARY_OP_NOT_EQUAL) { + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, uint8_t, int8_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, uint8_t, int16_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, !=); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, int8_t, int8_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, int8_t, uint16_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, int8_t, int16_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, !=); + } else { + return ndarray_binary_op(op, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, uint16_t, int16_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, !=); + } else { + return ndarray_binary_op(op, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, int16_t, int16_t, larray, lstrides, rarray, rstrides, !=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, int16_t, mp_float_t, larray, lstrides, rarray, rstrides, !=); + } else { + return ndarray_binary_op(op, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, !=); + } else { + return ndarray_binary_op(op, rhs, lhs); + } + } + } + #endif /* NDARRAY_HAS_BINARY_OP_NOT_EQUAL */ + + return MP_OBJ_FROM_PTR(results); +} +#endif /* NDARRAY_HAS_BINARY_OP_EQUAL | NDARRAY_HAS_BINARY_OP_NOT_EQUAL */ + +#if NDARRAY_HAS_BINARY_OP_ADD +mp_obj_t ndarray_binary_add(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + #if ULAB_SUPPORTS_COMPLEX + if((lhs->dtype == NDARRAY_COMPLEX) || (rhs->dtype == NDARRAY_COMPLEX)) { + return carray_binary_add(lhs, rhs, ndim, shape, lstrides, rstrides); + } + #endif + + ndarray_obj_t *results = NULL; + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, uint8_t, int8_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, uint8_t, int16_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, +); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT8); + BINARY_LOOP(results, int8_t, int8_t, int8_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int8_t, uint16_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int8_t, int16_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, +); + } else { + return ndarray_binary_op(MP_BINARY_OP_ADD, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint16_t, int16_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, +); + } else { + return ndarray_binary_op(MP_BINARY_OP_ADD, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int16_t, int16_t, larray, lstrides, rarray, rstrides, +); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, int16_t, mp_float_t, larray, lstrides, rarray, rstrides, +); + } else { + return ndarray_binary_op(MP_BINARY_OP_ADD, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, +); + } else { + return ndarray_binary_op(MP_BINARY_OP_ADD, rhs, lhs); + } + } + + return MP_OBJ_FROM_PTR(results); +} +#endif /* NDARRAY_HAS_BINARY_OP_ADD */ + +#if NDARRAY_HAS_BINARY_OP_MULTIPLY +mp_obj_t ndarray_binary_multiply(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + #if ULAB_SUPPORTS_COMPLEX + if((lhs->dtype == NDARRAY_COMPLEX) || (rhs->dtype == NDARRAY_COMPLEX)) { + return carray_binary_multiply(lhs, rhs, ndim, shape, lstrides, rstrides); + } + #endif + + ndarray_obj_t *results = NULL; + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, uint8_t, int8_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, uint8_t, int16_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, *); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT8); + BINARY_LOOP(results, int8_t, int8_t, int8_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int8_t, uint16_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int8_t, int16_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, *); + } else { + return ndarray_binary_op(MP_BINARY_OP_MULTIPLY, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint16_t, int16_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, *); + } else { + return ndarray_binary_op(MP_BINARY_OP_MULTIPLY, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int16_t, int16_t, larray, lstrides, rarray, rstrides, *); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, int16_t, mp_float_t, larray, lstrides, rarray, rstrides, *); + } else { + return ndarray_binary_op(MP_BINARY_OP_MULTIPLY, rhs, lhs); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, *); + } else { + return ndarray_binary_op(MP_BINARY_OP_MULTIPLY, rhs, lhs); + } + } + + return MP_OBJ_FROM_PTR(results); +} +#endif /* NDARRAY_HAS_BINARY_OP_MULTIPLY */ + +#if NDARRAY_HAS_BINARY_OP_MORE | NDARRAY_HAS_BINARY_OP_MORE_EQUAL | NDARRAY_HAS_BINARY_OP_LESS | NDARRAY_HAS_BINARY_OP_LESS_EQUAL +mp_obj_t ndarray_binary_more(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides, mp_binary_op_t op) { + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT8); + results->boolean = 1; + uint8_t *array = (uint8_t *)results->array; + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + #if NDARRAY_HAS_BINARY_OP_MORE | NDARRAY_HAS_BINARY_OP_LESS + if(op == MP_BINARY_OP_MORE) { + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, uint8_t, int8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, uint8_t, int16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, >); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, int8_t, uint8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, int8_t, int8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, int8_t, uint16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, int8_t, int16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, >); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, uint16_t, uint8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, uint16_t, int8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, uint16_t, int16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, >); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, int16_t, uint8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, int16_t, int8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, int16_t, uint16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, int16_t, int16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, >); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, mp_float_t, uint8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, mp_float_t, int8_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, mp_float_t, uint16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, mp_float_t, int16_t, larray, lstrides, rarray, rstrides, >); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, >); + } + } + } + #endif /* NDARRAY_HAS_BINARY_OP_MORE | NDARRAY_HAS_BINARY_OP_LESS*/ + #if NDARRAY_HAS_BINARY_OP_MORE_EQUAL | NDARRAY_HAS_BINARY_OP_LESS_EQUAL + if(op == MP_BINARY_OP_MORE_EQUAL) { + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, uint8_t, int8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, uint8_t, int16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, >=); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, int8_t, uint8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, int8_t, int8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, int8_t, uint16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, int8_t, int16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, >=); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, uint16_t, uint8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, uint16_t, int8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, uint16_t, int16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, >=); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, int16_t, uint8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, int16_t, int8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, int16_t, uint16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, int16_t, int16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, >=); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_UINT8) { + EQUALITY_LOOP(results, array, mp_float_t, uint8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT8) { + EQUALITY_LOOP(results, array, mp_float_t, int8_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_UINT16) { + EQUALITY_LOOP(results, array, mp_float_t, uint16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_INT16) { + EQUALITY_LOOP(results, array, mp_float_t, int16_t, larray, lstrides, rarray, rstrides, >=); + } else if(rhs->dtype == NDARRAY_FLOAT) { + EQUALITY_LOOP(results, array, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, >=); + } + } + } + #endif /* NDARRAY_HAS_BINARY_OP_MORE_EQUAL | NDARRAY_HAS_BINARY_OP_LESS_EQUAL */ + + return MP_OBJ_FROM_PTR(results); +} +#endif /* NDARRAY_HAS_BINARY_OP_MORE | NDARRAY_HAS_BINARY_OP_MORE_EQUAL | NDARRAY_HAS_BINARY_OP_LESS | NDARRAY_HAS_BINARY_OP_LESS_EQUAL */ + +#if NDARRAY_HAS_BINARY_OP_SUBTRACT +mp_obj_t ndarray_binary_subtract(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + #if ULAB_SUPPORTS_COMPLEX + if((lhs->dtype == NDARRAY_COMPLEX) || (rhs->dtype == NDARRAY_COMPLEX)) { + return carray_binary_subtract(lhs, rhs, ndim, shape, lstrides, rstrides); + } + #endif + + ndarray_obj_t *results = NULL; + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT8); + BINARY_LOOP(results, uint8_t, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, uint8_t, int8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, uint8_t, int16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, -); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_UINT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int8_t, uint8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT8); + BINARY_LOOP(results, int8_t, int8_t, int8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int8_t, uint16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int8_t, int16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, -); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint16_t, uint8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint16_t, int8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT16); + BINARY_LOOP(results, uint16_t, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint16_t, int16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, -); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_UINT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int16_t, uint8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int16_t, int8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, int16_t, uint16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_INT16); + BINARY_LOOP(results, int16_t, int16_t, int16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, -); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_UINT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, mp_float_t, uint8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT8) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, mp_float_t, int8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_UINT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, mp_float_t, uint16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT16) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, mp_float_t, int16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_FLOAT) { + results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + BINARY_LOOP(results, mp_float_t, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, -); + } + } + + return MP_OBJ_FROM_PTR(results); +} +#endif /* NDARRAY_HAS_BINARY_OP_SUBTRACT */ + +#if NDARRAY_HAS_BINARY_OP_TRUE_DIVIDE +mp_obj_t ndarray_binary_true_divide(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + #if ULAB_SUPPORTS_COMPLEX + if((lhs->dtype == NDARRAY_COMPLEX) || (rhs->dtype == NDARRAY_COMPLEX)) { + return carray_binary_divide(lhs, rhs, ndim, shape, lstrides, rstrides); + } + #endif + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + #if NDARRAY_BINARY_USES_FUN_POINTER + mp_float_t (*get_lhs)(void *) = ndarray_get_float_function(lhs->dtype); + mp_float_t (*get_rhs)(void *) = ndarray_get_float_function(rhs->dtype); + + uint8_t *array = (uint8_t *)results->array; + void (*set_result)(void *, mp_float_t ) = ndarray_set_float_function(NDARRAY_FLOAT); + + // Note that lvalue and rvalue are local variables in the macro itself + FUNC_POINTER_LOOP(results, array, get_lhs, get_rhs, larray, lstrides, rarray, rstrides, lvalue/rvalue); + + #else + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + BINARY_LOOP(results, mp_float_t, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT8) { + BINARY_LOOP(results, mp_float_t, uint8_t, int8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_UINT16) { + BINARY_LOOP(results, mp_float_t, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT16) { + BINARY_LOOP(results, mp_float_t, uint8_t, int16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_FLOAT) { + BINARY_LOOP(results, mp_float_t, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, /); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_UINT8) { + BINARY_LOOP(results, mp_float_t, int8_t, uint8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT8) { + BINARY_LOOP(results, mp_float_t, int8_t, int8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_UINT16) { + BINARY_LOOP(results, mp_float_t, int8_t, uint16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT16) { + BINARY_LOOP(results, mp_float_t, int8_t, int16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_FLOAT) { + BINARY_LOOP(results, mp_float_t, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, /); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT8) { + BINARY_LOOP(results, mp_float_t, uint16_t, uint8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT8) { + BINARY_LOOP(results, mp_float_t, uint16_t, int8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_UINT16) { + BINARY_LOOP(results, mp_float_t, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT16) { + BINARY_LOOP(results, mp_float_t, uint16_t, int16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_FLOAT) { + BINARY_LOOP(results, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, /); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_UINT8) { + BINARY_LOOP(results, mp_float_t, int16_t, uint8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT8) { + BINARY_LOOP(results, mp_float_t, int16_t, int8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_UINT16) { + BINARY_LOOP(results, mp_float_t, int16_t, uint16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT16) { + BINARY_LOOP(results, mp_float_t, int16_t, int16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_FLOAT) { + BINARY_LOOP(results, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, /); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_UINT8) { + BINARY_LOOP(results, mp_float_t, mp_float_t, uint8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT8) { + BINARY_LOOP(results, mp_float_t, mp_float_t, int8_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_UINT16) { + BINARY_LOOP(results, mp_float_t, mp_float_t, uint16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_INT16) { + BINARY_LOOP(results, mp_float_t, mp_float_t, int16_t, larray, lstrides, rarray, rstrides, /); + } else if(rhs->dtype == NDARRAY_FLOAT) { + BINARY_LOOP(results, mp_float_t, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, /); + } + } + #endif /* NDARRAY_BINARY_USES_FUN_POINTER */ + + return MP_OBJ_FROM_PTR(results); +} +#endif /* NDARRAY_HAS_BINARY_OP_TRUE_DIVIDE */ + +#if NDARRAY_HAS_BINARY_OP_POWER +mp_obj_t ndarray_binary_power(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + // Note that numpy upcasts the results to int64, if the inputs are of integer type, + // while we always return a float array. + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + #if NDARRAY_BINARY_USES_FUN_POINTER + mp_float_t (*get_lhs)(void *) = ndarray_get_float_function(lhs->dtype); + mp_float_t (*get_rhs)(void *) = ndarray_get_float_function(rhs->dtype); + + uint8_t *array = (uint8_t *)results->array; + void (*set_result)(void *, mp_float_t ) = ndarray_set_float_function(NDARRAY_FLOAT); + + // Note that lvalue and rvalue are local variables in the macro itself + FUNC_POINTER_LOOP(results, array, get_lhs, get_rhs, larray, lstrides, rarray, rstrides, MICROPY_FLOAT_C_FUN(pow)(lvalue, rvalue)); + + #else + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + POWER_LOOP(results, mp_float_t, uint8_t, uint8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT8) { + POWER_LOOP(results, mp_float_t, uint8_t, int8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_UINT16) { + POWER_LOOP(results, mp_float_t, uint8_t, uint16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT16) { + POWER_LOOP(results, mp_float_t, uint8_t, int16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_FLOAT) { + POWER_LOOP(results, mp_float_t, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_UINT8) { + POWER_LOOP(results, mp_float_t, int8_t, uint8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT8) { + POWER_LOOP(results, mp_float_t, int8_t, int8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_UINT16) { + POWER_LOOP(results, mp_float_t, int8_t, uint16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT16) { + POWER_LOOP(results, mp_float_t, int8_t, int16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_FLOAT) { + POWER_LOOP(results, mp_float_t, int8_t, mp_float_t, larray, lstrides, rarray, rstrides); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT8) { + POWER_LOOP(results, mp_float_t, uint16_t, uint8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT8) { + POWER_LOOP(results, mp_float_t, uint16_t, int8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_UINT16) { + POWER_LOOP(results, mp_float_t, uint16_t, uint16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT16) { + POWER_LOOP(results, mp_float_t, uint16_t, int16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_FLOAT) { + POWER_LOOP(results, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_UINT8) { + POWER_LOOP(results, mp_float_t, int16_t, uint8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT8) { + POWER_LOOP(results, mp_float_t, int16_t, int8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_UINT16) { + POWER_LOOP(results, mp_float_t, int16_t, uint16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT16) { + POWER_LOOP(results, mp_float_t, int16_t, int16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_FLOAT) { + POWER_LOOP(results, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_UINT8) { + POWER_LOOP(results, mp_float_t, mp_float_t, uint8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT8) { + POWER_LOOP(results, mp_float_t, mp_float_t, int8_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_UINT16) { + POWER_LOOP(results, mp_float_t, mp_float_t, uint16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT16) { + POWER_LOOP(results, mp_float_t, mp_float_t, int16_t, larray, lstrides, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_FLOAT) { + POWER_LOOP(results, mp_float_t, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides); + } + } + #endif /* NDARRAY_BINARY_USES_FUN_POINTER */ + + return MP_OBJ_FROM_PTR(results); +} +#endif /* NDARRAY_HAS_BINARY_OP_POWER */ + +#if NDARRAY_HAS_INPLACE_ADD || NDARRAY_HAS_INPLACE_MULTIPLY || NDARRAY_HAS_INPLACE_SUBTRACT +mp_obj_t ndarray_inplace_ams(ndarray_obj_t *lhs, ndarray_obj_t *rhs, int32_t *rstrides, uint8_t optype) { + + if((lhs->dtype != NDARRAY_FLOAT) && (rhs->dtype == NDARRAY_FLOAT)) { + mp_raise_TypeError(translate("cannot cast output with casting rule")); + } + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + #if NDARRAY_HAS_INPLACE_ADD + if(optype == MP_BINARY_OP_INPLACE_ADD) { + UNWRAP_INPLACE_OPERATOR(lhs, larray, rarray, rstrides, +=); + } + #endif + #if NDARRAY_HAS_INPLACE_ADD + if(optype == MP_BINARY_OP_INPLACE_MULTIPLY) { + UNWRAP_INPLACE_OPERATOR(lhs, larray, rarray, rstrides, *=); + } + #endif + #if NDARRAY_HAS_INPLACE_SUBTRACT + if(optype == MP_BINARY_OP_INPLACE_SUBTRACT) { + UNWRAP_INPLACE_OPERATOR(lhs, larray, rarray, rstrides, -=); + } + #endif + + return MP_OBJ_FROM_PTR(lhs); +} +#endif /* NDARRAY_HAS_INPLACE_ADD || NDARRAY_HAS_INPLACE_MULTIPLY || NDARRAY_HAS_INPLACE_SUBTRACT */ + +#if NDARRAY_HAS_INPLACE_TRUE_DIVIDE +mp_obj_t ndarray_inplace_divide(ndarray_obj_t *lhs, ndarray_obj_t *rhs, int32_t *rstrides) { + + if((lhs->dtype != NDARRAY_FLOAT)) { + mp_raise_TypeError(translate("results cannot be cast to specified type")); + } + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + if(rhs->dtype == NDARRAY_UINT8) { + INPLACE_LOOP(lhs, mp_float_t, uint8_t, larray, rarray, rstrides, /=); + } else if(rhs->dtype == NDARRAY_INT8) { + INPLACE_LOOP(lhs, mp_float_t, int8_t, larray, rarray, rstrides, /=); + } else if(rhs->dtype == NDARRAY_UINT16) { + INPLACE_LOOP(lhs, mp_float_t, uint16_t, larray, rarray, rstrides, /=); + } else if(rhs->dtype == NDARRAY_INT16) { + INPLACE_LOOP(lhs, mp_float_t, int16_t, larray, rarray, rstrides, /=); + } else if(lhs->dtype == NDARRAY_FLOAT) { + INPLACE_LOOP(lhs, mp_float_t, mp_float_t, larray, rarray, rstrides, /=); + } + return MP_OBJ_FROM_PTR(lhs); +} +#endif /* NDARRAY_HAS_INPLACE_DIVIDE */ + +#if NDARRAY_HAS_INPLACE_POWER +mp_obj_t ndarray_inplace_power(ndarray_obj_t *lhs, ndarray_obj_t *rhs, int32_t *rstrides) { + + if((lhs->dtype != NDARRAY_FLOAT)) { + mp_raise_TypeError(translate("results cannot be cast to specified type")); + } + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + if(rhs->dtype == NDARRAY_UINT8) { + INPLACE_POWER(lhs, mp_float_t, uint8_t, larray, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT8) { + INPLACE_POWER(lhs, mp_float_t, int8_t, larray, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_UINT16) { + INPLACE_POWER(lhs, mp_float_t, uint16_t, larray, rarray, rstrides); + } else if(rhs->dtype == NDARRAY_INT16) { + INPLACE_POWER(lhs, mp_float_t, int16_t, larray, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_FLOAT) { + INPLACE_POWER(lhs, mp_float_t, mp_float_t, larray, rarray, rstrides); + } + return MP_OBJ_FROM_PTR(lhs); +} +#endif /* NDARRAY_HAS_INPLACE_POWER */ diff --git a/circuitpython/extmod/ulab/code/ndarray_operators.h b/circuitpython/extmod/ulab/code/ndarray_operators.h new file mode 100644 index 0000000..7849e03 --- /dev/null +++ b/circuitpython/extmod/ulab/code/ndarray_operators.h @@ -0,0 +1,277 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös +*/ + +#include "ndarray.h" + +mp_obj_t ndarray_binary_equality(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *, mp_binary_op_t ); +mp_obj_t ndarray_binary_add(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); +mp_obj_t ndarray_binary_multiply(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); +mp_obj_t ndarray_binary_more(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *, mp_binary_op_t ); +mp_obj_t ndarray_binary_power(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); +mp_obj_t ndarray_binary_subtract(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); +mp_obj_t ndarray_binary_true_divide(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); + +mp_obj_t ndarray_inplace_ams(ndarray_obj_t *, ndarray_obj_t *, int32_t *, uint8_t ); +mp_obj_t ndarray_inplace_power(ndarray_obj_t *, ndarray_obj_t *, int32_t *); +mp_obj_t ndarray_inplace_divide(ndarray_obj_t *, ndarray_obj_t *, int32_t *); + +#define UNWRAP_INPLACE_OPERATOR(lhs, larray, rarray, rstrides, OPERATOR)\ +({\ + if((lhs)->dtype == NDARRAY_UINT8) {\ + if((rhs)->dtype == NDARRAY_UINT8) {\ + INPLACE_LOOP((lhs), uint8_t, uint8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_INT8) {\ + INPLACE_LOOP((lhs), uint8_t, int8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_UINT16) {\ + INPLACE_LOOP((lhs), uint8_t, uint16_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else {\ + INPLACE_LOOP((lhs), uint8_t, int16_t, (larray), (rarray), (rstrides), OPERATOR);\ + }\ + } else if(lhs->dtype == NDARRAY_INT8) {\ + if(rhs->dtype == NDARRAY_UINT8) {\ + INPLACE_LOOP((lhs), int8_t, uint8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_INT8) {\ + INPLACE_LOOP((lhs), int8_t, int8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_UINT16) {\ + INPLACE_LOOP((lhs), int8_t, uint16_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else {\ + INPLACE_LOOP((lhs), int8_t, int16_t, (larray), (rarray), (rstrides), OPERATOR);\ + }\ + } else if(lhs->dtype == NDARRAY_UINT16) {\ + if(rhs->dtype == NDARRAY_UINT8) {\ + INPLACE_LOOP((lhs), uint16_t, uint8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_INT8) {\ + INPLACE_LOOP((lhs), uint16_t, int8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_UINT16) {\ + INPLACE_LOOP((lhs), uint16_t, uint16_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else {\ + INPLACE_LOOP((lhs), uint16_t, int16_t, (larray), (rarray), (rstrides), OPERATOR);\ + }\ + } else if(lhs->dtype == NDARRAY_INT16) {\ + if(rhs->dtype == NDARRAY_UINT8) {\ + INPLACE_LOOP((lhs), int16_t, uint8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_INT8) {\ + INPLACE_LOOP((lhs), int16_t, int8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_UINT16) {\ + INPLACE_LOOP((lhs), int16_t, uint16_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else {\ + INPLACE_LOOP((lhs), int16_t, int16_t, (larray), (rarray), (rstrides), OPERATOR);\ + }\ + } else if(lhs->dtype == NDARRAY_FLOAT) {\ + if(rhs->dtype == NDARRAY_UINT8) {\ + INPLACE_LOOP((lhs), mp_float_t, uint8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_INT8) {\ + INPLACE_LOOP((lhs), mp_float_t, int8_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_UINT16) {\ + INPLACE_LOOP((lhs), mp_float_t, uint16_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else if(rhs->dtype == NDARRAY_INT16) {\ + INPLACE_LOOP((lhs), mp_float_t, int16_t, (larray), (rarray), (rstrides), OPERATOR);\ + } else {\ + INPLACE_LOOP((lhs), mp_float_t, mp_float_t, (larray), (rarray), (rstrides), OPERATOR);\ + }\ + }\ +}) + +#if ULAB_MAX_DIMS == 1 +#define INPLACE_POWER(results, type_left, type_right, larray, rarray, rstrides)\ +({ size_t l = 0;\ + do {\ + *((type_left *)(larray)) = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ +}) + +#define FUNC_POINTER_LOOP(results, array, get_lhs, get_rhs, larray, lstrides, rarray, rstrides, OPERATION)\ +({ size_t l = 0;\ + do {\ + mp_float_t lvalue = (get_lhs)((larray));\ + mp_float_t rvalue = (get_rhs)((rarray));\ + (set_result)((array), OPERATION);\ + (array) += (results)->itemsize;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ +}) +#endif /* ULAB_MAX_DIMS == 1 */ + +#if ULAB_MAX_DIMS == 2 +#define INPLACE_POWER(results, type_left, type_right, larray, rarray, rstrides)\ +({ size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_left *)(larray)) = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ +}) + +#define FUNC_POINTER_LOOP(results, array, get_lhs, get_rhs, larray, lstrides, rarray, rstrides, OPERATION)\ +({ size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + mp_float_t lvalue = (get_lhs)((larray));\ + mp_float_t rvalue = (get_rhs)((rarray));\ + (set_result)((array), OPERATION);\ + (array) += (results)->itemsize;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < results->shape[ULAB_MAX_DIMS - 2]);\ +}) +#endif /* ULAB_MAX_DIMS == 2 */ + +#if ULAB_MAX_DIMS == 3 +#define INPLACE_POWER(results, type_left, type_right, larray, rarray, rstrides)\ +({ size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_left *)(larray)) = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ +}) + + +#define FUNC_POINTER_LOOP(results, array, get_lhs, get_rhs, larray, lstrides, rarray, rstrides, OPERATION)\ +({ size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + mp_float_t lvalue = (get_lhs)((larray));\ + mp_float_t rvalue = (get_rhs)((rarray));\ + (set_result)((array), OPERATION);\ + (array) += (results)->itemsize;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < results->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ +}) +#endif /* ULAB_MAX_DIMS == 3 */ + +#if ULAB_MAX_DIMS == 4 +#define INPLACE_POWER(results, type_left, type_right, larray, rarray, rstrides)\ +({ size_t i = 0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_left *)(larray)) = MICROPY_FLOAT_C_FUN(pow)(*((type_left *)(larray)), *((type_right *)(rarray)));\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ +}) + +#define FUNC_POINTER_LOOP(results, array, get_lhs, get_rhs, larray, lstrides, rarray, rstrides, OPERATION)\ +({ size_t i = 0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + mp_float_t lvalue = (get_lhs)((larray));\ + mp_float_t rvalue = (get_rhs)((rarray));\ + (set_result)((array), OPERATION);\ + (array) += (results)->itemsize;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < results->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + (larray) -= (results)->strides[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (larray) += (results)->strides[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS-3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ +}) +#endif /* ULAB_MAX_DIMS == 4 */ diff --git a/circuitpython/extmod/ulab/code/ndarray_properties.c b/circuitpython/extmod/ulab/code/ndarray_properties.c new file mode 100644 index 0000000..5464b31 --- /dev/null +++ b/circuitpython/extmod/ulab/code/ndarray_properties.c @@ -0,0 +1,123 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2021 Zoltán Vörös + * +*/ + +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" + +#include "ulab.h" +#include "ndarray.h" +#include "numpy/ndarray/ndarray_iter.h" +#if ULAB_SUPPORTS_COMPLEX +#include "numpy/carray/carray.h" +#endif + +#ifndef CIRCUITPY + +// a somewhat hackish implementation of property getters/setters; +// this functions is hooked into the attr member of ndarray + +STATIC void call_local_method(mp_obj_t obj, qstr attr, mp_obj_t *dest) { + const mp_obj_type_t *type = mp_obj_get_type(obj); + while (type->locals_dict != NULL) { + assert(type->locals_dict->base.type == &mp_type_dict); // MicroPython restriction, for now + mp_map_t *locals_map = &type->locals_dict->map; + mp_map_elem_t *elem = mp_map_lookup(locals_map, MP_OBJ_NEW_QSTR(attr), MP_MAP_LOOKUP); + if (elem != NULL) { + mp_convert_member_lookup(obj, type, elem->value, dest); + break; + } + if (type->parent == NULL) { + break; + } + type = type->parent; + } +} + + +void ndarray_properties_attr(mp_obj_t self_in, qstr attr, mp_obj_t *dest) { + if (dest[0] == MP_OBJ_NULL) { + switch(attr) { + #if NDARRAY_HAS_DTYPE + case MP_QSTR_dtype: + dest[0] = ndarray_dtype(self_in); + break; + #endif + #if NDARRAY_HAS_FLATITER + case MP_QSTR_flat: + dest[0] = ndarray_flatiter_make_new(self_in); + break; + #endif + #if NDARRAY_HAS_ITEMSIZE + case MP_QSTR_itemsize: + dest[0] = ndarray_itemsize(self_in); + break; + #endif + #if NDARRAY_HAS_SHAPE + case MP_QSTR_shape: + dest[0] = ndarray_shape(self_in); + break; + #endif + #if NDARRAY_HAS_SIZE + case MP_QSTR_size: + dest[0] = ndarray_size(self_in); + break; + #endif + #if NDARRAY_HAS_STRIDES + case MP_QSTR_strides: + dest[0] = ndarray_strides(self_in); + break; + #endif + #if NDARRAY_HAS_TRANSPOSE + case MP_QSTR_T: + dest[0] = ndarray_transpose(self_in); + break; + #endif + #if ULAB_SUPPORTS_COMPLEX + #if ULAB_NUMPY_HAS_IMAG + case MP_QSTR_imag: + dest[0] = carray_imag(self_in); + break; + #endif + #if ULAB_NUMPY_HAS_IMAG + case MP_QSTR_real: + dest[0] = carray_real(self_in); + break; + #endif + #endif /* ULAB_SUPPORTS_COMPLEX */ + default: + call_local_method(self_in, attr, dest); + break; + } + } else { + if(dest[1]) { + switch(attr) { + #if ULAB_MAX_DIMS > 1 + #if NDARRAY_HAS_RESHAPE + case MP_QSTR_shape: + ndarray_reshape_core(self_in, dest[1], 1); + break; + #endif + #endif + default: + return; + break; + } + dest[0] = MP_OBJ_NULL; + } + } +} + +#endif /* CIRCUITPY */
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/code/ndarray_properties.h b/circuitpython/extmod/ulab/code/ndarray_properties.h new file mode 100644 index 0000000..28da7c0 --- /dev/null +++ b/circuitpython/extmod/ulab/code/ndarray_properties.h @@ -0,0 +1,104 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020-2021 Zoltán Vörös +*/ + +#ifndef _NDARRAY_PROPERTIES_ +#define _NDARRAY_PROPERTIES_ + +#include "py/runtime.h" +#include "py/binary.h" +#include "py/obj.h" +#include "py/objarray.h" + +#include "ulab.h" +#include "ndarray.h" +#include "numpy/ndarray/ndarray_iter.h" + +#if CIRCUITPY +typedef struct _mp_obj_property_t { + mp_obj_base_t base; + mp_obj_t proxy[3]; // getter, setter, deleter +} mp_obj_property_t; + +#if NDARRAY_HAS_DTYPE +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_get_dtype_obj, ndarray_dtype); +STATIC const mp_obj_property_t ndarray_dtype_obj = { + .base.type = &mp_type_property, + .proxy = {(mp_obj_t)&ndarray_get_dtype_obj, + mp_const_none, + mp_const_none }, +}; +#endif /* NDARRAY_HAS_DTYPE */ + +#if NDARRAY_HAS_FLATITER +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_flatiter_make_new_obj, ndarray_flatiter_make_new); +STATIC const mp_obj_property_t ndarray_flat_obj = { + .base.type = &mp_type_property, + .proxy = {(mp_obj_t)&ndarray_flatiter_make_new_obj, + mp_const_none, + mp_const_none }, +}; +#endif /* NDARRAY_HAS_FLATITER */ + +#if NDARRAY_HAS_ITEMSIZE +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_get_itemsize_obj, ndarray_itemsize); +STATIC const mp_obj_property_t ndarray_itemsize_obj = { + .base.type = &mp_type_property, + .proxy = {(mp_obj_t)&ndarray_get_itemsize_obj, + mp_const_none, + mp_const_none }, +}; +#endif /* NDARRAY_HAS_ITEMSIZE */ + +#if NDARRAY_HAS_SHAPE +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_get_shape_obj, ndarray_shape); +STATIC const mp_obj_property_t ndarray_shape_obj = { + .base.type = &mp_type_property, + .proxy = {(mp_obj_t)&ndarray_get_shape_obj, + mp_const_none, + mp_const_none }, +}; +#endif /* NDARRAY_HAS_SHAPE */ + +#if NDARRAY_HAS_SIZE +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_get_size_obj, ndarray_size); +STATIC const mp_obj_property_t ndarray_size_obj = { + .base.type = &mp_type_property, + .proxy = {(mp_obj_t)&ndarray_get_size_obj, + mp_const_none, + mp_const_none }, +}; +#endif /* NDARRAY_HAS_SIZE */ + +#if NDARRAY_HAS_STRIDES +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_get_strides_obj, ndarray_strides); +STATIC const mp_obj_property_t ndarray_strides_obj = { + .base.type = &mp_type_property, + .proxy = {(mp_obj_t)&ndarray_get_strides_obj, + mp_const_none, + mp_const_none }, +}; +#endif /* NDARRAY_HAS_STRIDES */ + +#else + +void ndarray_properties_attr(mp_obj_t , qstr , mp_obj_t *); + +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_dtype_obj, ndarray_dtype); +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_flatiter_make_new_obj, ndarray_flatiter_make_new); +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_itemsize_obj, ndarray_itemsize); +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_shape_obj, ndarray_shape); +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_size_obj, ndarray_size); +MP_DEFINE_CONST_FUN_OBJ_1(ndarray_strides_obj, ndarray_strides); + +#endif /* CIRCUITPY */ + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/approx.c b/circuitpython/extmod/ulab/code/numpy/approx.c new file mode 100644 index 0000000..85cdbf7 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/approx.c @@ -0,0 +1,227 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös + * 2020 Diego Elio Pettenò + * 2020 Taku Fukada +*/ + +#include <math.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../ulab.h" +#include "../ulab_tools.h" +#include "carray/carray_tools.h" +#include "approx.h" + +//| """Numerical approximation methods""" +//| + +const mp_obj_float_t approx_trapz_dx = {{&mp_type_float}, MICROPY_FLOAT_CONST(1.0)}; + +#if ULAB_NUMPY_HAS_INTERP +//| def interp( +//| x: ulab.numpy.ndarray, +//| xp: ulab.numpy.ndarray, +//| fp: ulab.numpy.ndarray, +//| *, +//| left: Optional[_float] = None, +//| right: Optional[_float] = None +//| ) -> ulab.numpy.ndarray: +//| """ +//| :param ulab.numpy.ndarray x: The x-coordinates at which to evaluate the interpolated values. +//| :param ulab.numpy.ndarray xp: The x-coordinates of the data points, must be increasing +//| :param ulab.numpy.ndarray fp: The y-coordinates of the data points, same length as xp +//| :param left: Value to return for ``x < xp[0]``, default is ``fp[0]``. +//| :param right: Value to return for ``x > xp[-1]``, default is ``fp[-1]``. +//| +//| Returns the one-dimensional piecewise linear interpolant to a function with given discrete data points (xp, fp), evaluated at x.""" +//| ... +//| + +STATIC mp_obj_t approx_interp(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_left, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} }, + { MP_QSTR_right, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} }, + }; + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + ndarray_obj_t *x = ndarray_from_mp_obj(args[0].u_obj, 0); + ndarray_obj_t *xp = ndarray_from_mp_obj(args[1].u_obj, 0); // xp must hold an increasing sequence of independent values + ndarray_obj_t *fp = ndarray_from_mp_obj(args[2].u_obj, 0); + COMPLEX_DTYPE_NOT_IMPLEMENTED(x->dtype) + COMPLEX_DTYPE_NOT_IMPLEMENTED(xp->dtype) + COMPLEX_DTYPE_NOT_IMPLEMENTED(fp->dtype) + if((xp->ndim != 1) || (fp->ndim != 1) || (xp->len < 2) || (fp->len < 2) || (xp->len != fp->len)) { + mp_raise_ValueError(translate("interp is defined for 1D iterables of equal length")); + } + + ndarray_obj_t *y = ndarray_new_linear_array(x->len, NDARRAY_FLOAT); + mp_float_t left_value, right_value; + uint8_t *xparray = (uint8_t *)xp->array; + + mp_float_t xp_left = ndarray_get_float_value(xparray, xp->dtype); + xparray += (xp->len-1) * xp->strides[ULAB_MAX_DIMS - 1]; + mp_float_t xp_right = ndarray_get_float_value(xparray, xp->dtype); + + uint8_t *fparray = (uint8_t *)fp->array; + + if(args[3].u_obj == mp_const_none) { + left_value = ndarray_get_float_value(fparray, fp->dtype); + } else { + left_value = mp_obj_get_float(args[3].u_obj); + } + if(args[4].u_obj == mp_const_none) { + fparray += (fp->len-1) * fp->strides[ULAB_MAX_DIMS - 1]; + right_value = ndarray_get_float_value(fparray, fp->dtype); + } else { + right_value = mp_obj_get_float(args[4].u_obj); + } + + xparray = xp->array; + fparray = fp->array; + + uint8_t *xarray = (uint8_t *)x->array; + mp_float_t *yarray = (mp_float_t *)y->array; + uint8_t *temp; + + for(size_t i=0; i < x->len; i++, yarray++) { + mp_float_t x_value = ndarray_get_float_value(xarray, x->dtype); + xarray += x->strides[ULAB_MAX_DIMS - 1]; + if(x_value < xp_left) { + *yarray = left_value; + } else if(x_value > xp_right) { + *yarray = right_value; + } else { // do the binary search here + mp_float_t xp_left_, xp_right_; + mp_float_t fp_left, fp_right; + size_t left_index = 0, right_index = xp->len - 1, middle_index; + while(right_index - left_index > 1) { + middle_index = left_index + (right_index - left_index) / 2; + temp = xparray + middle_index * xp->strides[ULAB_MAX_DIMS - 1]; + mp_float_t xp_middle = ndarray_get_float_value(temp, xp->dtype); + if(x_value <= xp_middle) { + right_index = middle_index; + } else { + left_index = middle_index; + } + } + temp = xparray + left_index * xp->strides[ULAB_MAX_DIMS - 1]; + xp_left_ = ndarray_get_float_value(temp, xp->dtype); + + temp = xparray + right_index * xp->strides[ULAB_MAX_DIMS - 1]; + xp_right_ = ndarray_get_float_value(temp, xp->dtype); + + temp = fparray + left_index * fp->strides[ULAB_MAX_DIMS - 1]; + fp_left = ndarray_get_float_value(temp, fp->dtype); + + temp = fparray + right_index * fp->strides[ULAB_MAX_DIMS - 1]; + fp_right = ndarray_get_float_value(temp, fp->dtype); + + *yarray = fp_left + (x_value - xp_left_) * (fp_right - fp_left) / (xp_right_ - xp_left_); + } + } + return MP_OBJ_FROM_PTR(y); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(approx_interp_obj, 2, approx_interp); +#endif + +#if ULAB_NUMPY_HAS_TRAPZ +//| def trapz(y: ulab.numpy.ndarray, x: Optional[ulab.numpy.ndarray] = None, dx: _float = 1.0) -> _float: +//| """ +//| :param 1D ulab.numpy.ndarray y: the values of the dependent variable +//| :param 1D ulab.numpy.ndarray x: optional, the coordinates of the independent variable. Defaults to uniformly spaced values. +//| :param float dx: the spacing between sample points, if x=None +//| +//| Returns the integral of y(x) using the trapezoidal rule. +//| """ +//| ... +//| + +STATIC mp_obj_t approx_trapz(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_x, MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_dx, MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&approx_trapz_dx)} }, + }; + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + ndarray_obj_t *y = ndarray_from_mp_obj(args[0].u_obj, 0); + COMPLEX_DTYPE_NOT_IMPLEMENTED(y->dtype) + ndarray_obj_t *x; + mp_float_t mean = MICROPY_FLOAT_CONST(0.0); + if(y->len < 2) { + return mp_obj_new_float(mean); + } + if((y->ndim != 1)) { + mp_raise_ValueError(translate("trapz is defined for 1D iterables")); + } + + mp_float_t (*funcy)(void *) = ndarray_get_float_function(y->dtype); + uint8_t *yarray = (uint8_t *)y->array; + + size_t count = 1; + mp_float_t y1, y2, m; + + if(args[1].u_obj != mp_const_none) { + x = ndarray_from_mp_obj(args[1].u_obj, 0); // x must hold an increasing sequence of independent values + COMPLEX_DTYPE_NOT_IMPLEMENTED(x->dtype) + if((x->ndim != 1) || (y->len != x->len)) { + mp_raise_ValueError(translate("trapz is defined for 1D arrays of equal length")); + } + + mp_float_t (*funcx)(void *) = ndarray_get_float_function(x->dtype); + uint8_t *xarray = (uint8_t *)x->array; + mp_float_t x1, x2; + + y1 = funcy(yarray); + yarray += y->strides[ULAB_MAX_DIMS - 1]; + x1 = funcx(xarray); + xarray += x->strides[ULAB_MAX_DIMS - 1]; + + for(size_t i=1; i < y->len; i++) { + y2 = funcy(yarray); + yarray += y->strides[ULAB_MAX_DIMS - 1]; + x2 = funcx(xarray); + xarray += x->strides[ULAB_MAX_DIMS - 1]; + mp_float_t value = (x2 - x1) * (y2 + y1); + m = mean + (value - mean) / (mp_float_t)count; + mean = m; + x1 = x2; + y1 = y2; + count++; + } + } else { + mp_float_t dx = mp_obj_get_float(args[2].u_obj); + y1 = funcy(yarray); + yarray += y->strides[ULAB_MAX_DIMS - 1]; + + for(size_t i=1; i < y->len; i++) { + y2 = ndarray_get_float_index(y->array, y->dtype, i); + mp_float_t value = (y2 + y1); + m = mean + (value - mean) / (mp_float_t)count; + mean = m; + y1 = y2; + count++; + } + mean *= dx; + } + return mp_obj_new_float(MICROPY_FLOAT_CONST(0.5)*mean*(y->len-1)); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(approx_trapz_obj, 1, approx_trapz); +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/approx.h b/circuitpython/extmod/ulab/code/numpy/approx.h new file mode 100644 index 0000000..487a98b --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/approx.h @@ -0,0 +1,29 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös +*/ + +#ifndef _APPROX_ +#define _APPROX_ + +#include "../ulab.h" +#include "../ndarray.h" + +#define APPROX_EPS MICROPY_FLOAT_CONST(1.0e-4) +#define APPROX_NONZDELTA MICROPY_FLOAT_CONST(0.05) +#define APPROX_ZDELTA MICROPY_FLOAT_CONST(0.00025) +#define APPROX_ALPHA MICROPY_FLOAT_CONST(1.0) +#define APPROX_BETA MICROPY_FLOAT_CONST(2.0) +#define APPROX_GAMMA MICROPY_FLOAT_CONST(0.5) +#define APPROX_DELTA MICROPY_FLOAT_CONST(0.5) + +MP_DECLARE_CONST_FUN_OBJ_KW(approx_interp_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(approx_trapz_obj); + +#endif /* _APPROX_ */ diff --git a/circuitpython/extmod/ulab/code/numpy/carray/carray.c b/circuitpython/extmod/ulab/code/numpy/carray/carray.c new file mode 100644 index 0000000..a5f8a2b --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/carray/carray.c @@ -0,0 +1,826 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2021-2022 Zoltán Vörös +*/ + +#include <math.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/objint.h" +#include "py/runtime.h" +#include "py/builtin.h" +#include "py/misc.h" + +#include "../../ulab.h" +#include "../../ndarray.h" +#include "../../ulab_tools.h" +#include "carray.h" + +#if ULAB_SUPPORTS_COMPLEX + +//| import ulab.numpy + +//| def real(val): +//| """ +//| Return the real part of the complex argument, which can be +//| either an ndarray, or a scalar.""" +//| ... +//| + +mp_obj_t carray_real(mp_obj_t _source) { + if(mp_obj_is_type(_source, &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(_source); + if(source->dtype != NDARRAY_COMPLEX) { + ndarray_obj_t *target = ndarray_new_dense_ndarray(source->ndim, source->shape, source->dtype); + ndarray_copy_array(source, target, 0); + return MP_OBJ_FROM_PTR(target); + } else { // the input is most definitely a complex array + ndarray_obj_t *target = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_FLOAT); + ndarray_copy_array(source, target, 0); + return MP_OBJ_FROM_PTR(target); + } + } else { + mp_raise_NotImplementedError(translate("function is implemented for ndarrays only")); + } + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_1(carray_real_obj, carray_real); + +//| def imag(val): +//| """ +//| Return the imaginary part of the complex argument, which can be +//| either an ndarray, or a scalar.""" +//| ... +//| + +mp_obj_t carray_imag(mp_obj_t _source) { + if(mp_obj_is_type(_source, &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(_source); + if(source->dtype != NDARRAY_COMPLEX) { // if not complex, then the imaginary part is zero + ndarray_obj_t *target = ndarray_new_dense_ndarray(source->ndim, source->shape, source->dtype); + return MP_OBJ_FROM_PTR(target); + } else { // the input is most definitely a complex array + ndarray_obj_t *target = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_FLOAT); + ndarray_copy_array(source, target, source->itemsize / 2); + return MP_OBJ_FROM_PTR(target); + } + } else { + mp_raise_NotImplementedError(translate("function is implemented for ndarrays only")); + } + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_1(carray_imag_obj, carray_imag); + +#if ULAB_NUMPY_HAS_CONJUGATE + +//| def conjugate(val): +//| """ +//| Return the conjugate of the complex argument, which can be +//| either an ndarray, or a scalar.""" +//| ... +//| +mp_obj_t carray_conjugate(mp_obj_t _source) { + if(mp_obj_is_type(_source, &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(_source); + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, source->dtype); + ndarray_copy_array(source, ndarray, 0); + if(source->dtype == NDARRAY_COMPLEX) { + mp_float_t *array = (mp_float_t *)ndarray->array; + array++; + for(size_t i = 0; i < ndarray->len; i++) { + *array *= MICROPY_FLOAT_CONST(-1.0); + array += 2; + } + } + return MP_OBJ_FROM_PTR(ndarray); + } else { + if(mp_obj_is_type(_source, &mp_type_complex)) { + mp_float_t real, imag; + mp_obj_get_complex(_source, &real, &imag); + imag = imag * MICROPY_FLOAT_CONST(-1.0); + return mp_obj_new_complex(real, imag); + } else if(mp_obj_is_int(_source) || mp_obj_is_float(_source)) { + return _source; + } else { + mp_raise_TypeError(translate("input must be an ndarray, or a scalar")); + } + } + // this should never happen + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_1(carray_conjugate_obj, carray_conjugate); +#endif + +#if ULAB_NUMPY_HAS_SORT_COMPLEX +//| def sort_complex(a: ulab.numpy.ndarray) -> ulab.numpy.ndarray: +//| """ +//| .. param: a +//| a one-dimensional ndarray +//| +//| Sort a complex array using the real part first, then the imaginary part. +//| Always returns a sorted complex array, even if the input was real.""" +//| ... +//| + +static void carray_sort_complex_(mp_float_t *array, size_t len) { + // array is assumed to be a floating vector containing the real and imaginary parts + // of a complex array at alternating positions as + // array[0] = real[0] + // array[1] = imag[0] + // array[2] = real[1] + // array[3] = imag[1] + + mp_float_t real, imag; + size_t c, q = len, p, r = len >> 1; + for (;;) { + if (r > 0) { + r--; + real = array[2 * r]; + imag = array[2 * r + 1]; + } else { + q--; + if(q == 0) { + break; + } + real = array[2 * q]; + imag = array[2 * q + 1]; + array[2 * q] = array[0]; + array[2 * q + 1] = array[1]; + } + p = r; + c = r + r + 1; + while (c < q) { + if(c + 1 < q) { + if((array[2 * (c+1)] > array[2 * c]) || + ((array[2 * (c+1)] == array[2 * c]) && (array[2 * (c+1) + 1] > array[2 * c + 1]))) { + c++; + } + } + if((array[2 * c] > real) || + ((array[2 * c] == real) && (array[2 * c + 1] > imag))) { + array[2 * p] = array[2 * c]; // real part + array[2 * p + 1] = array[2 * c + 1]; // imag part + p = c; + c = p + p + 1; + } else { + break; + } + } + array[2 * p] = real; + array[2 * p + 1] = imag; + } +} + +mp_obj_t carray_sort_complex(mp_obj_t _source) { + if(!mp_obj_is_type(_source, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("input must be a 1D ndarray")); + } + ndarray_obj_t *source = MP_OBJ_TO_PTR(_source); + if(source->ndim != 1) { + mp_raise_TypeError(translate("input must be a 1D ndarray")); + } + + ndarray_obj_t *ndarray = ndarray_copy_view_convert_type(source, NDARRAY_COMPLEX); + mp_float_t *array = (mp_float_t *)ndarray->array; + carray_sort_complex_(array, ndarray->len); + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_1(carray_sort_complex_obj, carray_sort_complex); +#endif + +//| def abs(a: ulab.numpy.ndarray) -> ulab.numpy.ndarray: +//| """ +//| .. param: a +//| a one-dimensional ndarray +//| +//| Return the absolute value of complex ndarray.""" +//| ... +//| + +mp_obj_t carray_abs(ndarray_obj_t *source, ndarray_obj_t *target) { + // calculates the absolute value of a complex array and returns a dense array + uint8_t *sarray = (uint8_t *)source->array; + mp_float_t *tarray = (mp_float_t *)target->array; + uint8_t itemsize = mp_binary_get_size('@', NDARRAY_FLOAT, NULL); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t rvalue = *(mp_float_t *)sarray; + mp_float_t ivalue = *(mp_float_t *)(sarray + itemsize); + *tarray++ = MICROPY_FLOAT_C_FUN(sqrt)(rvalue * rvalue + ivalue * ivalue); + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif + return MP_OBJ_FROM_PTR(target); +} + +static void carray_copy_part(uint8_t *tarray, uint8_t *sarray, size_t *shape, int32_t *strides) { + // copies the real or imaginary part of an array + // into the respective part of a dense complex array + uint8_t sz = sizeof(mp_float_t); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + memcpy(tarray, sarray, sz); + tarray += 2 * sz; + sarray += strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= strides[ULAB_MAX_DIMS - 1] * shape[ULAB_MAX_DIMS-1]; + sarray += strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + sarray -= strides[ULAB_MAX_DIMS - 2] * shape[ULAB_MAX_DIMS-2]; + sarray += strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + sarray -= strides[ULAB_MAX_DIMS - 3] * shape[ULAB_MAX_DIMS-3]; + sarray += strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ +} + +mp_obj_t carray_binary_equal_not_equal(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides, mp_binary_op_t op) { + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_UINT8); + results->boolean = 1; + uint8_t *array = (uint8_t *)results->array; + + if(op == MP_BINARY_OP_NOT_EQUAL) { + memset(array, 1, results->len); + } + + if((lhs->dtype == NDARRAY_COMPLEX) && (rhs->dtype == NDARRAY_COMPLEX)) { + mp_float_t *larray = (mp_float_t *)lhs->array; + mp_float_t *rarray = (mp_float_t *)rhs->array; + + ulab_rescale_float_strides(lstrides); + ulab_rescale_float_strides(rstrides); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + if((larray[0] == rarray[0]) && (larray[1] == rarray[1])) { + *array ^= 0x01; + } + array++; + larray += lstrides[ULAB_MAX_DIMS - 1]; + rarray += rstrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < results->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + larray -= lstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + larray += lstrides[ULAB_MAX_DIMS - 2]; + rarray -= rstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + rarray += rstrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < results->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + larray -= lstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + larray += lstrides[ULAB_MAX_DIMS - 3]; + rarray -= rstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < results->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + larray -= lstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + larray += lstrides[ULAB_MAX_DIMS - 4]; + rarray -= rstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + rarray += rstrides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < results->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + } else { // only one of the operands is complex + mp_float_t *larray = (mp_float_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + // align the complex array to the left + uint8_t rdtype = rhs->dtype; + int32_t *lstrides_ = lstrides; + int32_t *rstrides_ = rstrides; + + if(rhs->dtype == NDARRAY_COMPLEX) { + larray = (mp_float_t *)rhs->array; + rarray = (uint8_t *)lhs->array; + lstrides_ = rstrides; + rstrides_ = lstrides; + rdtype = lhs->dtype; + } + + ulab_rescale_float_strides(lstrides_); + + if(rdtype == NDARRAY_UINT8) { + BINARY_LOOP_COMPLEX_EQUAL(results, array, uint8_t, larray, lstrides_, rarray, rstrides_); + } else if(rdtype == NDARRAY_INT8) { + BINARY_LOOP_COMPLEX_EQUAL(results, array, int8_t, larray, lstrides_, rarray, rstrides_); + } else if(rdtype == NDARRAY_UINT16) { + BINARY_LOOP_COMPLEX_EQUAL(results, array, uint16_t, larray, lstrides_, rarray, rstrides_); + } else if(rdtype == NDARRAY_INT16) { + BINARY_LOOP_COMPLEX_EQUAL(results, array, int16_t, larray, lstrides_, rarray, rstrides_); + } else if(rdtype == NDARRAY_FLOAT) { + BINARY_LOOP_COMPLEX_EQUAL(results, array, mp_float_t, larray, lstrides_, rarray, rstrides_); + } + } + return MP_OBJ_FROM_PTR(results); +} + +mp_obj_t carray_binary_add(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_COMPLEX); + mp_float_t *resarray = (mp_float_t *)results->array; + + if((lhs->dtype == NDARRAY_COMPLEX) && (rhs->dtype == NDARRAY_COMPLEX)) { + mp_float_t *larray = (mp_float_t *)lhs->array; + mp_float_t *rarray = (mp_float_t *)rhs->array; + + ulab_rescale_float_strides(lstrides); + ulab_rescale_float_strides(rstrides); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + // real part + *resarray++ = larray[0] + rarray[0]; + // imaginary part + *resarray++ = larray[1] + rarray[1]; + larray += lstrides[ULAB_MAX_DIMS - 1]; + rarray += rstrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < results->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + larray -= lstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + larray += lstrides[ULAB_MAX_DIMS - 2]; + rarray -= rstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + rarray += rstrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < results->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + larray -= lstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + larray += lstrides[ULAB_MAX_DIMS - 3]; + rarray -= rstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < results->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + larray -= lstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + larray += lstrides[ULAB_MAX_DIMS - 4]; + rarray -= rstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + rarray += rstrides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < results->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + } else { // only one of the operands is complex + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + // align the complex array to the left + uint8_t rdtype = rhs->dtype; + int32_t *lstrides_ = lstrides; + int32_t *rstrides_ = rstrides; + + if(rhs->dtype == NDARRAY_COMPLEX) { + larray = (uint8_t *)rhs->array; + rarray = (uint8_t *)lhs->array; + lstrides_ = rstrides; + rstrides_ = lstrides; + rdtype = lhs->dtype; + } + + if(rdtype == NDARRAY_UINT8) { + BINARY_LOOP_COMPLEX(results, resarray, uint8_t, larray, lstrides_, rarray, rstrides_, +); + } else if(rdtype == NDARRAY_INT8) { + BINARY_LOOP_COMPLEX(results, resarray, int8_t, larray, lstrides_, rarray, rstrides_, +); + } else if(rdtype == NDARRAY_UINT16) { + BINARY_LOOP_COMPLEX(results, resarray, uint16_t, larray, lstrides_, rarray, rstrides_, +); + } else if(rdtype == NDARRAY_INT16) { + BINARY_LOOP_COMPLEX(results, resarray, int16_t, larray, lstrides_, rarray, rstrides_, +); + } else if(rdtype == NDARRAY_FLOAT) { + BINARY_LOOP_COMPLEX(results, resarray, mp_float_t, larray, lstrides_, rarray, rstrides_, +); + } + + // simply copy the imaginary part + uint8_t *tarray = (uint8_t *)results->array; + tarray += sizeof(mp_float_t); + + if(lhs->dtype == NDARRAY_COMPLEX) { + rarray = (uint8_t *)lhs->array; + rstrides = lstrides; + } else { + rarray = (uint8_t *)rhs->array; + } + rarray += sizeof(mp_float_t); + carray_copy_part(tarray, rarray, results->shape, rstrides); + } + return MP_OBJ_FROM_PTR(results); +} + +static void carray_binary_multiply_(ndarray_obj_t *results, mp_float_t *resarray, uint8_t *larray, uint8_t *rarray, + int32_t *lstrides, int32_t *rstrides, uint8_t rdtype) { + + if(rdtype == NDARRAY_UINT8) { + BINARY_LOOP_COMPLEX(results, resarray, uint8_t, larray, lstrides, rarray, rstrides, *); + } else if(rdtype == NDARRAY_INT8) { + BINARY_LOOP_COMPLEX(results, resarray, int8_t, larray, lstrides, rarray, rstrides, *); + } else if(rdtype == NDARRAY_UINT16) { + BINARY_LOOP_COMPLEX(results, resarray, uint16_t, larray, lstrides, rarray, rstrides, *); + } else if(rdtype == NDARRAY_INT16) { + BINARY_LOOP_COMPLEX(results, resarray, int16_t, larray, lstrides, rarray, rstrides, *); + } else if(rdtype == NDARRAY_FLOAT) { + BINARY_LOOP_COMPLEX(results, resarray, mp_float_t, larray, lstrides, rarray, rstrides, *); + } +} + +mp_obj_t carray_binary_multiply(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_COMPLEX); + mp_float_t *resarray = (mp_float_t *)results->array; + + if((lhs->dtype == NDARRAY_COMPLEX) && (rhs->dtype == NDARRAY_COMPLEX)) { + mp_float_t *larray = (mp_float_t *)lhs->array; + mp_float_t *rarray = (mp_float_t *)rhs->array; + + ulab_rescale_float_strides(lstrides); + ulab_rescale_float_strides(rstrides); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + // real part + *resarray++ = larray[0] * rarray[0] - larray[1] * rarray[1]; + // imaginary part + *resarray++ = larray[0] * rarray[1] + larray[1] * rarray[0]; + larray += lstrides[ULAB_MAX_DIMS - 1]; + rarray += rstrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < results->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + larray -= lstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + larray += lstrides[ULAB_MAX_DIMS - 2]; + rarray -= rstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + rarray += rstrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < results->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + larray -= lstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + larray += lstrides[ULAB_MAX_DIMS - 3]; + rarray -= rstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < results->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + larray -= lstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + larray += lstrides[ULAB_MAX_DIMS - 4]; + rarray -= rstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + rarray += rstrides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < results->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + } else { // only one of the operands is complex + + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + uint8_t *lo = larray, *ro = rarray; + int32_t *left_strides = lstrides; + int32_t *right_strides = rstrides; + uint8_t rdtype = rhs->dtype; + + // align the complex array to the left + if(rhs->dtype == NDARRAY_COMPLEX) { + lo = (uint8_t *)rhs->array; + ro = (uint8_t *)lhs->array; + rdtype = lhs->dtype; + left_strides = rstrides; + right_strides = lstrides; + } + + larray = lo; + rarray = ro; + // real part + carray_binary_multiply_(results, resarray, larray, rarray, left_strides, right_strides, rdtype); + + larray = lo + sizeof(mp_float_t); + rarray = ro; + resarray = (mp_float_t *)results->array; + resarray++; + // imaginary part + carray_binary_multiply_(results, resarray, larray, rarray, left_strides, right_strides, rdtype); + } + return MP_OBJ_FROM_PTR(results); +} + +mp_obj_t carray_binary_subtract(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_COMPLEX); + mp_float_t *resarray = (mp_float_t *)results->array; + + if((lhs->dtype == NDARRAY_COMPLEX) && (rhs->dtype == NDARRAY_COMPLEX)) { + mp_float_t *larray = (mp_float_t *)lhs->array; + mp_float_t *rarray = (mp_float_t *)rhs->array; + + ulab_rescale_float_strides(lstrides); + ulab_rescale_float_strides(rstrides); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + // real part + *resarray++ = larray[0] - rarray[0]; + // imaginary part + *resarray++ = larray[1] - rarray[1]; + larray += lstrides[ULAB_MAX_DIMS - 1]; + rarray += rstrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < results->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + larray -= lstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + larray += lstrides[ULAB_MAX_DIMS - 2]; + rarray -= rstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + rarray += rstrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < results->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + larray -= lstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + larray += lstrides[ULAB_MAX_DIMS - 3]; + rarray -= rstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < results->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + larray -= lstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + larray += lstrides[ULAB_MAX_DIMS - 4]; + rarray -= rstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + rarray += rstrides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < results->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + } else { + uint8_t *larray = (uint8_t *)lhs->array; + if(lhs->dtype == NDARRAY_COMPLEX) { + uint8_t *rarray = (uint8_t *)rhs->array; + if(rhs->dtype == NDARRAY_UINT8) { + BINARY_LOOP_COMPLEX(results, resarray, uint8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT8) { + BINARY_LOOP_COMPLEX(results, resarray, int8_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_UINT16) { + BINARY_LOOP_COMPLEX(results, resarray, uint16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_INT16) { + BINARY_LOOP_COMPLEX(results, resarray, int16_t, larray, lstrides, rarray, rstrides, -); + } else if(rhs->dtype == NDARRAY_FLOAT) { + BINARY_LOOP_COMPLEX(results, resarray, mp_float_t, larray, lstrides, rarray, rstrides, -); + } + // copy the imaginary part + uint8_t *tarray = (uint8_t *)results->array; + tarray += sizeof(mp_float_t); + + larray = (uint8_t *)lhs->array; + larray += sizeof(mp_float_t); + + carray_copy_part(tarray, larray, results->shape, lstrides); + } else if(rhs->dtype == NDARRAY_COMPLEX) { + mp_float_t *rarray = (mp_float_t *)rhs->array; + ulab_rescale_float_strides(rstrides); + + if(lhs->dtype == NDARRAY_UINT8) { + BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT(results, resarray, uint8_t, larray, lstrides, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_INT8) { + BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT(results, resarray, int8_t, larray, lstrides, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_UINT16) { + BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT(results, resarray, uint16_t, larray, lstrides, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_INT16) { + BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT(results, resarray, int16_t, larray, lstrides, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_FLOAT) { + BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT(results, resarray, mp_float_t, larray, lstrides, rarray, rstrides); + } + } + } + + return MP_OBJ_FROM_PTR(results); +} + +static void carray_binary_left_divide_(ndarray_obj_t *results, mp_float_t *resarray, uint8_t *larray, uint8_t *rarray, + int32_t *lstrides, int32_t *rstrides, uint8_t rdtype) { + + if(rdtype == NDARRAY_UINT8) { + BINARY_LOOP_COMPLEX(results, resarray, uint8_t, larray, lstrides, rarray, rstrides, /); + } else if(rdtype == NDARRAY_INT8) { + BINARY_LOOP_COMPLEX(results, resarray, int8_t, larray, lstrides, rarray, rstrides, /); + } else if(rdtype == NDARRAY_UINT16) { + BINARY_LOOP_COMPLEX(results, resarray, uint16_t, larray, lstrides, rarray, rstrides, /); + } else if(rdtype == NDARRAY_INT16) { + BINARY_LOOP_COMPLEX(results, resarray, int16_t, larray, lstrides, rarray, rstrides, /); + } else if(rdtype == NDARRAY_FLOAT) { + BINARY_LOOP_COMPLEX(results, resarray, mp_float_t, larray, lstrides, rarray, rstrides, /); + } +} + +mp_obj_t carray_binary_divide(ndarray_obj_t *lhs, ndarray_obj_t *rhs, + uint8_t ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_COMPLEX); + mp_float_t *resarray = (mp_float_t *)results->array; + + if((lhs->dtype == NDARRAY_COMPLEX) && (rhs->dtype == NDARRAY_COMPLEX)) { + mp_float_t *larray = (mp_float_t *)lhs->array; + mp_float_t *rarray = (mp_float_t *)rhs->array; + + ulab_rescale_float_strides(lstrides); + ulab_rescale_float_strides(rstrides); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + // (a + bi) / (c + di) = + // (ac + bd) / (c^2 + d^2) + i (bc - ad) / (c^2 + d^2) + // denominator + mp_float_t denom = rarray[0] * rarray[0] + rarray[1] * rarray[1]; + + // real part + *resarray++ = (larray[0] * rarray[0] + larray[1] * rarray[1]) / denom; + // imaginary part + *resarray++ = (larray[1] * rarray[0] - larray[0] * rarray[1]) / denom; + larray += lstrides[ULAB_MAX_DIMS - 1]; + rarray += rstrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < results->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + larray -= lstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + larray += lstrides[ULAB_MAX_DIMS - 2]; + rarray -= rstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + rarray += rstrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < results->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + larray -= lstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + larray += lstrides[ULAB_MAX_DIMS - 3]; + rarray -= rstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < results->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + larray -= lstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + larray += lstrides[ULAB_MAX_DIMS - 4]; + rarray -= rstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + rarray += rstrides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < results->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + } else { + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + if(lhs->dtype == NDARRAY_COMPLEX) { + // real part + carray_binary_left_divide_(results, resarray, larray, rarray, lstrides, rstrides, rhs->dtype); + // imaginary part + resarray = (mp_float_t *)results->array; + resarray++; + larray = (uint8_t *)lhs->array; + larray += sizeof(mp_float_t); + rarray = (uint8_t *)rhs->array; + carray_binary_left_divide_(results, resarray, larray, rarray, lstrides, rstrides, rhs->dtype); + } else { + if(lhs->dtype == NDARRAY_UINT8) { + BINARY_LOOP_COMPLEX_RIGHT_DIVIDE(results, resarray, uint8_t, larray, lstrides, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_INT8) { + BINARY_LOOP_COMPLEX_RIGHT_DIVIDE(results, resarray, int8_t, larray, lstrides, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_UINT16) { + BINARY_LOOP_COMPLEX_RIGHT_DIVIDE(results, resarray, uint16_t, larray, lstrides, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_INT16) { + BINARY_LOOP_COMPLEX_RIGHT_DIVIDE(results, resarray, int16_t, larray, lstrides, rarray, rstrides); + } else if(lhs->dtype == NDARRAY_FLOAT) { + BINARY_LOOP_COMPLEX_RIGHT_DIVIDE(results, resarray, mp_float_t, larray, lstrides, rarray, rstrides); + } + } + } + + return MP_OBJ_FROM_PTR(results); +} + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/carray/carray.h b/circuitpython/extmod/ulab/code/numpy/carray/carray.h new file mode 100644 index 0000000..8ca5de2 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/carray/carray.h @@ -0,0 +1,237 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2021-2022 Zoltán Vörös +*/ + +#ifndef _CARRAY_ +#define _CARRAY_ + +MP_DECLARE_CONST_FUN_OBJ_1(carray_real_obj); +MP_DECLARE_CONST_FUN_OBJ_1(carray_imag_obj); +MP_DECLARE_CONST_FUN_OBJ_1(carray_conjugate_obj); +MP_DECLARE_CONST_FUN_OBJ_1(carray_sort_complex_obj); + + +mp_obj_t carray_imag(mp_obj_t ); +mp_obj_t carray_real(mp_obj_t ); + +mp_obj_t carray_abs(ndarray_obj_t *, ndarray_obj_t *); +mp_obj_t carray_binary_add(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); +mp_obj_t carray_binary_multiply(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); +mp_obj_t carray_binary_subtract(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); +mp_obj_t carray_binary_divide(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *); +mp_obj_t carray_binary_equal_not_equal(ndarray_obj_t *, ndarray_obj_t *, uint8_t , size_t *, int32_t *, int32_t *, mp_binary_op_t ); + +#define BINARY_LOOP_COMPLEX1(results, resarray, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t l = 0;\ + do {\ + *(resarray) = *((mp_float_t *)(larray)) OPERATOR *((type_right *)(rarray));\ + (resarray) += 2;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#define BINARY_LOOP_COMPLEX2(results, resarray, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t k = 0;\ + do {\ + BINARY_LOOP_COMPLEX1((results), (resarray), type_right, (larray), (lstrides), (rarray), (rstrides), OPERATOR);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#define BINARY_LOOP_COMPLEX3(results, resarray, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t j = 0;\ + do {\ + BINARY_LOOP_COMPLEX2((results), (resarray), type_right, (larray), (lstrides), (rarray), (rstrides), OPERATOR);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#define BINARY_LOOP_COMPLEX4(results, resarray, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t i = 0;\ + do {\ + BINARY_LOOP_COMPLEX3((results), (resarray), type_right, (larray), (lstrides), (rarray), (rstrides), OPERATOR);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + +#define BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT1(results, resarray, type_left, larray, lstrides, rarray, rstrides)\ + size_t l = 0;\ + do {\ + *(resarray)++ = *((type_left *)(larray)) - (rarray)[0];\ + *(resarray)++ = -(rarray)[1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#define BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT2(results, resarray, type_left, larray, lstrides, rarray, rstrides)\ + size_t k = 0;\ + do {\ + BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT1((results), (resarray), type_left, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#define BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT3(results, resarray, type_left, larray, lstrides, rarray, rstrides)\ + size_t j = 0;\ + do {\ + BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT2((results), (resarray), type_left, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#define BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT4(results, resarray, type_left, larray, lstrides, rarray, rstrides)\ + size_t i = 0;\ + do {\ + BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT3((results), (resarray), type_left, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + +#define BINARY_LOOP_COMPLEX_RIGHT_DIVIDE1(results, resarray, type_left, larray, lstrides, rarray, rstrides)\ + size_t l = 0;\ + do {\ + mp_float_t *c = (mp_float_t *)(rarray);\ + mp_float_t denom = c[0] * c[0] + c[1] * c[1];\ + mp_float_t a = *((type_left *)(larray)) / denom;\ + *(resarray)++ = a * c[0];\ + *(resarray)++ = -a * c[1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#define BINARY_LOOP_COMPLEX_RIGHT_DIVIDE2(results, resarray, type_left, larray, lstrides, rarray, rstrides)\ + size_t k = 0;\ + do {\ + BINARY_LOOP_COMPLEX_RIGHT_DIVIDE1((results), (resarray), type_left, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#define BINARY_LOOP_COMPLEX_RIGHT_DIVIDE3(results, resarray, type_left, larray, lstrides, rarray, rstrides)\ + size_t j = 0;\ + do {\ + BINARY_LOOP_COMPLEX_RIGHT_DIVIDE2((results), (resarray), type_left, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#define BINARY_LOOP_COMPLEX_RIGHT_DIVIDE4(results, resarray, type_left, larray, lstrides, rarray, rstrides)\ + size_t i = 0;\ + do {\ + BINARY_LOOP_COMPLEX_RIGHT_DIVIDE3((results), (resarray), type_left, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + + +#define BINARY_LOOP_COMPLEX_EQUAL1(results, array, type_right, larray, lstrides, rarray, rstrides)\ + size_t l = 0;\ + do {\ + if((*(larray) == *((type_right *)(rarray))) && ((larray)[1] == MICROPY_FLOAT_CONST(0.0))) {\ + *(array) ^= 0x01;\ + }\ + (array)++;\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\ + +#define BINARY_LOOP_COMPLEX_EQUAL2(results, array, type_right, larray, lstrides, rarray, rstrides)\ + size_t k = 0;\ + do {\ + BINARY_LOOP_COMPLEX_EQUAL1((results), (array), type_right, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\ + +#define BINARY_LOOP_COMPLEX_EQUAL3(results, array, type_right, larray, lstrides, rarray, rstrides)\ + size_t j = 0;\ + do {\ + BINARY_LOOP_COMPLEX_EQUAL2((results), (array), type_right, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\ + +#define BINARY_LOOP_COMPLEX_EQUAL4(results, array, type_right, larray, lstrides, rarray, rstrides)\ + size_t i = 0;\ + do {\ + BINARY_LOOP_COMPLEX_EQUAL3((results), (array), type_right, (larray), (lstrides), (rarray), (rstrides));\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (results)->shape[ULAB_MAX_DIMS - 4]);\ + +#if ULAB_MAX_DIMS == 1 +#define BINARY_LOOP_COMPLEX BINARY_LOOP_COMPLEX1 +#define BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT1 +#define BINARY_LOOP_COMPLEX_RIGHT_DIVIDE BINARY_LOOP_COMPLEX_RIGHT_DIVIDE1 +#define BINARY_LOOP_COMPLEX_EQUAL BINARY_LOOP_COMPLEX_EQUAL1 +#endif /* ULAB_MAX_DIMS == 1 */ + +#if ULAB_MAX_DIMS == 2 +#define BINARY_LOOP_COMPLEX BINARY_LOOP_COMPLEX2 +#define BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT2 +#define BINARY_LOOP_COMPLEX_RIGHT_DIVIDE BINARY_LOOP_COMPLEX_RIGHT_DIVIDE2 +#define BINARY_LOOP_COMPLEX_EQUAL BINARY_LOOP_COMPLEX_EQUAL2 +#endif /* ULAB_MAX_DIMS == 2 */ + +#if ULAB_MAX_DIMS == 3 +#define BINARY_LOOP_COMPLEX BINARY_LOOP_COMPLEX3 +#define BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT3 +#define BINARY_LOOP_COMPLEX_RIGHT_DIVIDE BINARY_LOOP_COMPLEX_RIGHT_DIVIDE3 +#define BINARY_LOOP_COMPLEX_EQUAL BINARY_LOOP_COMPLEX_EQUAL3 +#endif /* ULAB_MAX_DIMS == 3 */ + +#if ULAB_MAX_DIMS == 4 +#define BINARY_LOOP_COMPLEX BINARY_LOOP_COMPLEX4 +#define BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT BINARY_LOOP_COMPLEX_REVERSED_SUBTRACT4 +#define BINARY_LOOP_COMPLEX_RIGHT_DIVIDE BINARY_LOOP_COMPLEX_RIGHT_DIVIDE4 +#define BINARY_LOOP_COMPLEX_EQUAL BINARY_LOOP_COMPLEX_EQUAL4 +#endif /* ULAB_MAX_DIMS == 4 */ + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/carray/carray_tools.c b/circuitpython/extmod/ulab/code/numpy/carray/carray_tools.c new file mode 100644 index 0000000..7b623d3 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/carray/carray_tools.c @@ -0,0 +1,28 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2022 Zoltán Vörös +*/ + +#include <math.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../../ulab.h" +#include "../../ndarray.h" + +#if ULAB_SUPPORTS_COMPLEX + +void raise_complex_NotImplementedError(void) { + mp_raise_NotImplementedError(translate("not implemented for complex dtype")); +} + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/carray/carray_tools.h b/circuitpython/extmod/ulab/code/numpy/carray/carray_tools.h new file mode 100644 index 0000000..3ac79b5 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/carray/carray_tools.h @@ -0,0 +1,25 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2022 Zoltán Vörös +*/ + +#ifndef _CARRAY_TOOLS_ +#define _CARRAY_TOOLS_ + +void raise_complex_NotImplementedError(void); + +#if ULAB_SUPPORTS_COMPLEX + #define NOT_IMPLEMENTED_FOR_COMPLEX() raise_complex_NotImplementedError(); + #define COMPLEX_DTYPE_NOT_IMPLEMENTED(dtype) if((dtype) == NDARRAY_COMPLEX) raise_complex_NotImplementedError(); +#else + #define NOT_IMPLEMENTED_FOR_COMPLEX() // do nothing + #define COMPLEX_DTYPE_NOT_IMPLEMENTED(dtype) // do nothing +#endif + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/compare.c b/circuitpython/extmod/ulab/code/numpy/compare.c new file mode 100644 index 0000000..5a82072 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/compare.c @@ -0,0 +1,428 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös + * 2020 Jeff Epler for Adafruit Industries +*/ + +#include <math.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../ulab.h" +#include "../ndarray_operators.h" +#include "../ulab_tools.h" +#include "carray/carray_tools.h" +#include "compare.h" + +static mp_obj_t compare_function(mp_obj_t x1, mp_obj_t x2, uint8_t op) { + ndarray_obj_t *lhs = ndarray_from_mp_obj(x1, 0); + ndarray_obj_t *rhs = ndarray_from_mp_obj(x2, 0); + #if ULAB_SUPPORTS_COMPLEX + if((lhs->dtype == NDARRAY_COMPLEX) || (rhs->dtype == NDARRAY_COMPLEX)) { + NOT_IMPLEMENTED_FOR_COMPLEX() + } + #endif + uint8_t ndim = 0; + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + int32_t *lstrides = m_new(int32_t, ULAB_MAX_DIMS); + int32_t *rstrides = m_new(int32_t, ULAB_MAX_DIMS); + if(!ndarray_can_broadcast(lhs, rhs, &ndim, shape, lstrides, rstrides)) { + mp_raise_ValueError(translate("operands could not be broadcast together")); + m_del(size_t, shape, ULAB_MAX_DIMS); + m_del(int32_t, lstrides, ULAB_MAX_DIMS); + m_del(int32_t, rstrides, ULAB_MAX_DIMS); + } + + uint8_t *larray = (uint8_t *)lhs->array; + uint8_t *rarray = (uint8_t *)rhs->array; + + if(op == COMPARE_EQUAL) { + return ndarray_binary_equality(lhs, rhs, ndim, shape, lstrides, rstrides, MP_BINARY_OP_EQUAL); + } else if(op == COMPARE_NOT_EQUAL) { + return ndarray_binary_equality(lhs, rhs, ndim, shape, lstrides, rstrides, MP_BINARY_OP_NOT_EQUAL); + } + // These are the upcasting rules + // float always becomes float + // operation on identical types preserves type + // uint8 + int8 => int16 + // uint8 + int16 => int16 + // uint8 + uint16 => uint16 + // int8 + int16 => int16 + // int8 + uint16 => uint16 + // uint16 + int16 => float + // The parameters of RUN_COMPARE_LOOP are + // typecode of result, type_out, type_left, type_right, lhs operand, rhs operand, operator + if(lhs->dtype == NDARRAY_UINT8) { + if(rhs->dtype == NDARRAY_UINT8) { + RUN_COMPARE_LOOP(NDARRAY_UINT8, uint8_t, uint8_t, uint8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT8) { + RUN_COMPARE_LOOP(NDARRAY_INT16, int16_t, uint8_t, int8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_UINT16) { + RUN_COMPARE_LOOP(NDARRAY_UINT16, uint16_t, uint8_t, uint16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT16) { + RUN_COMPARE_LOOP(NDARRAY_INT16, int16_t, uint8_t, int16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_FLOAT) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, uint8_t, mp_float_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } + } else if(lhs->dtype == NDARRAY_INT8) { + if(rhs->dtype == NDARRAY_UINT8) { + RUN_COMPARE_LOOP(NDARRAY_INT16, int16_t, int8_t, uint8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT8) { + RUN_COMPARE_LOOP(NDARRAY_INT8, int8_t, int8_t, int8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_UINT16) { + RUN_COMPARE_LOOP(NDARRAY_INT16, int16_t, int8_t, uint16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT16) { + RUN_COMPARE_LOOP(NDARRAY_INT16, int16_t, int8_t, int16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_FLOAT) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, int8_t, mp_float_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } + } else if(lhs->dtype == NDARRAY_UINT16) { + if(rhs->dtype == NDARRAY_UINT8) { + RUN_COMPARE_LOOP(NDARRAY_UINT16, uint16_t, uint16_t, uint8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT8) { + RUN_COMPARE_LOOP(NDARRAY_UINT16, uint16_t, uint16_t, int8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_UINT16) { + RUN_COMPARE_LOOP(NDARRAY_UINT16, uint16_t, uint16_t, uint16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT16) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, uint16_t, int16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_FLOAT) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, uint16_t, mp_float_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } + } else if(lhs->dtype == NDARRAY_INT16) { + if(rhs->dtype == NDARRAY_UINT8) { + RUN_COMPARE_LOOP(NDARRAY_INT16, int16_t, int16_t, uint8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT8) { + RUN_COMPARE_LOOP(NDARRAY_INT16, int16_t, int16_t, int8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_UINT16) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, int16_t, uint16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT16) { + RUN_COMPARE_LOOP(NDARRAY_INT16, int16_t, int16_t, int16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_FLOAT) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, int16_t, mp_float_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } + } else if(lhs->dtype == NDARRAY_FLOAT) { + if(rhs->dtype == NDARRAY_UINT8) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, mp_float_t, uint8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT8) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, mp_float_t, int8_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_UINT16) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, mp_float_t, uint16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_INT16) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, mp_float_t, int16_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } else if(rhs->dtype == NDARRAY_FLOAT) { + RUN_COMPARE_LOOP(NDARRAY_FLOAT, mp_float_t, mp_float_t, mp_float_t, larray, lstrides, rarray, rstrides, ndim, shape, op); + } + } + return mp_const_none; // we should never reach this point +} + +static mp_obj_t compare_equal_helper(mp_obj_t x1, mp_obj_t x2, uint8_t comptype) { + // scalar comparisons should return a single object of mp_obj_t type + mp_obj_t result = compare_function(x1, x2, comptype); + if((mp_obj_is_int(x1) || mp_obj_is_float(x1)) && (mp_obj_is_int(x2) || mp_obj_is_float(x2))) { + mp_obj_iter_buf_t iter_buf; + mp_obj_t iterable = mp_getiter(result, &iter_buf); + mp_obj_t item = mp_iternext(iterable); + return item; + } + return result; +} + +#if ULAB_NUMPY_HAS_CLIP + +mp_obj_t compare_clip(mp_obj_t x1, mp_obj_t x2, mp_obj_t x3) { + // Note: this function could be made faster by implementing a single-loop comparison in + // RUN_COMPARE_LOOP. However, that would add around 2 kB of compile size, while we + // would not gain a factor of two in speed, since the two comparisons should still be + // evaluated. In contrast, calling the function twice adds only 140 bytes to the firmware + if(mp_obj_is_int(x1) || mp_obj_is_float(x1)) { + mp_float_t v1 = mp_obj_get_float(x1); + mp_float_t v2 = mp_obj_get_float(x2); + mp_float_t v3 = mp_obj_get_float(x3); + if(v1 < v2) { + return x2; + } else if(v1 > v3) { + return x3; + } else { + return x1; + } + } else { // assume ndarrays + return compare_function(x2, compare_function(x1, x3, COMPARE_MINIMUM), COMPARE_MAXIMUM); + } +} + +MP_DEFINE_CONST_FUN_OBJ_3(compare_clip_obj, compare_clip); +#endif + +#if ULAB_NUMPY_HAS_EQUAL + +mp_obj_t compare_equal(mp_obj_t x1, mp_obj_t x2) { + return compare_equal_helper(x1, x2, COMPARE_EQUAL); +} + +MP_DEFINE_CONST_FUN_OBJ_2(compare_equal_obj, compare_equal); +#endif + +#if ULAB_NUMPY_HAS_NOTEQUAL + +mp_obj_t compare_not_equal(mp_obj_t x1, mp_obj_t x2) { + return compare_equal_helper(x1, x2, COMPARE_NOT_EQUAL); +} + +MP_DEFINE_CONST_FUN_OBJ_2(compare_not_equal_obj, compare_not_equal); +#endif + +#if ULAB_NUMPY_HAS_ISFINITE | ULAB_NUMPY_HAS_ISINF +static mp_obj_t compare_isinf_isfinite(mp_obj_t _x, uint8_t mask) { + // mask should signify, whether the function is called from isinf (mask = 1), + // or from isfinite (mask = 0) + if(mp_obj_is_int(_x)) { + if(mask) { + return mp_const_false; + } else { + return mp_const_true; + } + } else if(mp_obj_is_float(_x)) { + mp_float_t x = mp_obj_get_float(_x); + if(isnan(x)) { + return mp_const_false; + } + if(mask) { // called from isinf + return isinf(x) ? mp_const_true : mp_const_false; + } else { // called from isfinite + return isinf(x) ? mp_const_false : mp_const_true; + } + } else if(mp_obj_is_type(_x, &ulab_ndarray_type)) { + ndarray_obj_t *x = MP_OBJ_TO_PTR(_x); + COMPLEX_DTYPE_NOT_IMPLEMENTED(x->dtype) + ndarray_obj_t *results = ndarray_new_dense_ndarray(x->ndim, x->shape, NDARRAY_BOOL); + // At this point, results is all False + uint8_t *rarray = (uint8_t *)results->array; + if(x->dtype != NDARRAY_FLOAT) { + // int types can never be infinite... + if(!mask) { + // ...so flip all values in the array, if the function was called from isfinite + memset(rarray, 1, results->len); + } + return results; + } + uint8_t *xarray = (uint8_t *)x->array; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t value = *(mp_float_t *)xarray; + if(isnan(value)) { + *rarray++ = 0; + } else { + *rarray++ = isinf(value) ? mask : 1 - mask; + } + xarray += x->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < x->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + xarray -= x->strides[ULAB_MAX_DIMS - 1] * x->shape[ULAB_MAX_DIMS-1]; + xarray += x->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < x->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + xarray -= x->strides[ULAB_MAX_DIMS - 2] * x->shape[ULAB_MAX_DIMS-2]; + xarray += x->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < x->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + xarray -= x->strides[ULAB_MAX_DIMS - 3] * x->shape[ULAB_MAX_DIMS-3]; + xarray += x->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < x->shape[ULAB_MAX_DIMS - 4]); + #endif + + return results; + } else { + mp_raise_TypeError(translate("wrong input type")); + } + return mp_const_none; +} +#endif + +#if ULAB_NUMPY_HAS_ISFINITE +mp_obj_t compare_isfinite(mp_obj_t _x) { + return compare_isinf_isfinite(_x, 0); +} + +MP_DEFINE_CONST_FUN_OBJ_1(compare_isfinite_obj, compare_isfinite); +#endif + +#if ULAB_NUMPY_HAS_ISINF +mp_obj_t compare_isinf(mp_obj_t _x) { + return compare_isinf_isfinite(_x, 1); +} + +MP_DEFINE_CONST_FUN_OBJ_1(compare_isinf_obj, compare_isinf); +#endif + +#if ULAB_NUMPY_HAS_MAXIMUM +mp_obj_t compare_maximum(mp_obj_t x1, mp_obj_t x2) { + // extra round, so that we can return maximum(3, 4) properly + mp_obj_t result = compare_function(x1, x2, COMPARE_MAXIMUM); + if((mp_obj_is_int(x1) || mp_obj_is_float(x1)) && (mp_obj_is_int(x2) || mp_obj_is_float(x2))) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(result); + return mp_binary_get_val_array(ndarray->dtype, ndarray->array, 0); + } + return result; +} + +MP_DEFINE_CONST_FUN_OBJ_2(compare_maximum_obj, compare_maximum); +#endif + +#if ULAB_NUMPY_HAS_MINIMUM + +mp_obj_t compare_minimum(mp_obj_t x1, mp_obj_t x2) { + // extra round, so that we can return minimum(3, 4) properly + mp_obj_t result = compare_function(x1, x2, COMPARE_MINIMUM); + if((mp_obj_is_int(x1) || mp_obj_is_float(x1)) && (mp_obj_is_int(x2) || mp_obj_is_float(x2))) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(result); + return mp_binary_get_val_array(ndarray->dtype, ndarray->array, 0); + } + return result; +} + +MP_DEFINE_CONST_FUN_OBJ_2(compare_minimum_obj, compare_minimum); +#endif + +#if ULAB_NUMPY_HAS_WHERE + +mp_obj_t compare_where(mp_obj_t _condition, mp_obj_t _x, mp_obj_t _y) { + // this implementation will work with ndarrays, and scalars only + ndarray_obj_t *c = ndarray_from_mp_obj(_condition, 0); + ndarray_obj_t *x = ndarray_from_mp_obj(_x, 0); + ndarray_obj_t *y = ndarray_from_mp_obj(_y, 0); + + COMPLEX_DTYPE_NOT_IMPLEMENTED(c->dtype) + COMPLEX_DTYPE_NOT_IMPLEMENTED(x->dtype) + COMPLEX_DTYPE_NOT_IMPLEMENTED(y->dtype) + + int32_t *cstrides = m_new(int32_t, ULAB_MAX_DIMS); + int32_t *xstrides = m_new(int32_t, ULAB_MAX_DIMS); + int32_t *ystrides = m_new(int32_t, ULAB_MAX_DIMS); + + size_t *oshape = m_new(size_t, ULAB_MAX_DIMS); + + uint8_t ndim; + + // establish the broadcasting conditions first + // if any two of the arrays can be broadcast together, then + // the three arrays can also be broadcast together + if(!ndarray_can_broadcast(c, x, &ndim, oshape, cstrides, ystrides) || + !ndarray_can_broadcast(c, y, &ndim, oshape, cstrides, ystrides) || + !ndarray_can_broadcast(x, y, &ndim, oshape, xstrides, ystrides)) { + mp_raise_ValueError(translate("operands could not be broadcast together")); + } + + ndim = MAX(MAX(c->ndim, x->ndim), y->ndim); + + for(uint8_t i = 1; i <= ndim; i++) { + cstrides[ULAB_MAX_DIMS - i] = c->shape[ULAB_MAX_DIMS - i] < 2 ? 0 : c->strides[ULAB_MAX_DIMS - i]; + xstrides[ULAB_MAX_DIMS - i] = x->shape[ULAB_MAX_DIMS - i] < 2 ? 0 : x->strides[ULAB_MAX_DIMS - i]; + ystrides[ULAB_MAX_DIMS - i] = y->shape[ULAB_MAX_DIMS - i] < 2 ? 0 : y->strides[ULAB_MAX_DIMS - i]; + oshape[ULAB_MAX_DIMS - i] = MAX(MAX(c->shape[ULAB_MAX_DIMS - i], x->shape[ULAB_MAX_DIMS - i]), y->shape[ULAB_MAX_DIMS - i]); + } + + uint8_t out_dtype = ndarray_upcast_dtype(x->dtype, y->dtype); + ndarray_obj_t *out = ndarray_new_dense_ndarray(ndim, oshape, out_dtype); + + mp_float_t (*cfunc)(void *) = ndarray_get_float_function(c->dtype); + mp_float_t (*xfunc)(void *) = ndarray_get_float_function(x->dtype); + mp_float_t (*yfunc)(void *) = ndarray_get_float_function(y->dtype); + mp_float_t (*ofunc)(void *, mp_float_t ) = ndarray_set_float_function(out->dtype); + + uint8_t *oarray = (uint8_t *)out->array; + uint8_t *carray = (uint8_t *)c->array; + uint8_t *xarray = (uint8_t *)x->array; + uint8_t *yarray = (uint8_t *)y->array; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t value; + mp_float_t cvalue = cfunc(carray); + if(cvalue != MICROPY_FLOAT_CONST(0.0)) { + value = xfunc(xarray); + } else { + value = yfunc(yarray); + } + ofunc(oarray, value); + oarray += out->itemsize; + carray += cstrides[ULAB_MAX_DIMS - 1]; + xarray += xstrides[ULAB_MAX_DIMS - 1]; + yarray += ystrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < out->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + carray -= cstrides[ULAB_MAX_DIMS - 1] * c->shape[ULAB_MAX_DIMS-1]; + carray += cstrides[ULAB_MAX_DIMS - 2]; + xarray -= xstrides[ULAB_MAX_DIMS - 1] * x->shape[ULAB_MAX_DIMS-1]; + xarray += xstrides[ULAB_MAX_DIMS - 2]; + yarray -= ystrides[ULAB_MAX_DIMS - 1] * y->shape[ULAB_MAX_DIMS-1]; + yarray += ystrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < out->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + carray -= cstrides[ULAB_MAX_DIMS - 2] * c->shape[ULAB_MAX_DIMS-2]; + carray += cstrides[ULAB_MAX_DIMS - 3]; + xarray -= xstrides[ULAB_MAX_DIMS - 2] * x->shape[ULAB_MAX_DIMS-2]; + xarray += xstrides[ULAB_MAX_DIMS - 3]; + yarray -= ystrides[ULAB_MAX_DIMS - 2] * y->shape[ULAB_MAX_DIMS-2]; + yarray += ystrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < out->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + carray -= cstrides[ULAB_MAX_DIMS - 3] * c->shape[ULAB_MAX_DIMS-3]; + carray += cstrides[ULAB_MAX_DIMS - 4]; + xarray -= xstrides[ULAB_MAX_DIMS - 3] * x->shape[ULAB_MAX_DIMS-3]; + xarray += xstrides[ULAB_MAX_DIMS - 4]; + yarray -= ystrides[ULAB_MAX_DIMS - 3] * y->shape[ULAB_MAX_DIMS-3]; + yarray += ystrides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < out->shape[ULAB_MAX_DIMS - 4]); + #endif + return MP_OBJ_FROM_PTR(out); +} + +MP_DEFINE_CONST_FUN_OBJ_3(compare_where_obj, compare_where); +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/compare.h b/circuitpython/extmod/ulab/code/numpy/compare.h new file mode 100644 index 0000000..90ceaf7 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/compare.h @@ -0,0 +1,150 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös +*/ + +#ifndef _COMPARE_ +#define _COMPARE_ + +#include "../ulab.h" +#include "../ndarray.h" + +enum COMPARE_FUNCTION_TYPE { + COMPARE_EQUAL, + COMPARE_NOT_EQUAL, + COMPARE_MINIMUM, + COMPARE_MAXIMUM, + COMPARE_CLIP, +}; + +MP_DECLARE_CONST_FUN_OBJ_3(compare_clip_obj); +MP_DECLARE_CONST_FUN_OBJ_2(compare_equal_obj); +MP_DECLARE_CONST_FUN_OBJ_2(compare_isfinite_obj); +MP_DECLARE_CONST_FUN_OBJ_2(compare_isinf_obj); +MP_DECLARE_CONST_FUN_OBJ_2(compare_minimum_obj); +MP_DECLARE_CONST_FUN_OBJ_2(compare_maximum_obj); +MP_DECLARE_CONST_FUN_OBJ_2(compare_not_equal_obj); +MP_DECLARE_CONST_FUN_OBJ_3(compare_where_obj); + +#if ULAB_MAX_DIMS == 1 +#define COMPARE_LOOP(results, array, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t l = 0;\ + do {\ + *((type_out *)(array)) = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? (type_out)(*((type_left *)(larray))) : (type_out)(*((type_right *)(rarray)));\ + (array) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < results->shape[ULAB_MAX_DIMS - 1]);\ + return MP_OBJ_FROM_PTR(results);\ + +#endif // ULAB_MAX_DIMS == 1 + +#if ULAB_MAX_DIMS == 2 +#define COMPARE_LOOP(results, array, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_out *)(array)) = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? (type_out)(*((type_left *)(larray))) : (type_out)(*((type_right *)(rarray)));\ + (array) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < results->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < results->shape[ULAB_MAX_DIMS - 2]);\ + return MP_OBJ_FROM_PTR(results);\ + +#endif // ULAB_MAX_DIMS == 2 + +#if ULAB_MAX_DIMS == 3 +#define COMPARE_LOOP(results, array, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_out *)(array)) = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? (type_out)(*((type_left *)(larray))) : (type_out)(*((type_right *)(rarray)));\ + (array) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < results->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < results->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < results->shape[ULAB_MAX_DIMS - 3]);\ + return MP_OBJ_FROM_PTR(results);\ + +#endif // ULAB_MAX_DIMS == 3 + +#if ULAB_MAX_DIMS == 4 +#define COMPARE_LOOP(results, array, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\ + size_t i = 0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *((type_out *)(array)) = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)) ? (type_out)(*((type_left *)(larray))) : (type_out)(*((type_right *)(rarray)));\ + (array) += (results)->strides[ULAB_MAX_DIMS - 1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < results->shape[ULAB_MAX_DIMS - 1]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < results->shape[ULAB_MAX_DIMS - 2]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < results->shape[ULAB_MAX_DIMS - 3]);\ + (larray) -= (lstrides)[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3];\ + (larray) += (lstrides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3];\ + (rarray) += (rstrides)[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < results->shape[ULAB_MAX_DIMS - 4]);\ + return MP_OBJ_FROM_PTR(results);\ + +#endif // ULAB_MAX_DIMS == 4 + +#define RUN_COMPARE_LOOP(dtype, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, ndim, shape, op) do {\ + ndarray_obj_t *results = ndarray_new_dense_ndarray((ndim), (shape), (dtype));\ + uint8_t *array = (uint8_t *)results->array;\ + if((op) == COMPARE_MINIMUM) {\ + COMPARE_LOOP(results, array, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, <);\ + }\ + if((op) == COMPARE_MAXIMUM) {\ + COMPARE_LOOP(results, array, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, >);\ + }\ +} while(0) + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/create.c b/circuitpython/extmod/ulab/code/numpy/create.c new file mode 100644 index 0000000..5777070 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/create.c @@ -0,0 +1,783 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2019-2021 Zoltán Vörös + * 2020 Taku Fukada +*/ + +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" + +#include "../ulab.h" +#include "create.h" +#include "../ulab_tools.h" + +#if ULAB_NUMPY_HAS_ONES | ULAB_NUMPY_HAS_ZEROS | ULAB_NUMPY_HAS_FULL | ULAB_NUMPY_HAS_EMPTY +static mp_obj_t create_zeros_ones_full(mp_obj_t oshape, uint8_t dtype, mp_obj_t value) { + if(!mp_obj_is_int(oshape) && !mp_obj_is_type(oshape, &mp_type_tuple) && !mp_obj_is_type(oshape, &mp_type_list)) { + mp_raise_TypeError(translate("input argument must be an integer, a tuple, or a list")); + } + ndarray_obj_t *ndarray = NULL; + if(mp_obj_is_int(oshape)) { + size_t n = mp_obj_get_int(oshape); + ndarray = ndarray_new_linear_array(n, dtype); + } else if(mp_obj_is_type(oshape, &mp_type_tuple) || mp_obj_is_type(oshape, &mp_type_list)) { + uint8_t len = (uint8_t)mp_obj_get_int(mp_obj_len_maybe(oshape)); + if(len > ULAB_MAX_DIMS) { + mp_raise_TypeError(translate("too many dimensions")); + } + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, ULAB_MAX_DIMS * sizeof(size_t)); + size_t i = 0; + mp_obj_iter_buf_t iter_buf; + mp_obj_t item, iterable = mp_getiter(oshape, &iter_buf); + while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION){ + shape[ULAB_MAX_DIMS - len + i] = (size_t)mp_obj_get_int(item); + i++; + } + ndarray = ndarray_new_dense_ndarray(len, shape, dtype); + } + if(value != mp_const_none) { + if(dtype == NDARRAY_BOOL) { + dtype = NDARRAY_UINT8; + if(mp_obj_is_true(value)) { + value = mp_obj_new_int(1); + } else { + value = mp_obj_new_int(0); + } + } + for(size_t i=0; i < ndarray->len; i++) { + #if ULAB_SUPPORTS_COMPLEX + if(dtype == NDARRAY_COMPLEX) { + ndarray_set_complex_value(ndarray->array, i, value); + } else { + ndarray_set_value(dtype, ndarray->array, i, value); + } + #else + ndarray_set_value(dtype, ndarray->array, i, value); + #endif + } + } + // if zeros calls the function, we don't have to do anything + return MP_OBJ_FROM_PTR(ndarray); +} +#endif + +#if ULAB_NUMPY_HAS_ARANGE | ULAB_NUMPY_HAS_LINSPACE +static ndarray_obj_t *create_linspace_arange(mp_float_t start, mp_float_t step, mp_float_t stop, size_t len, uint8_t dtype) { + mp_float_t value = start; + + ndarray_obj_t *ndarray = ndarray_new_linear_array(len, dtype); + if(ndarray->boolean == NDARRAY_BOOLEAN) { + uint8_t *array = (uint8_t *)ndarray->array; + for(size_t i=0; i < len; i++, value += step) { + *array++ = value == MICROPY_FLOAT_CONST(0.0) ? 0 : 1; + } + } else if(dtype == NDARRAY_UINT8) { + ARANGE_LOOP(uint8_t, ndarray, len, step, stop); + } else if(dtype == NDARRAY_INT8) { + ARANGE_LOOP(int8_t, ndarray, len, step, stop); + } else if(dtype == NDARRAY_UINT16) { + ARANGE_LOOP(uint16_t, ndarray, len, step, stop); + } else if(dtype == NDARRAY_INT16) { + ARANGE_LOOP(int16_t, ndarray, len, step, stop); + } else { + ARANGE_LOOP(mp_float_t, ndarray, len, step, stop); + } + return ndarray; +} +#endif + +#if ULAB_NUMPY_HAS_ARANGE +//| @overload +//| def arange(stop: _float, step: _float = 1, *, dtype: _DType = ulab.numpy.float) -> ulab.numpy.ndarray: ... +//| @overload +//| def arange(start: _float, stop: _float, step: _float = 1, *, dtype: _DType = ulab.numpy.float) -> ulab.numpy.ndarray: +//| """ +//| .. param: start +//| First value in the array, optional, defaults to 0 +//| .. param: stop +//| Final value in the array +//| .. param: step +//| Difference between consecutive elements, optional, defaults to 1.0 +//| .. param: dtype +//| Type of values in the array +//| +//| Return a new 1-D array with elements ranging from ``start`` to ``stop``, with step size ``step``.""" +//| ... +//| + +mp_obj_t create_arange(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + uint8_t dtype = NDARRAY_FLOAT; + mp_float_t start, stop, step; + if(n_args == 1) { + start = MICROPY_FLOAT_CONST(0.0); + stop = mp_obj_get_float(args[0].u_obj); + step = MICROPY_FLOAT_CONST(1.0); + if(mp_obj_is_int(args[0].u_obj)) dtype = NDARRAY_INT16; + } else if(n_args == 2) { + start = mp_obj_get_float(args[0].u_obj); + stop = mp_obj_get_float(args[1].u_obj); + step = MICROPY_FLOAT_CONST(1.0); + if(mp_obj_is_int(args[0].u_obj) && mp_obj_is_int(args[1].u_obj)) dtype = NDARRAY_INT16; + } else if(n_args == 3) { + start = mp_obj_get_float(args[0].u_obj); + stop = mp_obj_get_float(args[1].u_obj); + step = mp_obj_get_float(args[2].u_obj); + if(mp_obj_is_int(args[0].u_obj) && mp_obj_is_int(args[1].u_obj) && mp_obj_is_int(args[2].u_obj)) dtype = NDARRAY_INT16; + } else { + mp_raise_TypeError(translate("wrong number of arguments")); + } + if((MICROPY_FLOAT_C_FUN(fabs)(stop) > 32768) || (MICROPY_FLOAT_C_FUN(fabs)(start) > 32768) || (MICROPY_FLOAT_C_FUN(fabs)(step) > 32768)) { + dtype = NDARRAY_FLOAT; + } + if(args[3].u_obj != mp_const_none) { + dtype = (uint8_t)mp_obj_get_int(args[3].u_obj); + } + ndarray_obj_t *ndarray; + if((stop - start)/step < 0) { + ndarray = ndarray_new_linear_array(0, dtype); + } else { + size_t len = (size_t)(MICROPY_FLOAT_C_FUN(ceil)((stop - start) / step)); + stop = start + (len - 1) * step; + ndarray = create_linspace_arange(start, step, stop, len, dtype); + } + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_arange_obj, 1, create_arange); +#endif + +#if ULAB_NUMPY_HAS_CONCATENATE +//| def concatenate(arrays: Tuple[ulab.numpy.ndarray], *, axis: int = 0) -> ulab.numpy.ndarray: +//| """ +//| .. param: arrays +//| tuple of ndarrays +//| .. param: axis +//| axis along which the arrays will be joined +//| +//| Join a sequence of arrays along an existing axis.""" +//| ... +//| + +mp_obj_t create_concatenate(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = 0 } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(!mp_obj_is_type(args[0].u_obj, &mp_type_tuple)) { + mp_raise_TypeError(translate("first argument must be a tuple of ndarrays")); + } + int8_t axis = (int8_t)args[1].u_int; + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + mp_obj_tuple_t *ndarrays = MP_OBJ_TO_PTR(args[0].u_obj); + + // first check, whether the arrays are compatible + ndarray_obj_t *_ndarray = MP_OBJ_TO_PTR(ndarrays->items[0]); + uint8_t dtype = _ndarray->dtype; + uint8_t ndim = _ndarray->ndim; + if(axis < 0) { + axis += ndim; + } + if((axis < 0) || (axis >= ndim)) { + mp_raise_ValueError(translate("wrong axis specified")); + } + // shift axis + axis = ULAB_MAX_DIMS - ndim + axis; + for(uint8_t j=0; j < ULAB_MAX_DIMS; j++) { + shape[j] = _ndarray->shape[j]; + } + + for(uint8_t i=1; i < ndarrays->len; i++) { + _ndarray = MP_OBJ_TO_PTR(ndarrays->items[i]); + // check, whether the arrays are compatible + if((dtype != _ndarray->dtype) || (ndim != _ndarray->ndim)) { + mp_raise_ValueError(translate("input arrays are not compatible")); + } + for(uint8_t j=0; j < ULAB_MAX_DIMS; j++) { + if(j == axis) { + shape[j] += _ndarray->shape[j]; + } else { + if(shape[j] != _ndarray->shape[j]) { + mp_raise_ValueError(translate("input arrays are not compatible")); + } + } + } + } + + ndarray_obj_t *target = ndarray_new_dense_ndarray(ndim, shape, dtype); + uint8_t *tpos = (uint8_t *)target->array; + uint8_t *tarray; + + for(uint8_t p=0; p < ndarrays->len; p++) { + // reset the pointer along the axis + ndarray_obj_t *source = MP_OBJ_TO_PTR(ndarrays->items[p]); + uint8_t *sarray = (uint8_t *)source->array; + tarray = tpos; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + memcpy(tarray, sarray, source->itemsize); + tarray += target->strides[ULAB_MAX_DIMS - 1]; + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + tarray -= target->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + tarray += target->strides[ULAB_MAX_DIMS - 2]; + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + tarray -= target->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + tarray += target->strides[ULAB_MAX_DIMS - 3]; + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + tarray -= target->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + tarray += target->strides[ULAB_MAX_DIMS - 4]; + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif + if(p < ndarrays->len - 1) { + tpos += target->strides[axis] * source->shape[axis]; + } + } + return MP_OBJ_FROM_PTR(target); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_concatenate_obj, 1, create_concatenate); +#endif + +#if ULAB_MAX_DIMS > 1 +#if ULAB_NUMPY_HAS_DIAG +//| def diag(a: ulab.numpy.ndarray, *, k: int = 0) -> ulab.numpy.ndarray: +//| """ +//| .. param: a +//| an ndarray +//| .. param: k +//| Offset of the diagonal from the main diagonal. Can be positive or negative. +//| +//| Return specified diagonals.""" +//| ... +//| + +mp_obj_t create_diag(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_k, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = 0 } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("input must be an ndarray")); + } + ndarray_obj_t *source = MP_OBJ_TO_PTR(args[0].u_obj); + if(source->ndim == 1) { // return a rank-2 tensor with the prescribed diagonal + ndarray_obj_t *target = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, source->len, source->len), source->dtype); + uint8_t *sarray = (uint8_t *)source->array; + uint8_t *tarray = (uint8_t *)target->array; + for(size_t i=0; i < source->len; i++) { + memcpy(tarray, sarray, source->itemsize); + sarray += source->strides[ULAB_MAX_DIMS - 1]; + tarray += (source->len + 1) * target->itemsize; + } + return MP_OBJ_FROM_PTR(target); + } + if(source->ndim > 2) { + mp_raise_TypeError(translate("input must be a tensor of rank 2")); + } + int32_t k = args[1].u_int; + size_t len = 0; + uint8_t *sarray = (uint8_t *)source->array; + if(k < 0) { // move the pointer "vertically" + if(-k < (int32_t)source->shape[ULAB_MAX_DIMS - 2]) { + sarray -= k * source->strides[ULAB_MAX_DIMS - 2]; + len = MIN(source->shape[ULAB_MAX_DIMS - 2] + k, source->shape[ULAB_MAX_DIMS - 1]); + } + } else { // move the pointer "horizontally" + if(k < (int32_t)source->shape[ULAB_MAX_DIMS - 1]) { + sarray += k * source->strides[ULAB_MAX_DIMS - 1]; + len = MIN(source->shape[ULAB_MAX_DIMS - 1] - k, source->shape[ULAB_MAX_DIMS - 2]); + } + } + + if(len == 0) { + mp_raise_ValueError(translate("offset is too large")); + } + + ndarray_obj_t *target = ndarray_new_linear_array(len, source->dtype); + uint8_t *tarray = (uint8_t *)target->array; + + for(size_t i=0; i < len; i++) { + memcpy(tarray, sarray, source->itemsize); + sarray += source->strides[ULAB_MAX_DIMS - 2]; + sarray += source->strides[ULAB_MAX_DIMS - 1]; + tarray += source->itemsize; + } + return MP_OBJ_FROM_PTR(target); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_diag_obj, 1, create_diag); +#endif /* ULAB_NUMPY_HAS_DIAG */ + +#if ULAB_NUMPY_HAS_EMPTY +// This function is bound in numpy.c to numpy.zeros(), and is simply an alias for that + +//| def empty(shape: Union[int, Tuple[int, ...]], *, dtype: _DType = ulab.numpy.float) -> ulab.numpy.ndarray: +//| """ +//| .. param: shape +//| Shape of the array, either an integer (for a 1-D array) or a tuple of 2 integers (for a 2-D array) +//| .. param: dtype +//| Type of values in the array +//| +//| Return a new array of the given shape with all elements set to 0. An alias for numpy.zeros.""" +//| ... +//| +#endif + +#if ULAB_NUMPY_HAS_EYE +//| def eye(size: int, *, M: Optional[int] = None, k: int = 0, dtype: _DType = ulab.numpy.float) -> ulab.numpy.ndarray: +//| """Return a new square array of size, with the diagonal elements set to 1 +//| and the other elements set to 0. If k is given, the diagonal is shifted by the specified amount.""" +//| ... +//| + +mp_obj_t create_eye(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_INT, { .u_int = 0 } }, + { MP_QSTR_M, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_k, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = 0 } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = NDARRAY_FLOAT } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + size_t n = args[0].u_int, m; + size_t k = args[2].u_int > 0 ? (size_t)args[2].u_int : (size_t)(-args[2].u_int); + uint8_t dtype = args[3].u_int; + if(args[1].u_rom_obj == mp_const_none) { + m = n; + } else { + m = mp_obj_get_int(args[1].u_rom_obj); + } + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, n, m), dtype); + if(dtype == NDARRAY_BOOL) { + dtype = NDARRAY_UINT8; + } + mp_obj_t one = mp_obj_new_int(1); + size_t i = 0; + if((args[2].u_int >= 0)) { + while(k < m) { + ndarray_set_value(dtype, ndarray->array, i*m+k, one); + k++; + i++; + } + } else { + while(k < n) { + ndarray_set_value(dtype, ndarray->array, k*m+i, one); + k++; + i++; + } + } + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_eye_obj, 1, create_eye); +#endif /* ULAB_NUMPY_HAS_EYE */ +#endif /* ULAB_MAX_DIMS > 1 */ + +#if ULAB_NUMPY_HAS_FULL +//| def full(shape: Union[int, Tuple[int, ...]], fill_value: Union[_float, _bool], *, dtype: _DType = ulab.numpy.float) -> ulab.numpy.ndarray: +//| """ +//| .. param: shape +//| Shape of the array, either an integer (for a 1-D array) or a tuple of integers (for tensors of higher rank) +//| .. param: fill_value +//| scalar, the value with which the array is filled +//| .. param: dtype +//| Type of values in the array +//| +//| Return a new array of the given shape with all elements set to 0.""" +//| ... +//| + +mp_obj_t create_full(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_obj = MP_OBJ_NULL } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_obj = MP_OBJ_NULL } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = NDARRAY_FLOAT } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + uint8_t dtype = args[2].u_int; + + return create_zeros_ones_full(args[0].u_obj, dtype, args[1].u_obj); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_full_obj, 0, create_full); +#endif + + +#if ULAB_NUMPY_HAS_LINSPACE +//| def linspace( +//| start: _float, +//| stop: _float, +//| *, +//| dtype: _DType = ulab.numpy.float, +//| num: int = 50, +//| endpoint: _bool = True, +//| retstep: _bool = False +//| ) -> ulab.numpy.ndarray: +//| """ +//| .. param: start +//| First value in the array +//| .. param: stop +//| Final value in the array +//| .. param int: num +//| Count of values in the array. +//| .. param: dtype +//| Type of values in the array +//| .. param bool: endpoint +//| Whether the ``stop`` value is included. Note that even when +//| endpoint=True, the exact ``stop`` value may not be included due to the +//| inaccuracy of floating point arithmetic. +//| .. param bool: retstep, +//| If True, return (`samples`, `step`), where `step` is the spacing between samples. +//| +//| Return a new 1-D array with ``num`` elements ranging from ``start`` to ``stop`` linearly.""" +//| ... +//| + +mp_obj_t create_linspace(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_num, MP_ARG_INT, { .u_int = 50 } }, + { MP_QSTR_endpoint, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_true } }, + { MP_QSTR_retstep, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_false } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = NDARRAY_FLOAT } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(args[2].u_int < 2) { + mp_raise_ValueError(translate("number of points must be at least 2")); + } + size_t len = (size_t)args[2].u_int; + mp_float_t start, step, stop; + + ndarray_obj_t *ndarray = NULL; + + #if ULAB_SUPPORTS_COMPLEX + mp_float_t step_real, step_imag; + bool complex_out = false; + + if(mp_obj_is_type(args[0].u_obj, &mp_type_complex) || mp_obj_is_type(args[1].u_obj, &mp_type_complex)) { + complex_out = true; + ndarray = ndarray_new_linear_array(len, NDARRAY_COMPLEX); + mp_float_t *array = (mp_float_t *)ndarray->array; + mp_float_t start_real, start_imag; + mp_float_t stop_real, stop_imag; + + mp_obj_get_complex(args[0].u_obj, &start_real, &start_imag); + mp_obj_get_complex(args[1].u_obj, &stop_real, &stop_imag); + if(args[3].u_obj == mp_const_true) { + step_real = (stop_real - start_real) / (len - 1); + step_imag = (stop_imag - start_imag) / (len - 1); + } else { + step_real = (stop_real - start_real) / len; + step_imag = (stop_imag - start_imag) / len; + } + + for(size_t i = 0; i < len; i++) { + *array++ = start_real; + *array++ = start_imag; + start_real += step_real; + start_imag += step_imag; + } + } else { + #endif + start = mp_obj_get_float(args[0].u_obj); + stop = mp_obj_get_float(args[1].u_obj); + + uint8_t typecode = args[5].u_int; + + if(args[3].u_obj == mp_const_true) { + step = (stop - start) / (len - 1); + } else { + step = (stop - start) / len; + stop = start + step * (len - 1); + } + + ndarray = create_linspace_arange(start, step, stop, len, typecode); + #if ULAB_SUPPORTS_COMPLEX + } + #endif + + if(args[4].u_obj == mp_const_false) { + return MP_OBJ_FROM_PTR(ndarray); + } else { + mp_obj_t tuple[2]; + tuple[0] = ndarray; + #if ULAB_SUPPORTS_COMPLEX + if(complex_out) { + tuple[1] = mp_obj_new_complex(step_real, step_imag); + } else { + tuple[1] = mp_obj_new_float(step); + } + #else /* ULAB_SUPPORTS_COMPLEX */ + tuple[1] = mp_obj_new_float(step); + #endif + + return mp_obj_new_tuple(2, tuple); + } +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_linspace_obj, 2, create_linspace); +#endif + +#if ULAB_NUMPY_HAS_LOGSPACE +//| def logspace( +//| start: _float, +//| stop: _float, +//| *, +//| dtype: _DType = ulab.numpy.float, +//| num: int = 50, +//| endpoint: _bool = True, +//| base: _float = 10.0 +//| ) -> ulab.numpy.ndarray: +//| """ +//| .. param: start +//| First value in the array +//| .. param: stop +//| Final value in the array +//| .. param int: num +//| Count of values in the array. Defaults to 50. +//| .. param: base +//| The base of the log space. The step size between the elements in +//| ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform. Defaults to 10.0. +//| .. param: dtype +//| Type of values in the array +//| .. param bool: endpoint +//| Whether the ``stop`` value is included. Note that even when +//| endpoint=True, the exact ``stop`` value may not be included due to the +//| inaccuracy of floating point arithmetic. Defaults to True. +//| +//| Return a new 1-D array with ``num`` evenly spaced elements on a log scale. +//| The sequence starts at ``base ** start``, and ends with ``base ** stop``.""" +//| ... +//| + +const mp_obj_float_t create_float_const_ten = {{&mp_type_float}, MICROPY_FLOAT_CONST(10.0)}; + +mp_obj_t create_logspace(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_num, MP_ARG_INT, { .u_int = 50 } }, + { MP_QSTR_base, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_PTR(&create_float_const_ten) } }, + { MP_QSTR_endpoint, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_true } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = NDARRAY_FLOAT } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(args[2].u_int < 2) { + mp_raise_ValueError(translate("number of points must be at least 2")); + } + size_t len = (size_t)args[2].u_int; + mp_float_t start, step, quotient; + start = mp_obj_get_float(args[0].u_obj); + uint8_t dtype = args[5].u_int; + mp_float_t base = mp_obj_get_float(args[3].u_obj); + if(args[4].u_obj == mp_const_true) step = (mp_obj_get_float(args[1].u_obj) - start)/(len - 1); + else step = (mp_obj_get_float(args[1].u_obj) - start) / len; + quotient = MICROPY_FLOAT_C_FUN(pow)(base, step); + ndarray_obj_t *ndarray = ndarray_new_linear_array(len, dtype); + + mp_float_t value = MICROPY_FLOAT_C_FUN(pow)(base, start); + if(ndarray->dtype == NDARRAY_UINT8) { + uint8_t *array = (uint8_t *)ndarray->array; + if(ndarray->boolean) { + memset(array, 1, len); + } else { + for(size_t i=0; i < len; i++, value *= quotient) *array++ = (uint8_t)value; + } + } else if(ndarray->dtype == NDARRAY_INT8) { + int8_t *array = (int8_t *)ndarray->array; + for(size_t i=0; i < len; i++, value *= quotient) *array++ = (int8_t)value; + } else if(ndarray->dtype == NDARRAY_UINT16) { + uint16_t *array = (uint16_t *)ndarray->array; + for(size_t i=0; i < len; i++, value *= quotient) *array++ = (uint16_t)value; + } else if(ndarray->dtype == NDARRAY_INT16) { + int16_t *array = (int16_t *)ndarray->array; + for(size_t i=0; i < len; i++, value *= quotient) *array++ = (int16_t)value; + } else { + mp_float_t *array = (mp_float_t *)ndarray->array; + for(size_t i=0; i < len; i++, value *= quotient) *array++ = value; + } + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_logspace_obj, 2, create_logspace); +#endif + +#if ULAB_NUMPY_HAS_ONES +//| def ones(shape: Union[int, Tuple[int, ...]], *, dtype: _DType = ulab.numpy.float) -> ulab.numpy.ndarray: +//| """ +//| .. param: shape +//| Shape of the array, either an integer (for a 1-D array) or a tuple of 2 integers (for a 2-D array) +//| .. param: dtype +//| Type of values in the array +//| +//| Return a new array of the given shape with all elements set to 1.""" +//| ... +//| + +mp_obj_t create_ones(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_obj = MP_OBJ_NULL } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = NDARRAY_FLOAT } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + uint8_t dtype = args[1].u_int; + mp_obj_t one = mp_obj_new_int(1); + return create_zeros_ones_full(args[0].u_obj, dtype, one); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_ones_obj, 0, create_ones); +#endif + +#if ULAB_NUMPY_HAS_ZEROS +//| def zeros(shape: Union[int, Tuple[int, ...]], *, dtype: _DType = ulab.numpy.float) -> ulab.numpy.ndarray: +//| """ +//| .. param: shape +//| Shape of the array, either an integer (for a 1-D array) or a tuple of 2 integers (for a 2-D array) +//| .. param: dtype +//| Type of values in the array +//| +//| Return a new array of the given shape with all elements set to 0.""" +//| ... +//| + +mp_obj_t create_zeros(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_obj = MP_OBJ_NULL } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = NDARRAY_FLOAT } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + uint8_t dtype = args[1].u_int; + return create_zeros_ones_full(args[0].u_obj, dtype, mp_const_none); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_zeros_obj, 0, create_zeros); +#endif + +#if ULAB_NUMPY_HAS_FROMBUFFER +mp_obj_t create_frombuffer(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_INT(NDARRAY_FLOAT) } }, + { MP_QSTR_count, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_INT(-1) } }, + { MP_QSTR_offset, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_INT(0) } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + uint8_t dtype = mp_obj_get_int(args[1].u_obj); + size_t offset = mp_obj_get_int(args[3].u_obj); + + mp_buffer_info_t bufinfo; + if(mp_get_buffer(args[0].u_obj, &bufinfo, MP_BUFFER_READ)) { + size_t sz = ulab_binary_get_size(dtype); + + if(bufinfo.len < offset) { + mp_raise_ValueError(translate("offset must be non-negative and no greater than buffer length")); + } + size_t len = (bufinfo.len - offset) / sz; + if((len * sz) != (bufinfo.len - offset)) { + mp_raise_ValueError(translate("buffer size must be a multiple of element size")); + } + if(mp_obj_get_int(args[2].u_obj) > 0) { + size_t count = mp_obj_get_int(args[2].u_obj); + if(len < count) { + mp_raise_ValueError(translate("buffer is smaller than requested size")); + } else { + len = count; + } + } + ndarray_obj_t *ndarray = m_new_obj(ndarray_obj_t); + ndarray->base.type = &ulab_ndarray_type; + ndarray->dtype = dtype == NDARRAY_BOOL ? NDARRAY_UINT8 : dtype; + ndarray->boolean = dtype == NDARRAY_BOOL ? NDARRAY_BOOLEAN : NDARRAY_NUMERIC; + ndarray->ndim = 1; + ndarray->len = len; + ndarray->itemsize = sz; + ndarray->shape[ULAB_MAX_DIMS - 1] = len; + ndarray->strides[ULAB_MAX_DIMS - 1] = sz; + + uint8_t *buffer = bufinfo.buf; + ndarray->array = buffer + offset; + return MP_OBJ_FROM_PTR(ndarray); + } + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(create_frombuffer_obj, 1, create_frombuffer); +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/create.h b/circuitpython/extmod/ulab/code/numpy/create.h new file mode 100644 index 0000000..18f636c --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/create.h @@ -0,0 +1,79 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2019-2021 Zoltán Vörös +*/ + +#ifndef _CREATE_ +#define _CREATE_ + +#include "../ulab.h" +#include "../ndarray.h" + +#if ULAB_NUMPY_HAS_ARANGE +mp_obj_t create_arange(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_arange_obj); +#endif + +#if ULAB_NUMPY_HAS_CONCATENATE +mp_obj_t create_concatenate(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_concatenate_obj); +#endif + +#if ULAB_NUMPY_HAS_DIAG +mp_obj_t create_diag(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_diag_obj); +#endif + +#if ULAB_MAX_DIMS > 1 +#if ULAB_NUMPY_HAS_EYE +mp_obj_t create_eye(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_eye_obj); +#endif +#endif + +#if ULAB_NUMPY_HAS_FULL +mp_obj_t create_full(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_full_obj); +#endif + +#if ULAB_NUMPY_HAS_LINSPACE +mp_obj_t create_linspace(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_linspace_obj); +#endif + +#if ULAB_NUMPY_HAS_LOGSPACE +mp_obj_t create_logspace(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_logspace_obj); +#endif + +#if ULAB_NUMPY_HAS_ONES +mp_obj_t create_ones(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_ones_obj); +#endif + +#if ULAB_NUMPY_HAS_ZEROS +mp_obj_t create_zeros(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_zeros_obj); +#endif + +#if ULAB_NUMPY_HAS_FROMBUFFER +mp_obj_t create_frombuffer(size_t , const mp_obj_t *, mp_map_t *); +MP_DECLARE_CONST_FUN_OBJ_KW(create_frombuffer_obj); +#endif + +#define ARANGE_LOOP(type_, ndarray, len, step, stop) \ +({\ + type_ *array = (type_ *)(ndarray)->array;\ + for (size_t i = 0; i < (len) - 1; i++, (value) += (step)) {\ + *array++ = (type_)(value);\ + }\ + *array = (type_)(stop);\ +}) + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/fft/fft.c b/circuitpython/extmod/ulab/code/numpy/fft/fft.c new file mode 100644 index 0000000..27cb79c --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/fft/fft.c @@ -0,0 +1,102 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * 2020 Scott Shawcroft for Adafruit Industries + * 2020 Taku Fukada +*/ + +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include "py/runtime.h" +#include "py/builtin.h" +#include "py/binary.h" +#include "py/obj.h" +#include "py/objarray.h" + +#include "../carray/carray_tools.h" +#include "fft.h" + +//| """Frequency-domain functions""" +//| +//| import ulab.numpy + + +//| def fft(r: ulab.numpy.ndarray, c: Optional[ulab.numpy.ndarray] = None) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]: +//| """ +//| :param ulab.numpy.ndarray r: A 1-dimension array of values whose size is a power of 2 +//| :param ulab.numpy.ndarray c: An optional 1-dimension array of values whose size is a power of 2, giving the complex part of the value +//| :return tuple (r, c): The real and complex parts of the FFT +//| +//| Perform a Fast Fourier Transform from the time domain into the frequency domain +//| +//| See also ~ulab.extras.spectrum, which computes the magnitude of the fft, +//| rather than separately returning its real and imaginary parts.""" +//| ... +//| +#if ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE +static mp_obj_t fft_fft(mp_obj_t arg) { + return fft_fft_ifft_spectrogram(arg, FFT_FFT); +} + +MP_DEFINE_CONST_FUN_OBJ_1(fft_fft_obj, fft_fft); +#else +static mp_obj_t fft_fft(size_t n_args, const mp_obj_t *args) { + if(n_args == 2) { + return fft_fft_ifft_spectrogram(n_args, args[0], args[1], FFT_FFT); + } else { + return fft_fft_ifft_spectrogram(n_args, args[0], mp_const_none, FFT_FFT); + } +} + +MP_DEFINE_CONST_FUN_OBJ_VAR_BETWEEN(fft_fft_obj, 1, 2, fft_fft); +#endif + +//| def ifft(r: ulab.numpy.ndarray, c: Optional[ulab.numpy.ndarray] = None) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]: +//| """ +//| :param ulab.numpy.ndarray r: A 1-dimension array of values whose size is a power of 2 +//| :param ulab.numpy.ndarray c: An optional 1-dimension array of values whose size is a power of 2, giving the complex part of the value +//| :return tuple (r, c): The real and complex parts of the inverse FFT +//| +//| Perform an Inverse Fast Fourier Transform from the frequeny domain into the time domain""" +//| ... +//| + +#if ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE +static mp_obj_t fft_ifft(mp_obj_t arg) { + return fft_fft_ifft_spectrogram(arg, FFT_IFFT); +} + +MP_DEFINE_CONST_FUN_OBJ_1(fft_ifft_obj, fft_ifft); +#else +static mp_obj_t fft_ifft(size_t n_args, const mp_obj_t *args) { + NOT_IMPLEMENTED_FOR_COMPLEX() + if(n_args == 2) { + return fft_fft_ifft_spectrogram(n_args, args[0], args[1], FFT_IFFT); + } else { + return fft_fft_ifft_spectrogram(n_args, args[0], mp_const_none, FFT_IFFT); + } +} + +MP_DEFINE_CONST_FUN_OBJ_VAR_BETWEEN(fft_ifft_obj, 1, 2, fft_ifft); +#endif + +STATIC const mp_rom_map_elem_t ulab_fft_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_fft) }, + { MP_OBJ_NEW_QSTR(MP_QSTR_fft), (mp_obj_t)&fft_fft_obj }, + { MP_OBJ_NEW_QSTR(MP_QSTR_ifft), (mp_obj_t)&fft_ifft_obj }, +}; + +STATIC MP_DEFINE_CONST_DICT(mp_module_ulab_fft_globals, ulab_fft_globals_table); + +const mp_obj_module_t ulab_fft_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_fft_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_fft, ulab_fft_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); diff --git a/circuitpython/extmod/ulab/code/numpy/fft/fft.h b/circuitpython/extmod/ulab/code/numpy/fft/fft.h new file mode 100644 index 0000000..1e50a8d --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/fft/fft.h @@ -0,0 +1,30 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#ifndef _FFT_ +#define _FFT_ + +#include "../../ulab.h" +#include "../../ulab_tools.h" +#include "../../ndarray.h" +#include "fft_tools.h" + +extern const mp_obj_module_t ulab_fft_module; + +#if ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE +MP_DECLARE_CONST_FUN_OBJ_3(fft_fft_obj); +MP_DECLARE_CONST_FUN_OBJ_3(fft_ifft_obj); +#else +MP_DECLARE_CONST_FUN_OBJ_VAR_BETWEEN(fft_fft_obj); +MP_DECLARE_CONST_FUN_OBJ_VAR_BETWEEN(fft_ifft_obj); +#endif + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/fft/fft_tools.c b/circuitpython/extmod/ulab/code/numpy/fft/fft_tools.c new file mode 100644 index 0000000..8a55927 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/fft/fft_tools.c @@ -0,0 +1,287 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#include <math.h> +#include <string.h> +#include "py/runtime.h" + +#include "../../ndarray.h" +#include "../../ulab_tools.h" +#include "../carray/carray_tools.h" +#include "fft_tools.h" + +#ifndef MP_PI +#define MP_PI MICROPY_FLOAT_CONST(3.14159265358979323846) +#endif +#ifndef MP_E +#define MP_E MICROPY_FLOAT_CONST(2.71828182845904523536) +#endif + +/* Kernel implementation for the case, when ulab has no complex support + + * The following function takes two arrays, namely, the real and imaginary + * parts of a complex array, and calculates the Fourier transform in place. + * + * The function is basically a modification of four1 from Numerical Recipes, + * has no dependencies beyond micropython itself (for the definition of mp_float_t), + * and can be used independent of ulab. + */ + +#if ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE +/* Kernel implementation for the complex case. Data are contained in data as + + data[0], data[1], data[2], data[3], .... , data[2n - 2], data[2n-1] + real[0], imag[0], real[1], imag[1], .... , real[n-1], imag[n-1] + + In general + real[i] = data[2i] + imag[i] = data[2i+1] + +*/ +void fft_kernel_complex(mp_float_t *data, size_t n, int isign) { + size_t j, m, mmax, istep; + mp_float_t tempr, tempi; + mp_float_t wtemp, wr, wpr, wpi, wi, theta; + + j = 0; + for(size_t i = 0; i < n; i++) { + if (j > i) { + SWAP(mp_float_t, data[2*i], data[2*j]); + SWAP(mp_float_t, data[2*i+1], data[2*j+1]); + } + m = n >> 1; + while (j >= m && m > 0) { + j -= m; + m >>= 1; + } + j += m; + } + + mmax = 1; + while (n > mmax) { + istep = mmax << 1; + theta = MICROPY_FLOAT_CONST(-2.0)*isign*MP_PI/istep; + wtemp = MICROPY_FLOAT_C_FUN(sin)(MICROPY_FLOAT_CONST(0.5) * theta); + wpr = MICROPY_FLOAT_CONST(-2.0) * wtemp * wtemp; + wpi = MICROPY_FLOAT_C_FUN(sin)(theta); + wr = MICROPY_FLOAT_CONST(1.0); + wi = MICROPY_FLOAT_CONST(0.0); + for(m = 0; m < mmax; m++) { + for(size_t i = m; i < n; i += istep) { + j = i + mmax; + tempr = wr * data[2*j] - wi * data[2*j+1]; + tempi = wr * data[2*j+1] + wi * data[2*j]; + data[2*j] = data[2*i] - tempr; + data[2*j+1] = data[2*i+1] - tempi; + data[2*i] += tempr; + data[2*i+1] += tempi; + } + wtemp = wr; + wr = wr*wpr - wi*wpi + wr; + wi = wi*wpr + wtemp*wpi + wi; + } + mmax = istep; + } +} + +/* + * The following function is a helper interface to the python side. + * It has been factored out from fft.c, so that the same argument parsing + * routine can be called from scipy.signal.spectrogram. + */ +mp_obj_t fft_fft_ifft_spectrogram(mp_obj_t data_in, uint8_t type) { + if(!mp_obj_is_type(data_in, &ulab_ndarray_type)) { + mp_raise_NotImplementedError(translate("FFT is defined for ndarrays only")); + } + ndarray_obj_t *in = MP_OBJ_TO_PTR(data_in); + #if ULAB_MAX_DIMS > 1 + if(in->ndim != 1) { + mp_raise_TypeError(translate("FFT is implemented for linear arrays only")); + } + #endif + size_t len = in->len; + // Check if input is of length of power of 2 + if((len & (len-1)) != 0) { + mp_raise_ValueError(translate("input array length must be power of 2")); + } + + ndarray_obj_t *out = ndarray_new_linear_array(len, NDARRAY_COMPLEX); + mp_float_t *data = (mp_float_t *)out->array; + uint8_t *array = (uint8_t *)in->array; + + if(in->dtype == NDARRAY_COMPLEX) { + uint8_t sz = 2 * sizeof(mp_float_t); + uint8_t *data_ = (uint8_t *)out->array; + for(size_t i = 0; i < len; i++) { + memcpy(data_, array, sz); + array += in->strides[ULAB_MAX_DIMS - 1]; + } + } else { + mp_float_t (*func)(void *) = ndarray_get_float_function(in->dtype); + for(size_t i = 0; i < len; i++) { + // real part; the imaginary part is 0, no need to assign + *data = func(array); + data += 2; + array += in->strides[ULAB_MAX_DIMS - 1]; + } + } + data -= 2 * len; + + if((type == FFT_FFT) || (type == FFT_SPECTROGRAM)) { + fft_kernel_complex(data, len, 1); + if(type == FFT_SPECTROGRAM) { + ndarray_obj_t *spectrum = ndarray_new_linear_array(len, NDARRAY_FLOAT); + mp_float_t *sarray = (mp_float_t *)spectrum->array; + for(size_t i = 0; i < len; i++) { + *sarray++ = MICROPY_FLOAT_C_FUN(sqrt)(data[0] * data[0] + data[1] * data[1]); + data += 2; + } + m_del(mp_float_t, data, 2 * len); + return MP_OBJ_FROM_PTR(spectrum); + } + } else { // inverse transform + fft_kernel_complex(data, len, -1); + // TODO: numpy accepts the norm keyword argument + for(size_t i = 0; i < len; i++) { + *data++ /= len; + } + } + return MP_OBJ_FROM_PTR(out); +} +#else /* ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE */ +void fft_kernel(mp_float_t *real, mp_float_t *imag, size_t n, int isign) { + size_t j, m, mmax, istep; + mp_float_t tempr, tempi; + mp_float_t wtemp, wr, wpr, wpi, wi, theta; + + j = 0; + for(size_t i = 0; i < n; i++) { + if (j > i) { + SWAP(mp_float_t, real[i], real[j]); + SWAP(mp_float_t, imag[i], imag[j]); + } + m = n >> 1; + while (j >= m && m > 0) { + j -= m; + m >>= 1; + } + j += m; + } + + mmax = 1; + while (n > mmax) { + istep = mmax << 1; + theta = MICROPY_FLOAT_CONST(-2.0)*isign*MP_PI/istep; + wtemp = MICROPY_FLOAT_C_FUN(sin)(MICROPY_FLOAT_CONST(0.5) * theta); + wpr = MICROPY_FLOAT_CONST(-2.0) * wtemp * wtemp; + wpi = MICROPY_FLOAT_C_FUN(sin)(theta); + wr = MICROPY_FLOAT_CONST(1.0); + wi = MICROPY_FLOAT_CONST(0.0); + for(m = 0; m < mmax; m++) { + for(size_t i = m; i < n; i += istep) { + j = i + mmax; + tempr = wr * real[j] - wi * imag[j]; + tempi = wr * imag[j] + wi * real[j]; + real[j] = real[i] - tempr; + imag[j] = imag[i] - tempi; + real[i] += tempr; + imag[i] += tempi; + } + wtemp = wr; + wr = wr*wpr - wi*wpi + wr; + wi = wi*wpr + wtemp*wpi + wi; + } + mmax = istep; + } +} + +mp_obj_t fft_fft_ifft_spectrogram(size_t n_args, mp_obj_t arg_re, mp_obj_t arg_im, uint8_t type) { + if(!mp_obj_is_type(arg_re, &ulab_ndarray_type)) { + mp_raise_NotImplementedError(translate("FFT is defined for ndarrays only")); + } + if(n_args == 2) { + if(!mp_obj_is_type(arg_im, &ulab_ndarray_type)) { + mp_raise_NotImplementedError(translate("FFT is defined for ndarrays only")); + } + } + ndarray_obj_t *re = MP_OBJ_TO_PTR(arg_re); + #if ULAB_MAX_DIMS > 1 + if(re->ndim != 1) { + COMPLEX_DTYPE_NOT_IMPLEMENTED(re->dtype) + mp_raise_TypeError(translate("FFT is implemented for linear arrays only")); + } + #endif + size_t len = re->len; + // Check if input is of length of power of 2 + if((len & (len-1)) != 0) { + mp_raise_ValueError(translate("input array length must be power of 2")); + } + + ndarray_obj_t *out_re = ndarray_new_linear_array(len, NDARRAY_FLOAT); + mp_float_t *data_re = (mp_float_t *)out_re->array; + + uint8_t *array = (uint8_t *)re->array; + mp_float_t (*func)(void *) = ndarray_get_float_function(re->dtype); + + for(size_t i=0; i < len; i++) { + *data_re++ = func(array); + array += re->strides[ULAB_MAX_DIMS - 1]; + } + data_re -= len; + ndarray_obj_t *out_im = ndarray_new_linear_array(len, NDARRAY_FLOAT); + mp_float_t *data_im = (mp_float_t *)out_im->array; + + if(n_args == 2) { + ndarray_obj_t *im = MP_OBJ_TO_PTR(arg_im); + #if ULAB_MAX_DIMS > 1 + if(im->ndim != 1) { + COMPLEX_DTYPE_NOT_IMPLEMENTED(im->dtype) + mp_raise_TypeError(translate("FFT is implemented for linear arrays only")); + } + #endif + if (re->len != im->len) { + mp_raise_ValueError(translate("real and imaginary parts must be of equal length")); + } + array = (uint8_t *)im->array; + func = ndarray_get_float_function(im->dtype); + for(size_t i=0; i < len; i++) { + *data_im++ = func(array); + array += im->strides[ULAB_MAX_DIMS - 1]; + } + data_im -= len; + } + + if((type == FFT_FFT) || (type == FFT_SPECTROGRAM)) { + fft_kernel(data_re, data_im, len, 1); + if(type == FFT_SPECTROGRAM) { + for(size_t i=0; i < len; i++) { + *data_re = MICROPY_FLOAT_C_FUN(sqrt)(*data_re * *data_re + *data_im * *data_im); + data_re++; + data_im++; + } + } + } else { // inverse transform + fft_kernel(data_re, data_im, len, -1); + // TODO: numpy accepts the norm keyword argument + for(size_t i=0; i < len; i++) { + *data_re++ /= len; + *data_im++ /= len; + } + } + if(type == FFT_SPECTROGRAM) { + return MP_OBJ_TO_PTR(out_re); + } else { + mp_obj_t tuple[2]; + tuple[0] = out_re; + tuple[1] = out_im; + return mp_obj_new_tuple(2, tuple); + } +} +#endif /* ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE */ diff --git a/circuitpython/extmod/ulab/code/numpy/fft/fft_tools.h b/circuitpython/extmod/ulab/code/numpy/fft/fft_tools.h new file mode 100644 index 0000000..9444232 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/fft/fft_tools.h @@ -0,0 +1,28 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#ifndef _FFT_TOOLS_ +#define _FFT_TOOLS_ + +enum FFT_TYPE { + FFT_FFT, + FFT_IFFT, + FFT_SPECTROGRAM, +}; + +#if ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE +void fft_kernel(mp_float_t *, size_t , int ); +mp_obj_t fft_fft_ifft_spectrogram(mp_obj_t , uint8_t ); +#else +void fft_kernel(mp_float_t *, mp_float_t *, size_t , int ); +mp_obj_t fft_fft_ifft_spectrogram(size_t , mp_obj_t , mp_obj_t , uint8_t ); +#endif /* ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE */ + +#endif /* _FFT_TOOLS_ */ diff --git a/circuitpython/extmod/ulab/code/numpy/filter.c b/circuitpython/extmod/ulab/code/numpy/filter.c new file mode 100644 index 0000000..057cd6d --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/filter.c @@ -0,0 +1,132 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020 Scott Shawcroft for Adafruit Industries + * 2020-2021 Zoltán Vörös + * 2020 Taku Fukada +*/ + +#include <math.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../ulab.h" +#include "../scipy/signal/signal.h" +#include "carray/carray_tools.h" +#include "filter.h" + +#if ULAB_NUMPY_HAS_CONVOLVE + +mp_obj_t filter_convolve(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_a, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_v, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type) || !mp_obj_is_type(args[1].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("convolve arguments must be ndarrays")); + } + + ndarray_obj_t *a = MP_OBJ_TO_PTR(args[0].u_obj); + ndarray_obj_t *c = MP_OBJ_TO_PTR(args[1].u_obj); + // deal with linear arrays only + #if ULAB_MAX_DIMS > 1 + if((a->ndim != 1) || (c->ndim != 1)) { + mp_raise_TypeError(translate("convolve arguments must be linear arrays")); + } + #endif + size_t len_a = a->len; + size_t len_c = c->len; + if(len_a == 0 || len_c == 0) { + mp_raise_TypeError(translate("convolve arguments must not be empty")); + } + + int len = len_a + len_c - 1; // convolve mode "full" + int32_t off = len_c - 1; + uint8_t dtype = NDARRAY_FLOAT; + + #if ULAB_SUPPORTS_COMPLEX + if((a->dtype == NDARRAY_COMPLEX) || (c->dtype == NDARRAY_COMPLEX)) { + dtype = NDARRAY_COMPLEX; + } + #endif + ndarray_obj_t *ndarray = ndarray_new_linear_array(len, dtype); + mp_float_t *array = (mp_float_t *)ndarray->array; + + uint8_t *aarray = (uint8_t *)a->array; + uint8_t *carray = (uint8_t *)c->array; + + int32_t as = a->strides[ULAB_MAX_DIMS - 1] / a->itemsize; + int32_t cs = c->strides[ULAB_MAX_DIMS - 1] / c->itemsize; + + + #if ULAB_SUPPORTS_COMPLEX + if(dtype == NDARRAY_COMPLEX) { + mp_float_t a_real, a_imag; + mp_float_t c_real, c_imag = MICROPY_FLOAT_CONST(0.0); + for(int32_t k = -off; k < len-off; k++) { + mp_float_t accum_real = MICROPY_FLOAT_CONST(0.0); + mp_float_t accum_imag = MICROPY_FLOAT_CONST(0.0); + + int32_t top_n = MIN(len_c, len_a - k); + int32_t bot_n = MAX(-k, 0); + + for(int32_t n = bot_n; n < top_n; n++) { + int32_t idx_c = (len_c - n - 1) * cs; + int32_t idx_a = (n + k) * as; + if(a->dtype != NDARRAY_COMPLEX) { + a_real = ndarray_get_float_index(aarray, a->dtype, idx_a); + a_imag = MICROPY_FLOAT_CONST(0.0); + } else { + a_real = ndarray_get_float_index(aarray, NDARRAY_FLOAT, 2 * idx_a); + a_imag = ndarray_get_float_index(aarray, NDARRAY_FLOAT, 2 * idx_a + 1); + } + + if(c->dtype != NDARRAY_COMPLEX) { + c_real = ndarray_get_float_index(carray, c->dtype, idx_c); + c_imag = MICROPY_FLOAT_CONST(0.0); + } else { + c_real = ndarray_get_float_index(carray, NDARRAY_FLOAT, 2 * idx_c); + c_imag = ndarray_get_float_index(carray, NDARRAY_FLOAT, 2 * idx_c + 1); + } + accum_real += a_real * c_real - a_imag * c_imag; + accum_imag += a_real * c_imag + a_imag * c_real; + } + *array++ = accum_real; + *array++ = accum_imag; + } + return MP_OBJ_FROM_PTR(ndarray); + } + #endif + + for(int32_t k = -off; k < len-off; k++) { + mp_float_t accum = MICROPY_FLOAT_CONST(0.0); + int32_t top_n = MIN(len_c, len_a - k); + int32_t bot_n = MAX(-k, 0); + for(int32_t n = bot_n; n < top_n; n++) { + int32_t idx_c = (len_c - n - 1) * cs; + int32_t idx_a = (n + k) * as; + mp_float_t ai = ndarray_get_float_index(aarray, a->dtype, idx_a); + mp_float_t ci = ndarray_get_float_index(carray, c->dtype, idx_c); + accum += ai * ci; + } + *array++ = accum; + } + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(filter_convolve_obj, 2, filter_convolve); + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/filter.h b/circuitpython/extmod/ulab/code/numpy/filter.h new file mode 100644 index 0000000..d6d0f17 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/filter.h @@ -0,0 +1,20 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020-2021 Zoltán Vörös +*/ + +#ifndef _FILTER_ +#define _FILTER_ + +#include "../ulab.h" +#include "../ndarray.h" + +MP_DECLARE_CONST_FUN_OBJ_KW(filter_convolve_obj); +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/linalg/linalg.c b/circuitpython/extmod/ulab/code/numpy/linalg/linalg.c new file mode 100644 index 0000000..11dc7de --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/linalg/linalg.c @@ -0,0 +1,541 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * 2020 Scott Shawcroft for Adafruit Industries + * 2020 Roberto Colistete Jr. + * 2020 Taku Fukada + * +*/ + +#include <stdlib.h> +#include <string.h> +#include <math.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../../ulab.h" +#include "../../ulab_tools.h" +#include "../carray/carray_tools.h" +#include "linalg.h" + +#if ULAB_NUMPY_HAS_LINALG_MODULE +//| +//| import ulab.numpy +//| +//| """Linear algebra functions""" +//| + +#if ULAB_MAX_DIMS > 1 +//| def cholesky(A: ulab.numpy.ndarray) -> ulab.numpy.ndarray: +//| """ +//| :param ~ulab.numpy.ndarray A: a positive definite, symmetric square matrix +//| :return ~ulab.numpy.ndarray L: a square root matrix in the lower triangular form +//| :raises ValueError: If the input does not fulfill the necessary conditions +//| +//| The returned matrix satisfies the equation m=LL*""" +//| ... +//| + +static mp_obj_t linalg_cholesky(mp_obj_t oin) { + ndarray_obj_t *ndarray = tools_object_is_square(oin); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + ndarray_obj_t *L = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, ndarray->shape[ULAB_MAX_DIMS - 1], ndarray->shape[ULAB_MAX_DIMS - 1]), NDARRAY_FLOAT); + mp_float_t *Larray = (mp_float_t *)L->array; + + size_t N = ndarray->shape[ULAB_MAX_DIMS - 1]; + uint8_t *array = (uint8_t *)ndarray->array; + mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype); + + for(size_t m=0; m < N; m++) { // rows + for(size_t n=0; n < N; n++) { // columns + *Larray++ = func(array); + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + } + array -= ndarray->strides[ULAB_MAX_DIMS - 1] * N; + array += ndarray->strides[ULAB_MAX_DIMS - 2]; + } + Larray -= N*N; + // make sure the matrix is symmetric + for(size_t m=0; m < N; m++) { // rows + for(size_t n=m+1; n < N; n++) { // columns + // compare entry (m, n) to (n, m) + if(LINALG_EPSILON < MICROPY_FLOAT_C_FUN(fabs)(Larray[m * N + n] - Larray[n * N + m])) { + mp_raise_ValueError(translate("input matrix is asymmetric")); + } + } + } + + // this is actually not needed, but Cholesky in numpy returns the lower triangular matrix + for(size_t i=0; i < N; i++) { // rows + for(size_t j=i+1; j < N; j++) { // columns + Larray[i*N + j] = MICROPY_FLOAT_CONST(0.0); + } + } + mp_float_t sum = 0.0; + for(size_t i=0; i < N; i++) { // rows + for(size_t j=0; j <= i; j++) { // columns + sum = Larray[i * N + j]; + for(size_t k=0; k < j; k++) { + sum -= Larray[i * N + k] * Larray[j * N + k]; + } + if(i == j) { + if(sum <= MICROPY_FLOAT_CONST(0.0)) { + mp_raise_ValueError(translate("matrix is not positive definite")); + } else { + Larray[i * N + i] = MICROPY_FLOAT_C_FUN(sqrt)(sum); + } + } else { + Larray[i * N + j] = sum / Larray[j * N + j]; + } + } + } + return MP_OBJ_FROM_PTR(L); +} + +MP_DEFINE_CONST_FUN_OBJ_1(linalg_cholesky_obj, linalg_cholesky); + +//| def det(m: ulab.numpy.ndarray) -> float: +//| """ +//| :param: m, a square matrix +//| :return float: The determinant of the matrix +//| +//| Computes the eigenvalues and eigenvectors of a square matrix""" +//| ... +//| + +static mp_obj_t linalg_det(mp_obj_t oin) { + ndarray_obj_t *ndarray = tools_object_is_square(oin); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + uint8_t *array = (uint8_t *)ndarray->array; + size_t N = ndarray->shape[ULAB_MAX_DIMS - 1]; + mp_float_t *tmp = m_new(mp_float_t, N * N); + for(size_t m=0; m < N; m++) { // rows + for(size_t n=0; n < N; n++) { // columns + *tmp++ = ndarray_get_float_value(array, ndarray->dtype); + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + } + array -= ndarray->strides[ULAB_MAX_DIMS - 1] * N; + array += ndarray->strides[ULAB_MAX_DIMS - 2]; + } + + // re-wind the pointer + tmp -= N*N; + + mp_float_t c; + mp_float_t det_sign = 1.0; + + for(size_t m=0; m < N-1; m++){ + if(MICROPY_FLOAT_C_FUN(fabs)(tmp[m * (N+1)]) < LINALG_EPSILON) { + size_t m1 = m + 1; + for(; m1 < N; m1++) { + if(!(MICROPY_FLOAT_C_FUN(fabs)(tmp[m1*N+m]) < LINALG_EPSILON)) { + //look for a line to swap + for(size_t m2=0; m2 < N; m2++) { + mp_float_t swapVal = tmp[m*N+m2]; + tmp[m*N+m2] = tmp[m1*N+m2]; + tmp[m1*N+m2] = swapVal; + } + det_sign = -det_sign; + break; + } + } + if (m1 >= N) { + m_del(mp_float_t, tmp, N * N); + return mp_obj_new_float(0.0); + } + } + for(size_t n=0; n < N; n++) { + if(m != n) { + c = tmp[N * n + m] / tmp[m * (N+1)]; + for(size_t k=0; k < N; k++){ + tmp[N * n + k] -= c * tmp[N * m + k]; + } + } + } + } + mp_float_t det = det_sign; + + for(size_t m=0; m < N; m++){ + det *= tmp[m * (N+1)]; + } + m_del(mp_float_t, tmp, N * N); + return mp_obj_new_float(det); +} + +MP_DEFINE_CONST_FUN_OBJ_1(linalg_det_obj, linalg_det); + +#endif + +#if ULAB_MAX_DIMS > 1 +//| def eig(m: ulab.numpy.ndarray) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]: +//| """ +//| :param m: a square matrix +//| :return tuple (eigenvectors, eigenvalues): +//| +//| Computes the eigenvalues and eigenvectors of a square matrix""" +//| ... +//| + +static mp_obj_t linalg_eig(mp_obj_t oin) { + ndarray_obj_t *in = tools_object_is_square(oin); + COMPLEX_DTYPE_NOT_IMPLEMENTED(in->dtype) + uint8_t *iarray = (uint8_t *)in->array; + size_t S = in->shape[ULAB_MAX_DIMS - 1]; + mp_float_t *array = m_new(mp_float_t, S*S); + for(size_t i=0; i < S; i++) { // rows + for(size_t j=0; j < S; j++) { // columns + *array++ = ndarray_get_float_value(iarray, in->dtype); + iarray += in->strides[ULAB_MAX_DIMS - 1]; + } + iarray -= in->strides[ULAB_MAX_DIMS - 1] * S; + iarray += in->strides[ULAB_MAX_DIMS - 2]; + } + array -= S * S; + // make sure the matrix is symmetric + for(size_t m=0; m < S; m++) { + for(size_t n=m+1; n < S; n++) { + // compare entry (m, n) to (n, m) + // TODO: this must probably be scaled! + if(LINALG_EPSILON < MICROPY_FLOAT_C_FUN(fabs)(array[m * S + n] - array[n * S + m])) { + mp_raise_ValueError(translate("input matrix is asymmetric")); + } + } + } + + // if we got this far, then the matrix will be symmetric + + ndarray_obj_t *eigenvectors = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, S, S), NDARRAY_FLOAT); + mp_float_t *eigvectors = (mp_float_t *)eigenvectors->array; + + size_t iterations = linalg_jacobi_rotations(array, eigvectors, S); + + if(iterations == 0) { + // the computation did not converge; numpy raises LinAlgError + m_del(mp_float_t, array, in->len); + mp_raise_ValueError(translate("iterations did not converge")); + } + ndarray_obj_t *eigenvalues = ndarray_new_linear_array(S, NDARRAY_FLOAT); + mp_float_t *eigvalues = (mp_float_t *)eigenvalues->array; + for(size_t i=0; i < S; i++) { + eigvalues[i] = array[i * (S + 1)]; + } + m_del(mp_float_t, array, in->len); + + mp_obj_tuple_t *tuple = MP_OBJ_TO_PTR(mp_obj_new_tuple(2, NULL)); + tuple->items[0] = MP_OBJ_FROM_PTR(eigenvalues); + tuple->items[1] = MP_OBJ_FROM_PTR(eigenvectors); + return tuple; +} + +MP_DEFINE_CONST_FUN_OBJ_1(linalg_eig_obj, linalg_eig); + +//| def inv(m: ulab.numpy.ndarray) -> ulab.numpy.ndarray: +//| """ +//| :param ~ulab.numpy.ndarray m: a square matrix +//| :return: The inverse of the matrix, if it exists +//| :raises ValueError: if the matrix is not invertible +//| +//| Computes the inverse of a square matrix""" +//| ... +//| +static mp_obj_t linalg_inv(mp_obj_t o_in) { + ndarray_obj_t *ndarray = tools_object_is_square(o_in); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + uint8_t *array = (uint8_t *)ndarray->array; + size_t N = ndarray->shape[ULAB_MAX_DIMS - 1]; + ndarray_obj_t *inverted = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, N, N), NDARRAY_FLOAT); + mp_float_t *iarray = (mp_float_t *)inverted->array; + + mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype); + + for(size_t i=0; i < N; i++) { // rows + for(size_t j=0; j < N; j++) { // columns + *iarray++ = func(array); + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + } + array -= ndarray->strides[ULAB_MAX_DIMS - 1] * N; + array += ndarray->strides[ULAB_MAX_DIMS - 2]; + } + // re-wind the pointer + iarray -= N*N; + + if(!linalg_invert_matrix(iarray, N)) { + mp_raise_ValueError(translate("input matrix is singular")); + } + return MP_OBJ_FROM_PTR(inverted); +} + +MP_DEFINE_CONST_FUN_OBJ_1(linalg_inv_obj, linalg_inv); +#endif + +//| def norm(x: ulab.numpy.ndarray) -> float: +//| """ +//| :param ~ulab.numpy.ndarray x: a vector or a matrix +//| +//| Computes the 2-norm of a vector or a matrix, i.e., ``sqrt(sum(x*x))``, however, without the RAM overhead.""" +//| ... +//| + +static mp_obj_t linalg_norm(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none} } , + { MP_QSTR_axis, MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t x = args[0].u_obj; + mp_obj_t axis = args[1].u_obj; + + mp_float_t dot = 0.0, value; + size_t count = 1; + + if(mp_obj_is_type(x, &mp_type_tuple) || mp_obj_is_type(x, &mp_type_list) || mp_obj_is_type(x, &mp_type_range)) { + mp_obj_iter_buf_t iter_buf; + mp_obj_t item, iterable = mp_getiter(x, &iter_buf); + while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + value = mp_obj_get_float(item); + // we could simply take the sum of value ** 2, + // but this method is numerically stable + dot = dot + (value * value - dot) / count++; + } + return mp_obj_new_float(MICROPY_FLOAT_C_FUN(sqrt)(dot * (count - 1))); + } else if(mp_obj_is_type(x, &ulab_ndarray_type)) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(x); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + uint8_t *array = (uint8_t *)ndarray->array; + // always get a float, so that we don't have to resolve the dtype later + mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype); + shape_strides _shape_strides = tools_reduce_axes(ndarray, axis); + ndarray_obj_t *results = ndarray_new_dense_ndarray(_shape_strides.ndim, _shape_strides.shape, NDARRAY_FLOAT); + mp_float_t *rarray = (mp_float_t *)results->array; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + if(axis != mp_const_none) { + count = 1; + dot = 0.0; + } + do { + value = func(array); + dot = dot + (value * value - dot) / count++; + array += _shape_strides.strides[0]; + l++; + } while(l < _shape_strides.shape[0]); + *rarray = MICROPY_FLOAT_C_FUN(sqrt)(dot * (count - 1)); + #if ULAB_MAX_DIMS > 1 + rarray += _shape_strides.increment; + array -= _shape_strides.strides[0] * _shape_strides.shape[0]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 1]; + k++; + } while(k < _shape_strides.shape[ULAB_MAX_DIMS - 1]); + #endif + #if ULAB_MAX_DIMS > 2 + array -= _shape_strides.strides[ULAB_MAX_DIMS - 1] * _shape_strides.shape[ULAB_MAX_DIMS - 1]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 2]; + j++; + } while(j < _shape_strides.shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 3 + array -= _shape_strides.strides[ULAB_MAX_DIMS - 2] * _shape_strides.shape[ULAB_MAX_DIMS - 2]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 3]; + i++; + } while(i < _shape_strides.shape[ULAB_MAX_DIMS - 3]); + #endif + if(results->ndim == 0) { + return mp_obj_new_float(*rarray); + } + return results; + } + return mp_const_none; // we should never reach this point +} + +MP_DEFINE_CONST_FUN_OBJ_KW(linalg_norm_obj, 1, linalg_norm); + +#if ULAB_MAX_DIMS > 1 +//| def qr(m: ulab.numpy.ndarray) -> Tuple[ulab.numpy.ndarray, ulab.numpy.ndarray]: +//| """ +//| :param m: a matrix +//| :return tuple (Q, R): +//| +//| Factor the matrix a as QR, where Q is orthonormal and R is upper-triangular. +//| """ +//| ... +//| + +static mp_obj_t linalg_qr(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_mode, MP_ARG_OBJ, { .u_rom_obj = MP_ROM_QSTR(MP_QSTR_reduced) } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("operation is defined for ndarrays only")); + } + ndarray_obj_t *source = MP_OBJ_TO_PTR(args[0].u_obj); + if(source->ndim != 2) { + mp_raise_ValueError(translate("operation is defined for 2D arrays only")); + } + + size_t m = source->shape[ULAB_MAX_DIMS - 2]; // rows + size_t n = source->shape[ULAB_MAX_DIMS - 1]; // columns + + ndarray_obj_t *Q = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, m, m), NDARRAY_FLOAT); + ndarray_obj_t *R = ndarray_new_dense_ndarray(2, source->shape, NDARRAY_FLOAT); + + mp_float_t *qarray = (mp_float_t *)Q->array; + mp_float_t *rarray = (mp_float_t *)R->array; + + // simply copy the entries of source to a float array + mp_float_t (*func)(void *) = ndarray_get_float_function(source->dtype); + uint8_t *sarray = (uint8_t *)source->array; + + for(size_t i = 0; i < m; i++) { + for(size_t j = 0; j < n; j++) { + *rarray++ = func(sarray); + sarray += source->strides[ULAB_MAX_DIMS - 1]; + } + sarray -= n * source->strides[ULAB_MAX_DIMS - 1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + } + rarray -= m * n; + + // start with the unit matrix + for(size_t i = 0; i < m; i++) { + qarray[i * (m + 1)] = 1.0; + } + + for(size_t j = 0; j < n; j++) { // columns + for(size_t i = m - 1; i > j; i--) { // rows + mp_float_t c, s; + // Givens matrix: note that numpy uses a strange form of the rotation + // [[c s], + // [s -c]] + if(MICROPY_FLOAT_C_FUN(fabs)(rarray[i * n + j]) < LINALG_EPSILON) { // r[i, j] + c = (rarray[(i - 1) * n + j] >= 0.0) ? 1.0 : -1.0; // r[i-1, j] + s = 0.0; + } else if(MICROPY_FLOAT_C_FUN(fabs)(rarray[(i - 1) * n + j]) < LINALG_EPSILON) { // r[i-1, j] + c = 0.0; + s = (rarray[i * n + j] >= 0.0) ? -1.0 : 1.0; // r[i, j] + } else { + mp_float_t t, u; + if(MICROPY_FLOAT_C_FUN(fabs)(rarray[(i - 1) * n + j]) > MICROPY_FLOAT_C_FUN(fabs)(rarray[i * n + j])) { // r[i-1, j], r[i, j] + t = rarray[i * n + j] / rarray[(i - 1) * n + j]; // r[i, j]/r[i-1, j] + u = MICROPY_FLOAT_C_FUN(sqrt)(1 + t * t); + c = -1.0 / u; + s = c * t; + } else { + t = rarray[(i - 1) * n + j] / rarray[i * n + j]; // r[i-1, j]/r[i, j] + u = MICROPY_FLOAT_C_FUN(sqrt)(1 + t * t); + s = -1.0 / u; + c = s * t; + } + } + + mp_float_t r1, r2; + // update R: multiply with the rotation matrix from the left + for(size_t k = 0; k < n; k++) { + r1 = rarray[(i - 1) * n + k]; // r[i-1, k] + r2 = rarray[i * n + k]; // r[i, k] + rarray[(i - 1) * n + k] = c * r1 + s * r2; // r[i-1, k] + rarray[i * n + k] = s * r1 - c * r2; // r[i, k] + } + + // update Q: multiply with the transpose of the rotation matrix from the right + for(size_t k = 0; k < m; k++) { + r1 = qarray[k * m + (i - 1)]; + r2 = qarray[k * m + i]; + qarray[k * m + (i - 1)] = c * r1 + s * r2; + qarray[k * m + i] = s * r1 - c * r2; + } + } + } + + mp_obj_tuple_t *tuple = MP_OBJ_TO_PTR(mp_obj_new_tuple(2, NULL)); + GET_STR_DATA_LEN(args[1].u_obj, mode, len); + if(memcmp(mode, "complete", 8) == 0) { + tuple->items[0] = MP_OBJ_FROM_PTR(Q); + tuple->items[1] = MP_OBJ_FROM_PTR(R); + } else if(memcmp(mode, "reduced", 7) == 0) { + size_t k = MAX(m, n) - MIN(m, n); + ndarray_obj_t *q = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, m, m - k), NDARRAY_FLOAT); + ndarray_obj_t *r = ndarray_new_dense_ndarray(2, ndarray_shape_vector(0, 0, m - k, n), NDARRAY_FLOAT); + mp_float_t *qa = (mp_float_t *)q->array; + mp_float_t *ra = (mp_float_t *)r->array; + for(size_t i = 0; i < m; i++) { + memcpy(qa, qarray, (m - k) * q->itemsize); + qa += (m - k); + qarray += m; + } + for(size_t i = 0; i < m - k; i++) { + memcpy(ra, rarray, n * r->itemsize); + ra += n; + rarray += n; + } + tuple->items[0] = MP_OBJ_FROM_PTR(q); + tuple->items[1] = MP_OBJ_FROM_PTR(r); + } else { + mp_raise_ValueError(translate("mode must be complete, or reduced")); + } + return tuple; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(linalg_qr_obj, 1, linalg_qr); +#endif + +STATIC const mp_rom_map_elem_t ulab_linalg_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_linalg) }, + #if ULAB_MAX_DIMS > 1 + #if ULAB_LINALG_HAS_CHOLESKY + { MP_ROM_QSTR(MP_QSTR_cholesky), (mp_obj_t)&linalg_cholesky_obj }, + #endif + #if ULAB_LINALG_HAS_DET + { MP_ROM_QSTR(MP_QSTR_det), (mp_obj_t)&linalg_det_obj }, + #endif + #if ULAB_LINALG_HAS_EIG + { MP_ROM_QSTR(MP_QSTR_eig), (mp_obj_t)&linalg_eig_obj }, + #endif + #if ULAB_LINALG_HAS_INV + { MP_ROM_QSTR(MP_QSTR_inv), (mp_obj_t)&linalg_inv_obj }, + #endif + #if ULAB_LINALG_HAS_QR + { MP_ROM_QSTR(MP_QSTR_qr), (mp_obj_t)&linalg_qr_obj }, + #endif + #endif + #if ULAB_LINALG_HAS_NORM + { MP_ROM_QSTR(MP_QSTR_norm), (mp_obj_t)&linalg_norm_obj }, + #endif +}; + +STATIC MP_DEFINE_CONST_DICT(mp_module_ulab_linalg_globals, ulab_linalg_globals_table); + +const mp_obj_module_t ulab_linalg_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_linalg_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_linalg, ulab_linalg_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/linalg/linalg.h b/circuitpython/extmod/ulab/code/numpy/linalg/linalg.h new file mode 100644 index 0000000..35fc403 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/linalg/linalg.h @@ -0,0 +1,27 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#ifndef _LINALG_ +#define _LINALG_ + +#include "../../ulab.h" +#include "../../ndarray.h" +#include "linalg_tools.h" + +extern const mp_obj_module_t ulab_linalg_module; + +MP_DECLARE_CONST_FUN_OBJ_1(linalg_cholesky_obj); +MP_DECLARE_CONST_FUN_OBJ_1(linalg_det_obj); +MP_DECLARE_CONST_FUN_OBJ_1(linalg_eig_obj); +MP_DECLARE_CONST_FUN_OBJ_1(linalg_inv_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(linalg_norm_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(linalg_qr_obj); +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/linalg/linalg_tools.c b/circuitpython/extmod/ulab/code/numpy/linalg/linalg_tools.c new file mode 100644 index 0000000..5e03a50 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/linalg/linalg_tools.c @@ -0,0 +1,171 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2010 Zoltán Vörös +*/ + +#include <math.h> +#include <string.h> +#include "py/runtime.h" + +#include "linalg_tools.h" + +/* + * The following function inverts a matrix, whose entries are given in the input array + * The function has no dependencies beyond micropython itself (for the definition of mp_float_t), + * and can be used independent of ulab. + */ + +bool linalg_invert_matrix(mp_float_t *data, size_t N) { + // returns true, of the inversion was successful, + // false, if the matrix is singular + + // initially, this is the unit matrix: the contents of this matrix is what + // will be returned after all the transformations + mp_float_t *unit = m_new(mp_float_t, N*N); + mp_float_t elem = 1.0; + // initialise the unit matrix + memset(unit, 0, sizeof(mp_float_t)*N*N); + for(size_t m=0; m < N; m++) { + memcpy(&unit[m * (N+1)], &elem, sizeof(mp_float_t)); + } + for(size_t m=0; m < N; m++){ + // this could be faster with ((c < epsilon) && (c > -epsilon)) + if(MICROPY_FLOAT_C_FUN(fabs)(data[m * (N+1)]) < LINALG_EPSILON) { + //look for a line to swap + size_t m1 = m + 1; + for(; m1 < N; m1++) { + if(!(MICROPY_FLOAT_C_FUN(fabs)(data[m1*N + m]) < LINALG_EPSILON)) { + for(size_t m2=0; m2 < N; m2++) { + mp_float_t swapVal = data[m*N+m2]; + data[m*N+m2] = data[m1*N+m2]; + data[m1*N+m2] = swapVal; + swapVal = unit[m*N+m2]; + unit[m*N+m2] = unit[m1*N+m2]; + unit[m1*N+m2] = swapVal; + } + break; + } + } + if (m1 >= N) { + m_del(mp_float_t, unit, N*N); + return false; + } + } + for(size_t n=0; n < N; n++) { + if(m != n){ + elem = data[N * n + m] / data[m * (N+1)]; + for(size_t k=0; k < N; k++) { + data[N * n + k] -= elem * data[N * m + k]; + unit[N * n + k] -= elem * unit[N * m + k]; + } + } + } + } + for(size_t m=0; m < N; m++) { + elem = data[m * (N+1)]; + for(size_t n=0; n < N; n++) { + data[N * m + n] /= elem; + unit[N * m + n] /= elem; + } + } + memcpy(data, unit, sizeof(mp_float_t)*N*N); + m_del(mp_float_t, unit, N * N); + return true; +} + +/* + * The following function calculates the eigenvalues and eigenvectors of a symmetric + * real matrix, whose entries are given in the input array. + * The function has no dependencies beyond micropython itself (for the definition of mp_float_t), + * and can be used independent of ulab. + */ + +size_t linalg_jacobi_rotations(mp_float_t *array, mp_float_t *eigvectors, size_t S) { + // eigvectors should be a 0-array; start out with the unit matrix + for(size_t m=0; m < S; m++) { + eigvectors[m * (S+1)] = 1.0; + } + mp_float_t largest, w, t, c, s, tau, aMk, aNk, vm, vn; + size_t M, N; + size_t iterations = JACOBI_MAX * S * S; + do { + iterations--; + // find the pivot here + M = 0; + N = 0; + largest = 0.0; + for(size_t m=0; m < S-1; m++) { // -1: no need to inspect last row + for(size_t n=m+1; n < S; n++) { + w = MICROPY_FLOAT_C_FUN(fabs)(array[m * S + n]); + if((largest < w) && (LINALG_EPSILON < w)) { + M = m; + N = n; + largest = w; + } + } + } + if(M + N == 0) { // all entries are smaller than epsilon, there is not much we can do... + break; + } + // at this point, we have the pivot, and it is the entry (M, N) + // now we have to find the rotation angle + w = (array[N * S + N] - array[M * S + M]) / (MICROPY_FLOAT_CONST(2.0)*array[M * S + N]); + // The following if/else chooses the smaller absolute value for the tangent + // of the rotation angle. Going with the smaller should be numerically stabler. + if(w > 0) { + t = MICROPY_FLOAT_C_FUN(sqrt)(w*w + MICROPY_FLOAT_CONST(1.0)) - w; + } else { + t = MICROPY_FLOAT_CONST(-1.0)*(MICROPY_FLOAT_C_FUN(sqrt)(w*w + MICROPY_FLOAT_CONST(1.0)) + w); + } + s = t / MICROPY_FLOAT_C_FUN(sqrt)(t*t + MICROPY_FLOAT_CONST(1.0)); // the sine of the rotation angle + c = MICROPY_FLOAT_CONST(1.0) / MICROPY_FLOAT_C_FUN(sqrt)(t*t + MICROPY_FLOAT_CONST(1.0)); // the cosine of the rotation angle + tau = (MICROPY_FLOAT_CONST(1.0)-c)/s; // this is equal to the tangent of the half of the rotation angle + + // at this point, we have the rotation angles, so we can transform the matrix + // first the two diagonal elements + // a(M, M) = a(M, M) - t*a(M, N) + array[M * S + M] = array[M * S + M] - t * array[M * S + N]; + // a(N, N) = a(N, N) + t*a(M, N) + array[N * S + N] = array[N * S + N] + t * array[M * S + N]; + // after the rotation, the a(M, N), and a(N, M) entries should become zero + array[M * S + N] = array[N * S + M] = MICROPY_FLOAT_CONST(0.0); + // then all other elements in the column + for(size_t k=0; k < S; k++) { + if((k == M) || (k == N)) { + continue; + } + aMk = array[M * S + k]; + aNk = array[N * S + k]; + // a(M, k) = a(M, k) - s*(a(N, k) + tau*a(M, k)) + array[M * S + k] -= s * (aNk + tau * aMk); + // a(N, k) = a(N, k) + s*(a(M, k) - tau*a(N, k)) + array[N * S + k] += s * (aMk - tau * aNk); + // a(k, M) = a(M, k) + array[k * S + M] = array[M * S + k]; + // a(k, N) = a(N, k) + array[k * S + N] = array[N * S + k]; + } + // now we have to update the eigenvectors + // the rotation matrix, R, multiplies from the right + // R is the unit matrix, except for the + // R(M,M) = R(N, N) = c + // R(N, M) = s + // (M, N) = -s + // entries. This means that only the Mth, and Nth columns will change + for(size_t m=0; m < S; m++) { + vm = eigvectors[m * S + M]; + vn = eigvectors[m * S + N]; + // the new value of eigvectors(m, M) + eigvectors[m * S + M] = c * vm - s * vn; + // the new value of eigvectors(m, N) + eigvectors[m * S + N] = s * vm + c * vn; + } + } while(iterations > 0); + + return iterations; +} diff --git a/circuitpython/extmod/ulab/code/numpy/linalg/linalg_tools.h b/circuitpython/extmod/ulab/code/numpy/linalg/linalg_tools.h new file mode 100644 index 0000000..942da00 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/linalg/linalg_tools.h @@ -0,0 +1,28 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#ifndef _TOOLS_TOOLS_ +#define _TOOLS_TOOLS_ + +#ifndef LINALG_EPSILON +#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT +#define LINALG_EPSILON MICROPY_FLOAT_CONST(1.2e-7) +#elif MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE +#define LINALG_EPSILON MICROPY_FLOAT_CONST(2.3e-16) +#endif +#endif /* LINALG_EPSILON */ + +#define JACOBI_MAX 20 + +bool linalg_invert_matrix(mp_float_t *, size_t ); +size_t linalg_jacobi_rotations(mp_float_t *, mp_float_t *, size_t ); + +#endif /* _TOOLS_TOOLS_ */ + diff --git a/circuitpython/extmod/ulab/code/numpy/ndarray/ndarray_iter.c b/circuitpython/extmod/ulab/code/numpy/ndarray/ndarray_iter.c new file mode 100644 index 0000000..8704836 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/ndarray/ndarray_iter.c @@ -0,0 +1,66 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2021 Zoltán Vörös + * +*/ + +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" + +#include "ndarray_iter.h" + +#ifdef NDARRAY_HAS_FLATITER +mp_obj_t ndarray_flatiter_make_new(mp_obj_t self_in) { + ndarray_flatiter_t *flatiter = m_new_obj(ndarray_flatiter_t); + flatiter->base.type = &ndarray_flatiter_type; + flatiter->iternext = ndarray_flatiter_next; + flatiter->ndarray = MP_OBJ_TO_PTR(self_in); + flatiter->cur = 0; + return flatiter; +} + +mp_obj_t ndarray_flatiter_next(mp_obj_t self_in) { + ndarray_flatiter_t *self = MP_OBJ_TO_PTR(self_in); + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(self->ndarray); + uint8_t *array = (uint8_t *)ndarray->array; + + if(self->cur < ndarray->len) { + uint32_t remainder = self->cur; + uint8_t i = ULAB_MAX_DIMS - 1; + do { + size_t div = (remainder / ndarray->shape[i]); + array += remainder * ndarray->strides[i]; + remainder -= div * ndarray->shape[i]; + i--; + } while(i > ULAB_MAX_DIMS - ndarray->ndim); + self->cur++; + return ndarray_get_item(ndarray, array); + } + return MP_OBJ_STOP_ITERATION; +} + +mp_obj_t ndarray_new_flatiterator(mp_obj_t flatiter_in, mp_obj_iter_buf_t *iter_buf) { + assert(sizeof(ndarray_flatiter_t) <= sizeof(mp_obj_iter_buf_t)); + ndarray_flatiter_t *iter = (ndarray_flatiter_t *)iter_buf; + ndarray_flatiter_t *flatiter = MP_OBJ_TO_PTR(flatiter_in); + iter->base.type = &mp_type_polymorph_iter; + iter->iternext = ndarray_flatiter_next; + iter->ndarray = flatiter->ndarray; + iter->cur = 0; + return MP_OBJ_FROM_PTR(iter); +} + +mp_obj_t ndarray_get_flatiterator(mp_obj_t o_in, mp_obj_iter_buf_t *iter_buf) { + return ndarray_new_flatiterator(o_in, iter_buf); +} +#endif /* NDARRAY_HAS_FLATITER */ diff --git a/circuitpython/extmod/ulab/code/numpy/ndarray/ndarray_iter.h b/circuitpython/extmod/ulab/code/numpy/ndarray/ndarray_iter.h new file mode 100644 index 0000000..b3fc48d --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/ndarray/ndarray_iter.h @@ -0,0 +1,36 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020-2021 Zoltán Vörös +*/ + +#ifndef _NDARRAY_ITER_ +#define _NDARRAY_ITER_ + +#include "py/runtime.h" +#include "py/binary.h" +#include "py/obj.h" +#include "py/objarray.h" + +#include "../../ulab.h" +#include "../../ndarray.h" + +// TODO: take simply mp_obj_ndarray_it_t from ndarray.c +typedef struct _mp_obj_ndarray_flatiter_t { + mp_obj_base_t base; + mp_fun_1_t iternext; + mp_obj_t ndarray; + size_t cur; +} ndarray_flatiter_t; + +mp_obj_t ndarray_get_flatiterator(mp_obj_t , mp_obj_iter_buf_t *); +mp_obj_t ndarray_flatiter_make_new(mp_obj_t ); +mp_obj_t ndarray_flatiter_next(mp_obj_t ); + +#endif
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/code/numpy/numerical.c b/circuitpython/extmod/ulab/code/numpy/numerical.c new file mode 100644 index 0000000..d6983c0 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/numerical.c @@ -0,0 +1,1402 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * 2020 Scott Shawcroft for Adafruit Industries + * 2020 Taku Fukada +*/ + +#include <math.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/objint.h" +#include "py/runtime.h" +#include "py/builtin.h" +#include "py/misc.h" + +#include "../ulab.h" +#include "../ulab_tools.h" +#include "./carray/carray_tools.h" +#include "numerical.h" + +enum NUMERICAL_FUNCTION_TYPE { + NUMERICAL_ALL, + NUMERICAL_ANY, + NUMERICAL_ARGMAX, + NUMERICAL_ARGMIN, + NUMERICAL_MAX, + NUMERICAL_MEAN, + NUMERICAL_MIN, + NUMERICAL_STD, + NUMERICAL_SUM, +}; + +//| """Numerical and Statistical functions +//| +//| Most of these functions take an "axis" argument, which indicates whether to +//| operate over the flattened array (None), or a particular axis (integer).""" +//| +//| from typing import Dict +//| +//| _ArrayLike = Union[ndarray, List[_float], Tuple[_float], range] +//| +//| _DType = int +//| """`ulab.numpy.int8`, `ulab.numpy.uint8`, `ulab.numpy.int16`, `ulab.numpy.uint16`, `ulab.numpy.float` or `ulab.numpy.bool`""" +//| +//| from builtins import float as _float +//| from builtins import bool as _bool +//| +//| int8: _DType +//| """Type code for signed integers in the range -128 .. 127 inclusive, like the 'b' typecode of `array.array`""" +//| +//| int16: _DType +//| """Type code for signed integers in the range -32768 .. 32767 inclusive, like the 'h' typecode of `array.array`""" +//| +//| float: _DType +//| """Type code for floating point values, like the 'f' typecode of `array.array`""" +//| +//| uint8: _DType +//| """Type code for unsigned integers in the range 0 .. 255 inclusive, like the 'H' typecode of `array.array`""" +//| +//| uint16: _DType +//| """Type code for unsigned integers in the range 0 .. 65535 inclusive, like the 'h' typecode of `array.array`""" +//| +//| bool: _DType +//| """Type code for boolean values""" +//| + +static void numerical_reduce_axes(ndarray_obj_t *ndarray, int8_t axis, size_t *shape, int32_t *strides) { + // removes the values corresponding to a single axis from the shape and strides array + uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + axis; + if((ndarray->ndim == 1) && (axis == 0)) { + index = 0; + shape[ULAB_MAX_DIMS - 1] = 1; + return; + } + for(uint8_t i = ULAB_MAX_DIMS - 1; i > 0; i--) { + if(i > index) { + shape[i] = ndarray->shape[i]; + strides[i] = ndarray->strides[i]; + } else { + shape[i] = ndarray->shape[i-1]; + strides[i] = ndarray->strides[i-1]; + } + } +} + +#if ULAB_NUMPY_HAS_ALL | ULAB_NUMPY_HAS_ANY +static mp_obj_t numerical_all_any(mp_obj_t oin, mp_obj_t axis, uint8_t optype) { + bool anytype = optype == NUMERICAL_ALL ? 1 : 0; + if(mp_obj_is_type(oin, &ulab_ndarray_type)) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(oin); + uint8_t *array = (uint8_t *)ndarray->array; + if(ndarray->len == 0) { // return immediately with empty arrays + if(optype == NUMERICAL_ALL) { + return mp_const_true; + } else { + return mp_const_false; + } + } + // always get a float, so that we don't have to resolve the dtype later + mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype); + ndarray_obj_t *results = NULL; + uint8_t *rarray = NULL; + shape_strides _shape_strides = tools_reduce_axes(ndarray, axis); + if(axis != mp_const_none) { + results = ndarray_new_dense_ndarray(_shape_strides.ndim, _shape_strides.shape, NDARRAY_BOOL); + rarray = results->array; + if(optype == NUMERICAL_ALL) { + memset(rarray, 1, results->len); + } + } + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + if(axis == mp_const_none) { + do { + #if ULAB_SUPPORTS_COMPLEX + if(ndarray->dtype == NDARRAY_COMPLEX) { + mp_float_t real = *((mp_float_t *)array); + mp_float_t imag = *((mp_float_t *)(array + sizeof(mp_float_t))); + if(((real != MICROPY_FLOAT_CONST(0.0)) | (imag != MICROPY_FLOAT_CONST(0.0))) & !anytype) { + // optype = NUMERICAL_ANY + return mp_const_true; + } else if(((real == MICROPY_FLOAT_CONST(0.0)) & (imag == MICROPY_FLOAT_CONST(0.0))) & anytype) { + // optype == NUMERICAL_ALL + return mp_const_false; + } + } else { + #endif + mp_float_t value = func(array); + if((value != MICROPY_FLOAT_CONST(0.0)) & !anytype) { + // optype = NUMERICAL_ANY + return mp_const_true; + } else if((value == MICROPY_FLOAT_CONST(0.0)) & anytype) { + // optype == NUMERICAL_ALL + return mp_const_false; + } + #if ULAB_SUPPORTS_COMPLEX + } + #endif + array += _shape_strides.strides[0]; + l++; + } while(l < _shape_strides.shape[0]); + } else { // a scalar axis keyword was supplied + do { + #if ULAB_SUPPORTS_COMPLEX + if(ndarray->dtype == NDARRAY_COMPLEX) { + mp_float_t real = *((mp_float_t *)array); + mp_float_t imag = *((mp_float_t *)(array + sizeof(mp_float_t))); + if(((real != MICROPY_FLOAT_CONST(0.0)) | (imag != MICROPY_FLOAT_CONST(0.0))) & !anytype) { + // optype = NUMERICAL_ANY + *rarray = 1; + // since we are breaking out of the loop, move the pointer forward + array += _shape_strides.strides[0] * (_shape_strides.shape[0] - l); + break; + } else if(((real == MICROPY_FLOAT_CONST(0.0)) & (imag == MICROPY_FLOAT_CONST(0.0))) & anytype) { + // optype == NUMERICAL_ALL + *rarray = 0; + // since we are breaking out of the loop, move the pointer forward + array += _shape_strides.strides[0] * (_shape_strides.shape[0] - l); + break; + } + } else { + #endif + mp_float_t value = func(array); + if((value != MICROPY_FLOAT_CONST(0.0)) & !anytype) { + // optype == NUMERICAL_ANY + *rarray = 1; + // since we are breaking out of the loop, move the pointer forward + array += _shape_strides.strides[0] * (_shape_strides.shape[0] - l); + break; + } else if((value == MICROPY_FLOAT_CONST(0.0)) & anytype) { + // optype == NUMERICAL_ALL + *rarray = 0; + // since we are breaking out of the loop, move the pointer forward + array += _shape_strides.strides[0] * (_shape_strides.shape[0] - l); + break; + } + #if ULAB_SUPPORTS_COMPLEX + } + #endif + array += _shape_strides.strides[0]; + l++; + } while(l < _shape_strides.shape[0]); + } + #if ULAB_MAX_DIMS > 1 + rarray += _shape_strides.increment; + array -= _shape_strides.strides[0] * _shape_strides.shape[0]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 1]; + k++; + } while(k < _shape_strides.shape[ULAB_MAX_DIMS - 1]); + #endif + #if ULAB_MAX_DIMS > 2 + array -= _shape_strides.strides[ULAB_MAX_DIMS - 1] * _shape_strides.shape[ULAB_MAX_DIMS - 1]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 2]; + j++; + } while(j < _shape_strides.shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 3 + array -= _shape_strides.strides[ULAB_MAX_DIMS - 2] * _shape_strides.shape[ULAB_MAX_DIMS - 2]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 3]; + i++; + } while(i < _shape_strides.shape[ULAB_MAX_DIMS - 3]); + #endif + if(axis == mp_const_none) { + // the innermost loop fell through, so return the result here + if(!anytype) { + return mp_const_false; + } else { + return mp_const_true; + } + } + return results; + } else if(mp_obj_is_int(oin) || mp_obj_is_float(oin)) { + return mp_obj_is_true(oin) ? mp_const_true : mp_const_false; + } else { + mp_obj_iter_buf_t iter_buf; + mp_obj_t item, iterable = mp_getiter(oin, &iter_buf); + while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + if(!mp_obj_is_true(item) & !anytype) { + return mp_const_false; + } else if(mp_obj_is_true(item) & anytype) { + return mp_const_true; + } + } + } + return anytype ? mp_const_true : mp_const_false; +} +#endif + +#if ULAB_NUMPY_HAS_SUM | ULAB_NUMPY_HAS_MEAN | ULAB_NUMPY_HAS_STD +static mp_obj_t numerical_sum_mean_std_iterable(mp_obj_t oin, uint8_t optype, size_t ddof) { + mp_float_t value = MICROPY_FLOAT_CONST(0.0); + mp_float_t M = MICROPY_FLOAT_CONST(0.0); + mp_float_t m = MICROPY_FLOAT_CONST(0.0); + mp_float_t S = MICROPY_FLOAT_CONST(0.0); + mp_float_t s = MICROPY_FLOAT_CONST(0.0); + size_t count = 0; + mp_obj_iter_buf_t iter_buf; + mp_obj_t item, iterable = mp_getiter(oin, &iter_buf); + while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + value = mp_obj_get_float(item); + m = M + (value - M) / (count + 1); + s = S + (value - M) * (value - m); + M = m; + S = s; + count++; + } + if(optype == NUMERICAL_SUM) { + return mp_obj_new_float(m * count); + } else if(optype == NUMERICAL_MEAN) { + return count > 0 ? mp_obj_new_float(m) : mp_obj_new_float(MICROPY_FLOAT_CONST(0.0)); + } else { // this should be the case of the standard deviation + return count > ddof ? mp_obj_new_float(MICROPY_FLOAT_C_FUN(sqrt)(s / (count - ddof))) : mp_obj_new_float(MICROPY_FLOAT_CONST(0.0)); + } +} + +static mp_obj_t numerical_sum_mean_std_ndarray(ndarray_obj_t *ndarray, mp_obj_t axis, uint8_t optype, size_t ddof) { + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + uint8_t *array = (uint8_t *)ndarray->array; + shape_strides _shape_strides = tools_reduce_axes(ndarray, axis); + + if(axis == mp_const_none) { + // work with the flattened array + if((optype == NUMERICAL_STD) && (ddof > ndarray->len)) { + // if there are too many degrees of freedom, there is no point in calculating anything + return mp_obj_new_float(MICROPY_FLOAT_CONST(0.0)); + } + mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype); + mp_float_t M = MICROPY_FLOAT_CONST(0.0); + mp_float_t m = MICROPY_FLOAT_CONST(0.0); + mp_float_t S = MICROPY_FLOAT_CONST(0.0); + mp_float_t s = MICROPY_FLOAT_CONST(0.0); + size_t count = 0; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + count++; + mp_float_t value = func(array); + m = M + (value - M) / (mp_float_t)count; + if(optype == NUMERICAL_STD) { + s = S + (value - M) * (value - m); + S = s; + } + M = m; + array += _shape_strides.strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < _shape_strides.shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + array -= _shape_strides.strides[ULAB_MAX_DIMS - 1] * _shape_strides.shape[ULAB_MAX_DIMS - 1]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < _shape_strides.shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + array -= _shape_strides.strides[ULAB_MAX_DIMS - 2] * _shape_strides.shape[ULAB_MAX_DIMS - 2]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < _shape_strides.shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + array -= _shape_strides.strides[ULAB_MAX_DIMS - 3] * _shape_strides.shape[ULAB_MAX_DIMS - 3]; + array += _shape_strides.strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < _shape_strides.shape[ULAB_MAX_DIMS - 4]); + #endif + if(optype == NUMERICAL_SUM) { + // numpy returns an integer for integer input types + if(ndarray->dtype == NDARRAY_FLOAT) { + return mp_obj_new_float(M * ndarray->len); + } else { + return mp_obj_new_int((int32_t)MICROPY_FLOAT_C_FUN(round)(M * ndarray->len)); + } + } else if(optype == NUMERICAL_MEAN) { + return mp_obj_new_float(M); + } else { // this must be the case of the standard deviation + // we have already made certain that ddof < ndarray->len holds + return mp_obj_new_float(MICROPY_FLOAT_C_FUN(sqrt)(S / (ndarray->len - ddof))); + } + } else { + ndarray_obj_t *results = NULL; + uint8_t *rarray = NULL; + mp_float_t *farray = NULL; + if(optype == NUMERICAL_SUM) { + results = ndarray_new_dense_ndarray(_shape_strides.ndim, _shape_strides.shape, ndarray->dtype); + rarray = (uint8_t *)results->array; + // TODO: numpy promotes the output to the highest integer type + if(ndarray->dtype == NDARRAY_UINT8) { + RUN_SUM(uint8_t, array, results, rarray, _shape_strides); + } else if(ndarray->dtype == NDARRAY_INT8) { + RUN_SUM(int8_t, array, results, rarray, _shape_strides); + } else if(ndarray->dtype == NDARRAY_UINT16) { + RUN_SUM(uint16_t, array, results, rarray, _shape_strides); + } else if(ndarray->dtype == NDARRAY_INT16) { + RUN_SUM(int16_t, array, results, rarray, _shape_strides); + } else { + // for floats, the sum might be inaccurate with the naive summation + // call mean, and multiply with the number of samples + farray = (mp_float_t *)results->array; + RUN_MEAN_STD(mp_float_t, array, farray, _shape_strides, MICROPY_FLOAT_CONST(0.0), 0); + mp_float_t norm = (mp_float_t)_shape_strides.shape[0]; + // re-wind the array here + farray = (mp_float_t *)results->array; + for(size_t i=0; i < results->len; i++) { + *farray++ *= norm; + } + } + } else { + bool isStd = optype == NUMERICAL_STD ? 1 : 0; + results = ndarray_new_dense_ndarray(_shape_strides.ndim, _shape_strides.shape, NDARRAY_FLOAT); + farray = (mp_float_t *)results->array; + // we can return the 0 array here, if the degrees of freedom is larger than the length of the axis + if((optype == NUMERICAL_STD) && (_shape_strides.shape[0] <= ddof)) { + return MP_OBJ_FROM_PTR(results); + } + mp_float_t div = optype == NUMERICAL_STD ? (mp_float_t)(_shape_strides.shape[0] - ddof) : MICROPY_FLOAT_CONST(0.0); + if(ndarray->dtype == NDARRAY_UINT8) { + RUN_MEAN_STD(uint8_t, array, farray, _shape_strides, div, isStd); + } else if(ndarray->dtype == NDARRAY_INT8) { + RUN_MEAN_STD(int8_t, array, farray, _shape_strides, div, isStd); + } else if(ndarray->dtype == NDARRAY_UINT16) { + RUN_MEAN_STD(uint16_t, array, farray, _shape_strides, div, isStd); + } else if(ndarray->dtype == NDARRAY_INT16) { + RUN_MEAN_STD(int16_t, array, farray, _shape_strides, div, isStd); + } else { + RUN_MEAN_STD(mp_float_t, array, farray, _shape_strides, div, isStd); + } + } + if(results->ndim == 0) { // return a scalar here + return mp_binary_get_val_array(results->dtype, results->array, 0); + } + return MP_OBJ_FROM_PTR(results); + } + return mp_const_none; +} +#endif + +#if ULAB_NUMPY_HAS_ARGMINMAX +static mp_obj_t numerical_argmin_argmax_iterable(mp_obj_t oin, uint8_t optype) { + if(MP_OBJ_SMALL_INT_VALUE(mp_obj_len_maybe(oin)) == 0) { + mp_raise_ValueError(translate("attempt to get argmin/argmax of an empty sequence")); + } + size_t idx = 0, best_idx = 0; + mp_obj_iter_buf_t iter_buf; + mp_obj_t iterable = mp_getiter(oin, &iter_buf); + mp_obj_t item; + uint8_t op = 0; // argmin, min + if((optype == NUMERICAL_ARGMAX) || (optype == NUMERICAL_MAX)) op = 1; + item = mp_iternext(iterable); + mp_obj_t best_obj = item; + mp_float_t value, best_value = mp_obj_get_float(item); + value = best_value; + while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + idx++; + value = mp_obj_get_float(item); + if((op == 0) && (value < best_value)) { + best_obj = item; + best_idx = idx; + best_value = value; + } else if((op == 1) && (value > best_value)) { + best_obj = item; + best_idx = idx; + best_value = value; + } + } + if((optype == NUMERICAL_ARGMIN) || (optype == NUMERICAL_ARGMAX)) { + return MP_OBJ_NEW_SMALL_INT(best_idx); + } else { + return best_obj; + } +} + +static mp_obj_t numerical_argmin_argmax_ndarray(ndarray_obj_t *ndarray, mp_obj_t axis, uint8_t optype) { + // TODO: treat the flattened array + if(ndarray->len == 0) { + mp_raise_ValueError(translate("attempt to get (arg)min/(arg)max of empty sequence")); + } + + if(axis == mp_const_none) { + // work with the flattened array + mp_float_t (*func)(void *) = ndarray_get_float_function(ndarray->dtype); + uint8_t *array = (uint8_t *)ndarray->array; + mp_float_t best_value = func(array); + mp_float_t value; + size_t index = 0, best_index = 0; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + value = func(array); + if((optype == NUMERICAL_ARGMAX) || (optype == NUMERICAL_MAX)) { + if(best_value < value) { + best_value = value; + best_index = index; + } + } else { + if(best_value > value) { + best_value = value; + best_index = index; + } + } + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + l++; + index++; + } while(l < ndarray->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + array -= ndarray->strides[ULAB_MAX_DIMS - 1] * ndarray->shape[ULAB_MAX_DIMS-1]; + array += ndarray->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < ndarray->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + array -= ndarray->strides[ULAB_MAX_DIMS - 2] * ndarray->shape[ULAB_MAX_DIMS-2]; + array += ndarray->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < ndarray->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + array -= ndarray->strides[ULAB_MAX_DIMS - 3] * ndarray->shape[ULAB_MAX_DIMS-3]; + array += ndarray->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < ndarray->shape[ULAB_MAX_DIMS - 4]); + #endif + + if((optype == NUMERICAL_ARGMIN) || (optype == NUMERICAL_ARGMAX)) { + return mp_obj_new_int(best_index); + } else { + if(ndarray->dtype == NDARRAY_FLOAT) { + return mp_obj_new_float(best_value); + } else { + return MP_OBJ_NEW_SMALL_INT((int32_t)best_value); + } + } + } else { + int8_t ax = tools_get_axis(axis, ndarray->ndim); + + uint8_t *array = (uint8_t *)ndarray->array; + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS); + numerical_reduce_axes(ndarray, ax, shape, strides); + uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + ax; + + ndarray_obj_t *results = NULL; + + if((optype == NUMERICAL_ARGMIN) || (optype == NUMERICAL_ARGMAX)) { + results = ndarray_new_dense_ndarray(MAX(1, ndarray->ndim-1), shape, NDARRAY_INT16); + } else { + results = ndarray_new_dense_ndarray(MAX(1, ndarray->ndim-1), shape, ndarray->dtype); + } + + uint8_t *rarray = (uint8_t *)results->array; + + if(ndarray->dtype == NDARRAY_UINT8) { + RUN_ARGMIN(ndarray, uint8_t, array, results, rarray, shape, strides, index, optype); + } else if(ndarray->dtype == NDARRAY_INT8) { + RUN_ARGMIN(ndarray, int8_t, array, results, rarray, shape, strides, index, optype); + } else if(ndarray->dtype == NDARRAY_UINT16) { + RUN_ARGMIN(ndarray, uint16_t, array, results, rarray, shape, strides, index, optype); + } else if(ndarray->dtype == NDARRAY_INT16) { + RUN_ARGMIN(ndarray, int16_t, array, results, rarray, shape, strides, index, optype); + } else { + RUN_ARGMIN(ndarray, mp_float_t, array, results, rarray, shape, strides, index, optype); + } + if(results->len == 1) { + return mp_binary_get_val_array(results->dtype, results->array, 0); + } + return MP_OBJ_FROM_PTR(results); + } + return mp_const_none; +} +#endif + +static mp_obj_t numerical_function(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args, uint8_t optype) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none} } , + { MP_QSTR_axis, MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t oin = args[0].u_obj; + mp_obj_t axis = args[1].u_obj; + if((axis != mp_const_none) && (!mp_obj_is_int(axis))) { + mp_raise_TypeError(translate("axis must be None, or an integer")); + } + + if((optype == NUMERICAL_ALL) || (optype == NUMERICAL_ANY)) { + return numerical_all_any(oin, axis, optype); + } + if(mp_obj_is_type(oin, &mp_type_tuple) || mp_obj_is_type(oin, &mp_type_list) || + mp_obj_is_type(oin, &mp_type_range)) { + switch(optype) { + case NUMERICAL_MIN: + case NUMERICAL_ARGMIN: + case NUMERICAL_MAX: + case NUMERICAL_ARGMAX: + return numerical_argmin_argmax_iterable(oin, optype); + case NUMERICAL_SUM: + case NUMERICAL_MEAN: + return numerical_sum_mean_std_iterable(oin, optype, 0); + default: // we should never reach this point, but whatever + return mp_const_none; + } + } else if(mp_obj_is_type(oin, &ulab_ndarray_type)) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(oin); + switch(optype) { + case NUMERICAL_MIN: + case NUMERICAL_MAX: + case NUMERICAL_ARGMIN: + case NUMERICAL_ARGMAX: + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + return numerical_argmin_argmax_ndarray(ndarray, axis, optype); + case NUMERICAL_SUM: + case NUMERICAL_MEAN: + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + return numerical_sum_mean_std_ndarray(ndarray, axis, optype, 0); + default: + mp_raise_NotImplementedError(translate("operation is not implemented on ndarrays")); + } + } else { + mp_raise_TypeError(translate("input must be tuple, list, range, or ndarray")); + } + return mp_const_none; +} + +#if ULAB_NUMPY_HAS_SORT | NDARRAY_HAS_SORT +static mp_obj_t numerical_sort_helper(mp_obj_t oin, mp_obj_t axis, uint8_t inplace) { + if(!mp_obj_is_type(oin, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("sort argument must be an ndarray")); + } + + ndarray_obj_t *ndarray; + if(inplace == 1) { + ndarray = MP_OBJ_TO_PTR(oin); + } else { + ndarray = ndarray_copy_view(MP_OBJ_TO_PTR(oin)); + } + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + + int8_t ax = 0; + if(axis == mp_const_none) { + // flatten the array + #if ULAB_MAX_DIMS > 1 + for(uint8_t i=0; i < ULAB_MAX_DIMS - 1; i++) { + ndarray->shape[i] = 0; + ndarray->strides[i] = 0; + } + ndarray->shape[ULAB_MAX_DIMS - 1] = ndarray->len; + ndarray->strides[ULAB_MAX_DIMS - 1] = ndarray->itemsize; + ndarray->ndim = 1; + #endif + } else { + ax = tools_get_axis(axis, ndarray->ndim); + } + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS); + numerical_reduce_axes(ndarray, ax, shape, strides); + ax = ULAB_MAX_DIMS - ndarray->ndim + ax; + // we work with the typed array, so re-scale the stride + int32_t increment = ndarray->strides[ax] / ndarray->itemsize; + + uint8_t *array = (uint8_t *)ndarray->array; + if((ndarray->dtype == NDARRAY_UINT8) || (ndarray->dtype == NDARRAY_INT8)) { + HEAPSORT(ndarray, uint8_t, array, shape, strides, ax, increment, ndarray->shape[ax]); + } else if((ndarray->dtype == NDARRAY_INT16) || (ndarray->dtype == NDARRAY_INT16)) { + HEAPSORT(ndarray, uint16_t, array, shape, strides, ax, increment, ndarray->shape[ax]); + } else { + HEAPSORT(ndarray, mp_float_t, array, shape, strides, ax, increment, ndarray->shape[ax]); + } + if(inplace == 1) { + return mp_const_none; + } else { + return MP_OBJ_FROM_PTR(ndarray); + } +} +#endif /* ULAB_NUMERICAL_HAS_SORT | NDARRAY_HAS_SORT */ + +#if ULAB_NUMPY_HAS_ALL +mp_obj_t numerical_all(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return numerical_function(n_args, pos_args, kw_args, NUMERICAL_ALL); +} +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_all_obj, 1, numerical_all); +#endif + +#if ULAB_NUMPY_HAS_ANY +mp_obj_t numerical_any(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return numerical_function(n_args, pos_args, kw_args, NUMERICAL_ANY); +} +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_any_obj, 1, numerical_any); +#endif + +#if ULAB_NUMPY_HAS_ARGMINMAX +//| def argmax(array: _ArrayLike, *, axis: Optional[int] = None) -> int: +//| """Return the index of the maximum element of the 1D array""" +//| ... +//| + +mp_obj_t numerical_argmax(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return numerical_function(n_args, pos_args, kw_args, NUMERICAL_ARGMAX); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_argmax_obj, 1, numerical_argmax); + +//| def argmin(array: _ArrayLike, *, axis: Optional[int] = None) -> int: +//| """Return the index of the minimum element of the 1D array""" +//| ... +//| + +static mp_obj_t numerical_argmin(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return numerical_function(n_args, pos_args, kw_args, NUMERICAL_ARGMIN); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_argmin_obj, 1, numerical_argmin); +#endif + +#if ULAB_NUMPY_HAS_ARGSORT +//| def argsort(array: ulab.numpy.ndarray, *, axis: int = -1) -> ulab.numpy.ndarray: +//| """Returns an array which gives indices into the input array from least to greatest.""" +//| ... +//| + +mp_obj_t numerical_argsort(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + }; + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("argsort argument must be an ndarray")); + } + + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + if(args[1].u_obj == mp_const_none) { + // bail out, though dense arrays could still be sorted + mp_raise_NotImplementedError(translate("argsort is not implemented for flattened arrays")); + } + // Since we are returning an NDARRAY_UINT16 array, bail out, + // if the axis is longer than what we can hold + for(uint8_t i=0; i < ULAB_MAX_DIMS; i++) { + if(ndarray->shape[i] > 65535) { + mp_raise_ValueError(translate("axis too long")); + } + } + int8_t ax = tools_get_axis(args[1].u_obj, ndarray->ndim); + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS); + numerical_reduce_axes(ndarray, ax, shape, strides); + + // We could return an NDARRAY_UINT8 array, if all lengths are shorter than 256 + ndarray_obj_t *indices = ndarray_new_ndarray(ndarray->ndim, ndarray->shape, NULL, NDARRAY_UINT16); + int32_t *istrides = m_new(int32_t, ULAB_MAX_DIMS); + memset(istrides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS); + numerical_reduce_axes(indices, ax, shape, istrides); + for(uint8_t i=0; i < ULAB_MAX_DIMS; i++) { + istrides[i] /= sizeof(uint16_t); + } + + ax = ULAB_MAX_DIMS - ndarray->ndim + ax; + // we work with the typed array, so re-scale the stride + int32_t increment = ndarray->strides[ax] / ndarray->itemsize; + uint16_t iincrement = indices->strides[ax] / sizeof(uint16_t); + + uint8_t *array = (uint8_t *)ndarray->array; + uint16_t *iarray = (uint16_t *)indices->array; + + // fill in the index values + #if ULAB_MAX_DIMS > 3 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t k = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t l = 0; + do { + #endif + uint16_t m = 0; + do { + *iarray = m++; + iarray += iincrement; + } while(m < indices->shape[ax]); + #if ULAB_MAX_DIMS > 1 + iarray -= iincrement * indices->shape[ax]; + iarray += istrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < shape[ULAB_MAX_DIMS - 1]); + iarray -= istrides[ULAB_MAX_DIMS - 1] * shape[ULAB_MAX_DIMS - 1]; + iarray += istrides[ULAB_MAX_DIMS - 2]; + #endif + #if ULAB_MAX_DIMS > 2 + k++; + } while(k < shape[ULAB_MAX_DIMS - 2]); + iarray -= istrides[ULAB_MAX_DIMS - 2] * shape[ULAB_MAX_DIMS - 2]; + iarray += istrides[ULAB_MAX_DIMS - 3]; + #endif + #if ULAB_MAX_DIMS > 3 + j++; + } while(j < shape[ULAB_MAX_DIMS - 3]); + #endif + // reset the array + iarray = indices->array; + + if((ndarray->dtype == NDARRAY_UINT8) || (ndarray->dtype == NDARRAY_INT8)) { + HEAP_ARGSORT(ndarray, uint8_t, array, shape, strides, ax, increment, ndarray->shape[ax], iarray, istrides, iincrement); + } else if((ndarray->dtype == NDARRAY_UINT16) || (ndarray->dtype == NDARRAY_INT16)) { + HEAP_ARGSORT(ndarray, uint16_t, array, shape, strides, ax, increment, ndarray->shape[ax], iarray, istrides, iincrement); + } else { + HEAP_ARGSORT(ndarray, mp_float_t, array, shape, strides, ax, increment, ndarray->shape[ax], iarray, istrides, iincrement); + } + return MP_OBJ_FROM_PTR(indices); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_argsort_obj, 1, numerical_argsort); +#endif + +#if ULAB_NUMPY_HAS_CROSS +//| def cross(a: ulab.numpy.ndarray, b: ulab.numpy.ndarray) -> ulab.numpy.ndarray: +//| """Return the cross product of two vectors of length 3""" +//| ... +//| + +static mp_obj_t numerical_cross(mp_obj_t _a, mp_obj_t _b) { + if (!mp_obj_is_type(_a, &ulab_ndarray_type) || !mp_obj_is_type(_b, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("arguments must be ndarrays")); + } + ndarray_obj_t *a = MP_OBJ_TO_PTR(_a); + ndarray_obj_t *b = MP_OBJ_TO_PTR(_b); + COMPLEX_DTYPE_NOT_IMPLEMENTED(a->dtype) + COMPLEX_DTYPE_NOT_IMPLEMENTED(b->dtype) + if((a->ndim != 1) || (b->ndim != 1) || (a->len != b->len) || (a->len != 3)) { + mp_raise_ValueError(translate("cross is defined for 1D arrays of length 3")); + } + + mp_float_t *results = m_new(mp_float_t, 3); + results[0] = ndarray_get_float_index(a->array, a->dtype, 1) * ndarray_get_float_index(b->array, b->dtype, 2); + results[0] -= ndarray_get_float_index(a->array, a->dtype, 2) * ndarray_get_float_index(b->array, b->dtype, 1); + results[1] = -ndarray_get_float_index(a->array, a->dtype, 0) * ndarray_get_float_index(b->array, b->dtype, 2); + results[1] += ndarray_get_float_index(a->array, a->dtype, 2) * ndarray_get_float_index(b->array, b->dtype, 0); + results[2] = ndarray_get_float_index(a->array, a->dtype, 0) * ndarray_get_float_index(b->array, b->dtype, 1); + results[2] -= ndarray_get_float_index(a->array, a->dtype, 1) * ndarray_get_float_index(b->array, b->dtype, 0); + + /* The upcasting happens here with the rules + + - if one of the operarands is a float, the result is always float + - operation on identical types preserves type + + uint8 + int8 => int16 + uint8 + int16 => int16 + uint8 + uint16 => uint16 + int8 + int16 => int16 + int8 + uint16 => uint16 + uint16 + int16 => float + + */ + + uint8_t dtype = NDARRAY_FLOAT; + if(a->dtype == b->dtype) { + dtype = a->dtype; + } else if(((a->dtype == NDARRAY_UINT8) && (b->dtype == NDARRAY_INT8)) || ((a->dtype == NDARRAY_INT8) && (b->dtype == NDARRAY_UINT8))) { + dtype = NDARRAY_INT16; + } else if(((a->dtype == NDARRAY_UINT8) && (b->dtype == NDARRAY_INT16)) || ((a->dtype == NDARRAY_INT16) && (b->dtype == NDARRAY_UINT8))) { + dtype = NDARRAY_INT16; + } else if(((a->dtype == NDARRAY_UINT8) && (b->dtype == NDARRAY_UINT16)) || ((a->dtype == NDARRAY_UINT16) && (b->dtype == NDARRAY_UINT8))) { + dtype = NDARRAY_UINT16; + } else if(((a->dtype == NDARRAY_INT8) && (b->dtype == NDARRAY_INT16)) || ((a->dtype == NDARRAY_INT16) && (b->dtype == NDARRAY_INT8))) { + dtype = NDARRAY_INT16; + } else if(((a->dtype == NDARRAY_INT8) && (b->dtype == NDARRAY_UINT16)) || ((a->dtype == NDARRAY_UINT16) && (b->dtype == NDARRAY_INT8))) { + dtype = NDARRAY_UINT16; + } + + ndarray_obj_t *ndarray = ndarray_new_linear_array(3, dtype); + if(dtype == NDARRAY_UINT8) { + uint8_t *array = (uint8_t *)ndarray->array; + for(uint8_t i=0; i < 3; i++) array[i] = (uint8_t)results[i]; + } else if(dtype == NDARRAY_INT8) { + int8_t *array = (int8_t *)ndarray->array; + for(uint8_t i=0; i < 3; i++) array[i] = (int8_t)results[i]; + } else if(dtype == NDARRAY_UINT16) { + uint16_t *array = (uint16_t *)ndarray->array; + for(uint8_t i=0; i < 3; i++) array[i] = (uint16_t)results[i]; + } else if(dtype == NDARRAY_INT16) { + int16_t *array = (int16_t *)ndarray->array; + for(uint8_t i=0; i < 3; i++) array[i] = (int16_t)results[i]; + } else { + mp_float_t *array = (mp_float_t *)ndarray->array; + for(uint8_t i=0; i < 3; i++) array[i] = results[i]; + } + m_del(mp_float_t, results, 3); + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_2(numerical_cross_obj, numerical_cross); + +#endif /* ULAB_NUMERICAL_HAS_CROSS */ + +#if ULAB_NUMPY_HAS_DIFF +//| def diff(array: ulab.numpy.ndarray, *, n: int = 1, axis: int = -1) -> ulab.numpy.ndarray: +//| """Return the numerical derivative of successive elements of the array, as +//| an array. axis=None is not supported.""" +//| ... +//| + +mp_obj_t numerical_diff(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_n, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 1 } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = -1 } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("diff argument must be an ndarray")); + } + + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + int8_t ax = args[2].u_int; + if(ax < 0) ax += ndarray->ndim; + + if((ax < 0) || (ax > ndarray->ndim - 1)) { + mp_raise_ValueError(translate("index out of range")); + } + + if((args[1].u_int < 0) || (args[1].u_int > 9)) { + mp_raise_ValueError(translate("differentiation order out of range")); + } + uint8_t N = (uint8_t)args[1].u_int; + uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + ax; + if(N > ndarray->shape[index]) { + mp_raise_ValueError(translate("differentiation order out of range")); + } + + int8_t *stencil = m_new(int8_t, N+1); + stencil[0] = 1; + for(uint8_t i=1; i < N+1; i++) { + stencil[i] = -stencil[i-1]*(N-i+1)/i; + } + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + for(uint8_t i=0; i < ULAB_MAX_DIMS; i++) { + shape[i] = ndarray->shape[i]; + if(i == index) { + shape[i] -= N; + } + } + uint8_t *array = (uint8_t *)ndarray->array; + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim, shape, ndarray->dtype); + uint8_t *rarray = (uint8_t *)results->array; + + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memset(strides, 0, sizeof(int32_t)*ULAB_MAX_DIMS); + numerical_reduce_axes(ndarray, ax, shape, strides); + + if(ndarray->dtype == NDARRAY_UINT8) { + RUN_DIFF(ndarray, uint8_t, array, results, rarray, shape, strides, index, stencil, N); + } else if(ndarray->dtype == NDARRAY_INT8) { + RUN_DIFF(ndarray, int8_t, array, results, rarray, shape, strides, index, stencil, N); + } else if(ndarray->dtype == NDARRAY_UINT16) { + RUN_DIFF(ndarray, uint16_t, array, results, rarray, shape, strides, index, stencil, N); + } else if(ndarray->dtype == NDARRAY_INT16) { + RUN_DIFF(ndarray, int16_t, array, results, rarray, shape, strides, index, stencil, N); + } else { + RUN_DIFF(ndarray, mp_float_t, array, results, rarray, shape, strides, index, stencil, N); + } + m_del(int8_t, stencil, N+1); + m_del(size_t, shape, ULAB_MAX_DIMS); + m_del(int32_t, strides, ULAB_MAX_DIMS); + return MP_OBJ_FROM_PTR(results); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_diff_obj, 1, numerical_diff); +#endif + +#if ULAB_NUMPY_HAS_FLIP +//| def flip(array: ulab.numpy.ndarray, *, axis: Optional[int] = None) -> ulab.numpy.ndarray: +//| """Returns a new array that reverses the order of the elements along the +//| given axis, or along all axes if axis is None.""" +//| ... +//| + +mp_obj_t numerical_flip(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("flip argument must be an ndarray")); + } + + ndarray_obj_t *results = NULL; + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj); + if(args[1].u_obj == mp_const_none) { // flip the flattened array + results = ndarray_new_linear_array(ndarray->len, ndarray->dtype); + ndarray_copy_array(ndarray, results, 0); + uint8_t *rarray = (uint8_t *)results->array; + rarray += (results->len - 1) * results->itemsize; + results->array = rarray; + results->strides[ULAB_MAX_DIMS - 1] = -results->strides[ULAB_MAX_DIMS - 1]; + } else if(mp_obj_is_int(args[1].u_obj)){ + int8_t ax = tools_get_axis(args[1].u_obj, ndarray->ndim); + + ax = ULAB_MAX_DIMS - ndarray->ndim + ax; + int32_t offset = (ndarray->shape[ax] - 1) * ndarray->strides[ax]; + results = ndarray_new_view(ndarray, ndarray->ndim, ndarray->shape, ndarray->strides, offset); + results->strides[ax] = -results->strides[ax]; + } else { + mp_raise_TypeError(translate("wrong axis index")); + } + return results; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_flip_obj, 1, numerical_flip); +#endif + +#if ULAB_NUMPY_HAS_MINMAX +//| def max(array: _ArrayLike, *, axis: Optional[int] = None) -> _float: +//| """Return the maximum element of the 1D array""" +//| ... +//| + +mp_obj_t numerical_max(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return numerical_function(n_args, pos_args, kw_args, NUMERICAL_MAX); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_max_obj, 1, numerical_max); +#endif + +#if ULAB_NUMPY_HAS_MEAN +//| def mean(array: _ArrayLike, *, axis: Optional[int] = None) -> _float: +//| """Return the mean element of the 1D array, as a number if axis is None, otherwise as an array.""" +//| ... +//| + +mp_obj_t numerical_mean(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return numerical_function(n_args, pos_args, kw_args, NUMERICAL_MEAN); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_mean_obj, 1, numerical_mean); +#endif + +#if ULAB_NUMPY_HAS_MEDIAN +//| def median(array: ulab.numpy.ndarray, *, axis: int = -1) -> ulab.numpy.ndarray: +//| """Find the median value in an array along the given axis, or along all axes if axis is None.""" +//| ... +//| + +mp_obj_t numerical_median(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("median argument must be an ndarray")); + } + + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj); + if(ndarray->len == 0) { + return mp_obj_new_float(MICROPY_FLOAT_C_FUN(nan)("")); + } + + ndarray = numerical_sort_helper(args[0].u_obj, args[1].u_obj, 0); + + if((args[1].u_obj == mp_const_none) || (ndarray->ndim == 1)) { + // at this point, the array holding the sorted values should be flat + uint8_t *array = (uint8_t *)ndarray->array; + size_t len = ndarray->len; + array += (len >> 1) * ndarray->itemsize; + mp_float_t median = ndarray_get_float_value(array, ndarray->dtype); + if(!(len & 0x01)) { // len is an even number + array -= ndarray->itemsize; + median += ndarray_get_float_value(array, ndarray->dtype); + median *= MICROPY_FLOAT_CONST(0.5); + } + return mp_obj_new_float(median); + } else { + int8_t ax = tools_get_axis(args[1].u_obj, ndarray->ndim); + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS); + numerical_reduce_axes(ndarray, ax, shape, strides); + ax = ULAB_MAX_DIMS - ndarray->ndim + ax; + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim-1, shape, NDARRAY_FLOAT); + mp_float_t *rarray = (mp_float_t *)results->array; + + uint8_t *array = (uint8_t *)ndarray->array; + + size_t len = ndarray->shape[ax]; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + size_t k = 0; + do { + array += ndarray->strides[ax] * (len >> 1); + mp_float_t median = ndarray_get_float_value(array, ndarray->dtype); + if(!(len & 0x01)) { // len is an even number + array -= ndarray->strides[ax]; + median += ndarray_get_float_value(array, ndarray->dtype); + median *= MICROPY_FLOAT_CONST(0.5); + array += ndarray->strides[ax]; + } + array -= ndarray->strides[ax] * (len >> 1); + array += strides[ULAB_MAX_DIMS - 1]; + *rarray = median; + rarray++; + k++; + } while(k < shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 2 + array -= strides[ULAB_MAX_DIMS - 1] * shape[ULAB_MAX_DIMS - 1]; + array += strides[ULAB_MAX_DIMS - 2]; + j++; + } while(j < shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 3 + array -= strides[ULAB_MAX_DIMS - 2] * shape[ULAB_MAX_DIMS-2]; + array += strides[ULAB_MAX_DIMS - 3]; + i++; + } while(i < shape[ULAB_MAX_DIMS - 3]); + #endif + + return MP_OBJ_FROM_PTR(results); + } + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_median_obj, 1, numerical_median); +#endif + +#if ULAB_NUMPY_HAS_MINMAX +//| def min(array: _ArrayLike, *, axis: Optional[int] = None) -> _float: +//| """Return the minimum element of the 1D array""" +//| ... +//| + +mp_obj_t numerical_min(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return numerical_function(n_args, pos_args, kw_args, NUMERICAL_MIN); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_min_obj, 1, numerical_min); +#endif + +#if ULAB_NUMPY_HAS_ROLL +//| def roll(array: ulab.numpy.ndarray, distance: int, *, axis: Optional[int] = None) -> None: +//| """Shift the content of a vector by the positions given as the second +//| argument. If the ``axis`` keyword is supplied, the shift is applied to +//| the given axis. The array is modified in place.""" +//| ... +//| + +mp_obj_t numerical_roll(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("roll argument must be an ndarray")); + } + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0].u_obj); + uint8_t *array = ndarray->array; + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim, ndarray->shape, ndarray->dtype); + + int32_t shift = mp_obj_get_int(args[1].u_obj); + int32_t _shift = shift < 0 ? -shift : shift; + + size_t counter; + uint8_t *rarray = (uint8_t *)results->array; + + if(args[2].u_obj == mp_const_none) { // roll the flattened array + _shift = _shift % results->len; + if(shift > 0) { // shift to the right + rarray += _shift * results->itemsize; + counter = results->len - _shift; + } else { // shift to the left + rarray += (results->len - _shift) * results->itemsize; + counter = _shift; + } + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + memcpy(rarray, array, ndarray->itemsize); + rarray += results->itemsize; + array += ndarray->strides[ULAB_MAX_DIMS - 1]; + l++; + if(--counter == 0) { + rarray = results->array; + } + } while(l < ndarray->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + array -= ndarray->strides[ULAB_MAX_DIMS - 1] * ndarray->shape[ULAB_MAX_DIMS-1]; + array += ndarray->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < ndarray->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + array -= ndarray->strides[ULAB_MAX_DIMS - 2] * ndarray->shape[ULAB_MAX_DIMS-2]; + array += ndarray->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < ndarray->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + array -= ndarray->strides[ULAB_MAX_DIMS - 3] * ndarray->shape[ULAB_MAX_DIMS-3]; + array += ndarray->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < ndarray->shape[ULAB_MAX_DIMS - 4]); + #endif + } else if(mp_obj_is_int(args[2].u_obj)){ + int8_t ax = tools_get_axis(args[2].u_obj, ndarray->ndim); + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memset(strides, 0, sizeof(int32_t)*ULAB_MAX_DIMS); + numerical_reduce_axes(ndarray, ax, shape, strides); + + size_t *rshape = m_new(size_t, ULAB_MAX_DIMS); + memset(rshape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *rstrides = m_new(int32_t, ULAB_MAX_DIMS); + memset(rstrides, 0, sizeof(int32_t)*ULAB_MAX_DIMS); + numerical_reduce_axes(results, ax, rshape, rstrides); + + ax = ULAB_MAX_DIMS - ndarray->ndim + ax; + uint8_t *_rarray; + _shift = _shift % results->shape[ax]; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + _rarray = rarray; + if(shift < 0) { + rarray += (results->shape[ax] - _shift) * results->strides[ax]; + counter = _shift; + } else { + rarray += _shift * results->strides[ax]; + counter = results->shape[ax] - _shift; + } + do { + memcpy(rarray, array, ndarray->itemsize); + array += ndarray->strides[ax]; + rarray += results->strides[ax]; + if(--counter == 0) { + rarray = _rarray; + } + l++; + } while(l < ndarray->shape[ax]); + #if ULAB_MAX_DIMS > 1 + rarray = _rarray; + rarray += rstrides[ULAB_MAX_DIMS - 1]; + array -= ndarray->strides[ax] * ndarray->shape[ax]; + array += strides[ULAB_MAX_DIMS - 1]; + k++; + } while(k < shape[ULAB_MAX_DIMS - 1]); + #endif + #if ULAB_MAX_DIMS > 2 + rarray -= rstrides[ULAB_MAX_DIMS - 1] * rshape[ULAB_MAX_DIMS-1]; + rarray += rstrides[ULAB_MAX_DIMS - 2]; + array -= strides[ULAB_MAX_DIMS - 1] * shape[ULAB_MAX_DIMS-1]; + array += strides[ULAB_MAX_DIMS - 2]; + j++; + } while(j < shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 3 + rarray -= rstrides[ULAB_MAX_DIMS - 2] * rshape[ULAB_MAX_DIMS-2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + array -= strides[ULAB_MAX_DIMS - 2] * shape[ULAB_MAX_DIMS-2]; + array += strides[ULAB_MAX_DIMS - 3]; + i++; + } while(i < shape[ULAB_MAX_DIMS - 3]); + #endif + } else { + mp_raise_TypeError(translate("wrong axis index")); + } + return results; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_roll_obj, 2, numerical_roll); +#endif + +#if ULAB_NUMPY_HAS_SORT +//| def sort(array: ulab.numpy.ndarray, *, axis: int = -1) -> ulab.numpy.ndarray: +//| """Sort the array along the given axis, or along all axes if axis is None. +//| The array is modified in place.""" +//| ... +//| + +mp_obj_t numerical_sort(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + return numerical_sort_helper(args[0].u_obj, args[1].u_obj, 0); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_sort_obj, 1, numerical_sort); +#endif + +#if NDARRAY_HAS_SORT +// method of an ndarray +static mp_obj_t numerical_sort_inplace(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_int = -1 } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + return numerical_sort_helper(args[0].u_obj, args[1].u_obj, 1); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_sort_inplace_obj, 1, numerical_sort_inplace); +#endif /* NDARRAY_HAS_SORT */ + +#if ULAB_NUMPY_HAS_STD +//| def std(array: _ArrayLike, *, axis: Optional[int] = None, ddof: int = 0) -> _float: +//| """Return the standard deviation of the array, as a number if axis is None, otherwise as an array.""" +//| ... +//| + +mp_obj_t numerical_std(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } } , + { MP_QSTR_axis, MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_ddof, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 0} }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t oin = args[0].u_obj; + mp_obj_t axis = args[1].u_obj; + size_t ddof = args[2].u_int; + if((axis != mp_const_none) && (mp_obj_get_int(axis) != 0) && (mp_obj_get_int(axis) != 1)) { + // this seems to pass with False, and True... + mp_raise_ValueError(translate("axis must be None, or an integer")); + } + if(mp_obj_is_type(oin, &mp_type_tuple) || mp_obj_is_type(oin, &mp_type_list) || mp_obj_is_type(oin, &mp_type_range)) { + return numerical_sum_mean_std_iterable(oin, NUMERICAL_STD, ddof); + } else if(mp_obj_is_type(oin, &ulab_ndarray_type)) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(oin); + return numerical_sum_mean_std_ndarray(ndarray, axis, NUMERICAL_STD, ddof); + } else { + mp_raise_TypeError(translate("input must be tuple, list, range, or ndarray")); + } + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_std_obj, 1, numerical_std); +#endif + +#if ULAB_NUMPY_HAS_SUM +//| def sum(array: _ArrayLike, *, axis: Optional[int] = None) -> Union[_float, int, ulab.numpy.ndarray]: +//| """Return the sum of the array, as a number if axis is None, otherwise as an array.""" +//| ... +//| + +mp_obj_t numerical_sum(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return numerical_function(n_args, pos_args, kw_args, NUMERICAL_SUM); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(numerical_sum_obj, 1, numerical_sum); +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/numerical.h b/circuitpython/extmod/ulab/code/numpy/numerical.h new file mode 100644 index 0000000..8d2971c --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/numerical.h @@ -0,0 +1,652 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#ifndef _NUMERICAL_ +#define _NUMERICAL_ + +#include "../ulab.h" +#include "../ndarray.h" + +// TODO: implement cumsum + +#define RUN_ARGMIN1(ndarray, type, array, results, rarray, index, op)\ +({\ + uint16_t best_index = 0;\ + type best_value = *((type *)(array));\ + if(((op) == NUMERICAL_MAX) || ((op) == NUMERICAL_ARGMAX)) {\ + for(uint16_t i=0; i < (ndarray)->shape[(index)]; i++) {\ + if(*((type *)(array)) > best_value) {\ + best_index = i;\ + best_value = *((type *)(array));\ + }\ + (array) += (ndarray)->strides[(index)];\ + }\ + } else {\ + for(uint16_t i=0; i < (ndarray)->shape[(index)]; i++) {\ + if(*((type *)(array)) < best_value) {\ + best_index = i;\ + best_value = *((type *)(array));\ + }\ + (array) += (ndarray)->strides[(index)];\ + }\ + }\ + if(((op) == NUMERICAL_ARGMAX) || ((op) == NUMERICAL_ARGMIN)) {\ + memcpy((rarray), &best_index, (results)->itemsize);\ + } else {\ + memcpy((rarray), &best_value, (results)->itemsize);\ + }\ + (rarray) += (results)->itemsize;\ +}) + +#define RUN_SUM1(type, array, results, rarray, ss)\ +({\ + type sum = 0;\ + for(size_t i=0; i < (ss).shape[0]; i++) {\ + sum += *((type *)(array));\ + (array) += (ss).strides[0];\ + }\ + memcpy((rarray), &sum, (results)->itemsize);\ + (rarray) += (results)->itemsize;\ +}) + +// The mean could be calculated by simply dividing the sum by +// the number of elements, but that method is numerically unstable +#define RUN_MEAN1(type, array, rarray, ss)\ +({\ + mp_float_t M = 0.0;\ + for(size_t i=0; i < (ss).shape[0]; i++) {\ + mp_float_t value = (mp_float_t)(*(type *)(array));\ + M = M + (value - M) / (mp_float_t)(i+1);\ + (array) += (ss).strides[0];\ + }\ + *(rarray)++ = M;\ +}) + +// Instead of the straightforward implementation of the definition, +// we take the numerically stable Welford algorithm here +// https://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-computing-standard-deviation/ +#define RUN_STD1(type, array, rarray, ss, div)\ +({\ + mp_float_t M = 0.0, m = 0.0, S = 0.0;\ + for(size_t i=0; i < (ss).shape[0]; i++) {\ + mp_float_t value = (mp_float_t)(*(type *)(array));\ + m = M + (value - M) / (mp_float_t)(i+1);\ + S = S + (value - M) * (value - m);\ + M = m;\ + (array) += (ss).strides[0];\ + }\ + *(rarray)++ = MICROPY_FLOAT_C_FUN(sqrt)(S / (div));\ +}) + +#define RUN_MEAN_STD1(type, array, rarray, ss, div, isStd)\ +({\ + mp_float_t M = 0.0, m = 0.0, S = 0.0;\ + for(size_t i=0; i < (ss).shape[0]; i++) {\ + mp_float_t value = (mp_float_t)(*(type *)(array));\ + m = M + (value - M) / (mp_float_t)(i+1);\ + if(isStd) {\ + S += (value - M) * (value - m);\ + }\ + M = m;\ + (array) += (ss).strides[0];\ + }\ + *(rarray)++ = isStd ? MICROPY_FLOAT_C_FUN(sqrt)(S / (div)) : M;\ +}) + +#define RUN_DIFF1(ndarray, type, array, results, rarray, index, stencil, N)\ +({\ + for(size_t i=0; i < (results)->shape[ULAB_MAX_DIMS - 1]; i++) {\ + type sum = 0;\ + uint8_t *source = (array);\ + for(uint8_t d=0; d < (N)+1; d++) {\ + sum -= (stencil)[d] * *((type *)source);\ + source += (ndarray)->strides[(index)];\ + }\ + (array) += (ndarray)->strides[ULAB_MAX_DIMS - 1];\ + *(type *)(rarray) = sum;\ + (rarray) += (results)->itemsize;\ + }\ +}) + +#define HEAPSORT1(type, array, increment, N)\ +({\ + type *_array = (type *)array;\ + type tmp;\ + size_t c, q = (N), p, r = (N) >> 1;\ + for (;;) {\ + if (r > 0) {\ + tmp = _array[(--r)*(increment)];\ + } else {\ + q--;\ + if(q == 0) {\ + break;\ + }\ + tmp = _array[q*(increment)];\ + _array[q*(increment)] = _array[0];\ + }\ + p = r;\ + c = r + r + 1;\ + while (c < q) {\ + if((c + 1 < q) && (_array[(c+1)*(increment)] > _array[c*(increment)])) {\ + c++;\ + }\ + if(_array[c*(increment)] > tmp) {\ + _array[p*(increment)] = _array[c*(increment)];\ + p = c;\ + c = p + p + 1;\ + } else {\ + break;\ + }\ + }\ + _array[p*(increment)] = tmp;\ + }\ +}) + +#define HEAP_ARGSORT1(type, array, increment, N, iarray, iincrement)\ +({\ + type *_array = (type *)array;\ + type tmp;\ + uint16_t itmp, c, q = (N), p, r = (N) >> 1;\ + for (;;) {\ + if (r > 0) {\ + r--;\ + itmp = (iarray)[r*(iincrement)];\ + tmp = _array[itmp*(increment)];\ + } else {\ + q--;\ + if(q == 0) {\ + break;\ + }\ + itmp = (iarray)[q*(iincrement)];\ + tmp = _array[itmp*(increment)];\ + (iarray)[q*(iincrement)] = (iarray)[0];\ + }\ + p = r;\ + c = r + r + 1;\ + while (c < q) {\ + if((c + 1 < q) && (_array[(iarray)[(c+1)*(iincrement)]*(increment)] > _array[(iarray)[c*(iincrement)]*(increment)])) {\ + c++;\ + }\ + if(_array[(iarray)[c*(iincrement)]*(increment)] > tmp) {\ + (iarray)[p*(iincrement)] = (iarray)[c*(iincrement)];\ + p = c;\ + c = p + p + 1;\ + } else {\ + break;\ + }\ + }\ + (iarray)[p*(iincrement)] = itmp;\ + }\ +}) + +#if ULAB_MAX_DIMS == 1 +#define RUN_SUM(type, array, results, rarray, ss) do {\ + RUN_SUM1(type, (array), (results), (rarray), (ss));\ +} while(0) + +#define RUN_MEAN(type, array, rarray, ss) do {\ + RUN_MEAN1(type, (array), (rarray), (ss));\ +} while(0) + +#define RUN_STD(type, array, rarray, ss, div) do {\ + RUN_STD1(type, (array), (results), (rarray), (ss), (div));\ +} while(0) + +#define RUN_MEAN_STD(type, array, rarray, ss, div, isStd) do {\ + RUN_MEAN_STD1(type, (array), (rarray), (ss), (div), (isStd));\ +} while(0) + +#define RUN_ARGMIN(ndarray, type, array, results, rarray, shape, strides, index, op) do {\ + RUN_ARGMIN1((ndarray), type, (array), (results), (rarray), (index), (op));\ +} while(0) + +#define RUN_DIFF(ndarray, type, array, results, rarray, shape, strides, index, stencil, N) do {\ + RUN_DIFF1((ndarray), type, (array), (results), (rarray), (index), (stencil), (N));\ +} while(0) + +#define HEAPSORT(ndarray, type, array, shape, strides, index, increment, N) do {\ + HEAPSORT1(type, (array), (increment), (N));\ +} while(0) + +#define HEAP_ARGSORT(ndarray, type, array, shape, strides, index, increment, N, iarray, istrides, iincrement) do {\ + HEAP_ARGSORT1(type, (array), (increment), (N), (iarray), (iincrement));\ +} while(0) + +#endif + +#if ULAB_MAX_DIMS == 2 +#define RUN_SUM(type, array, results, rarray, ss) do {\ + size_t l = 0;\ + do {\ + RUN_SUM1(type, (array), (results), (rarray), (ss));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ +} while(0) + +#define RUN_MEAN(type, array, rarray, ss) do {\ + size_t l = 0;\ + do {\ + RUN_MEAN1(type, (array), (rarray), (ss));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ +} while(0) + +#define RUN_STD(type, array, rarray, ss, div) do {\ + size_t l = 0;\ + do {\ + RUN_STD1(type, (array), (rarray), (ss), (div));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ +} while(0) + +#define RUN_MEAN_STD(type, array, rarray, ss, div, isStd) do {\ + size_t l = 0;\ + do {\ + RUN_MEAN_STD1(type, (array), (rarray), (ss), (div), (isStd));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ +} while(0) + + +#define RUN_ARGMIN(ndarray, type, array, results, rarray, shape, strides, index, op) do {\ + size_t l = 0;\ + do {\ + RUN_ARGMIN1((ndarray), type, (array), (results), (rarray), (index), (op));\ + (array) -= (ndarray)->strides[(index)] * (ndarray)->shape[(index)];\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ +} while(0) + +#define RUN_DIFF(ndarray, type, array, results, rarray, shape, strides, index, stencil, N) do {\ + size_t l = 0;\ + do {\ + RUN_DIFF1((ndarray), type, (array), (results), (rarray), (index), (stencil), (N));\ + (array) -= (ndarray)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (array) += (ndarray)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (rarray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + l++;\ + } while(l < (results)->shape[ULAB_MAX_DIMS - 2]);\ +} while(0) + +#define HEAPSORT(ndarray, type, array, shape, strides, index, increment, N) do {\ + size_t l = 0;\ + do {\ + HEAPSORT1(type, (array), (increment), (N));\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ +} while(0) + +#define HEAP_ARGSORT(ndarray, type, array, shape, strides, index, increment, N, iarray, istrides, iincrement) do {\ + size_t l = 0;\ + do {\ + HEAP_ARGSORT1(type, (array), (increment), (N), (iarray), (iincrement));\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + (iarray) += (istrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ +} while(0) + +#endif + +#if ULAB_MAX_DIMS == 3 +#define RUN_SUM(type, array, results, rarray, ss) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_SUM1(type, (array), (results), (rarray), (ss));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 1] * (ss).shape[ULAB_MAX_DIMS - 1];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (ss).shape[ULAB_MAX_DIMS - 2]);\ +} while(0) + +#define RUN_MEAN(type, array, rarray, ss) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_MEAN1(type, (array), (rarray), (ss));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 1] * (ss).shape[ULAB_MAX_DIMS - 1];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (ss).shape[ULAB_MAX_DIMS - 2]);\ +} while(0) + +#define RUN_STD(type, array, rarray, ss, div) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_STD1(type, (array), (rarray), (ss), (div));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 1] * (ss).shape[ULAB_MAX_DIMS - 1];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (ss).shape[ULAB_MAX_DIMS - 2]);\ +} while(0) + +#define RUN_MEAN_STD(type, array, rarray, ss, div, isStd) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_MEAN_STD1(type, (array), (rarray), (ss), (div), (isStd));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 1] * (ss).shape[ULAB_MAX_DIMS - 1];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (ss).shape[ULAB_MAX_DIMS - 2]);\ +} while(0) + +#define RUN_ARGMIN(ndarray, type, array, results, rarray, shape, strides, index, op) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_ARGMIN1((ndarray), type, (array), (results), (rarray), (index), (op));\ + (array) -= (ndarray)->strides[(index)] * (ndarray)->shape[(index)];\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ + (array) -= (strides)[ULAB_MAX_DIMS - 1] * (shape)[ULAB_MAX_DIMS-1];\ + (array) += (strides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (shape)[ULAB_MAX_DIMS - 2]);\ +} while(0) + +#define RUN_DIFF(ndarray, type, array, results, rarray, shape, strides, index, stencil, N) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_DIFF1((ndarray), type, (array), (results), (rarray), (index), (stencil), (N));\ + (array) -= (ndarray)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (array) += (ndarray)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (rarray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 2]);\ + (array) -= (ndarray)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS-2];\ + (array) += (ndarray)->strides[ULAB_MAX_DIMS - 3];\ + (rarray) -= (results)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (rarray) += (results)->strides[ULAB_MAX_DIMS - 3];\ + k++;\ + } while(k < (shape)[ULAB_MAX_DIMS - 3]);\ +} while(0) + +#define HEAPSORT(ndarray, type, array, shape, strides, index, increment, N) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + HEAPSORT1(type, (array), (increment), (N));\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ + (array) -= (strides)[ULAB_MAX_DIMS - 1] * (shape)[ULAB_MAX_DIMS-1];\ + (array) += (strides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (shape)[ULAB_MAX_DIMS - 2]);\ +} while(0) + +#define HEAP_ARGSORT(ndarray, type, array, shape, strides, index, increment, N, iarray, istrides, iincrement) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + HEAP_ARGSORT1(type, (array), (increment), (N), (iarray), (iincrement));\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + (iarray) += (istrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ + (iarray) -= (istrides)[ULAB_MAX_DIMS - 1] * (shape)[ULAB_MAX_DIMS-1];\ + (iarray) += (istrides)[ULAB_MAX_DIMS - 2];\ + (array) -= (strides)[ULAB_MAX_DIMS - 1] * (shape)[ULAB_MAX_DIMS-1];\ + (array) += (strides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (shape)[ULAB_MAX_DIMS - 2]);\ +} while(0) + +#endif + +#if ULAB_MAX_DIMS == 4 +#define RUN_SUM(type, array, results, rarray, ss) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_SUM1(type, (array), (results), (rarray), (ss));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 1] * (ss).shape[ULAB_MAX_DIMS - 1];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (ss).shape[ULAB_MAX_DIMS - 2]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 2] * (ss).shape[ULAB_MAX_DIMS - 2];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (ss).shape[ULAB_MAX_DIMS - 3]);\ +} while(0) + +#define RUN_MEAN(type, array, rarray, ss) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_MEAN1(type, (array), (rarray), (ss));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 1] * (ss).shape[ULAB_MAX_DIMS - 1];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (ss).shape[ULAB_MAX_DIMS - 2]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 2] * (ss).shape[ULAB_MAX_DIMS - 2];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (ss).shape[ULAB_MAX_DIMS - 3]);\ +} while(0) + +#define RUN_STD(type, array, rarray, ss, div) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_STD1(type, (array), (rarray), (ss), (div));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 1] * (ss).shape[ULAB_MAX_DIMS - 1];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (ss).shape[ULAB_MAX_DIMS - 2]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 2] * (ss).shape[ULAB_MAX_DIMS - 2];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (ss).shape[ULAB_MAX_DIMS - 3]);\ +} while(0) + +#define RUN_MEAN_STD(type, array, rarray, ss, div, isStd) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_MEAN_STD1(type, (array), (rarray), (ss), (div), (isStd));\ + (array) -= (ss).strides[0] * (ss).shape[0];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (ss).shape[ULAB_MAX_DIMS - 1]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 1] * (ss).shape[ULAB_MAX_DIMS - 1];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (ss).shape[ULAB_MAX_DIMS - 2]);\ + (array) -= (ss).strides[ULAB_MAX_DIMS - 2] * (ss).shape[ULAB_MAX_DIMS - 2];\ + (array) += (ss).strides[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (ss).shape[ULAB_MAX_DIMS - 3]);\ +} while(0) + +#define RUN_ARGMIN(ndarray, type, array, results, rarray, shape, strides, index, op) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_ARGMIN1((ndarray), type, (array), (results), (rarray), (index), (op));\ + (array) -= (ndarray)->strides[(index)] * (ndarray)->shape[(index)];\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ + (array) -= (strides)[ULAB_MAX_DIMS - 1] * (shape)[ULAB_MAX_DIMS-1];\ + (array) += (strides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (shape)[ULAB_MAX_DIMS - 2]);\ + (array) -= (strides)[ULAB_MAX_DIMS - 2] * (shape)[ULAB_MAX_DIMS-2];\ + (array) += (strides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (shape)[ULAB_MAX_DIMS - 3]);\ +} while(0) + +#define RUN_DIFF(ndarray, type, array, results, rarray, shape, strides, index, stencil, N) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + RUN_DIFF1((ndarray), type, (array), (results), (rarray), (index), (stencil), (N));\ + (array) -= (ndarray)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (array) += (ndarray)->strides[ULAB_MAX_DIMS - 2];\ + (rarray) -= (results)->strides[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS - 1];\ + (rarray) += (results)->strides[ULAB_MAX_DIMS - 2];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 2]);\ + (array) -= (strides)[ULAB_MAX_DIMS - 2] * (shape)[ULAB_MAX_DIMS-2];\ + (array) += (strides)[ULAB_MAX_DIMS - 3];\ + (rarray) -= (results)->strides[ULAB_MAX_DIMS - 2] * (results)->shape[ULAB_MAX_DIMS - 2];\ + (rarray) += (results)->strides[ULAB_MAX_DIMS - 3];\ + k++;\ + } while(k < (shape)[ULAB_MAX_DIMS - 3]);\ + (array) -= (strides)[ULAB_MAX_DIMS - 3] * (shape)[ULAB_MAX_DIMS-3];\ + (array) += (strides)[ULAB_MAX_DIMS - 4];\ + (rarray) -= (results)->strides[ULAB_MAX_DIMS - 3] * (results)->shape[ULAB_MAX_DIMS - 3];\ + (rarray) += (results)->strides[ULAB_MAX_DIMS - 4];\ + j++;\ + } while(j < (shape)[ULAB_MAX_DIMS - 4]);\ +} while(0) + +#define HEAPSORT(ndarray, type, array, shape, strides, index, increment, N) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + HEAPSORT1(type, (array), (increment), (N));\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ + (array) -= (strides)[ULAB_MAX_DIMS - 1] * (shape)[ULAB_MAX_DIMS-1];\ + (array) += (strides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (shape)[ULAB_MAX_DIMS - 2]);\ + (array) -= (strides)[ULAB_MAX_DIMS - 2] * (shape)[ULAB_MAX_DIMS-2];\ + (array) += (strides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (shape)[ULAB_MAX_DIMS - 3]);\ +} while(0) + +#define HEAP_ARGSORT(ndarray, type, array, shape, strides, index, increment, N, iarray, istrides, iincrement) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + HEAP_ARGSORT1(type, (array), (increment), (N), (iarray), (iincrement));\ + (array) += (strides)[ULAB_MAX_DIMS - 1];\ + (iarray) += (istrides)[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (shape)[ULAB_MAX_DIMS - 1]);\ + (iarray) -= (istrides)[ULAB_MAX_DIMS - 1] * (shape)[ULAB_MAX_DIMS-1];\ + (iarray) += (istrides)[ULAB_MAX_DIMS - 2];\ + (array) -= (strides)[ULAB_MAX_DIMS - 1] * (shape)[ULAB_MAX_DIMS-1];\ + (array) += (strides)[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (shape)[ULAB_MAX_DIMS - 2]);\ + (iarray) -= (istrides)[ULAB_MAX_DIMS - 2] * (shape)[ULAB_MAX_DIMS-2];\ + (iarray) += (istrides)[ULAB_MAX_DIMS - 3];\ + (array) -= (strides)[ULAB_MAX_DIMS - 2] * (shape)[ULAB_MAX_DIMS-2];\ + (array) += (strides)[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (shape)[ULAB_MAX_DIMS - 3]);\ +} while(0) + +#endif + +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_all_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_any_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_argmax_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_argmin_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_argsort_obj); +MP_DECLARE_CONST_FUN_OBJ_2(numerical_cross_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_diff_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_flip_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_max_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_mean_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_median_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_min_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_roll_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_std_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_sum_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_sort_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(numerical_sort_inplace_obj); + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/numpy.c b/circuitpython/extmod/ulab/code/numpy/numpy.c new file mode 100644 index 0000000..ebd171d --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/numpy.c @@ -0,0 +1,383 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020 Scott Shawcroft for Adafruit Industries + * 2020-2022 Zoltán Vörös + * 2020 Taku Fukada +*/ + +#include <math.h> +#include <string.h> +#include "py/runtime.h" + +#include "numpy.h" +#include "approx.h" +#include "carray/carray.h" +#include "compare.h" +#include "create.h" +#include "fft/fft.h" +#include "filter.h" +#include "linalg/linalg.h" +#include "numerical.h" +#include "stats.h" +#include "transform.h" +#include "poly.h" +#include "vector.h" + +//| """Compatibility layer for numpy""" +//| + +//| class ndarray: ... + +//| def get_printoptions() -> Dict[str, int]: +//| """Get printing options""" +//| ... +//| +//| def set_printoptions(threshold: Optional[int] = None, edgeitems: Optional[int] = None) -> None: +//| """Set printing options""" +//| ... +//| +//| def ndinfo(array: ulab.numpy.ndarray) -> None: +//| ... +//| +//| def array( +//| values: Union[ndarray, Iterable[Union[_float, _bool, Iterable[Any]]]], +//| *, +//| dtype: _DType = ulab.numpy.float +//| ) -> ulab.numpy.ndarray: +//| """alternate constructor function for `ulab.numpy.ndarray`. Mirrors numpy.array""" +//| ... + +// math constants +#if ULAB_NUMPY_HAS_E +#if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C +#define ulab_const_float_e MP_ROM_PTR((mp_obj_t)(((0x402df854 & ~3) | 2) + 0x80800000)) +#elif MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_D +#define ulab_const_float_e {((mp_obj_t)((uint64_t)0x4005bf0a8b145769 + 0x8004000000000000))} +#else +mp_obj_float_t ulab_const_float_e_obj = {{&mp_type_float}, MP_E}; +#define ulab_const_float_e MP_ROM_PTR(&ulab_const_float_e_obj) +#endif +#endif + +#if ULAB_NUMPY_HAS_INF +#if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C +#define numpy_const_float_inf MP_ROM_PTR((mp_obj_t)(0x7f800002 + 0x80800000)) +#elif MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_D +#define numpy_const_float_inf {((mp_obj_t)((uint64_t)0x7ff0000000000000 + 0x8004000000000000))} +#else +mp_obj_float_t numpy_const_float_inf_obj = {{&mp_type_float}, (mp_float_t)INFINITY}; +#define numpy_const_float_inf MP_ROM_PTR(&numpy_const_float_inf_obj) +#endif +#endif + +#if ULAB_NUMPY_HAS_NAN +#if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C +#define numpy_const_float_nan MP_ROM_PTR((mp_obj_t)(0x7fc00002 + 0x80800000)) +#elif MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_D +#define numpy_const_float_nan {((mp_obj_t)((uint64_t)0x7ff8000000000000 + 0x8004000000000000))} +#else +mp_obj_float_t numpy_const_float_nan_obj = {{&mp_type_float}, (mp_float_t)NAN}; +#define numpy_const_float_nan MP_ROM_PTR(&numpy_const_float_nan_obj) +#endif +#endif + +#if ULAB_NUMPY_HAS_PI +#if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_C +#define ulab_const_float_pi MP_ROM_PTR((mp_obj_t)(((0x40490fdb & ~3) | 2) + 0x80800000)) +#elif MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_D +#define ulab_const_float_pi {((mp_obj_t)((uint64_t)0x400921fb54442d18 + 0x8004000000000000))} +#else +mp_obj_float_t ulab_const_float_pi_obj = {{&mp_type_float}, MP_PI}; +#define ulab_const_float_pi MP_ROM_PTR(&ulab_const_float_pi_obj) +#endif +#endif + +static const mp_rom_map_elem_t ulab_numpy_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_numpy) }, + { MP_OBJ_NEW_QSTR(MP_QSTR_ndarray), (mp_obj_t)&ulab_ndarray_type }, + { MP_OBJ_NEW_QSTR(MP_QSTR_array), MP_ROM_PTR(&ndarray_array_constructor_obj) }, + #if ULAB_NUMPY_HAS_FROMBUFFER + { MP_ROM_QSTR(MP_QSTR_frombuffer), MP_ROM_PTR(&create_frombuffer_obj) }, + #endif + // math constants + #if ULAB_NUMPY_HAS_E + { MP_ROM_QSTR(MP_QSTR_e), ulab_const_float_e }, + #endif + #if ULAB_NUMPY_HAS_INF + { MP_ROM_QSTR(MP_QSTR_inf), numpy_const_float_inf }, + #endif + #if ULAB_NUMPY_HAS_NAN + { MP_ROM_QSTR(MP_QSTR_nan), numpy_const_float_nan }, + #endif + #if ULAB_NUMPY_HAS_PI + { MP_ROM_QSTR(MP_QSTR_pi), ulab_const_float_pi }, + #endif + // class constants, always included + { MP_ROM_QSTR(MP_QSTR_bool), MP_ROM_INT(NDARRAY_BOOL) }, + { MP_ROM_QSTR(MP_QSTR_uint8), MP_ROM_INT(NDARRAY_UINT8) }, + { MP_ROM_QSTR(MP_QSTR_int8), MP_ROM_INT(NDARRAY_INT8) }, + { MP_ROM_QSTR(MP_QSTR_uint16), MP_ROM_INT(NDARRAY_UINT16) }, + { MP_ROM_QSTR(MP_QSTR_int16), MP_ROM_INT(NDARRAY_INT16) }, + { MP_ROM_QSTR(MP_QSTR_float), MP_ROM_INT(NDARRAY_FLOAT) }, + #if ULAB_SUPPORTS_COMPLEX + { MP_ROM_QSTR(MP_QSTR_complex), MP_ROM_INT(NDARRAY_COMPLEX) }, + #endif + // modules of numpy + #if ULAB_NUMPY_HAS_FFT_MODULE + { MP_ROM_QSTR(MP_QSTR_fft), MP_ROM_PTR(&ulab_fft_module) }, + #endif + #if ULAB_NUMPY_HAS_LINALG_MODULE + { MP_ROM_QSTR(MP_QSTR_linalg), MP_ROM_PTR(&ulab_linalg_module) }, + #endif + #if ULAB_HAS_PRINTOPTIONS + { MP_ROM_QSTR(MP_QSTR_set_printoptions), (mp_obj_t)&ndarray_set_printoptions_obj }, + { MP_ROM_QSTR(MP_QSTR_get_printoptions), (mp_obj_t)&ndarray_get_printoptions_obj }, + #endif + #if ULAB_NUMPY_HAS_NDINFO + { MP_ROM_QSTR(MP_QSTR_ndinfo), (mp_obj_t)&ndarray_info_obj }, + #endif + #if ULAB_NUMPY_HAS_ARANGE + { MP_ROM_QSTR(MP_QSTR_arange), (mp_obj_t)&create_arange_obj }, + #endif + #if ULAB_NUMPY_HAS_COMPRESS + { MP_ROM_QSTR(MP_QSTR_compress), (mp_obj_t)&transform_compress_obj }, + #endif + #if ULAB_NUMPY_HAS_CONCATENATE + { MP_ROM_QSTR(MP_QSTR_concatenate), (mp_obj_t)&create_concatenate_obj }, + #endif + #if ULAB_NUMPY_HAS_DIAG + #if ULAB_MAX_DIMS > 1 + { MP_ROM_QSTR(MP_QSTR_diag), (mp_obj_t)&create_diag_obj }, + #endif + #endif + #if ULAB_NUMPY_HAS_EMPTY + { MP_ROM_QSTR(MP_QSTR_empty), (mp_obj_t)&create_zeros_obj }, + #endif + #if ULAB_MAX_DIMS > 1 + #if ULAB_NUMPY_HAS_EYE + { MP_ROM_QSTR(MP_QSTR_eye), (mp_obj_t)&create_eye_obj }, + #endif + #endif /* ULAB_MAX_DIMS */ + // functions of the approx sub-module + #if ULAB_NUMPY_HAS_INTERP + { MP_OBJ_NEW_QSTR(MP_QSTR_interp), (mp_obj_t)&approx_interp_obj }, + #endif + #if ULAB_NUMPY_HAS_TRAPZ + { MP_OBJ_NEW_QSTR(MP_QSTR_trapz), (mp_obj_t)&approx_trapz_obj }, + #endif + // functions of the create sub-module + #if ULAB_NUMPY_HAS_FULL + { MP_ROM_QSTR(MP_QSTR_full), (mp_obj_t)&create_full_obj }, + #endif + #if ULAB_NUMPY_HAS_LINSPACE + { MP_ROM_QSTR(MP_QSTR_linspace), (mp_obj_t)&create_linspace_obj }, + #endif + #if ULAB_NUMPY_HAS_LOGSPACE + { MP_ROM_QSTR(MP_QSTR_logspace), (mp_obj_t)&create_logspace_obj }, + #endif + #if ULAB_NUMPY_HAS_ONES + { MP_ROM_QSTR(MP_QSTR_ones), (mp_obj_t)&create_ones_obj }, + #endif + #if ULAB_NUMPY_HAS_ZEROS + { MP_ROM_QSTR(MP_QSTR_zeros), (mp_obj_t)&create_zeros_obj }, + #endif + // functions of the compare sub-module + #if ULAB_NUMPY_HAS_CLIP + { MP_OBJ_NEW_QSTR(MP_QSTR_clip), (mp_obj_t)&compare_clip_obj }, + #endif + #if ULAB_NUMPY_HAS_EQUAL + { MP_OBJ_NEW_QSTR(MP_QSTR_equal), (mp_obj_t)&compare_equal_obj }, + #endif + #if ULAB_NUMPY_HAS_NOTEQUAL + { MP_OBJ_NEW_QSTR(MP_QSTR_not_equal), (mp_obj_t)&compare_not_equal_obj }, + #endif + #if ULAB_NUMPY_HAS_ISFINITE + { MP_OBJ_NEW_QSTR(MP_QSTR_isfinite), (mp_obj_t)&compare_isfinite_obj }, + #endif + #if ULAB_NUMPY_HAS_ISINF + { MP_OBJ_NEW_QSTR(MP_QSTR_isinf), (mp_obj_t)&compare_isinf_obj }, + #endif + #if ULAB_NUMPY_HAS_MAXIMUM + { MP_OBJ_NEW_QSTR(MP_QSTR_maximum), (mp_obj_t)&compare_maximum_obj }, + #endif + #if ULAB_NUMPY_HAS_MINIMUM + { MP_OBJ_NEW_QSTR(MP_QSTR_minimum), (mp_obj_t)&compare_minimum_obj }, + #endif + #if ULAB_NUMPY_HAS_WHERE + { MP_OBJ_NEW_QSTR(MP_QSTR_where), (mp_obj_t)&compare_where_obj }, + #endif + // functions of the filter sub-module + #if ULAB_NUMPY_HAS_CONVOLVE + { MP_OBJ_NEW_QSTR(MP_QSTR_convolve), (mp_obj_t)&filter_convolve_obj }, + #endif + // functions of the numerical sub-module + #if ULAB_NUMPY_HAS_ALL + { MP_OBJ_NEW_QSTR(MP_QSTR_all), (mp_obj_t)&numerical_all_obj }, + #endif + #if ULAB_NUMPY_HAS_ANY + { MP_OBJ_NEW_QSTR(MP_QSTR_any), (mp_obj_t)&numerical_any_obj }, + #endif + #if ULAB_NUMPY_HAS_ARGMINMAX + { MP_OBJ_NEW_QSTR(MP_QSTR_argmax), (mp_obj_t)&numerical_argmax_obj }, + { MP_OBJ_NEW_QSTR(MP_QSTR_argmin), (mp_obj_t)&numerical_argmin_obj }, + #endif + #if ULAB_NUMPY_HAS_ARGSORT + { MP_OBJ_NEW_QSTR(MP_QSTR_argsort), (mp_obj_t)&numerical_argsort_obj }, + #endif + #if ULAB_NUMPY_HAS_CROSS + { MP_OBJ_NEW_QSTR(MP_QSTR_cross), (mp_obj_t)&numerical_cross_obj }, + #endif + #if ULAB_NUMPY_HAS_DIFF + { MP_OBJ_NEW_QSTR(MP_QSTR_diff), (mp_obj_t)&numerical_diff_obj }, + #endif + #if ULAB_NUMPY_HAS_DOT + #if ULAB_MAX_DIMS > 1 + { MP_OBJ_NEW_QSTR(MP_QSTR_dot), (mp_obj_t)&transform_dot_obj }, + #endif + #endif + #if ULAB_NUMPY_HAS_TRACE + #if ULAB_MAX_DIMS > 1 + { MP_ROM_QSTR(MP_QSTR_trace), (mp_obj_t)&stats_trace_obj }, + #endif + #endif + #if ULAB_NUMPY_HAS_FLIP + { MP_OBJ_NEW_QSTR(MP_QSTR_flip), (mp_obj_t)&numerical_flip_obj }, + #endif + #if ULAB_NUMPY_HAS_MINMAX + { MP_OBJ_NEW_QSTR(MP_QSTR_max), (mp_obj_t)&numerical_max_obj }, + #endif + #if ULAB_NUMPY_HAS_MEAN + { MP_OBJ_NEW_QSTR(MP_QSTR_mean), (mp_obj_t)&numerical_mean_obj }, + #endif + #if ULAB_NUMPY_HAS_MEDIAN + { MP_OBJ_NEW_QSTR(MP_QSTR_median), (mp_obj_t)&numerical_median_obj }, + #endif + #if ULAB_NUMPY_HAS_MINMAX + { MP_OBJ_NEW_QSTR(MP_QSTR_min), (mp_obj_t)&numerical_min_obj }, + #endif + #if ULAB_NUMPY_HAS_ROLL + { MP_OBJ_NEW_QSTR(MP_QSTR_roll), (mp_obj_t)&numerical_roll_obj }, + #endif + #if ULAB_NUMPY_HAS_SORT + { MP_OBJ_NEW_QSTR(MP_QSTR_sort), (mp_obj_t)&numerical_sort_obj }, + #endif + #if ULAB_NUMPY_HAS_STD + { MP_OBJ_NEW_QSTR(MP_QSTR_std), (mp_obj_t)&numerical_std_obj }, + #endif + #if ULAB_NUMPY_HAS_SUM + { MP_OBJ_NEW_QSTR(MP_QSTR_sum), (mp_obj_t)&numerical_sum_obj }, + #endif + // functions of the poly sub-module + #if ULAB_NUMPY_HAS_POLYFIT + { MP_OBJ_NEW_QSTR(MP_QSTR_polyfit), (mp_obj_t)&poly_polyfit_obj }, + #endif + #if ULAB_NUMPY_HAS_POLYVAL + { MP_OBJ_NEW_QSTR(MP_QSTR_polyval), (mp_obj_t)&poly_polyval_obj }, + #endif + // functions of the vector sub-module + #if ULAB_NUMPY_HAS_ACOS + { MP_OBJ_NEW_QSTR(MP_QSTR_acos), (mp_obj_t)&vector_acos_obj }, + #endif + #if ULAB_NUMPY_HAS_ACOSH + { MP_OBJ_NEW_QSTR(MP_QSTR_acosh), (mp_obj_t)&vector_acosh_obj }, + #endif + #if ULAB_NUMPY_HAS_ARCTAN2 + { MP_OBJ_NEW_QSTR(MP_QSTR_arctan2), (mp_obj_t)&vector_arctan2_obj }, + #endif + #if ULAB_NUMPY_HAS_AROUND + { MP_OBJ_NEW_QSTR(MP_QSTR_around), (mp_obj_t)&vector_around_obj }, + #endif + #if ULAB_NUMPY_HAS_ASIN + { MP_OBJ_NEW_QSTR(MP_QSTR_asin), (mp_obj_t)&vector_asin_obj }, + #endif + #if ULAB_NUMPY_HAS_ASINH + { MP_OBJ_NEW_QSTR(MP_QSTR_asinh), (mp_obj_t)&vector_asinh_obj }, + #endif + #if ULAB_NUMPY_HAS_ATAN + { MP_OBJ_NEW_QSTR(MP_QSTR_atan), (mp_obj_t)&vector_atan_obj }, + #endif + #if ULAB_NUMPY_HAS_ATANH + { MP_OBJ_NEW_QSTR(MP_QSTR_atanh), (mp_obj_t)&vector_atanh_obj }, + #endif + #if ULAB_NUMPY_HAS_CEIL + { MP_OBJ_NEW_QSTR(MP_QSTR_ceil), (mp_obj_t)&vector_ceil_obj }, + #endif + #if ULAB_NUMPY_HAS_COS + { MP_OBJ_NEW_QSTR(MP_QSTR_cos), (mp_obj_t)&vector_cos_obj }, + #endif + #if ULAB_NUMPY_HAS_COSH + { MP_OBJ_NEW_QSTR(MP_QSTR_cosh), (mp_obj_t)&vector_cosh_obj }, + #endif + #if ULAB_NUMPY_HAS_DEGREES + { MP_OBJ_NEW_QSTR(MP_QSTR_degrees), (mp_obj_t)&vector_degrees_obj }, + #endif + #if ULAB_NUMPY_HAS_EXP + { MP_OBJ_NEW_QSTR(MP_QSTR_exp), (mp_obj_t)&vector_exp_obj }, + #endif + #if ULAB_NUMPY_HAS_EXPM1 + { MP_OBJ_NEW_QSTR(MP_QSTR_expm1), (mp_obj_t)&vector_expm1_obj }, + #endif + #if ULAB_NUMPY_HAS_FLOOR + { MP_OBJ_NEW_QSTR(MP_QSTR_floor), (mp_obj_t)&vector_floor_obj }, + #endif + #if ULAB_NUMPY_HAS_LOG + { MP_OBJ_NEW_QSTR(MP_QSTR_log), (mp_obj_t)&vector_log_obj }, + #endif + #if ULAB_NUMPY_HAS_LOG10 + { MP_OBJ_NEW_QSTR(MP_QSTR_log10), (mp_obj_t)&vector_log10_obj }, + #endif + #if ULAB_NUMPY_HAS_LOG2 + { MP_OBJ_NEW_QSTR(MP_QSTR_log2), (mp_obj_t)&vector_log2_obj }, + #endif + #if ULAB_NUMPY_HAS_RADIANS + { MP_OBJ_NEW_QSTR(MP_QSTR_radians), (mp_obj_t)&vector_radians_obj }, + #endif + #if ULAB_NUMPY_HAS_SIN + { MP_OBJ_NEW_QSTR(MP_QSTR_sin), (mp_obj_t)&vector_sin_obj }, + #endif + #if ULAB_NUMPY_HAS_SINH + { MP_OBJ_NEW_QSTR(MP_QSTR_sinh), (mp_obj_t)&vector_sinh_obj }, + #endif + #if ULAB_NUMPY_HAS_SQRT + { MP_OBJ_NEW_QSTR(MP_QSTR_sqrt), (mp_obj_t)&vector_sqrt_obj }, + #endif + #if ULAB_NUMPY_HAS_TAN + { MP_OBJ_NEW_QSTR(MP_QSTR_tan), (mp_obj_t)&vector_tan_obj }, + #endif + #if ULAB_NUMPY_HAS_TANH + { MP_OBJ_NEW_QSTR(MP_QSTR_tanh), (mp_obj_t)&vector_tanh_obj }, + #endif + #if ULAB_NUMPY_HAS_VECTORIZE + { MP_OBJ_NEW_QSTR(MP_QSTR_vectorize), (mp_obj_t)&vector_vectorize_obj }, + #endif + #if ULAB_SUPPORTS_COMPLEX + #if ULAB_NUMPY_HAS_REAL + { MP_OBJ_NEW_QSTR(MP_QSTR_real), (mp_obj_t)&carray_real_obj }, + #endif + #if ULAB_NUMPY_HAS_IMAG + { MP_OBJ_NEW_QSTR(MP_QSTR_imag), (mp_obj_t)&carray_imag_obj }, + #endif + #if ULAB_NUMPY_HAS_CONJUGATE + { MP_ROM_QSTR(MP_QSTR_conjugate), (mp_obj_t)&carray_conjugate_obj }, + #endif + #if ULAB_NUMPY_HAS_SORT_COMPLEX + { MP_ROM_QSTR(MP_QSTR_sort_complex), (mp_obj_t)&carray_sort_complex_obj }, + #endif + #endif +}; + +static MP_DEFINE_CONST_DICT(mp_module_ulab_numpy_globals, ulab_numpy_globals_table); + +const mp_obj_module_t ulab_numpy_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_numpy_globals, +}; + +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_numpy, ulab_numpy_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); diff --git a/circuitpython/extmod/ulab/code/numpy/numpy.h b/circuitpython/extmod/ulab/code/numpy/numpy.h new file mode 100644 index 0000000..f1348f3 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/numpy.h @@ -0,0 +1,21 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös + * +*/ + +#ifndef _NUMPY_ +#define _NUMPY_ + +#include "../ulab.h" +#include "../ndarray.h" + +extern const mp_obj_module_t ulab_numpy_module; + +#endif /* _NUMPY_ */ diff --git a/circuitpython/extmod/ulab/code/numpy/poly.c b/circuitpython/extmod/ulab/code/numpy/poly.c new file mode 100644 index 0000000..97ee5c7 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/poly.c @@ -0,0 +1,250 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * 2020 Jeff Epler for Adafruit Industries + * 2020 Scott Shawcroft for Adafruit Industries + * 2020 Taku Fukada +*/ + +#include "py/obj.h" +#include "py/runtime.h" +#include "py/objarray.h" + +#include "../ulab.h" +#include "linalg/linalg_tools.h" +#include "../ulab_tools.h" +#include "carray/carray_tools.h" +#include "poly.h" + +#if ULAB_NUMPY_HAS_POLYFIT + +mp_obj_t poly_polyfit(size_t n_args, const mp_obj_t *args) { + if(!ndarray_object_is_array_like(args[0])) { + mp_raise_ValueError(translate("input data must be an iterable")); + } + #if ULAB_SUPPORTS_COMPLEX + if(mp_obj_is_type(args[0], &ulab_ndarray_type)) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[0]); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + } + #endif + size_t lenx = 0, leny = 0; + uint8_t deg = 0; + mp_float_t *x, *XT, *y, *prod; + + if(n_args == 2) { // only the y values are supplied + // TODO: this is actually not enough: the first argument can very well be a matrix, + // in which case we are between the rock and a hard place + leny = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[0])); + deg = (uint8_t)mp_obj_get_int(args[1]); + if(leny < deg) { + mp_raise_ValueError(translate("more degrees of freedom than data points")); + } + lenx = leny; + x = m_new(mp_float_t, lenx); // assume uniformly spaced data points + for(size_t i=0; i < lenx; i++) { + x[i] = i; + } + y = m_new(mp_float_t, leny); + fill_array_iterable(y, args[0]); + } else /* n_args == 3 */ { + if(!ndarray_object_is_array_like(args[1])) { + mp_raise_ValueError(translate("input data must be an iterable")); + } + lenx = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[0])); + leny = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[1])); + if(lenx != leny) { + mp_raise_ValueError(translate("input vectors must be of equal length")); + } + deg = (uint8_t)mp_obj_get_int(args[2]); + if(leny < deg) { + mp_raise_ValueError(translate("more degrees of freedom than data points")); + } + x = m_new(mp_float_t, lenx); + fill_array_iterable(x, args[0]); + y = m_new(mp_float_t, leny); + fill_array_iterable(y, args[1]); + } + + // one could probably express X as a function of XT, + // and thereby save RAM, because X is used only in the product + XT = m_new(mp_float_t, (deg+1)*leny); // XT is a matrix of shape (deg+1, len) (rows, columns) + for(size_t i=0; i < leny; i++) { // column index + XT[i+0*lenx] = 1.0; // top row + for(uint8_t j=1; j < deg+1; j++) { // row index + XT[i+j*leny] = XT[i+(j-1)*leny]*x[i]; + } + } + + prod = m_new(mp_float_t, (deg+1)*(deg+1)); // the product matrix is of shape (deg+1, deg+1) + mp_float_t sum; + for(uint8_t i=0; i < deg+1; i++) { // column index + for(uint8_t j=0; j < deg+1; j++) { // row index + sum = 0.0; + for(size_t k=0; k < lenx; k++) { + // (j, k) * (k, i) + // Note that the second matrix is simply the transpose of the first: + // X(k, i) = XT(i, k) = XT[k*lenx+i] + sum += XT[j*lenx+k]*XT[i*lenx+k]; // X[k*(deg+1)+i]; + } + prod[j*(deg+1)+i] = sum; + } + } + if(!linalg_invert_matrix(prod, deg+1)) { + // Although X was a Vandermonde matrix, whose inverse is guaranteed to exist, + // we bail out here, if prod couldn't be inverted: if the values in x are not all + // distinct, prod is singular + m_del(mp_float_t, XT, (deg+1)*lenx); + m_del(mp_float_t, x, lenx); + m_del(mp_float_t, y, lenx); + m_del(mp_float_t, prod, (deg+1)*(deg+1)); + mp_raise_ValueError(translate("could not invert Vandermonde matrix")); + } + // at this point, we have the inverse of X^T * X + // y is a column vector; x is free now, we can use it for storing intermediate values + for(uint8_t i=0; i < deg+1; i++) { // row index + sum = 0.0; + for(size_t j=0; j < lenx; j++) { // column index + sum += XT[i*lenx+j]*y[j]; + } + x[i] = sum; + } + // XT is no longer needed + m_del(mp_float_t, XT, (deg+1)*leny); + + ndarray_obj_t *beta = ndarray_new_linear_array(deg+1, NDARRAY_FLOAT); + mp_float_t *betav = (mp_float_t *)beta->array; + // x[0..(deg+1)] contains now the product X^T * y; we can get rid of y + m_del(float, y, leny); + + // now, we calculate beta, i.e., we apply prod = (X^T * X)^(-1) on x = X^T * y; x is a column vector now + for(uint8_t i=0; i < deg+1; i++) { + sum = 0.0; + for(uint8_t j=0; j < deg+1; j++) { + sum += prod[i*(deg+1)+j]*x[j]; + } + betav[i] = sum; + } + m_del(mp_float_t, x, lenx); + m_del(mp_float_t, prod, (deg+1)*(deg+1)); + for(uint8_t i=0; i < (deg+1)/2; i++) { + // We have to reverse the array, for the leading coefficient comes first. + SWAP(mp_float_t, betav[i], betav[deg-i]); + } + return MP_OBJ_FROM_PTR(beta); +} + +MP_DEFINE_CONST_FUN_OBJ_VAR_BETWEEN(poly_polyfit_obj, 2, 3, poly_polyfit); +#endif + +#if ULAB_NUMPY_HAS_POLYVAL + +mp_obj_t poly_polyval(mp_obj_t o_p, mp_obj_t o_x) { + if(!ndarray_object_is_array_like(o_p) || !ndarray_object_is_array_like(o_x)) { + mp_raise_TypeError(translate("inputs are not iterable")); + } + #if ULAB_SUPPORTS_COMPLEX + ndarray_obj_t *input; + if(mp_obj_is_type(o_p, &ulab_ndarray_type)) { + input = MP_OBJ_TO_PTR(o_p); + COMPLEX_DTYPE_NOT_IMPLEMENTED(input->dtype) + } + if(mp_obj_is_type(o_x, &ulab_ndarray_type)) { + input = MP_OBJ_TO_PTR(o_x); + COMPLEX_DTYPE_NOT_IMPLEMENTED(input->dtype) + } + #endif + // p had better be a one-dimensional standard iterable + uint8_t plen = mp_obj_get_int(mp_obj_len_maybe(o_p)); + mp_float_t *p = m_new(mp_float_t, plen); + mp_obj_iter_buf_t p_buf; + mp_obj_t p_item, p_iterable = mp_getiter(o_p, &p_buf); + uint8_t i = 0; + while((p_item = mp_iternext(p_iterable)) != MP_OBJ_STOP_ITERATION) { + p[i] = mp_obj_get_float(p_item); + i++; + } + + // polynomials are going to be of type float, except, when both + // the coefficients and the independent variable are integers + ndarray_obj_t *ndarray; + if(mp_obj_is_type(o_x, &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(o_x); + uint8_t *sarray = (uint8_t *)source->array; + ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_FLOAT); + mp_float_t *array = (mp_float_t *)ndarray->array; + + mp_float_t (*func)(void *) = ndarray_get_float_function(source->dtype); + + // TODO: these loops are really nothing, but the re-impplementation of + // ITERATE_VECTOR from vectorise.c. We could pass a function pointer here + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t y = p[0]; + mp_float_t _x = func(sarray); + for(uint8_t m=0; m < plen-1; m++) { + y *= _x; + y += p[m+1]; + } + *array++ = y; + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif + } else { + // o_x had better be a one-dimensional standard iterable + ndarray = ndarray_new_linear_array(mp_obj_get_int(mp_obj_len_maybe(o_x)), NDARRAY_FLOAT); + mp_float_t *array = (mp_float_t *)ndarray->array; + mp_obj_iter_buf_t x_buf; + mp_obj_t x_item, x_iterable = mp_getiter(o_x, &x_buf); + while ((x_item = mp_iternext(x_iterable)) != MP_OBJ_STOP_ITERATION) { + mp_float_t _x = mp_obj_get_float(x_item); + mp_float_t y = p[0]; + for(uint8_t j=0; j < plen-1; j++) { + y *= _x; + y += p[j+1]; + } + *array++ = y; + } + } + m_del(mp_float_t, p, plen); + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_2(poly_polyval_obj, poly_polyval); +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/poly.h b/circuitpython/extmod/ulab/code/numpy/poly.h new file mode 100644 index 0000000..59cb9f5 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/poly.h @@ -0,0 +1,21 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#ifndef _POLY_ +#define _POLY_ + +#include "../ulab.h" +#include "../ndarray.h" + +MP_DECLARE_CONST_FUN_OBJ_VAR_BETWEEN(poly_polyfit_obj); +MP_DECLARE_CONST_FUN_OBJ_2(poly_polyval_obj); + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/stats.c b/circuitpython/extmod/ulab/code/numpy/stats.c new file mode 100644 index 0000000..2d34889 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/stats.c @@ -0,0 +1,54 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * 2020 Scott Shawcroft for Adafruit Industries + * 2020 Roberto Colistete Jr. + * 2020 Taku Fukada + * +*/ + +#include <stdlib.h> +#include <string.h> +#include <math.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../ulab.h" +#include "../ulab_tools.h" +#include "carray/carray_tools.h" +#include "stats.h" + +#if ULAB_MAX_DIMS > 1 +#if ULAB_NUMPY_HAS_TRACE + +//| def trace(m: ulab.numpy.ndarray) -> _float: +//| """ +//| :param m: a square matrix +//| +//| Compute the trace of the matrix, the sum of its diagonal elements.""" +//| ... +//| + +static mp_obj_t stats_trace(mp_obj_t oin) { + ndarray_obj_t *ndarray = tools_object_is_square(oin); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + mp_float_t trace = 0.0; + for(size_t i=0; i < ndarray->shape[ULAB_MAX_DIMS - 1]; i++) { + int32_t pos = i * (ndarray->strides[ULAB_MAX_DIMS - 1] + ndarray->strides[ULAB_MAX_DIMS - 2]); + trace += ndarray_get_float_index(ndarray->array, ndarray->dtype, pos/ndarray->itemsize); + } + if(ndarray->dtype == NDARRAY_FLOAT) { + return mp_obj_new_float(trace); + } + return mp_obj_new_int_from_float(trace); +} + +MP_DEFINE_CONST_FUN_OBJ_1(stats_trace_obj, stats_trace); +#endif +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/stats.h b/circuitpython/extmod/ulab/code/numpy/stats.h new file mode 100644 index 0000000..62bba9f --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/stats.h @@ -0,0 +1,20 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#ifndef _STATS_ +#define _STATS_ + +#include "../ulab.h" +#include "../ndarray.h" + +MP_DECLARE_CONST_FUN_OBJ_1(stats_trace_obj); + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/transform.c b/circuitpython/extmod/ulab/code/numpy/transform.c new file mode 100644 index 0000000..f0e3e70 --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/transform.c @@ -0,0 +1,224 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * +*/ + +#include <stdlib.h> +#include <string.h> +#include <math.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../ulab.h" +#include "../ulab_tools.h" +#include "carray/carray_tools.h" +#include "transform.h" + +#if ULAB_NUMPY_HAS_COMPRESS +static mp_obj_t transform_compress(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_axis, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t condition = args[0].u_obj; + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[1].u_obj); + uint8_t *array = (uint8_t *)ndarray->array; + mp_obj_t axis = args[2].u_obj; + + size_t len = MP_OBJ_SMALL_INT_VALUE(mp_obj_len_maybe(condition)); + int8_t ax, shift_ax; + + if(axis != mp_const_none) { + ax = tools_get_axis(axis, ndarray->ndim); + shift_ax = ULAB_MAX_DIMS - ndarray->ndim + ax; + } + + if(((axis == mp_const_none) && (len != ndarray->len)) || + ((axis != mp_const_none) && (len != ndarray->shape[shift_ax]))) { + mp_raise_ValueError(translate("wrong length of condition array")); + } + + size_t true_count = 0; + mp_obj_iter_buf_t iter_buf; + mp_obj_t item, iterable = mp_getiter(condition, &iter_buf); + while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + if(mp_obj_is_true(item)) { + true_count++; + } + } + + iterable = mp_getiter(condition, &iter_buf); + + ndarray_obj_t *result = NULL; + uint8_t *rarray = NULL; + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memcpy(shape, ndarray->shape, ULAB_MAX_DIMS * sizeof(size_t)); + + size_t *rshape = m_new(size_t, ULAB_MAX_DIMS); + memcpy(rshape, ndarray->shape, ULAB_MAX_DIMS * sizeof(size_t)); + + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memcpy(strides, ndarray->strides, ULAB_MAX_DIMS * sizeof(int32_t)); + + int32_t *rstrides = m_new(int32_t, ULAB_MAX_DIMS); + + if(axis == mp_const_none) { + result = ndarray_new_linear_array(true_count, ndarray->dtype); + rarray = (uint8_t *)result->array; + memset(rstrides, 0, ndarray->ndim * sizeof(int32_t)); + rstrides[ULAB_MAX_DIMS - 1] = ndarray->itemsize; + rshape[ULAB_MAX_DIMS - 1] = 0; + } else { + rshape[shift_ax] = true_count; + + result = ndarray_new_dense_ndarray(ndarray->ndim, rshape, ndarray->dtype); + rarray = (uint8_t *)result->array; + + SWAP(size_t, shape[shift_ax], shape[ULAB_MAX_DIMS - 1]); + SWAP(size_t, rshape[shift_ax], rshape[ULAB_MAX_DIMS - 1]); + SWAP(int32_t, strides[shift_ax], strides[ULAB_MAX_DIMS - 1]); + + memcpy(rstrides, result->strides, ULAB_MAX_DIMS * sizeof(int32_t)); + SWAP(int32_t, rstrides[shift_ax], rstrides[ULAB_MAX_DIMS - 1]); + } + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + if(axis != mp_const_none) { + iterable = mp_getiter(condition, &iter_buf); + } + do { + item = mp_iternext(iterable); + if(mp_obj_is_true(item)) { + memcpy(rarray, array, ndarray->itemsize); + rarray += rstrides[ULAB_MAX_DIMS - 1]; + } + array += strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + array -= strides[ULAB_MAX_DIMS - 1] * shape[ULAB_MAX_DIMS - 1]; + array += strides[ULAB_MAX_DIMS - 2]; + rarray -= rstrides[ULAB_MAX_DIMS - 1] * rshape[ULAB_MAX_DIMS - 1]; + rarray += rstrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + array -= strides[ULAB_MAX_DIMS - 2] * shape[ULAB_MAX_DIMS - 2]; + array += strides[ULAB_MAX_DIMS - 3]; + rarray -= rstrides[ULAB_MAX_DIMS - 2] * rshape[ULAB_MAX_DIMS - 2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + array -= strides[ULAB_MAX_DIMS - 3] * shape[ULAB_MAX_DIMS - 3]; + array += strides[ULAB_MAX_DIMS - 4]; + rarray -= rstrides[ULAB_MAX_DIMS - 2] * rshape[ULAB_MAX_DIMS - 2]; + rarray += rstrides[ULAB_MAX_DIMS - 3]; + i++; + } while(i < shape[ULAB_MAX_DIMS - 4]); + #endif + + return result; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(transform_compress_obj, 2, transform_compress); +#endif /* ULAB_NUMPY_HAS_COMPRESS */ + +#if ULAB_MAX_DIMS > 1 +#if ULAB_NUMPY_HAS_DOT +//| def dot(m1: ulab.numpy.ndarray, m2: ulab.numpy.ndarray) -> Union[ulab.numpy.ndarray, _float]: +//| """ +//| :param ~ulab.numpy.ndarray m1: a matrix, or a vector +//| :param ~ulab.numpy.ndarray m2: a matrix, or a vector +//| +//| Computes the product of two matrices, or two vectors. In the letter case, the inner product is returned.""" +//| ... +//| + +mp_obj_t transform_dot(mp_obj_t _m1, mp_obj_t _m2) { + // TODO: should the results be upcast? + // This implements 2D operations only! + if(!mp_obj_is_type(_m1, &ulab_ndarray_type) || !mp_obj_is_type(_m2, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("arguments must be ndarrays")); + } + ndarray_obj_t *m1 = MP_OBJ_TO_PTR(_m1); + ndarray_obj_t *m2 = MP_OBJ_TO_PTR(_m2); + COMPLEX_DTYPE_NOT_IMPLEMENTED(m1->dtype) + COMPLEX_DTYPE_NOT_IMPLEMENTED(m2->dtype) + + uint8_t *array1 = (uint8_t *)m1->array; + uint8_t *array2 = (uint8_t *)m2->array; + + mp_float_t (*func1)(void *) = ndarray_get_float_function(m1->dtype); + mp_float_t (*func2)(void *) = ndarray_get_float_function(m2->dtype); + + if(m1->shape[ULAB_MAX_DIMS - 1] != m2->shape[ULAB_MAX_DIMS - m2->ndim]) { + mp_raise_ValueError(translate("dimensions do not match")); + } + uint8_t ndim = MIN(m1->ndim, m2->ndim); + size_t shape1 = m1->ndim == 2 ? m1->shape[ULAB_MAX_DIMS - m1->ndim] : 1; + size_t shape2 = m2->ndim == 2 ? m2->shape[ULAB_MAX_DIMS - 1] : 1; + + size_t *shape = NULL; + if(ndim == 2) { // matrix times matrix -> matrix + shape = ndarray_shape_vector(0, 0, shape1, shape2); + } else { // matrix times vector -> vector, vector times vector -> vector (size 1) + shape = ndarray_shape_vector(0, 0, 0, shape1); + } + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + mp_float_t *rarray = (mp_float_t *)results->array; + + for(size_t i=0; i < shape1; i++) { // rows of m1 + for(size_t j=0; j < shape2; j++) { // columns of m2 + mp_float_t dot = 0.0; + for(size_t k=0; k < m1->shape[ULAB_MAX_DIMS - 1]; k++) { + // (i, k) * (k, j) + dot += func1(array1) * func2(array2); + array1 += m1->strides[ULAB_MAX_DIMS - 1]; + array2 += m2->strides[ULAB_MAX_DIMS - m2->ndim]; + } + *rarray++ = dot; + array1 -= m1->strides[ULAB_MAX_DIMS - 1] * m1->shape[ULAB_MAX_DIMS - 1]; + array2 -= m2->strides[ULAB_MAX_DIMS - m2->ndim] * m2->shape[ULAB_MAX_DIMS - m2->ndim]; + array2 += m2->strides[ULAB_MAX_DIMS - 1]; + } + array1 += m1->strides[ULAB_MAX_DIMS - m1->ndim]; + array2 = m2->array; + } + if((m1->ndim * m2->ndim) == 1) { // return a scalar, if product of two vectors + return mp_obj_new_float(*(--rarray)); + } else { + return MP_OBJ_FROM_PTR(results); + } +} + +MP_DEFINE_CONST_FUN_OBJ_2(transform_dot_obj, transform_dot); +#endif +#endif
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/code/numpy/transform.h b/circuitpython/extmod/ulab/code/numpy/transform.h new file mode 100644 index 0000000..039dcea --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/transform.h @@ -0,0 +1,29 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * +*/ + +#ifndef _TRANSFORM_ +#define _TRANSFORM_ + +#include <stdlib.h> +#include <string.h> +#include <math.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../ulab.h" +#include "../ulab_tools.h" +#include "transform.h" + +MP_DECLARE_CONST_FUN_OBJ_KW(transform_compress_obj); +MP_DECLARE_CONST_FUN_OBJ_2(transform_dot_obj); + +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/vector.c b/circuitpython/extmod/ulab/code/numpy/vector.c new file mode 100644 index 0000000..97ab66d --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/vector.c @@ -0,0 +1,844 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * 2020 Jeff Epler for Adafruit Industries + * 2020 Scott Shawcroft for Adafruit Industries + * 2020 Taku Fukada +*/ + +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include "py/runtime.h" +#include "py/binary.h" +#include "py/obj.h" +#include "py/objarray.h" + +#include "../ulab.h" +#include "../ulab_tools.h" +#include "carray/carray_tools.h" +#include "vector.h" + +//| """Element-by-element functions +//| +//| These functions can operate on numbers, 1-D iterables, and arrays of 1 to 4 dimensions by +//| applying the function to every element in the array. This is typically +//| much more efficient than expressing the same operation as a Python loop.""" +//| + +static mp_obj_t vector_generic_vector(mp_obj_t o_in, mp_float_t (*f)(mp_float_t)) { + // Return a single value, if o_in is not iterable + if(mp_obj_is_float(o_in) || mp_obj_is_int(o_in)) { + return mp_obj_new_float(f(mp_obj_get_float(o_in))); + } + ndarray_obj_t *ndarray = NULL; + if(mp_obj_is_type(o_in, &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(o_in); + COMPLEX_DTYPE_NOT_IMPLEMENTED(source->dtype) + uint8_t *sarray = (uint8_t *)source->array; + ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_FLOAT); + mp_float_t *array = (mp_float_t *)ndarray->array; + + #if ULAB_VECTORISE_USES_FUN_POINTER + + mp_float_t (*func)(void *) = ndarray_get_float_function(source->dtype); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t value = func(sarray); + *array++ = f(value); + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + #else + if(source->dtype == NDARRAY_UINT8) { + ITERATE_VECTOR(uint8_t, array, source, sarray); + } else if(source->dtype == NDARRAY_INT8) { + ITERATE_VECTOR(int8_t, array, source, sarray); + } else if(source->dtype == NDARRAY_UINT16) { + ITERATE_VECTOR(uint16_t, array, source, sarray); + } else if(source->dtype == NDARRAY_INT16) { + ITERATE_VECTOR(int16_t, array, source, sarray); + } else { + ITERATE_VECTOR(mp_float_t, array, source, sarray); + } + #endif /* ULAB_VECTORISE_USES_FUN_POINTER */ + } else { + ndarray = ndarray_from_mp_obj(o_in, 0); + mp_float_t *narray = (mp_float_t *)ndarray->array; + for(size_t i = 0; i < ndarray->len; i++) { + *narray = f(*narray); + narray++; + } + } + return MP_OBJ_FROM_PTR(ndarray); +} + +#if ULAB_NUMPY_HAS_ACOS +//| def acos(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the inverse cosine function""" +//| ... +//| + +MATH_FUN_1(acos, acos); +MP_DEFINE_CONST_FUN_OBJ_1(vector_acos_obj, vector_acos); +#endif + +#if ULAB_NUMPY_HAS_ACOSH +//| def acosh(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the inverse hyperbolic cosine function""" +//| ... +//| + +MATH_FUN_1(acosh, acosh); +MP_DEFINE_CONST_FUN_OBJ_1(vector_acosh_obj, vector_acosh); +#endif + +#if ULAB_NUMPY_HAS_ASIN +//| def asin(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the inverse sine function""" +//| ... +//| + +MATH_FUN_1(asin, asin); +MP_DEFINE_CONST_FUN_OBJ_1(vector_asin_obj, vector_asin); +#endif + +#if ULAB_NUMPY_HAS_ASINH +//| def asinh(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the inverse hyperbolic sine function""" +//| ... +//| + +MATH_FUN_1(asinh, asinh); +MP_DEFINE_CONST_FUN_OBJ_1(vector_asinh_obj, vector_asinh); +#endif + +#if ULAB_NUMPY_HAS_AROUND +//| def around(a: _ArrayLike, *, decimals: int = 0) -> ulab.numpy.ndarray: +//| """Returns a new float array in which each element is rounded to +//| ``decimals`` places.""" +//| ... +//| + +mp_obj_t vector_around(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} }, + { MP_QSTR_decimals, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 0 } } + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("first argument must be an ndarray")); + } + int8_t n = args[1].u_int; + mp_float_t mul = MICROPY_FLOAT_C_FUN(pow)(10.0, n); + ndarray_obj_t *source = MP_OBJ_TO_PTR(args[0].u_obj); + COMPLEX_DTYPE_NOT_IMPLEMENTED(source->dtype) + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_FLOAT); + mp_float_t *narray = (mp_float_t *)ndarray->array; + uint8_t *sarray = (uint8_t *)source->array; + + mp_float_t (*func)(void *) = ndarray_get_float_function(source->dtype); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t f = func(sarray); + *narray++ = MICROPY_FLOAT_C_FUN(round)(f * mul) / mul; + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif + return MP_OBJ_FROM_PTR(ndarray); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(vector_around_obj, 1, vector_around); +#endif + +#if ULAB_NUMPY_HAS_ATAN +//| def atan(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the inverse tangent function; the return values are in the +//| range [-pi/2,pi/2].""" +//| ... +//| + +MATH_FUN_1(atan, atan); +MP_DEFINE_CONST_FUN_OBJ_1(vector_atan_obj, vector_atan); +#endif + +#if ULAB_NUMPY_HAS_ARCTAN2 +//| def arctan2(ya: _ArrayLike, xa: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the inverse tangent function of y/x; the return values are in +//| the range [-pi, pi].""" +//| ... +//| + +mp_obj_t vector_arctan2(mp_obj_t y, mp_obj_t x) { + ndarray_obj_t *ndarray_x = ndarray_from_mp_obj(x, 0); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray_x->dtype) + + ndarray_obj_t *ndarray_y = ndarray_from_mp_obj(y, 0); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray_y->dtype) + + uint8_t ndim = 0; + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + int32_t *xstrides = m_new(int32_t, ULAB_MAX_DIMS); + int32_t *ystrides = m_new(int32_t, ULAB_MAX_DIMS); + if(!ndarray_can_broadcast(ndarray_x, ndarray_y, &ndim, shape, xstrides, ystrides)) { + mp_raise_ValueError(translate("operands could not be broadcast together")); + m_del(size_t, shape, ULAB_MAX_DIMS); + m_del(int32_t, xstrides, ULAB_MAX_DIMS); + m_del(int32_t, ystrides, ULAB_MAX_DIMS); + } + + uint8_t *xarray = (uint8_t *)ndarray_x->array; + uint8_t *yarray = (uint8_t *)ndarray_y->array; + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + mp_float_t *rarray = (mp_float_t *)results->array; + + mp_float_t (*funcx)(void *) = ndarray_get_float_function(ndarray_x->dtype); + mp_float_t (*funcy)(void *) = ndarray_get_float_function(ndarray_y->dtype); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t _x = funcx(xarray); + mp_float_t _y = funcy(yarray); + *rarray++ = MICROPY_FLOAT_C_FUN(atan2)(_y, _x); + xarray += xstrides[ULAB_MAX_DIMS - 1]; + yarray += ystrides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < results->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + xarray -= xstrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + xarray += xstrides[ULAB_MAX_DIMS - 2]; + yarray -= ystrides[ULAB_MAX_DIMS - 1] * results->shape[ULAB_MAX_DIMS-1]; + yarray += ystrides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < results->shape[ULAB_MAX_DIMS - 2]); + #endif + #if ULAB_MAX_DIMS > 2 + xarray -= xstrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + xarray += xstrides[ULAB_MAX_DIMS - 3]; + yarray -= ystrides[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + yarray += ystrides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < results->shape[ULAB_MAX_DIMS - 3]); + #endif + #if ULAB_MAX_DIMS > 3 + xarray -= xstrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + xarray += xstrides[ULAB_MAX_DIMS - 4]; + yarray -= ystrides[ULAB_MAX_DIMS - 3] * results->shape[ULAB_MAX_DIMS-3]; + yarray += ystrides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < results->shape[ULAB_MAX_DIMS - 4]); + #endif + + return MP_OBJ_FROM_PTR(results); +} + +MP_DEFINE_CONST_FUN_OBJ_2(vector_arctan2_obj, vector_arctan2); +#endif /* ULAB_VECTORISE_HAS_ARCTAN2 */ + +#if ULAB_NUMPY_HAS_ATANH +//| def atanh(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the inverse hyperbolic tangent function""" +//| ... +//| + +MATH_FUN_1(atanh, atanh); +MP_DEFINE_CONST_FUN_OBJ_1(vector_atanh_obj, vector_atanh); +#endif + +#if ULAB_NUMPY_HAS_CEIL +//| def ceil(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Rounds numbers up to the next whole number""" +//| ... +//| + +MATH_FUN_1(ceil, ceil); +MP_DEFINE_CONST_FUN_OBJ_1(vector_ceil_obj, vector_ceil); +#endif + +#if ULAB_NUMPY_HAS_COS +//| def cos(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the cosine function""" +//| ... +//| + +MATH_FUN_1(cos, cos); +MP_DEFINE_CONST_FUN_OBJ_1(vector_cos_obj, vector_cos); +#endif + +#if ULAB_NUMPY_HAS_COSH +//| def cosh(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the hyperbolic cosine function""" +//| ... +//| + +MATH_FUN_1(cosh, cosh); +MP_DEFINE_CONST_FUN_OBJ_1(vector_cosh_obj, vector_cosh); +#endif + +#if ULAB_NUMPY_HAS_DEGREES +//| def degrees(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Converts angles from radians to degrees""" +//| ... +//| + +static mp_float_t vector_degrees_(mp_float_t value) { + return value * MICROPY_FLOAT_CONST(180.0) / MP_PI; +} + +static mp_obj_t vector_degrees(mp_obj_t x_obj) { + return vector_generic_vector(x_obj, vector_degrees_); +} + +MP_DEFINE_CONST_FUN_OBJ_1(vector_degrees_obj, vector_degrees); +#endif + +#if ULAB_SCIPY_SPECIAL_HAS_ERF +//| def erf(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the error function, which has applications in statistics""" +//| ... +//| + +MATH_FUN_1(erf, erf); +MP_DEFINE_CONST_FUN_OBJ_1(vector_erf_obj, vector_erf); +#endif + +#if ULAB_SCIPY_SPECIAL_HAS_ERFC +//| def erfc(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the complementary error function, which has applications in statistics""" +//| ... +//| + +MATH_FUN_1(erfc, erfc); +MP_DEFINE_CONST_FUN_OBJ_1(vector_erfc_obj, vector_erfc); +#endif + +#if ULAB_NUMPY_HAS_EXP +//| def exp(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the exponent function.""" +//| ... +//| + +static mp_obj_t vector_exp(mp_obj_t o_in) { + #if ULAB_SUPPORTS_COMPLEX + if(mp_obj_is_type(o_in, &mp_type_complex)) { + mp_float_t real, imag; + mp_obj_get_complex(o_in, &real, &imag); + mp_float_t exp_real = MICROPY_FLOAT_C_FUN(exp)(real); + return mp_obj_new_complex(exp_real * MICROPY_FLOAT_C_FUN(cos)(imag), exp_real * MICROPY_FLOAT_C_FUN(sin)(imag)); + } else if(mp_obj_is_type(o_in, &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(o_in); + if(source->dtype == NDARRAY_COMPLEX) { + uint8_t *sarray = (uint8_t *)source->array; + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_COMPLEX); + mp_float_t *array = (mp_float_t *)ndarray->array; + uint8_t itemsize = sizeof(mp_float_t); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t real = *(mp_float_t *)sarray; + mp_float_t imag = *(mp_float_t *)(sarray + itemsize); + mp_float_t exp_real = MICROPY_FLOAT_C_FUN(exp)(real); + *array++ = exp_real * MICROPY_FLOAT_C_FUN(cos)(imag); + *array++ = exp_real * MICROPY_FLOAT_C_FUN(sin)(imag); + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + return MP_OBJ_FROM_PTR(ndarray); + } + } + #endif + return vector_generic_vector(o_in, MICROPY_FLOAT_C_FUN(exp)); +} + +MP_DEFINE_CONST_FUN_OBJ_1(vector_exp_obj, vector_exp); +#endif + +#if ULAB_NUMPY_HAS_EXPM1 +//| def expm1(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes $e^x-1$. In certain applications, using this function preserves numeric accuracy better than the `exp` function.""" +//| ... +//| + +MATH_FUN_1(expm1, expm1); +MP_DEFINE_CONST_FUN_OBJ_1(vector_expm1_obj, vector_expm1); +#endif + +#if ULAB_NUMPY_HAS_FLOOR +//| def floor(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Rounds numbers up to the next whole number""" +//| ... +//| + +MATH_FUN_1(floor, floor); +MP_DEFINE_CONST_FUN_OBJ_1(vector_floor_obj, vector_floor); +#endif + +#if ULAB_SCIPY_SPECIAL_HAS_GAMMA +//| def gamma(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the gamma function""" +//| ... +//| + +MATH_FUN_1(gamma, tgamma); +MP_DEFINE_CONST_FUN_OBJ_1(vector_gamma_obj, vector_gamma); +#endif + +#if ULAB_SCIPY_SPECIAL_HAS_GAMMALN +//| def lgamma(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the natural log of the gamma function""" +//| ... +//| + +MATH_FUN_1(lgamma, lgamma); +MP_DEFINE_CONST_FUN_OBJ_1(vector_lgamma_obj, vector_lgamma); +#endif + +#if ULAB_NUMPY_HAS_LOG +//| def log(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the natural log""" +//| ... +//| + +MATH_FUN_1(log, log); +MP_DEFINE_CONST_FUN_OBJ_1(vector_log_obj, vector_log); +#endif + +#if ULAB_NUMPY_HAS_LOG10 +//| def log10(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the log base 10""" +//| ... +//| + +MATH_FUN_1(log10, log10); +MP_DEFINE_CONST_FUN_OBJ_1(vector_log10_obj, vector_log10); +#endif + +#if ULAB_NUMPY_HAS_LOG2 +//| def log2(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the log base 2""" +//| ... +//| + +MATH_FUN_1(log2, log2); +MP_DEFINE_CONST_FUN_OBJ_1(vector_log2_obj, vector_log2); +#endif + +#if ULAB_NUMPY_HAS_RADIANS +//| def radians(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Converts angles from degrees to radians""" +//| ... +//| + +static mp_float_t vector_radians_(mp_float_t value) { + return value * MP_PI / MICROPY_FLOAT_CONST(180.0); +} + +static mp_obj_t vector_radians(mp_obj_t x_obj) { + return vector_generic_vector(x_obj, vector_radians_); +} + +MP_DEFINE_CONST_FUN_OBJ_1(vector_radians_obj, vector_radians); +#endif + +#if ULAB_NUMPY_HAS_SIN +//| def sin(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the sine function""" +//| ... +//| + +MATH_FUN_1(sin, sin); +MP_DEFINE_CONST_FUN_OBJ_1(vector_sin_obj, vector_sin); +#endif + +#if ULAB_NUMPY_HAS_SINH +//| def sinh(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the hyperbolic sine""" +//| ... +//| + +MATH_FUN_1(sinh, sinh); +MP_DEFINE_CONST_FUN_OBJ_1(vector_sinh_obj, vector_sinh); +#endif + + +#if ULAB_NUMPY_HAS_SQRT +//| def sqrt(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the square root""" +//| ... +//| + +#if ULAB_SUPPORTS_COMPLEX +mp_obj_t vector_sqrt(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_dtype, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_INT(NDARRAY_FLOAT) } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t o_in = args[0].u_obj; + uint8_t dtype = mp_obj_get_int(args[1].u_obj); + if((dtype != NDARRAY_FLOAT) && (dtype != NDARRAY_COMPLEX)) { + mp_raise_TypeError(translate("dtype must be float, or complex")); + } + + if(mp_obj_is_type(o_in, &mp_type_complex)) { + mp_float_t real, imag; + mp_obj_get_complex(o_in, &real, &imag); + mp_float_t sqrt_abs = MICROPY_FLOAT_C_FUN(sqrt)(real * real + imag * imag); + sqrt_abs = MICROPY_FLOAT_C_FUN(sqrt)(sqrt_abs); + mp_float_t theta = MICROPY_FLOAT_CONST(0.5) * MICROPY_FLOAT_C_FUN(atan2)(imag, real); + return mp_obj_new_complex(sqrt_abs * MICROPY_FLOAT_C_FUN(cos)(theta), sqrt_abs * MICROPY_FLOAT_C_FUN(sin)(theta)); + } else if(mp_obj_is_type(o_in, &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(o_in); + if((source->dtype == NDARRAY_COMPLEX) && (dtype == NDARRAY_FLOAT)) { + mp_raise_TypeError(translate("can't convert complex to float")); + } + + if(dtype == NDARRAY_COMPLEX) { + if(source->dtype == NDARRAY_COMPLEX) { + uint8_t *sarray = (uint8_t *)source->array; + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_COMPLEX); + mp_float_t *array = (mp_float_t *)ndarray->array; + uint8_t itemsize = sizeof(mp_float_t); + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t real = *(mp_float_t *)sarray; + mp_float_t imag = *(mp_float_t *)(sarray + itemsize); + mp_float_t sqrt_abs = MICROPY_FLOAT_C_FUN(sqrt)(real * real + imag * imag); + sqrt_abs = MICROPY_FLOAT_C_FUN(sqrt)(sqrt_abs); + mp_float_t theta = MICROPY_FLOAT_CONST(0.5) * MICROPY_FLOAT_C_FUN(atan2)(imag, real); + *array++ = sqrt_abs * MICROPY_FLOAT_C_FUN(cos)(theta); + *array++ = sqrt_abs * MICROPY_FLOAT_C_FUN(sin)(theta); + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + return MP_OBJ_FROM_PTR(ndarray); + } else if(source->dtype == NDARRAY_FLOAT) { + uint8_t *sarray = (uint8_t *)source->array; + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, NDARRAY_COMPLEX); + mp_float_t *array = (mp_float_t *)ndarray->array; + + #if ULAB_MAX_DIMS > 3 + size_t i = 0; + do { + #endif + #if ULAB_MAX_DIMS > 2 + size_t j = 0; + do { + #endif + #if ULAB_MAX_DIMS > 1 + size_t k = 0; + do { + #endif + size_t l = 0; + do { + mp_float_t value = *(mp_float_t *)sarray; + if(value >= MICROPY_FLOAT_CONST(0.0)) { + *array++ = MICROPY_FLOAT_C_FUN(sqrt)(value); + array++; + } else { + array++; + *array++ = MICROPY_FLOAT_C_FUN(sqrt)(-value); + } + sarray += source->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < source->shape[ULAB_MAX_DIMS - 1]); + #if ULAB_MAX_DIMS > 1 + sarray -= source->strides[ULAB_MAX_DIMS - 1] * source->shape[ULAB_MAX_DIMS-1]; + sarray += source->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < source->shape[ULAB_MAX_DIMS - 2]); + #endif /* ULAB_MAX_DIMS > 1 */ + #if ULAB_MAX_DIMS > 2 + sarray -= source->strides[ULAB_MAX_DIMS - 2] * source->shape[ULAB_MAX_DIMS-2]; + sarray += source->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < source->shape[ULAB_MAX_DIMS - 3]); + #endif /* ULAB_MAX_DIMS > 2 */ + #if ULAB_MAX_DIMS > 3 + sarray -= source->strides[ULAB_MAX_DIMS - 3] * source->shape[ULAB_MAX_DIMS-3]; + sarray += source->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < source->shape[ULAB_MAX_DIMS - 4]); + #endif /* ULAB_MAX_DIMS > 3 */ + return MP_OBJ_FROM_PTR(ndarray); + } else { + mp_raise_TypeError(translate("input dtype must be float or complex")); + } + } + } + return vector_generic_vector(o_in, MICROPY_FLOAT_C_FUN(sqrt)); +} +MP_DEFINE_CONST_FUN_OBJ_KW(vector_sqrt_obj, 1, vector_sqrt); +#else +MATH_FUN_1(sqrt, sqrt); +MP_DEFINE_CONST_FUN_OBJ_1(vector_sqrt_obj, vector_sqrt); +#endif /* ULAB_SUPPORTS_COMPLEX */ + +#endif /* ULAB_NUMPY_HAS_SQRT */ + +#if ULAB_NUMPY_HAS_TAN +//| def tan(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the tangent""" +//| ... +//| + +MATH_FUN_1(tan, tan); +MP_DEFINE_CONST_FUN_OBJ_1(vector_tan_obj, vector_tan); +#endif + +#if ULAB_NUMPY_HAS_TANH +//| def tanh(a: _ArrayLike) -> ulab.numpy.ndarray: +//| """Computes the hyperbolic tangent""" +//| ... + +MATH_FUN_1(tanh, tanh); +MP_DEFINE_CONST_FUN_OBJ_1(vector_tanh_obj, vector_tanh); +#endif + +#if ULAB_NUMPY_HAS_VECTORIZE +static mp_obj_t vector_vectorized_function_call(mp_obj_t self_in, size_t n_args, size_t n_kw, const mp_obj_t *args) { + (void) n_args; + (void) n_kw; + vectorized_function_obj_t *self = MP_OBJ_TO_PTR(self_in); + mp_obj_t avalue[1]; + mp_obj_t fvalue; + if(mp_obj_is_type(args[0], &ulab_ndarray_type)) { + ndarray_obj_t *source = MP_OBJ_TO_PTR(args[0]); + COMPLEX_DTYPE_NOT_IMPLEMENTED(source->dtype) + ndarray_obj_t *ndarray = ndarray_new_dense_ndarray(source->ndim, source->shape, self->otypes); + for(size_t i=0; i < source->len; i++) { + avalue[0] = mp_binary_get_val_array(source->dtype, source->array, i); + fvalue = self->type->MP_TYPE_CALL(self->fun, 1, 0, avalue); + ndarray_set_value(self->otypes, ndarray->array, i, fvalue); + } + return MP_OBJ_FROM_PTR(ndarray); + } else if(mp_obj_is_type(args[0], &mp_type_tuple) || mp_obj_is_type(args[0], &mp_type_list) || + mp_obj_is_type(args[0], &mp_type_range)) { // i.e., the input is a generic iterable + size_t len = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[0])); + ndarray_obj_t *ndarray = ndarray_new_linear_array(len, self->otypes); + mp_obj_iter_buf_t iter_buf; + mp_obj_t iterable = mp_getiter(args[0], &iter_buf); + size_t i=0; + while ((avalue[0] = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + fvalue = self->type->MP_TYPE_CALL(self->fun, 1, 0, avalue); + ndarray_set_value(self->otypes, ndarray->array, i, fvalue); + i++; + } + return MP_OBJ_FROM_PTR(ndarray); + } else if(mp_obj_is_int(args[0]) || mp_obj_is_float(args[0])) { + ndarray_obj_t *ndarray = ndarray_new_linear_array(1, self->otypes); + fvalue = self->type->MP_TYPE_CALL(self->fun, 1, 0, args); + ndarray_set_value(self->otypes, ndarray->array, 0, fvalue); + return MP_OBJ_FROM_PTR(ndarray); + } else { + mp_raise_ValueError(translate("wrong input type")); + } + return mp_const_none; +} + +const mp_obj_type_t vector_function_type = { + { &mp_type_type }, + .flags = MP_TYPE_FLAG_EXTENDED, + .name = MP_QSTR_, + MP_TYPE_EXTENDED_FIELDS( + .call = vector_vectorized_function_call, + ) +}; + +//| def vectorize( +//| f: Union[Callable[[int], _float], Callable[[_float], _float]], +//| *, +//| otypes: Optional[_DType] = None +//| ) -> Callable[[_ArrayLike], ulab.numpy.ndarray]: +//| """ +//| :param callable f: The function to wrap +//| :param otypes: List of array types that may be returned by the function. None is interpreted to mean the return value is float. +//| +//| Wrap a Python function ``f`` so that it can be applied to arrays. +//| The callable must return only values of the types specified by ``otypes``, or the result is undefined.""" +//| ... +//| + +static mp_obj_t vector_vectorize(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} }, + { MP_QSTR_otypes, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} } + }; + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + const mp_obj_type_t *type = mp_obj_get_type(args[0].u_obj); + if(mp_type_get_call_slot(type) == NULL) { + mp_raise_TypeError(translate("first argument must be a callable")); + } + mp_obj_t _otypes = args[1].u_obj; + uint8_t otypes = NDARRAY_FLOAT; + if(_otypes == mp_const_none) { + // TODO: is this what numpy does? + otypes = NDARRAY_FLOAT; + } else if(mp_obj_is_int(_otypes)) { + otypes = mp_obj_get_int(_otypes); + if(otypes != NDARRAY_FLOAT && otypes != NDARRAY_UINT8 && otypes != NDARRAY_INT8 && + otypes != NDARRAY_UINT16 && otypes != NDARRAY_INT16) { + mp_raise_ValueError(translate("wrong output type")); + } + } + else { + mp_raise_ValueError(translate("wrong output type")); + } + vectorized_function_obj_t *function = m_new_obj(vectorized_function_obj_t); + function->base.type = &vector_function_type; + function->otypes = otypes; + function->fun = args[0].u_obj; + function->type = type; + return MP_OBJ_FROM_PTR(function); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(vector_vectorize_obj, 1, vector_vectorize); +#endif diff --git a/circuitpython/extmod/ulab/code/numpy/vector.h b/circuitpython/extmod/ulab/code/numpy/vector.h new file mode 100644 index 0000000..ea38b0f --- /dev/null +++ b/circuitpython/extmod/ulab/code/numpy/vector.h @@ -0,0 +1,161 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös +*/ + +#ifndef _VECTOR_ +#define _VECTOR_ + +#include "../ulab.h" +#include "../ndarray.h" + +MP_DECLARE_CONST_FUN_OBJ_1(vector_acos_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_acosh_obj); +MP_DECLARE_CONST_FUN_OBJ_2(vector_arctan2_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(vector_around_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_asin_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_asinh_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_atan_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_atanh_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_ceil_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_cos_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_cosh_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_degrees_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_erf_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_erfc_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_exp_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_expm1_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_floor_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_gamma_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_lgamma_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_log_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_log10_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_log2_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_radians_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_sin_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_sinh_obj); +#if ULAB_SUPPORTS_COMPLEX +MP_DECLARE_CONST_FUN_OBJ_KW(vector_sqrt_obj); +#else +MP_DECLARE_CONST_FUN_OBJ_1(vector_sqrt_obj); +#endif +MP_DECLARE_CONST_FUN_OBJ_1(vector_tan_obj); +MP_DECLARE_CONST_FUN_OBJ_1(vector_tanh_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(vector_vectorize_obj); + +typedef struct _vectorized_function_obj_t { + mp_obj_base_t base; + uint8_t otypes; + mp_obj_t fun; + const mp_obj_type_t *type; +} vectorized_function_obj_t; + +#if ULAB_HAS_FUNCTION_ITERATOR +#define ITERATE_VECTOR(type, array, source, sarray, shift)\ +({\ + size_t *scoords = ndarray_new_coords((source)->ndim);\ + for(size_t i=0; i < (source)->len/(source)->shape[ULAB_MAX_DIMS -1]; i++) {\ + for(size_t l=0; l < (source)->shape[ULAB_MAX_DIMS - 1]; l++) {\ + *(array) = f(*((type *)(sarray)));\ + (array) += (shift);\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 1];\ + }\ + ndarray_rewind_array((source)->ndim, sarray, (source)->shape, (source)->strides, scoords);\ + }\ +}) + +#else + +#if ULAB_MAX_DIMS == 4 +#define ITERATE_VECTOR(type, array, source, sarray) do {\ + size_t i=0;\ + do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *(array)++ = f(*((type *)(sarray)));\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (source)->shape[ULAB_MAX_DIMS-1]);\ + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1];\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (source)->shape[ULAB_MAX_DIMS-2]);\ + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 2] * (source)->shape[ULAB_MAX_DIMS-2];\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (source)->shape[ULAB_MAX_DIMS-3]);\ + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 3] * (source)->shape[ULAB_MAX_DIMS-3];\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 4];\ + i++;\ + } while(i < (source)->shape[ULAB_MAX_DIMS-4]);\ +} while(0) +#endif /* ULAB_MAX_DIMS == 4 */ + +#if ULAB_MAX_DIMS == 3 +#define ITERATE_VECTOR(type, array, source, sarray) do {\ + size_t j = 0;\ + do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *(array)++ = f(*((type *)(sarray)));\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (source)->shape[ULAB_MAX_DIMS-1]);\ + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1];\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (source)->shape[ULAB_MAX_DIMS-2]);\ + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 2] * (source)->shape[ULAB_MAX_DIMS-2];\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 3];\ + j++;\ + } while(j < (source)->shape[ULAB_MAX_DIMS-3]);\ +} while(0) +#endif /* ULAB_MAX_DIMS == 3 */ + +#if ULAB_MAX_DIMS == 2 +#define ITERATE_VECTOR(type, array, source, sarray) do {\ + size_t k = 0;\ + do {\ + size_t l = 0;\ + do {\ + *(array)++ = f(*((type *)(sarray)));\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (source)->shape[ULAB_MAX_DIMS-1]);\ + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1];\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 2];\ + k++;\ + } while(k < (source)->shape[ULAB_MAX_DIMS-2]);\ +} while(0) +#endif /* ULAB_MAX_DIMS == 2 */ + +#if ULAB_MAX_DIMS == 1 +#define ITERATE_VECTOR(type, array, source, sarray) do {\ + size_t l = 0;\ + do {\ + *(array)++ = f(*((type *)(sarray)));\ + (sarray) += (source)->strides[ULAB_MAX_DIMS - 1];\ + l++;\ + } while(l < (source)->shape[ULAB_MAX_DIMS-1]);\ +} while(0) +#endif /* ULAB_MAX_DIMS == 1 */ +#endif /* ULAB_HAS_FUNCTION_ITERATOR */ + +#define MATH_FUN_1(py_name, c_name) \ + static mp_obj_t vector_ ## py_name(mp_obj_t x_obj) { \ + return vector_generic_vector(x_obj, MICROPY_FLOAT_C_FUN(c_name)); \ +} + +#endif /* _VECTOR_ */ diff --git a/circuitpython/extmod/ulab/code/scipy/linalg/linalg.c b/circuitpython/extmod/ulab/code/scipy/linalg/linalg.c new file mode 100644 index 0000000..d211f72 --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/linalg/linalg.c @@ -0,0 +1,280 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2021 Vikas Udupa + * +*/ + +#include <stdlib.h> +#include <string.h> +#include <math.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../../ulab.h" +#include "../../ulab_tools.h" +#include "../../numpy/linalg/linalg_tools.h" +#include "linalg.h" + +#if ULAB_SCIPY_HAS_LINALG_MODULE +//| +//| import ulab.scipy +//| import ulab.numpy +//| +//| """Linear algebra functions""" +//| + +#if ULAB_MAX_DIMS > 1 + +//| def solve_triangular(A: ulab.numpy.ndarray, b: ulab.numpy.ndarray, lower: bool) -> ulab.numpy.ndarray: +//| """ +//| :param ~ulab.numpy.ndarray A: a matrix +//| :param ~ulab.numpy.ndarray b: a vector +//| :param ~bool lower: if true, use only data contained in lower triangle of A, else use upper triangle of A +//| :return: solution to the system A x = b. Shape of return matches b +//| :raises TypeError: if A and b are not of type ndarray and are not dense +//| :raises ValueError: if A is a singular matrix +//| +//| Solve the equation A x = b for x, assuming A is a triangular matrix""" +//| ... +//| + +static mp_obj_t solve_triangular(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + + size_t i, j; + + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none} } , + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none} } , + { MP_QSTR_lower, MP_ARG_OBJ, { .u_rom_obj = mp_const_false } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(!mp_obj_is_type(args[0].u_obj, &ulab_ndarray_type) || !mp_obj_is_type(args[1].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("first two arguments must be ndarrays")); + } + + ndarray_obj_t *A = MP_OBJ_TO_PTR(args[0].u_obj); + ndarray_obj_t *b = MP_OBJ_TO_PTR(args[1].u_obj); + + if(!ndarray_is_dense(A) || !ndarray_is_dense(b)) { + mp_raise_TypeError(translate("input must be a dense ndarray")); + } + + size_t A_rows = A->shape[ULAB_MAX_DIMS - 2]; + size_t A_cols = A->shape[ULAB_MAX_DIMS - 1]; + + uint8_t *A_arr = (uint8_t *)A->array; + uint8_t *b_arr = (uint8_t *)b->array; + + mp_float_t (*get_A_ele)(void *) = ndarray_get_float_function(A->dtype); + mp_float_t (*get_b_ele)(void *) = ndarray_get_float_function(b->dtype); + + uint8_t *temp_A = A_arr; + + // check if input matrix A is singular + for (i = 0; i < A_rows; i++) { + if (MICROPY_FLOAT_C_FUN(fabs)(get_A_ele(A_arr)) < LINALG_EPSILON) + mp_raise_ValueError(translate("input matrix is singular")); + A_arr += A->strides[ULAB_MAX_DIMS - 2]; + A_arr += A->strides[ULAB_MAX_DIMS - 1]; + } + + A_arr = temp_A; + + ndarray_obj_t *x = ndarray_new_dense_ndarray(b->ndim, b->shape, NDARRAY_FLOAT); + mp_float_t *x_arr = (mp_float_t *)x->array; + + if (mp_obj_is_true(args[2].u_obj)) { + // Solve the lower triangular matrix by iterating each row of A. + // Start by finding the first unknown using the first row. + // On finding this unknown, find the second unknown using the second row. + // Continue the same till the last unknown is found using the last row. + + for (i = 0; i < A_rows; i++) { + mp_float_t sum = 0.0; + for (j = 0; j < i; j++) { + sum += (get_A_ele(A_arr) * (*x_arr++)); + A_arr += A->strides[ULAB_MAX_DIMS - 1]; + } + + sum = (get_b_ele(b_arr) - sum) / (get_A_ele(A_arr)); + *x_arr = sum; + + x_arr -= j; + A_arr -= A->strides[ULAB_MAX_DIMS - 1] * j; + A_arr += A->strides[ULAB_MAX_DIMS - 2]; + b_arr += b->strides[ULAB_MAX_DIMS - 1]; + } + } else { + // Solve the upper triangular matrix by iterating each row of A. + // Start by finding the last unknown using the last row. + // On finding this unknown, find the last-but-one unknown using the last-but-one row. + // Continue the same till the first unknown is found using the first row. + + A_arr += (A->strides[ULAB_MAX_DIMS - 2] * A_rows); + b_arr += (b->strides[ULAB_MAX_DIMS - 1] * A_cols); + x_arr += A_cols; + + for (i = A_rows - 1; i < A_rows; i--) { + mp_float_t sum = 0.0; + for (j = i + 1; j < A_cols; j++) { + sum += (get_A_ele(A_arr) * (*x_arr++)); + A_arr += A->strides[ULAB_MAX_DIMS - 1]; + } + + x_arr -= (j - i); + A_arr -= (A->strides[ULAB_MAX_DIMS - 1] * (j - i)); + b_arr -= b->strides[ULAB_MAX_DIMS - 1]; + + sum = (get_b_ele(b_arr) - sum) / get_A_ele(A_arr); + *x_arr = sum; + + A_arr -= A->strides[ULAB_MAX_DIMS - 2]; + } + } + + return MP_OBJ_FROM_PTR(x); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(linalg_solve_triangular_obj, 2, solve_triangular); + +//| def cho_solve(L: ulab.numpy.ndarray, b: ulab.numpy.ndarray) -> ulab.numpy.ndarray: +//| """ +//| :param ~ulab.numpy.ndarray L: the lower triangular, Cholesky factorization of A +//| :param ~ulab.numpy.ndarray b: right-hand-side vector b +//| :return: solution to the system A x = b. Shape of return matches b +//| :raises TypeError: if L and b are not of type ndarray and are not dense +//| +//| Solve the linear equations A x = b, given the Cholesky factorization of A as input""" +//| ... +//| + +static mp_obj_t cho_solve(mp_obj_t _L, mp_obj_t _b) { + + if(!mp_obj_is_type(_L, &ulab_ndarray_type) || !mp_obj_is_type(_b, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("first two arguments must be ndarrays")); + } + + ndarray_obj_t *L = MP_OBJ_TO_PTR(_L); + ndarray_obj_t *b = MP_OBJ_TO_PTR(_b); + + if(!ndarray_is_dense(L) || !ndarray_is_dense(b)) { + mp_raise_TypeError(translate("input must be a dense ndarray")); + } + + mp_float_t (*get_L_ele)(void *) = ndarray_get_float_function(L->dtype); + mp_float_t (*get_b_ele)(void *) = ndarray_get_float_function(b->dtype); + void (*set_L_ele)(void *, mp_float_t) = ndarray_set_float_function(L->dtype); + + size_t L_rows = L->shape[ULAB_MAX_DIMS - 2]; + size_t L_cols = L->shape[ULAB_MAX_DIMS - 1]; + + // Obtain transpose of the input matrix L in L_t + size_t L_t_shape[ULAB_MAX_DIMS]; + size_t L_t_rows = L_t_shape[ULAB_MAX_DIMS - 2] = L_cols; + size_t L_t_cols = L_t_shape[ULAB_MAX_DIMS - 1] = L_rows; + ndarray_obj_t *L_t = ndarray_new_dense_ndarray(L->ndim, L_t_shape, L->dtype); + + uint8_t *L_arr = (uint8_t *)L->array; + uint8_t *L_t_arr = (uint8_t *)L_t->array; + uint8_t *b_arr = (uint8_t *)b->array; + + size_t i, j; + + uint8_t *L_ptr = L_arr; + uint8_t *L_t_ptr = L_t_arr; + for (i = 0; i < L_rows; i++) { + for (j = 0; j < L_cols; j++) { + set_L_ele(L_t_ptr, get_L_ele(L_ptr)); + L_t_ptr += L_t->strides[ULAB_MAX_DIMS - 2]; + L_ptr += L->strides[ULAB_MAX_DIMS - 1]; + } + + L_t_ptr -= j * L_t->strides[ULAB_MAX_DIMS - 2]; + L_t_ptr += L_t->strides[ULAB_MAX_DIMS - 1]; + L_ptr -= j * L->strides[ULAB_MAX_DIMS - 1]; + L_ptr += L->strides[ULAB_MAX_DIMS - 2]; + } + + ndarray_obj_t *x = ndarray_new_dense_ndarray(b->ndim, b->shape, NDARRAY_FLOAT); + mp_float_t *x_arr = (mp_float_t *)x->array; + + ndarray_obj_t *y = ndarray_new_dense_ndarray(b->ndim, b->shape, NDARRAY_FLOAT); + mp_float_t *y_arr = (mp_float_t *)y->array; + + // solve L y = b to obtain y, where L_t x = y + for (i = 0; i < L_rows; i++) { + mp_float_t sum = 0.0; + for (j = 0; j < i; j++) { + sum += (get_L_ele(L_arr) * (*y_arr++)); + L_arr += L->strides[ULAB_MAX_DIMS - 1]; + } + + sum = (get_b_ele(b_arr) - sum) / (get_L_ele(L_arr)); + *y_arr = sum; + + y_arr -= j; + L_arr -= L->strides[ULAB_MAX_DIMS - 1] * j; + L_arr += L->strides[ULAB_MAX_DIMS - 2]; + b_arr += b->strides[ULAB_MAX_DIMS - 1]; + } + + // using y, solve L_t x = y to obtain x + L_t_arr += (L_t->strides[ULAB_MAX_DIMS - 2] * L_t_rows); + y_arr += L_t_cols; + x_arr += L_t_cols; + + for (i = L_t_rows - 1; i < L_t_rows; i--) { + mp_float_t sum = 0.0; + for (j = i + 1; j < L_t_cols; j++) { + sum += (get_L_ele(L_t_arr) * (*x_arr++)); + L_t_arr += L_t->strides[ULAB_MAX_DIMS - 1]; + } + + x_arr -= (j - i); + L_t_arr -= (L_t->strides[ULAB_MAX_DIMS - 1] * (j - i)); + y_arr--; + + sum = ((*y_arr) - sum) / get_L_ele(L_t_arr); + *x_arr = sum; + + L_t_arr -= L_t->strides[ULAB_MAX_DIMS - 2]; + } + + return MP_OBJ_FROM_PTR(x); +} + +MP_DEFINE_CONST_FUN_OBJ_2(linalg_cho_solve_obj, cho_solve); + +#endif + +static const mp_rom_map_elem_t ulab_scipy_linalg_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_linalg) }, + #if ULAB_MAX_DIMS > 1 + #if ULAB_SCIPY_LINALG_HAS_SOLVE_TRIANGULAR + { MP_ROM_QSTR(MP_QSTR_solve_triangular), (mp_obj_t)&linalg_solve_triangular_obj }, + #endif + #if ULAB_SCIPY_LINALG_HAS_CHO_SOLVE + { MP_ROM_QSTR(MP_QSTR_cho_solve), (mp_obj_t)&linalg_cho_solve_obj }, + #endif + #endif +}; + +static MP_DEFINE_CONST_DICT(mp_module_ulab_scipy_linalg_globals, ulab_scipy_linalg_globals_table); + +const mp_obj_module_t ulab_scipy_linalg_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_scipy_linalg_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_scipy_dot_linalg, ulab_scipy_linalg_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); + +#endif diff --git a/circuitpython/extmod/ulab/code/scipy/linalg/linalg.h b/circuitpython/extmod/ulab/code/scipy/linalg/linalg.h new file mode 100644 index 0000000..628051f --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/linalg/linalg.h @@ -0,0 +1,21 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2021 Vikas Udupa + * +*/ + +#ifndef _SCIPY_LINALG_ +#define _SCIPY_LINALG_ + +extern const mp_obj_module_t ulab_scipy_linalg_module; + +MP_DECLARE_CONST_FUN_OBJ_KW(linalg_solve_triangular_obj); +MP_DECLARE_CONST_FUN_OBJ_2(linalg_cho_solve_obj); + +#endif /* _SCIPY_LINALG_ */ diff --git a/circuitpython/extmod/ulab/code/scipy/optimize/optimize.c b/circuitpython/extmod/ulab/code/scipy/optimize/optimize.c new file mode 100644 index 0000000..f1c746a --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/optimize/optimize.c @@ -0,0 +1,415 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020 Scott Shawcroft for Adafruit Industries + * 2020-2021 Zoltán Vörös + * 2020 Taku Fukada +*/ + +#include <math.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" + +#include "../../ndarray.h" +#include "../../ulab.h" +#include "../../ulab_tools.h" +#include "optimize.h" + +const mp_obj_float_t xtolerance = {{&mp_type_float}, MICROPY_FLOAT_CONST(2.4e-7)}; +const mp_obj_float_t rtolerance = {{&mp_type_float}, MICROPY_FLOAT_CONST(0.0)}; + +static mp_float_t optimize_python_call(const mp_obj_type_t *type, mp_obj_t fun, mp_float_t x, mp_obj_t *fargs, uint8_t nparams) { + // Helper function for calculating the value of f(x, a, b, c, ...), + // where f is defined in python. Takes a float, returns a float. + // The array of mp_obj_t type must be supplied, as must the number of parameters (a, b, c...) in nparams + fargs[0] = mp_obj_new_float(x); + return mp_obj_get_float(type->MP_TYPE_CALL(fun, nparams+1, 0, fargs)); +} + +#if ULAB_SCIPY_OPTIMIZE_HAS_BISECT +//| def bisect( +//| fun: Callable[[float], float], +//| a: float, +//| b: float, +//| *, +//| xtol: float = 2.4e-7, +//| maxiter: int = 100 +//| ) -> float: +//| """ +//| :param callable f: The function to bisect +//| :param float a: The left side of the interval +//| :param float b: The right side of the interval +//| :param float xtol: The tolerance value +//| :param float maxiter: The maximum number of iterations to perform +//| +//| Find a solution (zero) of the function ``f(x)`` on the interval +//| (``a``..``b``) using the bisection method. The result is accurate to within +//| ``xtol`` unless more than ``maxiter`` steps are required.""" +//| ... +//| + +STATIC mp_obj_t optimize_bisect(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + // Simple bisection routine + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_xtol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} }, + { MP_QSTR_maxiter, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 100} }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t fun = args[0].u_obj; + const mp_obj_type_t *type = mp_obj_get_type(fun); + if(mp_type_get_call_slot(type) == NULL) { + mp_raise_TypeError(translate("first argument must be a function")); + } + mp_float_t xtol = mp_obj_get_float(args[3].u_obj); + mp_obj_t *fargs = m_new(mp_obj_t, 1); + mp_float_t left, right; + mp_float_t x_mid; + mp_float_t a = mp_obj_get_float(args[1].u_obj); + mp_float_t b = mp_obj_get_float(args[2].u_obj); + left = optimize_python_call(type, fun, a, fargs, 0); + right = optimize_python_call(type, fun, b, fargs, 0); + if(left * right > 0) { + mp_raise_ValueError(translate("function has the same sign at the ends of interval")); + } + mp_float_t rtb = left < MICROPY_FLOAT_CONST(0.0) ? a : b; + mp_float_t dx = left < MICROPY_FLOAT_CONST(0.0) ? b - a : a - b; + if(args[4].u_int < 0) { + mp_raise_ValueError(translate("maxiter should be > 0")); + } + for(uint16_t i=0; i < args[4].u_int; i++) { + dx *= MICROPY_FLOAT_CONST(0.5); + x_mid = rtb + dx; + if(optimize_python_call(type, fun, x_mid, fargs, 0) < MICROPY_FLOAT_CONST(0.0)) { + rtb = x_mid; + } + if(MICROPY_FLOAT_C_FUN(fabs)(dx) < xtol) break; + } + return mp_obj_new_float(rtb); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(optimize_bisect_obj, 3, optimize_bisect); +#endif + +#if ULAB_SCIPY_OPTIMIZE_HAS_FMIN +//| def fmin( +//| fun: Callable[[float], float], +//| x0: float, +//| *, +//| xatol: float = 2.4e-7, +//| fatol: float = 2.4e-7, +//| maxiter: int = 200 +//| ) -> float: +//| """ +//| :param callable f: The function to bisect +//| :param float x0: The initial x value +//| :param float xatol: The absolute tolerance value +//| :param float fatol: The relative tolerance value +//| +//| Find a minimum of the function ``f(x)`` using the downhill simplex method. +//| The located ``x`` is within ``fxtol`` of the actual minimum, and ``f(x)`` +//| is within ``fatol`` of the actual minimum unless more than ``maxiter`` +//| steps are requried.""" +//| ... +//| + +STATIC mp_obj_t optimize_fmin(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + // downhill simplex method in 1D + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_xatol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} }, + { MP_QSTR_fatol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} }, + { MP_QSTR_maxiter, MP_ARG_KW_ONLY | MP_ARG_INT, {.u_int = 200} }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t fun = args[0].u_obj; + const mp_obj_type_t *type = mp_obj_get_type(fun); + if(mp_type_get_call_slot(type) == NULL) { + mp_raise_TypeError(translate("first argument must be a function")); + } + + // parameters controlling convergence conditions + mp_float_t xatol = mp_obj_get_float(args[2].u_obj); + mp_float_t fatol = mp_obj_get_float(args[3].u_obj); + if(args[4].u_int <= 0) { + mp_raise_ValueError(translate("maxiter must be > 0")); + } + uint16_t maxiter = (uint16_t)args[4].u_int; + + mp_float_t x0 = mp_obj_get_float(args[1].u_obj); + mp_float_t x1 = MICROPY_FLOAT_C_FUN(fabs)(x0) > OPTIMIZE_EPSILON ? (MICROPY_FLOAT_CONST(1.0) + OPTIMIZE_NONZDELTA) * x0 : OPTIMIZE_ZDELTA; + mp_obj_t *fargs = m_new(mp_obj_t, 1); + mp_float_t f0 = optimize_python_call(type, fun, x0, fargs, 0); + mp_float_t f1 = optimize_python_call(type, fun, x1, fargs, 0); + if(f1 < f0) { + SWAP(mp_float_t, x0, x1); + SWAP(mp_float_t, f0, f1); + } + for(uint16_t i=0; i < maxiter; i++) { + uint8_t shrink = 0; + f0 = optimize_python_call(type, fun, x0, fargs, 0); + f1 = optimize_python_call(type, fun, x1, fargs, 0); + + // reflection + mp_float_t xr = (MICROPY_FLOAT_CONST(1.0) + OPTIMIZE_ALPHA) * x0 - OPTIMIZE_ALPHA * x1; + mp_float_t fr = optimize_python_call(type, fun, xr, fargs, 0); + if(fr < f0) { // expansion + mp_float_t xe = (1 + OPTIMIZE_ALPHA * OPTIMIZE_BETA) * x0 - OPTIMIZE_ALPHA * OPTIMIZE_BETA * x1; + mp_float_t fe = optimize_python_call(type, fun, xe, fargs, 0); + if(fe < fr) { + x1 = xe; + f1 = fe; + } else { + x1 = xr; + f1 = fr; + } + } else { + if(fr < f1) { // contraction + mp_float_t xc = (1 + OPTIMIZE_GAMMA * OPTIMIZE_ALPHA) * x0 - OPTIMIZE_GAMMA * OPTIMIZE_ALPHA * x1; + mp_float_t fc = optimize_python_call(type, fun, xc, fargs, 0); + if(fc < fr) { + x1 = xc; + f1 = fc; + } else { + shrink = 1; + } + } else { // inside contraction + mp_float_t xc = (MICROPY_FLOAT_CONST(1.0) - OPTIMIZE_GAMMA) * x0 + OPTIMIZE_GAMMA * x1; + mp_float_t fc = optimize_python_call(type, fun, xc, fargs, 0); + if(fc < f1) { + x1 = xc; + f1 = fc; + } else { + shrink = 1; + } + } + if(shrink == 1) { + x1 = x0 + OPTIMIZE_DELTA * (x1 - x0); + f1 = optimize_python_call(type, fun, x1, fargs, 0); + } + if((MICROPY_FLOAT_C_FUN(fabs)(f1 - f0) < fatol) || + (MICROPY_FLOAT_C_FUN(fabs)(x1 - x0) < xatol)) { + break; + } + if(f1 < f0) { + SWAP(mp_float_t, x0, x1); + SWAP(mp_float_t, f0, f1); + } + } + } + return mp_obj_new_float(x0); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(optimize_fmin_obj, 2, optimize_fmin); +#endif + +#if ULAB_SCIPY_OPTIMIZE_HAS_CURVE_FIT +static void optimize_jacobi(const mp_obj_type_t *type, mp_obj_t fun, mp_float_t *x, mp_float_t *y, uint16_t len, mp_float_t *params, uint8_t nparams, mp_float_t *jacobi, mp_float_t *grad) { + /* Calculates the Jacobian and the gradient of the cost function + * + * The entries in the Jacobian are + * J(m, n) = de_m/da_n, + * + * where + * + * e_m = (f(x_m, a1, a2, ...) - y_m)/sigma_m is the error at x_m, + * + * and + * + * a1, a2, ..., a_n are the free parameters + */ + mp_obj_t *fargs0 = m_new(mp_obj_t, lenp+1); + mp_obj_t *fargs1 = m_new(mp_obj_t, lenp+1); + for(uint8_t p=0; p < nparams; p++) { + fargs0[p+1] = mp_obj_new_float(params[p]); + fargs1[p+1] = mp_obj_new_float(params[p]); + } + for(uint8_t p=0; p < nparams; p++) { + mp_float_t da = params[p] != MICROPY_FLOAT_CONST(0.0) ? (MICROPY_FLOAT_CONST(1.0) + APPROX_NONZDELTA) * params[p] : APPROX_ZDELTA; + fargs1[p+1] = mp_obj_new_float(params[p] + da); + grad[p] = MICROPY_FLOAT_CONST(0.0); + for(uint16_t i=0; i < len; i++) { + mp_float_t f0 = optimize_python_call(type, fun, x[i], fargs0, nparams); + mp_float_t f1 = optimize_python_call(type, fun, x[i], fargs1, nparams); + jacobi[i*nparamp+p] = (f1 - f0) / da; + grad[p] += (f0 - y[i]) * jacobi[i*nparamp+p]; + } + fargs1[p+1] = fargs0[p+1]; // set back to the original value + } +} + +static void optimize_delta(mp_float_t *jacobi, mp_float_t *grad, uint16_t len, uint8_t nparams, mp_float_t lambda) { + // +} + +mp_obj_t optimize_curve_fit(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + // Levenberg-Marquardt non-linear fit + // The implementation follows the introductory discussion in Mark Tanstrum's paper, https://arxiv.org/abs/1201.5885 + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_p0, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_xatol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} }, + { MP_QSTR_fatol, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = MP_ROM_PTR(&xtolerance)} }, + { MP_QSTR_maxiter, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none} }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t fun = args[0].u_obj; + const mp_obj_type_t *type = mp_obj_get_type(fun); + if(mp_type_get_call_slot(type) == NULL) { + mp_raise_TypeError(translate("first argument must be a function")); + } + + mp_obj_t x_obj = args[1].u_obj; + mp_obj_t y_obj = args[2].u_obj; + mp_obj_t p0_obj = args[3].u_obj; + if(!ndarray_object_is_array_like(x_obj) || !ndarray_object_is_array_like(y_obj)) { + mp_raise_TypeError(translate("data must be iterable")); + } + if(!ndarray_object_is_nditerable(p0_obj)) { + mp_raise_TypeError(translate("initial values must be iterable")); + } + size_t len = (size_t)mp_obj_get_int(mp_obj_len_maybe(x_obj)); + uint8_t lenp = (uint8_t)mp_obj_get_int(mp_obj_len_maybe(p0_obj)); + if(len != (uint16_t)mp_obj_get_int(mp_obj_len_maybe(y_obj))) { + mp_raise_ValueError(translate("data must be of equal length")); + } + + mp_float_t *x = m_new(mp_float_t, len); + fill_array_iterable(x, x_obj); + mp_float_t *y = m_new(mp_float_t, len); + fill_array_iterable(y, y_obj); + mp_float_t *p0 = m_new(mp_float_t, lenp); + fill_array_iterable(p0, p0_obj); + mp_float_t *grad = m_new(mp_float_t, len); + mp_float_t *jacobi = m_new(mp_float_t, len*len); + mp_obj_t *fargs = m_new(mp_obj_t, lenp+1); + + m_del(mp_float_t, p0, lenp); + // parameters controlling convergence conditions + //mp_float_t xatol = mp_obj_get_float(args[2].u_obj); + //mp_float_t fatol = mp_obj_get_float(args[3].u_obj); + + // this has finite binary representation; we will multiply/divide by 4 + //mp_float_t lambda = 0.0078125; + + //linalg_invert_matrix(mp_float_t *data, size_t N) + + m_del(mp_float_t, x, len); + m_del(mp_float_t, y, len); + m_del(mp_float_t, grad, len); + m_del(mp_float_t, jacobi, len*len); + m_del(mp_obj_t, fargs, lenp+1); + return mp_const_none; +} + +MP_DEFINE_CONST_FUN_OBJ_KW(optimize_curve_fit_obj, 2, optimize_curve_fit); +#endif + +#if ULAB_SCIPY_OPTIMIZE_HAS_NEWTON +//| def newton( +//| fun: Callable[[float], float], +//| x0: float, +//| *, +//| xtol: float = 2.4e-7, +//| rtol: float = 0.0, +//| maxiter: int = 50 +//| ) -> float: +//| """ +//| :param callable f: The function to bisect +//| :param float x0: The initial x value +//| :param float xtol: The absolute tolerance value +//| :param float rtol: The relative tolerance value +//| :param float maxiter: The maximum number of iterations to perform +//| +//| Find a solution (zero) of the function ``f(x)`` using Newton's Method. +//| The result is accurate to within ``xtol * rtol * |f(x)|`` unless more than +//| ``maxiter`` steps are requried.""" +//| ... +//| + +static mp_obj_t optimize_newton(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + // this is actually the secant method, as the first derivative of the function + // is not accepted as an argument. The function whose root we want to solve for + // must depend on a single variable without parameters, i.e., f(x) + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_tol, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_PTR(&xtolerance) } }, + { MP_QSTR_rtol, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_PTR(&rtolerance) } }, + { MP_QSTR_maxiter, MP_ARG_KW_ONLY | MP_ARG_INT, { .u_int = 50 } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + mp_obj_t fun = args[0].u_obj; + const mp_obj_type_t *type = mp_obj_get_type(fun); + if(mp_type_get_call_slot(type) == NULL) { + mp_raise_TypeError(translate("first argument must be a function")); + } + mp_float_t x = mp_obj_get_float(args[1].u_obj); + mp_float_t tol = mp_obj_get_float(args[2].u_obj); + mp_float_t rtol = mp_obj_get_float(args[3].u_obj); + mp_float_t dx, df, fx; + dx = x > MICROPY_FLOAT_CONST(0.0) ? OPTIMIZE_EPS * x : -OPTIMIZE_EPS * x; + mp_obj_t *fargs = m_new(mp_obj_t, 1); + if(args[4].u_int <= 0) { + mp_raise_ValueError(translate("maxiter must be > 0")); + } + for(uint16_t i=0; i < args[4].u_int; i++) { + fx = optimize_python_call(type, fun, x, fargs, 0); + df = (optimize_python_call(type, fun, x + dx, fargs, 0) - fx) / dx; + dx = fx / df; + x -= dx; + if(MICROPY_FLOAT_C_FUN(fabs)(dx) < (tol + rtol * MICROPY_FLOAT_C_FUN(fabs)(x))) break; + } + return mp_obj_new_float(x); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(optimize_newton_obj, 2, optimize_newton); +#endif + +static const mp_rom_map_elem_t ulab_scipy_optimize_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_optimize) }, + #if ULAB_SCIPY_OPTIMIZE_HAS_BISECT + { MP_OBJ_NEW_QSTR(MP_QSTR_bisect), (mp_obj_t)&optimize_bisect_obj }, + #endif + #if ULAB_SCIPY_OPTIMIZE_HAS_CURVE_FIT + { MP_OBJ_NEW_QSTR(MP_QSTR_curve_fit), (mp_obj_t)&optimize_curve_fit_obj }, + #endif + #if ULAB_SCIPY_OPTIMIZE_HAS_FMIN + { MP_OBJ_NEW_QSTR(MP_QSTR_fmin), (mp_obj_t)&optimize_fmin_obj }, + #endif + #if ULAB_SCIPY_OPTIMIZE_HAS_NEWTON + { MP_OBJ_NEW_QSTR(MP_QSTR_newton), (mp_obj_t)&optimize_newton_obj }, + #endif +}; + +static MP_DEFINE_CONST_DICT(mp_module_ulab_scipy_optimize_globals, ulab_scipy_optimize_globals_table); + +const mp_obj_module_t ulab_scipy_optimize_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_scipy_optimize_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_scipy_dot_optimize, ulab_scipy_optimize_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); diff --git a/circuitpython/extmod/ulab/code/scipy/optimize/optimize.h b/circuitpython/extmod/ulab/code/scipy/optimize/optimize.h new file mode 100644 index 0000000..174b386 --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/optimize/optimize.h @@ -0,0 +1,41 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös + * +*/ + +#ifndef _SCIPY_OPTIMIZE_ +#define _SCIPY_OPTIMIZE_ + +#include "../../ulab_tools.h" + +#ifndef OPTIMIZE_EPSILON +#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT +#define OPTIMIZE_EPSILON MICROPY_FLOAT_CONST(1.2e-7) +#elif MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE +#define OPTIMIZE_EPSILON MICROPY_FLOAT_CONST(2.3e-16) +#endif +#endif + +#define OPTIMIZE_EPS MICROPY_FLOAT_CONST(1.0e-4) +#define OPTIMIZE_NONZDELTA MICROPY_FLOAT_CONST(0.05) +#define OPTIMIZE_ZDELTA MICROPY_FLOAT_CONST(0.00025) +#define OPTIMIZE_ALPHA MICROPY_FLOAT_CONST(1.0) +#define OPTIMIZE_BETA MICROPY_FLOAT_CONST(2.0) +#define OPTIMIZE_GAMMA MICROPY_FLOAT_CONST(0.5) +#define OPTIMIZE_DELTA MICROPY_FLOAT_CONST(0.5) + +extern const mp_obj_module_t ulab_scipy_optimize_module; + +MP_DECLARE_CONST_FUN_OBJ_KW(optimize_bisect_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(optimize_curve_fit_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(optimize_fmin_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(optimize_newton_obj); + +#endif /* _SCIPY_OPTIMIZE_ */ diff --git a/circuitpython/extmod/ulab/code/scipy/scipy.c b/circuitpython/extmod/ulab/code/scipy/scipy.c new file mode 100644 index 0000000..ba37dde --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/scipy.c @@ -0,0 +1,52 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020 Scott Shawcroft for Adafruit Industries + * 2020-2021 Zoltán Vörös + * 2020 Taku Fukada +*/ + +#include <math.h> +#include "py/runtime.h" + +#include "../ulab.h" +#include "optimize/optimize.h" +#include "signal/signal.h" +#include "special/special.h" +#include "linalg/linalg.h" + +#if ULAB_HAS_SCIPY + +//| """Compatibility layer for scipy""" +//| + +static const mp_rom_map_elem_t ulab_scipy_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_scipy) }, + #if ULAB_SCIPY_HAS_LINALG_MODULE + { MP_ROM_QSTR(MP_QSTR_linalg), MP_ROM_PTR(&ulab_scipy_linalg_module) }, + #endif + #if ULAB_SCIPY_HAS_OPTIMIZE_MODULE + { MP_ROM_QSTR(MP_QSTR_optimize), MP_ROM_PTR(&ulab_scipy_optimize_module) }, + #endif + #if ULAB_SCIPY_HAS_SIGNAL_MODULE + { MP_ROM_QSTR(MP_QSTR_signal), MP_ROM_PTR(&ulab_scipy_signal_module) }, + #endif + #if ULAB_SCIPY_HAS_SPECIAL_MODULE + { MP_ROM_QSTR(MP_QSTR_special), MP_ROM_PTR(&ulab_scipy_special_module) }, + #endif +}; + +static MP_DEFINE_CONST_DICT(mp_module_ulab_scipy_globals, ulab_scipy_globals_table); + +const mp_obj_module_t ulab_scipy_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_scipy_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_scipy, ulab_scipy_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); +#endif diff --git a/circuitpython/extmod/ulab/code/scipy/scipy.h b/circuitpython/extmod/ulab/code/scipy/scipy.h new file mode 100644 index 0000000..ec8c804 --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/scipy.h @@ -0,0 +1,21 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös + * +*/ + +#ifndef _SCIPY_ +#define _SCIPY_ + +#include "../ulab.h" +#include "../ndarray.h" + +extern const mp_obj_module_t ulab_scipy_module; + +#endif /* _SCIPY_ */ diff --git a/circuitpython/extmod/ulab/code/scipy/signal/signal.c b/circuitpython/extmod/ulab/code/scipy/signal/signal.c new file mode 100644 index 0000000..69d5609 --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/signal/signal.c @@ -0,0 +1,172 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020 Scott Shawcroft for Adafruit Industries + * 2020-2021 Zoltán Vörös + * 2020 Taku Fukada +*/ + +#include <math.h> +#include <string.h> +#include "py/runtime.h" + +#include "../../ulab.h" +#include "../../ndarray.h" +#include "../../numpy/carray/carray_tools.h" +#include "../../numpy/fft/fft_tools.h" + +#if ULAB_SCIPY_SIGNAL_HAS_SPECTROGRAM +//| import ulab.numpy +//| +//| def spectrogram(r: ulab.numpy.ndarray) -> ulab.numpy.ndarray: +//| """ +//| :param ulab.numpy.ndarray r: A 1-dimension array of values whose size is a power of 2 +//| +//| Computes the spectrum of the input signal. This is the absolute value of the (complex-valued) fft of the signal. +//| This function is similar to scipy's ``scipy.signal.spectrogram``.""" +//| ... +//| + +mp_obj_t signal_spectrogram(size_t n_args, const mp_obj_t *args) { + #if ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE + return fft_fft_ifft_spectrogram(args[0], FFT_SPECTROGRAM); + #else + if(n_args == 2) { + return fft_fft_ifft_spectrogram(n_args, args[0], args[1], FFT_SPECTROGRAM); + } else { + return fft_fft_ifft_spectrogram(n_args, args[0], mp_const_none, FFT_SPECTROGRAM); + } + #endif +} + +#if ULAB_SUPPORTS_COMPLEX & ULAB_FFT_IS_NUMPY_COMPATIBLE +MP_DEFINE_CONST_FUN_OBJ_VAR_BETWEEN(signal_spectrogram_obj, 1, 1, signal_spectrogram); +#else +MP_DEFINE_CONST_FUN_OBJ_VAR_BETWEEN(signal_spectrogram_obj, 1, 2, signal_spectrogram); +#endif + +#endif /* ULAB_SCIPY_SIGNAL_HAS_SPECTROGRAM */ + +#if ULAB_SCIPY_SIGNAL_HAS_SOSFILT +static void signal_sosfilt_array(mp_float_t *x, const mp_float_t *coeffs, mp_float_t *zf, const size_t len) { + for(size_t i=0; i < len; i++) { + mp_float_t xn = *x; + *x = coeffs[0] * xn + zf[0]; + zf[0] = zf[1] + coeffs[1] * xn - coeffs[4] * *x; + zf[1] = coeffs[2] * xn - coeffs[5] * *x; + x++; + } + x -= len; +} + +mp_obj_t signal_sosfilt(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_sos, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_x, MP_ARG_REQUIRED | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + { MP_QSTR_zi, MP_ARG_KW_ONLY | MP_ARG_OBJ, {.u_rom_obj = mp_const_none } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + if(!ndarray_object_is_array_like(args[0].u_obj) || !ndarray_object_is_array_like(args[1].u_obj)) { + mp_raise_TypeError(translate("sosfilt requires iterable arguments")); + } + #if ULAB_SUPPORTS_COMPLEX + if(mp_obj_is_type(args[1].u_obj, &ulab_ndarray_type)) { + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(args[1].u_obj); + COMPLEX_DTYPE_NOT_IMPLEMENTED(ndarray->dtype) + } + #endif + size_t lenx = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[1].u_obj)); + ndarray_obj_t *y = ndarray_new_linear_array(lenx, NDARRAY_FLOAT); + mp_float_t *yarray = (mp_float_t *)y->array; + mp_float_t coeffs[6]; + if(mp_obj_is_type(args[1].u_obj, &ulab_ndarray_type)) { + ndarray_obj_t *inarray = MP_OBJ_TO_PTR(args[1].u_obj); + #if ULAB_MAX_DIMS > 1 + if(inarray->ndim > 1) { + mp_raise_ValueError(translate("input must be one-dimensional")); + } + #endif + uint8_t *iarray = (uint8_t *)inarray->array; + for(size_t i=0; i < lenx; i++) { + *yarray++ = ndarray_get_float_value(iarray, inarray->dtype); + iarray += inarray->strides[ULAB_MAX_DIMS - 1]; + } + yarray -= lenx; + } else { + fill_array_iterable(yarray, args[1].u_obj); + } + + mp_obj_iter_buf_t iter_buf; + mp_obj_t item, iterable = mp_getiter(args[0].u_obj, &iter_buf); + size_t lensos = (size_t)mp_obj_get_int(mp_obj_len_maybe(args[0].u_obj)); + + size_t *shape = ndarray_shape_vector(0, 0, lensos, 2); + ndarray_obj_t *zf = ndarray_new_dense_ndarray(2, shape, NDARRAY_FLOAT); + mp_float_t *zf_array = (mp_float_t *)zf->array; + + if(args[2].u_obj != mp_const_none) { + if(!mp_obj_is_type(args[2].u_obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("zi must be an ndarray")); + } else { + ndarray_obj_t *zi = MP_OBJ_TO_PTR(args[2].u_obj); + if((zi->shape[ULAB_MAX_DIMS - 1] != lensos) || (zi->shape[ULAB_MAX_DIMS - 1] != 2)) { + mp_raise_ValueError(translate("zi must be of shape (n_section, 2)")); + } + if(zi->dtype != NDARRAY_FLOAT) { + mp_raise_ValueError(translate("zi must be of float type")); + } + // TODO: this won't work with sparse arrays + memcpy(zf_array, zi->array, 2*lensos*sizeof(mp_float_t)); + } + } + while((item = mp_iternext(iterable)) != MP_OBJ_STOP_ITERATION) { + if(mp_obj_get_int(mp_obj_len_maybe(item)) != 6) { + mp_raise_ValueError(translate("sos array must be of shape (n_section, 6)")); + } else { + fill_array_iterable(coeffs, item); + if(coeffs[3] != MICROPY_FLOAT_CONST(1.0)) { + mp_raise_ValueError(translate("sos[:, 3] should be all ones")); + } + signal_sosfilt_array(yarray, coeffs, zf_array, lenx); + zf_array += 2; + } + } + if(args[2].u_obj == mp_const_none) { + return MP_OBJ_FROM_PTR(y); + } else { + mp_obj_tuple_t *tuple = MP_OBJ_TO_PTR(mp_obj_new_tuple(2, NULL)); + tuple->items[0] = MP_OBJ_FROM_PTR(y); + tuple->items[1] = MP_OBJ_FROM_PTR(zf); + return tuple; + } +} + +MP_DEFINE_CONST_FUN_OBJ_KW(signal_sosfilt_obj, 2, signal_sosfilt); +#endif /* ULAB_SCIPY_SIGNAL_HAS_SOSFILT */ + +static const mp_rom_map_elem_t ulab_scipy_signal_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_signal) }, + #if ULAB_SCIPY_SIGNAL_HAS_SPECTROGRAM + { MP_OBJ_NEW_QSTR(MP_QSTR_spectrogram), (mp_obj_t)&signal_spectrogram_obj }, + #endif + #if ULAB_SCIPY_SIGNAL_HAS_SOSFILT + { MP_OBJ_NEW_QSTR(MP_QSTR_sosfilt), (mp_obj_t)&signal_sosfilt_obj }, + #endif +}; + +static MP_DEFINE_CONST_DICT(mp_module_ulab_scipy_signal_globals, ulab_scipy_signal_globals_table); + +const mp_obj_module_t ulab_scipy_signal_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_scipy_signal_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_scipy_dot_signal, ulab_scipy_signal_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); diff --git a/circuitpython/extmod/ulab/code/scipy/signal/signal.h b/circuitpython/extmod/ulab/code/scipy/signal/signal.h new file mode 100644 index 0000000..21299a6 --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/signal/signal.h @@ -0,0 +1,24 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös + * +*/ + +#ifndef _SCIPY_SIGNAL_ +#define _SCIPY_SIGNAL_ + +#include "../../ulab.h" +#include "../../ndarray.h" + +extern const mp_obj_module_t ulab_scipy_signal_module; + +MP_DECLARE_CONST_FUN_OBJ_VAR_BETWEEN(signal_spectrogram_obj); +MP_DECLARE_CONST_FUN_OBJ_KW(signal_sosfilt_obj); + +#endif /* _SCIPY_SIGNAL_ */ diff --git a/circuitpython/extmod/ulab/code/scipy/special/special.c b/circuitpython/extmod/ulab/code/scipy/special/special.c new file mode 100644 index 0000000..decfde0 --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/special/special.c @@ -0,0 +1,43 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020 Jeff Epler for Adafruit Industries + * 2020 Scott Shawcroft for Adafruit Industries + * 2020-2021 Zoltán Vörös + * 2020 Taku Fukada +*/ + +#include <math.h> +#include "py/runtime.h" + +#include "../../ulab.h" +#include "../../numpy/vector.h" + +static const mp_rom_map_elem_t ulab_scipy_special_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_special) }, + #if ULAB_SCIPY_SPECIAL_HAS_ERF + { MP_OBJ_NEW_QSTR(MP_QSTR_erf), (mp_obj_t)&vector_erf_obj }, + #endif + #if ULAB_SCIPY_SPECIAL_HAS_ERFC + { MP_OBJ_NEW_QSTR(MP_QSTR_erfc), (mp_obj_t)&vector_erfc_obj }, + #endif + #if ULAB_SCIPY_SPECIAL_HAS_GAMMA + { MP_OBJ_NEW_QSTR(MP_QSTR_gamma), (mp_obj_t)&vector_gamma_obj }, + #endif + #if ULAB_SCIPY_SPECIAL_HAS_GAMMALN + { MP_OBJ_NEW_QSTR(MP_QSTR_gammaln), (mp_obj_t)&vector_lgamma_obj }, + #endif +}; + +static MP_DEFINE_CONST_DICT(mp_module_ulab_scipy_special_globals, ulab_scipy_special_globals_table); + +const mp_obj_module_t ulab_scipy_special_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_scipy_special_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_scipy_dot_special, ulab_scipy_special_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); diff --git a/circuitpython/extmod/ulab/code/scipy/special/special.h b/circuitpython/extmod/ulab/code/scipy/special/special.h new file mode 100644 index 0000000..bb34e27 --- /dev/null +++ b/circuitpython/extmod/ulab/code/scipy/special/special.h @@ -0,0 +1,21 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös + * +*/ + +#ifndef _SCIPY_SPECIAL_ +#define _SCIPY_SPECIAL_ + +#include "../../ulab.h" +#include "../../ndarray.h" + +extern const mp_obj_module_t ulab_scipy_special_module; + +#endif /* _SCIPY_SPECIAL_ */ diff --git a/circuitpython/extmod/ulab/code/ulab.c b/circuitpython/extmod/ulab/code/ulab.c new file mode 100644 index 0000000..e8dfe0e --- /dev/null +++ b/circuitpython/extmod/ulab/code/ulab.c @@ -0,0 +1,185 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2021 Zoltán Vörös + * 2020 Jeff Epler for Adafruit Industries +*/ + +#include <math.h> +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include "py/runtime.h" +#include "py/binary.h" +#include "py/obj.h" +#include "py/objarray.h" + +#include "ulab.h" +#include "ndarray.h" +#include "ndarray_properties.h" +#include "numpy/create.h" +#include "numpy/ndarray/ndarray_iter.h" + +#include "numpy/numpy.h" +#include "scipy/scipy.h" +// TODO: we should get rid of this; array.sort depends on it +#include "numpy/numerical.h" + +#include "user/user.h" +#include "utils/utils.h" + +#define ULAB_VERSION 4.0.0 +#define xstr(s) str(s) +#define str(s) #s + +#if ULAB_SUPPORTS_COMPLEX +#define ULAB_VERSION_STRING xstr(ULAB_VERSION) xstr(-) xstr(ULAB_MAX_DIMS) xstr(D-c) +#else +#define ULAB_VERSION_STRING xstr(ULAB_VERSION) xstr(-) xstr(ULAB_MAX_DIMS) xstr(D) +#endif + +STATIC MP_DEFINE_STR_OBJ(ulab_version_obj, ULAB_VERSION_STRING); + + +STATIC const mp_rom_map_elem_t ulab_ndarray_locals_dict_table[] = { + #if ULAB_MAX_DIMS > 1 + #if NDARRAY_HAS_RESHAPE + { MP_ROM_QSTR(MP_QSTR_reshape), MP_ROM_PTR(&ndarray_reshape_obj) }, + #endif + #if NDARRAY_HAS_TRANSPOSE + { MP_ROM_QSTR(MP_QSTR_transpose), MP_ROM_PTR(&ndarray_transpose_obj) }, + #endif + #endif + #if NDARRAY_HAS_BYTESWAP + { MP_ROM_QSTR(MP_QSTR_byteswap), MP_ROM_PTR(&ndarray_byteswap_obj) }, + #endif + #if NDARRAY_HAS_COPY + { MP_ROM_QSTR(MP_QSTR_copy), MP_ROM_PTR(&ndarray_copy_obj) }, + #endif + #if NDARRAY_HAS_FLATTEN + { MP_ROM_QSTR(MP_QSTR_flatten), MP_ROM_PTR(&ndarray_flatten_obj) }, + #endif + #if NDARRAY_HAS_TOBYTES + { MP_ROM_QSTR(MP_QSTR_tobytes), MP_ROM_PTR(&ndarray_tobytes_obj) }, + #endif + #if NDARRAY_HAS_TOLIST + { MP_ROM_QSTR(MP_QSTR_tolist), MP_ROM_PTR(&ndarray_tolist_obj) }, + #endif + #if NDARRAY_HAS_SORT + { MP_ROM_QSTR(MP_QSTR_sort), MP_ROM_PTR(&numerical_sort_inplace_obj) }, + #endif + #ifdef CIRCUITPY + #if NDARRAY_HAS_DTYPE + { MP_ROM_QSTR(MP_QSTR_dtype), MP_ROM_PTR(&ndarray_dtype_obj) }, + #endif + #if NDARRAY_HAS_FLATITER + { MP_ROM_QSTR(MP_QSTR_flat), MP_ROM_PTR(&ndarray_flat_obj) }, + #endif + #if NDARRAY_HAS_ITEMSIZE + { MP_ROM_QSTR(MP_QSTR_itemsize), MP_ROM_PTR(&ndarray_itemsize_obj) }, + #endif + #if NDARRAY_HAS_SHAPE + { MP_ROM_QSTR(MP_QSTR_shape), MP_ROM_PTR(&ndarray_shape_obj) }, + #endif + #if NDARRAY_HAS_SIZE + { MP_ROM_QSTR(MP_QSTR_size), MP_ROM_PTR(&ndarray_size_obj) }, + #endif + #if NDARRAY_HAS_STRIDES + { MP_ROM_QSTR(MP_QSTR_strides), MP_ROM_PTR(&ndarray_strides_obj) }, + #endif + #endif /* CIRCUITPY */ +}; + +STATIC MP_DEFINE_CONST_DICT(ulab_ndarray_locals_dict, ulab_ndarray_locals_dict_table); + +const mp_obj_type_t ulab_ndarray_type = { + { &mp_type_type }, + .flags = MP_TYPE_FLAG_EXTENDED + #if defined(MP_TYPE_FLAG_EQ_CHECKS_OTHER_TYPE) && defined(MP_TYPE_FLAG_EQ_HAS_NEQ_TEST) + | MP_TYPE_FLAG_EQ_CHECKS_OTHER_TYPE | MP_TYPE_FLAG_EQ_HAS_NEQ_TEST, + #endif + .name = MP_QSTR_ndarray, + .print = ndarray_print, + .make_new = ndarray_make_new, + .locals_dict = (mp_obj_dict_t*)&ulab_ndarray_locals_dict, + MP_TYPE_EXTENDED_FIELDS( + #if NDARRAY_IS_SLICEABLE + .subscr = ndarray_subscr, + #endif + #if NDARRAY_IS_ITERABLE + .getiter = ndarray_getiter, + #endif + #if NDARRAY_HAS_UNARY_OPS + .unary_op = ndarray_unary_op, + #endif + #if NDARRAY_HAS_BINARY_OPS + .binary_op = ndarray_binary_op, + #endif + #ifndef CIRCUITPY + .attr = ndarray_properties_attr, + #endif + .buffer_p = { .get_buffer = ndarray_get_buffer, }, + ) +}; + +#if ULAB_HAS_DTYPE_OBJECT +const mp_obj_type_t ulab_dtype_type = { + { &mp_type_type }, + .name = MP_QSTR_dtype, + .print = ndarray_dtype_print, + .make_new = ndarray_dtype_make_new, +}; +#endif + +#if NDARRAY_HAS_FLATITER +const mp_obj_type_t ndarray_flatiter_type = { + { &mp_type_type }, + .name = MP_QSTR_flatiter, + MP_TYPE_EXTENDED_FIELDS( + .getiter = ndarray_get_flatiterator, + ) +}; +#endif + +STATIC const mp_map_elem_t ulab_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_ulab) }, + { MP_ROM_QSTR(MP_QSTR___version__), MP_ROM_PTR(&ulab_version_obj) }, + #if ULAB_HAS_DTYPE_OBJECT + { MP_OBJ_NEW_QSTR(MP_QSTR_dtype), (mp_obj_t)&ulab_dtype_type }, + #else + #if NDARRAY_HAS_DTYPE + { MP_OBJ_NEW_QSTR(MP_QSTR_dtype), (mp_obj_t)&ndarray_dtype_obj }, + #endif /* NDARRAY_HAS_DTYPE */ + #endif /* ULAB_HAS_DTYPE_OBJECT */ + { MP_ROM_QSTR(MP_QSTR_numpy), MP_ROM_PTR((mp_obj_t)&ulab_numpy_module) }, + #if ULAB_HAS_SCIPY + { MP_ROM_QSTR(MP_QSTR_scipy), MP_ROM_PTR((mp_obj_t)&ulab_scipy_module) }, + #endif + #if ULAB_HAS_USER_MODULE + { MP_ROM_QSTR(MP_QSTR_user), MP_ROM_PTR((mp_obj_t)&ulab_user_module) }, + #endif + #if ULAB_HAS_UTILS_MODULE + { MP_ROM_QSTR(MP_QSTR_utils), MP_ROM_PTR((mp_obj_t)&ulab_utils_module) }, + #endif +}; + +STATIC MP_DEFINE_CONST_DICT ( + mp_module_ulab_globals, + ulab_globals_table +); + +#ifdef OPENMV +const struct _mp_obj_module_t ulab_user_cmodule = { +#else +const mp_obj_module_t ulab_user_cmodule = { +#endif + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_globals, +}; + +MP_REGISTER_MODULE(MP_QSTR_ulab, ulab_user_cmodule, MODULE_ULAB_ENABLED); diff --git a/circuitpython/extmod/ulab/code/ulab.h b/circuitpython/extmod/ulab/code/ulab.h new file mode 100644 index 0000000..924f4c7 --- /dev/null +++ b/circuitpython/extmod/ulab/code/ulab.h @@ -0,0 +1,712 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2019-2022 Zoltán Vörös +*/ + +#ifndef __ULAB__ +#define __ULAB__ + + + +// The pre-processor constants in this file determine how ulab behaves: +// +// - how many dimensions ulab can handle +// - which functions are included in the compiled firmware +// - whether arrays can be sliced and iterated over +// - which binary/unary operators are supported +// - whether ulab can deal with complex numbers +// +// A considerable amount of flash space can be saved by removing (setting +// the corresponding constants to 0) the unnecessary functions and features. + +// Values defined here can be overridden by your own config file as +// make -DULAB_CONFIG_FILE="my_ulab_config.h" +#if defined(ULAB_CONFIG_FILE) +#include ULAB_CONFIG_FILE +#endif + +// Adds support for complex ndarrays +#ifndef ULAB_SUPPORTS_COMPLEX +#define ULAB_SUPPORTS_COMPLEX (1) +#endif + +// Determines, whether scipy is defined in ulab. The sub-modules and functions +// of scipy have to be defined separately +#ifndef ULAB_HAS_SCIPY +#define ULAB_HAS_SCIPY (1) +#endif + +// The maximum number of dimensions the firmware should be able to support +// Possible values lie between 1, and 4, inclusive +#ifndef ULAB_MAX_DIMS +#define ULAB_MAX_DIMS 2 +#endif + +// By setting this constant to 1, iteration over array dimensions will be implemented +// as a function (ndarray_rewind_array), instead of writing out the loops in macros +// This reduces firmware size at the expense of speed +#ifndef ULAB_HAS_FUNCTION_ITERATOR +#define ULAB_HAS_FUNCTION_ITERATOR (0) +#endif + +// If NDARRAY_IS_ITERABLE is 1, the ndarray object defines its own iterator function +// This option saves approx. 250 bytes of flash space +#ifndef NDARRAY_IS_ITERABLE +#define NDARRAY_IS_ITERABLE (1) +#endif + +// Slicing can be switched off by setting this variable to 0 +#ifndef NDARRAY_IS_SLICEABLE +#define NDARRAY_IS_SLICEABLE (1) +#endif + +// The default threshold for pretty printing. These variables can be overwritten +// at run-time via the set_printoptions() function +#ifndef ULAB_HAS_PRINTOPTIONS +#define ULAB_HAS_PRINTOPTIONS (1) +#endif +#define NDARRAY_PRINT_THRESHOLD 10 +#define NDARRAY_PRINT_EDGEITEMS 3 + +// determines, whether the dtype is an object, or simply a character +// the object implementation is numpythonic, but requires more space +#ifndef ULAB_HAS_DTYPE_OBJECT +#define ULAB_HAS_DTYPE_OBJECT (0) +#endif + +// the ndarray binary operators +#ifndef NDARRAY_HAS_BINARY_OPS +#define NDARRAY_HAS_BINARY_OPS (1) +#endif + +// Firmware size can be reduced at the expense of speed by using function +// pointers in iterations. For each operator, he function pointer saves around +// 2 kB in the two-dimensional case, and around 4 kB in the four-dimensional case. + +#ifndef NDARRAY_BINARY_USES_FUN_POINTER +#define NDARRAY_BINARY_USES_FUN_POINTER (0) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_ADD +#define NDARRAY_HAS_BINARY_OP_ADD (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_EQUAL +#define NDARRAY_HAS_BINARY_OP_EQUAL (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_LESS +#define NDARRAY_HAS_BINARY_OP_LESS (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_LESS_EQUAL +#define NDARRAY_HAS_BINARY_OP_LESS_EQUAL (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_MORE +#define NDARRAY_HAS_BINARY_OP_MORE (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_MORE_EQUAL +#define NDARRAY_HAS_BINARY_OP_MORE_EQUAL (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_MULTIPLY +#define NDARRAY_HAS_BINARY_OP_MULTIPLY (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_NOT_EQUAL +#define NDARRAY_HAS_BINARY_OP_NOT_EQUAL (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_POWER +#define NDARRAY_HAS_BINARY_OP_POWER (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_SUBTRACT +#define NDARRAY_HAS_BINARY_OP_SUBTRACT (1) +#endif + +#ifndef NDARRAY_HAS_BINARY_OP_TRUE_DIVIDE +#define NDARRAY_HAS_BINARY_OP_TRUE_DIVIDE (1) +#endif + +#ifndef NDARRAY_HAS_INPLACE_OPS +#define NDARRAY_HAS_INPLACE_OPS (1) +#endif + +#ifndef NDARRAY_HAS_INPLACE_ADD +#define NDARRAY_HAS_INPLACE_ADD (1) +#endif + +#ifndef NDARRAY_HAS_INPLACE_MULTIPLY +#define NDARRAY_HAS_INPLACE_MULTIPLY (1) +#endif + +#ifndef NDARRAY_HAS_INPLACE_POWER +#define NDARRAY_HAS_INPLACE_POWER (1) +#endif + +#ifndef NDARRAY_HAS_INPLACE_SUBTRACT +#define NDARRAY_HAS_INPLACE_SUBTRACT (1) +#endif + +#ifndef NDARRAY_HAS_INPLACE_TRUE_DIVIDE +#define NDARRAY_HAS_INPLACE_TRUE_DIVIDE (1) +#endif + +// the ndarray unary operators +#ifndef NDARRAY_HAS_UNARY_OPS +#define NDARRAY_HAS_UNARY_OPS (1) +#endif + +#ifndef NDARRAY_HAS_UNARY_OP_ABS +#define NDARRAY_HAS_UNARY_OP_ABS (1) +#endif + +#ifndef NDARRAY_HAS_UNARY_OP_INVERT +#define NDARRAY_HAS_UNARY_OP_INVERT (1) +#endif + +#ifndef NDARRAY_HAS_UNARY_OP_LEN +#define NDARRAY_HAS_UNARY_OP_LEN (1) +#endif + +#ifndef NDARRAY_HAS_UNARY_OP_NEGATIVE +#define NDARRAY_HAS_UNARY_OP_NEGATIVE (1) +#endif + +#ifndef NDARRAY_HAS_UNARY_OP_POSITIVE +#define NDARRAY_HAS_UNARY_OP_POSITIVE (1) +#endif + + +// determines, which ndarray methods are available +#ifndef NDARRAY_HAS_BYTESWAP +#define NDARRAY_HAS_BYTESWAP (1) +#endif + +#ifndef NDARRAY_HAS_COPY +#define NDARRAY_HAS_COPY (1) +#endif + +#ifndef NDARRAY_HAS_DTYPE +#define NDARRAY_HAS_DTYPE (1) +#endif + +#ifndef NDARRAY_HAS_FLATTEN +#define NDARRAY_HAS_FLATTEN (1) +#endif + +#ifndef NDARRAY_HAS_ITEMSIZE +#define NDARRAY_HAS_ITEMSIZE (1) +#endif + +#ifndef NDARRAY_HAS_RESHAPE +#define NDARRAY_HAS_RESHAPE (1) +#endif + +#ifndef NDARRAY_HAS_SHAPE +#define NDARRAY_HAS_SHAPE (1) +#endif + +#ifndef NDARRAY_HAS_SIZE +#define NDARRAY_HAS_SIZE (1) +#endif + +#ifndef NDARRAY_HAS_SORT +#define NDARRAY_HAS_SORT (1) +#endif + +#ifndef NDARRAY_HAS_STRIDES +#define NDARRAY_HAS_STRIDES (1) +#endif + +#ifndef NDARRAY_HAS_TOBYTES +#define NDARRAY_HAS_TOBYTES (1) +#endif + +#ifndef NDARRAY_HAS_TOLIST +#define NDARRAY_HAS_TOLIST (1) +#endif + +#ifndef NDARRAY_HAS_TRANSPOSE +#define NDARRAY_HAS_TRANSPOSE (1) +#endif + +// Firmware size can be reduced at the expense of speed by using a function +// pointer in iterations. Setting ULAB_VECTORISE_USES_FUNCPOINTER to 1 saves +// around 800 bytes in the four-dimensional case, and around 200 in two dimensions. +#ifndef ULAB_VECTORISE_USES_FUN_POINTER +#define ULAB_VECTORISE_USES_FUN_POINTER (1) +#endif + +// determines, whether e is defined in ulab.numpy itself +#ifndef ULAB_NUMPY_HAS_E +#define ULAB_NUMPY_HAS_E (1) +#endif + +// ulab defines infinite as a class constant in ulab.numpy +#ifndef ULAB_NUMPY_HAS_INF +#define ULAB_NUMPY_HAS_INF (1) +#endif + +// ulab defines NaN as a class constant in ulab.numpy +#ifndef ULAB_NUMPY_HAS_NAN +#define ULAB_NUMPY_HAS_NAN (1) +#endif + +// determines, whether pi is defined in ulab.numpy itself +#ifndef ULAB_NUMPY_HAS_PI +#define ULAB_NUMPY_HAS_PI (1) +#endif + +// determines, whether the ndinfo function is available +#ifndef ULAB_NUMPY_HAS_NDINFO +#define ULAB_NUMPY_HAS_NDINFO (1) +#endif + +// if this constant is set to 1, the interpreter can iterate +// over the flat array without copying any data +#ifndef NDARRAY_HAS_FLATITER +#define NDARRAY_HAS_FLATITER (1) +#endif + +// frombuffer adds 600 bytes to the firmware +#ifndef ULAB_NUMPY_HAS_FROMBUFFER +#define ULAB_NUMPY_HAS_FROMBUFFER (1) +#endif + +// functions that create an array +#ifndef ULAB_NUMPY_HAS_ARANGE +#define ULAB_NUMPY_HAS_ARANGE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_CONCATENATE +#define ULAB_NUMPY_HAS_CONCATENATE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_DIAG +#define ULAB_NUMPY_HAS_DIAG (1) +#endif + +#ifndef ULAB_NUMPY_HAS_EMPTY +#define ULAB_NUMPY_HAS_EMPTY (1) +#endif + +#ifndef ULAB_NUMPY_HAS_EYE +#define ULAB_NUMPY_HAS_EYE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_FULL +#define ULAB_NUMPY_HAS_FULL (1) +#endif + +#ifndef ULAB_NUMPY_HAS_LINSPACE +#define ULAB_NUMPY_HAS_LINSPACE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_LOGSPACE +#define ULAB_NUMPY_HAS_LOGSPACE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ONES +#define ULAB_NUMPY_HAS_ONES (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ZEROS +#define ULAB_NUMPY_HAS_ZEROS (1) +#endif + +// functions that compare arrays +#ifndef ULAB_NUMPY_HAS_CLIP +#define ULAB_NUMPY_HAS_CLIP (1) +#endif + +#ifndef ULAB_NUMPY_HAS_EQUAL +#define ULAB_NUMPY_HAS_EQUAL (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ISFINITE +#define ULAB_NUMPY_HAS_ISFINITE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ISINF +#define ULAB_NUMPY_HAS_ISINF (1) +#endif + +#ifndef ULAB_NUMPY_HAS_MAXIMUM +#define ULAB_NUMPY_HAS_MAXIMUM (1) +#endif + +#ifndef ULAB_NUMPY_HAS_MINIMUM +#define ULAB_NUMPY_HAS_MINIMUM (1) +#endif + +#ifndef ULAB_NUMPY_HAS_NOTEQUAL +#define ULAB_NUMPY_HAS_NOTEQUAL (1) +#endif + +#ifndef ULAB_NUMPY_HAS_WHERE +#define ULAB_NUMPY_HAS_WHERE (1) +#endif + +// the linalg module; functions of the linalg module still have +// to be defined separately +#ifndef ULAB_NUMPY_HAS_LINALG_MODULE +#define ULAB_NUMPY_HAS_LINALG_MODULE (1) +#endif + +#ifndef ULAB_LINALG_HAS_CHOLESKY +#define ULAB_LINALG_HAS_CHOLESKY (1) +#endif + +#ifndef ULAB_LINALG_HAS_DET +#define ULAB_LINALG_HAS_DET (1) +#endif + +#ifndef ULAB_LINALG_HAS_EIG +#define ULAB_LINALG_HAS_EIG (1) +#endif + +#ifndef ULAB_LINALG_HAS_INV +#define ULAB_LINALG_HAS_INV (1) +#endif + +#ifndef ULAB_LINALG_HAS_NORM +#define ULAB_LINALG_HAS_NORM (1) +#endif + +#ifndef ULAB_LINALG_HAS_QR +#define ULAB_LINALG_HAS_QR (1) +#endif + +// the FFT module; functions of the fft module still have +// to be defined separately +#ifndef ULAB_NUMPY_HAS_FFT_MODULE +#define ULAB_NUMPY_HAS_FFT_MODULE (1) +#endif + +// By setting this constant to 1, the FFT routine will behave in a +// numpy-compatible way, i.e., it will output a complex array +// This setting has no effect, if ULAB_SUPPORTS_COMPLEX is 0 +// Note that in this case, the input also must be numpythonic, +// i.e., the real an imaginary parts cannot be passed as two arguments +#ifndef ULAB_FFT_IS_NUMPY_COMPATIBLE +#define ULAB_FFT_IS_NUMPY_COMPATIBLE (0) +#endif + +#ifndef ULAB_FFT_HAS_FFT +#define ULAB_FFT_HAS_FFT (1) +#endif + +#ifndef ULAB_FFT_HAS_IFFT +#define ULAB_FFT_HAS_IFFT (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ALL +#define ULAB_NUMPY_HAS_ALL (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ANY +#define ULAB_NUMPY_HAS_ANY (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ARGMINMAX +#define ULAB_NUMPY_HAS_ARGMINMAX (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ARGSORT +#define ULAB_NUMPY_HAS_ARGSORT (1) +#endif + +#ifndef ULAB_NUMPY_HAS_COMPRESS +#define ULAB_NUMPY_HAS_COMPRESS (1) +#endif + +#ifndef ULAB_NUMPY_HAS_CONVOLVE +#define ULAB_NUMPY_HAS_CONVOLVE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_CROSS +#define ULAB_NUMPY_HAS_CROSS (1) +#endif + +#ifndef ULAB_NUMPY_HAS_DIFF +#define ULAB_NUMPY_HAS_DIFF (1) +#endif + +#ifndef ULAB_NUMPY_HAS_DOT +#define ULAB_NUMPY_HAS_DOT (1) +#endif + +#ifndef ULAB_NUMPY_HAS_FLIP +#define ULAB_NUMPY_HAS_FLIP (1) +#endif + +#ifndef ULAB_NUMPY_HAS_INTERP +#define ULAB_NUMPY_HAS_INTERP (1) +#endif + +#ifndef ULAB_NUMPY_HAS_MEAN +#define ULAB_NUMPY_HAS_MEAN (1) +#endif + +#ifndef ULAB_NUMPY_HAS_MEDIAN +#define ULAB_NUMPY_HAS_MEDIAN (1) +#endif + +#ifndef ULAB_NUMPY_HAS_MINMAX +#define ULAB_NUMPY_HAS_MINMAX (1) +#endif + +#ifndef ULAB_NUMPY_HAS_POLYFIT +#define ULAB_NUMPY_HAS_POLYFIT (1) +#endif + +#ifndef ULAB_NUMPY_HAS_POLYVAL +#define ULAB_NUMPY_HAS_POLYVAL (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ROLL +#define ULAB_NUMPY_HAS_ROLL (1) +#endif + +#ifndef ULAB_NUMPY_HAS_SORT +#define ULAB_NUMPY_HAS_SORT (1) +#endif + +#ifndef ULAB_NUMPY_HAS_STD +#define ULAB_NUMPY_HAS_STD (1) +#endif + +#ifndef ULAB_NUMPY_HAS_SUM +#define ULAB_NUMPY_HAS_SUM (1) +#endif + +#ifndef ULAB_NUMPY_HAS_TRACE +#define ULAB_NUMPY_HAS_TRACE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_TRAPZ +#define ULAB_NUMPY_HAS_TRAPZ (1) +#endif + +// vectorised versions of the functions of the math python module, with +// the exception of the functions listed in scipy.special +#ifndef ULAB_NUMPY_HAS_ACOS +#define ULAB_NUMPY_HAS_ACOS (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ACOSH +#define ULAB_NUMPY_HAS_ACOSH (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ARCTAN2 +#define ULAB_NUMPY_HAS_ARCTAN2 (1) +#endif + +#ifndef ULAB_NUMPY_HAS_AROUND +#define ULAB_NUMPY_HAS_AROUND (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ASIN +#define ULAB_NUMPY_HAS_ASIN (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ASINH +#define ULAB_NUMPY_HAS_ASINH (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ATAN +#define ULAB_NUMPY_HAS_ATAN (1) +#endif + +#ifndef ULAB_NUMPY_HAS_ATANH +#define ULAB_NUMPY_HAS_ATANH (1) +#endif + +#ifndef ULAB_NUMPY_HAS_CEIL +#define ULAB_NUMPY_HAS_CEIL (1) +#endif + +#ifndef ULAB_NUMPY_HAS_COS +#define ULAB_NUMPY_HAS_COS (1) +#endif + +#ifndef ULAB_NUMPY_HAS_COSH +#define ULAB_NUMPY_HAS_COSH (1) +#endif + +#ifndef ULAB_NUMPY_HAS_DEGREES +#define ULAB_NUMPY_HAS_DEGREES (1) +#endif + +#ifndef ULAB_NUMPY_HAS_EXP +#define ULAB_NUMPY_HAS_EXP (1) +#endif + +#ifndef ULAB_NUMPY_HAS_EXPM1 +#define ULAB_NUMPY_HAS_EXPM1 (1) +#endif + +#ifndef ULAB_NUMPY_HAS_FLOOR +#define ULAB_NUMPY_HAS_FLOOR (1) +#endif + +#ifndef ULAB_NUMPY_HAS_LOG +#define ULAB_NUMPY_HAS_LOG (1) +#endif + +#ifndef ULAB_NUMPY_HAS_LOG10 +#define ULAB_NUMPY_HAS_LOG10 (1) +#endif + +#ifndef ULAB_NUMPY_HAS_LOG2 +#define ULAB_NUMPY_HAS_LOG2 (1) +#endif + +#ifndef ULAB_NUMPY_HAS_RADIANS +#define ULAB_NUMPY_HAS_RADIANS (1) +#endif + +#ifndef ULAB_NUMPY_HAS_SIN +#define ULAB_NUMPY_HAS_SIN (1) +#endif + +#ifndef ULAB_NUMPY_HAS_SINH +#define ULAB_NUMPY_HAS_SINH (1) +#endif + +#ifndef ULAB_NUMPY_HAS_SQRT +#define ULAB_NUMPY_HAS_SQRT (1) +#endif + +#ifndef ULAB_NUMPY_HAS_TAN +#define ULAB_NUMPY_HAS_TAN (1) +#endif + +#ifndef ULAB_NUMPY_HAS_TANH +#define ULAB_NUMPY_HAS_TANH (1) +#endif + +#ifndef ULAB_NUMPY_HAS_VECTORIZE +#define ULAB_NUMPY_HAS_VECTORIZE (1) +#endif + +// Complex functions. The implementations are compiled into +// the firmware, only if ULAB_SUPPORTS_COMPLEX is set to 1 +#ifndef ULAB_NUMPY_HAS_CONJUGATE +#define ULAB_NUMPY_HAS_CONJUGATE (1) +#endif + +#ifndef ULAB_NUMPY_HAS_IMAG +#define ULAB_NUMPY_HAS_IMAG (1) +#endif + +#ifndef ULAB_NUMPY_HAS_REAL +#define ULAB_NUMPY_HAS_REAL (1) +#endif + +#ifndef ULAB_NUMPY_HAS_SORT_COMPLEX +#define ULAB_NUMPY_HAS_SORT_COMPLEX (1) +#endif + +// scipy modules +#ifndef ULAB_SCIPY_HAS_LINALG_MODULE +#define ULAB_SCIPY_HAS_LINALG_MODULE (1) +#endif + +#ifndef ULAB_SCIPY_LINALG_HAS_CHO_SOLVE +#define ULAB_SCIPY_LINALG_HAS_CHO_SOLVE (1) +#endif + +#ifndef ULAB_SCIPY_LINALG_HAS_SOLVE_TRIANGULAR +#define ULAB_SCIPY_LINALG_HAS_SOLVE_TRIANGULAR (1) +#endif + +#ifndef ULAB_SCIPY_HAS_SIGNAL_MODULE +#define ULAB_SCIPY_HAS_SIGNAL_MODULE (1) +#endif + +#ifndef ULAB_SCIPY_SIGNAL_HAS_SPECTROGRAM +#define ULAB_SCIPY_SIGNAL_HAS_SPECTROGRAM (1) +#endif + +#ifndef ULAB_SCIPY_SIGNAL_HAS_SOSFILT +#define ULAB_SCIPY_SIGNAL_HAS_SOSFILT (1) +#endif + +#ifndef ULAB_SCIPY_HAS_OPTIMIZE_MODULE +#define ULAB_SCIPY_HAS_OPTIMIZE_MODULE (1) +#endif + +#ifndef ULAB_SCIPY_OPTIMIZE_HAS_BISECT +#define ULAB_SCIPY_OPTIMIZE_HAS_BISECT (1) +#endif + +#ifndef ULAB_SCIPY_OPTIMIZE_HAS_CURVE_FIT +#define ULAB_SCIPY_OPTIMIZE_HAS_CURVE_FIT (0) // not fully implemented +#endif + +#ifndef ULAB_SCIPY_OPTIMIZE_HAS_FMIN +#define ULAB_SCIPY_OPTIMIZE_HAS_FMIN (1) +#endif + +#ifndef ULAB_SCIPY_OPTIMIZE_HAS_NEWTON +#define ULAB_SCIPY_OPTIMIZE_HAS_NEWTON (1) +#endif + +#ifndef ULAB_SCIPY_HAS_SPECIAL_MODULE +#define ULAB_SCIPY_HAS_SPECIAL_MODULE (1) +#endif + +#ifndef ULAB_SCIPY_SPECIAL_HAS_ERF +#define ULAB_SCIPY_SPECIAL_HAS_ERF (1) +#endif + +#ifndef ULAB_SCIPY_SPECIAL_HAS_ERFC +#define ULAB_SCIPY_SPECIAL_HAS_ERFC (1) +#endif + +#ifndef ULAB_SCIPY_SPECIAL_HAS_GAMMA +#define ULAB_SCIPY_SPECIAL_HAS_GAMMA (1) +#endif + +#ifndef ULAB_SCIPY_SPECIAL_HAS_GAMMALN +#define ULAB_SCIPY_SPECIAL_HAS_GAMMALN (1) +#endif + +// user-defined module; source of the module and +// its sub-modules should be placed in code/user/ +#ifndef ULAB_HAS_USER_MODULE +#define ULAB_HAS_USER_MODULE (0) +#endif + +#ifndef ULAB_HAS_UTILS_MODULE +#define ULAB_HAS_UTILS_MODULE (1) +#endif + +#ifndef ULAB_UTILS_HAS_FROM_INT16_BUFFER +#define ULAB_UTILS_HAS_FROM_INT16_BUFFER (1) +#endif + +#ifndef ULAB_UTILS_HAS_FROM_UINT16_BUFFER +#define ULAB_UTILS_HAS_FROM_UINT16_BUFFER (1) +#endif + +#ifndef ULAB_UTILS_HAS_FROM_INT32_BUFFER +#define ULAB_UTILS_HAS_FROM_INT32_BUFFER (1) +#endif + +#ifndef ULAB_UTILS_HAS_FROM_UINT32_BUFFER +#define ULAB_UTILS_HAS_FROM_UINT32_BUFFER (1) +#endif + +#endif diff --git a/circuitpython/extmod/ulab/code/ulab_tools.c b/circuitpython/extmod/ulab/code/ulab_tools.c new file mode 100644 index 0000000..7fb6363 --- /dev/null +++ b/circuitpython/extmod/ulab/code/ulab_tools.c @@ -0,0 +1,260 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2022 Zoltán Vörös + */ + + +#include <string.h> +#include "py/runtime.h" + +#include "ulab.h" +#include "ndarray.h" +#include "ulab_tools.h" + +// The following five functions return a float from a void type +// The value in question is supposed to be located at the head of the pointer + +mp_float_t ndarray_get_float_uint8(void *data) { + // Returns a float value from an uint8_t type + return (mp_float_t)(*(uint8_t *)data); +} + +mp_float_t ndarray_get_float_int8(void *data) { + // Returns a float value from an int8_t type + return (mp_float_t)(*(int8_t *)data); +} + +mp_float_t ndarray_get_float_uint16(void *data) { + // Returns a float value from an uint16_t type + return (mp_float_t)(*(uint16_t *)data); +} + +mp_float_t ndarray_get_float_int16(void *data) { + // Returns a float value from an int16_t type + return (mp_float_t)(*(int16_t *)data); +} + + +mp_float_t ndarray_get_float_float(void *data) { + // Returns a float value from an mp_float_t type + return *((mp_float_t *)data); +} + +// returns a single function pointer, depending on the dtype +void *ndarray_get_float_function(uint8_t dtype) { + if(dtype == NDARRAY_UINT8) { + return ndarray_get_float_uint8; + } else if(dtype == NDARRAY_INT8) { + return ndarray_get_float_int8; + } else if(dtype == NDARRAY_UINT16) { + return ndarray_get_float_uint16; + } else if(dtype == NDARRAY_INT16) { + return ndarray_get_float_int16; + } else { + return ndarray_get_float_float; + } +} + +mp_float_t ndarray_get_float_index(void *data, uint8_t dtype, size_t index) { + // returns a single float value from an array located at index + if(dtype == NDARRAY_UINT8) { + return (mp_float_t)((uint8_t *)data)[index]; + } else if(dtype == NDARRAY_INT8) { + return (mp_float_t)((int8_t *)data)[index]; + } else if(dtype == NDARRAY_UINT16) { + return (mp_float_t)((uint16_t *)data)[index]; + } else if(dtype == NDARRAY_INT16) { + return (mp_float_t)((int16_t *)data)[index]; + } else { + return (mp_float_t)((mp_float_t *)data)[index]; + } +} + +mp_float_t ndarray_get_float_value(void *data, uint8_t dtype) { + // Returns a float value from an arbitrary data type + // The value in question is supposed to be located at the head of the pointer + if(dtype == NDARRAY_UINT8) { + return (mp_float_t)(*(uint8_t *)data); + } else if(dtype == NDARRAY_INT8) { + return (mp_float_t)(*(int8_t *)data); + } else if(dtype == NDARRAY_UINT16) { + return (mp_float_t)(*(uint16_t *)data); + } else if(dtype == NDARRAY_INT16) { + return (mp_float_t)(*(int16_t *)data); + } else { + return *((mp_float_t *)data); + } +} + +#if NDARRAY_BINARY_USES_FUN_POINTER | ULAB_NUMPY_HAS_WHERE +uint8_t ndarray_upcast_dtype(uint8_t ldtype, uint8_t rdtype) { + // returns a single character that corresponds to the broadcasting rules + // - if one of the operarands is a float, the result is always float + // - operation on identical types preserves type + // + // uint8 + int8 => int16 + // uint8 + int16 => int16 + // uint8 + uint16 => uint16 + // int8 + int16 => int16 + // int8 + uint16 => uint16 + // uint16 + int16 => float + + if(ldtype == rdtype) { + // if the two dtypes are equal, the result is also of that type + return ldtype; + } else if(((ldtype == NDARRAY_UINT8) && (rdtype == NDARRAY_INT8)) || + ((ldtype == NDARRAY_INT8) && (rdtype == NDARRAY_UINT8)) || + ((ldtype == NDARRAY_UINT8) && (rdtype == NDARRAY_INT16)) || + ((ldtype == NDARRAY_INT16) && (rdtype == NDARRAY_UINT8)) || + ((ldtype == NDARRAY_INT8) && (rdtype == NDARRAY_INT16)) || + ((ldtype == NDARRAY_INT16) && (rdtype == NDARRAY_INT8))) { + return NDARRAY_INT16; + } else if(((ldtype == NDARRAY_UINT8) && (rdtype == NDARRAY_UINT16)) || + ((ldtype == NDARRAY_UINT16) && (rdtype == NDARRAY_UINT8)) || + ((ldtype == NDARRAY_INT8) && (rdtype == NDARRAY_UINT16)) || + ((ldtype == NDARRAY_UINT16) && (rdtype == NDARRAY_INT8))) { + return NDARRAY_UINT16; + } + return NDARRAY_FLOAT; +} + +// The following five functions are the inverse of the ndarray_get_... functions, +// and write a floating point datum into a void pointer + +void ndarray_set_float_uint8(void *data, mp_float_t datum) { + *((uint8_t *)data) = (uint8_t)datum; +} + +void ndarray_set_float_int8(void *data, mp_float_t datum) { + *((int8_t *)data) = (int8_t)datum; +} + +void ndarray_set_float_uint16(void *data, mp_float_t datum) { + *((uint16_t *)data) = (uint16_t)datum; +} + +void ndarray_set_float_int16(void *data, mp_float_t datum) { + *((int16_t *)data) = (int16_t)datum; +} + +void ndarray_set_float_float(void *data, mp_float_t datum) { + *((mp_float_t *)data) = datum; +} + +// returns a single function pointer, depending on the dtype +void *ndarray_set_float_function(uint8_t dtype) { + if(dtype == NDARRAY_UINT8) { + return ndarray_set_float_uint8; + } else if(dtype == NDARRAY_INT8) { + return ndarray_set_float_int8; + } else if(dtype == NDARRAY_UINT16) { + return ndarray_set_float_uint16; + } else if(dtype == NDARRAY_INT16) { + return ndarray_set_float_int16; + } else { + return ndarray_set_float_float; + } +} +#endif /* NDARRAY_BINARY_USES_FUN_POINTER */ + +shape_strides tools_reduce_axes(ndarray_obj_t *ndarray, mp_obj_t axis) { + // TODO: replace numerical_reduce_axes with this function, wherever applicable + // This function should be used, whenever a tensor is contracted; + // The shape and strides at `axis` are moved to the zeroth position, + // everything else is aligned to the right + if(!mp_obj_is_int(axis) & (axis != mp_const_none)) { + mp_raise_TypeError(translate("axis must be None, or an integer")); + } + shape_strides _shape_strides; + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS + 1); + _shape_strides.shape = shape; + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS + 1); + _shape_strides.strides = strides; + + _shape_strides.increment = 0; + // this is the contracted dimension (won't be overwritten for axis == None) + _shape_strides.ndim = 0; + + memcpy(_shape_strides.shape, ndarray->shape, sizeof(size_t) * ULAB_MAX_DIMS); + memcpy(_shape_strides.strides, ndarray->strides, sizeof(int32_t) * ULAB_MAX_DIMS); + + if(axis == mp_const_none) { + return _shape_strides; + } + + uint8_t index = ULAB_MAX_DIMS - 1; // value of index for axis == mp_const_none (won't be overwritten) + + if(axis != mp_const_none) { // i.e., axis is an integer + int8_t ax = mp_obj_get_int(axis); + if(ax < 0) ax += ndarray->ndim; + if((ax < 0) || (ax > ndarray->ndim - 1)) { + mp_raise_ValueError(translate("index out of range")); + } + index = ULAB_MAX_DIMS - ndarray->ndim + ax; + _shape_strides.ndim = ndarray->ndim - 1; + } + + // move the value stored at index to the leftmost position, and align everything else to the right + _shape_strides.shape[0] = ndarray->shape[index]; + _shape_strides.strides[0] = ndarray->strides[index]; + for(uint8_t i = 0; i < index; i++) { + // entries to the right of index must be shifted by one position to the left + _shape_strides.shape[i + 1] = ndarray->shape[i]; + _shape_strides.strides[i + 1] = ndarray->strides[i]; + } + + if(_shape_strides.ndim != 0) { + _shape_strides.increment = 1; + } + + return _shape_strides; +} + +int8_t tools_get_axis(mp_obj_t axis, uint8_t ndim) { + int8_t ax = mp_obj_get_int(axis); + if(ax < 0) ax += ndim; + if((ax < 0) || (ax > ndim - 1)) { + mp_raise_ValueError(translate("axis is out of bounds")); + } + return ax; +} + +#if ULAB_MAX_DIMS > 1 +ndarray_obj_t *tools_object_is_square(mp_obj_t obj) { + // Returns an ndarray, if the object is a square ndarray, + // raises the appropriate exception otherwise + if(!mp_obj_is_type(obj, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("size is defined for ndarrays only")); + } + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(obj); + if((ndarray->shape[ULAB_MAX_DIMS - 1] != ndarray->shape[ULAB_MAX_DIMS - 2]) || (ndarray->ndim != 2)) { + mp_raise_ValueError(translate("input must be square matrix")); + } + return ndarray; +} +#endif + +uint8_t ulab_binary_get_size(uint8_t dtype) { + #if ULAB_SUPPORTS_COMPLEX + if(dtype == NDARRAY_COMPLEX) { + return 2 * (uint8_t)sizeof(mp_float_t); + } + #endif + return dtype == NDARRAY_BOOL ? 1 : mp_binary_get_size('@', dtype, NULL); +} + +#if ULAB_SUPPORTS_COMPLEX +void ulab_rescale_float_strides(int32_t *strides) { + // re-scale the strides, so that we can work with floats, when iterating + uint8_t sz = sizeof(mp_float_t); + for(uint8_t i = 0; i < ULAB_MAX_DIMS; i++) { + strides[i] /= sz; + } +} +#endif
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/code/ulab_tools.h b/circuitpython/extmod/ulab/code/ulab_tools.h new file mode 100644 index 0000000..2898ef1 --- /dev/null +++ b/circuitpython/extmod/ulab/code/ulab_tools.h @@ -0,0 +1,45 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2022 Zoltán Vörös +*/ + +#ifndef _TOOLS_ +#define _TOOLS_ + +#include "ndarray.h" + +#define SWAP(t, a, b) { t tmp = a; a = b; b = tmp; } + +typedef struct _shape_strides_t { + uint8_t increment; + uint8_t ndim; + size_t *shape; + int32_t *strides; +} shape_strides; + +mp_float_t ndarray_get_float_uint8(void *); +mp_float_t ndarray_get_float_int8(void *); +mp_float_t ndarray_get_float_uint16(void *); +mp_float_t ndarray_get_float_int16(void *); +mp_float_t ndarray_get_float_float(void *); +void *ndarray_get_float_function(uint8_t ); + +uint8_t ndarray_upcast_dtype(uint8_t , uint8_t ); +void *ndarray_set_float_function(uint8_t ); + +shape_strides tools_reduce_axes(ndarray_obj_t *, mp_obj_t ); +int8_t tools_get_axis(mp_obj_t , uint8_t ); +ndarray_obj_t *tools_object_is_square(mp_obj_t ); + +uint8_t ulab_binary_get_size(uint8_t ); + +#if ULAB_SUPPORTS_COMPLEX +void ulab_rescale_float_strides(int32_t *); +#endif + +#endif diff --git a/circuitpython/extmod/ulab/code/user/user.c b/circuitpython/extmod/ulab/code/user/user.c new file mode 100644 index 0000000..5ee890a --- /dev/null +++ b/circuitpython/extmod/ulab/code/user/user.c @@ -0,0 +1,96 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös +*/ + +#include <math.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" +#include "user.h" + +#if ULAB_HAS_USER_MODULE + +//| """This module should hold arbitrary user-defined functions.""" +//| + +static mp_obj_t user_square(mp_obj_t arg) { + // the function takes a single dense ndarray, and calculates the + // element-wise square of its entries + + // raise a TypeError exception, if the input is not an ndarray + if(!mp_obj_is_type(arg, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("input must be an ndarray")); + } + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(arg); + + // make sure that the input is a dense array + if(!ndarray_is_dense(ndarray)) { + mp_raise_TypeError(translate("input must be a dense ndarray")); + } + + // if the input is a dense array, create `results` with the same number of + // dimensions, shape, and dtype + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim, ndarray->shape, ndarray->dtype); + + // since in a dense array the iteration over the elements is trivial, we + // can cast the data arrays ndarray->array and results->array to the actual type + if(ndarray->dtype == NDARRAY_UINT8) { + uint8_t *array = (uint8_t *)ndarray->array; + uint8_t *rarray = (uint8_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } else if(ndarray->dtype == NDARRAY_INT8) { + int8_t *array = (int8_t *)ndarray->array; + int8_t *rarray = (int8_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } else if(ndarray->dtype == NDARRAY_UINT16) { + uint16_t *array = (uint16_t *)ndarray->array; + uint16_t *rarray = (uint16_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } else if(ndarray->dtype == NDARRAY_INT16) { + int16_t *array = (int16_t *)ndarray->array; + int16_t *rarray = (int16_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } else { // if we end up here, the dtype is NDARRAY_FLOAT + mp_float_t *array = (mp_float_t *)ndarray->array; + mp_float_t *rarray = (mp_float_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } + // at the end, return a micrppython object + return MP_OBJ_FROM_PTR(results); +} + +MP_DEFINE_CONST_FUN_OBJ_1(user_square_obj, user_square); + +static const mp_rom_map_elem_t ulab_user_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_user) }, + { MP_OBJ_NEW_QSTR(MP_QSTR_square), (mp_obj_t)&user_square_obj }, +}; + +static MP_DEFINE_CONST_DICT(mp_module_ulab_user_globals, ulab_user_globals_table); + +const mp_obj_module_t ulab_user_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_user_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_user, ulab_user_module, ULAB_HAS_USER_MODULE && CIRCUITPY_ULAB); + +#endif diff --git a/circuitpython/extmod/ulab/code/user/user.h b/circuitpython/extmod/ulab/code/user/user.h new file mode 100644 index 0000000..ff274f4 --- /dev/null +++ b/circuitpython/extmod/ulab/code/user/user.h @@ -0,0 +1,20 @@ + +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös +*/ + +#ifndef _USER_ +#define _USER_ + +#include "../ulab.h" +#include "../ndarray.h" + +extern const mp_obj_module_t ulab_user_module; + +#endif diff --git a/circuitpython/extmod/ulab/code/utils/utils.c b/circuitpython/extmod/ulab/code/utils/utils.c new file mode 100644 index 0000000..c265d49 --- /dev/null +++ b/circuitpython/extmod/ulab/code/utils/utils.c @@ -0,0 +1,216 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös +*/ + +#include <math.h> +#include <stdlib.h> +#include <string.h> +#include "py/obj.h" +#include "py/runtime.h" +#include "py/misc.h" +#include "utils.h" + +#if ULAB_HAS_UTILS_MODULE + +enum UTILS_BUFFER_TYPE { + UTILS_INT16_BUFFER, + UTILS_UINT16_BUFFER, + UTILS_INT32_BUFFER, + UTILS_UINT32_BUFFER, +}; + +#if ULAB_UTILS_HAS_FROM_INT16_BUFFER | ULAB_UTILS_HAS_FROM_UINT16_BUFFER | ULAB_UTILS_HAS_FROM_INT32_BUFFER | ULAB_UTILS_HAS_FROM_UINT32_BUFFER +static mp_obj_t utils_from_intbuffer_helper(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args, uint8_t buffer_type) { + static const mp_arg_t allowed_args[] = { + { MP_QSTR_, MP_ARG_REQUIRED | MP_ARG_OBJ, { .u_rom_obj = mp_const_none } } , + { MP_QSTR_count, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_INT(-1) } }, + { MP_QSTR_offset, MP_ARG_KW_ONLY | MP_ARG_OBJ, { .u_rom_obj = MP_ROM_INT(0) } }, + { MP_QSTR_out, MP_ARG_OBJ, { .u_rom_obj = mp_const_none } }, + { MP_QSTR_byteswap, MP_ARG_OBJ, { .u_rom_obj = mp_const_false } }, + }; + + mp_arg_val_t args[MP_ARRAY_SIZE(allowed_args)]; + mp_arg_parse_all(n_args, pos_args, kw_args, MP_ARRAY_SIZE(allowed_args), allowed_args, args); + + ndarray_obj_t *ndarray = NULL; + + if(args[3].u_obj != mp_const_none) { + ndarray = MP_OBJ_TO_PTR(args[3].u_obj); + if((ndarray->dtype != NDARRAY_FLOAT) || !ndarray_is_dense(ndarray)) { + mp_raise_TypeError(translate("out must be a float dense array")); + } + } + + size_t offset = mp_obj_get_int(args[2].u_obj); + + mp_buffer_info_t bufinfo; + if(mp_get_buffer(args[0].u_obj, &bufinfo, MP_BUFFER_READ)) { + if(bufinfo.len < offset) { + mp_raise_ValueError(translate("offset is too large")); + } + uint8_t sz = sizeof(int16_t); + #if ULAB_UTILS_HAS_FROM_INT32_BUFFER | ULAB_UTILS_HAS_FROM_UINT32_BUFFER + if((buffer_type == UTILS_INT32_BUFFER) || (buffer_type == UTILS_UINT32_BUFFER)) { + sz = sizeof(int32_t); + } + #endif + + size_t len = (bufinfo.len - offset) / sz; + if((len * sz) != (bufinfo.len - offset)) { + mp_raise_ValueError(translate("buffer size must be a multiple of element size")); + } + if(mp_obj_get_int(args[1].u_obj) > 0) { + size_t count = mp_obj_get_int(args[1].u_obj); + if(len < count) { + mp_raise_ValueError(translate("buffer is smaller than requested size")); + } else { + len = count; + } + } + if(args[3].u_obj == mp_const_none) { + ndarray = ndarray_new_linear_array(len, NDARRAY_FLOAT); + } else { + if(ndarray->len < len) { + mp_raise_ValueError(translate("out array is too small")); + } + } + uint8_t *buffer = bufinfo.buf; + + mp_float_t *array = (mp_float_t *)ndarray->array; + if(args[4].u_obj == mp_const_true) { + // swap the bytes before conversion + uint8_t *tmpbuff = m_new(uint8_t, sz); + #if ULAB_UTILS_HAS_FROM_INT16_BUFFER | ULAB_UTILS_HAS_FROM_UINT16_BUFFER + if((buffer_type == UTILS_INT16_BUFFER) || (buffer_type == UTILS_UINT16_BUFFER)) { + for(size_t i = 0; i < len; i++) { + tmpbuff += sz; + for(uint8_t j = 0; j < sz; j++) { + memcpy(--tmpbuff, buffer++, 1); + } + if(buffer_type == UTILS_INT16_BUFFER) { + *array++ = (mp_float_t)(*(int16_t *)tmpbuff); + } else { + *array++ = (mp_float_t)(*(uint16_t *)tmpbuff); + } + } + } + #endif + #if ULAB_UTILS_HAS_FROM_INT32_BUFFER | ULAB_UTILS_HAS_FROM_UINT32_BUFFER + if((buffer_type == UTILS_INT32_BUFFER) || (buffer_type == UTILS_UINT32_BUFFER)) { + for(size_t i = 0; i < len; i++) { + tmpbuff += sz; + for(uint8_t j = 0; j < sz; j++) { + memcpy(--tmpbuff, buffer++, 1); + } + if(buffer_type == UTILS_INT32_BUFFER) { + *array++ = (mp_float_t)(*(int32_t *)tmpbuff); + } else { + *array++ = (mp_float_t)(*(uint32_t *)tmpbuff); + } + } + } + #endif + } else { + #if ULAB_UTILS_HAS_FROM_INT16_BUFFER + if(buffer_type == UTILS_INT16_BUFFER) { + for(size_t i = 0; i < len; i++) { + *array++ = (mp_float_t)(*(int16_t *)buffer); + buffer += sz; + } + } + #endif + #if ULAB_UTILS_HAS_FROM_UINT16_BUFFER + if(buffer_type == UTILS_UINT16_BUFFER) { + for(size_t i = 0; i < len; i++) { + *array++ = (mp_float_t)(*(uint16_t *)buffer); + buffer += sz; + } + } + #endif + #if ULAB_UTILS_HAS_FROM_INT32_BUFFER + if(buffer_type == UTILS_INT32_BUFFER) { + for(size_t i = 0; i < len; i++) { + *array++ = (mp_float_t)(*(int32_t *)buffer); + buffer += sz; + } + } + #endif + #if ULAB_UTILS_HAS_FROM_UINT32_BUFFER + if(buffer_type == UTILS_UINT32_BUFFER) { + for(size_t i = 0; i < len; i++) { + *array++ = (mp_float_t)(*(uint32_t *)buffer); + buffer += sz; + } + } + #endif + } + return MP_OBJ_FROM_PTR(ndarray); + } + return mp_const_none; +} + +#ifdef ULAB_UTILS_HAS_FROM_INT16_BUFFER +static mp_obj_t utils_from_int16_buffer(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return utils_from_intbuffer_helper(n_args, pos_args, kw_args, UTILS_INT16_BUFFER); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(utils_from_int16_buffer_obj, 1, utils_from_int16_buffer); +#endif + +#ifdef ULAB_UTILS_HAS_FROM_UINT16_BUFFER +static mp_obj_t utils_from_uint16_buffer(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return utils_from_intbuffer_helper(n_args, pos_args, kw_args, UTILS_UINT16_BUFFER); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(utils_from_uint16_buffer_obj, 1, utils_from_uint16_buffer); +#endif + +#ifdef ULAB_UTILS_HAS_FROM_INT32_BUFFER +static mp_obj_t utils_from_int32_buffer(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return utils_from_intbuffer_helper(n_args, pos_args, kw_args, UTILS_INT32_BUFFER); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(utils_from_int32_buffer_obj, 1, utils_from_int32_buffer); +#endif + +#ifdef ULAB_UTILS_HAS_FROM_UINT32_BUFFER +static mp_obj_t utils_from_uint32_buffer(size_t n_args, const mp_obj_t *pos_args, mp_map_t *kw_args) { + return utils_from_intbuffer_helper(n_args, pos_args, kw_args, UTILS_UINT32_BUFFER); +} + +MP_DEFINE_CONST_FUN_OBJ_KW(utils_from_uint32_buffer_obj, 1, utils_from_uint32_buffer); +#endif + +#endif + +static const mp_rom_map_elem_t ulab_utils_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_utils) }, + #if ULAB_UTILS_HAS_FROM_INT16_BUFFER + { MP_OBJ_NEW_QSTR(MP_QSTR_from_int16_buffer), (mp_obj_t)&utils_from_int16_buffer_obj }, + #endif + #if ULAB_UTILS_HAS_FROM_UINT16_BUFFER + { MP_OBJ_NEW_QSTR(MP_QSTR_from_uint16_buffer), (mp_obj_t)&utils_from_uint16_buffer_obj }, + #endif + #if ULAB_UTILS_HAS_FROM_INT32_BUFFER + { MP_OBJ_NEW_QSTR(MP_QSTR_from_int32_buffer), (mp_obj_t)&utils_from_int32_buffer_obj }, + #endif + #if ULAB_UTILS_HAS_FROM_UINT32_BUFFER + { MP_OBJ_NEW_QSTR(MP_QSTR_from_uint32_buffer), (mp_obj_t)&utils_from_uint32_buffer_obj }, + #endif +}; + +static MP_DEFINE_CONST_DICT(mp_module_ulab_utils_globals, ulab_utils_globals_table); + +const mp_obj_module_t ulab_utils_module = { + .base = { &mp_type_module }, + .globals = (mp_obj_dict_t*)&mp_module_ulab_utils_globals, +}; +MP_REGISTER_MODULE(MP_QSTR_ulab_dot_utils, ulab_utils_module, MODULE_ULAB_ENABLED && CIRCUITPY_ULAB); + +#endif diff --git a/circuitpython/extmod/ulab/code/utils/utils.h b/circuitpython/extmod/ulab/code/utils/utils.h new file mode 100644 index 0000000..b2155c3 --- /dev/null +++ b/circuitpython/extmod/ulab/code/utils/utils.h @@ -0,0 +1,19 @@ +/* + * This file is part of the micropython-ulab project, + * + * https://github.com/v923z/micropython-ulab + * + * The MIT License (MIT) + * + * Copyright (c) 2020-2021 Zoltán Vörös +*/ + +#ifndef _UTILS_ +#define _UTILS_ + +#include "../ulab.h" +#include "../ndarray.h" + +extern const mp_obj_module_t ulab_utils_module; + +#endif diff --git a/circuitpython/extmod/ulab/docs/manual/Makefile b/circuitpython/extmod/ulab/docs/manual/Makefile new file mode 100644 index 0000000..a97f725 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/Makefile @@ -0,0 +1,24 @@ +# Minimal makefile for Sphinx documentation +# + +# You can set these variables from the command line, and also +# from the environment for the first two. +SPHINXOPTS ?= +SPHINXBUILD ?= sphinx-build +SOURCEDIR = source +BUILDDIR = build + +# Put it first so that "make" without argument is like "make help". +help: + @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +.PHONY: help Makefile + +clean: + rm -rf "$(BUILDDIR)" + + +# Catch-all target: route all unknown targets to Sphinx using the new +# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). +%: Makefile + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) diff --git a/circuitpython/extmod/ulab/docs/manual/make.bat b/circuitpython/extmod/ulab/docs/manual/make.bat new file mode 100644 index 0000000..6247f7e --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/make.bat @@ -0,0 +1,35 @@ +@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+ set SPHINXBUILD=sphinx-build
+)
+set SOURCEDIR=source
+set BUILDDIR=build
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+ echo.
+ echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+ echo.installed, then set the SPHINXBUILD environment variable to point
+ echo.to the full path of the 'sphinx-build' executable. Alternatively you
+ echo.may add the Sphinx directory to PATH.
+ echo.
+ echo.If you don't have Sphinx installed, grab it from
+ echo.http://sphinx-doc.org/
+ exit /b 1
+)
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+
+:end
+popd
diff --git a/circuitpython/extmod/ulab/docs/manual/source/conf.py b/circuitpython/extmod/ulab/docs/manual/source/conf.py new file mode 100644 index 0000000..5c7b7dc --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/conf.py @@ -0,0 +1,112 @@ +# Configuration file for the Sphinx documentation builder. +# +# This file only contains a selection of the most common options. For a full +# list see the documentation: +# http://www.sphinx-doc.org/en/master/config + +# -- Path setup -------------------------------------------------------------- + +# If extensions (or modules to document with autodoc) are in another directory, +# add these directories to sys.path here. If the directory is relative to the +# documentation root, use os.path.abspath to make it absolute, like shown here. +# +import os +# import sys +# sys.path.insert(0, os.path.abspath('.')) + +#import sphinx_rtd_theme + +from sphinx.transforms import SphinxTransform +from docutils import nodes +from sphinx import addnodes + +# -- Project information ----------------------------------------------------- + +project = 'The ulab book' +copyright = '2019-2022, Zoltán Vörös and contributors' +author = 'Zoltán Vörös' + +# The full version, including alpha/beta/rc tags +release = '4.0.0' + + +# -- General configuration --------------------------------------------------- + +# Add any Sphinx extension module names here, as strings. They can be +# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom +# ones. +extensions = [ +] + +# Add any paths that contain templates here, relative to this directory. +templates_path = ['_templates'] + +# List of patterns, relative to source directory, that match files and +# directories to ignore when looking for source files. +# This pattern also affects html_static_path and html_extra_path. +exclude_patterns = [] + + +# Add any paths that contain custom static files (such as style sheets) here, +# relative to this directory. They are copied after the builtin static files, +# so a file named "default.css" will overwrite the builtin "default.css". +html_static_path = ['_static'] + +latex_maketitle = r''' +\begin{titlepage} +\begin{flushright} +\Huge\textbf{The $\mu$lab book} +\vskip 0.5em +\LARGE +\textbf{Release %s} +\vskip 5em +\huge\textbf{Zoltán Vörös} +\end{flushright} +\begin{flushright} +\LARGE +\vskip 2em +with contributions by +\vskip 2em +\textbf{Roberto Colistete Jr.} +\vskip 0.2em +\textbf{Jeff Epler} +\vskip 0.2em +\textbf{Taku Fukada} +\vskip 0.2em +\textbf{Diego Elio Pettenò} +\vskip 0.2em +\textbf{Scott Shawcroft} +\vskip 5em +\today +\end{flushright} +\end{titlepage} +'''%release + +latex_elements = { + 'maketitle': latex_maketitle +} + + +master_doc = 'index' + +author=u'Zoltán Vörös' +copyright=author +language='en' + +latex_documents = [ +(master_doc, 'the-ulab-book.tex', 'The $\mu$lab book', +'Zoltán Vörös', 'manual'), +] + +# Read the docs theme +on_rtd = os.environ.get('READTHEDOCS', None) == 'True' +if not on_rtd: + try: + import sphinx_rtd_theme + html_theme = 'sphinx_rtd_theme' + html_theme_path = [sphinx_rtd_theme.get_html_theme_path(), '.'] + except ImportError: + html_theme = 'default' + html_theme_path = ['.'] +else: + html_theme_path = ['.'] diff --git a/circuitpython/extmod/ulab/docs/manual/source/index.rst b/circuitpython/extmod/ulab/docs/manual/source/index.rst new file mode 100644 index 0000000..1bae7a3 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/index.rst @@ -0,0 +1,38 @@ + +.. ulab-manual documentation master file, created by + sphinx-quickstart on Sat Oct 19 12:48:00 2019. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +Welcome to the ulab book! +======================================= + +.. toctree:: + :maxdepth: 2 + :caption: Introduction + + ulab-intro + +.. toctree:: + :maxdepth: 2 + :caption: User's guide: + + ulab-ndarray + numpy-functions + numpy-universal + numpy-fft + numpy-linalg + scipy-linalg + scipy-optimize + scipy-signal + scipy-special + ulab-utils + ulab-tricks + ulab-programming + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` +* :ref:`search` diff --git a/circuitpython/extmod/ulab/docs/manual/source/numpy-fft.rst b/circuitpython/extmod/ulab/docs/manual/source/numpy-fft.rst new file mode 100644 index 0000000..7da9b60 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/numpy-fft.rst @@ -0,0 +1,197 @@ + +numpy.fft +========= + +Functions related to Fourier transforms can be called by prepending them +with ``numpy.fft.``. The module defines the following two functions: + +1. `numpy.fft.fft <#fft>`__ +2. `numpy.fft.ifft <#ifft>`__ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.fft.ifft.html + +fft +--- + +Since ``ulab``\ ’s ``ndarray`` does not support complex numbers, the +invocation of the Fourier transform differs from that in ``numpy``. In +``numpy``, you can simply pass an array or iterable to the function, and +it will be treated as a complex array: + +.. code:: + + # code to be run in CPython + + fft.fft([1, 2, 3, 4, 1, 2, 3, 4]) + + + +.. parsed-literal:: + + array([20.+0.j, 0.+0.j, -4.+4.j, 0.+0.j, -4.+0.j, 0.+0.j, -4.-4.j, + 0.+0.j]) + + + +**WARNING:** The array returned is also complex, i.e., the real and +imaginary components are cast together. In ``ulab``, the real and +imaginary parts are treated separately: you have to pass two +``ndarray``\ s to the function, although, the second argument is +optional, in which case the imaginary part is assumed to be zero. + +**WARNING:** The function, as opposed to ``numpy``, returns a 2-tuple, +whose elements are two ``ndarray``\ s, holding the real and imaginary +parts of the transform separately. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + x = np.linspace(0, 10, num=1024) + y = np.sin(x) + z = np.zeros(len(x)) + + a, b = np.fft.fft(x) + print('real part:\t', a) + print('\nimaginary part:\t', b) + + c, d = np.fft.fft(x, z) + print('\nreal part:\t', c) + print('\nimaginary part:\t', d) + +.. parsed-literal:: + + real part: array([5119.996, -5.004663, -5.004798, ..., -5.005482, -5.005643, -5.006577], dtype=float)
+
+ imaginary part: array([0.0, 1631.333, 815.659, ..., -543.764, -815.6588, -1631.333], dtype=float)
+
+ real part: array([5119.996, -5.004663, -5.004798, ..., -5.005482, -5.005643, -5.006577], dtype=float)
+
+ imaginary part: array([0.0, 1631.333, 815.659, ..., -543.764, -815.6588, -1631.333], dtype=float)
+ + + +ulab with complex support +~~~~~~~~~~~~~~~~~~~~~~~~~ + +If the ``ULAB_SUPPORTS_COMPLEX``, and ``ULAB_FFT_IS_NUMPY_COMPATIBLE`` +pre-processor constants are set to 1 in +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__ +as + +.. code:: c + + // Adds support for complex ndarrays + #ifndef ULAB_SUPPORTS_COMPLEX + #define ULAB_SUPPORTS_COMPLEX (1) + #endif + +.. code:: c + + #ifndef ULAB_FFT_IS_NUMPY_COMPATIBLE + #define ULAB_FFT_IS_NUMPY_COMPATIBLE (1) + #endif + +then the FFT routine will behave in a ``numpy``-compatible way: the +single input array can either be real, in which case the imaginary part +is assumed to be zero, or complex. The output is also complex. + +While ``numpy``-compatibility might be a desired feature, it has one +side effect, namely, the FFT routine consumes approx. 50% more RAM. The +reason for this lies in the implementation details. + +ifft +---- + +The above-mentioned rules apply to the inverse Fourier transform. The +inverse is also normalised by ``N``, the number of elements, as is +customary in ``numpy``. With the normalisation, we can ascertain that +the inverse of the transform is equal to the original array. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + x = np.linspace(0, 10, num=1024) + y = np.sin(x) + + a, b = np.fft.fft(y) + + print('original vector:\t', y) + + y, z = np.fft.ifft(a, b) + # the real part should be equal to y + print('\nreal part of inverse:\t', y) + # the imaginary part should be equal to zero + print('\nimaginary part of inverse:\t', z) + +.. parsed-literal:: + + original vector: array([0.0, 0.009775016, 0.0195491, ..., -0.5275068, -0.5357859, -0.5440139], dtype=float) + + real part of inverse: array([-2.980232e-08, 0.0097754, 0.0195494, ..., -0.5275064, -0.5357857, -0.5440133], dtype=float) + + imaginary part of inverse: array([-2.980232e-08, -1.451171e-07, 3.693752e-08, ..., 6.44871e-08, 9.34986e-08, 2.18336e-07], dtype=float) + + + +Note that unlike in ``numpy``, the length of the array on which the +Fourier transform is carried out must be a power of 2. If this is not +the case, the function raises a ``ValueError`` exception. + +ulab with complex support +~~~~~~~~~~~~~~~~~~~~~~~~~ + +The ``fft.ifft`` function can also be made ``numpy``-compatible by +setting the ``ULAB_SUPPORTS_COMPLEX``, and +``ULAB_FFT_IS_NUMPY_COMPATIBLE`` pre-processor constants to 1. + +Computation and storage costs +----------------------------- + +RAM +~~~ + +The FFT routine of ``ulab`` calculates the transform in place. This +means that beyond reserving space for the two ``ndarray``\ s that will +be returned (the computation uses these two as intermediate storage +space), only a handful of temporary variables, all floats or 32-bit +integers, are required. + +Speed of FFTs +~~~~~~~~~~~~~ + +A comment on the speed: a 1024-point transform implemented in python +would cost around 90 ms, and 13 ms in assembly, if the code runs on the +pyboard, v.1.1. You can gain a factor of four by moving to the D series +https://github.com/peterhinch/micropython-fourier/blob/master/README.md#8-performance. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + x = np.linspace(0, 10, num=1024) + y = np.sin(x) + + @timeit + def np_fft(y): + return np.fft.fft(y) + + a, b = np_fft(y) + +.. parsed-literal:: + + execution time: 1985 us + + + +The C implementation runs in less than 2 ms on the pyboard (we have just +measured that), and has been reported to run in under 0.8 ms on the D +series board. That is an improvement of at least a factor of four. diff --git a/circuitpython/extmod/ulab/docs/manual/source/numpy-functions.rst b/circuitpython/extmod/ulab/docs/manual/source/numpy-functions.rst new file mode 100644 index 0000000..206d641 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/numpy-functions.rst @@ -0,0 +1,1664 @@ + +Numpy functions +=============== + +This section of the manual discusses those functions that were adapted +from ``numpy``. Starred functions accept complex arrays as arguments, if +the firmware was compiled with complex support. + +1. `numpy.all\* <#all>`__ +2. `numpy.any\* <#any>`__ +3. `numpy.argmax <#argmax>`__ +4. `numpy.argmin <#argmin>`__ +5. `numpy.argsort <#argsort>`__ +6. `numpy.clip <#clip>`__ +7. `numpy.compress\* <#compress>`__ +8. `numpy.conjugate\* <#conjugate>`__ +9. `numpy.convolve\* <#convolve>`__ +10. `numpy.diff <#diff>`__ +11. `numpy.dot <#dot>`__ +12. `numpy.equal <#equal>`__ +13. `numpy.flip\* <#flip>`__ +14. `numpy.imag\* <#imag>`__ +15. `numpy.interp <#interp>`__ +16. `numpy.isfinite <#isfinite>`__ +17. `numpy.isinf <#isinf>`__ +18. `numpy.max <#max>`__ +19. `numpy.maximum <#maximum>`__ +20. `numpy.mean <#mean>`__ +21. `numpy.median <#median>`__ +22. `numpy.min <#min>`__ +23. `numpy.minimum <#minimum>`__ +24. `numpy.not_equal <#equal>`__ +25. `numpy.polyfit <#polyfit>`__ +26. `numpy.polyval <#polyval>`__ +27. `numpy.real\* <#real>`__ +28. `numpy.roll <#roll>`__ +29. `numpy.sort <#sort>`__ +30. `numpy.sort_complex\* <#sort_complex>`__ +31. `numpy.std <#std>`__ +32. `numpy.sum <#sum>`__ +33. `numpy.trace <#trace>`__ +34. `numpy.trapz <#trapz>`__ +35. `numpy.where <#where>`__ + +all +--- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.all.html + +The function takes one positional, and one keyword argument, the +``axis``, with a default value of ``None``, and tests, whether *all* +array elements along the given axis evaluate to ``True``. If the keyword +argument is ``None``, the flattened array is inspected. + +Elements of an array evaluate to ``True``, if they are not equal to +zero, or the Boolean ``False``. The return value if a Boolean +``ndarray``. + +If the firmware was compiled with complex support, the function can +accept complex arrays. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(12)).reshape((3, 4)) + + print('\na:\n', a) + + b = np.all(a) + print('\nall of the flattened array:\n', b) + + c = np.all(a, axis=0) + print('\nall of a along 0th axis:\n', c) + + d = np.all(a, axis=1) + print('\nall of a along 1st axis:\n', d) + +.. parsed-literal:: + + + a: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0]], dtype=float64) + + all of the flattened array: + False + + all of a along 0th axis: + array([False, True, True, True], dtype=bool) + + all of a along 1st axis: + array([False, True, True], dtype=bool) + + + + +any +--- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.any.html + +The function takes one positional, and one keyword argument, the +``axis``, with a default value of ``None``, and tests, whether *any* +array element along the given axis evaluates to ``True``. If the keyword +argument is ``None``, the flattened array is inspected. + +Elements of an array evaluate to ``True``, if they are not equal to +zero, or the Boolean ``False``. The return value if a Boolean +``ndarray``. + +If the firmware was compiled with complex support, the function can +accept complex arrays. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(12)).reshape((3, 4)) + + print('\na:\n', a) + + b = np.any(a) + print('\nany of the flattened array:\n', b) + + c = np.any(a, axis=0) + print('\nany of a along 0th axis:\n', c) + + d = np.any(a, axis=1) + print('\nany of a along 1st axis:\n', d) + +.. parsed-literal:: + + + a: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0]], dtype=float64) + + any of the flattened array: + True + + any of a along 0th axis: + array([True, True, True, True], dtype=bool) + + any of a along 1st axis: + array([True, True, True], dtype=bool) + + + + +argmax +------ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html + +See `numpy.max <#max>`__. + +argmin +------ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmin.html + +See `numpy.max <#max>`__. + +argsort +------- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.argsort.html + +Similarly to `sort <#sort>`__, ``argsort`` takes a positional, and a +keyword argument, and returns an unsigned short index array of type +``ndarray`` with the same dimensions as the input, or, if ``axis=None``, +as a row vector with length equal to the number of elements in the input +(i.e., the flattened array). The indices in the output sort the input in +ascending order. The routine in ``argsort`` is the same as in ``sort``, +therefore, the comments on computational expenses (time and RAM) also +apply. In particular, since no copy of the original data is required, +virtually no RAM beyond the output array is used. + +Since the underlying container of the output array is of type +``uint16_t``, neither of the output dimensions should be larger than +65535. If that happens to be the case, the function will bail out with a +``ValueError``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.float) + print('\na:\n', a) + b = np.argsort(a, axis=0) + print('\na sorted along vertical axis:\n', b) + + c = np.argsort(a, axis=1) + print('\na sorted along horizontal axis:\n', c) + + c = np.argsort(a, axis=None) + print('\nflattened a sorted:\n', c) + +.. parsed-literal:: + + + a: + array([[1.0, 12.0, 3.0, 0.0], + [5.0, 3.0, 4.0, 1.0], + [9.0, 11.0, 1.0, 8.0], + [7.0, 10.0, 0.0, 1.0]], dtype=float64) + + a sorted along vertical axis: + array([[0, 1, 3, 0], + [1, 3, 2, 1], + [3, 2, 0, 3], + [2, 0, 1, 2]], dtype=uint16) + + a sorted along horizontal axis: + array([[3, 0, 2, 1], + [3, 1, 2, 0], + [2, 3, 0, 1], + [2, 3, 0, 1]], dtype=uint16) + + Traceback (most recent call last): + File "/dev/shm/micropython.py", line 12, in <module> + NotImplementedError: argsort is not implemented for flattened arrays + + + +Since during the sorting, only the indices are shuffled, ``argsort`` +does not modify the input array, as one can verify this by the following +example: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([0, 5, 1, 3, 2, 4], dtype=np.uint8) + print('\na:\n', a) + b = np.argsort(a, axis=0) + print('\nsorting indices:\n', b) + print('\nthe original array:\n', a) + +.. parsed-literal:: + + + a: + array([0, 5, 1, 3, 2, 4], dtype=uint8) + + sorting indices: + array([0, 2, 4, 3, 5, 1], dtype=uint16) + + the original array: + array([0, 5, 1, 3, 2, 4], dtype=uint8) + + + + +clip +---- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.clip.html + +Clips an array, i.e., values that are outside of an interval are clipped +to the interval edges. The function is equivalent to +``maximum(a_min, minimum(a, a_max))`` broadcasting takes place exactly +as in `minimum <#minimum>`__. If the arrays are of different ``dtype``, +the output is upcast as in `Binary operators <#Binary-operators>`__. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(9), dtype=np.uint8) + print('a:\t\t', a) + print('clipped:\t', np.clip(a, 3, 7)) + + b = 3 * np.ones(len(a), dtype=np.float) + print('\na:\t\t', a) + print('b:\t\t', b) + print('clipped:\t', np.clip(a, b, 7)) + +.. parsed-literal:: + + a: array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8) + clipped: array([3, 3, 3, 3, 4, 5, 6, 7, 7], dtype=uint8) + + a: array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8) + b: array([3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0], dtype=float64) + clipped: array([3.0, 3.0, 3.0, 3.0, 4.0, 5.0, 6.0, 7.0, 7.0], dtype=float64) + + + + +compress +-------- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.compress.html + +The function returns selected slices of an array along given axis. If +the axis keyword is ``None``, the flattened array is used. + +If the firmware was compiled with complex support, the function can +accept complex arguments. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(6)).reshape((2, 3)) + + print('a:\n', a) + print('\ncompress(a):\n', np.compress([0, 1], a, axis=0)) + +.. parsed-literal:: + + a: + array([[0.0, 1.0, 2.0], + [3.0, 4.0, 5.0]], dtype=float64) + + compress(a): + array([[3.0, 4.0, 5.0]], dtype=float64) + + + + +conjugate +--------- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.conjugate.html + +If the firmware was compiled with complex support, the function +calculates the complex conjugate of the input array. If the input array +is of real ``dtype``, then the output is simply a copy, preserving the +``dtype``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4], dtype=np.uint8) + b = np.array([1+1j, 2-2j, 3+3j, 4-4j], dtype=np.complex) + + print('a:\t\t', a) + print('conjugate(a):\t', np.conjugate(a)) + print() + print('b:\t\t', b) + print('conjugate(b):\t', np.conjugate(b)) + +.. parsed-literal:: + + a: array([1, 2, 3, 4], dtype=uint8) + conjugate(a): array([1, 2, 3, 4], dtype=uint8) + + b: array([1.0+1.0j, 2.0-2.0j, 3.0+3.0j, 4.0-4.0j], dtype=complex) + conjugate(b): array([1.0-1.0j, 2.0+2.0j, 3.0-3.0j, 4.0+4.0j], dtype=complex) + + + + +convolve +-------- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html + +Returns the discrete, linear convolution of two one-dimensional arrays. + +Only the ``full`` mode is supported, and the ``mode`` named parameter is +not accepted. Note that all other modes can be had by slicing a ``full`` +result. + +If the firmware was compiled with complex support, the function can +accept complex arrays. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + x = np.array((1, 2, 3)) + y = np.array((1, 10, 100, 1000)) + + print(np.convolve(x, y)) + +.. parsed-literal:: + + array([1.0, 12.0, 123.0, 1230.0, 2300.0, 3000.0], dtype=float64) + + + + +diff +---- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.diff.html + +The ``diff`` function returns the numerical derivative of the forward +scheme, or more accurately, the differences of an ``ndarray`` along a +given axis. The order of derivative can be stipulated with the ``n`` +keyword argument, which should be between 0, and 9. Default is 1. If +higher order derivatives are required, they can be gotten by repeated +calls to the function. The ``axis`` keyword argument should be -1 (last +axis, in ``ulab`` equivalent to the second axis, and this also happens +to be the default value), 0, or 1. + +Beyond the output array, the function requires only a couple of bytes of +extra RAM for the differentiation stencil. (The stencil is an ``int8`` +array, one byte longer than ``n``. This also explains, why the highest +order is 9: the coefficients of a ninth-order stencil all fit in signed +bytes, while 10 would require ``int16``.) Note that as usual in +numerical differentiation (and also in ``numpy``), the length of the +respective axis will be reduced by ``n`` after the operation. If ``n`` +is larger than, or equal to the length of the axis, an empty array will +be returned. + +**WARNING**: the ``diff`` function does not implement the ``prepend`` +and ``append`` keywords that can be found in ``numpy``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(9), dtype=np.uint8) + a[3] = 10 + print('a:\n', a) + + print('\nfirst derivative:\n', np.diff(a, n=1)) + print('\nsecond derivative:\n', np.diff(a, n=2)) + + c = np.array([[1, 2, 3, 4], [4, 3, 2, 1], [1, 4, 9, 16], [0, 0, 0, 0]]) + print('\nc:\n', c) + print('\nfirst derivative, first axis:\n', np.diff(c, axis=0)) + print('\nfirst derivative, second axis:\n', np.diff(c, axis=1)) + +.. parsed-literal:: + + a: + array([0, 1, 2, 10, 4, 5, 6, 7, 8], dtype=uint8) + + first derivative: + array([1, 1, 8, 250, 1, 1, 1, 1], dtype=uint8) + + second derivative: + array([0, 249, 14, 249, 0, 0, 0], dtype=uint8) + + c: + array([[1.0, 2.0, 3.0, 4.0], + [4.0, 3.0, 2.0, 1.0], + [1.0, 4.0, 9.0, 16.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) + + first derivative, first axis: + array([[3.0, 1.0, -1.0, -3.0], + [-3.0, 1.0, 7.0, 15.0], + [-1.0, -4.0, -9.0, -16.0]], dtype=float64) + + first derivative, second axis: + array([[1.0, 1.0, 1.0], + [-1.0, -1.0, -1.0], + [3.0, 5.0, 7.0], + [0.0, 0.0, 0.0]], dtype=float64) + + + + +dot +--- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html + +**WARNING:** numpy applies upcasting rules for the multiplication of +matrices, while ``ulab`` simply returns a float matrix. + +Once you can invert a matrix, you might want to know, whether the +inversion is correct. You can simply take the original matrix and its +inverse, and multiply them by calling the ``dot`` function, which takes +the two matrices as its arguments. If the matrix dimensions do not +match, the function raises a ``ValueError``. The result of the +multiplication is expected to be the unit matrix, which is demonstrated +below. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + m = np.array([[1, 2, 3], [4, 5, 6], [7, 10, 9]], dtype=np.uint8) + n = np.linalg.inv(m) + print("m:\n", m) + print("\nm^-1:\n", n) + # this should be the unit matrix + print("\nm*m^-1:\n", np.dot(m, n)) + +.. parsed-literal:: + + m: + array([[1, 2, 3], + [4, 5, 6], + [7, 10, 9]], dtype=uint8) + + m^-1: + array([[-1.25, 1.0, -0.25], + [0.4999999999999998, -1.0, 0.5], + [0.4166666666666668, 0.3333333333333333, -0.25]], dtype=float64) + + m*m^-1: + array([[1.0, 0.0, 0.0], + [4.440892098500626e-16, 1.0, 0.0], + [8.881784197001252e-16, 0.0, 1.0]], dtype=float64) + + + + +Note that for matrix multiplication you don’t necessarily need square +matrices, it is enough, if their dimensions are compatible (i.e., the +the left-hand-side matrix has as many columns, as does the +right-hand-side matrix rows): + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + m = np.array([[1, 2, 3, 4], [5, 6, 7, 8]], dtype=np.uint8) + n = np.array([[1, 2], [3, 4], [5, 6], [7, 8]], dtype=np.uint8) + print(m) + print(n) + print(np.dot(m, n)) + +.. parsed-literal:: + + array([[1, 2, 3, 4], + [5, 6, 7, 8]], dtype=uint8) + array([[1, 2], + [3, 4], + [5, 6], + [7, 8]], dtype=uint8) + array([[50.0, 60.0], + [114.0, 140.0]], dtype=float64) + + + + +equal +----- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.equal.html + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.not_equal.html + +In ``micropython``, equality of arrays or scalars can be established by +utilising the ``==``, ``!=``, ``<``, ``>``, ``<=``, or ``=>`` binary +operators. In ``circuitpython``, ``==`` and ``!=`` will produce +unexpected results. In order to avoid this discrepancy, and to maintain +compatibility with ``numpy``, ``ulab`` implements the ``equal`` and +``not_equal`` operators that return the same results, irrespective of +the ``python`` implementation. + +These two functions take two ``ndarray``\ s, or scalars as their +arguments. No keyword arguments are implemented. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(9)) + b = np.zeros(9) + + print('a: ', a) + print('b: ', b) + print('\na == b: ', np.equal(a, b)) + print('a != b: ', np.not_equal(a, b)) + + # comparison with scalars + print('a == 2: ', np.equal(a, 2)) + +.. parsed-literal:: + + a: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64) + b: array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], dtype=float64) + + a == b: array([True, False, False, False, False, False, False, False, False], dtype=bool) + a != b: array([False, True, True, True, True, True, True, True, True], dtype=bool) + a == 2: array([False, False, True, False, False, False, False, False, False], dtype=bool) + + + + +flip +---- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.flip.html + +The ``flip`` function takes one positional, an ``ndarray``, and one +keyword argument, ``axis = None``, and reverses the order of elements +along the given axis. If the keyword argument is ``None``, the matrix’ +entries are flipped along all axes. ``flip`` returns a new copy of the +array. + +If the firmware was compiled with complex support, the function can +accept complex arrays. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5]) + print("a: \t", a) + print("a flipped:\t", np.flip(a)) + + a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.uint8) + print("\na flipped horizontally\n", np.flip(a, axis=1)) + print("\na flipped vertically\n", np.flip(a, axis=0)) + print("\na flipped horizontally+vertically\n", np.flip(a)) + +.. parsed-literal:: + + a: array([1.0, 2.0, 3.0, 4.0, 5.0], dtype=float64) + a flipped: array([5.0, 4.0, 3.0, 2.0, 1.0], dtype=float64) + + a flipped horizontally + array([[3, 2, 1], + [6, 5, 4], + [9, 8, 7]], dtype=uint8) + + a flipped vertically + array([[7, 8, 9], + [4, 5, 6], + [1, 2, 3]], dtype=uint8) + + a flipped horizontally+vertically + array([9, 8, 7, 6, 5, 4, 3, 2, 1], dtype=uint8) + + + + +imag +---- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.imag.html + +The ``imag`` function returns the imaginary part of an array, or scalar. +It cannot accept a generic iterable as its argument. The function is +defined only, if the firmware was compiled with complex support. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3], dtype=np.uint16) + print("a:\t\t", a) + print("imag(a):\t", np.imag(a)) + + b = np.array([1, 2+1j, 3-1j], dtype=np.complex) + print("\nb:\t\t", b) + print("imag(b):\t", np.imag(b)) + +.. parsed-literal:: + + a: array([1, 2, 3], dtype=uint16) + imag(a): array([0, 0, 0], dtype=uint16) + + b: array([1.0+0.0j, 2.0+1.0j, 3.0-1.0j], dtype=complex) + imag(b): array([0.0, 1.0, -1.0], dtype=float64) + + + + +interp +------ + +``numpy``: https://docs.scipy.org/doc/numpy/numpy.interp + +The ``interp`` function returns the linearly interpolated values of a +one-dimensional numerical array. It requires three positional +arguments,\ ``x``, at which the interpolated values are evaluated, +``xp``, the array of the independent data variable, and ``fp``, the +array of the dependent values of the data. ``xp`` must be a +monotonically increasing sequence of numbers. + +Two keyword arguments, ``left``, and ``right`` can also be supplied; +these determine the return values, if ``x < xp[0]``, and ``x > xp[-1]``, +respectively. If these arguments are not supplied, ``left``, and +``right`` default to ``fp[0]``, and ``fp[-1]``, respectively. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + x = np.array([1, 2, 3, 4, 5]) - 0.2 + xp = np.array([1, 2, 3, 4]) + fp = np.array([1, 2, 3, 5]) + + print(x) + print(np.interp(x, xp, fp)) + print(np.interp(x, xp, fp, left=0.0)) + print(np.interp(x, xp, fp, right=10.0)) + +.. parsed-literal:: + + array([0.8, 1.8, 2.8, 3.8, 4.8], dtype=float64) + array([1.0, 1.8, 2.8, 4.6, 5.0], dtype=float64) + array([0.0, 1.8, 2.8, 4.6, 5.0], dtype=float64) + array([1.0, 1.8, 2.8, 4.6, 10.0], dtype=float64) + + + + +isfinite +-------- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.isfinite.html + +Returns a Boolean array of the same shape as the input, or a +``True/False``, if the input is a scalar. In the return value, all +elements are ``True`` at positions, where the input value was finite. +Integer types are automatically finite, therefore, if the input is of +integer type, the output will be the ``True`` tensor. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + print('isfinite(0): ', np.isfinite(0)) + + a = np.array([1, 2, np.nan]) + print('\n' + '='*20) + print('a:\n', a) + print('\nisfinite(a):\n', np.isfinite(a)) + + b = np.array([1, 2, np.inf]) + print('\n' + '='*20) + print('b:\n', b) + print('\nisfinite(b):\n', np.isfinite(b)) + + c = np.array([1, 2, 3], dtype=np.uint16) + print('\n' + '='*20) + print('c:\n', c) + print('\nisfinite(c):\n', np.isfinite(c)) + +.. parsed-literal:: + + isfinite(0): True + + ==================== + a: + array([1.0, 2.0, nan], dtype=float64) + + isfinite(a): + array([True, True, False], dtype=bool) + + ==================== + b: + array([1.0, 2.0, inf], dtype=float64) + + isfinite(b): + array([True, True, False], dtype=bool) + + ==================== + c: + array([1, 2, 3], dtype=uint16) + + isfinite(c): + array([True, True, True], dtype=bool) + + + + +isinf +----- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.isinf.html + +Similar to `isfinite <#isfinite>`__, but the output is ``True`` at +positions, where the input is infinite. Integer types return the +``False`` tensor. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + print('isinf(0): ', np.isinf(0)) + + a = np.array([1, 2, np.nan]) + print('\n' + '='*20) + print('a:\n', a) + print('\nisinf(a):\n', np.isinf(a)) + + b = np.array([1, 2, np.inf]) + print('\n' + '='*20) + print('b:\n', b) + print('\nisinf(b):\n', np.isinf(b)) + + c = np.array([1, 2, 3], dtype=np.uint16) + print('\n' + '='*20) + print('c:\n', c) + print('\nisinf(c):\n', np.isinf(c)) + +.. parsed-literal:: + + isinf(0): False + + ==================== + a: + array([1.0, 2.0, nan], dtype=float64) + + isinf(a): + array([False, False, False], dtype=bool) + + ==================== + b: + array([1.0, 2.0, inf], dtype=float64) + + isinf(b): + array([False, False, True], dtype=bool) + + ==================== + c: + array([1, 2, 3], dtype=uint16) + + isinf(c): + array([False, False, False], dtype=bool) + + + + +mean +---- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html + +If the axis keyword is not specified, it assumes the default value of +``None``, and returns the result of the computation for the flattened +array. Otherwise, the calculation is along the given axis. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + print('a: \n', a) + print('mean, flat: ', np.mean(a)) + print('mean, horizontal: ', np.mean(a, axis=1)) + print('mean, vertical: ', np.mean(a, axis=0)) + +.. parsed-literal:: + + a: + array([[1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0]], dtype=float64) + mean, flat: 5.0 + mean, horizontal: array([2.0, 5.0, 8.0], dtype=float64) + mean, vertical: array([4.0, 5.0, 6.0], dtype=float64) + + + + +max +--- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.max.html + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.min.html + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmin.html + +**WARNING:** Difference to ``numpy``: the ``out`` keyword argument is +not implemented. + +These functions follow the same pattern, and work with generic +iterables, and ``ndarray``\ s. ``min``, and ``max`` return the minimum +or maximum of a sequence. If the input array is two-dimensional, the +``axis`` keyword argument can be supplied, in which case the +minimum/maximum along the given axis will be returned. If ``axis=None`` +(this is also the default value), the minimum/maximum of the flattened +array will be determined. + +``argmin/argmax`` return the position (index) of the minimum/maximum in +the sequence. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 0, 1, 10]) + print('a:', a) + print('min of a:', np.min(a)) + print('argmin of a:', np.argmin(a)) + + b = np.array([[1, 2, 0], [1, 10, -1]]) + print('\nb:\n', b) + print('min of b (flattened):', np.min(b)) + print('min of b (axis=0):', np.min(b, axis=0)) + print('min of b (axis=1):', np.min(b, axis=1)) + +.. parsed-literal:: + + a: array([1.0, 2.0, 0.0, 1.0, 10.0], dtype=float64) + min of a: 0.0 + argmin of a: 2 + + b: + array([[1.0, 2.0, 0.0], + [1.0, 10.0, -1.0]], dtype=float64) + min of b (flattened): -1.0 + min of b (axis=0): array([1.0, 2.0, -1.0], dtype=float64) + min of b (axis=1): array([0.0, -1.0], dtype=float64) + + + + +median +------ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.median.html + +The function computes the median along the specified axis, and returns +the median of the array elements. If the ``axis`` keyword argument is +``None``, the arrays is flattened first. The ``dtype`` of the results is +always float. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(12), dtype=np.int8).reshape((3, 4)) + print('a:\n', a) + print('\nmedian of the flattened array: ', np.median(a)) + print('\nmedian along the vertical axis: ', np.median(a, axis=0)) + print('\nmedian along the horizontal axis: ', np.median(a, axis=1)) + +.. parsed-literal:: + + a: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11]], dtype=int8) + + median of the flattened array: 5.5 + + median along the vertical axis: array([4.0, 5.0, 6.0, 7.0], dtype=float64) + + median along the horizontal axis: array([1.5, 5.5, 9.5], dtype=float64) + + + + +min +--- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.min.html + +See `numpy.max <#max>`__. + +minimum +------- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.minimum.html + +See `numpy.maximum <#maximum>`__ + +maximum +------- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.maximum.html + +Returns the maximum of two arrays, or two scalars, or an array, and a +scalar. If the arrays are of different ``dtype``, the output is upcast +as in `Binary operators <#Binary-operators>`__. If both inputs are +scalars, a scalar is returned. Only positional arguments are +implemented. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5], dtype=np.uint8) + b = np.array([5, 4, 3, 2, 1], dtype=np.float) + print('minimum of a, and b:') + print(np.minimum(a, b)) + + print('\nmaximum of a, and b:') + print(np.maximum(a, b)) + + print('\nmaximum of 1, and 5.5:') + print(np.maximum(1, 5.5)) + +.. parsed-literal:: + + minimum of a, and b: + array([1.0, 2.0, 3.0, 2.0, 1.0], dtype=float64) + + maximum of a, and b: + array([5.0, 4.0, 3.0, 4.0, 5.0], dtype=float64) + + maximum of 1, and 5.5: + 5.5 + + + + +not_equal +--------- + +See `numpy.equal <#equal>`__. + +polyfit +------- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html + +polyfit takes two, or three arguments. The last one is the degree of the +polynomial that will be fitted, the last but one is an array or iterable +with the ``y`` (dependent) values, and the first one, an array or +iterable with the ``x`` (independent) values, can be dropped. If that is +the case, ``x`` will be generated in the function as ``range(len(y))``. + +If the lengths of ``x``, and ``y`` are not the same, the function raises +a ``ValueError``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + x = np.array([0, 1, 2, 3, 4, 5, 6]) + y = np.array([9, 4, 1, 0, 1, 4, 9]) + print('independent values:\t', x) + print('dependent values:\t', y) + print('fitted values:\t\t', np.polyfit(x, y, 2)) + + # the same with missing x + print('\ndependent values:\t', y) + print('fitted values:\t\t', np.polyfit(y, 2)) + +.. parsed-literal:: + + independent values: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float64) + dependent values: array([9.0, 4.0, 1.0, 0.0, 1.0, 4.0, 9.0], dtype=float64) + fitted values: array([1.0, -6.0, 9.000000000000004], dtype=float64) + + dependent values: array([9.0, 4.0, 1.0, 0.0, 1.0, 4.0, 9.0], dtype=float64) + fitted values: array([1.0, -6.0, 9.000000000000004], dtype=float64) + + + + +Execution time +~~~~~~~~~~~~~~ + +``polyfit`` is based on the inversion of a matrix (there is more on the +background in https://en.wikipedia.org/wiki/Polynomial_regression), and +it requires the intermediate storage of ``2*N*(deg+1)`` floats, where +``N`` is the number of entries in the input array, and ``deg`` is the +fit’s degree. The additional computation costs of the matrix inversion +discussed in `linalg.inv <#inv>`__ also apply. The example from above +needs around 150 microseconds to return: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + @timeit + def time_polyfit(x, y, n): + return np.polyfit(x, y, n) + + x = np.array([0, 1, 2, 3, 4, 5, 6]) + y = np.array([9, 4, 1, 0, 1, 4, 9]) + + time_polyfit(x, y, 2) + +.. parsed-literal:: + + execution time: 153 us + + +polyval +------- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyval.html + +``polyval`` takes two arguments, both arrays or generic ``micropython`` +iterables returning scalars. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + p = [1, 1, 1, 0] + x = [0, 1, 2, 3, 4] + print('coefficients: ', p) + print('independent values: ', x) + print('\nvalues of p(x): ', np.polyval(p, x)) + + # the same works with one-dimensional ndarrays + a = np.array(x) + print('\nndarray (a): ', a) + print('value of p(a): ', np.polyval(p, a)) + +.. parsed-literal:: + + coefficients: [1, 1, 1, 0] + independent values: [0, 1, 2, 3, 4] + + values of p(x): array([0.0, 3.0, 14.0, 39.0, 84.0], dtype=float64) + + ndarray (a): array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) + value of p(a): array([0.0, 3.0, 14.0, 39.0, 84.0], dtype=float64) + + + + +real +---- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.real.html + +The ``real`` function returns the real part of an array, or scalar. It +cannot accept a generic iterable as its argument. The function is +defined only, if the firmware was compiled with complex support. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3], dtype=np.uint16) + print("a:\t\t", a) + print("real(a):\t", np.real(a)) + + b = np.array([1, 2+1j, 3-1j], dtype=np.complex) + print("\nb:\t\t", b) + print("real(b):\t", np.real(b)) + +.. parsed-literal:: + + a: array([1, 2, 3], dtype=uint16) + real(a): array([1, 2, 3], dtype=uint16) + + b: array([1.0+0.0j, 2.0+1.0j, 3.0-1.0j], dtype=complex) + real(b): array([1.0, 2.0, 3.0], dtype=float64) + + + + +roll +---- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.roll.html + +The roll function shifts the content of a vector by the positions given +as the second argument. If the ``axis`` keyword is supplied, the shift +is applied to the given axis. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5, 6, 7, 8]) + print("a:\t\t\t", a) + + a = np.roll(a, 2) + print("a rolled to the left:\t", a) + + # this should be the original vector + a = np.roll(a, -2) + print("a rolled to the right:\t", a) + +.. parsed-literal:: + + a: array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64) + a rolled to the left: array([7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float64) + a rolled to the right: array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64) + + + + +Rolling works with matrices, too. If the ``axis`` keyword is 0, the +matrix is rolled along its vertical axis, otherwise, horizontally. + +Horizontal rolls are faster, because they require fewer steps, and +larger memory chunks are copied, however, they also require more RAM: +basically the whole row must be stored internally. Most expensive are +the ``None`` keyword values, because with ``axis = None``, the array is +flattened first, hence the row’s length is the size of the whole matrix. + +Vertical rolls require two internal copies of single columns. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(12)).reshape((3, 4)) + print("a:\n", a) + a = np.roll(a, 2, axis=0) + print("\na rolled up:\n", a) + + a = np.array(range(12)).reshape((3, 4)) + print("a:\n", a) + a = np.roll(a, -1, axis=1) + print("\na rolled to the left:\n", a) + + a = np.array(range(12)).reshape((3, 4)) + print("a:\n", a) + a = np.roll(a, 1, axis=None) + print("\na rolled with None:\n", a) + +.. parsed-literal:: + + a: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0]], dtype=float64) + + a rolled up: + array([[4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0], + [0.0, 1.0, 2.0, 3.0]], dtype=float64) + a: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0]], dtype=float64) + + a rolled to the left: + array([[1.0, 2.0, 3.0, 0.0], + [5.0, 6.0, 7.0, 4.0], + [9.0, 10.0, 11.0, 8.0]], dtype=float64) + a: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0]], dtype=float64) + + a rolled with None: + array([[11.0, 0.0, 1.0, 2.0], + [3.0, 4.0, 5.0, 6.0], + [7.0, 8.0, 9.0, 10.0]], dtype=float64) + + + + +sort +---- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html + +The sort function takes an ndarray, and sorts its elements in ascending +order along the specified axis using a heap sort algorithm. As opposed +to the ``.sort()`` method discussed earlier, this function creates a +copy of its input before sorting, and at the end, returns this copy. +Sorting takes place in place, without auxiliary storage. The ``axis`` +keyword argument takes on the possible values of -1 (the last axis, in +``ulab`` equivalent to the second axis, and this also happens to be the +default value), 0, 1, or ``None``. The first three cases are identical +to those in `diff <#diff>`__, while the last one flattens the array +before sorting. + +If descending order is required, the result can simply be ``flip``\ ped, +see `flip <#flip>`__. + +**WARNING:** ``numpy`` defines the ``kind``, and ``order`` keyword +arguments that are not implemented here. The function in ``ulab`` always +uses heap sort, and since ``ulab`` does not have the concept of data +fields, the ``order`` keyword argument would have no meaning. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.float) + print('\na:\n', a) + b = np.sort(a, axis=0) + print('\na sorted along vertical axis:\n', b) + + c = np.sort(a, axis=1) + print('\na sorted along horizontal axis:\n', c) + + c = np.sort(a, axis=None) + print('\nflattened a sorted:\n', c) + +.. parsed-literal:: + + + a: + array([[1.0, 12.0, 3.0, 0.0], + [5.0, 3.0, 4.0, 1.0], + [9.0, 11.0, 1.0, 8.0], + [7.0, 10.0, 0.0, 1.0]], dtype=float64) + + a sorted along vertical axis: + array([[1.0, 3.0, 0.0, 0.0], + [5.0, 10.0, 1.0, 1.0], + [7.0, 11.0, 3.0, 1.0], + [9.0, 12.0, 4.0, 8.0]], dtype=float64) + + a sorted along horizontal axis: + array([[0.0, 1.0, 3.0, 12.0], + [1.0, 3.0, 4.0, 5.0], + [1.0, 8.0, 9.0, 11.0], + [0.0, 1.0, 7.0, 10.0]], dtype=float64) + + flattened a sorted: + array([0.0, 0.0, 1.0, ..., 10.0, 11.0, 12.0], dtype=float64) + + + + +Heap sort requires :math:`\sim N\log N` operations, and notably, the +worst case costs only 20% more time than the average. In order to get an +order-of-magnitude estimate, we will take the sine of 1000 uniformly +spaced numbers between 0, and two pi, and sort them: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + @timeit + def sort_time(array): + return nup.sort(array) + + b = np.sin(np.linspace(0, 6.28, num=1000)) + print('b: ', b) + sort_time(b) + print('\nb sorted:\n', b) +sort_complex +------------ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.sort_complex.html + +If the firmware was compiled with complex support, the functions sorts +the input array first according to its real part, and then the imaginary +part. The input must be a one-dimensional array. The output is always of +``dtype`` complex, even if the input was real integer. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([5, 4, 3, 2, 1], dtype=np.int16) + print('a:\t\t\t', a) + print('sort_complex(a):\t', np.sort_complex(a)) + print() + + b = np.array([5, 4+3j, 4-2j, 0, 1j], dtype=np.complex) + print('b:\t\t\t', b) + print('sort_complex(b):\t', np.sort_complex(b)) + +.. parsed-literal:: + + a: array([5, 4, 3, 2, 1], dtype=int16) + sort_complex(a): array([1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j], dtype=complex) + + b: array([5.0+0.0j, 4.0+3.0j, 4.0-2.0j, 0.0+0.0j, 0.0+1.0j], dtype=complex) + sort_complex(b): array([0.0+0.0j, 0.0+1.0j, 4.0-2.0j, 4.0+3.0j, 5.0+0.0j], dtype=complex) + + + + +std +--- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html + +If the axis keyword is not specified, it assumes the default value of +``None``, and returns the result of the computation for the flattened +array. Otherwise, the calculation is along the given axis. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + print('a: \n', a) + print('sum, flat array: ', np.std(a)) + print('std, vertical: ', np.std(a, axis=0)) + print('std, horizonal: ', np.std(a, axis=1)) + +.. parsed-literal:: + + a: + array([[1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0]], dtype=float64) + sum, flat array: 2.581988897471611 + std, vertical: array([2.449489742783178, 2.449489742783178, 2.449489742783178], dtype=float64) + std, horizonal: array([0.8164965809277261, 0.8164965809277261, 0.8164965809277261], dtype=float64) + + + + +sum +--- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.sum.html + +If the axis keyword is not specified, it assumes the default value of +``None``, and returns the result of the computation for the flattened +array. Otherwise, the calculation is along the given axis. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + print('a: \n', a) + + print('sum, flat array: ', np.sum(a)) + print('sum, horizontal: ', np.sum(a, axis=1)) + print('std, vertical: ', np.sum(a, axis=0)) + +.. parsed-literal:: + + a: + array([[1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0]], dtype=float64) + sum, flat array: 45.0 + sum, horizontal: array([6.0, 15.0, 24.0], dtype=float64) + std, vertical: array([12.0, 15.0, 18.0], dtype=float64) + + + + +trace +----- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.trace.html + +The ``trace`` function returns the sum of the diagonal elements of a +square matrix. If the input argument is not a square matrix, an +exception will be raised. + +The scalar so returned will inherit the type of the input array, i.e., +integer arrays have integer trace, and floating point arrays a floating +point trace. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[25, 15, -5], [15, 18, 0], [-5, 0, 11]], dtype=np.int8) + print('a: ', a) + print('\ntrace of a: ', np.trace(a)) + + b = np.array([[25, 15, -5], [15, 18, 0], [-5, 0, 11]], dtype=np.float) + + print('='*20 + '\nb: ', b) + print('\ntrace of b: ', np.trace(b)) + +.. parsed-literal:: + + a: array([[25, 15, -5], + [15, 18, 0], + [-5, 0, 11]], dtype=int8) + + trace of a: 54 + ==================== + b: array([[25.0, 15.0, -5.0], + [15.0, 18.0, 0.0], + [-5.0, 0.0, 11.0]], dtype=float64) + + trace of b: 54.0 + + + + +trapz +----- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.trapz.html + +The function takes one or two one-dimensional ``ndarray``\ s, and +integrates the dependent values (``y``) using the trapezoidal rule. If +the independent variable (``x``) is given, that is taken as the sample +points corresponding to ``y``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + x = np.linspace(0, 9, num=10) + y = x*x + + print('x: ', x) + print('y: ', y) + print('============================') + print('integral of y: ', np.trapz(y)) + print('integral of y at x: ', np.trapz(y, x=x)) + +.. parsed-literal:: + + x: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64) + y: array([0.0, 1.0, 4.0, 9.0, 16.0, 25.0, 36.0, 49.0, 64.0, 81.0], dtype=float64) + ============================ + integral of y: 244.5 + integral of y at x: 244.5 + + + + +where +----- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.where.html + +The function takes three positional arguments, ``condition``, ``x``, and +``y``, and returns a new ``ndarray``, whose values are taken from either +``x``, or ``y``, depending on the truthness of ``condition``. The three +arguments are broadcast together, and the function raises a +``ValueError`` exception, if broadcasting is not possible. + +The function is implemented for ``ndarray``\ s only: other iterable +types can be passed after casting them to an ``ndarray`` by calling the +``array`` constructor. + +If the ``dtype``\ s of ``x``, and ``y`` differ, the output is upcast as +discussed earlier. + +Note that the ``condition`` is expanded into an Boolean ``ndarray``. +This means that the storage required to hold the condition should be +taken into account, whenever the function is called. + +The following example returns an ``ndarray`` of length 4, with 1 at +positions, where ``condition`` is smaller than 3, and with -1 otherwise. + +.. code:: + + # code to be run in micropython + + + from ulab import numpy as np + + condition = np.array([1, 2, 3, 4], dtype=np.uint8) + print(np.where(condition < 3, 1, -1)) + +.. parsed-literal:: + + array([1, 1, -1, -1], dtype=int16) + + + + +The next snippet shows, how values from two arrays can be fed into the +output: + +.. code:: + + # code to be run in micropython + + + from ulab import numpy as np + + condition = np.array([1, 2, 3, 4], dtype=np.uint8) + x = np.array([11, 22, 33, 44], dtype=np.uint8) + y = np.array([1, 2, 3, 4], dtype=np.uint8) + print(np.where(condition < 3, x, y)) + +.. parsed-literal:: + + array([11, 22, 3, 4], dtype=uint8) + + + diff --git a/circuitpython/extmod/ulab/docs/manual/source/numpy-linalg.rst b/circuitpython/extmod/ulab/docs/manual/source/numpy-linalg.rst new file mode 100644 index 0000000..8439f33 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/numpy-linalg.rst @@ -0,0 +1,386 @@ + +numpy.linalg +============ + +Functions in the ``linalg`` module can be called by prepending them by +``numpy.linalg.``. The module defines the following seven functions: + +1. `numpy.linalg.cholesky <#cholesky>`__ +2. `numpy.linalg.det <#det>`__ +3. `numpy.linalg.eig <#eig>`__ +4. `numpy.linalg.inv <#inv>`__ +5. `numpy.linalg.norm <#norm>`__ +6. `numpy.linalg.qr <#qr>`__ + +cholesky +-------- + +``numpy``: +https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.linalg.cholesky.html + +The function of the Cholesky decomposition takes a positive definite, +symmetric square matrix as its single argument, and returns the *square +root matrix* in the lower triangular form. If the input argument does +not fulfill the positivity or symmetry condition, a ``ValueError`` is +raised. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[25, 15, -5], [15, 18, 0], [-5, 0, 11]]) + print('a: ', a) + print('\n' + '='*20 + '\nCholesky decomposition\n', np.linalg.cholesky(a)) + +.. parsed-literal:: + + a: array([[25.0, 15.0, -5.0], + [15.0, 18.0, 0.0], + [-5.0, 0.0, 11.0]], dtype=float) + + ==================== + Cholesky decomposition + array([[5.0, 0.0, 0.0], + [3.0, 3.0, 0.0], + [-1.0, 1.0, 3.0]], dtype=float) + + + + +det +--- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.det.html + +The ``det`` function takes a square matrix as its single argument, and +calculates the determinant. The calculation is based on successive +elimination of the matrix elements, and the return value is a float, +even if the input array was of integer type. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2], [3, 4]], dtype=np.uint8) + print(np.linalg.det(a)) + +.. parsed-literal:: + + -2.0 + + + +Benchmark +~~~~~~~~~ + +Since the routine for calculating the determinant is pretty much the +same as for finding the `inverse of a matrix <#inv>`__, the execution +times are similar: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + @timeit + def matrix_det(m): + return np.linalg.inv(m) + + m = np.array([[1, 2, 3, 4, 5, 6, 7, 8], [0, 5, 6, 4, 5, 6, 4, 5], + [0, 0, 9, 7, 8, 9, 7, 8], [0, 0, 0, 10, 11, 12, 11, 12], + [0, 0, 0, 0, 4, 6, 7, 8], [0, 0, 0, 0, 0, 5, 6, 7], + [0, 0, 0, 0, 0, 0, 7, 6], [0, 0, 0, 0, 0, 0, 0, 2]]) + + matrix_det(m) + +.. parsed-literal:: + + execution time: 294 us + + + +eig +--- + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html + +The ``eig`` function calculates the eigenvalues and the eigenvectors of +a real, symmetric square matrix. If the matrix is not symmetric, a +``ValueError`` will be raised. The function takes a single argument, and +returns a tuple with the eigenvalues, and eigenvectors. With the help of +the eigenvectors, amongst other things, you can implement sophisticated +stabilisation routines for robots. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2, 1, 4], [2, 5, 3, 5], [1, 3, 6, 1], [4, 5, 1, 7]], dtype=np.uint8) + x, y = np.linalg.eig(a) + print('eigenvectors of a:\n', y) + print('\neigenvalues of a:\n', x) + +.. parsed-literal:: + + eigenvectors of a: + array([[0.8151560042509081, -0.4499411232970823, -0.1644660242574522, 0.3256141906686505], + [0.2211334179893007, 0.7846992598235538, 0.08372081379922657, 0.5730077734355189], + [-0.1340114162071679, -0.3100776411558949, 0.8742786816656, 0.3486109343758527], + [-0.5183258053659028, -0.292663481927148, -0.4489749870391468, 0.6664142156731531]], dtype=float) + + eigenvalues of a: + array([-1.165288365404889, 0.8029365530314914, 5.585625756072663, 13.77672605630074], dtype=float) + + + + +The same matrix diagonalised with ``numpy`` yields: + +.. code:: + + # code to be run in CPython + + a = array([[1, 2, 1, 4], [2, 5, 3, 5], [1, 3, 6, 1], [4, 5, 1, 7]], dtype=np.uint8) + x, y = eig(a) + print('eigenvectors of a:\n', y) + print('\neigenvalues of a:\n', x) + +.. parsed-literal:: + + eigenvectors of a: + [[ 0.32561419 0.815156 0.44994112 -0.16446602] + [ 0.57300777 0.22113342 -0.78469926 0.08372081] + [ 0.34861093 -0.13401142 0.31007764 0.87427868] + [ 0.66641421 -0.51832581 0.29266348 -0.44897499]] + + eigenvalues of a: + [13.77672606 -1.16528837 0.80293655 5.58562576] + + +When comparing results, we should keep two things in mind: + +1. the eigenvalues and eigenvectors are not necessarily sorted in the + same way +2. an eigenvector can be multiplied by an arbitrary non-zero scalar, and + it is still an eigenvector with the same eigenvalue. This is why all + signs of the eigenvector belonging to 5.58, and 0.80 are flipped in + ``ulab`` with respect to ``numpy``. This difference, however, is of + absolutely no consequence. + +Computation expenses +~~~~~~~~~~~~~~~~~~~~ + +Since the function is based on `Givens +rotations <https://en.wikipedia.org/wiki/Givens_rotation>`__ and runs +till convergence is achieved, or till the maximum number of allowed +rotations is exhausted, there is no universal estimate for the time +required to find the eigenvalues. However, an order of magnitude can, at +least, be guessed based on the measurement below: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + @timeit + def matrix_eig(a): + return np.linalg.eig(a) + + a = np.array([[1, 2, 1, 4], [2, 5, 3, 5], [1, 3, 6, 1], [4, 5, 1, 7]], dtype=np.uint8) + + matrix_eig(a) + +.. parsed-literal:: + + execution time: 111 us + + + +inv +--- + +``numpy``: +https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.linalg.inv.html + +A square matrix, provided that it is not singular, can be inverted by +calling the ``inv`` function that takes a single argument. The inversion +is based on successive elimination of elements in the lower left +triangle, and raises a ``ValueError`` exception, if the matrix turns out +to be singular (i.e., one of the diagonal entries is zero). + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + m = np.array([[1, 2, 3, 4], [4, 5, 6, 4], [7, 8.6, 9, 4], [3, 4, 5, 6]]) + + print(np.linalg.inv(m)) + +.. parsed-literal:: + + array([[-2.166666666666667, 1.500000000000001, -0.8333333333333337, 1.0], + [1.666666666666667, -3.333333333333335, 1.666666666666668, -0.0], + [0.1666666666666666, 2.166666666666668, -0.8333333333333337, -1.0], + [-0.1666666666666667, -0.3333333333333333, 0.0, 0.5]], dtype=float64) + + + + +Computation expenses +~~~~~~~~~~~~~~~~~~~~ + +Note that the cost of inverting a matrix is approximately twice as many +floats (RAM), as the number of entries in the original matrix, and +approximately as many operations, as the number of entries. Here are a +couple of numbers: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + @timeit + def invert_matrix(m): + return np.linalg.inv(m) + + m = np.array([[1, 2,], [4, 5]]) + print('2 by 2 matrix:') + invert_matrix(m) + + m = np.array([[1, 2, 3, 4], [4, 5, 6, 4], [7, 8.6, 9, 4], [3, 4, 5, 6]]) + print('\n4 by 4 matrix:') + invert_matrix(m) + + m = np.array([[1, 2, 3, 4, 5, 6, 7, 8], [0, 5, 6, 4, 5, 6, 4, 5], + [0, 0, 9, 7, 8, 9, 7, 8], [0, 0, 0, 10, 11, 12, 11, 12], + [0, 0, 0, 0, 4, 6, 7, 8], [0, 0, 0, 0, 0, 5, 6, 7], + [0, 0, 0, 0, 0, 0, 7, 6], [0, 0, 0, 0, 0, 0, 0, 2]]) + print('\n8 by 8 matrix:') + invert_matrix(m) + +.. parsed-literal:: + + 2 by 2 matrix: + execution time: 65 us + + 4 by 4 matrix: + execution time: 105 us + + 8 by 8 matrix: + execution time: 299 us + + + +The above-mentioned scaling is not obeyed strictly. The reason for the +discrepancy is that the function call is still the same for all three +cases: the input must be inspected, the output array must be created, +and so on. + +norm +---- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html + +The function takes a vector or matrix without options, and returns its +2-norm, i.e., the square root of the sum of the square of the elements. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5]) + b = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) + + print('norm of a:', np.linalg.norm(a)) + print('norm of b:', np.linalg.norm(b)) + +.. parsed-literal:: + + norm of a: 7.416198487095663 + norm of b: 16.88194301613414 + + + + +qr +-- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.linalg.qr.html + +The function computes the QR decomposition of a matrix ``m`` of +dimensions ``(M, N)``, i.e., it returns two such matrices, ``q``\ ’, and +``r``, that ``m = qr``, where ``q`` is orthonormal, and ``r`` is upper +triangular. In addition to the input matrix, which is the first +positional argument, the function accepts the ``mode`` keyword argument +with a default value of ``reduced``. If ``mode`` is ``reduced``, ``q``, +and ``r`` are returned in the reduced representation. Otherwise, the +outputs will have dimensions ``(M, M)``, and ``(M, N)``, respectively. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + A = np.arange(6).reshape((3, 2)) + print('A: \n', A) + + print('complete decomposition') + q, r = np.linalg.qr(A, mode='complete') + print('q: \n', q) + print() + print('r: \n', r) + + print('\n\nreduced decomposition') + q, r = np.linalg.qr(A, mode='reduced') + print('q: \n', q) + print() + print('r: \n', r) + +.. parsed-literal:: + + A: + array([[0, 1], + [2, 3], + [4, 5]], dtype=int16) + complete decomposition + q: + array([[0.0, -0.9128709291752768, 0.408248290463863], + [-0.447213595499958, -0.3651483716701107, -0.8164965809277261], + [-0.8944271909999159, 0.1825741858350553, 0.408248290463863]], dtype=float64) + + r: + array([[-4.47213595499958, -5.813776741499454], + [0.0, -1.095445115010332], + [0.0, 0.0]], dtype=float64) + + + reduced decomposition + q: + array([[0.0, -0.9128709291752768], + [-0.447213595499958, -0.3651483716701107], + [-0.8944271909999159, 0.1825741858350553]], dtype=float64) + + r: + array([[-4.47213595499958, -5.813776741499454], + [0.0, -1.095445115010332]], dtype=float64) + + + diff --git a/circuitpython/extmod/ulab/docs/manual/source/numpy-universal.rst b/circuitpython/extmod/ulab/docs/manual/source/numpy-universal.rst new file mode 100644 index 0000000..b9b7f9f --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/numpy-universal.rst @@ -0,0 +1,487 @@ + +Universal functions +=================== + +Standard mathematical functions can be calculated on any scalar, +scalar-valued iterable (ranges, lists, tuples containing numbers), and +on ``ndarray``\ s without having to change the call signature. In all +cases the functions return a new ``ndarray`` of typecode ``float`` +(since these functions usually generate float values, anyway). The only +exceptions to this rule are the ``exp``, and ``sqrt`` functions, which, +if ``ULAB_SUPPORTS_COMPLEX`` is set to 1 in +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__, +can return complex arrays, depending on the argument. All functions +execute faster with ``ndarray`` arguments than with iterables, because +the values of the input vector can be extracted faster. + +At present, the following functions are supported (starred functions can +operate on, or can return complex arrays): + +``acos``, ``acosh``, ``arctan2``, ``around``, ``asin``, ``asinh``, +``atan``, ``arctan2``, ``atanh``, ``ceil``, ``cos``, ``degrees``, +``exp*``, ``expm1``, ``floor``, ``log``, ``log10``, ``log2``, +``radians``, ``sin``, ``sinh``, ``sqrt*``, ``tan``, ``tanh``. + +These functions are applied element-wise to the arguments, thus, e.g., +the exponential of a matrix cannot be calculated in this way, only the +exponential of the matrix entries. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = range(9) + b = np.array(a) + + # works with ranges, lists, tuples etc. + print('a:\t', a) + print('exp(a):\t', np.exp(a)) + + # with 1D arrays + print('\n=============\nb:\n', b) + print('exp(b):\n', np.exp(b)) + + # as well as with matrices + c = np.array(range(9)).reshape((3, 3)) + print('\n=============\nc:\n', c) + print('exp(c):\n', np.exp(c)) + +.. parsed-literal:: + + a: range(0, 9) + exp(a): array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767, 54.59815003314424, 148.4131591025766, 403.4287934927351, 1096.633158428459, 2980.957987041728], dtype=float64) + + ============= + b: + array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64) + exp(b): + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767, 54.59815003314424, 148.4131591025766, 403.4287934927351, 1096.633158428459, 2980.957987041728], dtype=float64) + + ============= + c: + array([[0.0, 1.0, 2.0], + [3.0, 4.0, 5.0], + [6.0, 7.0, 8.0]], dtype=float64) + exp(c): + array([[1.0, 2.718281828459045, 7.38905609893065], + [20.08553692318767, 54.59815003314424, 148.4131591025766], + [403.4287934927351, 1096.633158428459, 2980.957987041728]], dtype=float64) + + + + +Computation expenses +-------------------- + +The overhead for calculating with micropython iterables is quite +significant: for the 1000 samples below, the difference is more than 800 +microseconds, because internally the function has to create the +``ndarray`` for the output, has to fetch the iterable’s items of unknown +type, and then convert them to floats. All these steps are skipped for +``ndarray``\ s, because these pieces of information are already known. + +Doing the same with ``list`` comprehension requires 30 times more time +than with the ``ndarray``, which would become even more, if we converted +the resulting list to an ``ndarray``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + import math + + a = [0]*1000 + b = np.array(a) + + @timeit + def timed_vector(iterable): + return np.exp(iterable) + + @timeit + def timed_list(iterable): + return [math.exp(i) for i in iterable] + + print('iterating over ndarray in ulab') + timed_vector(b) + + print('\niterating over list in ulab') + timed_vector(a) + + print('\niterating over list in python') + timed_list(a) + +.. parsed-literal:: + + iterating over ndarray in ulab
+ execution time: 441 us
+
+ iterating over list in ulab
+ execution time: 1266 us
+
+ iterating over list in python
+ execution time: 11379 us
+ + + +arctan2 +------- + +``numpy``: +https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.arctan2.html + +The two-argument inverse tangent function is also part of the ``vector`` +sub-module. The function implements broadcasting as discussed in the +section on ``ndarray``\ s. Scalars (``micropython`` integers or floats) +are also allowed. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2.2, 33.33, 444.444]) + print('a:\n', a) + print('\narctan2(a, 1.0)\n', np.arctan2(a, 1.0)) + print('\narctan2(1.0, a)\n', np.arctan2(1.0, a)) + print('\narctan2(a, a): \n', np.arctan2(a, a)) + +.. parsed-literal:: + + a: + array([1.0, 2.2, 33.33, 444.444], dtype=float64) + + arctan2(a, 1.0) + array([0.7853981633974483, 1.14416883366802, 1.5408023243361, 1.568546328341769], dtype=float64) + + arctan2(1.0, a) + array([0.7853981633974483, 0.426627493126876, 0.02999400245879636, 0.002249998453127392], dtype=float64) + + arctan2(a, a): + array([0.7853981633974483, 0.7853981633974483, 0.7853981633974483, 0.7853981633974483], dtype=float64) + + + + +around +------ + +``numpy``: +https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.around.html + +``numpy``\ ’s ``around`` function can also be found in the ``vector`` +sub-module. The function implements the ``decimals`` keyword argument +with default value ``0``. The first argument must be an ``ndarray``. If +this is not the case, the function raises a ``TypeError`` exception. +Note that ``numpy`` accepts general iterables. The ``out`` keyword +argument known from ``numpy`` is not accepted. The function always +returns an ndarray of type ``mp_float_t``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2.2, 33.33, 444.444]) + print('a:\t\t', a) + print('\ndecimals = 0\t', np.around(a, decimals=0)) + print('\ndecimals = 1\t', np.around(a, decimals=1)) + print('\ndecimals = -1\t', np.around(a, decimals=-1)) + +.. parsed-literal:: + + a: array([1.0, 2.2, 33.33, 444.444], dtype=float64) + + decimals = 0 array([1.0, 2.0, 33.0, 444.0], dtype=float64) + + decimals = 1 array([1.0, 2.2, 33.3, 444.4], dtype=float64) + + decimals = -1 array([0.0, 0.0, 30.0, 440.0], dtype=float64) + + + + +exp +--- + +If ``ULAB_SUPPORTS_COMPLEX`` is set to 1 in +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__, +the exponential function can also take complex arrays as its argument, +in which case the return value is also complex. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3]) + print('a:\t\t', a) + print('exp(a):\t\t', np.exp(a)) + print() + + b = np.array([1+1j, 2+2j, 3+3j], dtype=np.complex) + print('b:\t\t', b) + print('exp(b):\t\t', np.exp(b)) + +.. parsed-literal:: + + a: array([1.0, 2.0, 3.0], dtype=float64) + exp(a): array([2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + + b: array([1.0+1.0j, 2.0+2.0j, 3.0+3.0j], dtype=complex) + exp(b): array([1.468693939915885+2.287355287178842j, -3.074932320639359+6.71884969742825j, -19.88453084414699+2.834471132487004j], dtype=complex) + + + + +sqrt +---- + +If ``ULAB_SUPPORTS_COMPLEX`` is set to 1 in +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__, +the exponential function can also take complex arrays as its argument, +in which case the return value is also complex. If the input is real, +but the results might be complex, the user is supposed to specify the +output ``dtype`` in the function call. Otherwise, the square roots of +negative numbers will result in ``NaN``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, -1]) + print('a:\t\t', a) + print('sqrt(a):\t\t', np.sqrt(a)) + print('sqrt(a):\t\t', np.sqrt(a, dtype=np.complex)) + +.. parsed-literal:: + + a: array([1.0, -1.0], dtype=float64) + sqrt(a): array([1.0, nan], dtype=float64) + sqrt(a): array([1.0+0.0j, 0.0+1.0j], dtype=complex) + + + + +Vectorising generic python functions +------------------------------------ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.vectorize.html + +The examples above use factory functions. In fact, they are nothing but +the vectorised versions of the standard mathematical functions. +User-defined ``python`` functions can also be vectorised by help of +``vectorize``. This function takes a positional argument, namely, the +``python`` function that you want to vectorise, and a non-mandatory +keyword argument, ``otypes``, which determines the ``dtype`` of the +output array. The ``otypes`` must be ``None`` (default), or any of the +``dtypes`` defined in ``ulab``. With ``None``, the output is +automatically turned into a float array. + +The return value of ``vectorize`` is a ``micropython`` object that can +be called as a standard function, but which now accepts either a scalar, +an ``ndarray``, or a generic ``micropython`` iterable as its sole +argument. Note that the function that is to be vectorised must have a +single argument. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + def f(x): + return x*x + + vf = np.vectorize(f) + + # calling with a scalar + print('{:20}'.format('f on a scalar: '), vf(44.0)) + + # calling with an ndarray + a = np.array([1, 2, 3, 4]) + print('{:20}'.format('f on an ndarray: '), vf(a)) + + # calling with a list + print('{:20}'.format('f on a list: '), vf([2, 3, 4])) + +.. parsed-literal:: + + f on a scalar: array([1936.0], dtype=float64) + f on an ndarray: array([1.0, 4.0, 9.0, 16.0], dtype=float64) + f on a list: array([4.0, 9.0, 16.0], dtype=float64) + + + + +As mentioned, the ``dtype`` of the resulting ``ndarray`` can be +specified via the ``otypes`` keyword. The value is bound to the function +object that ``vectorize`` returns, therefore, if the same function is to +be vectorised with different output types, then for each type a new +function object must be created. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + l = [1, 2, 3, 4] + def f(x): + return x*x + + vf1 = np.vectorize(f, otypes=np.uint8) + vf2 = np.vectorize(f, otypes=np.float) + + print('{:20}'.format('output is uint8: '), vf1(l)) + print('{:20}'.format('output is float: '), vf2(l)) + +.. parsed-literal:: + + output is uint8: array([1, 4, 9, 16], dtype=uint8) + output is float: array([1.0, 4.0, 9.0, 16.0], dtype=float64) + + + + +The ``otypes`` keyword argument cannot be used for type coercion: if the +function evaluates to a float, but ``otypes`` would dictate an integer +type, an exception will be raised: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + int_list = [1, 2, 3, 4] + float_list = [1.0, 2.0, 3.0, 4.0] + def f(x): + return x*x + + vf = np.vectorize(f, otypes=np.uint8) + + print('{:20}'.format('integer list: '), vf(int_list)) + # this will raise a TypeError exception + print(vf(float_list)) + +.. parsed-literal:: + + integer list: array([1, 4, 9, 16], dtype=uint8) + + Traceback (most recent call last): + File "/dev/shm/micropython.py", line 14, in <module> + TypeError: can't convert float to int + + + +Benchmarks +~~~~~~~~~~ + +It should be pointed out that the ``vectorize`` function produces the +pseudo-vectorised version of the ``python`` function that is fed into +it, i.e., on the C level, the same ``python`` function is called, with +the all-encompassing ``mp_obj_t`` type arguments, and all that happens +is that the ``for`` loop in ``[f(i) for i in iterable]`` runs purely in +C. Since type checking and type conversion in ``f()`` is expensive, the +speed-up is not so spectacular as when iterating over an ``ndarray`` +with a factory function: a gain of approximately 30% can be expected, +when a native ``python`` type (e.g., ``list``) is returned by the +function, and this becomes around 50% (a factor of 2), if conversion to +an ``ndarray`` is also counted. + +The following code snippet calculates the square of a 1000 numbers with +the vectorised function (which returns an ``ndarray``), with ``list`` +comprehension, and with ``list`` comprehension followed by conversion to +an ``ndarray``. For comparison, the execution time is measured also for +the case, when the square is calculated entirely in ``ulab``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + def f(x): + return x*x + + vf = np.vectorize(f) + + @timeit + def timed_vectorised_square(iterable): + return vf(iterable) + + @timeit + def timed_python_square(iterable): + return [f(i) for i in iterable] + + @timeit + def timed_ndarray_square(iterable): + return np.array([f(i) for i in iterable]) + + @timeit + def timed_ulab_square(ndarray): + return ndarray**2 + + print('vectorised function') + squares = timed_vectorised_square(range(1000)) + + print('\nlist comprehension') + squares = timed_python_square(range(1000)) + + print('\nlist comprehension + ndarray conversion') + squares = timed_ndarray_square(range(1000)) + + print('\nsquaring an ndarray entirely in ulab') + a = np.array(range(1000)) + squares = timed_ulab_square(a) + +.. parsed-literal:: + + vectorised function
+ execution time: 7237 us
+
+ list comprehension
+ execution time: 10248 us
+
+ list comprehension + ndarray conversion
+ execution time: 12562 us
+
+ squaring an ndarray entirely in ulab
+ execution time: 560 us
+ + + +From the comparisons above, it is obvious that ``python`` functions +should only be vectorised, when the same effect cannot be gotten in +``ulab`` only. However, although the time savings are not significant, +there is still a good reason for caring about vectorised functions. +Namely, user-defined ``python`` functions become universal, i.e., they +can accept generic iterables as well as ``ndarray``\ s as their +arguments. A vectorised function is still a one-liner, resulting in +transparent and elegant code. + +A final comment on this subject: the ``f(x)`` that we defined is a +*generic* ``python`` function. This means that it is not required that +it just crunches some numbers. It has to return a number object, but it +can still access the hardware in the meantime. So, e.g., + +.. code:: python + + + led = pyb.LED(2) + + def f(x): + if x < 100: + led.toggle() + return x*x + +is perfectly valid code. diff --git a/circuitpython/extmod/ulab/docs/manual/source/scipy-linalg.rst b/circuitpython/extmod/ulab/docs/manual/source/scipy-linalg.rst new file mode 100644 index 0000000..5259682 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/scipy-linalg.rst @@ -0,0 +1,151 @@ + +scipy.linalg +============ + +``scipy``\ ’s ``linalg`` module contains two functions, +``solve_triangular``, and ``cho_solve``. The functions can be called by +prepending them by ``scipy.linalg.``. + +1. `scipy.linalg.solve_cho <#cho_solve>`__ +2. `scipy.linalg.solve_triangular <#solve_triangular>`__ + +cho_solve +--------- + +``scipy``: +https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.cho_solve.html + +Solve the linear equations + +:raw-latex:`\begin{equation} +\mathbf{A}\cdot\mathbf{x} = \mathbf{b} +\end{equation}` + +given the Cholesky factorization of :math:`\mathbf{A}`. As opposed to +``scipy``, the function simply takes the Cholesky-factorised matrix, +:math:`\mathbf{A}`, and :math:`\mathbf{b}` as inputs. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + A = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 2, 1, 8]]) + b = np.array([4, 2, 4, 2]) + + print(spy.linalg.cho_solve(A, b)) + +.. parsed-literal:: + + array([-0.01388888888888906, -0.6458333333333331, 2.677083333333333, -0.01041666666666667], dtype=float64) + + + + +solve_triangular +---------------- + +``scipy``: +https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_triangular.html + +Solve the linear equation + +:raw-latex:`\begin{equation} +\mathbf{a}\cdot\mathbf{x} = \mathbf{b} +\end{equation}` + +with the assumption that :math:`\mathbf{a}` is a triangular matrix. The +two position arguments are :math:`\mathbf{a}`, and :math:`\mathbf{b}`, +and the optional keyword argument is ``lower`` with a default value of +``False``. ``lower`` determines, whether data are taken from the lower, +or upper triangle of :math:`\mathbf{a}`. + +Note that :math:`\mathbf{a}` itself does not have to be a triangular +matrix: if it is not, then the values are simply taken to be 0 in the +upper or lower triangle, as dictated by ``lower``. However, +:math:`\mathbf{a}\cdot\mathbf{x}` will yield :math:`\mathbf{b}` only, +when :math:`\mathbf{a}` is triangular. You should keep this in mind, +when trying to establish the validity of the solution by back +substitution. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + a = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 2, 1, 8]]) + b = np.array([4, 2, 4, 2]) + + print('a:\n') + print(a) + print('\nb: ', b) + + x = spy.linalg.solve_triangular(a, b, lower=True) + + print('='*20) + print('x: ', x) + print('\ndot(a, x): ', np.dot(a, x)) + +.. parsed-literal:: + + a: + + array([[3.0, 0.0, 0.0, 0.0], + [2.0, 1.0, 0.0, 0.0], + [1.0, 0.0, 1.0, 0.0], + [1.0, 2.0, 1.0, 8.0]], dtype=float64) + + b: array([4.0, 2.0, 4.0, 2.0], dtype=float64) + ==================== + x: array([1.333333333333333, -0.6666666666666665, 2.666666666666667, -0.08333333333333337], dtype=float64) + + dot(a, x): array([4.0, 2.0, 4.0, 2.0], dtype=float64) + + + + +With get the same solution, :math:`\mathbf{x}`, with the following +matrix, but the dot product of :math:`\mathbf{a}`, and +:math:`\mathbf{x}` is no longer :math:`\mathbf{b}`: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + a = np.array([[3, 2, 1, 0], [2, 1, 0, 1], [1, 0, 1, 4], [1, 2, 1, 8]]) + b = np.array([4, 2, 4, 2]) + + print('a:\n') + print(a) + print('\nb: ', b) + + x = spy.linalg.solve_triangular(a, b, lower=True) + + print('='*20) + print('x: ', x) + print('\ndot(a, x): ', np.dot(a, x)) + +.. parsed-literal:: + + a: + + array([[3.0, 2.0, 1.0, 0.0], + [2.0, 1.0, 0.0, 1.0], + [1.0, 0.0, 1.0, 4.0], + [1.0, 2.0, 1.0, 8.0]], dtype=float64) + + b: array([4.0, 2.0, 4.0, 2.0], dtype=float64) + ==================== + x: array([1.333333333333333, -0.6666666666666665, 2.666666666666667, -0.08333333333333337], dtype=float64) + + dot(a, x): array([5.333333333333334, 1.916666666666666, 3.666666666666667, 2.0], dtype=float64) + + + diff --git a/circuitpython/extmod/ulab/docs/manual/source/scipy-optimize.rst b/circuitpython/extmod/ulab/docs/manual/source/scipy-optimize.rst new file mode 100644 index 0000000..63d60dd --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/scipy-optimize.rst @@ -0,0 +1,173 @@ + +scipy.optimize +============== + +Functions in the ``optimize`` module can be called by prepending them by +``scipy.optimize.``. The module defines the following three functions: + +1. `scipy.optimize.bisect <#bisect>`__ +2. `scipy.optimize.fmin <#fmin>`__ +3. `scipy.optimize.newton <#newton>`__ + +Note that routines that work with user-defined functions still have to +call the underlying ``python`` code, and therefore, gains in speed are +not as significant as with other vectorised operations. As a rule of +thumb, a factor of two can be expected, when compared to an optimised +``python`` implementation. + +bisect +------ + +``scipy``: +https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.bisect.html + +``bisect`` finds the root of a function of one variable using a simple +bisection routine. It takes three positional arguments, the function +itself, and two starting points. The function must have opposite signs +at the starting points. Returned is the position of the root. + +Two keyword arguments, ``xtol``, and ``maxiter`` can be supplied to +control the accuracy, and the number of bisections, respectively. + +.. code:: + + # code to be run in micropython + + from ulab import scipy as spy + + def f(x): + return x*x - 1 + + print(spy.optimize.bisect(f, 0, 4)) + + print('only 8 bisections: ', spy.optimize.bisect(f, 0, 4, maxiter=8)) + + print('with 0.1 accuracy: ', spy.optimize.bisect(f, 0, 4, xtol=0.1)) + +.. parsed-literal:: + + 0.9999997615814209 + only 8 bisections: 0.984375 + with 0.1 accuracy: 0.9375 + + + + +Performance +~~~~~~~~~~~ + +Since the ``bisect`` routine calls user-defined ``python`` functions, +the speed gain is only about a factor of two, if compared to a purely +``python`` implementation. + +.. code:: + + # code to be run in micropython + + from ulab import scipy as spy + + def f(x): + return (x-1)*(x-1) - 2.0 + + def bisect(f, a, b, xtol=2.4e-7, maxiter=100): + if f(a) * f(b) > 0: + raise ValueError + + rtb = a if f(a) < 0.0 else b + dx = b - a if f(a) < 0.0 else a - b + for i in range(maxiter): + dx *= 0.5 + x_mid = rtb + dx + mid_value = f(x_mid) + if mid_value < 0: + rtb = x_mid + if abs(dx) < xtol: + break + + return rtb + + @timeit + def bisect_scipy(f, a, b): + return spy.optimize.bisect(f, a, b) + + @timeit + def bisect_timed(f, a, b): + return bisect(f, a, b) + + print('bisect running in python') + bisect_timed(f, 3, 2) + + print('bisect running in C') + bisect_scipy(f, 3, 2) + +.. parsed-literal:: + + bisect running in python
+ execution time: 1270 us
+ bisect running in C
+ execution time: 642 us
+ + + +fmin +---- + +``scipy``: +https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin.html + +The ``fmin`` function finds the position of the minimum of a +user-defined function by using the downhill simplex method. Requires two +positional arguments, the function, and the initial value. Three keyword +arguments, ``xatol``, ``fatol``, and ``maxiter`` stipulate conditions +for stopping. + +.. code:: + + # code to be run in micropython + + from ulab import scipy as spy + + def f(x): + return (x-1)**2 - 1 + + print(spy.optimize.fmin(f, 3.0)) + print(spy.optimize.fmin(f, 3.0, xatol=0.1)) + +.. parsed-literal:: + + 0.9996093749999952 + 1.199999999999996 + + + + +newton +------ + +``scipy``:https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.newton.html + +``newton`` finds a zero of a real, user-defined function using the +Newton-Raphson (or secant or Halley’s) method. The routine requires two +positional arguments, the function, and the initial value. Three keyword +arguments can be supplied to control the iteration. These are the +absolute and relative tolerances ``tol``, and ``rtol``, respectively, +and the number of iterations before stopping, ``maxiter``. The function +retuns a single scalar, the position of the root. + +.. code:: + + # code to be run in micropython + + from ulab import scipy as spy + + def f(x): + return x*x*x - 2.0 + + print(spy.optimize.newton(f, 3., tol=0.001, rtol=0.01)) + +.. parsed-literal:: + + 1.260135727246117 + + + diff --git a/circuitpython/extmod/ulab/docs/manual/source/scipy-signal.rst b/circuitpython/extmod/ulab/docs/manual/source/scipy-signal.rst new file mode 100644 index 0000000..b3bcd52 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/scipy-signal.rst @@ -0,0 +1,137 @@ + +scipy.signal +============ + +Functions in the ``signal`` module can be called by prepending them by +``scipy.signal.``. The module defines the following two functions: + +1. `scipy.signal.sosfilt <#sosfilt>`__ +2. `scipy.signal.spectrogram <#spectrogram>`__ + +sosfilt +------- + +``scipy``: +https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.sosfilt.html + +Filter data along one dimension using cascaded second-order sections. + +The function takes two positional arguments, ``sos``, the filter +segments of length 6, and the one-dimensional, uniformly sampled data +set to be filtered. Returns the filtered data, or the filtered data and +the final filter delays, if the ``zi`` keyword arguments is supplied. +The keyword argument must be a float ``ndarray`` of shape +``(n_sections, 2)``. If ``zi`` is not passed to the function, the +initial values are assumed to be 0. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) + sos = [[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]] + y = spy.signal.sosfilt(sos, x) + print('y: ', y) + +.. parsed-literal:: + + y: array([0.0, 1.0, -4.0, 24.0, -104.0, 440.0, -1728.0, 6532.000000000001, -23848.0, 84864.0], dtype=float) + + + + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) + sos = [[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]] + # initial conditions of the filter + zi = np.array([[1, 2], [3, 4]]) + + y, zf = spy.signal.sosfilt(sos, x, zi=zi) + print('y: ', y) + print('\n' + '='*40 + '\nzf: ', zf) + +.. parsed-literal:: + + y: array([4.0, -16.0, 63.00000000000001, -227.0, 802.9999999999999, -2751.0, 9271.000000000001, -30775.0, 101067.0, -328991.0000000001], dtype=float) + + ======================================== + zf: array([[37242.0, 74835.0], + [1026187.0, 1936542.0]], dtype=float) + + + + +spectrogram +----------- + +In addition to the Fourier transform and its inverse, ``ulab`` also +sports a function called ``spectrogram``, which returns the absolute +value of the Fourier transform. This could be used to find the dominant +spectral component in a time series. The arguments are treated in the +same way as in ``fft``, and ``ifft``. This means that, if the firmware +was compiled with complex support, the input can also be a complex +array. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + x = np.linspace(0, 10, num=1024) + y = np.sin(x) + + a = spy.signal.spectrogram(y) + + print('original vector:\t', y) + print('\nspectrum:\t', a) + +.. parsed-literal:: + + original vector: array([0.0, 0.009775015390171337, 0.01954909674625918, ..., -0.5275140569487312, -0.5357931822978732, -0.5440211108893639], dtype=float64) + + spectrum: array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64) + + + + +As such, ``spectrogram`` is really just a shorthand for +``np.sqrt(a*a + b*b)``: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + x = np.linspace(0, 10, num=1024) + y = np.sin(x) + + a, b = np.fft.fft(y) + + print('\nspectrum calculated the hard way:\t', np.sqrt(a*a + b*b)) + + a = spy.signal.spectrogram(y) + + print('\nspectrum calculated the lazy way:\t', a) + +.. parsed-literal:: + + + spectrum calculated the hard way: array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64) + + spectrum calculated the lazy way: array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64) + + + diff --git a/circuitpython/extmod/ulab/docs/manual/source/scipy-special.rst b/circuitpython/extmod/ulab/docs/manual/source/scipy-special.rst new file mode 100644 index 0000000..755a535 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/scipy-special.rst @@ -0,0 +1,44 @@ + +scipy.special +============= + +``scipy``\ ’s ``special`` module defines several functions that behave +as do the standard mathematical functions of the ``numpy``, i.e., they +can be called on any scalar, scalar-valued iterable (ranges, lists, +tuples containing numbers), and on ``ndarray``\ s without having to +change the call signature. In all cases the functions return a new +``ndarray`` of typecode ``float`` (since these functions usually +generate float values, anyway). + +At present, ``ulab``\ ’s ``special`` module contains the following +functions: + +``erf``, ``erfc``, ``gamma``, and ``gammaln``, and they can be called by +prepending them by ``scipy.special.``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + a = range(9) + b = np.array(a) + + print('a: ', a) + print(spy.special.erf(a)) + + print('\nb: ', b) + print(spy.special.erfc(b)) + +.. parsed-literal:: + + a: range(0, 9) + array([0.0, 0.8427007929497149, 0.9953222650189527, 0.9999779095030014, 0.9999999845827421, 1.0, 1.0, 1.0, 1.0], dtype=float64) + + b: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64) + array([1.0, 0.1572992070502851, 0.004677734981047265, 2.209049699858544e-05, 1.541725790028002e-08, 1.537459794428035e-12, 2.151973671249892e-17, 4.183825607779414e-23, 1.122429717298293e-29], dtype=float64) + + + diff --git a/circuitpython/extmod/ulab/docs/manual/source/ulab-intro.rst b/circuitpython/extmod/ulab/docs/manual/source/ulab-intro.rst new file mode 100644 index 0000000..81019e3 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/ulab-intro.rst @@ -0,0 +1,624 @@ + +Introduction +============ + +Enter ulab +---------- + +``ulab`` is a ``numpy``-like module for ``micropython`` and its +derivatives, meant to simplify and speed up common mathematical +operations on arrays. ``ulab`` implements a small subset of ``numpy`` +and ``scipy``. The functions were chosen such that they might be useful +in the context of a microcontroller. However, the project is a living +one, and suggestions for new features are always welcome. + +This document discusses how you can use the library, starting from +building your own firmware, through questions like what affects the +firmware size, what are the trade-offs, and what are the most important +differences to ``numpy`` and ``scipy``, respectively. The document is +organised as follows: + +The chapter after this one helps you with firmware customisation. + +The third chapter gives a very concise summary of the ``ulab`` functions +and array methods. This chapter can be used as a quick reference. + +The chapters after that are an in-depth review of most functions. Here +you can find usage examples, benchmarks, as well as a thorough +discussion of such concepts as broadcasting, and views versus copies. + +The final chapter of this book can be regarded as the programming +manual. The inner working of ``ulab`` is dissected here, and you will +also find hints as to how to implement your own ``numpy``-compatible +functions. + +Purpose +------- + +Of course, the first question that one has to answer is, why on Earth +one would need a fast math library on a microcontroller. After all, it +is not expected that heavy number crunching is going to take place on +bare metal. It is not meant to. On a PC, the main reason for writing +fast code is the sheer amount of data that one wants to process. On a +microcontroller, the data volume is probably small, but it might lead to +catastrophic system failure, if these data are not processed in time, +because the microcontroller is supposed to interact with the outside +world in a timely fashion. In fact, this latter objective was the +initiator of this project: I needed the Fourier transform of a signal +coming from the ADC of the ``pyboard``, and all available options were +simply too slow. + +In addition to speed, another issue that one has to keep in mind when +working with embedded systems is the amount of available RAM: I believe, +everything here could be implemented in pure ``python`` with relatively +little effort (in fact, there are a couple of ``python``-only +implementations of ``numpy`` functions out there), but the price we +would have to pay for that is not only speed, but RAM, too. ``python`` +code, if is not frozen, and compiled into the firmware, has to be +compiled at runtime, which is not exactly a cheap process. On top of +that, if numbers are stored in a list or tuple, which would be the +high-level container, then they occupy 8 bytes, no matter, whether they +are all smaller than 100, or larger than one hundred million. This is +obviously a waste of resources in an environment, where resources are +scarce. + +Finally, there is a reason for using ``micropython`` in the first place. +Namely, that a microcontroller can be programmed in a very elegant, and +*pythonic* way. But if it is so, why should we not extend this idea to +other tasks and concepts that might come up in this context? If there +was no other reason than this *elegance*, I would find that convincing +enough. + +Based on the above-mentioned considerations, all functions in ``ulab`` +are implemented in a way that + +1. conforms to ``numpy`` as much as possible +2. is so frugal with RAM as possible, +3. and yet, fast. Much faster than pure python. Think of speed-ups of + 30-50! + +The main points of ``ulab`` are + +- compact, iterable and slicable containers of numerical data in one to + four dimensions. These containers support all the relevant unary and + binary operators (e.g., ``len``, ==, +, \*, etc.) +- vectorised computations on ``micropython`` iterables and numerical + arrays (in ``numpy``-speak, universal functions) +- computing statistical properties (mean, standard deviation etc.) on + arrays +- basic linear algebra routines (matrix inversion, multiplication, + reshaping, transposition, determinant, and eigenvalues, Cholesky + decomposition and so on) +- polynomial fits to numerical data, and evaluation of polynomials +- fast Fourier transforms +- filtering of data (convolution and second-order filters) +- function minimisation, fitting, and numerical approximation routines +- interfacing between numerical data and peripheral hardware devices + +``ulab`` implements close to a hundred functions and array methods. At +the time of writing this manual (for version 4.0.0), the library adds +approximately 120 kB of extra compiled code to the ``micropython`` +(pyboard.v.1.17) firmware. However, if you are tight with flash space, +you can easily shave tens of kB off the firmware. In fact, if only a +small sub-set of functions are needed, you can get away with less than +10 kB of flash space. See the section on `customising +ulab <#Customising-the-firmware>`__. + +Resources and legal matters +--------------------------- + +The source code of the module can be found under +https://github.com/v923z/micropython-ulab/tree/master/code. while the +source of this user manual is under +https://github.com/v923z/micropython-ulab/tree/master/docs. + +The MIT licence applies to all material. + +Friendly request +---------------- + +If you use ``ulab``, and bump into a bug, or think that a particular +function is missing, or its behaviour does not conform to ``numpy``, +please, raise a `ulab +issue <#https://github.com/v923z/micropython-ulab/issues>`__ on github, +so that the community can profit from your experiences. + +Even better, if you find the project to be useful, and think that it +could be made better, faster, tighter, and shinier, please, consider +contributing, and issue a pull request with the implementation of your +improvements and new features. ``ulab`` can only become successful, if +it offers what the community needs. + +These last comments apply to the documentation, too. If, in your +opinion, the documentation is obscure, misleading, or not detailed +enough, please, let us know, so that *we* can fix it. + +Differences between micropython-ulab and circuitpython-ulab +----------------------------------------------------------- + +``ulab`` has originally been developed for ``micropython``, but has +since been integrated into a number of its flavours. Most of these are +simply forks of ``micropython`` itself, with some additional +functionality. One of the notable exceptions is ``circuitpython``, which +has slightly diverged at the core level, and this has some minor +consequences. Some of these concern the C implementation details only, +which all have been sorted out with the generous and enthusiastic +support of Jeff Epler from `Adafruit +Industries <http://www.adafruit.com>`__. + +There are, however, a couple of instances, where the two environments +differ at the python level in how the class properties can be accessed. +We will point out the differences and possible workarounds at the +relevant places in this document. + +Customising the firmware +======================== + +As mentioned above, ``ulab`` has considerably grown since its +conception, which also means that it might no longer fit on the +microcontroller of your choice. There are, however, a couple of ways of +customising the firmware, and thereby reducing its size. + +All ``ulab`` options are listed in a single header file, +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__, +which contains pre-processor flags for each feature that can be +fine-tuned. The first couple of lines of the file look like this + +.. code:: c + + // The pre-processor constants in this file determine how ulab behaves: + // + // - how many dimensions ulab can handle + // - which functions are included in the compiled firmware + // - whether the python syntax is numpy-like, or modular + // - whether arrays can be sliced and iterated over + // - which binary/unary operators are supported + // + // A considerable amount of flash space can be saved by removing (setting + // the corresponding constants to 0) the unnecessary functions and features. + + // Values defined here can be overridden by your own config file as + // make -DULAB_CONFIG_FILE="my_ulab_config.h" + #if defined(ULAB_CONFIG_FILE) + #include ULAB_CONFIG_FILE + #endif + + // Adds support for complex ndarrays + #ifndef ULAB_SUPPORTS_COMPLEX + #define ULAB_SUPPORTS_COMPLEX (1) + #endif + + // Determines, whether scipy is defined in ulab. The sub-modules and functions + // of scipy have to be defined separately + #define ULAB_HAS_SCIPY (1) + + // The maximum number of dimensions the firmware should be able to support + // Possible values lie between 1, and 4, inclusive + #define ULAB_MAX_DIMS 2 + + // By setting this constant to 1, iteration over array dimensions will be implemented + // as a function (ndarray_rewind_array), instead of writing out the loops in macros + // This reduces firmware size at the expense of speed + #define ULAB_HAS_FUNCTION_ITERATOR (0) + + // If NDARRAY_IS_ITERABLE is 1, the ndarray object defines its own iterator function + // This option saves approx. 250 bytes of flash space + #define NDARRAY_IS_ITERABLE (1) + + // Slicing can be switched off by setting this variable to 0 + #define NDARRAY_IS_SLICEABLE (1) + + // The default threshold for pretty printing. These variables can be overwritten + // at run-time via the set_printoptions() function + #define ULAB_HAS_PRINTOPTIONS (1) + #define NDARRAY_PRINT_THRESHOLD 10 + #define NDARRAY_PRINT_EDGEITEMS 3 + + // determines, whether the dtype is an object, or simply a character + // the object implementation is numpythonic, but requires more space + #define ULAB_HAS_DTYPE_OBJECT (0) + + // the ndarray binary operators + #define NDARRAY_HAS_BINARY_OPS (1) + + // Firmware size can be reduced at the expense of speed by using function + // pointers in iterations. For each operator, he function pointer saves around + // 2 kB in the two-dimensional case, and around 4 kB in the four-dimensional case. + + #define NDARRAY_BINARY_USES_FUN_POINTER (0) + + #define NDARRAY_HAS_BINARY_OP_ADD (1) + #define NDARRAY_HAS_BINARY_OP_EQUAL (1) + #define NDARRAY_HAS_BINARY_OP_LESS (1) + #define NDARRAY_HAS_BINARY_OP_LESS_EQUAL (1) + #define NDARRAY_HAS_BINARY_OP_MORE (1) + #define NDARRAY_HAS_BINARY_OP_MORE_EQUAL (1) + #define NDARRAY_HAS_BINARY_OP_MULTIPLY (1) + #define NDARRAY_HAS_BINARY_OP_NOT_EQUAL (1) + #define NDARRAY_HAS_BINARY_OP_POWER (1) + #define NDARRAY_HAS_BINARY_OP_SUBTRACT (1) + #define NDARRAY_HAS_BINARY_OP_TRUE_DIVIDE (1) + ... + +The meaning of flags with names ``_HAS_`` should be obvious, so we will +just explain the other options. + +To see how much you can gain by un-setting the functions that you do not +need, here are some pointers. In four dimensions, including all +functions adds around 120 kB to the ``micropython`` firmware. On the +other hand, if you are interested in Fourier transforms only, and strip +everything else, you get away with less than 5 kB extra. + +Compatibility with numpy +------------------------ + +The functions implemented in ``ulab`` are organised in four sub-modules +at the C level, namely, ``numpy``, ``scipy``, ``utils``, and ``user``. +This modularity is elevated to ``python``, meaning that in order to use +functions that are part of ``numpy``, you have to import ``numpy`` as + +.. code:: python + + from ulab import numpy as np + + x = np.array([4, 5, 6]) + p = np.array([1, 2, 3]) + np.polyval(p, x) + +There are a couple of exceptions to this rule, namely ``fft``, and +``linalg``, which are sub-modules even in ``numpy``, thus you have to +write them out as + +.. code:: python + + from ulab import numpy as np + + A = np.array([1, 2, 3, 4]).reshape() + np.linalg.trace(A) + +Some of the functions in ``ulab`` are re-implementations of ``scipy`` +functions, and they are to be imported as + +.. code:: python + + from ulab import numpy as np + from ulab import scipy as spy + + + x = np.array([1, 2, 3]) + spy.special.erf(x) + +``numpy``-compatibility has an enormous benefit : namely, by +``try``\ ing to ``import``, we can guarantee that the same, unmodified +code runs in ``CPython``, as in ``micropython``. The following snippet +is platform-independent, thus, the ``python`` code can be tested and +debugged on a computer before loading it onto the microcontroller. + +.. code:: python + + + try: + from ulab import numpy as np + from ulab import scipy as spy + except ImportError: + import numpy as np + import scipy as spy + + x = np.array([1, 2, 3]) + spy.special.erf(x) + +The impact of dimensionality +---------------------------- + +Reducing the number of dimensions +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +``ulab`` supports tensors of rank four, but this is expensive in terms +of flash: with all available functions and options, the library adds +around 100 kB to the firmware. However, if such high dimensions are not +required, significant reductions in size can be gotten by changing the +value of + +.. code:: c + + #define ULAB_MAX_DIMS 2 + +Two dimensions cost a bit more than half of four, while you can get away +with around 20 kB of flash in one dimension, because all those functions +that don’t make sense (e.g., matrix inversion, eigenvalues etc.) are +automatically stripped from the firmware. + +Using the function iterator +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +In higher dimensions, the firmware size increases, because each +dimension (axis) adds another level of nested loops. An example of this +is the macro of the binary operator in three dimensions + +.. code:: c + + #define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR) + type_out *array = (type_out *)results->array; + size_t j = 0; + do { + size_t k = 0; + do { + size_t l = 0; + do { + *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)); + (larray) += (lstrides)[ULAB_MAX_DIMS - 1]; + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1]; + l++; + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]); + (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1]; + (larray) += (lstrides)[ULAB_MAX_DIMS - 2]; + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1]; + (rarray) += (rstrides)[ULAB_MAX_DIMS - 2]; + k++; + } while(k < (results)->shape[ULAB_MAX_DIMS - 2]); + (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + (larray) += (lstrides)[ULAB_MAX_DIMS - 3]; + (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2]; + (rarray) += (rstrides)[ULAB_MAX_DIMS - 3]; + j++; + } while(j < (results)->shape[ULAB_MAX_DIMS - 3]); + +In order to reduce firmware size, it *might* make sense in higher +dimensions to make use of the function iterator by setting the + +.. code:: c + + #define ULAB_HAS_FUNCTION_ITERATOR (1) + +constant to 1. This allows the compiler to call the +``ndarray_rewind_array`` function, so that it doesn’t have to unwrap the +loops for ``k``, and ``j``. Instead of the macro above, we now have + +.. code:: c + + #define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR) + type_out *array = (type_out *)(results)->array; + size_t *lcoords = ndarray_new_coords((results)->ndim); + size_t *rcoords = ndarray_new_coords((results)->ndim); + for(size_t i=0; i < (results)->len/(results)->shape[ULAB_MAX_DIMS -1]; i++) { + size_t l = 0; + do { + *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray)); + (larray) += (lstrides)[ULAB_MAX_DIMS - 1]; + (rarray) += (rstrides)[ULAB_MAX_DIMS - 1]; + l++; + } while(l < (results)->shape[ULAB_MAX_DIMS - 1]); + ndarray_rewind_array((results)->ndim, larray, (results)->shape, lstrides, lcoords); + ndarray_rewind_array((results)->ndim, rarray, (results)->shape, rstrides, rcoords); + } while(0) + +Since the ``ndarray_rewind_array`` function is implemented only once, a +lot of space can be saved. Obviously, function calls cost time, thus +such trade-offs must be evaluated for each application. The gain also +depends on which functions and features you include. Operators and +functions that involve two arrays are expensive, because at the C level, +the number of cases that must be handled scales with the squares of the +number of data types. As an example, the innocent-looking expression + +.. code:: python + + + from ulab import numpy as np + + a = np.array([1, 2, 3]) + b = np.array([4, 5, 6]) + + c = a + b + +requires 25 loops in C, because the ``dtypes`` of both ``a``, and ``b`` +can assume 5 different values, and the addition has to be resolved for +all possible cases. Hint: each binary operator costs between 3 and 4 kB +in two dimensions. + +The ulab version string +----------------------- + +As is customary with ``python`` packages, information on the package +version can be found be querying the ``__version__`` string. + +.. code:: + + # code to be run in micropython + + import ulab + + print('you are running ulab version', ulab.__version__) + +.. parsed-literal:: + + you are running ulab version 2.1.0-2D + + + + +The first three numbers indicate the major, minor, and sub-minor +versions of ``ulab`` (defined by the ``ULAB_VERSION`` constant in +`ulab.c <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.c>`__). +We usually change the minor version, whenever a new function is added to +the code, and the sub-minor version will be incremented, if a bug fix is +implemented. + +``2D`` tells us that the particular firmware supports tensors of rank 2 +(defined by ``ULAB_MAX_DIMS`` in +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__). + +If you find a bug, please, include the version string in your report! + +Should you need the numerical value of ``ULAB_MAX_DIMS``, you can get it +from the version string in the following way: + +.. code:: + + # code to be run in micropython + + import ulab + + version = ulab.__version__ + version_dims = version.split('-')[1] + version_num = int(version_dims.replace('D', '')) + + print('version string: ', version) + print('version dimensions: ', version_dims) + print('numerical value of dimensions: ', version_num) + +.. parsed-literal:: + + version string: 2.1.0-2D + version dimensions: 2D + numerical value of dimensions: 2 + + + + +ulab with complex arrays +~~~~~~~~~~~~~~~~~~~~~~~~ + +If the firmware supports complex arrays, ``-c`` is appended to the +version string as can be seen below. + +.. code:: + + # code to be run in micropython + + import ulab + + version = ulab.__version__ + + print('version string: ', version) + +.. parsed-literal:: + + version string: 4.0.0-2D-c + + + + +Finding out what your firmware supports +--------------------------------------- + +``ulab`` implements a number of array operators and functions, but this +does not mean that all of these functions and methods are actually +compiled into the firmware. You can fine-tune your firmware by +setting/unsetting any of the ``_HAS_`` constants in +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__. + +Functions included in the firmware +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The version string will not tell you everything about your firmware, +because the supported functions and sub-modules can still arbitrarily be +included or excluded. One way of finding out what is compiled into the +firmware is calling ``dir`` with ``ulab`` as its argument. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import scipy as spy + + + print('===== constants, functions, and modules of numpy =====\n\n', dir(np)) + + # since fft and linalg are sub-modules, print them separately + print('\nfunctions included in the fft module:\n', dir(np.fft)) + print('\nfunctions included in the linalg module:\n', dir(np.linalg)) + + print('\n\n===== modules of scipy =====\n\n', dir(spy)) + print('\nfunctions included in the optimize module:\n', dir(spy.optimize)) + print('\nfunctions included in the signal module:\n', dir(spy.signal)) + print('\nfunctions included in the special module:\n', dir(spy.special)) + +.. parsed-literal:: + + ===== constants, functions, and modules of numpy ===== + + ['__class__', '__name__', 'bool', 'sort', 'sum', 'acos', 'acosh', 'arange', 'arctan2', 'argmax', 'argmin', 'argsort', 'around', 'array', 'asin', 'asinh', 'atan', 'atanh', 'ceil', 'clip', 'concatenate', 'convolve', 'cos', 'cosh', 'cross', 'degrees', 'diag', 'diff', 'e', 'equal', 'exp', 'expm1', 'eye', 'fft', 'flip', 'float', 'floor', 'frombuffer', 'full', 'get_printoptions', 'inf', 'int16', 'int8', 'interp', 'linalg', 'linspace', 'log', 'log10', 'log2', 'logspace', 'max', 'maximum', 'mean', 'median', 'min', 'minimum', 'nan', 'ndinfo', 'not_equal', 'ones', 'pi', 'polyfit', 'polyval', 'radians', 'roll', 'set_printoptions', 'sin', 'sinh', 'sqrt', 'std', 'tan', 'tanh', 'trapz', 'uint16', 'uint8', 'vectorize', 'zeros'] + + functions included in the fft module: + ['__class__', '__name__', 'fft', 'ifft'] + + functions included in the linalg module: + ['__class__', '__name__', 'cholesky', 'det', 'dot', 'eig', 'inv', 'norm', 'trace'] + + + ===== modules of scipy ===== + + ['__class__', '__name__', 'optimize', 'signal', 'special'] + + functions included in the optimize module: + ['__class__', '__name__', 'bisect', 'fmin', 'newton'] + + functions included in the signal module: + ['__class__', '__name__', 'sosfilt', 'spectrogram'] + + functions included in the special module: + ['__class__', '__name__', 'erf', 'erfc', 'gamma', 'gammaln'] + + + + +Methods included in the firmware +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The ``dir`` function applied to the module or its sub-modules gives +information on what the module and sub-modules include, but is not +enough to find out which methods the ``ndarray`` class supports. We can +list the methods by calling ``dir`` with the ``array`` object itself: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + print(dir(np.array)) + +.. parsed-literal:: + + ['__class__', '__name__', 'copy', 'sort', '__bases__', '__dict__', 'dtype', 'flatten', 'itemsize', 'reshape', 'shape', 'size', 'strides', 'tobytes', 'transpose'] + + + + +Operators included in the firmware +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A list of operators cannot be generated as shown above. If you really +need to find out, whether, e.g., the ``**`` operator is supported by the +firmware, you have to ``try`` it: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3]) + b = np.array([4, 5, 6]) + + try: + print(a ** b) + except Exception as e: + print('operator is not supported: ', e) + +.. parsed-literal:: + + operator is not supported: unsupported types for __pow__: 'ndarray', 'ndarray' + + + + +The exception above would be raised, if the firmware was compiled with +the + +.. code:: c + + #define NDARRAY_HAS_BINARY_OP_POWER (0) + +definition. diff --git a/circuitpython/extmod/ulab/docs/manual/source/ulab-ndarray.rst b/circuitpython/extmod/ulab/docs/manual/source/ulab-ndarray.rst new file mode 100644 index 0000000..a37cef7 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/ulab-ndarray.rst @@ -0,0 +1,2607 @@ + +ndarray, the base class +======================= + +The ``ndarray`` is the underlying container of numerical data. It can be +thought of as micropython’s own ``array`` object, but has a great number +of extra features starting with how it can be initialised, which +operations can be done on it, and which functions can accept it as an +argument. One important property of an ``ndarray`` is that it is also a +proper ``micropython`` iterable. + +The ``ndarray`` consists of a short header, and a pointer that holds the +data. The pointer always points to a contiguous segment in memory +(``numpy`` is more flexible in this regard), and the header tells the +interpreter, how the data from this segment is to be read out, and what +the bytes mean. Some operations, e.g., ``reshape``, are fast, because +they do not operate on the data, they work on the header, and therefore, +only a couple of bytes are manipulated, even if there are a million data +entries. A more detailed exposition of how operators are implemented can +be found in the section titled `Programming ulab <#Programming_ula>`__. + +Since the ``ndarray`` is a binary container, it is also compact, meaning +that it takes only a couple of bytes of extra RAM in addition to what is +required for storing the numbers themselves. ``ndarray``\ s are also +type-aware, i.e., one can save RAM by specifying a data type, and using +the smallest reasonable one. Five such types are defined, namely +``uint8``, ``int8``, which occupy a single byte of memory per datum, +``uint16``, and ``int16``, which occupy two bytes per datum, and +``float``, which occupies four or eight bytes per datum. The +precision/size of the ``float`` type depends on the definition of +``mp_float_t``. Some platforms, e.g., the PYBD, implement ``double``\ s, +but some, e.g., the pyboard.v.11, do not. You can find out, what type of +float your particular platform implements by looking at the output of +the `.itemsize <#.itemsize>`__ class property, or looking at the exact +``dtype``, when you print out an array. + +In addition to the five above-mentioned numerical types, it is also +possible to define Boolean arrays, which can be used in the indexing of +data. However, Boolean arrays are really nothing but arrays of type +``uint8`` with an extra flag. + +On the following pages, we will see how one can work with +``ndarray``\ s. Those familiar with ``numpy`` should find that the +nomenclature and naming conventions of ``numpy`` are adhered to as +closely as possible. We will point out the few differences, where +necessary. + +For the sake of comparison, in addition to the ``ulab`` code snippets, +sometimes the equivalent ``numpy`` code is also presented. You can find +out, where the snippet is supposed to run by looking at its first line, +the header of the code block. + +The ndinfo function +------------------- + +A concise summary of a couple of the properties of an ``ndarray`` can be +printed out by calling the ``ndinfo`` function. In addition to finding +out what the *shape* and *strides* of the array array, we also get the +``itemsize``, as well as the type. An interesting piece of information +is the *data pointer*, which tells us, what the address of the data +segment of the ``ndarray`` is. We will see the significance of this in +the section `Slicing and indexing <#Slicing-and-indexing>`__. + +Note that this function simply prints some information, but does not +return anything. If you need to get a handle of the data contained in +the printout, you should call the dedicated ``shape``, ``strides``, or +``itemsize`` functions directly. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(5), dtype=np.float) + b = np.array(range(25), dtype=np.uint8).reshape((5, 5)) + np.ndinfo(a) + print('\n') + np.ndinfo(b) + +.. parsed-literal:: + + class: ndarray + shape: (5,) + strides: (8,) + itemsize: 8 + data pointer: 0x7f8f6fa2e240 + type: float + + + class: ndarray + shape: (5, 5) + strides: (5, 1) + itemsize: 1 + data pointer: 0x7f8f6fa2e2e0 + type: uint8 + + + + +Initialising an array +--------------------- + +A new array can be created by passing either a standard micropython +iterable, or another ``ndarray`` into the constructor. + +Initialising by passing iterables +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +If the iterable is one-dimensional, i.e., one whose elements are +numbers, then a row vector will be created and returned. If the iterable +is two-dimensional, i.e., one whose elements are again iterables, a +matrix will be created. If the lengths of the iterables are not +consistent, a ``ValueError`` will be raised. Iterables of different +types can be mixed in the initialisation function. + +If the ``dtype`` keyword with the possible +``uint8/int8/uint16/int16/float`` values is supplied, the new +``ndarray`` will have that type, otherwise, it assumes ``float`` as +default. In addition, if ``ULAB_SUPPORTS_COMPLEX`` is set to 1 in +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__, +the ``dtype`` can also take on the value of ``complex``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = [1, 2, 3, 4, 5, 6, 7, 8] + b = np.array(a) + + print("a:\t", a) + print("b:\t", b) + + # a two-dimensional array with mixed-type initialisers + c = np.array([range(5), range(20, 25, 1), [44, 55, 66, 77, 88]], dtype=np.uint8) + print("\nc:\t", c) + + # and now we throw an exception + d = np.array([range(5), range(10), [44, 55, 66, 77, 88]], dtype=np.uint8) + print("\nd:\t", d) + +.. parsed-literal:: + + a: [1, 2, 3, 4, 5, 6, 7, 8] + b: array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64) + + c: array([[0, 1, 2, 3, 4], + [20, 21, 22, 23, 24], + [44, 55, 66, 77, 88]], dtype=uint8) + + Traceback (most recent call last): + File "/dev/shm/micropython.py", line 15, in <module> + ValueError: iterables are not of the same length + + + +Initialising by passing arrays +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +An ``ndarray`` can be initialised by supplying another array. This +statement is almost trivial, since ``ndarray``\ s are iterables +themselves, though it should be pointed out that initialising through +arrays is a bit faster. This statement is especially true, if the +``dtype``\ s of the source and output arrays are the same, because then +the contents can simply be copied without further ado. While type +conversion is also possible, it will always be slower than straight +copying. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = [1, 2, 3, 4, 5, 6, 7, 8] + b = np.array(a) + c = np.array(b) + d = np.array(b, dtype=np.uint8) + + print("a:\t", a) + print("\nb:\t", b) + print("\nc:\t", c) + print("\nd:\t", d) + +.. parsed-literal:: + + a: [1, 2, 3, 4, 5, 6, 7, 8] + + b: array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64) + + c: array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64) + + d: array([1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8) + + + + +Note that the default type of the ``ndarray`` is ``float``. Hence, if +the array is initialised from another array, type conversion will always +take place, except, when the output type is specifically supplied. I.e., + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(5), dtype=np.uint8) + b = np.array(a) + print("a:\t", a) + print("\nb:\t", b) + +.. parsed-literal:: + + a: array([0, 1, 2, 3, 4], dtype=uint8) + + b: array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) + + + + +will iterate over the elements in ``a``, since in the assignment +``b = np.array(a)``, no output type was given, therefore, ``float`` was +assumed. On the other hand, + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(5), dtype=np.uint8) + b = np.array(a, dtype=np.uint8) + print("a:\t", a) + print("\nb:\t", b) + +.. parsed-literal:: + + a: array([0, 1, 2, 3, 4], dtype=uint8) + + b: array([0, 1, 2, 3, 4], dtype=uint8) + + + + +will simply copy the content of ``a`` into ``b`` without any iteration, +and will, therefore, be faster. Keep this in mind, whenever the output +type, or performance is important. + +Array initialisation functions +------------------------------ + +There are nine functions that can be used for initialising an array. +Starred functions accept ``complex`` as the value of the ``dtype``, if +the firmware was compiled with complex support. + +1. `numpy.arange <#arange>`__ +2. `numpy.concatenate <#concatenate>`__ +3. `numpy.diag\* <#diag>`__ +4. `numpy.empty\* <#empty>`__ +5. `numpy.eye\* <#eye>`__ +6. `numpy.frombuffer <#frombuffer>`__ +7. `numpy.full\* <#full>`__ +8. `numpy.linspace\* <#linspace>`__ +9. `numpy.logspace <#logspace>`__ +10. `numpy.ones\* <#ones>`__ +11. `numpy.zeros\* <#zeros>`__ + +arange +~~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.arange.html + +The function returns a one-dimensional array with evenly spaced values. +Takes 3 positional arguments (two are optional), and the ``dtype`` +keyword argument. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + print(np.arange(10)) + print(np.arange(2, 10)) + print(np.arange(2, 10, 3)) + print(np.arange(2, 10, 3, dtype=np.float)) + +.. parsed-literal:: + + array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int16) + array([2, 3, 4, 5, 6, 7, 8, 9], dtype=int16) + array([2, 5, 8], dtype=int16) + array([2.0, 5.0, 8.0], dtype=float64) + + + + +concatenate +~~~~~~~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.concatenate.html + +The function joins a sequence of arrays, if they are compatible in +shape, i.e., if all shapes except the one along the joining axis are +equal. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(25), dtype=np.uint8).reshape((5, 5)) + b = np.array(range(15), dtype=np.uint8).reshape((3, 5)) + + c = np.concatenate((a, b), axis=0) + print(c) + +.. parsed-literal:: + + array([[0, 1, 2, 3, 4], + [5, 6, 7, 8, 9], + [10, 11, 12, 13, 14], + [15, 16, 17, 18, 19], + [20, 21, 22, 23, 24], + [0, 1, 2, 3, 4], + [5, 6, 7, 8, 9], + [10, 11, 12, 13, 14]], dtype=uint8) + + + + +**WARNING**: ``numpy`` accepts arbitrary ``dtype``\ s in the sequence of +arrays, in ``ulab`` the ``dtype``\ s must be identical. If you want to +concatenate different types, you have to convert all arrays to the same +type first. Here ``b`` is of ``float`` type, so it cannot directly be +concatenated to ``a``. However, if we cast the ``dtype`` of ``b``, the +concatenation works: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(25), dtype=np.uint8).reshape((5, 5)) + b = np.array(range(15), dtype=np.float).reshape((5, 3)) + d = np.array(b+1, dtype=np.uint8) + print('a: ', a) + print('='*20 + '\nd: ', d) + c = np.concatenate((d, a), axis=1) + print('='*20 + '\nc: ', c) + +.. parsed-literal:: + + a: array([[0, 1, 2, 3, 4], + [5, 6, 7, 8, 9], + [10, 11, 12, 13, 14], + [15, 16, 17, 18, 19], + [20, 21, 22, 23, 24]], dtype=uint8) + ==================== + d: array([[1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12], + [13, 14, 15]], dtype=uint8) + ==================== + c: array([[1, 2, 3, 0, 1, 2, 3, 4], + [4, 5, 6, 5, 6, 7, 8, 9], + [7, 8, 9, 10, 11, 12, 13, 14], + [10, 11, 12, 15, 16, 17, 18, 19], + [13, 14, 15, 20, 21, 22, 23, 24]], dtype=uint8) + + + + +diag +---- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.diag.html + +Extract a diagonal, or construct a diagonal array. + +The function takes two arguments, an ``ndarray``, and a shift. If the +first argument is a two-dimensional array, the function returns a +one-dimensional array containing the diagonal entries. The diagonal can +be shifted by an amount given in the second argument. + +If the first argument is a one-dimensional array, the function returns a +two-dimensional tensor with its diagonal elements given by the first +argument. + +The ``diag`` function can accept a complex array, if the firmware was +compiled with complex support. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4]) + print(np.diag(a)) + +.. parsed-literal:: + + array([[1.0, 0.0, 0.0, 0.0], + [0.0, 2.0, 0.0, 0.0], + [0.0, 0.0, 3.0, 0.0], + [0.0, 0.0, 0.0, 4.0]], dtype=float64) + + + + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(16)).reshape((4, 4)) + print('a: ', a) + print() + print('diagonal of a: ', np.diag(a)) + +.. parsed-literal:: + + a: array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0], + [12.0, 13.0, 14.0, 15.0]], dtype=float64) + + diagonal of a: array([0.0, 5.0, 10.0, 15.0], dtype=float64) + + + + +empty +----- + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.empty.html + +``empty`` is simply an alias for ``zeros``, i.e., as opposed to +``numpy``, the entries of the tensor will be initialised to zero. + +The ``empty`` function can accept complex as the value of the dtype, if +the firmware was compiled with complex support. + +eye +~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.eye.html + +Another special array method is the ``eye`` function, whose call +signature is + +.. code:: python + + eye(N, M, k=0, dtype=float) + +where ``N`` (``M``) specify the dimensions of the matrix (if only ``N`` +is supplied, then we get a square matrix, otherwise one with ``M`` rows, +and ``N`` columns), and ``k`` is the shift of the ones (the main +diagonal corresponds to ``k=0``). Here are a couple of examples. + +The ``eye`` function can accept ``complex`` as the value of the +``dtype``, if the firmware was compiled with complex support. + +With a single argument +^^^^^^^^^^^^^^^^^^^^^^ + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + print(np.eye(5)) + +.. parsed-literal:: + + array([[1.0, 0.0, 0.0, 0.0, 0.0], + [0.0, 1.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 1.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 1.0, 0.0], + [0.0, 0.0, 0.0, 0.0, 1.0]], dtype=float64) + + + + +Specifying the dimensions of the matrix +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + print(np.eye(4, M=6, k=-1, dtype=np.int16)) + +.. parsed-literal:: + + array([[0, 0, 0, 0, 0, 0], + [1, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0], + [0, 0, 1, 0, 0, 0]], dtype=int16) + + + + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + print(np.eye(4, M=6, dtype=np.int8)) + +.. parsed-literal:: + + array([[1, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0], + [0, 0, 1, 0, 0, 0], + [0, 0, 0, 1, 0, 0]], dtype=int8) + + + + +frombuffer +~~~~~~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.frombuffer.html + +The function interprets a contiguous buffer as a one-dimensional array, +and thus can be used for piping buffered data directly into an array. +This method of analysing, e.g., ADC data is much more efficient than +passing the ADC buffer into the ``array`` constructor, because +``frombuffer`` simply creates the ``ndarray`` header and blindly copies +the memory segment, without inspecting the underlying data. + +The function takes a single positional argument, the buffer, and three +keyword arguments. These are the ``dtype`` with a default value of +``float``, the ``offset``, with a default of 0, and the ``count``, with +a default of -1, meaning that all data are taken in. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + buffer = b'\x01\x02\x03\x04\x05\x06\x07\x08' + print('buffer: ', buffer) + + a = np.frombuffer(buffer, dtype=np.uint8) + print('a, all data read: ', a) + + b = np.frombuffer(buffer, dtype=np.uint8, offset=2) + print('b, all data with an offset: ', b) + + c = np.frombuffer(buffer, dtype=np.uint8, offset=2, count=3) + print('c, only 3 items with an offset: ', c) + +.. parsed-literal:: + + buffer: b'\x01\x02\x03\x04\x05\x06\x07\x08' + a, all data read: array([1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8) + b, all data with an offset: array([3, 4, 5, 6, 7, 8], dtype=uint8) + c, only 3 items with an offset: array([3, 4, 5], dtype=uint8) + + + + +full +~~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.full.html + +The function returns an array of arbitrary dimension, whose elements are +all equal to the second positional argument. The first argument is a +tuple describing the shape of the tensor. The ``dtype`` keyword argument +with a default value of ``float`` can also be supplied. + +The ``full`` function can accept a complex scalar, or ``complex`` as the +value of ``dtype``, if the firmware was compiled with complex support. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + # create an array with the default type + print(np.full((2, 4), 3)) + + print('\n' + '='*20 + '\n') + # the array type is uint8 now + print(np.full((2, 4), 3, dtype=np.uint8)) + +.. parsed-literal:: + + array([[3.0, 3.0, 3.0, 3.0], + [3.0, 3.0, 3.0, 3.0]], dtype=float64) + + ==================== + + array([[3, 3, 3, 3], + [3, 3, 3, 3]], dtype=uint8) + + + + +linspace +~~~~~~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html + +This function returns an array, whose elements are uniformly spaced +between the ``start``, and ``stop`` points. The number of intervals is +determined by the ``num`` keyword argument, whose default value is 50. +With the ``endpoint`` keyword argument (defaults to ``True``) one can +include ``stop`` in the sequence. In addition, the ``dtype`` keyword can +be supplied to force type conversion of the output. The default is +``float``. Note that, when ``dtype`` is of integer type, the sequence is +not necessarily evenly spaced. This is not an error, rather a +consequence of rounding. (This is also the ``numpy`` behaviour.) + +The ``linspace`` function can accept ``complex`` as the value of the +``dtype``, if the firmware was compiled with complex support. The output +``dtype`` is automatically complex, if either of the endpoints is a +complex scalar. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + # generate a sequence with defaults + print('default sequence:\t', np.linspace(0, 10)) + + # num=5 + print('num=5:\t\t\t', np.linspace(0, 10, num=5)) + + # num=5, endpoint=False + print('num=5:\t\t\t', np.linspace(0, 10, num=5, endpoint=False)) + + # num=5, endpoint=False, dtype=uint8 + print('num=5:\t\t\t', np.linspace(0, 5, num=7, endpoint=False, dtype=np.uint8)) + +.. parsed-literal:: + + default sequence: array([0.0, 0.2040816326530612, 0.4081632653061225, ..., 9.591836734693871, 9.795918367346932, 9.999999999999993], dtype=float64) + num=5: array([0.0, 2.5, 5.0, 7.5, 10.0], dtype=float64) + num=5: array([0.0, 2.0, 4.0, 6.0, 8.0], dtype=float64) + num=5: array([0, 0, 1, 2, 2, 3, 4], dtype=uint8) + + + + +logspace +~~~~~~~~ + +``linspace``\ ’ equivalent for logarithmically spaced data is +``logspace``. This function produces a sequence of numbers, in which the +quotient of consecutive numbers is constant. This is a geometric +sequence. + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.logspace.html + +This function returns an array, whose elements are uniformly spaced +between the ``start``, and ``stop`` points. The number of intervals is +determined by the ``num`` keyword argument, whose default value is 50. +With the ``endpoint`` keyword argument (defaults to ``True``) one can +include ``stop`` in the sequence. In addition, the ``dtype`` keyword can +be supplied to force type conversion of the output. The default is +``float``. Note that, exactly as in ``linspace``, when ``dtype`` is of +integer type, the sequence is not necessarily evenly spaced in log +space. + +In addition to the keyword arguments found in ``linspace``, ``logspace`` +also accepts the ``base`` argument. The default value is 10. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + # generate a sequence with defaults + print('default sequence:\t', np.logspace(0, 3)) + + # num=5 + print('num=5:\t\t\t', np.logspace(1, 10, num=5)) + + # num=5, endpoint=False + print('num=5:\t\t\t', np.logspace(1, 10, num=5, endpoint=False)) + + # num=5, endpoint=False + print('num=5:\t\t\t', np.logspace(1, 10, num=5, endpoint=False, base=2)) + +.. parsed-literal:: + + default sequence: array([1.0, 1.151395399326447, 1.325711365590109, ..., 754.3120063354646, 868.5113737513561, 1000.000000000004], dtype=float64) + num=5: array([10.0, 1778.279410038923, 316227.766016838, 56234132.5190349, 10000000000.0], dtype=float64) + num=5: array([10.0, 630.9573444801933, 39810.71705534974, 2511886.431509581, 158489319.2461114], dtype=float64) + num=5: array([2.0, 6.964404506368993, 24.25146506416637, 84.44850628946524, 294.066778879241], dtype=float64) + + + + +ones, zeros +~~~~~~~~~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.ones.html + +A couple of special arrays and matrices can easily be initialised by +calling one of the ``ones``, or ``zeros`` functions. ``ones`` and +``zeros`` follow the same pattern, and have the call signature + +.. code:: python + + ones(shape, dtype=float) + zeros(shape, dtype=float) + +where shape is either an integer, or a tuple specifying the shape. + +The ``ones/zeros`` functions can accept complex as the value of the +dtype, if the firmware was compiled with complex support. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + print(np.ones(6, dtype=np.uint8)) + + print(np.zeros((6, 4))) + +.. parsed-literal:: + + array([1, 1, 1, 1, 1, 1], dtype=uint8) + array([[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) + + + + +When specifying the shape, make sure that the length of the tuple is not +larger than the maximum dimension of your firmware. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + import ulab + + print('maximum number of dimensions: ', ulab.__version__) + + print(np.zeros((2, 2, 2))) + +.. parsed-literal:: + + maximum number of dimensions: 2.1.0-2D + + Traceback (most recent call last): + File "/dev/shm/micropython.py", line 7, in <module> + TypeError: too many dimensions + + + +Customising array printouts +--------------------------- + +``ndarray``\ s are pretty-printed, i.e., if the number of entries along +the last axis is larger than 10 (default value), then only the first and +last three entries will be printed. Also note that, as opposed to +``numpy``, the printout always contains the ``dtype``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(200)) + print("a:\t", a) + +.. parsed-literal:: + + a: array([0.0, 1.0, 2.0, ..., 197.0, 198.0, 199.0], dtype=float64) + + + + +set_printoptions +~~~~~~~~~~~~~~~~ + +The default values can be overwritten by means of the +``set_printoptions`` function +`numpy.set_printoptions <https://numpy.org/doc/1.18/reference/generated/numpy.set_printoptions.html>`__, +which accepts two keywords arguments, the ``threshold``, and the +``edgeitems``. The first of these arguments determines the length of the +longest array that will be printed in full, while the second is the +number of items that will be printed on the left and right hand side of +the ellipsis, if the array is longer than ``threshold``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(20)) + print("a printed with defaults:\t", a) + + np.set_printoptions(threshold=200) + print("\na printed in full:\t\t", a) + + np.set_printoptions(threshold=10, edgeitems=2) + print("\na truncated with 2 edgeitems:\t", a) + +.. parsed-literal:: + + a printed with defaults: array([0.0, 1.0, 2.0, ..., 17.0, 18.0, 19.0], dtype=float64) + + a printed in full: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0], dtype=float64) + + a truncated with 2 edgeitems: array([0.0, 1.0, ..., 18.0, 19.0], dtype=float64) + + + + +get_printoptions +~~~~~~~~~~~~~~~~ + +The set value of the ``threshold`` and ``edgeitems`` can be retrieved by +calling the ``get_printoptions`` function with no arguments. The +function returns a *dictionary* with two keys. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + np.set_printoptions(threshold=100, edgeitems=20) + print(np.get_printoptions()) + +.. parsed-literal:: + + {'threshold': 100, 'edgeitems': 20} + + + + +Methods and properties of ndarrays +---------------------------------- + +Arrays have several *properties* that can queried, and some methods that +can be called. With the exception of the flatten and transpose +operators, properties return an object that describe some feature of the +array, while the methods return a new array-like object. The ``imag``, +and ``real`` properties are included in the firmware only, when it was +compiled with complex support. + +1. `.byteswap <#.byteswap>`__ +2. `.copy <#.copy>`__ +3. `.dtype <#.dtype>`__ +4. `.flat <#.flat>`__ +5. `.flatten <#.flatten>`__ +6. `.imag\* <#.imag>`__ +7. `.itemsize <#.itemsize>`__ +8. `.real\* <#.real>`__ +9. `.reshape <#.reshape>`__ +10. `.shape <#.shape>`__ +11. `.size <#.size>`__ +12. `.T <#.transpose>`__ +13. `.tobytes <#.tobytes>`__ +14. `.tolist <#.tolist>`__ +15. `.transpose <#.transpose>`__ +16. `.sort <#.sort>`__ + +.byteswap +~~~~~~~~~ + +``numpy`` +https://numpy.org/doc/stable/reference/generated/numpy.char.chararray.byteswap.html + +The method takes a single keyword argument, ``inplace``, with values +``True`` or ``False``, and swaps the bytes in the array. If +``inplace = False``, a new ``ndarray`` is returned, otherwise the +original values are overwritten. + +The ``frombuffer`` function is a convenient way of receiving data from +peripheral devices that work with buffers. However, it is not guaranteed +that the byte order (in other words, the *endianness*) of the peripheral +device matches that of the microcontroller. The ``.byteswap`` method +makes it possible to change the endianness of the incoming data stream. + +Obviously, byteswapping makes sense only for those cases, when a datum +occupies more than one byte, i.e., for the ``uint16``, ``int16``, and +``float`` ``dtype``\ s. When ``dtype`` is either ``uint8``, or ``int8``, +the method simply returns a view or copy of self, depending upon the +value of ``inplace``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + buffer = b'\x01\x02\x03\x04\x05\x06\x07\x08' + print('buffer: ', buffer) + + a = np.frombuffer(buffer, dtype=np.uint16) + print('a: ', a) + b = a.byteswap() + print('b: ', b) + +.. parsed-literal:: + + buffer: b'\x01\x02\x03\x04\x05\x06\x07\x08' + a: array([513, 1027, 1541, 2055], dtype=uint16) + b: array([258, 772, 1286, 1800], dtype=uint16) + + + + +.copy +~~~~~ + +The ``.copy`` method creates a new *deep copy* of an array, i.e., the +entries of the source array are *copied* into the target array. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4], dtype=np.int8) + b = a.copy() + print('a: ', a) + print('='*20) + print('b: ', b) + +.. parsed-literal:: + + a: array([1, 2, 3, 4], dtype=int8) + ==================== + b: array([1, 2, 3, 4], dtype=int8) + + + + +.dtype +~~~~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.dtype.htm + +The ``.dtype`` property is the ``dtype`` of an array. This can then be +used for initialising another array with the matching type. ``ulab`` +implements two versions of ``dtype``; one that is ``numpy``-like, i.e., +one, which returns a ``dtype`` object, and one that is significantly +cheaper in terms of flash space, but does not define a ``dtype`` object, +and holds a single character (number) instead. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4], dtype=np.int8) + b = np.array([5, 6, 7], dtype=a.dtype) + print('a: ', a) + print('dtype of a: ', a.dtype) + print('\nb: ', b) + +.. parsed-literal:: + + a: array([1, 2, 3, 4], dtype=int8) + dtype of a: dtype('int8') + + b: array([5, 6, 7], dtype=int8) + + + + +If the ``ulab.h`` header file sets the pre-processor constant +``ULAB_HAS_DTYPE_OBJECT`` to 0 as + +.. code:: c + + #define ULAB_HAS_DTYPE_OBJECT (0) + +then the output of the previous snippet will be + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4], dtype=np.int8) + b = np.array([5, 6, 7], dtype=a.dtype) + print('a: ', a) + print('dtype of a: ', a.dtype) + print('\nb: ', b) + +.. parsed-literal:: + + a: array([1, 2, 3, 4], dtype=int8) + dtype of a: 98 + + b: array([5, 6, 7], dtype=int8) + + + + +Here 98 is nothing but the ASCII value of the character ``b``, which is +the type code for signed 8-bit integers. The object definition adds +around 600 bytes to the firmware. + +.flat +~~~~~ + +numpy: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flat.htm + +``.flat`` returns the array’s flat iterator. For one-dimensional objects +the flat iterator is equivalent to the standart iterator, while for +higher dimensional tensors, it amounts to first flattening the array, +and then iterating over it. Note, however, that the flat iterator does +not consume RAM beyond what is required for holding the position of the +iterator itself, while flattening produces a new copy. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4], dtype=np.int8) + for _a in a: + print(_a) + + a = np.array([[1, 2, 3, 4], [5, 6, 7, 8]], dtype=np.int8) + print('a:\n', a) + + for _a in a: + print(_a) + + for _a in a.flat: + print(_a) + +.. parsed-literal:: + + 1 + 2 + 3 + 4 + a: + array([[1, 2, 3, 4], + [5, 6, 7, 8]], dtype=int8) + array([1, 2, 3, 4], dtype=int8) + array([5, 6, 7, 8], dtype=int8) + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + + + + +.flatten +~~~~~~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flatten.htm + +``.flatten`` returns the flattened array. The array can be flattened in +``C`` style (i.e., moving along the last axis in the tensor), or in +``fortran`` style (i.e., moving along the first axis in the tensor). + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4], dtype=np.int8) + print("a: \t\t", a) + print("a flattened: \t", a.flatten()) + + b = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int8) + print("\nb:", b) + + print("b flattened (C): \t", b.flatten()) + print("b flattened (F): \t", b.flatten(order='F')) + +.. parsed-literal:: + + a: array([1, 2, 3, 4], dtype=int8) + a flattened: array([1, 2, 3, 4], dtype=int8) + + b: array([[1, 2, 3], + [4, 5, 6]], dtype=int8) + b flattened (C): array([1, 2, 3, 4, 5, 6], dtype=int8) + b flattened (F): array([1, 4, 2, 5, 3, 6], dtype=int8) + + + + +.imag +~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.ndarray.imag.html + +The ``.imag`` property is defined only, if the firmware was compiled +with complex support, and returns a copy with the imaginary part of an +array. If the array is real, then the output is straight zeros with the +``dtype`` of the input. If the input is complex, the output ``dtype`` is +always ``float``, irrespective of the values. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3], dtype=np.uint16) + print("a:\t", a) + print("a.imag:\t", a.imag) + + b = np.array([1, 2+1j, 3-1j], dtype=np.complex) + print("\nb:\t", b) + print("b.imag:\t", b.imag) + +.. parsed-literal:: + + a: array([1, 2, 3], dtype=uint16) + a.imag: array([0, 0, 0], dtype=uint16) + + b: array([1.0+0.0j, 2.0+1.0j, 3.0-1.0j], dtype=complex) + b.imag: array([0.0, 1.0, -1.0], dtype=float64) + + + + +.itemsize +~~~~~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.ndarray.itemsize.html + +The ``.itemsize`` property is an integer with the size of elements in +the array. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3], dtype=np.int8) + print("a:\n", a) + print("itemsize of a:", a.itemsize) + + b= np.array([[1, 2], [3, 4]], dtype=np.float) + print("\nb:\n", b) + print("itemsize of b:", b.itemsize) + +.. parsed-literal:: + + a: + array([1, 2, 3], dtype=int8) + itemsize of a: 1 + + b: + array([[1.0, 2.0], + [3.0, 4.0]], dtype=float64) + itemsize of b: 8 + + + + +.real +~~~~~ + +numpy: +https://numpy.org/doc/stable/reference/generated/numpy.ndarray.real.html + +The ``.real`` property is defined only, if the firmware was compiled +with complex support, and returns a copy with the real part of an array. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3], dtype=np.uint16) + print("a:\t", a) + print("a.real:\t", a.real) + + b = np.array([1, 2+1j, 3-1j], dtype=np.complex) + print("\nb:\t", b) + print("b.real:\t", b.real) + +.. parsed-literal:: + + a: array([1, 2, 3], dtype=uint16) + a.real: array([1, 2, 3], dtype=uint16) + + b: array([1.0+0.0j, 2.0+1.0j, 3.0-1.0j], dtype=complex) + b.real: array([1.0, 2.0, 3.0], dtype=float64) + + + + +.reshape +~~~~~~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.reshape.html + +``reshape`` re-writes the shape properties of an ``ndarray``, but the +array will not be modified in any other way. The function takes a single +2-tuple with two integers as its argument. The 2-tuple should specify +the desired number of rows and columns. If the new shape is not +consistent with the old, a ``ValueError`` exception will be raised. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]], dtype=np.uint8) + print('a (4 by 4):', a) + print('a (2 by 8):', a.reshape((2, 8))) + print('a (1 by 16):', a.reshape((1, 16))) + +.. parsed-literal:: + + a (4 by 4): array([[1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12], + [13, 14, 15, 16]], dtype=uint8) + a (2 by 8): array([[1, 2, 3, 4, 5, 6, 7, 8], + [9, 10, 11, 12, 13, 14, 15, 16]], dtype=uint8) + a (1 by 16): array([[1, 2, 3, ..., 14, 15, 16]], dtype=uint8) + + + + +.. code:: + + # code to be run in CPython + + Note that `ndarray.reshape()` can also be called by assigning to `ndarray.shape`. +.shape +~~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html + +The ``.shape`` property is a tuple whose elements are the length of the +array along each axis. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4], dtype=np.int8) + print("a:\n", a) + print("shape of a:", a.shape) + + b= np.array([[1, 2], [3, 4]], dtype=np.int8) + print("\nb:\n", b) + print("shape of b:", b.shape) + +.. parsed-literal:: + + a: + array([1, 2, 3, 4], dtype=int8) + shape of a: (4,) + + b: + array([[1, 2], + [3, 4]], dtype=int8) + shape of b: (2, 2) + + + + +By assigning a tuple to the ``.shape`` property, the array can be +``reshape``\ d: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9]) + print('a:\n', a) + + a.shape = (3, 3) + print('\na:\n', a) + +.. parsed-literal:: + + a: + array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64) + + a: + array([[1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0]], dtype=float64) + + + + +.size +~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.ndarray.size.html + +The ``.size`` property is an integer specifying the number of elements +in the array. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3], dtype=np.int8) + print("a:\n", a) + print("size of a:", a.size) + + b= np.array([[1, 2], [3, 4]], dtype=np.int8) + print("\nb:\n", b) + print("size of b:", b.size) + +.. parsed-literal:: + + a: + array([1, 2, 3], dtype=int8) + size of a: 3 + + b: + array([[1, 2], + [3, 4]], dtype=int8) + size of b: 4 + + + + +.T + +The ``.T`` property of the ``ndarray`` is equivalent to +`.transpose <#.transpose>`__. + +.tobytes +~~~~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tobytes.html + +The ``.tobytes`` method can be used for acquiring a handle of the +underlying data pointer of an array, and it returns a new ``bytearray`` +that can be fed into any method that can accep a ``bytearray``, e.g., +ADC data can be buffered into this ``bytearray``, or the ``bytearray`` +can be fed into a DAC. Since the ``bytearray`` is really nothing but the +bare data container of the array, any manipulation on the ``bytearray`` +automatically modifies the array itself. + +Note that the method raises a ``ValueError`` exception, if the array is +not dense (i.e., it has already been sliced). + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(8), dtype=np.uint8) + print('a: ', a) + b = a.tobytes() + print('b: ', b) + + # modify b + b[0] = 13 + + print('='*20) + print('b: ', b) + print('a: ', a) + +.. parsed-literal:: + + a: array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint8) + b: bytearray(b'\x00\x01\x02\x03\x04\x05\x06\x07') + ==================== + b: bytearray(b'\r\x01\x02\x03\x04\x05\x06\x07') + a: array([13, 1, 2, 3, 4, 5, 6, 7], dtype=uint8) + + + + +.tolist +~~~~~~~ + +``numpy``: +https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tolist.html + +The ``.tolist`` method can be used for converting the numerical array +into a (nested) ``python`` lists. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(4), dtype=np.uint8) + print('a: ', a) + b = a.tolist() + print('b: ', b) + + c = a.reshape((2, 2)) + print('='*20) + print('c: ', c) + d = c.tolist() + print('d: ', d) + +.. parsed-literal:: + + a: array([0, 1, 2, 3], dtype=uint8) + b: [0, 1, 2, 3] + ==================== + c: array([[0, 1], + [2, 3]], dtype=uint8) + d: [[0, 1], [2, 3]] + + + + +.transpose +~~~~~~~~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.transpose.html + +Returns the transposed array. Only defined, if the number of maximum +dimensions is larger than 1. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], dtype=np.uint8) + print('a:\n', a) + print('shape of a:', a.shape) + a.transpose() + print('\ntranspose of a:\n', a) + print('shape of a:', a.shape) + +.. parsed-literal:: + + a: + array([[1, 2, 3], + [4, 5, 6], + [7, 8, 9], + [10, 11, 12]], dtype=uint8) + shape of a: (4, 3) + + transpose of a: + array([[1, 4, 7, 10], + [2, 5, 8, 11], + [3, 6, 9, 12]], dtype=uint8) + shape of a: (3, 4) + + + + +The transpose of the array can also be gotten through the ``T`` +property: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.uint8) + print('a:\n', a) + print('\ntranspose of a:\n', a.T) + +.. parsed-literal:: + + a: + array([[1, 2, 3], + [4, 5, 6], + [7, 8, 9]], dtype=uint8) + + transpose of a: + array([[1, 4, 7], + [2, 5, 8], + [3, 6, 9]], dtype=uint8) + + + + +.sort +~~~~~ + +``numpy``: +https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html + +In-place sorting of an ``ndarray``. For a more detailed exposition, see +`sort <#sort>`__. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8) + print('\na:\n', a) + a.sort(axis=0) + print('\na sorted along vertical axis:\n', a) + + a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8) + a.sort(axis=1) + print('\na sorted along horizontal axis:\n', a) + + a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8) + a.sort(axis=None) + print('\nflattened a sorted:\n', a) + +.. parsed-literal:: + + + a: + array([[1, 12, 3, 0], + [5, 3, 4, 1], + [9, 11, 1, 8], + [7, 10, 0, 1]], dtype=uint8) + + a sorted along vertical axis: + array([[1, 3, 0, 0], + [5, 10, 1, 1], + [7, 11, 3, 1], + [9, 12, 4, 8]], dtype=uint8) + + a sorted along horizontal axis: + array([[0, 1, 3, 12], + [1, 3, 4, 5], + [1, 8, 9, 11], + [0, 1, 7, 10]], dtype=uint8) + + flattened a sorted: + array([0, 0, 1, ..., 10, 11, 12], dtype=uint8) + + + + +Unary operators +--------------- + +With the exception of ``len``, which returns a single number, all unary +operators manipulate the underlying data element-wise. + +len +~~~ + +This operator takes a single argument, the array, and returns either the +length of the first axis. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5], dtype=np.uint8) + b = np.array([range(5), range(5), range(5), range(5)], dtype=np.uint8) + + print("a:\t", a) + print("length of a: ", len(a)) + print("shape of a: ", a.shape) + print("\nb:\t", b) + print("length of b: ", len(b)) + print("shape of b: ", b.shape) + +.. parsed-literal:: + + a: array([1, 2, 3, 4, 5], dtype=uint8) + length of a: 5 + shape of a: (5,) + + b: array([[0, 1, 2, 3, 4], + [0, 1, 2, 3, 4], + [0, 1, 2, 3, 4], + [0, 1, 2, 3, 4]], dtype=uint8) + length of b: 2 + shape of b: (4, 5) + + + + +The number returned by ``len`` is also the length of the iterations, +when the array supplies the elements for an iteration (see later). + +invert +~~~~~~ + +The function is defined for integer data types (``uint8``, ``int8``, +``uint16``, and ``int16``) only, takes a single argument, and returns +the element-by-element, bit-wise inverse of the array. If a ``float`` is +supplied, the function raises a ``ValueError`` exception. + +With signed integers (``int8``, and ``int16``), the results might be +unexpected, as in the example below: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([0, -1, -100], dtype=np.int8) + print("a:\t\t", a) + print("inverse of a:\t", ~a) + + a = np.array([0, 1, 254, 255], dtype=np.uint8) + print("\na:\t\t", a) + print("inverse of a:\t", ~a) + +.. parsed-literal:: + + a: array([0, -1, -100], dtype=int8) + inverse of a: array([-1, 0, 99], dtype=int8) + + a: array([0, 1, 254, 255], dtype=uint8) + inverse of a: array([255, 254, 1, 0], dtype=uint8) + + + + +abs +~~~ + +This function takes a single argument, and returns the +element-by-element absolute value of the array. When the data type is +unsigned (``uint8``, or ``uint16``), a copy of the array will be +returned immediately, and no calculation takes place. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([0, -1, -100], dtype=np.int8) + print("a:\t\t\t ", a) + print("absolute value of a:\t ", abs(a)) + +.. parsed-literal:: + + a: array([0, -1, -100], dtype=int8) + absolute value of a: array([0, 1, 100], dtype=int8) + + + + +neg +~~~ + +This operator takes a single argument, and changes the sign of each +element in the array. Unsigned values are wrapped. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([10, -1, 1], dtype=np.int8) + print("a:\t\t", a) + print("negative of a:\t", -a) + + b = np.array([0, 100, 200], dtype=np.uint8) + print("\nb:\t\t", b) + print("negative of b:\t", -b) + +.. parsed-literal:: + + a: array([10, -1, 1], dtype=int8) + negative of a: array([-10, 1, -1], dtype=int8) + + b: array([0, 100, 200], dtype=uint8) + negative of b: array([0, 156, 56], dtype=uint8) + + + + +pos +~~~ + +This function takes a single argument, and simply returns a copy of the +array. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([10, -1, 1], dtype=np.int8) + print("a:\t\t", a) + print("positive of a:\t", +a) + +.. parsed-literal:: + + a: array([10, -1, 1], dtype=int8) + positive of a: array([10, -1, 1], dtype=int8) + + + + +Binary operators +---------------- + +``ulab`` implements the ``+``, ``-``, ``*``, ``/``, ``**``, ``<``, +``>``, ``<=``, ``>=``, ``==``, ``!=``, ``+=``, ``-=``, ``*=``, ``/=``, +``**=`` binary operators that work element-wise. Broadcasting is +available, meaning that the two operands do not even have to have the +same shape. If the lengths along the respective axes are equal, or one +of them is 1, or the axis is missing, the element-wise operation can +still be carried out. A thorough explanation of broadcasting can be +found under https://numpy.org/doc/stable/user/basics.broadcasting.html. + +**WARNING**: note that relational operators (``<``, ``>``, ``<=``, +``>=``, ``==``, ``!=``) should have the ``ndarray`` on their left hand +side, when compared to scalars. This means that the following works + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3]) + print(a > 2) + +.. parsed-literal:: + + array([False, False, True], dtype=bool) + + + + +while the equivalent statement, ``2 < a``, will raise a ``TypeError`` +exception: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3]) + print(2 < a) + +.. parsed-literal:: + + + Traceback (most recent call last): + File "/dev/shm/micropython.py", line 5, in <module> + TypeError: unsupported types for __lt__: 'int', 'ndarray' + + + +**WARNING:** ``circuitpython`` users should use the ``equal``, and +``not_equal`` operators instead of ``==``, and ``!=``. See the section +on `array comparison <#Comparison-of-arrays>`__ for details. + +Upcasting +~~~~~~~~~ + +Binary operations require special attention, because two arrays with +different typecodes can be the operands of an operation, in which case +it is not trivial, what the typecode of the result is. This decision on +the result’s typecode is called upcasting. Since the number of typecodes +in ``ulab`` is significantly smaller than in ``numpy``, we have to +define new upcasting rules. Where possible, I followed ``numpy``\ ’s +conventions. + +``ulab`` observes the following upcasting rules: + +1. Operations on two ``ndarray``\ s of the same ``dtype`` preserve their + ``dtype``, even when the results overflow. + +2. if either of the operands is a float, the result is automatically a + float + +3. When one of the operands is a scalar, it will internally be turned + into a single-element ``ndarray`` with the *smallest* possible + ``dtype``. Thus, e.g., if the scalar is 123, it will be converted + into an array of ``dtype`` ``uint8``, while -1000 will be converted + into ``int16``. An ``mp_obj_float``, will always be promoted to + ``dtype`` ``float``. Other micropython types (e.g., lists, tuples, + etc.) raise a ``TypeError`` exception. + +4. + +============== =============== =========== ============ +left hand side right hand side ulab result numpy result +============== =============== =========== ============ +``uint8`` ``int8`` ``int16`` ``int16`` +``uint8`` ``int16`` ``int16`` ``int16`` +``uint8`` ``uint16`` ``uint16`` ``uint16`` +``int8`` ``int16`` ``int16`` ``int16`` +``int8`` ``uint16`` ``uint16`` ``int32`` +``uint16`` ``int16`` ``float`` ``int32`` +============== =============== =========== ============ + +Note that the last two operations are promoted to ``int32`` in +``numpy``. + +**WARNING:** Due to the lower number of available data types, the +upcasting rules of ``ulab`` are slightly different to those of +``numpy``. Watch out for this, when porting code! + +Upcasting can be seen in action in the following snippet: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4], dtype=np.uint8) + b = np.array([1, 2, 3, 4], dtype=np.int8) + print("a:\t", a) + print("b:\t", b) + print("a+b:\t", a+b) + + c = np.array([1, 2, 3, 4], dtype=np.float) + print("\na:\t", a) + print("c:\t", c) + print("a*c:\t", a*c) + +.. parsed-literal:: + + a: array([1, 2, 3, 4], dtype=uint8) + b: array([1, 2, 3, 4], dtype=int8) + a+b: array([2, 4, 6, 8], dtype=int16) + + a: array([1, 2, 3, 4], dtype=uint8) + c: array([1.0, 2.0, 3.0, 4.0], dtype=float64) + a*c: array([1.0, 4.0, 9.0, 16.0], dtype=float64) + + + + +Benchmarks +~~~~~~~~~~ + +The following snippet compares the performance of binary operations to a +possible implementation in python. For the time measurement, we will +take the following snippet from the micropython manual: + +.. code:: + + # code to be run in micropython + + import utime + + def timeit(f, *args, **kwargs): + func_name = str(f).split(' ')[1] + def new_func(*args, **kwargs): + t = utime.ticks_us() + result = f(*args, **kwargs) + print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us') + return result + return new_func + +.. parsed-literal:: + + + + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + @timeit + def py_add(a, b): + return [a[i]+b[i] for i in range(1000)] + + @timeit + def py_multiply(a, b): + return [a[i]*b[i] for i in range(1000)] + + @timeit + def ulab_add(a, b): + return a + b + + @timeit + def ulab_multiply(a, b): + return a * b + + a = [0.0]*1000 + b = range(1000) + + print('python add:') + py_add(a, b) + + print('\npython multiply:') + py_multiply(a, b) + + a = np.linspace(0, 10, num=1000) + b = np.ones(1000) + + print('\nulab add:') + ulab_add(a, b) + + print('\nulab multiply:') + ulab_multiply(a, b) + +.. parsed-literal:: + + python add: + execution time: 10051 us + + python multiply: + execution time: 14175 us + + ulab add: + execution time: 222 us + + ulab multiply: + execution time: 213 us + + + +The python implementation above is not perfect, and certainly, there is +much room for improvement. However, the factor of 50 difference in +execution time is very spectacular. This is nothing but a consequence of +the fact that the ``ulab`` functions run ``C`` code, with very little +python overhead. The factor of 50 appears to be quite universal: the FFT +routine obeys similar scaling (see `Speed of FFTs <#Speed-of-FFTs>`__), +and this number came up with font rendering, too: `fast font rendering +on graphical +displays <https://forum.micropython.org/viewtopic.php?f=15&t=5815&p=33362&hilit=ufont#p33383>`__. + +Comparison operators +-------------------- + +The smaller than, greater than, smaller or equal, and greater or equal +operators return a vector of Booleans indicating the positions +(``True``), where the condition is satisfied. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5, 6, 7, 8], dtype=np.uint8) + print(a < 5) + +.. parsed-literal:: + + array([True, True, True, True, False, False, False, False], dtype=bool) + + + + +**WARNING**: at the moment, due to ``micropython``\ ’s implementation +details, the ``ndarray`` must be on the left hand side of the relational +operators. + +That is, while ``a < 5`` and ``5 > a`` have the same meaning, the +following code will not work: + +.. code:: + + # code to be run in micropython + + import ulab as np + + a = np.array([1, 2, 3, 4, 5, 6, 7, 8], dtype=np.uint8) + print(5 > a) + +.. parsed-literal:: + + + Traceback (most recent call last): + File "/dev/shm/micropython.py", line 5, in <module> + TypeError: unsupported types for __gt__: 'int', 'ndarray' + + + +Iterating over arrays +--------------------- + +``ndarray``\ s are iterable, which means that their elements can also be +accessed as can the elements of a list, tuple, etc. If the array is +one-dimensional, the iterator returns scalars, otherwise a new +reduced-dimensional *view* is created and returned. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5], dtype=np.uint8) + b = np.array([range(5), range(10, 15, 1), range(20, 25, 1), range(30, 35, 1)], dtype=np.uint8) + + print("a:\t", a) + + for i, _a in enumerate(a): + print("element %d in a:"%i, _a) + + print("\nb:\t", b) + + for i, _b in enumerate(b): + print("element %d in b:"%i, _b) + +.. parsed-literal:: + + a: array([1, 2, 3, 4, 5], dtype=uint8) + element 0 in a: 1 + element 1 in a: 2 + element 2 in a: 3 + element 3 in a: 4 + element 4 in a: 5 + + b: array([[0, 1, 2, 3, 4], + [10, 11, 12, 13, 14], + [20, 21, 22, 23, 24], + [30, 31, 32, 33, 34]], dtype=uint8) + element 0 in b: array([0, 1, 2, 3, 4], dtype=uint8) + element 1 in b: array([10, 11, 12, 13, 14], dtype=uint8) + element 2 in b: array([20, 21, 22, 23, 24], dtype=uint8) + element 3 in b: array([30, 31, 32, 33, 34], dtype=uint8) + + + + +Slicing and indexing +-------------------- + +Views vs. copies +~~~~~~~~~~~~~~~~ + +``numpy`` has a very important concept called *views*, which is a +powerful extension of ``python``\ ’s own notion of slicing. Slices are +special python objects of the form + +.. code:: python + + slice = start:end:stop + +where ``start``, ``end``, and ``stop`` are (not necessarily +non-negative) integers. Not all of these three numbers must be specified +in an index, in fact, all three of them can be missing. The interpreter +takes care of filling in the missing values. (Note that slices cannot be +defined in this way, only there, where an index is expected.) For a good +explanation on how slices work in python, you can read the stackoverflow +question +https://stackoverflow.com/questions/509211/understanding-slice-notation. + +In order to see what slicing does, let us take the string +``a = '012345679'``! We can extract every second character by creating +the slice ``::2``, which is equivalent to ``0:len(a):2``, i.e., +increments the character pointer by 2 starting from 0, and traversing +the string up to the very end. + +.. code:: + + # code to be run in CPython + + string = '0123456789' + string[::2] + + + +.. parsed-literal:: + + '02468' + + + +Now, we can do the same with numerical arrays. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(10), dtype=np.uint8) + print('a:\t', a) + + print('a[::2]:\t', a[::2]) + +.. parsed-literal:: + + a: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8) + a[::2]: array([0, 2, 4, 6, 8], dtype=uint8) + + + + +This looks similar to ``string`` above, but there is a very important +difference that is not so obvious. Namely, ``string[::2]`` produces a +partial copy of ``string``, while ``a[::2]`` only produces a *view* of +``a``. What this means is that ``a``, and ``a[::2]`` share their data, +and the only difference between the two is, how the data are read out. +In other words, internally, ``a[::2]`` has the same data pointer as +``a``. We can easily convince ourselves that this is indeed the case by +calling the `ndinfo <#The_ndinfo_function>`__ function: the *data +pointer* entry is the same in the two printouts. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(10), dtype=np.uint8) + print('a: ', a, '\n') + np.ndinfo(a) + print('\n' + '='*20) + print('a[::2]: ', a[::2], '\n') + np.ndinfo(a[::2]) + +.. parsed-literal:: + + a: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8) + + class: ndarray + shape: (10,) + strides: (1,) + itemsize: 1 + data pointer: 0x7ff6c6193220 + type: uint8 + + ==================== + a[::2]: array([0, 2, 4, 6, 8], dtype=uint8) + + class: ndarray + shape: (5,) + strides: (2,) + itemsize: 1 + data pointer: 0x7ff6c6193220 + type: uint8 + + + + +If you are still a bit confused about the meaning of *views*, the +section `Slicing and assigning to +slices <#Slicing-and-assigning-to-slices>`__ should clarify the issue. + +Indexing +~~~~~~~~ + +The simplest form of indexing is specifying a single integer between the +square brackets as in + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(10), dtype=np.uint8) + print("a: ", a) + print("the first, and last element of a:\n", a[0], a[-1]) + print("the second, and last but one element of a:\n", a[1], a[-2]) + +.. parsed-literal:: + + a: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8) + the first, and last element of a: + 0 9 + the second, and last but one element of a: + 1 8 + + + + +Indexing can be applied to higher-dimensional tensors, too. When the +length of the indexing sequences is smaller than the number of +dimensions, a new *view* is returned, otherwise, we get a single number. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(9), dtype=np.uint8).reshape((3, 3)) + print("a:\n", a) + print("a[0]:\n", a[0]) + print("a[1,1]: ", a[1,1]) + +.. parsed-literal:: + + a: + array([[0, 1, 2], + [3, 4, 5], + [6, 7, 8]], dtype=uint8) + a[0]: + array([[0, 1, 2]], dtype=uint8) + a[1,1]: 4 + + + + +Indices can also be a list of Booleans. By using a Boolean list, we can +select those elements of an array that satisfy a specific condition. At +the moment, such indexing is defined for row vectors only; when the rank +of the tensor is higher than 1, the function raises a +``NotImplementedError`` exception, though this will be rectified in a +future version of ``ulab``. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(9), dtype=np.float) + print("a:\t", a) + print("a < 5:\t", a[a < 5]) + +.. parsed-literal:: + + a: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float) + a < 5: array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float) + + + + +Indexing with Boolean arrays can take more complicated expressions. This +is a very concise way of comparing two vectors, e.g.: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(9), dtype=np.uint8) + b = np.array([4, 4, 4, 3, 3, 3, 13, 13, 13], dtype=np.uint8) + print("a:\t", a) + print("\na**2:\t", a*a) + print("\nb:\t", b) + print("\n100*sin(b):\t", np.sin(b)*100.0) + print("\na[a*a > np.sin(b)*100.0]:\t", a[a*a > np.sin(b)*100.0]) + +.. parsed-literal:: + + a: array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8) + + a**2: array([0, 1, 4, 9, 16, 25, 36, 49, 64], dtype=uint16) + + b: array([4, 4, 4, 3, 3, 3, 13, 13, 13], dtype=uint8) + + 100*sin(b): array([-75.68024953079282, -75.68024953079282, -75.68024953079282, 14.11200080598672, 14.11200080598672, 14.11200080598672, 42.01670368266409, 42.01670368266409, 42.01670368266409], dtype=float) + + a[a*a > np.sin(b)*100.0]: array([0, 1, 2, 4, 5, 7, 8], dtype=uint8) + + + + +Boolean indices can also be used in assignments, if the array is +one-dimensional. The following example replaces the data in an array, +wherever some condition is fulfilled. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(9), dtype=np.uint8) + b = np.array(range(9)) + 12 + + print(a[b < 15]) + + a[b < 15] = 123 + print(a) + +.. parsed-literal:: + + array([0, 1, 2], dtype=uint8) + array([123, 123, 123, 3, 4, 5, 6, 7, 8], dtype=uint8) + + + + +On the right hand side of the assignment we can even have another array. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array(range(9), dtype=np.uint8) + b = np.array(range(9)) + 12 + + print(a[b < 15], b[b < 15]) + + a[b < 15] = b[b < 15] + print(a) + +.. parsed-literal:: + + array([0, 1, 2], dtype=uint8) array([12.0, 13.0, 14.0], dtype=float) + array([12, 13, 14, 3, 4, 5, 6, 7, 8], dtype=uint8) + + + + +Slicing and assigning to slices +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +You can also generate sub-arrays by specifying slices as the index of an +array. Slices are special python objects of the form + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.uint8) + print('a:\n', a) + + # the first row + print('\na[0]:\n', a[0]) + + # the first two elements of the first row + print('\na[0,:2]:\n', a[0,:2]) + + # the zeroth element in each row (also known as the zeroth column) + print('\na[:,0]:\n', a[:,0]) + + # the last row + print('\na[-1]:\n', a[-1]) + + # the last two rows backwards + print('\na[-1:-3:-1]:\n', a[-1:-3:-1]) + +.. parsed-literal:: + + a: + array([[1, 2, 3], + [4, 5, 6], + [7, 8, 9]], dtype=uint8) + + a[0]: + array([[1, 2, 3]], dtype=uint8) + + a[0,:2]: + array([[1, 2]], dtype=uint8) + + a[:,0]: + array([[1], + [4], + [7]], dtype=uint8) + + a[-1]: + array([[7, 8, 9]], dtype=uint8) + + a[-1:-3:-1]: + array([[7, 8, 9], + [4, 5, 6]], dtype=uint8) + + + + +Assignment to slices can be done for the whole slice, per row, and per +column. A couple of examples should make these statements clearer: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.zeros((3, 3), dtype=np.uint8) + print('a:\n', a) + + # assigning to the whole row + a[0] = 1 + print('\na[0] = 1\n', a) + + a = np.zeros((3, 3), dtype=np.uint8) + + # assigning to a column + a[:,2] = 3.0 + print('\na[:,0]:\n', a) + +.. parsed-literal:: + + a: + array([[0, 0, 0], + [0, 0, 0], + [0, 0, 0]], dtype=uint8) + + a[0] = 1 + array([[1, 1, 1], + [0, 0, 0], + [0, 0, 0]], dtype=uint8) + + a[:,0]: + array([[0, 0, 3], + [0, 0, 3], + [0, 0, 3]], dtype=uint8) + + + + +Now, you should notice that we re-set the array ``a`` after the first +assignment. Do you care to see what happens, if we do not do that? Well, +here are the results: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.zeros((3, 3), dtype=np.uint8) + b = a[:,:] + # assign 1 to the first row + b[0] = 1 + + # assigning to the last column + b[:,2] = 3 + print('a: ', a) + +.. parsed-literal:: + + a: array([[1, 1, 3], + [0, 0, 3], + [0, 0, 3]], dtype=uint8) + + + + +Note that both assignments involved ``b``, and not ``a``, yet, when we +print out ``a``, its entries are updated. This proves our earlier +statement about the behaviour of *views*: in the statement +``b = a[:,:]`` we simply created a *view* of ``a``, and not a *deep* +copy of it, meaning that whenever we modify ``b``, we actually modify +``a``, because the underlying data container of ``a`` and ``b`` are +shared between the two object. Having a single data container for two +seemingly different objects provides an extremely powerful way of +manipulating sub-sets of numerical data. + +If you want to work on a *copy* of your data, you can use the ``.copy`` +method of the ``ndarray``. The following snippet should drive the point +home: + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.zeros((3, 3), dtype=np.uint8) + b = a.copy() + + # get the address of the underlying data pointer + + np.ndinfo(a) + print() + np.ndinfo(b) + + # assign 1 to the first row of b, and do not touch a + b[0] = 1 + + print() + print('a: ', a) + print('='*20) + print('b: ', b) + +.. parsed-literal:: + + class: ndarray + shape: (3, 3) + strides: (3, 1) + itemsize: 1 + data pointer: 0x7ff737ea3220 + type: uint8 + + class: ndarray + shape: (3, 3) + strides: (3, 1) + itemsize: 1 + data pointer: 0x7ff737ea3340 + type: uint8 + + a: array([[0, 0, 0], + [0, 0, 0], + [0, 0, 0]], dtype=uint8) + ==================== + b: array([[1, 1, 1], + [0, 0, 0], + [0, 0, 0]], dtype=uint8) + + + + +The ``.copy`` method can also be applied to views: below, ``a[0]`` is a +*view* of ``a``, out of which we create a *deep copy* called ``b``. This +is a row vector now. We can then do whatever we want to with ``b``, and +that leaves ``a`` unchanged. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + + a = np.zeros((3, 3), dtype=np.uint8) + b = a[0].copy() + print('b: ', b) + print('='*20) + # assign 1 to the first entry of b, and do not touch a + b[0] = 1 + print('a: ', a) + print('='*20) + print('b: ', b) + +.. parsed-literal:: + + b: array([0, 0, 0], dtype=uint8) + ==================== + a: array([[0, 0, 0], + [0, 0, 0], + [0, 0, 0]], dtype=uint8) + ==================== + b: array([1, 0, 0], dtype=uint8) + + + + +The fact that the underlying data of a view is the same as that of the +original array has another important consequence, namely, that the +creation of a view is cheap. Both in terms of RAM, and execution time. A +view is really nothing but a short header with a data array that already +exists, and is filled up. Hence, creating the view requires only the +creation of its header. This operation is fast, and uses virtually no +RAM. diff --git a/circuitpython/extmod/ulab/docs/manual/source/ulab-programming.rst b/circuitpython/extmod/ulab/docs/manual/source/ulab-programming.rst new file mode 100644 index 0000000..ff1788b --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/ulab-programming.rst @@ -0,0 +1,911 @@ + +Programming ulab +================ + +Earlier we have seen, how ``ulab``\ ’s functions and methods can be +accessed in ``micropython``. This last section of the book explains, how +these functions are implemented. By the end of this chapter, not only +would you be able to extend ``ulab``, and write your own +``numpy``-compatible functions, but through a deeper understanding of +the inner workings of the functions, you would also be able to see what +the trade-offs are at the ``python`` level. + +Code organisation +----------------- + +As mentioned earlier, the ``python`` functions are organised into +sub-modules at the C level. The C sub-modules can be found in +``./ulab/code/``. + +The ``ndarray`` object +---------------------- + +General comments +~~~~~~~~~~~~~~~~ + +``ndarrays`` are efficient containers of numerical data of the same type +(i.e., signed/unsigned chars, signed/unsigned integers or +``mp_float_t``\ s, which, depending on the platform, are either C +``float``\ s, or C ``double``\ s). Beyond storing the actual data in the +void pointer ``*array``, the type definition has eight additional +members (on top of the ``base`` type). Namely, the ``dtype``, which +tells us, how the bytes are to be interpreted. Moreover, the +``itemsize``, which stores the size of a single entry in the array, +``boolean``, an unsigned integer, which determines, whether the arrays +is to be treated as a set of Booleans, or as numerical data, ``ndim``, +the number of dimensions (``uint8_t``), ``len``, the length of the array +(the number of entries), the shape (``*size_t``), the strides +(``*int32_t``). The length is simply the product of the numbers in +``shape``. + +The type definition is as follows: + +.. code:: c + + typedef struct _ndarray_obj_t { + mp_obj_base_t base; + uint8_t dtype; + uint8_t itemsize; + uint8_t boolean; + uint8_t ndim; + size_t len; + size_t shape[ULAB_MAX_DIMS]; + int32_t strides[ULAB_MAX_DIMS]; + void *array; + } ndarray_obj_t; + +Memory layout +~~~~~~~~~~~~~ + +The values of an ``ndarray`` are stored in a contiguous segment in the +RAM. The ``ndarray`` can be dense, meaning that all numbers in the +linear memory segment belong to a linar combination of coordinates, and +it can also be sparse, i.e., some elements of the linear storage space +will be skipped, when the elements of the tensor are traversed. + +In the RAM, the position of the item +:math:`M(n_1, n_2, ..., n_{k-1}, n_k)` in a dense tensor of rank +:math:`k` is given by the linear combination + +:raw-latex:`\begin{equation} +P(n_1, n_2, ..., n_{k-1}, n_k) = n_1 s_1 + n_2 s_2 + ... + n_{k-1}s_{k-1} + n_ks_k = \sum_{i=1}^{k}n_is_i +\end{equation}` where :math:`s_i` are the strides of the tensor, defined +as + +:raw-latex:`\begin{equation} +s_i = \prod_{j=i+1}^k l_j +\end{equation}` + +where :math:`l_j` is length of the tensor along the :math:`j`\ th axis. +When the tensor is sparse (e.g., when the tensor is sliced), the strides +along a particular axis will be multiplied by a non-zero integer. If +this integer is different to :math:`\pm 1`, the linear combination above +cannot access all elements in the RAM, i.e., some numbers will be +skipped. Note that :math:`|s_1| > |s_2| > ... > |s_{k-1}| > |s_k|`, even +if the tensor is sparse. The statement is trivial for dense tensors, and +it follows from the definition of :math:`s_i`. For sparse tensors, a +slice cannot have a step larger than the shape along that axis. But for +dense tensors, :math:`s_i/s_{i+1} = l_i`. + +When creating a *view*, we simply re-calculate the ``strides``, and +re-set the ``*array`` pointer. + +Iterating over elements of a tensor +----------------------------------- + +The ``shape`` and ``strides`` members of the array tell us how we have +to move our pointer, when we want to read out the numbers. For technical +reasons that will become clear later, the numbers in ``shape`` and in +``strides`` are aligned to the right, and begin on the right hand side, +i.e., if the number of possible dimensions is ``ULAB_MAX_DIMS``, then +``shape[ULAB_MAX_DIMS-1]`` is the length of the last axis, +``shape[ULAB_MAX_DIMS-2]`` is the length of the last but one axis, and +so on. If the number of actual dimensions, ``ndim < ULAB_MAX_DIMS``, the +first ``ULAB_MAX_DIMS - ndim`` entries in ``shape`` and ``strides`` will +be equal to zero, but they could, in fact, be assigned any value, +because these will never be accessed in an operation. + +With this definition of the strides, the linear combination in +:math:`P(n_1, n_2, ..., n_{k-1}, n_k)` is a one-to-one mapping from the +space of tensor coordinates, :math:`(n_1, n_2, ..., n_{k-1}, n_k)`, and +the coordinate in the linear array, +:math:`n_1s_1 + n_2s_2 + ... + n_{k-1}s_{k-1} + n_ks_k`, i.e., no two +distinct sets of coordinates will result in the same position in the +linear array. + +Since the ``strides`` are given in terms of bytes, when we iterate over +an array, the void data pointer is usually cast to ``uint8_t``, and the +values are converted using the proper data type stored in +``ndarray->dtype``. However, there might be cases, when it makes perfect +sense to cast ``*array`` to a different type, in which case the +``strides`` have to be re-scaled by the value of ``ndarray->itemsize``. + +Iterating using the unwrapped loops +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The following macro definition is taken from +`vector.h <https://github.com/v923z/micropython-ulab/blob/master/code/numpy/vector/vector.h>`__, +and demonstrates, how we can iterate over a single array in four +dimensions. + +.. code:: c + + #define ITERATE_VECTOR(type, array, source, sarray) do { + size_t i=0; + do { + size_t j = 0; + do { + size_t k = 0; + do { + size_t l = 0; + do { + *(array)++ = f(*((type *)(sarray))); + (sarray) += (source)->strides[ULAB_MAX_DIMS - 1]; + l++; + } while(l < (source)->shape[ULAB_MAX_DIMS-1]); + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1]; + (sarray) += (source)->strides[ULAB_MAX_DIMS - 2]; + k++; + } while(k < (source)->shape[ULAB_MAX_DIMS-2]); + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 2] * (source)->shape[ULAB_MAX_DIMS-2]; + (sarray) += (source)->strides[ULAB_MAX_DIMS - 3]; + j++; + } while(j < (source)->shape[ULAB_MAX_DIMS-3]); + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 3] * (source)->shape[ULAB_MAX_DIMS-3]; + (sarray) += (source)->strides[ULAB_MAX_DIMS - 4]; + i++; + } while(i < (source)->shape[ULAB_MAX_DIMS-4]); + } while(0) + +We start with the innermost loop, the one recursing ``l``. ``array`` is +already of type ``mp_float_t``, while the source array, ``sarray``, has +been cast to ``uint8_t`` in the calling function. The numbers contained +in ``sarray`` have to be read out in the proper type dictated by +``ndarray->dtype``. This is what happens in the statement +``*((type *)(sarray))``, and this number is then fed into the function +``f``. Vectorised mathematical functions produce *dense* arrays, and for +this reason, we can simply advance the ``array`` pointer. + +The advancing of the ``sarray`` pointer is a bit more involving: first, +in the innermost loop, we simply move forward by the amount given by the +last stride, which is ``(source)->strides[ULAB_MAX_DIMS - 1]``, because +the ``shape`` and the ``strides`` are aligned to the right. We move the +pointer as many times as given by ``(source)->shape[ULAB_MAX_DIMS-1]``, +which is the length of the very last axis. Hence the the structure of +the loop + +.. code:: c + + size_t l = 0; + do { + ... + l++; + } while(l < (source)->shape[ULAB_MAX_DIMS-1]); + +Once we have exhausted the last axis, we have to re-wind the pointer, +and advance it by an amount given by the last but one stride. Keep in +mind that in the the innermost loop we moved our pointer +``(source)->shape[ULAB_MAX_DIMS-1]`` times by +``(source)->strides[ULAB_MAX_DIMS - 1]``, i.e., we re-wind it by moving +it backwards by +``(source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1]``. +In the next step, we move forward by +``(source)->strides[ULAB_MAX_DIMS - 2]``, which is the last but one +stride. + +.. code:: c + + (sarray) -= (source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1]; + (sarray) += (source)->strides[ULAB_MAX_DIMS - 2]; + +This pattern must be repeated for each axis of the array, and this is +how we arrive at the four nested loops listed above. + +Re-winding arrays by means of a function +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +In addition to un-wrapping the iteration loops by means of macros, there +is another way of traversing all elements of a tensor: we note that, +since :math:`|s_1| > |s_2| > ... > |s_{k-1}| > |s_k|`, +:math:`P(n1, n2, ..., n_{k-1}, n_k)` changes most slowly in the last +coordinate. Hence, if we start from the very beginning, (:math:`n_i = 0` +for all :math:`i`), and walk along the linear RAM segment, we increment +the value of :math:`n_k` as long as :math:`n_k < l_k`. Once +:math:`n_k = l_k`, we have to reset :math:`n_k` to 0, and increment +:math:`n_{k-1}` by one. After each such round, :math:`n_{k-1}` will be +incremented by one, as long as :math:`n_{k-1} < l_{k-1}`. Once +:math:`n_{k-1} = l_{k-1}`, we reset both :math:`n_k`, and +:math:`n_{k-1}` to 0, and increment :math:`n_{k-2}` by one. + +Rewinding the arrays in this way is implemented in the function +``ndarray_rewind_array`` in +`ndarray.c <https://github.com/v923z/micropython-ulab/blob/master/code/ndarray.c>`__. + +.. code:: c + + void ndarray_rewind_array(uint8_t ndim, uint8_t *array, size_t *shape, int32_t *strides, size_t *coords) { + // resets the data pointer of a single array, whenever an axis is full + // since we always iterate over the very last axis, we have to keep track of + // the last ndim-2 axes only + array -= shape[ULAB_MAX_DIMS - 1] * strides[ULAB_MAX_DIMS - 1]; + array += strides[ULAB_MAX_DIMS - 2]; + for(uint8_t i=1; i < ndim-1; i++) { + coords[ULAB_MAX_DIMS - 1 - i] += 1; + if(coords[ULAB_MAX_DIMS - 1 - i] == shape[ULAB_MAX_DIMS - 1 - i]) { // we are at a dimension boundary + array -= shape[ULAB_MAX_DIMS - 1 - i] * strides[ULAB_MAX_DIMS - 1 - i]; + array += strides[ULAB_MAX_DIMS - 2 - i]; + coords[ULAB_MAX_DIMS - 1 - i] = 0; + coords[ULAB_MAX_DIMS - 2 - i] += 1; + } else { // coordinates can change only, if the last coordinate changes + return; + } + } + } + +and the function would be called as in the snippet below. Note that the +innermost loop is factored out, so that we can save the ``if(...)`` +statement for the last axis. + +.. code:: c + + size_t *coords = ndarray_new_coords(results->ndim); + for(size_t i=0; i < results->len/results->shape[ULAB_MAX_DIMS -1]; i++) { + size_t l = 0; + do { + ... + l++; + } while(l < results->shape[ULAB_MAX_DIMS - 1]); + ndarray_rewind_array(results->ndim, array, results->shape, strides, coords); + } while(0) + +The advantage of this method is that the implementation is independent +of the number of dimensions: the iteration requires more or less the +same flash space for 2 dimensions as for 22. However, the price we have +to pay for this convenience is the extra function call. + +Iterating over two ndarrays simultaneously: broadcasting +-------------------------------------------------------- + +Whenever we invoke a binary operator, call a function with two arguments +of ``ndarray`` type, or assign something to an ``ndarray``, we have to +iterate over two views at the same time. The task is trivial, if the two +``ndarray``\ s in question have the same shape (but not necessarily the +same set of strides), because in this case, we can still iterate in the +same loop. All that happens is that we move two data pointers in sync. + +The problem becomes a bit more involving, when the shapes of the two +``ndarray``\ s are not identical. For such cases, ``numpy`` defines +so-called broadcasting, which boils down to two rules. + +1. The shapes in the tensor with lower rank has to be prepended with + axes of size 1 till the two ranks become equal. +2. Along all axes the two tensors should have the same size, or one of + the sizes must be 1. + +If, after applying the first rule the second is not satisfied, the two +``ndarray``\ s cannot be broadcast together. + +Now, let us suppose that we have two compatible ``ndarray``\ s, i.e., +after applying the first rule, the second is satisfied. How do we +iterate over the elements in the tensors? + +We should recall, what exactly we do, when iterating over a single +array: normally, we move the data pointer by the last stride, except, +when we arrive at a dimension boundary (when the last axis is +exhausted). At that point, we move the pointer by an amount dictated by +the strides. And this is the key: *dictated by the strides*. Now, if we +have two arrays that are originally not compatible, we define new +strides for them, and use these in the iteration. With that, we are back +to the case, where we had two compatible arrays. + +Now, let us look at the second broadcasting rule: if the two arrays have +the same size, we take both ``ndarray``\ s’ strides along that axis. If, +on the other hand, one of the ``ndarray``\ s is of length 1 along one of +its axes, we set the corresponding strides to 0. This will ensure that +that data pointer is not moved, when we iterate over both ``ndarray``\ s +at the same time. + +Thus, in order to implement broadcasting, we first have to check, +whether the two above-mentioned rules can be satisfied, and if so, we +have to find the two new sets strides. + +The ``ndarray_can_broadcast`` function from +`ndarray.c <https://github.com/v923z/micropython-ulab/blob/master/code/ndarray.c>`__ +takes two ``ndarray``\ s, and returns ``true``, if the two arrays can be +broadcast together. At the same time, it also calculates new strides for +the two arrays, so that they can be iterated over at the same time. + +.. code:: c + + bool ndarray_can_broadcast(ndarray_obj_t *lhs, ndarray_obj_t *rhs, uint8_t *ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) { + // returns True or False, depending on, whether the two arrays can be broadcast together + // numpy's broadcasting rules are as follows: + // + // 1. the two shapes are either equal + // 2. one of the shapes is 1 + memset(lstrides, 0, sizeof(size_t)*ULAB_MAX_DIMS); + memset(rstrides, 0, sizeof(size_t)*ULAB_MAX_DIMS); + lstrides[ULAB_MAX_DIMS - 1] = lhs->strides[ULAB_MAX_DIMS - 1]; + rstrides[ULAB_MAX_DIMS - 1] = rhs->strides[ULAB_MAX_DIMS - 1]; + for(uint8_t i=ULAB_MAX_DIMS; i > 0; i--) { + if((lhs->shape[i-1] == rhs->shape[i-1]) || (lhs->shape[i-1] == 0) || (lhs->shape[i-1] == 1) || + (rhs->shape[i-1] == 0) || (rhs->shape[i-1] == 1)) { + shape[i-1] = MAX(lhs->shape[i-1], rhs->shape[i-1]); + if(shape[i-1] > 0) (*ndim)++; + if(lhs->shape[i-1] < 2) { + lstrides[i-1] = 0; + } else { + lstrides[i-1] = lhs->strides[i-1]; + } + if(rhs->shape[i-1] < 2) { + rstrides[i-1] = 0; + } else { + rstrides[i-1] = rhs->strides[i-1]; + } + } else { + return false; + } + } + return true; + } + +A good example of how the function would be called can be found in +`vector.c <https://github.com/v923z/micropython-ulab/blob/master/code/numpy/vector/vector.c>`__, +in the ``vector_arctan2`` function: + +.. code:: c + + mp_obj_t vectorise_arctan2(mp_obj_t y, mp_obj_t x) { + ... + uint8_t ndim = 0; + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + int32_t *xstrides = m_new(int32_t, ULAB_MAX_DIMS); + int32_t *ystrides = m_new(int32_t, ULAB_MAX_DIMS); + if(!ndarray_can_broadcast(ndarray_x, ndarray_y, &ndim, shape, xstrides, ystrides)) { + mp_raise_ValueError(translate("operands could not be broadcast together")); + m_del(size_t, shape, ULAB_MAX_DIMS); + m_del(int32_t, xstrides, ULAB_MAX_DIMS); + m_del(int32_t, ystrides, ULAB_MAX_DIMS); + } + + uint8_t *xarray = (uint8_t *)ndarray_x->array; + uint8_t *yarray = (uint8_t *)ndarray_y->array; + + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT); + mp_float_t *rarray = (mp_float_t *)results->array; + ... + +After the new strides have been calculated, the iteration loop is +identical to what we discussed in the previous section. + +Contracting an ``ndarray`` +-------------------------- + +There are many operations that reduce the number of dimensions of an +``ndarray`` by 1, i.e., that remove an axis from the tensor. The drill +is the same as before, with the exception that first we have to remove +the ``strides`` and ``shape`` that corresponds to the axis along which +we intend to contract. The ``numerical_reduce_axes`` function from +`numerical.c <https://github.com/v923z/micropython-ulab/blob/master/code/numerical/numerical.c>`__ +does that. + +.. code:: c + + static void numerical_reduce_axes(ndarray_obj_t *ndarray, int8_t axis, size_t *shape, int32_t *strides) { + // removes the values corresponding to a single axis from the shape and strides array + uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + axis; + if((ndarray->ndim == 1) && (axis == 0)) { + index = 0; + shape[ULAB_MAX_DIMS - 1] = 0; + return; + } + for(uint8_t i = ULAB_MAX_DIMS - 1; i > 0; i--) { + if(i > index) { + shape[i] = ndarray->shape[i]; + strides[i] = ndarray->strides[i]; + } else { + shape[i] = ndarray->shape[i-1]; + strides[i] = ndarray->strides[i-1]; + } + } + } + +Once the reduced ``strides`` and ``shape`` are known, we place the axis +in question in the innermost loop, and wrap it with the loops, whose +coordinates are in the ``strides``, and ``shape`` arrays. The +``RUN_STD`` macro from +`numerical.h <https://github.com/v923z/micropython-ulab/blob/master/code/numpy/numerical/numerical.h>`__ +is a good example. The macro is expanded in the +``numerical_sum_mean_std_ndarray`` function. + +.. code:: c + + static mp_obj_t numerical_sum_mean_std_ndarray(ndarray_obj_t *ndarray, mp_obj_t axis, uint8_t optype, size_t ddof) { + uint8_t *array = (uint8_t *)ndarray->array; + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS); + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS); + + int8_t ax = mp_obj_get_int(axis); + if(ax < 0) ax += ndarray->ndim; + if((ax < 0) || (ax > ndarray->ndim - 1)) { + mp_raise_ValueError(translate("index out of range")); + } + numerical_reduce_axes(ndarray, ax, shape, strides); + uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + ax; + ndarray_obj_t *results = NULL; + uint8_t *rarray = NULL; + ... + +Here is the macro for the three-dimensional case: + +.. code:: c + + #define RUN_STD(ndarray, type, array, results, r, shape, strides, index, div) do { + size_t k = 0; + do { + size_t l = 0; + do { + RUN_STD1((ndarray), type, (array), (results), (r), (index), (div)); + (array) -= (ndarray)->strides[(index)] * (ndarray)->shape[(index)]; + (array) += (strides)[ULAB_MAX_DIMS - 1]; + l++; + } while(l < (shape)[ULAB_MAX_DIMS - 1]); + (array) -= (strides)[ULAB_MAX_DIMS - 2] * (shape)[ULAB_MAX_DIMS-2]; + (array) += (strides)[ULAB_MAX_DIMS - 3]; + k++; + } while(k < (shape)[ULAB_MAX_DIMS - 2]); + } while(0) + +In ``RUN_STD``, we simply move our pointers; the calculation itself +happens in the ``RUN_STD1`` macro below. (Note that this is the +implementation of the numerically stable Welford algorithm.) + +.. code:: c + + #define RUN_STD1(ndarray, type, array, results, r, index, div) + ({ + mp_float_t M, m, S = 0.0, s = 0.0; + M = m = *(mp_float_t *)((type *)(array)); + for(size_t i=1; i < (ndarray)->shape[(index)]; i++) { + (array) += (ndarray)->strides[(index)]; + mp_float_t value = *(mp_float_t *)((type *)(array)); + m = M + (value - M) / (mp_float_t)i; + s = S + (value - M) * (value - m); + M = m; + S = s; + } + (array) += (ndarray)->strides[(index)]; + *(r)++ = MICROPY_FLOAT_C_FUN(sqrt)((ndarray)->shape[(index)] * s / (div)); + }) + +Upcasting +--------- + +When in an operation the ``dtype``\ s of two arrays are different, the +result’s ``dtype`` will be decided by the following upcasting rules: + +1. Operations with two ``ndarray``\ s of the same ``dtype`` preserve + their ``dtype``, even when the results overflow. + +2. if either of the operands is a float, the result automatically + becomes a float + +3. otherwise + + - ``uint8`` + ``int8`` => ``int16``, + + - ``uint8`` + ``int16`` => ``int16`` + + - ``uint8`` + ``uint16`` => ``uint16`` + + - ``int8`` + ``int16`` => ``int16`` + + - ``int8`` + ``uint16`` => ``uint16`` (in numpy, the result is a + ``int32``) + + - ``uint16`` + ``int16`` => ``float`` (in numpy, the result is a + ``int32``) + +4. When one operand of a binary operation is a generic scalar + ``micropython`` variable, i.e., ``mp_obj_int``, or ``mp_obj_float``, + it will be converted to a linear array of length 1, and with the + smallest ``dtype`` that can accommodate the variable in question. + After that the broadcasting rules apply, as described in the section + `Iterating over two ndarrays simultaneously: + broadcasting <#Iterating_over_two_ndarrays_simultaneously:_broadcasting>`__ + +Upcasting is resolved in place, wherever it is required. Notable +examples can be found in +`ndarray_operators.c <https://github.com/v923z/micropython-ulab/blob/master/code/ndarray_operators.c>`__ + +Slicing and indexing +-------------------- + +An ``ndarray`` can be indexed with three types of objects: integer +scalars, slices, and another ``ndarray``, whose elements are either +integer scalars, or Booleans. Since slice and integer indices can be +thought of as modifications of the ``strides``, these indices return a +view of the ``ndarray``. This statement does not hold for ``ndarray`` +indices, and therefore, the return a copy of the array. + +Extending ulab +-------------- + +The ``user`` module is disabled by default, as can be seen from the last +couple of lines of +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__ + +.. code:: c + + // user-defined module + #ifndef ULAB_USER_MODULE + #define ULAB_USER_MODULE (0) + #endif + +The module contains a very simple function, ``user_dummy``, and this +function is bound to the module itself. In other words, even if the +module is enabled, one has to ``import``: + +.. code:: python + + + import ulab + from ulab import user + + user.dummy_function(2.5) + +which should just return 5.0. Even if ``numpy``-compatibility is +required (i.e., if most functions are bound at the top level to ``ulab`` +directly), having to ``import`` the module has a great advantage. +Namely, only the +`user.h <https://github.com/v923z/micropython-ulab/blob/master/code/user/user.h>`__ +and +`user.c <https://github.com/v923z/micropython-ulab/blob/master/code/user/user.c>`__ +files have to be modified, thus it should be relatively straightforward +to update your local copy from +`github <https://github.com/v923z/micropython-ulab/blob/master/>`__. + +Now, let us see, how we can add a more meaningful function. + +Creating a new ndarray +---------------------- + +In the `General comments <#General_comments>`__ sections we have seen +the type definition of an ``ndarray``. This structure can be generated +by means of a couple of functions listed in +`ndarray.c <https://github.com/v923z/micropython-ulab/blob/master/code/ndarray.c>`__. + +ndarray_new_ndarray +~~~~~~~~~~~~~~~~~~~ + +The ``ndarray_new_ndarray`` functions is called by all other +array-generating functions. It takes the number of dimensions, ``ndim``, +a ``uint8_t``, the ``shape``, a pointer to ``size_t``, the ``strides``, +a pointer to ``int32_t``, and ``dtype``, another ``uint8_t`` as its +arguments, and returns a new array with all entries initialised to 0. + +Assuming that ``ULAB_MAX_DIMS > 2``, a new dense array of dimension 3, +of ``shape`` (3, 4, 5), of ``strides`` (1000, 200, 10), and ``dtype`` +``uint16_t`` can be generated by the following instructions + +.. code:: c + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + shape[ULAB_MAX_DIMS - 1] = 5; + shape[ULAB_MAX_DIMS - 2] = 4; + shape[ULAB_MAX_DIMS - 3] = 3; + + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + strides[ULAB_MAX_DIMS - 1] = 10; + strides[ULAB_MAX_DIMS - 2] = 200; + strides[ULAB_MAX_DIMS - 3] = 1000; + + ndarray_obj_t *new_ndarray = ndarray_new_ndarray(3, shape, strides, NDARRAY_UINT16); + +ndarray_new_dense_ndarray +~~~~~~~~~~~~~~~~~~~~~~~~~ + +The functions simply calculates the ``strides`` from the ``shape``, and +calls ``ndarray_new_ndarray``. Assuming that ``ULAB_MAX_DIMS > 2``, a +new dense array of dimension 3, of ``shape`` (3, 4, 5), and ``dtype`` +``mp_float_t`` can be generated by the following instructions + +.. code:: c + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + shape[ULAB_MAX_DIMS - 1] = 5; + shape[ULAB_MAX_DIMS - 2] = 4; + shape[ULAB_MAX_DIMS - 3] = 3; + + ndarray_obj_t *new_ndarray = ndarray_new_dense_ndarray(3, shape, NDARRAY_FLOAT); + +ndarray_new_linear_array +~~~~~~~~~~~~~~~~~~~~~~~~ + +Since the dimensions of a linear array are known (1), the +``ndarray_new_linear_array`` takes the ``length``, a ``size_t``, and the +``dtype``, an ``uint8_t``. Internally, ``ndarray_new_linear_array`` +generates the ``shape`` array, and calls ``ndarray_new_dense_array`` +with ``ndim = 1``. + +A linear array of length 100, and ``dtype`` ``uint8`` could be created +by the function call + +.. code:: c + + ndarray_obj_t *new_ndarray = ndarray_new_linear_array(100, NDARRAY_UINT8) + +ndarray_new_ndarray_from_tuple +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This function takes a ``tuple``, which should hold the lengths of the +axes (in other words, the ``shape``), and the ``dtype``, and calls +internally ``ndarray_new_dense_array``. A new ``ndarray`` can be +generated by calling + +.. code:: c + + ndarray_obj_t *new_ndarray = ndarray_new_ndarray_from_tuple(shape, NDARRAY_FLOAT); + +where ``shape`` is a tuple. + +ndarray_new_view +~~~~~~~~~~~~~~~~ + +This function crates a *view*, and takes the source, an ``ndarray``, the +number of dimensions, an ``uint8_t``, the ``shape``, a pointer to +``size_t``, the ``strides``, a pointer to ``int32_t``, and the offset, +an ``int32_t`` as arguments. The offset is the number of bytes by which +the void ``array`` pointer is shifted. E.g., the ``python`` statement + +.. code:: python + + a = np.array([0, 1, 2, 3, 4, 5], dtype=uint8) + b = a[1::2] + +produces the array + +.. code:: python + + array([1, 3, 5], dtype=uint8) + +which holds its data at position ``x0 + 1``, if ``a``\ ’s pointer is at +``x0``. In this particular case, the offset is 1. + +The array ``b`` from the example above could be generated as + +.. code:: c + + size_t *shape = m_new(size_t, ULAB_MAX_DIMS); + shape[ULAB_MAX_DIMS - 1] = 3; + + int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS); + strides[ULAB_MAX_DIMS - 1] = 2; + + int32_t offset = 1; + uint8_t ndim = 1; + + ndarray_obj_t *new_ndarray = ndarray_new_view(ndarray_a, ndim, shape, strides, offset); + +ndarray_copy_array +~~~~~~~~~~~~~~~~~~ + +The ``ndarray_copy_array`` function can be used for copying the contents +of an array. Note that the target array has to be created beforehand. +E.g., a one-to-one copy can be gotten by + +.. code:: c + + ndarray_obj_t *new_ndarray = ndarray_new_ndarray(source->ndim, source->shape, source->strides, source->dtype); + ndarray_copy_array(source, new_ndarray); + +Note that the function cannot be used for forcing type conversion, i.e., +the input and output types must be identical, because the function +simply calls the ``memcpy`` function. On the other hand, the input and +output ``strides`` do not necessarily have to be equal. + +ndarray_copy_view +~~~~~~~~~~~~~~~~~ + +The ``ndarray_obj_t *new_ndarray = ...`` instruction can be saved by +calling the ``ndarray_copy_view`` function with the single ``source`` +argument. + +Accessing data in the ndarray +----------------------------- + +Having seen, how arrays can be generated and copied, it is time to look +at how the data in an ``ndarray`` can be accessed and modified. + +For starters, let us suppose that the object in question comes from the +user (i.e., via the ``micropython`` interface), First, we have to +acquire a pointer to the ``ndarray`` by calling + +.. code:: c + + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(object_in); + +If it is not clear, whether the object is an ``ndarray`` (e.g., if we +want to write a function that can take ``ndarray``\ s, and other +iterables as its argument), we find this out by evaluating + +.. code:: c + + mp_obj_is_type(object_in, &ulab_ndarray_type) + +which should return ``true``. Once the pointer is at our disposal, we +can get a pointer to the underlying numerical array as discussed +earlier, i.e., + +.. code:: c + + uint8_t *array = (uint8_t *)ndarray->array; + +If you need to find out the ``dtype`` of the array, you can get it by +accessing the ``dtype`` member of the ``ndarray``, i.e., + +.. code:: c + + ndarray->dtype + +should be equal to ``B``, ``b``, ``H``, ``h``, or ``f``. The size of a +single item is stored in the ``itemsize`` member. This number should be +equal to 1, if the ``dtype`` is ``B``, or ``b``, 2, if the ``dtype`` is +``H``, or ``h``, 4, if the ``dtype`` is ``f``, and 8 for ``d``. + +Boilerplate +----------- + +In the next section, we will construct a function that generates the +element-wise square of a dense array, otherwise, raises a ``TypeError`` +exception. Dense arrays can easily be iterated over, since we do not +have to care about the ``shape`` and the ``strides``. If the array is +sparse, the section `Iterating over elements of a +tensor <#Iterating-over-elements-of-a-tensor>`__ should contain hints as +to how the iteration can be implemented. + +The function is listed under +`user.c <https://github.com/v923z/micropython-ulab/tree/master/code/user/>`__. +The ``user`` module is bound to ``ulab`` in +`ulab.c <https://github.com/v923z/micropython-ulab/tree/master/code/ulab.c>`__ +in the lines + +.. code:: c + + #if ULAB_USER_MODULE + { MP_ROM_QSTR(MP_QSTR_user), MP_ROM_PTR(&ulab_user_module) }, + #endif + +which assumes that at the very end of +`ulab.h <https://github.com/v923z/micropython-ulab/tree/master/code/ulab.h>`__ +the + +.. code:: c + + // user-defined module + #ifndef ULAB_USER_MODULE + #define ULAB_USER_MODULE (1) + #endif + +constant has been set to 1. After compilation, you can call a particular +``user`` function in ``python`` by importing the module first, i.e., + +.. code:: python + + from ulab import numpy as np + from ulab import user + + user.some_function(...) + +This separation of user-defined functions from the rest of the code +ensures that the integrity of the main module and all its functions are +always preserved. Even in case of a catastrophic failure, you can +exclude the ``user`` module, and start over. + +And now the function: + +.. code:: c + + static mp_obj_t user_square(mp_obj_t arg) { + // the function takes a single dense ndarray, and calculates the + // element-wise square of its entries + + // raise a TypeError exception, if the input is not an ndarray + if(!mp_obj_is_type(arg, &ulab_ndarray_type)) { + mp_raise_TypeError(translate("input must be an ndarray")); + } + ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(arg); + + // make sure that the input is a dense array + if(!ndarray_is_dense(ndarray)) { + mp_raise_TypeError(translate("input must be a dense ndarray")); + } + + // if the input is a dense array, create `results` with the same number of + // dimensions, shape, and dtype + ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim, ndarray->shape, ndarray->dtype); + + // since in a dense array the iteration over the elements is trivial, we + // can cast the data arrays ndarray->array and results->array to the actual type + if(ndarray->dtype == NDARRAY_UINT8) { + uint8_t *array = (uint8_t *)ndarray->array; + uint8_t *rarray = (uint8_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } else if(ndarray->dtype == NDARRAY_INT8) { + int8_t *array = (int8_t *)ndarray->array; + int8_t *rarray = (int8_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } else if(ndarray->dtype == NDARRAY_UINT16) { + uint16_t *array = (uint16_t *)ndarray->array; + uint16_t *rarray = (uint16_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } else if(ndarray->dtype == NDARRAY_INT16) { + int16_t *array = (int16_t *)ndarray->array; + int16_t *rarray = (int16_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } else { // if we end up here, the dtype is NDARRAY_FLOAT + mp_float_t *array = (mp_float_t *)ndarray->array; + mp_float_t *rarray = (mp_float_t *)results->array; + for(size_t i=0; i < ndarray->len; i++, array++) { + *rarray++ = (*array) * (*array); + } + } + // at the end, return a micropython object + return MP_OBJ_FROM_PTR(results); + } + +To summarise, the steps for *implementing* a function are + +1. If necessary, inspect the type of the input object, which is always a + ``mp_obj_t`` object +2. If the input is an ``ndarray_obj_t``, acquire a pointer to it by + calling ``ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(arg);`` +3. Create a new array, or modify the existing one; get a pointer to the + data by calling ``uint8_t *array = (uint8_t *)ndarray->array;``, or + something equivalent +4. Once the new data have been calculated, return a ``micropython`` + object by calling ``MP_OBJ_FROM_PTR(...)``. + +The listing above contains the implementation of the function, but as +such, it cannot be called from ``python``: it still has to be bound to +the name space. This we do by first defining a function object in + +.. code:: c + + MP_DEFINE_CONST_FUN_OBJ_1(user_square_obj, user_square); + +``micropython`` defines a number of ``MP_DEFINE_CONST_FUN_OBJ_N`` macros +in +`obj.h <https://github.com/micropython/micropython/blob/master/py/obj.h>`__. +``N`` is always the number of arguments the function takes. We had a +function definition ``static mp_obj_t user_square(mp_obj_t arg)``, i.e., +we dealt with a single argument. + +Finally, we have to bind this function object in the globals table of +the ``user`` module: + +.. code:: c + + STATIC const mp_rom_map_elem_t ulab_user_globals_table[] = { + { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_user) }, + { MP_OBJ_NEW_QSTR(MP_QSTR_square), (mp_obj_t)&user_square_obj }, + }; + +Thus, the three steps required for the definition of a user-defined +function are + +1. The low-level implementation of the function itself +2. The definition of a function object by calling + MP_DEFINE_CONST_FUN_OBJ_N() +3. Binding this function object to the namespace in the + ``ulab_user_globals_table[]`` diff --git a/circuitpython/extmod/ulab/docs/manual/source/ulab-tricks.rst b/circuitpython/extmod/ulab/docs/manual/source/ulab-tricks.rst new file mode 100644 index 0000000..4c3802b --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/ulab-tricks.rst @@ -0,0 +1,268 @@ + +Tricks +====== + +This section of the book discusses a couple of tricks that can be +exploited to either speed up computations, or save on RAM. However, +there is probably no silver bullet, and you have to evaluate your code +in terms of execution speed (if the execution is time critical), or RAM +used. You should also keep in mind that, if a particular code snippet is +optimised on some hardware, there is no guarantee that on another piece +of hardware, you will get similar improvements. Hardware implementations +are vastly different. Some microcontrollers do not even have an FPU, so +you should not be surprised that you get significantly different +benchmarks. Just to underline this statement, you can study the +`collection of benchmarks <https://github.com/thiagofe/ulab_samples>`__. + +Use an ``ndarray``, if you can +------------------------------ + +Many functions in ``ulab`` are implemented in a universal fashion, +meaning that both generic ``micropython`` iterables, and ``ndarray``\ s +can be passed as an argument. E.g., both + +.. code:: python + + from ulab import numpy as np + + np.sum([1, 2, 3, 4, 5]) + +and + +.. code:: python + + from ulab import numpy as np + + a = np.array([1, 2, 3, 4, 5]) + np.sum(a) + +will return the ``micropython`` variable 15 as the result. Still, +``np.sum(a)`` is evaluated significantly faster, because in +``np.sum([1, 2, 3, 4, 5])``, the interpreter has to fetch 5 +``micropython`` variables, convert them to ``float``, and sum the +values, while the C type of ``a`` is known, thus the interpreter can +invoke a single ``for`` loop for the evaluation of the ``sum``. In the +``for`` loop, there are no function calls, the iteration simply walks +through the pointer holding the values of ``a``, and adds the values to +an accumulator. If the array ``a`` is already available, then you can +gain a factor of 3 in speed by calling ``sum`` on the array, instead of +using the list. Compared to the python implementation of the same +functionality, the speed-up is around 40 (again, this might depend on +the hardware). + +On the other hand, if the array is not available, then there is not much +point in converting the list to an ``ndarray`` and passing that to the +function. In fact, you should expect a slow-down: the constructor has to +iterate over the list elements, and has to convert them to a numerical +type. On top of that, it also has to reserve RAM for the ``ndarray``. + +Use a reasonable ``dtype`` +-------------------------- + +Just as in ``numpy``, the default ``dtype`` is ``float``. But this does +not mean that that is the most suitable one in all scenarios. If data +are streamed from an 8-bit ADC, and you only want to know the maximum, +or the sum, then it is quite reasonable to use ``uint8`` for the +``dtype``. Storing the same data in ``float`` array would cost 4 or 8 +times as much RAM, with absolutely no gain. Do not rely on the default +value of the constructor’s keyword argument, and choose one that fits! + +Beware the axis! +---------------- + +Whenever ``ulab`` iterates over multi-dimensional arrays, the outermost +loop is the first axis, then the second axis, and so on. E.g., when the +``sum`` of + +.. code:: python + + a = array([[1, 2, 3, 4], + [5, 6, 7, 8], + [9, 10, 11, 12]], dtype=uint8) + +is being calculated, first the data pointer walks along ``[1, 2, 3, 4]`` +(innermost loop, last axis), then is moved back to the position, where 5 +is stored (this is the nesting loop), and traverses ``[5, 6, 7, 8]``, +and so on. Moving the pointer back to 5 is more expensive, than moving +it along an axis, because the position of 5 has to be calculated, +whereas moving from 5 to 6 is simply an addition to the address. Thus, +while the matrix + +.. code:: python + + b = array([[1, 5, 9], + [2, 6, 10], + [3, 7, 11], + [4, 8, 12]], dtype=uint8) + +holds the same data as ``a``, the summation over the entries in ``b`` is +slower, because the pointer has to be re-wound three times, as opposed +to twice in ``a``. For small matrices the savings are not significant, +but you would definitely notice the difference, if you had + +:: + + a = array(range(2000)).reshape((2, 1000)) + b = array(range(2000)).reshape((1000, 2)) + +The moral is that, in order to improve on the execution speed, whenever +possible, you should try to make the last axis the longest. As a side +note, ``numpy`` can re-arrange its loops, and puts the longest axis in +the innermost loop. This is why the longest axis is sometimes referred +to as the fast axis. In ``ulab``, the order of the axes is fixed. + +Reduce the number of artifacts +------------------------------ + +Before showing a real-life example, let us suppose that we want to +interpolate uniformly sampled data, and the absolute magnitude is not +really important, we only care about the ratios between neighbouring +value. One way of achieving this is calling the ``interp`` functions. +However, we could just as well work with slices. + +.. code:: + + # code to be run in CPython + + a = array([0, 10, 2, 20, 4], dtype=np.uint8) + b = np.zeros(9, dtype=np.uint8) + + b[::2] = 2 * a + b[1::2] = a[:-1] + a[1:] + + b //= 2 + b + + + +.. parsed-literal:: + + array([ 0, 5, 10, 6, 2, 11, 20, 12, 4], dtype=uint8) + + + +``b`` now has values from ``a`` at every even position, and interpolates +the values on every odd position. If only the relative magnitudes are +important, then we can even save the division by 2, and we end up with + +.. code:: + + # code to be run in CPython + + a = array([0, 10, 2, 20, 4], dtype=np.uint8) + b = np.zeros(9, dtype=np.uint8) + + b[::2] = 2 * a + b[1::2] = a[:-1] + a[1:] + + b + + + +.. parsed-literal:: + + array([ 0, 10, 20, 12, 4, 22, 40, 24, 8], dtype=uint8) + + + +Importantly, we managed to keep the results in the smaller ``dtype``, +``uint8``. Now, while the two assignments above are terse and pythonic, +the code is not the most efficient: the right hand sides are compound +statements, generating intermediate results. To store them, RAM has to +be allocated. This takes time, and leads to memory fragmentation. Better +is to write out the assignments in 4 instructions: + +.. code:: + + # code to be run in CPython + + b = np.zeros(9, dtype=np.uint8) + + b[::2] = a + b[::2] += a + b[1::2] = a[:-1] + b[1::2] += a[1:] + + b + + + +.. parsed-literal:: + + array([ 0, 10, 20, 12, 4, 22, 40, 24, 8], dtype=uint8) + + + +The results are the same, but no extra RAM is allocated, except for the +views ``a[:-1]``, and ``a[1:]``, but those had to be created even in the +origin implementation. + +Upscaling images +~~~~~~~~~~~~~~~~ + +And now the example: there are low-resolution thermal cameras out there. +Low resolution might mean 8 by 8 pixels. Such a small number of pixels +is just not reasonable to plot, no matter how small the display is. If +you want to make the camera image a bit more pleasing, you can upscale +(stretch) it in both dimensions. This can be done exactly as we +up-scaled the linear array: + +.. code:: + + # code to be run in CPython + + b = np.zeros((15, 15), dtype=np.uint8) + + b[1::2,::2] = a[:-1,:] + b[1::2,::2] += a[1:, :] + b[1::2,::2] //= 2 + b[::,1::2] = a[::,:-1:2] + b[::,1::2] += a[::,2::2] + b[::,1::2] //= 2 +Up-scaling by larger numbers can be done in a similar fashion, you +simply have more assignments. + +There are cases, when one cannot do away with the intermediate results. +Two prominent cases are the ``where`` function, and indexing by means of +a Boolean array. E.g., in + +.. code:: + + # code to be run in CPython + + a = array([1, 2, 3, 4, 5]) + b = a[a < 4] + b + + + +.. parsed-literal:: + + array([1, 2, 3]) + + + +the expression ``a < 4`` produces the Boolean array, + +.. code:: + + # code to be run in CPython + + a < 4 + + + +.. parsed-literal:: + + array([ True, True, True, False, False]) + + + +If you repeatedly have such conditions in a loop, you might have to +peridically call the garbage collector to remove the Boolean arrays that +are used only once. + +.. code:: + + # code to be run in CPython + diff --git a/circuitpython/extmod/ulab/docs/manual/source/ulab-utils.rst b/circuitpython/extmod/ulab/docs/manual/source/ulab-utils.rst new file mode 100644 index 0000000..15cf978 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/manual/source/ulab-utils.rst @@ -0,0 +1,143 @@ + +ulab utilities +============== + +There might be cases, when the format of your data does not conform to +``ulab``, i.e., there is no obvious way to map the data to any of the +five supported ``dtype``\ s. A trivial example is an ADC or microphone +signal with 32-bit resolution. For such cases, ``ulab`` defines the +``utils`` module, which, at the moment, has four functions that are not +``numpy`` compatible, but which should ease interfacing ``ndarray``\ s +to peripheral devices. + +The ``utils`` module can be enabled by setting the +``ULAB_HAS_UTILS_MODULE`` constant to 1 in +`ulab.h <https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h>`__: + +.. code:: c + + #ifndef ULAB_HAS_UTILS_MODULE + #define ULAB_HAS_UTILS_MODULE (1) + #endif + +This still does not compile any functions into the firmware. You can add +a function by setting the corresponding pre-processor constant to 1. +E.g., + +.. code:: c + + #ifndef ULAB_UTILS_HAS_FROM_INT16_BUFFER + #define ULAB_UTILS_HAS_FROM_INT16_BUFFER (1) + #endif + +from_int32_buffer, from_uint32_buffer +------------------------------------- + +With the help of ``utils.from_int32_buffer``, and +``utils.from_uint32_buffer``, it is possible to convert 32-bit integer +buffers to ``ndarrays`` of float type. These functions have a syntax +similar to ``numpy.frombuffer``; they support the ``count=-1``, and +``offset=0`` keyword arguments. However, in addition, they also accept +``out=None``, and ``byteswap=False``. + +Here is an example without keyword arguments + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import utils + + a = bytearray([1, 1, 0, 0, 0, 0, 0, 255]) + print('a: ', a) + print() + print('unsigned integers: ', utils.from_uint32_buffer(a)) + + b = bytearray([1, 1, 0, 0, 0, 0, 0, 255]) + print('\nb: ', b) + print() + print('signed integers: ', utils.from_int32_buffer(b)) + +.. parsed-literal:: + + a: bytearray(b'\x01\x01\x00\x00\x00\x00\x00\xff') + + unsigned integers: array([257.0, 4278190080.000001], dtype=float64) + + b: bytearray(b'\x01\x01\x00\x00\x00\x00\x00\xff') + + signed integers: array([257.0, -16777216.0], dtype=float64) + + + + +The meaning of ``count``, and ``offset`` is similar to that in +``numpy.frombuffer``. ``count`` is the number of floats that will be +converted, while ``offset`` would discard the first ``offset`` number of +bytes from the buffer before the conversion. + +In the example above, repeated calls to either of the functions returns +a new ``ndarray``. You can save RAM by supplying the ``out`` keyword +argument with a pre-defined ``ndarray`` of sufficient size, in which +case the results will be inserted into the ``ndarray``. If the ``dtype`` +of ``out`` is not ``float``, a ``TypeError`` exception will be raised. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import utils + + a = np.array([1, 2], dtype=np.float) + b = bytearray([1, 0, 1, 0, 0, 1, 0, 1]) + print('b: ', b) + utils.from_uint32_buffer(b, out=a) + print('a: ', a) + +.. parsed-literal:: + + b: bytearray(b'\x01\x00\x01\x00\x00\x01\x00\x01') + a: array([65537.0, 16777472.0], dtype=float64) + + + + +Finally, since there is no guarantee that the endianness of a particular +peripheral device supplying the buffer is the same as that of the +microcontroller, ``from_(u)intbuffer`` allows a conversion via the +``byteswap`` keyword argument. + +.. code:: + + # code to be run in micropython + + from ulab import numpy as np + from ulab import utils + + a = bytearray([1, 0, 0, 0, 0, 0, 0, 1]) + print('a: ', a) + print('buffer without byteswapping: ', utils.from_uint32_buffer(a)) + print('buffer with byteswapping: ', utils.from_uint32_buffer(a, byteswap=True)) + +.. parsed-literal:: + + a: bytearray(b'\x01\x00\x00\x00\x00\x00\x00\x01') + buffer without byteswapping: array([1.0, 16777216.0], dtype=float64) + buffer with byteswapping: array([16777216.0, 1.0], dtype=float64) + + + + +from_int16_buffer, from_uint16_buffer +------------------------------------- + +These two functions are identical to ``utils.from_int32_buffer``, and +``utils.from_uint32_buffer``, with the exception that they convert +16-bit integers to floating point ``ndarray``\ s. + +.. code:: + + # code to be run in CPython + diff --git a/circuitpython/extmod/ulab/docs/numpy-fft.ipynb b/circuitpython/extmod/ulab/docs/numpy-fft.ipynb new file mode 100644 index 0000000..803c923 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/numpy-fft.ipynb @@ -0,0 +1,546 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-01T09:27:13.438054Z", + "start_time": "2020-05-01T09:27:13.191491Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:24:48.499467Z", + "start_time": "2022-01-07T18:24:48.488004Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2020-07-23T20:31:25.296014Z", + "start_time": "2020-07-23T20:31:25.265937Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# numpy.fft\n", + "\n", + "Functions related to Fourier transforms can be called by prepending them with `numpy.fft.`. The module defines the following two functions:\n", + "\n", + "1. [numpy.fft.fft](#fft)\n", + "1. [numpy.fft.ifft](#ifft)\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.fft.ifft.html\n", + "\n", + "## fft\n", + "\n", + "Since `ulab`'s `ndarray` does not support complex numbers, the invocation of the Fourier transform differs from that in `numpy`. In `numpy`, you can simply pass an array or iterable to the function, and it will be treated as a complex array:" + ] + }, + { + "cell_type": "code", + "execution_count": 341, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-17T17:33:38.487729Z", + "start_time": "2019-10-17T17:33:38.473515Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([20.+0.j, 0.+0.j, -4.+4.j, 0.+0.j, -4.+0.j, 0.+0.j, -4.-4.j,\n", + " 0.+0.j])" + ] + }, + "execution_count": 341, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "fft.fft([1, 2, 3, 4, 1, 2, 3, 4])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**WARNING:** The array returned is also complex, i.e., the real and imaginary components are cast together. In `ulab`, the real and imaginary parts are treated separately: you have to pass two `ndarray`s to the function, although, the second argument is optional, in which case the imaginary part is assumed to be zero.\n", + "\n", + "**WARNING:** The function, as opposed to `numpy`, returns a 2-tuple, whose elements are two `ndarray`s, holding the real and imaginary parts of the transform separately. " + ] + }, + { + "cell_type": "code", + "execution_count": 114, + "metadata": { + "ExecuteTime": { + "end_time": "2020-02-16T18:38:07.294862Z", + "start_time": "2020-02-16T18:38:07.233842Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "real part:\t array([5119.996, -5.004663, -5.004798, ..., -5.005482, -5.005643, -5.006577], dtype=float)\r\n", + "\r\n", + "imaginary part:\t array([0.0, 1631.333, 815.659, ..., -543.764, -815.6588, -1631.333], dtype=float)\r\n", + "\r\n", + "real part:\t array([5119.996, -5.004663, -5.004798, ..., -5.005482, -5.005643, -5.006577], dtype=float)\r\n", + "\r\n", + "imaginary part:\t array([0.0, 1631.333, 815.659, ..., -543.764, -815.6588, -1631.333], dtype=float)\r\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.linspace(0, 10, num=1024)\n", + "y = np.sin(x)\n", + "z = np.zeros(len(x))\n", + "\n", + "a, b = np.fft.fft(x)\n", + "print('real part:\\t', a)\n", + "print('\\nimaginary part:\\t', b)\n", + "\n", + "c, d = np.fft.fft(x, z)\n", + "print('\\nreal part:\\t', c)\n", + "print('\\nimaginary part:\\t', d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ulab with complex support\n", + "\n", + "If the `ULAB_SUPPORTS_COMPLEX`, and `ULAB_FFT_IS_NUMPY_COMPATIBLE` pre-processor constants are set to 1 in [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h) as \n", + "\n", + "```c\n", + "// Adds support for complex ndarrays\n", + "#ifndef ULAB_SUPPORTS_COMPLEX\n", + "#define ULAB_SUPPORTS_COMPLEX (1)\n", + "#endif\n", + "```\n", + "\n", + "```c\n", + "#ifndef ULAB_FFT_IS_NUMPY_COMPATIBLE\n", + "#define ULAB_FFT_IS_NUMPY_COMPATIBLE (1)\n", + "#endif\n", + "```\n", + "then the FFT routine will behave in a `numpy`-compatible way: the single input array can either be real, in which case the imaginary part is assumed to be zero, or complex. The output is also complex. \n", + "\n", + "While `numpy`-compatibility might be a desired feature, it has one side effect, namely, the FFT routine consumes approx. 50% more RAM. The reason for this lies in the implementation details." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ifft\n", + "\n", + "The above-mentioned rules apply to the inverse Fourier transform. The inverse is also normalised by `N`, the number of elements, as is customary in `numpy`. With the normalisation, we can ascertain that the inverse of the transform is equal to the original array." + ] + }, + { + "cell_type": "code", + "execution_count": 459, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-19T13:08:17.647416Z", + "start_time": "2019-10-19T13:08:17.597456Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "original vector:\t array([0.0, 0.009775016, 0.0195491, ..., -0.5275068, -0.5357859, -0.5440139], dtype=float)\n", + "\n", + "real part of inverse:\t array([-2.980232e-08, 0.0097754, 0.0195494, ..., -0.5275064, -0.5357857, -0.5440133], dtype=float)\n", + "\n", + "imaginary part of inverse:\t array([-2.980232e-08, -1.451171e-07, 3.693752e-08, ..., 6.44871e-08, 9.34986e-08, 2.18336e-07], dtype=float)\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.linspace(0, 10, num=1024)\n", + "y = np.sin(x)\n", + "\n", + "a, b = np.fft.fft(y)\n", + "\n", + "print('original vector:\\t', y)\n", + "\n", + "y, z = np.fft.ifft(a, b)\n", + "# the real part should be equal to y\n", + "print('\\nreal part of inverse:\\t', y)\n", + "# the imaginary part should be equal to zero\n", + "print('\\nimaginary part of inverse:\\t', z)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that unlike in `numpy`, the length of the array on which the Fourier transform is carried out must be a power of 2. If this is not the case, the function raises a `ValueError` exception." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ulab with complex support\n", + "\n", + "The `fft.ifft` function can also be made `numpy`-compatible by setting the `ULAB_SUPPORTS_COMPLEX`, and `ULAB_FFT_IS_NUMPY_COMPATIBLE` pre-processor constants to 1." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computation and storage costs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### RAM\n", + "\n", + "The FFT routine of `ulab` calculates the transform in place. This means that beyond reserving space for the two `ndarray`s that will be returned (the computation uses these two as intermediate storage space), only a handful of temporary variables, all floats or 32-bit integers, are required. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Speed of FFTs\n", + "\n", + "A comment on the speed: a 1024-point transform implemented in python would cost around 90 ms, and 13 ms in assembly, if the code runs on the pyboard, v.1.1. You can gain a factor of four by moving to the D series \n", + "https://github.com/peterhinch/micropython-fourier/blob/master/README.md#8-performance. " + ] + }, + { + "cell_type": "code", + "execution_count": 494, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-19T13:25:40.540913Z", + "start_time": "2019-10-19T13:25:40.509598Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "execution time: 1985 us\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.linspace(0, 10, num=1024)\n", + "y = np.sin(x)\n", + "\n", + "@timeit\n", + "def np_fft(y):\n", + " return np.fft.fft(y)\n", + "\n", + "a, b = np_fft(y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The C implementation runs in less than 2 ms on the pyboard (we have just measured that), and has been reported to run in under 0.8 ms on the D series board. That is an improvement of at least a factor of four. " + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/numpy-functions.ipynb b/circuitpython/extmod/ulab/docs/numpy-functions.ipynb new file mode 100644 index 0000000..f115a41 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/numpy-functions.ipynb @@ -0,0 +1,2393 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-02-13T08:28:06.727371Z", + "start_time": "2021-02-13T08:28:04.925338Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:45:28.079350Z", + "start_time": "2022-01-07T19:45:28.073911Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:45:28.654136Z", + "start_time": "2022-01-07T19:45:28.634610Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../micropython/ports/unix/micropython-2\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Numpy functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This section of the manual discusses those functions that were adapted from `numpy`. Starred functions accept complex arrays as arguments, if the firmware was compiled with complex support.\n", + "\n", + "1. [numpy.all*](#all)\n", + "1. [numpy.any*](#any)\n", + "1. [numpy.argmax](#argmax)\n", + "1. [numpy.argmin](#argmin)\n", + "1. [numpy.argsort](#argsort)\n", + "1. [numpy.clip](#clip)\n", + "1. [numpy.compress*](#compress)\n", + "1. [numpy.conjugate*](#conjugate)\n", + "1. [numpy.convolve*](#convolve)\n", + "1. [numpy.diff](#diff)\n", + "1. [numpy.dot](#dot)\n", + "1. [numpy.equal](#equal)\n", + "1. [numpy.flip*](#flip)\n", + "1. [numpy.imag*](#imag)\n", + "1. [numpy.interp](#interp)\n", + "1. [numpy.isfinite](#isfinite)\n", + "1. [numpy.isinf](#isinf)\n", + "1. [numpy.max](#max)\n", + "1. [numpy.maximum](#maximum)\n", + "1. [numpy.mean](#mean)\n", + "1. [numpy.median](#median)\n", + "1. [numpy.min](#min)\n", + "1. [numpy.minimum](#minimum)\n", + "1. [numpy.not_equal](#equal)\n", + "1. [numpy.polyfit](#polyfit)\n", + "1. [numpy.polyval](#polyval)\n", + "1. [numpy.real*](#real)\n", + "1. [numpy.roll](#roll)\n", + "1. [numpy.sort](#sort)\n", + "1. [numpy.sort_complex*](#sort_complex)\n", + "1. [numpy.std](#std)\n", + "1. [numpy.sum](#sum)\n", + "1. [numpy.trace](#trace)\n", + "1. [numpy.trapz](#trapz)\n", + "1. [numpy.where](#where)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## all\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.all.html\n", + "\n", + "The function takes one positional, and one keyword argument, the `axis`, with a default value of `None`, and tests, whether *all* array elements along the given axis evaluate to `True`. If the keyword argument is `None`, the flattened array is inspected. \n", + "\n", + "Elements of an array evaluate to `True`, if they are not equal to zero, or the Boolean `False`. The return value if a Boolean `ndarray`.\n", + "\n", + "If the firmware was compiled with complex support, the function can accept complex arrays." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2021-02-08T16:54:57.117630Z", + "start_time": "2021-02-08T16:54:57.105337Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([[0.0, 1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0, 7.0],\n", + " [8.0, 9.0, 10.0, 11.0]], dtype=float64)\n", + "\n", + "all of the flattened array:\n", + " False\n", + "\n", + "all of a along 0th axis:\n", + " array([False, True, True, True], dtype=bool)\n", + "\n", + "all of a along 1st axis:\n", + " array([False, True, True], dtype=bool)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(12)).reshape((3, 4))\n", + "\n", + "print('\\na:\\n', a)\n", + "\n", + "b = np.all(a)\n", + "print('\\nall of the flattened array:\\n', b)\n", + "\n", + "c = np.all(a, axis=0)\n", + "print('\\nall of a along 0th axis:\\n', c)\n", + "\n", + "d = np.all(a, axis=1)\n", + "print('\\nall of a along 1st axis:\\n', d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## any\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.any.html\n", + "\n", + "The function takes one positional, and one keyword argument, the `axis`, with a default value of `None`, and tests, whether *any* array element along the given axis evaluates to `True`. If the keyword argument is `None`, the flattened array is inspected. \n", + "\n", + "Elements of an array evaluate to `True`, if they are not equal to zero, or the Boolean `False`. The return value if a Boolean `ndarray`.\n", + "\n", + "If the firmware was compiled with complex support, the function can accept complex arrays." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2021-02-08T16:54:14.704132Z", + "start_time": "2021-02-08T16:54:14.693700Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([[0.0, 1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0, 7.0],\n", + " [8.0, 9.0, 10.0, 11.0]], dtype=float64)\n", + "\n", + "any of the flattened array:\n", + " True\n", + "\n", + "any of a along 0th axis:\n", + " array([True, True, True, True], dtype=bool)\n", + "\n", + "any of a along 1st axis:\n", + " array([True, True, True], dtype=bool)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(12)).reshape((3, 4))\n", + "\n", + "print('\\na:\\n', a)\n", + "\n", + "b = np.any(a)\n", + "print('\\nany of the flattened array:\\n', b)\n", + "\n", + "c = np.any(a, axis=0)\n", + "print('\\nany of a along 0th axis:\\n', c)\n", + "\n", + "d = np.any(a, axis=1)\n", + "print('\\nany of a along 1st axis:\\n', d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## argmax\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html\n", + "\n", + "See [numpy.max](#max)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## argmin\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmin.html\n", + "\n", + "See [numpy.max](#max)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## argsort\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.argsort.html\n", + "\n", + "Similarly to [sort](#sort), `argsort` takes a positional, and a keyword argument, and returns an unsigned short index array of type `ndarray` with the same dimensions as the input, or, if `axis=None`, as a row vector with length equal to the number of elements in the input (i.e., the flattened array). The indices in the output sort the input in ascending order. The routine in `argsort` is the same as in `sort`, therefore, the comments on computational expenses (time and RAM) also apply. In particular, since no copy of the original data is required, virtually no RAM beyond the output array is used. \n", + "\n", + "Since the underlying container of the output array is of type `uint16_t`, neither of the output dimensions should be larger than 65535. If that happens to be the case, the function will bail out with a `ValueError`." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:33:33.292717Z", + "start_time": "2021-01-13T16:33:33.280144Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([[1.0, 12.0, 3.0, 0.0],\n", + " [5.0, 3.0, 4.0, 1.0],\n", + " [9.0, 11.0, 1.0, 8.0],\n", + " [7.0, 10.0, 0.0, 1.0]], dtype=float64)\n", + "\n", + "a sorted along vertical axis:\n", + " array([[0, 1, 3, 0],\n", + " [1, 3, 2, 1],\n", + " [3, 2, 0, 3],\n", + " [2, 0, 1, 2]], dtype=uint16)\n", + "\n", + "a sorted along horizontal axis:\n", + " array([[3, 0, 2, 1],\n", + " [3, 1, 2, 0],\n", + " [2, 3, 0, 1],\n", + " [2, 3, 0, 1]], dtype=uint16)\n", + "\n", + "Traceback (most recent call last):\n", + " File \"/dev/shm/micropython.py\", line 12, in <module>\n", + "NotImplementedError: argsort is not implemented for flattened arrays\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.float)\n", + "print('\\na:\\n', a)\n", + "b = np.argsort(a, axis=0)\n", + "print('\\na sorted along vertical axis:\\n', b)\n", + "\n", + "c = np.argsort(a, axis=1)\n", + "print('\\na sorted along horizontal axis:\\n', c)\n", + "\n", + "c = np.argsort(a, axis=None)\n", + "print('\\nflattened a sorted:\\n', c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since during the sorting, only the indices are shuffled, `argsort` does not modify the input array, as one can verify this by the following example:" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:34:48.446211Z", + "start_time": "2021-01-13T16:34:48.424276Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([0, 5, 1, 3, 2, 4], dtype=uint8)\n", + "\n", + "sorting indices:\n", + " array([0, 2, 4, 3, 5, 1], dtype=uint16)\n", + "\n", + "the original array:\n", + " array([0, 5, 1, 3, 2, 4], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([0, 5, 1, 3, 2, 4], dtype=np.uint8)\n", + "print('\\na:\\n', a)\n", + "b = np.argsort(a, axis=0)\n", + "print('\\nsorting indices:\\n', b)\n", + "print('\\nthe original array:\\n', a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## clip\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.clip.html\n", + "\n", + "Clips an array, i.e., values that are outside of an interval are clipped to the interval edges. The function is equivalent to `maximum(a_min, minimum(a, a_max))` broadcasting takes place exactly as in [minimum](#minimum). If the arrays are of different `dtype`, the output is upcast as in [Binary operators](#Binary-operators)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:22:14.147310Z", + "start_time": "2021-01-08T13:22:14.123961Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "clipped:\t array([3, 3, 3, 3, 4, 5, 6, 7, 7], dtype=uint8)\n", + "\n", + "a:\t\t array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "b:\t\t array([3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0], dtype=float64)\n", + "clipped:\t array([3.0, 3.0, 3.0, 3.0, 4.0, 5.0, 6.0, 7.0, 7.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9), dtype=np.uint8)\n", + "print('a:\\t\\t', a)\n", + "print('clipped:\\t', np.clip(a, 3, 7))\n", + "\n", + "b = 3 * np.ones(len(a), dtype=np.float)\n", + "print('\\na:\\t\\t', a)\n", + "print('b:\\t\\t', b)\n", + "print('clipped:\\t', np.clip(a, b, 7))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## compress\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.compress.html\n", + "\n", + "The function returns selected slices of an array along given axis. If the axis keyword is `None`, the flattened array is used.\n", + "\n", + "If the firmware was compiled with complex support, the function can accept complex arguments." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:51:44.994323Z", + "start_time": "2022-01-07T19:51:44.978185Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[0.0, 1.0, 2.0],\n", + " [3.0, 4.0, 5.0]], dtype=float64)\n", + "\n", + "compress(a):\n", + " array([[3.0, 4.0, 5.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(6)).reshape((2, 3))\n", + "\n", + "print('a:\\n', a)\n", + "print('\\ncompress(a):\\n', np.compress([0, 1], a, axis=0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## conjugate\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.conjugate.html\n", + "\n", + "If the firmware was compiled with complex support, the function calculates the complex conjugate of the input array. If the input array is of real `dtype`, then the output is simply a copy, preserving the `dtype`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:30:53.394539Z", + "start_time": "2022-01-07T19:30:53.374737Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([1, 2, 3, 4], dtype=uint8)\n", + "conjugate(a):\t array([1, 2, 3, 4], dtype=uint8)\n", + "\n", + "b:\t\t array([1.0+1.0j, 2.0-2.0j, 3.0+3.0j, 4.0-4.0j], dtype=complex)\n", + "conjugate(b):\t array([1.0-1.0j, 2.0+2.0j, 3.0-3.0j, 4.0+4.0j], dtype=complex)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4], dtype=np.uint8)\n", + "b = np.array([1+1j, 2-2j, 3+3j, 4-4j], dtype=np.complex)\n", + "\n", + "print('a:\\t\\t', a)\n", + "print('conjugate(a):\\t', np.conjugate(a))\n", + "print()\n", + "print('b:\\t\\t', b)\n", + "print('conjugate(b):\\t', np.conjugate(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## convolve\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.convolve.html\n", + "\n", + "Returns the discrete, linear convolution of two one-dimensional arrays.\n", + "\n", + "Only the ``full`` mode is supported, and the ``mode`` named parameter is not accepted. Note that all other modes can be had by slicing a ``full`` result.\n", + "\n", + "If the firmware was compiled with complex support, the function can accept complex arrays." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T15:57:39.028884Z", + "start_time": "2021-01-13T15:57:39.008749Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([1.0, 12.0, 123.0, 1230.0, 2300.0, 3000.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.array((1, 2, 3))\n", + "y = np.array((1, 10, 100, 1000))\n", + "\n", + "print(np.convolve(x, y))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## diff\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.diff.html\n", + "\n", + "The `diff` function returns the numerical derivative of the forward scheme, or more accurately, the differences of an `ndarray` along a given axis. The order of derivative can be stipulated with the `n` keyword argument, which should be between 0, and 9. Default is 1. If higher order derivatives are required, they can be gotten by repeated calls to the function. The `axis` keyword argument should be -1 (last axis, in `ulab` equivalent to the second axis, and this also happens to be the default value), 0, or 1. \n", + "\n", + "Beyond the output array, the function requires only a couple of bytes of extra RAM for the differentiation stencil. (The stencil is an `int8` array, one byte longer than `n`. This also explains, why the highest order is 9: the coefficients of a ninth-order stencil all fit in signed bytes, while 10 would require `int16`.) Note that as usual in numerical differentiation (and also in `numpy`), the length of the respective axis will be reduced by `n` after the operation. If `n` is larger than, or equal to the length of the axis, an empty array will be returned.\n", + "\n", + "**WARNING**: the `diff` function does not implement the `prepend` and `append` keywords that can be found in `numpy`. " + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-14T16:06:27.468909Z", + "start_time": "2021-01-14T16:06:27.439067Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([0, 1, 2, 10, 4, 5, 6, 7, 8], dtype=uint8)\n", + "\n", + "first derivative:\n", + " array([1, 1, 8, 250, 1, 1, 1, 1], dtype=uint8)\n", + "\n", + "second derivative:\n", + " array([0, 249, 14, 249, 0, 0, 0], dtype=uint8)\n", + "\n", + "c:\n", + " array([[1.0, 2.0, 3.0, 4.0],\n", + " [4.0, 3.0, 2.0, 1.0],\n", + " [1.0, 4.0, 9.0, 16.0],\n", + " [0.0, 0.0, 0.0, 0.0]], dtype=float64)\n", + "\n", + "first derivative, first axis:\n", + " array([[3.0, 1.0, -1.0, -3.0],\n", + " [-3.0, 1.0, 7.0, 15.0],\n", + " [-1.0, -4.0, -9.0, -16.0]], dtype=float64)\n", + "\n", + "first derivative, second axis:\n", + " array([[1.0, 1.0, 1.0],\n", + " [-1.0, -1.0, -1.0],\n", + " [3.0, 5.0, 7.0],\n", + " [0.0, 0.0, 0.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9), dtype=np.uint8)\n", + "a[3] = 10\n", + "print('a:\\n', a)\n", + "\n", + "print('\\nfirst derivative:\\n', np.diff(a, n=1))\n", + "print('\\nsecond derivative:\\n', np.diff(a, n=2))\n", + "\n", + "c = np.array([[1, 2, 3, 4], [4, 3, 2, 1], [1, 4, 9, 16], [0, 0, 0, 0]])\n", + "print('\\nc:\\n', c)\n", + "print('\\nfirst derivative, first axis:\\n', np.diff(c, axis=0))\n", + "print('\\nfirst derivative, second axis:\\n', np.diff(c, axis=1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## dot\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html\n", + "\n", + "\n", + "**WARNING:** numpy applies upcasting rules for the multiplication of matrices, while `ulab` simply returns a float matrix. \n", + "\n", + "Once you can invert a matrix, you might want to know, whether the inversion is correct. You can simply take the original matrix and its inverse, and multiply them by calling the `dot` function, which takes the two matrices as its arguments. If the matrix dimensions do not match, the function raises a `ValueError`. The result of the multiplication is expected to be the unit matrix, which is demonstrated below." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2021-02-13T08:32:09.139378Z", + "start_time": "2021-02-13T08:32:09.122083Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "m:\n", + " array([[1, 2, 3],\n", + " [4, 5, 6],\n", + " [7, 10, 9]], dtype=uint8)\n", + "\n", + "m^-1:\n", + " array([[-1.25, 1.0, -0.25],\n", + " [0.4999999999999998, -1.0, 0.5],\n", + " [0.4166666666666668, 0.3333333333333333, -0.25]], dtype=float64)\n", + "\n", + "m*m^-1:\n", + " array([[1.0, 0.0, 0.0],\n", + " [4.440892098500626e-16, 1.0, 0.0],\n", + " [8.881784197001252e-16, 0.0, 1.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "m = np.array([[1, 2, 3], [4, 5, 6], [7, 10, 9]], dtype=np.uint8)\n", + "n = np.linalg.inv(m)\n", + "print(\"m:\\n\", m)\n", + "print(\"\\nm^-1:\\n\", n)\n", + "# this should be the unit matrix\n", + "print(\"\\nm*m^-1:\\n\", np.dot(m, n))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that for matrix multiplication you don't necessarily need square matrices, it is enough, if their dimensions are compatible (i.e., the the left-hand-side matrix has as many columns, as does the right-hand-side matrix rows):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2021-02-13T08:33:07.630825Z", + "start_time": "2021-02-13T08:33:07.608260Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([[1, 2, 3, 4],\n", + " [5, 6, 7, 8]], dtype=uint8)\n", + "array([[1, 2],\n", + " [3, 4],\n", + " [5, 6],\n", + " [7, 8]], dtype=uint8)\n", + "array([[50.0, 60.0],\n", + " [114.0, 140.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "m = np.array([[1, 2, 3, 4], [5, 6, 7, 8]], dtype=np.uint8)\n", + "n = np.array([[1, 2], [3, 4], [5, 6], [7, 8]], dtype=np.uint8)\n", + "print(m)\n", + "print(n)\n", + "print(np.dot(m, n))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## equal\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.equal.html\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.not_equal.html\n", + "\n", + "In `micropython`, equality of arrays or scalars can be established by utilising the `==`, `!=`, `<`, `>`, `<=`, or `=>` binary operators. In `circuitpython`, `==` and `!=` will produce unexpected results. In order to avoid this discrepancy, and to maintain compatibility with `numpy`, `ulab` implements the `equal` and `not_equal` operators that return the same results, irrespective of the `python` implementation.\n", + "\n", + "These two functions take two `ndarray`s, or scalars as their arguments. No keyword arguments are implemented." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T14:22:13.990898Z", + "start_time": "2021-01-08T14:22:13.941896Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "b: array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], dtype=float64)\n", + "\n", + "a == b: array([True, False, False, False, False, False, False, False, False], dtype=bool)\n", + "a != b: array([False, True, True, True, True, True, True, True, True], dtype=bool)\n", + "a == 2: array([False, False, True, False, False, False, False, False, False], dtype=bool)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9))\n", + "b = np.zeros(9)\n", + "\n", + "print('a: ', a)\n", + "print('b: ', b)\n", + "print('\\na == b: ', np.equal(a, b))\n", + "print('a != b: ', np.not_equal(a, b))\n", + "\n", + "# comparison with scalars\n", + "print('a == 2: ', np.equal(a, 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## flip\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.flip.html\n", + "\n", + "The `flip` function takes one positional, an `ndarray`, and one keyword argument, `axis = None`, and reverses the order of elements along the given axis. If the keyword argument is `None`, the matrix' entries are flipped along all axes. `flip` returns a new copy of the array.\n", + "\n", + "If the firmware was compiled with complex support, the function can accept complex arrays." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:25:08.425583Z", + "start_time": "2021-01-13T16:25:08.407004Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: \t array([1.0, 2.0, 3.0, 4.0, 5.0], dtype=float64)\n", + "a flipped:\t array([5.0, 4.0, 3.0, 2.0, 1.0], dtype=float64)\n", + "\n", + "a flipped horizontally\n", + " array([[3, 2, 1],\n", + " [6, 5, 4],\n", + " [9, 8, 7]], dtype=uint8)\n", + "\n", + "a flipped vertically\n", + " array([[7, 8, 9],\n", + " [4, 5, 6],\n", + " [1, 2, 3]], dtype=uint8)\n", + "\n", + "a flipped horizontally+vertically\n", + " array([9, 8, 7, 6, 5, 4, 3, 2, 1], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5])\n", + "print(\"a: \\t\", a)\n", + "print(\"a flipped:\\t\", np.flip(a))\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.uint8)\n", + "print(\"\\na flipped horizontally\\n\", np.flip(a, axis=1))\n", + "print(\"\\na flipped vertically\\n\", np.flip(a, axis=0))\n", + "print(\"\\na flipped horizontally+vertically\\n\", np.flip(a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## imag\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.imag.html\n", + "\n", + "The `imag` function returns the imaginary part of an array, or scalar. It cannot accept a generic iterable as its argument. The function is defined only, if the firmware was compiled with complex support." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:26:42.901258Z", + "start_time": "2022-01-07T19:26:42.880755Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([1, 2, 3], dtype=uint16)\n", + "imag(a):\t array([0, 0, 0], dtype=uint16)\n", + "\n", + "b:\t\t array([1.0+0.0j, 2.0+1.0j, 3.0-1.0j], dtype=complex)\n", + "imag(b):\t array([0.0, 1.0, -1.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3], dtype=np.uint16)\n", + "print(\"a:\\t\\t\", a)\n", + "print(\"imag(a):\\t\", np.imag(a))\n", + "\n", + "b = np.array([1, 2+1j, 3-1j], dtype=np.complex)\n", + "print(\"\\nb:\\t\\t\", b)\n", + "print(\"imag(b):\\t\", np.imag(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## interp\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/numpy.interp\n", + "\n", + "The `interp` function returns the linearly interpolated values of a one-dimensional numerical array. It requires three positional arguments,`x`, at which the interpolated values are evaluated, `xp`, the array\n", + "of the independent data variable, and `fp`, the array of the dependent values of the data. `xp` must be a monotonically increasing sequence of numbers.\n", + "\n", + "Two keyword arguments, `left`, and `right` can also be supplied; these determine the return values, if `x < xp[0]`, and `x > xp[-1]`, respectively. If these arguments are not supplied, `left`, and `right` default to `fp[0]`, and `fp[-1]`, respectively." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:00:43.505722Z", + "start_time": "2021-01-13T16:00:43.489060Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([0.8, 1.8, 2.8, 3.8, 4.8], dtype=float64)\n", + "array([1.0, 1.8, 2.8, 4.6, 5.0], dtype=float64)\n", + "array([0.0, 1.8, 2.8, 4.6, 5.0], dtype=float64)\n", + "array([1.0, 1.8, 2.8, 4.6, 10.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.array([1, 2, 3, 4, 5]) - 0.2\n", + "xp = np.array([1, 2, 3, 4])\n", + "fp = np.array([1, 2, 3, 5])\n", + "\n", + "print(x)\n", + "print(np.interp(x, xp, fp))\n", + "print(np.interp(x, xp, fp, left=0.0))\n", + "print(np.interp(x, xp, fp, right=10.0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## isfinite\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.isfinite.html\n", + "\n", + "Returns a Boolean array of the same shape as the input, or a `True/False`, if the input is a scalar. In the return value, all elements are `True` at positions, where the input value was finite. Integer types are automatically finite, therefore, if the input is of integer type, the output will be the `True` tensor." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-29T21:34:42.026689Z", + "start_time": "2021-01-29T21:34:42.010935Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "isfinite(0): True\n", + "\n", + "====================\n", + "a:\n", + " array([1.0, 2.0, nan], dtype=float64)\n", + "\n", + "isfinite(a):\n", + " array([True, True, False], dtype=bool)\n", + "\n", + "====================\n", + "b:\n", + " array([1.0, 2.0, inf], dtype=float64)\n", + "\n", + "isfinite(b):\n", + " array([True, True, False], dtype=bool)\n", + "\n", + "====================\n", + "c:\n", + " array([1, 2, 3], dtype=uint16)\n", + "\n", + "isfinite(c):\n", + " array([True, True, True], dtype=bool)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "print('isfinite(0): ', np.isfinite(0))\n", + "\n", + "a = np.array([1, 2, np.nan])\n", + "print('\\n' + '='*20)\n", + "print('a:\\n', a)\n", + "print('\\nisfinite(a):\\n', np.isfinite(a))\n", + "\n", + "b = np.array([1, 2, np.inf])\n", + "print('\\n' + '='*20)\n", + "print('b:\\n', b)\n", + "print('\\nisfinite(b):\\n', np.isfinite(b))\n", + "\n", + "c = np.array([1, 2, 3], dtype=np.uint16)\n", + "print('\\n' + '='*20)\n", + "print('c:\\n', c)\n", + "print('\\nisfinite(c):\\n', np.isfinite(c))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## isinf\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.isinf.html\n", + "\n", + "Similar to [isfinite](#isfinite), but the output is `True` at positions, where the input is infinite. Integer types return the `False` tensor." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-29T21:35:21.938514Z", + "start_time": "2021-01-29T21:35:21.923741Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "isinf(0): False\n", + "\n", + "====================\n", + "a:\n", + " array([1.0, 2.0, nan], dtype=float64)\n", + "\n", + "isinf(a):\n", + " array([False, False, False], dtype=bool)\n", + "\n", + "====================\n", + "b:\n", + " array([1.0, 2.0, inf], dtype=float64)\n", + "\n", + "isinf(b):\n", + " array([False, False, True], dtype=bool)\n", + "\n", + "====================\n", + "c:\n", + " array([1, 2, 3], dtype=uint16)\n", + "\n", + "isinf(c):\n", + " array([False, False, False], dtype=bool)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "print('isinf(0): ', np.isinf(0))\n", + "\n", + "a = np.array([1, 2, np.nan])\n", + "print('\\n' + '='*20)\n", + "print('a:\\n', a)\n", + "print('\\nisinf(a):\\n', np.isinf(a))\n", + "\n", + "b = np.array([1, 2, np.inf])\n", + "print('\\n' + '='*20)\n", + "print('b:\\n', b)\n", + "print('\\nisinf(b):\\n', np.isinf(b))\n", + "\n", + "c = np.array([1, 2, 3], dtype=np.uint16)\n", + "print('\\n' + '='*20)\n", + "print('c:\\n', c)\n", + "print('\\nisinf(c):\\n', np.isinf(c))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## mean\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html\n", + "\n", + "If the axis keyword is not specified, it assumes the default value of `None`, and returns the result of the computation for the flattened array. Otherwise, the calculation is along the given axis." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:15:39.921212Z", + "start_time": "2021-01-13T16:15:39.908217Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: \n", + " array([[1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0],\n", + " [7.0, 8.0, 9.0]], dtype=float64)\n", + "mean, flat: 5.0\n", + "mean, horizontal: array([2.0, 5.0, 8.0], dtype=float64)\n", + "mean, vertical: array([4.0, 5.0, 6.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n", + "print('a: \\n', a)\n", + "print('mean, flat: ', np.mean(a))\n", + "print('mean, horizontal: ', np.mean(a, axis=1))\n", + "print('mean, vertical: ', np.mean(a, axis=0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## max\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.max.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.min.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmin.html\n", + "\n", + "**WARNING:** Difference to `numpy`: the `out` keyword argument is not implemented.\n", + "\n", + "These functions follow the same pattern, and work with generic iterables, and `ndarray`s. `min`, and `max` return the minimum or maximum of a sequence. If the input array is two-dimensional, the `axis` keyword argument can be supplied, in which case the minimum/maximum along the given axis will be returned. If `axis=None` (this is also the default value), the minimum/maximum of the flattened array will be determined.\n", + "\n", + "`argmin/argmax` return the position (index) of the minimum/maximum in the sequence." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:08:56.986619Z", + "start_time": "2021-01-13T16:08:56.964492Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([1.0, 2.0, 0.0, 1.0, 10.0], dtype=float64)\n", + "min of a: 0.0\n", + "argmin of a: 2\n", + "\n", + "b:\n", + " array([[1.0, 2.0, 0.0],\n", + " [1.0, 10.0, -1.0]], dtype=float64)\n", + "min of b (flattened): -1.0\n", + "min of b (axis=0): array([1.0, 2.0, -1.0], dtype=float64)\n", + "min of b (axis=1): array([0.0, -1.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 0, 1, 10])\n", + "print('a:', a)\n", + "print('min of a:', np.min(a))\n", + "print('argmin of a:', np.argmin(a))\n", + "\n", + "b = np.array([[1, 2, 0], [1, 10, -1]])\n", + "print('\\nb:\\n', b)\n", + "print('min of b (flattened):', np.min(b))\n", + "print('min of b (axis=0):', np.min(b, axis=0))\n", + "print('min of b (axis=1):', np.min(b, axis=1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## median\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.median.html\n", + "\n", + "The function computes the median along the specified axis, and returns the median of the array elements. If the `axis` keyword argument is `None`, the arrays is flattened first. The `dtype` of the results is always float." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:31:13.833800Z", + "start_time": "2021-01-13T16:31:13.809560Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[0, 1, 2, 3],\n", + " [4, 5, 6, 7],\n", + " [8, 9, 10, 11]], dtype=int8)\n", + "\n", + "median of the flattened array: 5.5\n", + "\n", + "median along the vertical axis: array([4.0, 5.0, 6.0, 7.0], dtype=float64)\n", + "\n", + "median along the horizontal axis: array([1.5, 5.5, 9.5], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(12), dtype=np.int8).reshape((3, 4))\n", + "print('a:\\n', a)\n", + "print('\\nmedian of the flattened array: ', np.median(a))\n", + "print('\\nmedian along the vertical axis: ', np.median(a, axis=0))\n", + "print('\\nmedian along the horizontal axis: ', np.median(a, axis=1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## min\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.min.html\n", + "\n", + "See [numpy.max](#max)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## minimum\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.minimum.html\n", + "\n", + "See [numpy.maximum](#maximum)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## maximum\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.maximum.html\n", + "\n", + "Returns the maximum of two arrays, or two scalars, or an array, and a scalar. If the arrays are of different `dtype`, the output is upcast as in [Binary operators](#Binary-operators). If both inputs are scalars, a scalar is returned. Only positional arguments are implemented." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:21:17.151280Z", + "start_time": "2021-01-08T13:21:17.123768Z" + }, + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum of a, and b:\n", + "array([1.0, 2.0, 3.0, 2.0, 1.0], dtype=float64)\n", + "\n", + "maximum of a, and b:\n", + "array([5.0, 4.0, 3.0, 4.0, 5.0], dtype=float64)\n", + "\n", + "maximum of 1, and 5.5:\n", + "5.5\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5], dtype=np.uint8)\n", + "b = np.array([5, 4, 3, 2, 1], dtype=np.float)\n", + "print('minimum of a, and b:')\n", + "print(np.minimum(a, b))\n", + "\n", + "print('\\nmaximum of a, and b:')\n", + "print(np.maximum(a, b))\n", + "\n", + "print('\\nmaximum of 1, and 5.5:')\n", + "print(np.maximum(1, 5.5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## not_equal\n", + "\n", + "See [numpy.equal](#equal)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## polyfit\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html\n", + "\n", + "polyfit takes two, or three arguments. The last one is the degree of the polynomial that will be fitted, the last but one is an array or iterable with the `y` (dependent) values, and the first one, an array or iterable with the `x` (independent) values, can be dropped. If that is the case, `x` will be generated in the function as `range(len(y))`.\n", + "\n", + "If the lengths of `x`, and `y` are not the same, the function raises a `ValueError`." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T18:23:39.238450Z", + "start_time": "2021-01-13T18:23:39.221063Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "independent values:\t array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float64)\n", + "dependent values:\t array([9.0, 4.0, 1.0, 0.0, 1.0, 4.0, 9.0], dtype=float64)\n", + "fitted values:\t\t array([1.0, -6.0, 9.000000000000004], dtype=float64)\n", + "\n", + "dependent values:\t array([9.0, 4.0, 1.0, 0.0, 1.0, 4.0, 9.0], dtype=float64)\n", + "fitted values:\t\t array([1.0, -6.0, 9.000000000000004], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.array([0, 1, 2, 3, 4, 5, 6])\n", + "y = np.array([9, 4, 1, 0, 1, 4, 9])\n", + "print('independent values:\\t', x)\n", + "print('dependent values:\\t', y)\n", + "print('fitted values:\\t\\t', np.polyfit(x, y, 2))\n", + "\n", + "# the same with missing x\n", + "print('\\ndependent values:\\t', y)\n", + "print('fitted values:\\t\\t', np.polyfit(y, 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Execution time\n", + "\n", + "`polyfit` is based on the inversion of a matrix (there is more on the background in https://en.wikipedia.org/wiki/Polynomial_regression), and it requires the intermediate storage of `2*N*(deg+1)` floats, where `N` is the number of entries in the input array, and `deg` is the fit's degree. The additional computation costs of the matrix inversion discussed in [linalg.inv](#inv) also apply. The example from above needs around 150 microseconds to return:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T18:31:40.919764Z", + "start_time": "2021-01-13T18:31:40.912817Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "execution time: 153 us\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "@timeit\n", + "def time_polyfit(x, y, n):\n", + " return np.polyfit(x, y, n)\n", + "\n", + "x = np.array([0, 1, 2, 3, 4, 5, 6])\n", + "y = np.array([9, 4, 1, 0, 1, 4, 9])\n", + "\n", + "time_polyfit(x, y, 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## polyval\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyval.html\n", + "\n", + "`polyval` takes two arguments, both arrays or generic `micropython` iterables returning scalars." + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T18:12:56.736643Z", + "start_time": "2021-01-13T18:12:56.668042Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "coefficients: [1, 1, 1, 0]\n", + "independent values: [0, 1, 2, 3, 4]\n", + "\n", + "values of p(x): array([0.0, 3.0, 14.0, 39.0, 84.0], dtype=float64)\n", + "\n", + "ndarray (a): array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64)\n", + "value of p(a): array([0.0, 3.0, 14.0, 39.0, 84.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "p = [1, 1, 1, 0]\n", + "x = [0, 1, 2, 3, 4]\n", + "print('coefficients: ', p)\n", + "print('independent values: ', x)\n", + "print('\\nvalues of p(x): ', np.polyval(p, x))\n", + "\n", + "# the same works with one-dimensional ndarrays\n", + "a = np.array(x)\n", + "print('\\nndarray (a): ', a)\n", + "print('value of p(a): ', np.polyval(p, a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## real\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.real.html\n", + "\n", + "The `real` function returns the real part of an array, or scalar. It cannot accept a generic iterable as its argument. The function is defined only, if the firmware was compiled with complex support." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:27:22.141930Z", + "start_time": "2022-01-07T19:27:22.122577Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([1, 2, 3], dtype=uint16)\n", + "real(a):\t array([1, 2, 3], dtype=uint16)\n", + "\n", + "b:\t\t array([1.0+0.0j, 2.0+1.0j, 3.0-1.0j], dtype=complex)\n", + "real(b):\t array([1.0, 2.0, 3.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3], dtype=np.uint16)\n", + "print(\"a:\\t\\t\", a)\n", + "print(\"real(a):\\t\", np.real(a))\n", + "\n", + "b = np.array([1, 2+1j, 3-1j], dtype=np.complex)\n", + "print(\"\\nb:\\t\\t\", b)\n", + "print(\"real(b):\\t\", np.real(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## roll\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.roll.html\n", + "\n", + "The roll function shifts the content of a vector by the positions given as the second argument. If the `axis` keyword is supplied, the shift is applied to the given axis." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:18:30.387043Z", + "start_time": "2021-01-13T16:18:30.363374Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t\t array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "a rolled to the left:\t array([7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float64)\n", + "a rolled to the right:\t array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n", + "print(\"a:\\t\\t\\t\", a)\n", + "\n", + "a = np.roll(a, 2)\n", + "print(\"a rolled to the left:\\t\", a)\n", + "\n", + "# this should be the original vector\n", + "a = np.roll(a, -2)\n", + "print(\"a rolled to the right:\\t\", a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Rolling works with matrices, too. If the `axis` keyword is 0, the matrix is rolled along its vertical axis, otherwise, horizontally. \n", + "\n", + "Horizontal rolls are faster, because they require fewer steps, and larger memory chunks are copied, however, they also require more RAM: basically the whole row must be stored internally. Most expensive are the `None` keyword values, because with `axis = None`, the array is flattened first, hence the row's length is the size of the whole matrix.\n", + "\n", + "Vertical rolls require two internal copies of single columns. " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:23:52.025977Z", + "start_time": "2021-01-13T16:23:52.001252Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[0.0, 1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0, 7.0],\n", + " [8.0, 9.0, 10.0, 11.0]], dtype=float64)\n", + "\n", + "a rolled up:\n", + " array([[4.0, 5.0, 6.0, 7.0],\n", + " [8.0, 9.0, 10.0, 11.0],\n", + " [0.0, 1.0, 2.0, 3.0]], dtype=float64)\n", + "a:\n", + " array([[0.0, 1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0, 7.0],\n", + " [8.0, 9.0, 10.0, 11.0]], dtype=float64)\n", + "\n", + "a rolled to the left:\n", + " array([[1.0, 2.0, 3.0, 0.0],\n", + " [5.0, 6.0, 7.0, 4.0],\n", + " [9.0, 10.0, 11.0, 8.0]], dtype=float64)\n", + "a:\n", + " array([[0.0, 1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0, 7.0],\n", + " [8.0, 9.0, 10.0, 11.0]], dtype=float64)\n", + "\n", + "a rolled with None:\n", + " array([[11.0, 0.0, 1.0, 2.0],\n", + " [3.0, 4.0, 5.0, 6.0],\n", + " [7.0, 8.0, 9.0, 10.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(12)).reshape((3, 4))\n", + "print(\"a:\\n\", a)\n", + "a = np.roll(a, 2, axis=0)\n", + "print(\"\\na rolled up:\\n\", a)\n", + "\n", + "a = np.array(range(12)).reshape((3, 4))\n", + "print(\"a:\\n\", a)\n", + "a = np.roll(a, -1, axis=1)\n", + "print(\"\\na rolled to the left:\\n\", a)\n", + "\n", + "a = np.array(range(12)).reshape((3, 4))\n", + "print(\"a:\\n\", a)\n", + "a = np.roll(a, 1, axis=None)\n", + "print(\"\\na rolled with None:\\n\", a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## sort\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html\n", + "\n", + "The sort function takes an ndarray, and sorts its elements in ascending order along the specified axis using a heap sort algorithm. As opposed to the `.sort()` method discussed earlier, this function creates a copy of its input before sorting, and at the end, returns this copy. Sorting takes place in place, without auxiliary storage. The `axis` keyword argument takes on the possible values of -1 (the last axis, in `ulab` equivalent to the second axis, and this also happens to be the default value), 0, 1, or `None`. The first three cases are identical to those in [diff](#diff), while the last one flattens the array before sorting. \n", + "\n", + "If descending order is required, the result can simply be `flip`ped, see [flip](#flip).\n", + "\n", + "**WARNING:** `numpy` defines the `kind`, and `order` keyword arguments that are not implemented here. The function in `ulab` always uses heap sort, and since `ulab` does not have the concept of data fields, the `order` keyword argument would have no meaning." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:32:07.748972Z", + "start_time": "2021-01-13T16:32:07.730498Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([[1.0, 12.0, 3.0, 0.0],\n", + " [5.0, 3.0, 4.0, 1.0],\n", + " [9.0, 11.0, 1.0, 8.0],\n", + " [7.0, 10.0, 0.0, 1.0]], dtype=float64)\n", + "\n", + "a sorted along vertical axis:\n", + " array([[1.0, 3.0, 0.0, 0.0],\n", + " [5.0, 10.0, 1.0, 1.0],\n", + " [7.0, 11.0, 3.0, 1.0],\n", + " [9.0, 12.0, 4.0, 8.0]], dtype=float64)\n", + "\n", + "a sorted along horizontal axis:\n", + " array([[0.0, 1.0, 3.0, 12.0],\n", + " [1.0, 3.0, 4.0, 5.0],\n", + " [1.0, 8.0, 9.0, 11.0],\n", + " [0.0, 1.0, 7.0, 10.0]], dtype=float64)\n", + "\n", + "flattened a sorted:\n", + " array([0.0, 0.0, 1.0, ..., 10.0, 11.0, 12.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.float)\n", + "print('\\na:\\n', a)\n", + "b = np.sort(a, axis=0)\n", + "print('\\na sorted along vertical axis:\\n', b)\n", + "\n", + "c = np.sort(a, axis=1)\n", + "print('\\na sorted along horizontal axis:\\n', c)\n", + "\n", + "c = np.sort(a, axis=None)\n", + "print('\\nflattened a sorted:\\n', c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Heap sort requires $\\sim N\\log N$ operations, and notably, the worst case costs only 20% more time than the average. In order to get an order-of-magnitude estimate, we will take the sine of 1000 uniformly spaced numbers between 0, and two pi, and sort them:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "@timeit\n", + "def sort_time(array):\n", + " return nup.sort(array)\n", + "\n", + "b = np.sin(np.linspace(0, 6.28, num=1000))\n", + "print('b: ', b)\n", + "sort_time(b)\n", + "print('\\nb sorted:\\n', b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## sort_complex\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.sort_complex.html\n", + "\n", + "If the firmware was compiled with complex support, the functions sorts the input array first according to its real part, and then the imaginary part. The input must be a one-dimensional array. The output is always of `dtype` complex, even if the input was real integer." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:36:15.750029Z", + "start_time": "2022-01-07T19:36:15.732210Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t\t array([5, 4, 3, 2, 1], dtype=int16)\n", + "sort_complex(a):\t array([1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j], dtype=complex)\n", + "\n", + "b:\t\t\t array([5.0+0.0j, 4.0+3.0j, 4.0-2.0j, 0.0+0.0j, 0.0+1.0j], dtype=complex)\n", + "sort_complex(b):\t array([0.0+0.0j, 0.0+1.0j, 4.0-2.0j, 4.0+3.0j, 5.0+0.0j], dtype=complex)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([5, 4, 3, 2, 1], dtype=np.int16)\n", + "print('a:\\t\\t\\t', a)\n", + "print('sort_complex(a):\\t', np.sort_complex(a))\n", + "print()\n", + "\n", + "b = np.array([5, 4+3j, 4-2j, 0, 1j], dtype=np.complex)\n", + "print('b:\\t\\t\\t', b)\n", + "print('sort_complex(b):\\t', np.sort_complex(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## std\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html\n", + "\n", + "If the axis keyword is not specified, it assumes the default value of `None`, and returns the result of the computation for the flattened array. Otherwise, the calculation is along the given axis." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:14:54.051061Z", + "start_time": "2021-01-13T16:14:54.029924Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: \n", + " array([[1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0],\n", + " [7.0, 8.0, 9.0]], dtype=float64)\n", + "sum, flat array: 2.581988897471611\n", + "std, vertical: array([2.449489742783178, 2.449489742783178, 2.449489742783178], dtype=float64)\n", + "std, horizonal: array([0.8164965809277261, 0.8164965809277261, 0.8164965809277261], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n", + "print('a: \\n', a)\n", + "print('sum, flat array: ', np.std(a))\n", + "print('std, vertical: ', np.std(a, axis=0))\n", + "print('std, horizonal: ', np.std(a, axis=1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## sum\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.sum.html\n", + "\n", + "If the axis keyword is not specified, it assumes the default value of `None`, and returns the result of the computation for the flattened array. Otherwise, the calculation is along the given axis." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:14:34.576723Z", + "start_time": "2021-01-13T16:14:34.556304Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: \n", + " array([[1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0],\n", + " [7.0, 8.0, 9.0]], dtype=float64)\n", + "sum, flat array: 45.0\n", + "sum, horizontal: array([6.0, 15.0, 24.0], dtype=float64)\n", + "std, vertical: array([12.0, 15.0, 18.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n", + "print('a: \\n', a)\n", + "\n", + "print('sum, flat array: ', np.sum(a))\n", + "print('sum, horizontal: ', np.sum(a, axis=1))\n", + "print('std, vertical: ', np.sum(a, axis=0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## trace\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.trace.html\n", + "\n", + "The `trace` function returns the sum of the diagonal elements of a square matrix. If the input argument is not a square matrix, an exception will be raised.\n", + "\n", + "The scalar so returned will inherit the type of the input array, i.e., integer arrays have integer trace, and floating point arrays a floating point trace." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2021-02-13T08:30:25.211965Z", + "start_time": "2021-02-13T08:30:25.195102Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([[25, 15, -5],\n", + " [15, 18, 0],\n", + " [-5, 0, 11]], dtype=int8)\n", + "\n", + "trace of a: 54\n", + "====================\n", + "b: array([[25.0, 15.0, -5.0],\n", + " [15.0, 18.0, 0.0],\n", + " [-5.0, 0.0, 11.0]], dtype=float64)\n", + "\n", + "trace of b: 54.0\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[25, 15, -5], [15, 18, 0], [-5, 0, 11]], dtype=np.int8)\n", + "print('a: ', a)\n", + "print('\\ntrace of a: ', np.trace(a))\n", + "\n", + "b = np.array([[25, 15, -5], [15, 18, 0], [-5, 0, 11]], dtype=np.float)\n", + "\n", + "print('='*20 + '\\nb: ', b)\n", + "print('\\ntrace of b: ', np.trace(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## trapz\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.trapz.html\n", + "\n", + "The function takes one or two one-dimensional `ndarray`s, and integrates the dependent values (`y`) using the trapezoidal rule. If the independent variable (`x`) is given, that is taken as the sample points corresponding to `y`." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T16:03:42.566302Z", + "start_time": "2021-01-13T16:03:42.545630Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64)\n", + "y: array([0.0, 1.0, 4.0, 9.0, 16.0, 25.0, 36.0, 49.0, 64.0, 81.0], dtype=float64)\n", + "============================\n", + "integral of y: 244.5\n", + "integral of y at x: 244.5\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.linspace(0, 9, num=10)\n", + "y = x*x\n", + "\n", + "print('x: ', x)\n", + "print('y: ', y)\n", + "print('============================')\n", + "print('integral of y: ', np.trapz(y))\n", + "print('integral of y at x: ', np.trapz(y, x=x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## where\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.where.html\n", + "\n", + "The function takes three positional arguments, `condition`, `x`, and `y`, and returns a new `ndarray`, whose values are taken from either `x`, or `y`, depending on the truthness of `condition`. The three arguments are broadcast together, and the function raises a `ValueError` exception, if broadcasting is not possible.\n", + "\n", + "The function is implemented for `ndarray`s only: other iterable types can be passed after casting them to an `ndarray` by calling the `array` constructor.\n", + "\n", + "If the `dtype`s of `x`, and `y` differ, the output is upcast as discussed earlier. \n", + "\n", + "Note that the `condition` is expanded into an Boolean `ndarray`. This means that the storage required to hold the condition should be taken into account, whenever the function is called." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following example returns an `ndarray` of length 4, with 1 at positions, where `condition` is smaller than 3, and with -1 otherwise." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-23T16:18:14.396840Z", + "start_time": "2021-03-23T16:18:14.385134Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([1, 1, -1, -1], dtype=int16)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "condition = np.array([1, 2, 3, 4], dtype=np.uint8)\n", + "print(np.where(condition < 3, 1, -1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The next snippet shows, how values from two arrays can be fed into the output:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-23T16:15:29.954224Z", + "start_time": "2021-03-23T16:15:29.937205Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([11, 22, 3, 4], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "condition = np.array([1, 2, 3, 4], dtype=np.uint8)\n", + "x = np.array([11, 22, 33, 44], dtype=np.uint8)\n", + "y = np.array([1, 2, 3, 4], dtype=np.uint8)\n", + "print(np.where(condition < 3, x, y))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/numpy-linalg.ipynb b/circuitpython/extmod/ulab/docs/numpy-linalg.ipynb new file mode 100644 index 0000000..e57e63a --- /dev/null +++ b/circuitpython/extmod/ulab/docs/numpy-linalg.ipynb @@ -0,0 +1,811 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "source": [ + "%pylab inline" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:16:40.844266Z", + "start_time": "2021-01-13T06:16:39.992092Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## Notebook magic" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 1, + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ], + "outputs": [], + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:16:40.857076Z", + "start_time": "2021-01-13T06:16:40.852721Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 2, + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ], + "outputs": [], + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:16:40.947944Z", + "start_time": "2021-01-13T06:16:40.865720Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## pyboard" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 57, + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ], + "outputs": [], + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 9, + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ], + "outputs": [], + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + } + }, + { + "cell_type": "code", + "execution_count": 58, + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "__END_OF_DEFS__" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "# numpy.linalg\n", + "\n", + "Functions in the `linalg` module can be called by prepending them by `numpy.linalg.`. The module defines the following seven functions:\n", + "\n", + "1. [numpy.linalg.cholesky](#cholesky)\n", + "1. [numpy.linalg.det](#det)\n", + "1. [numpy.linalg.eig](#eig)\n", + "1. [numpy.linalg.inv](#inv)\n", + "1. [numpy.linalg.norm](#norm)\n", + "1. [numpy.linalg.qr](#qr)" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## cholesky\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.linalg.cholesky.html\n", + "\n", + "The function of the Cholesky decomposition takes a positive definite, symmetric square matrix as its single argument, and returns the *square root matrix* in the lower triangular form. If the input argument does not fulfill the positivity or symmetry condition, a `ValueError` is raised." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 18, + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[25, 15, -5], [15, 18, 0], [-5, 0, 11]])\n", + "print('a: ', a)\n", + "print('\\n' + '='*20 + '\\nCholesky decomposition\\n', np.linalg.cholesky(a))" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "a: array([[25.0, 15.0, -5.0],\n", + "\t [15.0, 18.0, 0.0],\n", + "\t [-5.0, 0.0, 11.0]], dtype=float)\n", + "\n", + "====================\n", + "Cholesky decomposition\n", + " array([[5.0, 0.0, 0.0],\n", + "\t [3.0, 3.0, 0.0],\n", + "\t [-1.0, 1.0, 3.0]], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2020-03-10T19:25:21.754166Z", + "start_time": "2020-03-10T19:25:21.740726Z" + }, + "scrolled": true + } + }, + { + "cell_type": "markdown", + "source": [ + "## det\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.det.html\n", + "\n", + "The `det` function takes a square matrix as its single argument, and calculates the determinant. The calculation is based on successive elimination of the matrix elements, and the return value is a float, even if the input array was of integer type." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 495, + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2], [3, 4]], dtype=np.uint8)\n", + "print(np.linalg.det(a))" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "-2.0\n", + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-19T13:27:24.246995Z", + "start_time": "2019-10-19T13:27:24.228698Z" + }, + "scrolled": true + } + }, + { + "cell_type": "markdown", + "source": [ + "### Benchmark\n", + "\n", + "Since the routine for calculating the determinant is pretty much the same as for finding the [inverse of a matrix](#inv), the execution times are similar:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 557, + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "@timeit\n", + "def matrix_det(m):\n", + " return np.linalg.inv(m)\n", + "\n", + "m = np.array([[1, 2, 3, 4, 5, 6, 7, 8], [0, 5, 6, 4, 5, 6, 4, 5], \n", + " [0, 0, 9, 7, 8, 9, 7, 8], [0, 0, 0, 10, 11, 12, 11, 12], \n", + " [0, 0, 0, 0, 4, 6, 7, 8], [0, 0, 0, 0, 0, 5, 6, 7], \n", + " [0, 0, 0, 0, 0, 0, 7, 6], [0, 0, 0, 0, 0, 0, 0, 2]])\n", + "\n", + "matrix_det(m)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "execution time: 294 us\n", + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-20T07:14:59.778987Z", + "start_time": "2019-10-20T07:14:59.740021Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## eig\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html\n", + "\n", + "The `eig` function calculates the eigenvalues and the eigenvectors of a real, symmetric square matrix. If the matrix is not symmetric, a `ValueError` will be raised. The function takes a single argument, and returns a tuple with the eigenvalues, and eigenvectors. With the help of the eigenvectors, amongst other things, you can implement sophisticated stabilisation routines for robots." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 18, + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2, 1, 4], [2, 5, 3, 5], [1, 3, 6, 1], [4, 5, 1, 7]], dtype=np.uint8)\n", + "x, y = np.linalg.eig(a)\n", + "print('eigenvectors of a:\\n', y)\n", + "print('\\neigenvalues of a:\\n', x)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "eigenvectors of a:\n", + " array([[0.8151560042509081, -0.4499411232970823, -0.1644660242574522, 0.3256141906686505],\n", + " [0.2211334179893007, 0.7846992598235538, 0.08372081379922657, 0.5730077734355189],\n", + " [-0.1340114162071679, -0.3100776411558949, 0.8742786816656, 0.3486109343758527],\n", + " [-0.5183258053659028, -0.292663481927148, -0.4489749870391468, 0.6664142156731531]], dtype=float)\n", + "\n", + "eigenvalues of a:\n", + " array([-1.165288365404889, 0.8029365530314914, 5.585625756072663, 13.77672605630074], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2020-11-03T20:25:26.952290Z", + "start_time": "2020-11-03T20:25:26.930184Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "The same matrix diagonalised with `numpy` yields:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 6, + "source": [ + "a = array([[1, 2, 1, 4], [2, 5, 3, 5], [1, 3, 6, 1], [4, 5, 1, 7]], dtype=np.uint8)\n", + "x, y = eig(a)\n", + "print('eigenvectors of a:\\n', y)\n", + "print('\\neigenvalues of a:\\n', x)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "eigenvectors of a:\n", + " [[ 0.32561419 0.815156 0.44994112 -0.16446602]\n", + " [ 0.57300777 0.22113342 -0.78469926 0.08372081]\n", + " [ 0.34861093 -0.13401142 0.31007764 0.87427868]\n", + " [ 0.66641421 -0.51832581 0.29266348 -0.44897499]]\n", + "\n", + "eigenvalues of a:\n", + " [13.77672606 -1.16528837 0.80293655 5.58562576]\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2020-11-03T20:13:27.236159Z", + "start_time": "2020-11-03T20:13:27.069967Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "When comparing results, we should keep two things in mind: \n", + "\n", + "1. the eigenvalues and eigenvectors are not necessarily sorted in the same way\n", + "2. an eigenvector can be multiplied by an arbitrary non-zero scalar, and it is still an eigenvector with the same eigenvalue. This is why all signs of the eigenvector belonging to 5.58, and 0.80 are flipped in `ulab` with respect to `numpy`. This difference, however, is of absolutely no consequence. " + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Computation expenses\n", + "\n", + "Since the function is based on [Givens rotations](https://en.wikipedia.org/wiki/Givens_rotation) and runs till convergence is achieved, or till the maximum number of allowed rotations is exhausted, there is no universal estimate for the time required to find the eigenvalues. However, an order of magnitude can, at least, be guessed based on the measurement below:" + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 559, + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "@timeit\n", + "def matrix_eig(a):\n", + " return np.linalg.eig(a)\n", + "\n", + "a = np.array([[1, 2, 1, 4], [2, 5, 3, 5], [1, 3, 6, 1], [4, 5, 1, 7]], dtype=np.uint8)\n", + "\n", + "matrix_eig(a)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "execution time: 111 us\n", + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-20T07:18:52.520515Z", + "start_time": "2019-10-20T07:18:52.499653Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## inv\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.linalg.inv.html\n", + "\n", + "A square matrix, provided that it is not singular, can be inverted by calling the `inv` function that takes a single argument. The inversion is based on successive elimination of elements in the lower left triangle, and raises a `ValueError` exception, if the matrix turns out to be singular (i.e., one of the diagonal entries is zero)." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 5, + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "m = np.array([[1, 2, 3, 4], [4, 5, 6, 4], [7, 8.6, 9, 4], [3, 4, 5, 6]])\n", + "\n", + "print(np.linalg.inv(m))" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "array([[-2.166666666666667, 1.500000000000001, -0.8333333333333337, 1.0],\n", + " [1.666666666666667, -3.333333333333335, 1.666666666666668, -0.0],\n", + " [0.1666666666666666, 2.166666666666668, -0.8333333333333337, -1.0],\n", + " [-0.1666666666666667, -0.3333333333333333, 0.0, 0.5]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:17:13.053816Z", + "start_time": "2021-01-13T06:17:13.038403Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "### Computation expenses\n", + "\n", + "Note that the cost of inverting a matrix is approximately twice as many floats (RAM), as the number of entries in the original matrix, and approximately as many operations, as the number of entries. Here are a couple of numbers: " + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 552, + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "@timeit\n", + "def invert_matrix(m):\n", + " return np.linalg.inv(m)\n", + "\n", + "m = np.array([[1, 2,], [4, 5]])\n", + "print('2 by 2 matrix:')\n", + "invert_matrix(m)\n", + "\n", + "m = np.array([[1, 2, 3, 4], [4, 5, 6, 4], [7, 8.6, 9, 4], [3, 4, 5, 6]])\n", + "print('\\n4 by 4 matrix:')\n", + "invert_matrix(m)\n", + "\n", + "m = np.array([[1, 2, 3, 4, 5, 6, 7, 8], [0, 5, 6, 4, 5, 6, 4, 5], \n", + " [0, 0, 9, 7, 8, 9, 7, 8], [0, 0, 0, 10, 11, 12, 11, 12], \n", + " [0, 0, 0, 0, 4, 6, 7, 8], [0, 0, 0, 0, 0, 5, 6, 7], \n", + " [0, 0, 0, 0, 0, 0, 7, 6], [0, 0, 0, 0, 0, 0, 0, 2]])\n", + "print('\\n8 by 8 matrix:')\n", + "invert_matrix(m)" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "2 by 2 matrix:\n", + "execution time: 65 us\n", + "\n", + "4 by 4 matrix:\n", + "execution time: 105 us\n", + "\n", + "8 by 8 matrix:\n", + "execution time: 299 us\n", + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-20T07:10:39.190734Z", + "start_time": "2019-10-20T07:10:39.138872Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "The above-mentioned scaling is not obeyed strictly. The reason for the discrepancy is that the function call is still the same for all three cases: the input must be inspected, the output array must be created, and so on. " + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "## norm\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html\n", + "\n", + "The function takes a vector or matrix without options, and returns its 2-norm, i.e., the square root of the sum of the square of the elements." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 11, + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5])\n", + "b = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n", + "\n", + "print('norm of a:', np.linalg.norm(a))\n", + "print('norm of b:', np.linalg.norm(b))" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "norm of a: 7.416198487095663\n", + "norm of b: 16.88194301613414\n", + "\n", + "\n" + ] + } + ], + "metadata": { + "ExecuteTime": { + "end_time": "2020-07-23T20:41:10.341349Z", + "start_time": "2020-07-23T20:41:10.327624Z" + } + } + }, + { + "cell_type": "markdown", + "source": [ + "## qr\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.linalg.qr.html\n", + "\n", + "\n", + "The function computes the QR decomposition of a matrix `m` of dimensions `(M, N)`, i.e., it returns two such matrices, `q`', and `r`, that `m = qr`, where `q` is orthonormal, and `r` is upper triangular. In addition to the input matrix, which is the first positional argument, the function accepts the `mode` keyword argument with a default value of `reduced`. If `mode` is `reduced`, `q`, and `r` are returned in the reduced representation. Otherwise, the outputs will have dimensions `(M, M)`, and `(M, N)`, respectively." + ], + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 3, + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "A = np.arange(6).reshape((3, 2))\n", + "print('A: \\n', A)\n", + "\n", + "print('complete decomposition')\n", + "q, r = np.linalg.qr(A, mode='complete')\n", + "print('q: \\n', q)\n", + "print()\n", + "print('r: \\n', r)\n", + "\n", + "print('\\n\\nreduced decomposition')\n", + "q, r = np.linalg.qr(A, mode='reduced')\n", + "print('q: \\n', q)\n", + "print()\n", + "print('r: \\n', r)\n" + ], + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "A: \n", + " array([[0, 1],\n", + " [2, 3],\n", + " [4, 5]], dtype=int16)\n", + "complete decomposition\n", + "q: \n", + " array([[0.0, -0.9128709291752768, 0.408248290463863],\n", + " [-0.447213595499958, -0.3651483716701107, -0.8164965809277261],\n", + " [-0.8944271909999159, 0.1825741858350553, 0.408248290463863]], dtype=float64)\n", + "\n", + "r: \n", + " array([[-4.47213595499958, -5.813776741499454],\n", + " [0.0, -1.095445115010332],\n", + " [0.0, 0.0]], dtype=float64)\n", + "\n", + "\n", + "reduced decomposition\n", + "q: \n", + " array([[0.0, -0.9128709291752768],\n", + " [-0.447213595499958, -0.3651483716701107],\n", + " [-0.8944271909999159, 0.1825741858350553]], dtype=float64)\n", + "\n", + "r: \n", + " array([[-4.47213595499958, -5.813776741499454],\n", + " [0.0, -1.095445115010332]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "metadata": {} + } + ], + "metadata": { + "kernelspec": { + "name": "python3", + "display_name": "Python 3.8.5 64-bit ('base': conda)" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + }, + "interpreter": { + "hash": "ce9a02f9f7db620716422019cafa4bc1786ca85daa298b819f6da075e7993842" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/docs/numpy-universal.ipynb b/circuitpython/extmod/ulab/docs/numpy-universal.ipynb new file mode 100644 index 0000000..8934fa6 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/numpy-universal.ipynb @@ -0,0 +1,869 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T18:54:58.722373Z", + "start_time": "2021-01-13T18:54:57.178438Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:10:30.696795Z", + "start_time": "2022-01-07T19:10:30.690003Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:10:30.785887Z", + "start_time": "2022-01-07T19:10:30.710912Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../micropython/ports/unix/micropython-2\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Universal functions\n", + "\n", + "Standard mathematical functions can be calculated on any scalar, scalar-valued iterable (ranges, lists, tuples containing numbers), and on `ndarray`s without having to change the call signature. In all cases the functions return a new `ndarray` of typecode `float` (since these functions usually generate float values, anyway). The only exceptions to this rule are the `exp`, and `sqrt` functions, which, if `ULAB_SUPPORTS_COMPLEX` is set to 1 in [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h), can return complex arrays, depending on the argument. All functions execute faster with `ndarray` arguments than with iterables, because the values of the input vector can be extracted faster. \n", + "\n", + "At present, the following functions are supported (starred functions can operate on, or can return complex arrays):\n", + "\n", + "`acos`, `acosh`, `arctan2`, `around`, `asin`, `asinh`, `atan`, `arctan2`, `atanh`, `ceil`, `cos`, `degrees`, `exp*`, `expm1`, `floor`, `log`, `log10`, `log2`, `radians`, `sin`, `sinh`, `sqrt*`, `tan`, `tanh`.\n", + "\n", + "These functions are applied element-wise to the arguments, thus, e.g., the exponential of a matrix cannot be calculated in this way, only the exponential of the matrix entries." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T19:11:07.579601Z", + "start_time": "2021-01-13T19:11:07.554672Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t range(0, 9)\n", + "exp(a):\t array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767, 54.59815003314424, 148.4131591025766, 403.4287934927351, 1096.633158428459, 2980.957987041728], dtype=float64)\n", + "\n", + "=============\n", + "b:\n", + " array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "exp(b):\n", + " array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767, 54.59815003314424, 148.4131591025766, 403.4287934927351, 1096.633158428459, 2980.957987041728], dtype=float64)\n", + "\n", + "=============\n", + "c:\n", + " array([[0.0, 1.0, 2.0],\n", + " [3.0, 4.0, 5.0],\n", + " [6.0, 7.0, 8.0]], dtype=float64)\n", + "exp(c):\n", + " array([[1.0, 2.718281828459045, 7.38905609893065],\n", + " [20.08553692318767, 54.59815003314424, 148.4131591025766],\n", + " [403.4287934927351, 1096.633158428459, 2980.957987041728]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = range(9)\n", + "b = np.array(a)\n", + "\n", + "# works with ranges, lists, tuples etc.\n", + "print('a:\\t', a)\n", + "print('exp(a):\\t', np.exp(a))\n", + "\n", + "# with 1D arrays\n", + "print('\\n=============\\nb:\\n', b)\n", + "print('exp(b):\\n', np.exp(b))\n", + "\n", + "# as well as with matrices\n", + "c = np.array(range(9)).reshape((3, 3))\n", + "print('\\n=============\\nc:\\n', c)\n", + "print('exp(c):\\n', np.exp(c))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computation expenses\n", + "\n", + "The overhead for calculating with micropython iterables is quite significant: for the 1000 samples below, the difference is more than 800 microseconds, because internally the function has to create the `ndarray` for the output, has to fetch the iterable's items of unknown type, and then convert them to floats. All these steps are skipped for `ndarray`s, because these pieces of information are already known. \n", + "\n", + "Doing the same with `list` comprehension requires 30 times more time than with the `ndarray`, which would become even more, if we converted the resulting list to an `ndarray`. " + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:45.696282Z", + "start_time": "2020-05-07T07:35:45.629909Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iterating over ndarray in ulab\r\n", + "execution time: 441 us\r\n", + "\r\n", + "iterating over list in ulab\r\n", + "execution time: 1266 us\r\n", + "\r\n", + "iterating over list in python\r\n", + "execution time: 11379 us\r\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "import math\n", + "\n", + "a = [0]*1000\n", + "b = np.array(a)\n", + "\n", + "@timeit\n", + "def timed_vector(iterable):\n", + " return np.exp(iterable)\n", + "\n", + "@timeit\n", + "def timed_list(iterable):\n", + " return [math.exp(i) for i in iterable]\n", + "\n", + "print('iterating over ndarray in ulab')\n", + "timed_vector(b)\n", + "\n", + "print('\\niterating over list in ulab')\n", + "timed_vector(a)\n", + "\n", + "print('\\niterating over list in python')\n", + "timed_list(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## arctan2\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.arctan2.html\n", + "\n", + "The two-argument inverse tangent function is also part of the `vector` sub-module. The function implements broadcasting as discussed in the section on `ndarray`s. Scalars (`micropython` integers or floats) are also allowed." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T19:15:08.215912Z", + "start_time": "2021-01-13T19:15:08.189806Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([1.0, 2.2, 33.33, 444.444], dtype=float64)\n", + "\n", + "arctan2(a, 1.0)\n", + " array([0.7853981633974483, 1.14416883366802, 1.5408023243361, 1.568546328341769], dtype=float64)\n", + "\n", + "arctan2(1.0, a)\n", + " array([0.7853981633974483, 0.426627493126876, 0.02999400245879636, 0.002249998453127392], dtype=float64)\n", + "\n", + "arctan2(a, a): \n", + " array([0.7853981633974483, 0.7853981633974483, 0.7853981633974483, 0.7853981633974483], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2.2, 33.33, 444.444])\n", + "print('a:\\n', a)\n", + "print('\\narctan2(a, 1.0)\\n', np.arctan2(a, 1.0))\n", + "print('\\narctan2(1.0, a)\\n', np.arctan2(1.0, a))\n", + "print('\\narctan2(a, a): \\n', np.arctan2(a, a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## around\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy-1.17.0/reference/generated/numpy.around.html\n", + "\n", + "`numpy`'s `around` function can also be found in the `vector` sub-module. The function implements the `decimals` keyword argument with default value `0`. The first argument must be an `ndarray`. If this is not the case, the function raises a `TypeError` exception. Note that `numpy` accepts general iterables. The `out` keyword argument known from `numpy` is not accepted. The function always returns an ndarray of type `mp_float_t`." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T19:19:46.728823Z", + "start_time": "2021-01-13T19:19:46.703348Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([1.0, 2.2, 33.33, 444.444], dtype=float64)\n", + "\n", + "decimals = 0\t array([1.0, 2.0, 33.0, 444.0], dtype=float64)\n", + "\n", + "decimals = 1\t array([1.0, 2.2, 33.3, 444.4], dtype=float64)\n", + "\n", + "decimals = -1\t array([0.0, 0.0, 30.0, 440.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2.2, 33.33, 444.444])\n", + "print('a:\\t\\t', a)\n", + "print('\\ndecimals = 0\\t', np.around(a, decimals=0))\n", + "print('\\ndecimals = 1\\t', np.around(a, decimals=1))\n", + "print('\\ndecimals = -1\\t', np.around(a, decimals=-1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## exp\n", + "\n", + "If `ULAB_SUPPORTS_COMPLEX` is set to 1 in [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h), the exponential function can also take complex arrays as its argument, in which case the return value is also complex." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:41:51.865779Z", + "start_time": "2022-01-07T18:41:51.843897Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([1.0, 2.0, 3.0], dtype=float64)\n", + "exp(a):\t\t array([2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64)\n", + "\n", + "b:\t\t array([1.0+1.0j, 2.0+2.0j, 3.0+3.0j], dtype=complex)\n", + "exp(b):\t\t array([1.468693939915885+2.287355287178842j, -3.074932320639359+6.71884969742825j, -19.88453084414699+2.834471132487004j], dtype=complex)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3])\n", + "print('a:\\t\\t', a)\n", + "print('exp(a):\\t\\t', np.exp(a))\n", + "print()\n", + "\n", + "b = np.array([1+1j, 2+2j, 3+3j], dtype=np.complex)\n", + "print('b:\\t\\t', b)\n", + "print('exp(b):\\t\\t', np.exp(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## sqrt\n", + "\n", + "If `ULAB_SUPPORTS_COMPLEX` is set to 1 in [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h), the exponential function can also take complex arrays as its argument, in which case the return value is also complex. If the input is real, but the results might be complex, the user is supposed to specify the output `dtype` in the function call. Otherwise, the square roots of negative numbers will result in `NaN`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:45:26.554520Z", + "start_time": "2022-01-07T18:45:26.543552Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([1.0, -1.0], dtype=float64)\n", + "sqrt(a):\t\t array([1.0, nan], dtype=float64)\n", + "sqrt(a):\t\t array([1.0+0.0j, 0.0+1.0j], dtype=complex)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, -1])\n", + "print('a:\\t\\t', a)\n", + "print('sqrt(a):\\t\\t', np.sqrt(a))\n", + "print('sqrt(a):\\t\\t', np.sqrt(a, dtype=np.complex))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Vectorising generic python functions\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.vectorize.html\n", + "\n", + "The examples above use factory functions. In fact, they are nothing but the vectorised versions of the standard mathematical functions. User-defined `python` functions can also be vectorised by help of `vectorize`. This function takes a positional argument, namely, the `python` function that you want to vectorise, and a non-mandatory keyword argument, `otypes`, which determines the `dtype` of the output array. The `otypes` must be `None` (default), or any of the `dtypes` defined in `ulab`. With `None`, the output is automatically turned into a float array. \n", + "\n", + "The return value of `vectorize` is a `micropython` object that can be called as a standard function, but which now accepts either a scalar, an `ndarray`, or a generic `micropython` iterable as its sole argument. Note that the function that is to be vectorised must have a single argument." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T19:16:55.709617Z", + "start_time": "2021-01-13T19:16:55.688222Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "f on a scalar: array([1936.0], dtype=float64)\n", + "f on an ndarray: array([1.0, 4.0, 9.0, 16.0], dtype=float64)\n", + "f on a list: array([4.0, 9.0, 16.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "def f(x):\n", + " return x*x\n", + "\n", + "vf = np.vectorize(f)\n", + "\n", + "# calling with a scalar\n", + "print('{:20}'.format('f on a scalar: '), vf(44.0))\n", + "\n", + "# calling with an ndarray\n", + "a = np.array([1, 2, 3, 4])\n", + "print('{:20}'.format('f on an ndarray: '), vf(a))\n", + "\n", + "# calling with a list\n", + "print('{:20}'.format('f on a list: '), vf([2, 3, 4]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As mentioned, the `dtype` of the resulting `ndarray` can be specified via the `otypes` keyword. The value is bound to the function object that `vectorize` returns, therefore, if the same function is to be vectorised with different output types, then for each type a new function object must be created." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T19:19:36.090837Z", + "start_time": "2021-01-13T19:19:36.069088Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "output is uint8: array([1, 4, 9, 16], dtype=uint8)\n", + "output is float: array([1.0, 4.0, 9.0, 16.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "l = [1, 2, 3, 4]\n", + "def f(x):\n", + " return x*x\n", + "\n", + "vf1 = np.vectorize(f, otypes=np.uint8)\n", + "vf2 = np.vectorize(f, otypes=np.float)\n", + "\n", + "print('{:20}'.format('output is uint8: '), vf1(l))\n", + "print('{:20}'.format('output is float: '), vf2(l))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `otypes` keyword argument cannot be used for type coercion: if the function evaluates to a float, but `otypes` would dictate an integer type, an exception will be raised:" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-06T22:21:43.616220Z", + "start_time": "2020-05-06T22:21:43.601280Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "integer list: array([1, 4, 9, 16], dtype=uint8)\n", + "\n", + "Traceback (most recent call last):\n", + " File \"/dev/shm/micropython.py\", line 14, in <module>\n", + "TypeError: can't convert float to int\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "int_list = [1, 2, 3, 4]\n", + "float_list = [1.0, 2.0, 3.0, 4.0]\n", + "def f(x):\n", + " return x*x\n", + "\n", + "vf = np.vectorize(f, otypes=np.uint8)\n", + "\n", + "print('{:20}'.format('integer list: '), vf(int_list))\n", + "# this will raise a TypeError exception\n", + "print(vf(float_list))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Benchmarks\n", + "\n", + "It should be pointed out that the `vectorize` function produces the pseudo-vectorised version of the `python` function that is fed into it, i.e., on the C level, the same `python` function is called, with the all-encompassing `mp_obj_t` type arguments, and all that happens is that the `for` loop in `[f(i) for i in iterable]` runs purely in C. Since type checking and type conversion in `f()` is expensive, the speed-up is not so spectacular as when iterating over an `ndarray` with a factory function: a gain of approximately 30% can be expected, when a native `python` type (e.g., `list`) is returned by the function, and this becomes around 50% (a factor of 2), if conversion to an `ndarray` is also counted.\n", + "\n", + "The following code snippet calculates the square of a 1000 numbers with the vectorised function (which returns an `ndarray`), with `list` comprehension, and with `list` comprehension followed by conversion to an `ndarray`. For comparison, the execution time is measured also for the case, when the square is calculated entirely in `ulab`." + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:32:20.048553Z", + "start_time": "2020-05-07T07:32:19.951851Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "vectorised function\r\n", + "execution time: 7237 us\r\n", + "\r\n", + "list comprehension\r\n", + "execution time: 10248 us\r\n", + "\r\n", + "list comprehension + ndarray conversion\r\n", + "execution time: 12562 us\r\n", + "\r\n", + "squaring an ndarray entirely in ulab\r\n", + "execution time: 560 us\r\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "def f(x):\n", + " return x*x\n", + "\n", + "vf = np.vectorize(f)\n", + "\n", + "@timeit\n", + "def timed_vectorised_square(iterable):\n", + " return vf(iterable)\n", + "\n", + "@timeit\n", + "def timed_python_square(iterable):\n", + " return [f(i) for i in iterable]\n", + "\n", + "@timeit\n", + "def timed_ndarray_square(iterable):\n", + " return np.array([f(i) for i in iterable])\n", + "\n", + "@timeit\n", + "def timed_ulab_square(ndarray):\n", + " return ndarray**2\n", + "\n", + "print('vectorised function')\n", + "squares = timed_vectorised_square(range(1000))\n", + "\n", + "print('\\nlist comprehension')\n", + "squares = timed_python_square(range(1000))\n", + "\n", + "print('\\nlist comprehension + ndarray conversion')\n", + "squares = timed_ndarray_square(range(1000))\n", + "\n", + "print('\\nsquaring an ndarray entirely in ulab')\n", + "a = np.array(range(1000))\n", + "squares = timed_ulab_square(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From the comparisons above, it is obvious that `python` functions should only be vectorised, when the same effect cannot be gotten in `ulab` only. However, although the time savings are not significant, there is still a good reason for caring about vectorised functions. Namely, user-defined `python` functions become universal, i.e., they can accept generic iterables as well as `ndarray`s as their arguments. A vectorised function is still a one-liner, resulting in transparent and elegant code.\n", + "\n", + "A final comment on this subject: the `f(x)` that we defined is a *generic* `python` function. This means that it is not required that it just crunches some numbers. It has to return a number object, but it can still access the hardware in the meantime. So, e.g., \n", + "\n", + "```python\n", + "\n", + "led = pyb.LED(2)\n", + "\n", + "def f(x):\n", + " if x < 100:\n", + " led.toggle()\n", + " return x*x\n", + "```\n", + "\n", + "is perfectly valid code." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/scipy-linalg.ipynb b/circuitpython/extmod/ulab/docs/scipy-linalg.ipynb new file mode 100644 index 0000000..6adaa11 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/scipy-linalg.ipynb @@ -0,0 +1,474 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T18:54:58.722373Z", + "start_time": "2021-01-13T18:54:57.178438Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-05-09T05:37:22.600510Z", + "start_time": "2021-05-09T05:37:22.595924Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2021-05-09T05:37:26.429136Z", + "start_time": "2021-05-09T05:37:26.403191Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# scipy.linalg\n", + "\n", + "`scipy`'s `linalg` module contains two functions, `solve_triangular`, and `cho_solve`. The functions can be called by prepending them by `scipy.linalg.`.\n", + "\n", + "1. [scipy.linalg.solve_cho](#cho_solve)\n", + "2. [scipy.linalg.solve_triangular](#solve_triangular)" + ] + }, + { + "source": [ + "## cho_solve\n", + "\n", + "`scipy`: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.cho_solve.html\n", + "\n", + "Solve the linear equations \n", + "\n", + "\n", + "\\begin{equation}\n", + "\\mathbf{A}\\cdot\\mathbf{x} = \\mathbf{b}\n", + "\\end{equation}\n", + "\n", + "given the Cholesky factorization of $\\mathbf{A}$. As opposed to `scipy`, the function simply takes the Cholesky-factorised matrix, $\\mathbf{A}$, and $\\mathbf{b}$ as inputs." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "array([-0.01388888888888906, -0.6458333333333331, 2.677083333333333, -0.01041666666666667], dtype=float64)\n\n\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "A = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 2, 1, 8]])\n", + "b = np.array([4, 2, 4, 2])\n", + "\n", + "print(spy.linalg.cho_solve(A, b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## solve_triangular\n", + "\n", + "`scipy`: https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.solve_triangular.html \n", + "\n", + "Solve the linear equation \n", + "\n", + "\\begin{equation}\n", + "\\mathbf{a}\\cdot\\mathbf{x} = \\mathbf{b}\n", + "\\end{equation}\n", + "\n", + "with the assumption that $\\mathbf{a}$ is a triangular matrix. The two position arguments are $\\mathbf{a}$, and $\\mathbf{b}$, and the optional keyword argument is `lower` with a default value of `False`. `lower` determines, whether data are taken from the lower, or upper triangle of $\\mathbf{a}$. \n", + "\n", + "Note that $\\mathbf{a}$ itself does not have to be a triangular matrix: if it is not, then the values are simply taken to be 0 in the upper or lower triangle, as dictated by `lower`. However, $\\mathbf{a}\\cdot\\mathbf{x}$ will yield $\\mathbf{b}$ only, when $\\mathbf{a}$ is triangular. You should keep this in mind, when trying to establish the validity of the solution by back substitution." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "ExecuteTime": { + "end_time": "2021-05-09T05:56:57.449996Z", + "start_time": "2021-05-09T05:56:57.422515Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + "\n", + "array([[3.0, 0.0, 0.0, 0.0],\n", + " [2.0, 1.0, 0.0, 0.0],\n", + " [1.0, 0.0, 1.0, 0.0],\n", + " [1.0, 2.0, 1.0, 8.0]], dtype=float64)\n", + "\n", + "b: array([4.0, 2.0, 4.0, 2.0], dtype=float64)\n", + "====================\n", + "x: array([1.333333333333333, -0.6666666666666665, 2.666666666666667, -0.08333333333333337], dtype=float64)\n", + "\n", + "dot(a, x): array([4.0, 2.0, 4.0, 2.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "a = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 2, 1, 8]])\n", + "b = np.array([4, 2, 4, 2])\n", + "\n", + "print('a:\\n')\n", + "print(a)\n", + "print('\\nb: ', b)\n", + "\n", + "x = spy.linalg.solve_triangular(a, b, lower=True)\n", + "\n", + "print('='*20)\n", + "print('x: ', x)\n", + "print('\\ndot(a, x): ', np.dot(a, x))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With get the same solution, $\\mathbf{x}$, with the following matrix, but the dot product of $\\mathbf{a}$, and $\\mathbf{x}$ is no longer $\\mathbf{b}$:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "ExecuteTime": { + "end_time": "2021-05-09T06:03:30.853054Z", + "start_time": "2021-05-09T06:03:30.841500Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + "\n", + "array([[3.0, 2.0, 1.0, 0.0],\n", + " [2.0, 1.0, 0.0, 1.0],\n", + " [1.0, 0.0, 1.0, 4.0],\n", + " [1.0, 2.0, 1.0, 8.0]], dtype=float64)\n", + "\n", + "b: array([4.0, 2.0, 4.0, 2.0], dtype=float64)\n", + "====================\n", + "x: array([1.333333333333333, -0.6666666666666665, 2.666666666666667, -0.08333333333333337], dtype=float64)\n", + "\n", + "dot(a, x): array([5.333333333333334, 1.916666666666666, 3.666666666666667, 2.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "a = np.array([[3, 2, 1, 0], [2, 1, 0, 1], [1, 0, 1, 4], [1, 2, 1, 8]])\n", + "b = np.array([4, 2, 4, 2])\n", + "\n", + "print('a:\\n')\n", + "print(a)\n", + "print('\\nb: ', b)\n", + "\n", + "x = spy.linalg.solve_triangular(a, b, lower=True)\n", + "\n", + "print('='*20)\n", + "print('x: ', x)\n", + "print('\\ndot(a, x): ', np.dot(a, x))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/docs/scipy-optimize.ipynb b/circuitpython/extmod/ulab/docs/scipy-optimize.ipynb new file mode 100644 index 0000000..eea97b7 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/scipy-optimize.ipynb @@ -0,0 +1,515 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:50:51.417613Z", + "start_time": "2021-01-08T12:50:51.208257Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:50:52.581876Z", + "start_time": "2021-01-08T12:50:52.567901Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:50:53.516712Z", + "start_time": "2021-01-08T12:50:53.454984Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# scipy.optimize\n", + "\n", + "Functions in the `optimize` module can be called by prepending them by `scipy.optimize.`. The module defines the following three functions:\n", + "\n", + "1. [scipy.optimize.bisect](#bisect)\n", + "1. [scipy.optimize.fmin](#fmin)\n", + "1. [scipy.optimize.newton](#newton)\n", + "\n", + "Note that routines that work with user-defined functions still have to call the underlying `python` code, and therefore, gains in speed are not as significant as with other vectorised operations. As a rule of thumb, a factor of two can be expected, when compared to an optimised `python` implementation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## bisect \n", + "\n", + "`scipy`: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.bisect.html\n", + "\n", + "`bisect` finds the root of a function of one variable using a simple bisection routine. It takes three positional arguments, the function itself, and two starting points. The function must have opposite signs\n", + "at the starting points. Returned is the position of the root.\n", + "\n", + "Two keyword arguments, `xtol`, and `maxiter` can be supplied to control the accuracy, and the number of bisections, respectively." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:58:28.444300Z", + "start_time": "2021-01-08T12:58:28.421989Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9999997615814209\n", + "only 8 bisections: 0.984375\n", + "with 0.1 accuracy: 0.9375\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import scipy as spy\n", + " \n", + "def f(x):\n", + " return x*x - 1\n", + "\n", + "print(spy.optimize.bisect(f, 0, 4))\n", + "\n", + "print('only 8 bisections: ', spy.optimize.bisect(f, 0, 4, maxiter=8))\n", + "\n", + "print('with 0.1 accuracy: ', spy.optimize.bisect(f, 0, 4, xtol=0.1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Performance\n", + "\n", + "Since the `bisect` routine calls user-defined `python` functions, the speed gain is only about a factor of two, if compared to a purely `python` implementation." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:08:24.750562Z", + "start_time": "2020-05-19T19:08:24.682959Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "bisect running in python\r\n", + "execution time: 1270 us\r\n", + "bisect running in C\r\n", + "execution time: 642 us\r\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import scipy as spy\n", + "\n", + "def f(x):\n", + " return (x-1)*(x-1) - 2.0\n", + "\n", + "def bisect(f, a, b, xtol=2.4e-7, maxiter=100):\n", + " if f(a) * f(b) > 0:\n", + " raise ValueError\n", + "\n", + " rtb = a if f(a) < 0.0 else b\n", + " dx = b - a if f(a) < 0.0 else a - b\n", + " for i in range(maxiter):\n", + " dx *= 0.5\n", + " x_mid = rtb + dx\n", + " mid_value = f(x_mid)\n", + " if mid_value < 0:\n", + " rtb = x_mid\n", + " if abs(dx) < xtol:\n", + " break\n", + "\n", + " return rtb\n", + "\n", + "@timeit\n", + "def bisect_scipy(f, a, b):\n", + " return spy.optimize.bisect(f, a, b)\n", + "\n", + "@timeit\n", + "def bisect_timed(f, a, b):\n", + " return bisect(f, a, b)\n", + "\n", + "print('bisect running in python')\n", + "bisect_timed(f, 3, 2)\n", + "\n", + "print('bisect running in C')\n", + "bisect_scipy(f, 3, 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## fmin\n", + "\n", + "`scipy`: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin.html\n", + "\n", + "The `fmin` function finds the position of the minimum of a user-defined function by using the downhill simplex method. Requires two positional arguments, the function, and the initial value. Three keyword arguments, `xatol`, `fatol`, and `maxiter` stipulate conditions for stopping." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:00:26.729947Z", + "start_time": "2021-01-08T13:00:26.702748Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9996093749999952\n", + "1.199999999999996\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import scipy as spy\n", + "\n", + "def f(x):\n", + " return (x-1)**2 - 1\n", + "\n", + "print(spy.optimize.fmin(f, 3.0))\n", + "print(spy.optimize.fmin(f, 3.0, xatol=0.1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## newton\n", + "\n", + "`scipy`:https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.newton.html\n", + "\n", + "`newton` finds a zero of a real, user-defined function using the Newton-Raphson (or secant or Halley’s) method. The routine requires two positional arguments, the function, and the initial value. Three keyword\n", + "arguments can be supplied to control the iteration. These are the absolute and relative tolerances `tol`, and `rtol`, respectively, and the number of iterations before stopping, `maxiter`. The function retuns a single scalar, the position of the root." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:56:35.139958Z", + "start_time": "2021-01-08T12:56:35.119712Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.260135727246117\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import scipy as spy\n", + " \n", + "def f(x):\n", + " return x*x*x - 2.0\n", + "\n", + "print(spy.optimize.newton(f, 3., tol=0.001, rtol=0.01))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/scipy-signal.ipynb b/circuitpython/extmod/ulab/docs/scipy-signal.ipynb new file mode 100644 index 0000000..c4d5f85 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/scipy-signal.ipynb @@ -0,0 +1,482 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:11:12.111639Z", + "start_time": "2021-01-12T16:11:11.914041Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:20:19.755153Z", + "start_time": "2022-01-07T19:20:19.745524Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:20:27.595871Z", + "start_time": "2022-01-07T19:20:27.565514Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../micropython/ports/unix/micropython-2\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# scipy.signal\n", + "\n", + "Functions in the `signal` module can be called by prepending them by `scipy.signal.`. The module defines the following two functions:\n", + "\n", + "1. [scipy.signal.sosfilt](#sosfilt)\n", + "1. [scipy.signal.spectrogram](#spectrogram)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## sosfilt\n", + "\n", + "`scipy`: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.sosfilt.html \n", + "\n", + "Filter data along one dimension using cascaded second-order sections.\n", + "\n", + "The function takes two positional arguments, `sos`, the filter segments of length 6, and the one-dimensional, uniformly sampled data set to be filtered. Returns the filtered data, or the filtered data and the final filter delays, if the `zi` keyword arguments is supplied. The keyword argument must be a float `ndarray` of shape `(n_sections, 2)`. If `zi` is not passed to the function, the initial values are assumed to be 0." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2020-06-19T20:24:10.529668Z", + "start_time": "2020-06-19T20:24:10.520389Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "y: array([0.0, 1.0, -4.0, 24.0, -104.0, 440.0, -1728.0, 6532.000000000001, -23848.0, 84864.0], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", + "sos = [[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]]\n", + "y = spy.signal.sosfilt(sos, x)\n", + "print('y: ', y)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "ExecuteTime": { + "end_time": "2020-06-19T20:27:39.508508Z", + "start_time": "2020-06-19T20:27:39.498256Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "y: array([4.0, -16.0, 63.00000000000001, -227.0, 802.9999999999999, -2751.0, 9271.000000000001, -30775.0, 101067.0, -328991.0000000001], dtype=float)\n", + "\n", + "========================================\n", + "zf: array([[37242.0, 74835.0],\n", + "\t [1026187.0, 1936542.0]], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", + "sos = [[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]]\n", + "# initial conditions of the filter\n", + "zi = np.array([[1, 2], [3, 4]])\n", + "\n", + "y, zf = spy.signal.sosfilt(sos, x, zi=zi)\n", + "print('y: ', y)\n", + "print('\\n' + '='*40 + '\\nzf: ', zf)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## spectrogram\n", + "\n", + "In addition to the Fourier transform and its inverse, `ulab` also sports a function called `spectrogram`, which returns the absolute value of the Fourier transform. This could be used to find the dominant spectral component in a time series. The arguments are treated in the same way as in `fft`, and `ifft`. This means that, if the firmware was compiled with complex support, the input can also be a complex array." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:12:06.573408Z", + "start_time": "2021-01-12T16:12:06.560558Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "original vector:\t array([0.0, 0.009775015390171337, 0.01954909674625918, ..., -0.5275140569487312, -0.5357931822978732, -0.5440211108893639], dtype=float64)\n", + "\n", + "spectrum:\t array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "x = np.linspace(0, 10, num=1024)\n", + "y = np.sin(x)\n", + "\n", + "a = spy.signal.spectrogram(y)\n", + "\n", + "print('original vector:\\t', y)\n", + "print('\\nspectrum:\\t', a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As such, `spectrogram` is really just a shorthand for `np.sqrt(a*a + b*b)`:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:13:36.726662Z", + "start_time": "2021-01-12T16:13:36.705036Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "spectrum calculated the hard way:\t array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)\n", + "\n", + "spectrum calculated the lazy way:\t array([187.8635087634579, 315.3112063607119, 347.8814873399374, ..., 84.45888934298905, 347.8814873399374, 315.3112063607118], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "x = np.linspace(0, 10, num=1024)\n", + "y = np.sin(x)\n", + "\n", + "a, b = np.fft.fft(y)\n", + "\n", + "print('\\nspectrum calculated the hard way:\\t', np.sqrt(a*a + b*b))\n", + "\n", + "a = spy.signal.spectrogram(y)\n", + "\n", + "print('\\nspectrum calculated the lazy way:\\t', a)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/scipy-special.ipynb b/circuitpython/extmod/ulab/docs/scipy-special.ipynb new file mode 100644 index 0000000..c3a0cf8 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/scipy-special.ipynb @@ -0,0 +1,344 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T18:54:58.722373Z", + "start_time": "2021-01-13T18:54:57.178438Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T18:57:41.555892Z", + "start_time": "2021-01-13T18:57:41.551121Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T18:57:42.313231Z", + "start_time": "2021-01-13T18:57:42.288402Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# scipy.special\n", + "\n", + "`scipy`'s `special` module defines several functions that behave as do the standard mathematical functions of the `numpy`, i.e., they can be called on any scalar, scalar-valued iterable (ranges, lists, tuples containing numbers), and on `ndarray`s without having to change the call signature. In all cases the functions return a new `ndarray` of typecode `float` (since these functions usually generate float values, anyway). \n", + "\n", + "At present, `ulab`'s `special` module contains the following functions:\n", + "\n", + "`erf`, `erfc`, `gamma`, and `gammaln`, and they can be called by prepending them by `scipy.special.`." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T19:06:54.640444Z", + "start_time": "2021-01-13T19:06:54.623467Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: range(0, 9)\n", + "array([0.0, 0.8427007929497149, 0.9953222650189527, 0.9999779095030014, 0.9999999845827421, 1.0, 1.0, 1.0, 1.0], dtype=float64)\n", + "\n", + "b: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "array([1.0, 0.1572992070502851, 0.004677734981047265, 2.209049699858544e-05, 1.541725790028002e-08, 1.537459794428035e-12, 2.151973671249892e-17, 4.183825607779414e-23, 1.122429717298293e-29], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "a = range(9)\n", + "b = np.array(a)\n", + "\n", + "print('a: ', a)\n", + "print(spy.special.erf(a))\n", + "\n", + "print('\\nb: ', b)\n", + "print(spy.special.erfc(b))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/templates/manual.tpl b/circuitpython/extmod/ulab/docs/templates/manual.tpl new file mode 100644 index 0000000..ba6b73e --- /dev/null +++ b/circuitpython/extmod/ulab/docs/templates/manual.tpl @@ -0,0 +1,113 @@ + +{%- extends 'display_priority.tpl' -%} + + +{% block in_prompt %} +{% endblock in_prompt %} + +{% block output_prompt %} +{% endblock output_prompt %} + +{% block input scoped%} + +{%- if cell.source.split('\n')[0].startswith('%%micropython') -%} +.. code:: + +{{ '\n'.join(['# code to be run in micropython'] + cell.source.strip().split('\n')[1:]) | indent}} + +{%- else -%} +.. code:: + +{{ '\n'.join(['# code to be run in CPython\n'] + cell.source.strip().split('\n')) | indent}} +{%- endif -%} +{% endblock input %} + +{% block error %} +:: + +{{ super() }} +{% endblock error %} + +{% block traceback_line %} +{{ line | indent | strip_ansi }} +{% endblock traceback_line %} + +{% block execute_result %} +{% block data_priority scoped %} +{{ super() }} +{% endblock %} +{% endblock execute_result %} + +{% block stream %} +.. parsed-literal:: + +{{ output.text | indent }} +{% endblock stream %} + +{% block data_svg %} +.. image:: {{ output.metadata.filenames['image/svg+xml'] | urlencode }} +{% endblock data_svg %} + +{% block data_png %} +.. image:: {{ output.metadata.filenames['image/png'] | urlencode }} +{%- set width=output | get_metadata('width', 'image/png') -%} +{%- if width is not none %} + :width: {{ width }}px +{%- endif %} +{%- set height=output | get_metadata('height', 'image/png') -%} +{%- if height is not none %} + :height: {{ height }}px +{%- endif %} +{% endblock data_png %} + +{% block data_jpg %} +.. image:: {{ output.metadata.filenames['image/jpeg'] | urlencode }} +{%- set width=output | get_metadata('width', 'image/jpeg') -%} +{%- if width is not none %} + :width: {{ width }}px +{%- endif %} +{%- set height=output | get_metadata('height', 'image/jpeg') -%} +{%- if height is not none %} + :height: {{ height }}px +{%- endif %} +{% endblock data_jpg %} + +{% block data_markdown %} +{{ output.data['text/markdown'] | convert_pandoc("markdown", "rst") }} +{% endblock data_markdown %} + +{% block data_latex %} +.. math:: + +{{ output.data['text/latex'] | strip_dollars | indent }} +{% endblock data_latex %} + +{% block data_text scoped %} +.. parsed-literal:: + +{{ output.data['text/plain'] | indent }} +{% endblock data_text %} + +{% block data_html scoped %} +.. raw:: html + +{{ output.data['text/html'] | indent }} +{% endblock data_html %} + +{% block markdowncell scoped %} +{{ cell.source | convert_pandoc("markdown", "rst") }} +{% endblock markdowncell %} + +{%- block rawcell scoped -%} +{%- if cell.metadata.get('raw_mimetype', '').lower() in resources.get('raw_mimetypes', ['']) %} +{{cell.source}} +{% endif -%} +{%- endblock rawcell -%} + +{% block headingcell scoped %} +{{ ("#" * cell.level + cell.source) | replace('\n', ' ') | convert_pandoc("markdown", "rst") }} +{% endblock headingcell %} + +{% block unknowncell scoped %} +unknown type {{cell.type}} +{% endblock unknowncell %} diff --git a/circuitpython/extmod/ulab/docs/templates/rst.tpl b/circuitpython/extmod/ulab/docs/templates/rst.tpl new file mode 100644 index 0000000..479a69f --- /dev/null +++ b/circuitpython/extmod/ulab/docs/templates/rst.tpl @@ -0,0 +1,144 @@ + +{%- extends 'display_priority.tpl' -%} + + +{% block in_prompt %} +{% endblock in_prompt %} + +{% block output_prompt %} +{% endblock output_prompt %} + +{% block input scoped%} + +{%- if '%%ccode' in cell.source.strip().split('\n')[0] -%} + +{{ 'https://github.com/v923z/micropython-ulab/tree/master/code/' + cell.source.strip().split('\n')[0].split()[-1] }} + +.. code:: cpp + +{{ '\n'.join( cell.source.strip().split('\n')[1:] ) | indent }} + +{%- elif '%%makefile' in cell.source.strip().split('\n')[0] -%} + +{{ 'https://github.com/v923z/micropython-ulab/tree/master/code/' + cell.source.strip().split('\n')[0].split()[-1].split('/')[1] + '/micropython.mk' }} + +.. code:: make + +{{ '\n'.join( cell.source.strip().split('\n')[1:] ) | indent }} + +{%- elif cell.source.strip().split('\n')[0].startswith('!') -%} + +.. code:: bash + +{{ cell.source | indent }} + +{%- else -%} +{%- if 'magics_language' in cell.metadata -%} + {{ cell.metadata.magics_language}} +{%- elif 'pygments_lexer' in nb.metadata.get('language_info', {}) -%} + {{ nb.metadata.language_info.pygments_lexer }} +{%- elif 'name' in nb.metadata.get('language_info', {}) -%} + {{ nb.metadata.language_info.name }} +{%- endif -%} + +.. code :: + +{{ cell.source | indent}} +{%- endif -%} +{% endblock input %} + +{% block error %} +:: + +{{ super() }} +{% endblock error %} + +{% block traceback_line %} +{{ line | indent | strip_ansi }} +{% endblock traceback_line %} + +{% block execute_result %} +{% block data_priority scoped %} +{{ super() }} +{% endblock %} +{% endblock execute_result %} + +{% block stream %} +{%- if '%%ccode' in cell.source.strip().split('\n')[0] -%} +{%- else -%} + +.. parsed-literal:: + +{{ output.text | indent }} +{%- endif -%} +{% endblock stream %} + +{% block data_svg %} +.. image:: {{ output.metadata.filenames['image/svg+xml'] | urlencode }} +{% endblock data_svg %} + +{% block data_png %} +.. image:: {{ output.metadata.filenames['image/png'] | urlencode }} +{%- set width=output | get_metadata('width', 'image/png') -%} +{%- if width is not none %} + :width: {{ width }}px +{%- endif %} +{%- set height=output | get_metadata('height', 'image/png') -%} +{%- if height is not none %} + :height: {{ height }}px +{%- endif %} +{% endblock data_png %} + +{% block data_jpg %} +.. image:: {{ output.metadata.filenames['image/jpeg'] | urlencode }} +{%- set width=output | get_metadata('width', 'image/jpeg') -%} +{%- if width is not none %} + :width: {{ width }}px +{%- endif %} +{%- set height=output | get_metadata('height', 'image/jpeg') -%} +{%- if height is not none %} + :height: {{ height }}px +{%- endif %} +{% endblock data_jpg %} + +{% block data_markdown %} +{{ output.data['text/markdown'] | convert_pandoc("markdown", "rst") }} +{% endblock data_markdown %} + +{% block data_latex %} +.. math:: + +{{ output.data['text/latex'] | strip_dollars | indent }} +{% endblock data_latex %} + +{% block data_text scoped %} + +.. parsed-literal:: + +{{ output.data['text/plain'] | indent }} +{% endblock data_text %} + +{% block data_html scoped %} +.. raw:: html + +{{ output.data['text/html'] | indent }} +{% endblock data_html %} + +{% block markdowncell scoped %} +{{ cell.source | convert_pandoc("markdown", "rst") }} +{% endblock markdowncell %} + +{%- block rawcell scoped -%} +{%- if cell.metadata.get('raw_mimetype', '').lower() in resources.get('raw_mimetypes', ['']) %} +{{cell.source}} +{% endif -%} +{%- endblock rawcell -%} + +{% block headingcell scoped %} +{{ ("#" * cell.level + cell.source) | replace('\n', ' ') | convert_pandoc("markdown", "rst") }} + +{% endblock headingcell %} + +{% block unknowncell scoped %} +unknown type {{cell.type}} +{% endblock unknowncell %} diff --git a/circuitpython/extmod/ulab/docs/ulab-approx.ipynb b/circuitpython/extmod/ulab/docs/ulab-approx.ipynb new file mode 100644 index 0000000..52dc205 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-approx.ipynb @@ -0,0 +1,613 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:50:51.417613Z", + "start_time": "2021-01-08T12:50:51.208257Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:50:52.581876Z", + "start_time": "2021-01-08T12:50:52.567901Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:50:53.516712Z", + "start_time": "2021-01-08T12:50:53.454984Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Approximation methods\n", + "\n", + "`ulab` implements five functions that can be used for interpolating, root finding, and minimising arbitrary `python` functions in one dimension. Two of these functions, namely, `interp`, and `trapz` are defined in `numpy`, while the other three are parts of `scipy`'s `optimize` module. \n", + "\n", + "Note that routines that work with user-defined functions still have to call the underlying `python` code, and therefore, gains in speed are not as significant as with other vectorised operations. As a rule of thumb, a factor of two can be expected, when compared to an optimised `python` implementation." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## interp\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/numpy.interp\n", + "\n", + "The `interp` function returns the linearly interpolated values of a one-dimensional numerical array. It requires three positional arguments,`x`, at which the interpolated values are evaluated, `xp`, the array\n", + "of the independent data variable, and `fp`, the array of the dependent values of the data. `xp` must be a monotonically increasing sequence of numbers.\n", + "\n", + "Two keyword arguments, `left`, and `right` can also be supplied; these determine the return values, if `x < xp[0]`, and `x > xp[-1]`, respectively. If these arguments are not supplied, `left`, and `right` default to `fp[0]`, and `fp[-1]`, respectively." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:54:58.895801Z", + "start_time": "2021-01-08T12:54:58.869338Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([0.8, 1.8, 2.8, 3.8, 4.8], dtype=float64)\n", + "array([1.0, 1.8, 2.8, 4.6, 5.0], dtype=float64)\n", + "array([0.0, 1.8, 2.8, 4.6, 5.0], dtype=float64)\n", + "array([1.0, 1.8, 2.8, 4.6, 10.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.array([1, 2, 3, 4, 5]) - 0.2\n", + "xp = np.array([1, 2, 3, 4])\n", + "fp = np.array([1, 2, 3, 5])\n", + "\n", + "print(x)\n", + "print(np.interp(x, xp, fp))\n", + "print(np.interp(x, xp, fp, left=0.0))\n", + "print(np.interp(x, xp, fp, right=10.0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## newton\n", + "\n", + "`scipy`:https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.newton.html\n", + "\n", + "`newton` finds a zero of a real, user-defined function using the Newton-Raphson (or secant or Halley’s) method. The routine requires two positional arguments, the function, and the initial value. Three keyword\n", + "arguments can be supplied to control the iteration. These are the absolute and relative tolerances `tol`, and `rtol`, respectively, and the number of iterations before stopping, `maxiter`. The function retuns a single scalar, the position of the root." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:56:35.139958Z", + "start_time": "2021-01-08T12:56:35.119712Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.260135727246117\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import scipy as spy\n", + " \n", + "def f(x):\n", + " return x*x*x - 2.0\n", + "\n", + "print(spy.optimize.newton(f, 3., tol=0.001, rtol=0.01))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## bisect \n", + "\n", + "`scipy`: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.bisect.html\n", + "\n", + "`bisect` finds the root of a function of one variable using a simple bisection routine. It takes three positional arguments, the function itself, and two starting points. The function must have opposite signs\n", + "at the starting points. Returned is the position of the root.\n", + "\n", + "Two keyword arguments, `xtol`, and `maxiter` can be supplied to control the accuracy, and the number of bisections, respectively." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:58:28.444300Z", + "start_time": "2021-01-08T12:58:28.421989Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9999997615814209\n", + "only 8 bisections: 0.984375\n", + "with 0.1 accuracy: 0.9375\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import scipy as spy\n", + " \n", + "def f(x):\n", + " return x*x - 1\n", + "\n", + "print(spy.optimize.bisect(f, 0, 4))\n", + "\n", + "print('only 8 bisections: ', spy.optimize.bisect(f, 0, 4, maxiter=8))\n", + "\n", + "print('with 0.1 accuracy: ', spy.optimize.bisect(f, 0, 4, xtol=0.1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Performance\n", + "\n", + "Since the `bisect` routine calls user-defined `python` functions, the speed gain is only about a factor of two, if compared to a purely `python` implementation." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:08:24.750562Z", + "start_time": "2020-05-19T19:08:24.682959Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "bisect running in python\r\n", + "execution time: 1270 us\r\n", + "bisect running in C\r\n", + "execution time: 642 us\r\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import scipy as spy\n", + "\n", + "def f(x):\n", + " return (x-1)*(x-1) - 2.0\n", + "\n", + "def bisect(f, a, b, xtol=2.4e-7, maxiter=100):\n", + " if f(a) * f(b) > 0:\n", + " raise ValueError\n", + "\n", + " rtb = a if f(a) < 0.0 else b\n", + " dx = b - a if f(a) < 0.0 else a - b\n", + " for i in range(maxiter):\n", + " dx *= 0.5\n", + " x_mid = rtb + dx\n", + " mid_value = f(x_mid)\n", + " if mid_value < 0:\n", + " rtb = x_mid\n", + " if abs(dx) < xtol:\n", + " break\n", + "\n", + " return rtb\n", + "\n", + "@timeit\n", + "def bisect_scipy(f, a, b):\n", + " return spy.optimize.bisect(f, a, b)\n", + "\n", + "@timeit\n", + "def bisect_timed(f, a, b):\n", + " return bisect(f, a, b)\n", + "\n", + "print('bisect running in python')\n", + "bisect_timed(f, 3, 2)\n", + "\n", + "print('bisect running in C')\n", + "bisect_scipy(f, 3, 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## fmin\n", + "\n", + "`scipy`: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.fmin.html\n", + "\n", + "The `fmin` function finds the position of the minimum of a user-defined function by using the downhill simplex method. Requires two positional arguments, the function, and the initial value. Three keyword arguments, `xatol`, `fatol`, and `maxiter` stipulate conditions for stopping." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:00:26.729947Z", + "start_time": "2021-01-08T13:00:26.702748Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9996093749999952\n", + "1.199999999999996\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import scipy as spy\n", + "\n", + "def f(x):\n", + " return (x-1)**2 - 1\n", + "\n", + "print(spy.optimize.fmin(f, 3.0))\n", + "print(spy.optimize.fmin(f, 3.0, xatol=0.1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## trapz\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.trapz.html\n", + "\n", + "The function takes one or two one-dimensional `ndarray`s, and integrates the dependent values (`y`) using the trapezoidal rule. If the independent variable (`x`) is given, that is taken as the sample points corresponding to `y`." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:01:29.515166Z", + "start_time": "2021-01-08T13:01:29.494285Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64)\n", + "y: array([0.0, 1.0, 4.0, 9.0, 16.0, 25.0, 36.0, 49.0, 64.0, 81.0], dtype=float64)\n", + "============================\n", + "integral of y: 244.5\n", + "integral of y at x: 244.5\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "x = np.linspace(0, 9, num=10)\n", + "y = x*x\n", + "\n", + "print('x: ', x)\n", + "print('y: ', y)\n", + "print('============================')\n", + "print('integral of y: ', np.trapz(y))\n", + "print('integral of y at x: ', np.trapz(y, x=x))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/ulab-change-log.md b/circuitpython/extmod/ulab/docs/ulab-change-log.md new file mode 100644 index 0000000..be9dc5e --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-change-log.md @@ -0,0 +1,957 @@ +Fri, 3 Dec 2021 + +version 3.3.8 + + fix any/all function + +Tue, 30 Nov 2021 + +version 3.3.7 + + fix sum() for integer/Boolean types + +Sat, 20 Nov 2021 + +version 3.3.6 + + fix .shape for arrays of zero length (#454) + +Sun, 07 Nov 2021 + +version 3.3.5 + + fix cast in numpy/compare.c:compare_function() + +Sat, 07 Aug 2021 + +version 3.3.4 + + change default keyword value in linalg.qr + +Fri, 23 Jul 2021 + +version 3.3.3 + + fix compilation for one dimension + +Thu, 22 Jul 2021 + +version 3.3.2 + + fix compilation error on SAMD devices + +Thu, 22 Jul 2021 + +version 3.3.1 + + fix sum for 4D arrays + +Thu, 22 Jul 2021 + +version 3.3.0 + + add QR decomposition + +Tue, 13 Jul 2021 + +version 3.2.0 + + add flatiter/flat to ndarray methods + +Tue, 22 Jun 2021 + +version 3.1.1 + + fix float comparison in scipy/linalg.c + +Sat, 19 Jun 2021 + +version 3.1.0 + + ndarray.shape can now be assigned to + +Thu, 17 Jun 2021 + +version 3.0.1 + + add the .T ndarray property + +Wed, 9 Jun 2021 + +version 3.0.0 + + implement property getter/setter for micropython + +Thu, 3 Jun 2021 + +version 2.9.0 + + add empty as alias for zeros + +Thu, 3 Jun 2021 + +version 2.8.8 + + allow functions in approx to take iterables as argument + +Thu, 3 Jun 2021 + +version 2.8.7 + + simplify vectorised function code + +Wed, 2 Jun 2021 + +version 2.8.6 + + factor out array creation from iterables, so that generic iterables can be passed to numerical functions + +Tue, 1 Jun 2021 + +version 2.8.5 + + fix upcasting rules for ndarray + scalar + +Mon, 31 May 2021 + +version 2.8.4 + + initialise arange values via macro + +Mon, 24 May 2021 + +version 2.8.3 + + fix nan return value + +Sat, 22 May 2021 + +version 2.8.2 + + fix all/any/median for empty arrays + +Tue, 18 May 2021 + +version 2.8.1 + + fix array initialisation/print with empty iterables + +Sun, 16 May 2021 + +version 2.8.0 + + added cho_solve function in scipy.linalg module + +Thu, 13 May 2021 + +version 2.7.1 + + fix garbage collection problem + +Wed, 5 May 2021 + +version 2.7.0 + + added linalg module in scipy with solve_triangular function + +Mon, 26 Apr 2021 + +version 2.6.2 + + fix optimize zero condition + +Sat, 23 Apr 2021 + +version 2.6.1 + + fix implementation of math constants + + +Mon, 22 Mar 2021 + +version 2.6.0 + + add where function + +Mon, 8 Mar 2021 + +version 2.5.1 + + fix linspace/logspace/arange for Boolean dtypes + +Wed, 03 Mar 2021 + +version 2.5.0 + + added utils sub-module with from_intbuffer function + +Tue, 23 Feb 2021 + +version 2.4.5 + + fix dot function + +Sun, 21 Feb 2021 + +version 2.4.3 + + re-introduce ndarray_get_buffer, and buffer protocol + +Sun, 21 Feb 2021 + +version 2.4.2 + + fix ndarray_is_dense, eye, ones, full, and zeros for Boolean type + +Sat, 13 Feb 2021 + +version 2.4.1 + + fixed dot error + +Fri, 12 Feb 2021 + +version 2.4.0 + + added byteswap method + +Sun, 14 Feb 2021 + +version 2.3.7 + + fixed frombuffer implementation glitch + +Sat, 13 Feb 2021 + +version 2.3.6 + + moved trace and dot to the top level + +Wed, 10 Feb 2021 + +version 2.3.5 + + fixed invisible error in tools_reduce_axes, simplified the implementation of all/any + +Tue, 9 Feb 2021 + +version 2.3.4 + + removed redundant exception from linalg.norm, fixed exception message in tools_reduce_axes + +Tue, 9 Feb 2021 + +version 2.3.3 + + linalg.norm should now work with the axis keyword argument + +Mon, 8 Feb 2021 + +version 2.3.2 + + improved the accuracy of linalg.norm, and extended it to generic iterables + +Mon, 8 Feb 2021 + +version 2.3.1 + + partially fix https://github.com/v923z/micropython-ulab/issues/304, and len unary operator + +Mon, 8 Feb 2021 + +version 2.3.0 + + added any and all functions + +Fri, 29 Jan 2021 + +version 2.2.0 + + added isinf/infinite functions + +Fri, 29 Jan 2021 + +version 2.1.5 + + fixed error, when calculating standard deviation of iterables + +wed, 27 Jan 2021 + +version 2.1.4 + + arrays can now be initialised from nested iterables + +Thu, 21 Jan 2021 + +version 2.1.3 + + added ifndef/endif wrappers in ulab.h + +Fri, 15 Jan 2021 + +version 2.1.2 + + fixed small error in frombuffer + +Thu, 14 Jan 2021 + +version 2.1.1 + + fixed bad error in diff + +Thu, 26 Nov 2020 + +version 2.1.0 + + implemented frombuffer + +Tue, 24 Nov 2020 + +version 2.0.0 + + implemented numpy/scipy compatibility + +Tue, 24 Nov 2020 + +version 1.6.0 + + added Boolean initialisation option + +Mon, 23 Nov 2020 + +version 1.5.1 + + fixed nan definition + +version 1.5.0 + + added nan/inf class level constants + +version 1.4.10 + + fixed sosfilt + +version 1.4.9 + + added in-place sort + +version 1.4.8 + + fixed convolve + +version 1.4.7. + + fixed iteration loop in norm + +Fri, 20 Nov 2020 + +version 1.4.6 + + fixed interp + +Thu, 19 Nov 2020 + +version 1.4.5 + + eliminated fatal micropython error in ndarray_init_helper + +version 1.4.4 + + fixed min, max + +version 1.4.3 + + fixed full, zeros, ones + +version 1.4.2 + + fixed dtype + +Wed, 18 Nov 2020 + +version 1.4.1. + + fixed std + +version 1.4.0 + + removed size from linalg + +version 1.3.8 + + fixed trapz + +Tue, 17 Nov 2020 + +version 1.3.7 + + fixed in-place power, in-place divide, roll + +Mon, 16 Nov 2020 + +version 1.3.6 + + fixed eye + +Mon, 16 Nov 2020 + +version 1.3.5 + + fixed trace + +Mon, 16 Nov 2020 + +version 1.3.4 + + fixed clip + +Mon, 16 Nov 2020 + +version 1.3.3 + + added function pointer option to some binary operators + +Fri, 13 Nov 2020 + +version 1.3.2 + + implemented function pointer option in vectorise + +Thu, 12 Nov 2020 + +version 1.3.1 + + factored out some of the math functions in re-usable form + +Wed, 11 Nov 2020 + +version 1.3.0 + + added dtype function/method/property + +Wed, 11 Nov 2020 + +version 1.2.8 + + improved the accuracy of sum for float types + +Wed, 11 Nov 2020 + +version 1.2.7 + + fixed transpose + improved the accuracy of trapz + +Tue, 10 Nov 2020 + +version 1.2.6 + + fixed slicing + +Mon, 9 Nov 2020 + +version 1.2.5 + + fixed array casting glitch in make_new_core + +Mon, 9 Nov 2020 + +version 1.2.4 + + sum/mean/std can flatten the arrays now + +Tue, 3 Nov 2020 + +version 1.2.1 + + fixed pointer issue in eig, and corrected the docs + +Tue, 3 Nov 2020 + +version 1.2.0 + + added median function + +Tue, 3 Nov 2020 + +version 1.1.4 + + fixed norm and shape + +Mon, 2 Nov 2020 + +version 1.1.3 + + fixed small glitch in diagonal, and ndarray_make_new_core + +Sun, 1 Nov 2020 + +version 1.1.1 + + fixed compilation error for 4D + +Sat, 31 Oct 2020 + +version 1.1.0 + + added the diagonal function + +Fri, 30 Oct 2020 + +version 1.0.0 + + added : + support for tensors of rank 4 + proper broadcasting + views + .tobytes() + concatenate + cross + full + logspace + in-place operators + +Sat, 25 Oct 2020 + +version 0.54.5 + + wrong type in slices raise TypeError exception + +Fri, 23 Oct 2020 + +version 0.54.4 + + fixed indexing error in slices + +Mon, 17 Aug 2020 + +version 0.54.3 + + fixed small error in linalg + +Mon, 03 Aug 2020 + +version 0.54.2 + + argsort throws an error, if the array is longer than 65535 + +Wed, 29 Jul 2020 + +version 0.54.1 + + changed to size_t for the length of arrays + +Thu, 23 Jul 2020 + +version 0.54.0 + + added norm to linalg + +Wed, 22 Jul 2020 + +version 0.53.2 + + added circuitpython documentation stubs to the source files + +Wed, 22 Jul 2020 + +version 0.53.1 + + fixed arange with negative steps + +Mon, 20 Jul 2020 + +version 0.53.0 + + added arange to create.c + +Thu, 16 Jul 2020 + +version 0.52.0 + + added trapz to approx + +Mon, 29 Jun 2020 + +version 0.51.1 + + fixed argmin/argmax issue + +Fri, 19 Jun 2020 + +version 0.51.0 + + add sosfilt to the filter sub-module + +Fri, 12 Jun 2020 + +version 0.50.2 + + fixes compilation error in openmv + +Mon, 1 Jun 2020 + +version 0.50.1 + + fixes error in numerical max/min + +Mon, 18 May 2020 + +version 0.50.0 + + move interp to the approx sub-module + +Wed, 06 May 2020 + +version 0.46.0 + + add curve_fit to the approx sub-module + +version 0.44.0 + + add approx sub-module with newton, fmin, and bisect functions + +Thu, 30 Apr 2020 + +version 0.44.0 + + add approx sub-module with newton, fmin, and bisect functions + +Tue, 19 May 2020 + +version 0.46.1 + + fixed bad error in binary_op + +Wed, 6 May 2020 + +version 0.46 + + added vectorisation of python functions + +Sat, 2 May 2020 + +version 0.45.0 + + add equal/not_equal to the compare module + +Tue, 21 Apr 2020 + +version 0.42.0 + + add minimum/maximum/clip functions + +Mon, 20 Apr 2020 + +version 0.41.6 + + argument handling improvement in polyfit + +Mon, 20 Apr 2020 + +version 0.41.5 + + fix compilation errors due to https://github.com/micropython/micropython/commit/30840ebc9925bb8ef025dbc2d5982b1bfeb75f1b + +Sat, 18 Apr 2020 + +version 0.41.4 + + fix compilation error on hardware ports + +Tue, 14 Apr 2020 + +version 0.41.3 + + fix indexing error in dot function + +Thu, 9 Apr 2020 + +version 0.41.2 + + fix transpose function + +Tue, 7 Apr 2020 + +version 0.41.2 + + fix discrepancy in argmin/argmax behaviour + +Tue, 7 Apr 2020 + +version 0.41.1 + + fix error in argsort + +Sat, 4 Apr 2020 + +version 0.41.0 + + implemented == and != binary operators + +Fri, 3 Apr 2020 + +version 0.40.0 + + added trace to linalg + +Thu, 2 Apr 2020 + +version 0.39.0 + + added the ** operator, and operand swapping in binary operators + +Thu, 2 Apr 2020 + +version 0.38.1 + + added fast option, when initialising from ndarray_properties + +Thu, 12 Mar 2020 + +version 0.38.0 + + added initialisation from ndarray, and the around function + +Tue, 10 Mar 2020 + +version 0.37.0 + + added Cholesky decomposition to linalg.c + +Thu, 27 Feb 2020 + +version 0.36.0 + + moved zeros, ones, eye and linspace into separate module (they are still bound at the top level) + +Thu, 27 Feb 2020 + +version 0.35.0 + + Move zeros, ones back into top level ulab module + +Tue, 18 Feb 2020 + +version 0.34.0 + + split ulab into multiple modules + +Sun, 16 Feb 2020 + +version 0.33.2 + + moved properties into ndarray_properties.h, implemented pointer arithmetic in fft.c to save some time + +Fri, 14 Feb 2020 + +version 0.33.1 + + added the __name__attribute to all sub-modules + +Thu, 13 Feb 2020 + +version 0.33.0 + + sub-modules are now proper sub-modules of ulab + +Mon, 17 Feb 2020 + +version 0.32.1 + + temporary fix for issue #40 + +Tue, 11 Feb 2020 + +version 0.32.0 + + added itemsize, size and shape attributes to ndarrays, and removed rawsize + +Mon, 10 Feb 2020 + +version 0.31.0 + + removed asbytearray, and added buffer protocol to ndarrays, fixed bad error in filter.c + +Sun, 09 Feb 2020 + +version 0.30.2 + + fixed slice_length in ndarray.c + +Sat, 08 Feb 2020 + +version 0.30.1 + + fixed typecode error, added variable inspection, and replaced ternary operators in filter.c + +Fri, 07 Feb 2020 + +version 0.30.0 + + ulab functions can arbitrarily be excluded from the firmware via the ulab.h configuration file + +Thu, 06 Feb 2020 + +version 0.27.0 + + add convolve, the start of a 'filter' functionality group + +Wed, 29 Jan 2020 + +version 0.26.7 + + fixed indexing error in linalg.dot + +Mon, 20 Jan 2020 + +version 0.26.6 + + replaced MP_ROM_PTR(&mp_const_none_obj), so that module can be compiled for the nucleo board + +Tue, 7 Jan 2020 + +version 0.26.5 + + fixed glitch in numerical.c, numerical.h + +Mon, 6 Jan 2020 + +version 0.26.4 + + switched version constant to string + +Tue, 31 Dec 2019 + +version 0.263 + + changed declaration of ulab_ndarray_type to extern + +Fri, 29 Nov 2019 + +version 0.262 + + fixed error in macro in vectorise.h + +Thu, 28 Nov 2019 + +version 0.261 + + fixed bad indexing error in linalg.dot + +Tue, 6 Nov 2019 + +version 0.26 + + added in-place sorting (method of ndarray), and argsort + +Mon, 4 Nov 2019 + +version 0.25 + + added first implementation of sort, and fixed section on compiling the module in the manual + +Thu, 31 Oct 2019 + +version 0.24 + + added diff to numerical.c + +Tue, 29 Oct 2019 + +version 0.23 + + major revamp of subscription method + +Sat, 19 Oct 2019 + +version 0.21 + + fixed trivial bug in .rawsize() + +Sat, 19 Oct 2019 + +version 0.22 + + fixed small error in linalg_det, and implemented linalg_eig. + + +Thu, 17 Oct 2019 + +version 0.21 + + implemented uniform interface for fft, and spectrum, and added ifft. + +Wed, 16 Oct 2019 + +version 0.20 + + Added flip function to numerical.c, and moved the size function to linalg. In addition, + size is a function now, and not a method. + +Tue, 15 Oct 2019 + +version 0.19 + + fixed roll in numerical.c: it can now accept the axis=None keyword argument, added determinant to linalg.c + +Mon, 14 Oct 2019 + +version 0.18 + + fixed min/man function in numerical.c; it conforms to numpy behaviour + +Fri, 11 Oct 2019 + +version 0.171 + + found and fixed small bux in roll function + +Fri, 11 Oct 2019 + +version 0.17 + + universal function can now take arbitrary typecodes + +Fri, 11 Oct 2019 + +version 0.161 + + fixed bad error in iterator, and make_new_ndarray + +Thu, 10 Oct 2019 + +varsion 0.16 + + changed ndarray to array in ulab.c, so as to conform to numpy's notation + extended subscr method to include slices (partially works) + +Tue, 8 Oct 2019 + +version 0.15 + + added inv, neg, pos, and abs unary operators to ndarray.c + +Mon, 7 Oct 2019 + +version 0.14 + + made the internal binary_op function tighter, and added keyword arguments to linspace + +Sat, 4 Oct 2019 + +version 0.13 + + added the <, <=, >, >= binary operators to ndarray + +Fri, 4 Oct 2019 + +version 0.12 + + added .flatten to ndarray, ones, zeros, and eye to linalg + +Thu, 3 Oct 2019 + +version 0.11 + + binary operators are now based on macros diff --git a/circuitpython/extmod/ulab/docs/ulab-compare.ipynb b/circuitpython/extmod/ulab/docs/ulab-compare.ipynb new file mode 100644 index 0000000..69fa762 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-compare.ipynb @@ -0,0 +1,467 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:02:42.934528Z", + "start_time": "2021-01-08T13:02:42.720862Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:02:44.890094Z", + "start_time": "2021-01-08T13:02:44.878787Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:06:20.583308Z", + "start_time": "2021-01-08T13:06:20.525830Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Comparison of arrays" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## equal, not_equal\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.equal.html\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.not_equal.html\n", + "\n", + "In `micropython`, equality of arrays or scalars can be established by utilising the `==`, `!=`, `<`, `>`, `<=`, or `=>` binary operators. In `circuitpython`, `==` and `!=` will produce unexpected results. In order to avoid this discrepancy, and to maintain compatibility with `numpy`, `ulab` implements the `equal` and `not_equal` operators that return the same results, irrespective of the `python` implementation.\n", + "\n", + "These two functions take two `ndarray`s, or scalars as their arguments. No keyword arguments are implemented." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T14:22:13.990898Z", + "start_time": "2021-01-08T14:22:13.941896Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "b: array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], dtype=float64)\n", + "\n", + "a == b: array([True, False, False, False, False, False, False, False, False], dtype=bool)\n", + "a != b: array([False, True, True, True, True, True, True, True, True], dtype=bool)\n", + "a == 2: array([False, False, True, False, False, False, False, False, False], dtype=bool)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9))\n", + "b = np.zeros(9)\n", + "\n", + "print('a: ', a)\n", + "print('b: ', b)\n", + "print('\\na == b: ', np.equal(a, b))\n", + "print('a != b: ', np.not_equal(a, b))\n", + "\n", + "# comparison with scalars\n", + "print('a == 2: ', np.equal(a, 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## minimum\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.minimum.html\n", + "\n", + "Returns the minimum of two arrays, or two scalars, or an array, and a scalar. If the arrays are of different `dtype`, the output is upcast as in [Binary operators](#Binary-operators). If both inputs are scalars, a scalar is returned. Only positional arguments are implemented.\n", + "\n", + "## maximum\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.maximum.html\n", + "\n", + "Returns the maximum of two arrays, or two scalars, or an array, and a scalar. If the arrays are of different `dtype`, the output is upcast as in [Binary operators](#Binary-operators). If both inputs are scalars, a scalar is returned. Only positional arguments are implemented." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:21:17.151280Z", + "start_time": "2021-01-08T13:21:17.123768Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "minimum of a, and b:\n", + "array([1.0, 2.0, 3.0, 2.0, 1.0], dtype=float64)\n", + "\n", + "maximum of a, and b:\n", + "array([5.0, 4.0, 3.0, 4.0, 5.0], dtype=float64)\n", + "\n", + "maximum of 1, and 5.5:\n", + "5.5\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5], dtype=np.uint8)\n", + "b = np.array([5, 4, 3, 2, 1], dtype=np.float)\n", + "print('minimum of a, and b:')\n", + "print(np.minimum(a, b))\n", + "\n", + "print('\\nmaximum of a, and b:')\n", + "print(np.maximum(a, b))\n", + "\n", + "print('\\nmaximum of 1, and 5.5:')\n", + "print(np.maximum(1, 5.5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## clip\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.clip.html\n", + "\n", + "Clips an array, i.e., values that are outside of an interval are clipped to the interval edges. The function is equivalent to `maximum(a_min, minimum(a, a_max))` broadcasting takes place exactly as in [minimum](#minimum). If the arrays are of different `dtype`, the output is upcast as in [Binary operators](#Binary-operators)." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T13:22:14.147310Z", + "start_time": "2021-01-08T13:22:14.123961Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "clipped:\t array([3, 3, 3, 3, 4, 5, 6, 7, 7], dtype=uint8)\n", + "\n", + "a:\t\t array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "b:\t\t array([3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0], dtype=float64)\n", + "clipped:\t array([3.0, 3.0, 3.0, 3.0, 4.0, 5.0, 6.0, 7.0, 7.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9), dtype=np.uint8)\n", + "print('a:\\t\\t', a)\n", + "print('clipped:\\t', np.clip(a, 3, 7))\n", + "\n", + "b = 3 * np.ones(len(a), dtype=np.float)\n", + "print('\\na:\\t\\t', a)\n", + "print('b:\\t\\t', b)\n", + "print('clipped:\\t', np.clip(a, b, 7))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/ulab-convert.ipynb b/circuitpython/extmod/ulab/docs/ulab-convert.ipynb new file mode 100644 index 0000000..70c6fa4 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-convert.ipynb @@ -0,0 +1,507 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-01T09:27:13.438054Z", + "start_time": "2020-05-01T09:27:13.191491Z" + } + }, + "source": [ + "# conf.py" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:24:12.745063Z", + "start_time": "2022-01-07T18:24:12.733067Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting manual/source/conf.py\n" + ] + } + ], + "source": [ + "%%writefile manual/source/conf.py\n", + "# Configuration file for the Sphinx documentation builder.\n", + "#\n", + "# This file only contains a selection of the most common options. For a full\n", + "# list see the documentation:\n", + "# http://www.sphinx-doc.org/en/master/config\n", + "\n", + "# -- Path setup --------------------------------------------------------------\n", + "\n", + "# If extensions (or modules to document with autodoc) are in another directory,\n", + "# add these directories to sys.path here. If the directory is relative to the\n", + "# documentation root, use os.path.abspath to make it absolute, like shown here.\n", + "#\n", + "import os\n", + "# import sys\n", + "# sys.path.insert(0, os.path.abspath('.'))\n", + "\n", + "#import sphinx_rtd_theme\n", + "\n", + "from sphinx.transforms import SphinxTransform\n", + "from docutils import nodes\n", + "from sphinx import addnodes\n", + "\n", + "# -- Project information -----------------------------------------------------\n", + "\n", + "project = 'The ulab book'\n", + "copyright = '2019-2022, Zoltán Vörös and contributors'\n", + "author = 'Zoltán Vörös'\n", + "\n", + "# The full version, including alpha/beta/rc tags\n", + "release = '4.0.0'\n", + "\n", + "\n", + "# -- General configuration ---------------------------------------------------\n", + "\n", + "# Add any Sphinx extension module names here, as strings. They can be\n", + "# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom\n", + "# ones.\n", + "extensions = [\n", + "]\n", + "\n", + "# Add any paths that contain templates here, relative to this directory.\n", + "templates_path = ['_templates']\n", + "\n", + "# List of patterns, relative to source directory, that match files and\n", + "# directories to ignore when looking for source files.\n", + "# This pattern also affects html_static_path and html_extra_path.\n", + "exclude_patterns = []\n", + "\n", + "\n", + "# Add any paths that contain custom static files (such as style sheets) here,\n", + "# relative to this directory. They are copied after the builtin static files,\n", + "# so a file named \"default.css\" will overwrite the builtin \"default.css\".\n", + "html_static_path = ['_static']\n", + "\n", + "latex_maketitle = r'''\n", + "\\begin{titlepage}\n", + "\\begin{flushright}\n", + "\\Huge\\textbf{The $\\mu$lab book}\n", + "\\vskip 0.5em\n", + "\\LARGE\n", + "\\textbf{Release %s}\n", + "\\vskip 5em\n", + "\\huge\\textbf{Zoltán Vörös}\n", + "\\end{flushright}\n", + "\\begin{flushright}\n", + "\\LARGE\n", + "\\vskip 2em\n", + "with contributions by\n", + "\\vskip 2em\n", + "\\textbf{Roberto Colistete Jr.}\n", + "\\vskip 0.2em\n", + "\\textbf{Jeff Epler}\n", + "\\vskip 0.2em\n", + "\\textbf{Taku Fukada}\n", + "\\vskip 0.2em\n", + "\\textbf{Diego Elio Pettenò}\n", + "\\vskip 0.2em\n", + "\\textbf{Scott Shawcroft}\n", + "\\vskip 5em\n", + "\\today\n", + "\\end{flushright}\n", + "\\end{titlepage}\n", + "'''%release\n", + "\n", + "latex_elements = {\n", + " 'maketitle': latex_maketitle\n", + "}\n", + "\n", + "\n", + "master_doc = 'index'\n", + "\n", + "author=u'Zoltán Vörös'\n", + "copyright=author\n", + "language='en'\n", + "\n", + "latex_documents = [\n", + "(master_doc, 'the-ulab-book.tex', 'The $\\mu$lab book',\n", + "'Zoltán Vörös', 'manual'),\n", + "]\n", + "\n", + "# Read the docs theme\n", + "on_rtd = os.environ.get('READTHEDOCS', None) == 'True'\n", + "if not on_rtd:\n", + " try:\n", + " import sphinx_rtd_theme\n", + " html_theme = 'sphinx_rtd_theme'\n", + " html_theme_path = [sphinx_rtd_theme.get_html_theme_path(), '.']\n", + " except ImportError:\n", + " html_theme = 'default'\n", + " html_theme_path = ['.']\n", + "else:\n", + " html_theme_path = ['.']" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2021-05-09T06:06:28.491158Z", + "start_time": "2021-05-09T06:06:28.477127Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting manual/source/index.rst\n" + ] + } + ], + "source": [ + "%%writefile manual/source/index.rst\n", + "\n", + ".. ulab-manual documentation master file, created by\n", + " sphinx-quickstart on Sat Oct 19 12:48:00 2019.\n", + " You can adapt this file completely to your liking, but it should at least\n", + " contain the root `toctree` directive.\n", + "\n", + "Welcome to the ulab book!\n", + "=======================================\n", + "\n", + ".. toctree::\n", + " :maxdepth: 2\n", + " :caption: Introduction\n", + "\n", + " ulab-intro\n", + "\n", + ".. toctree::\n", + " :maxdepth: 2\n", + " :caption: User's guide:\n", + "\n", + " ulab-ndarray\n", + " numpy-functions\n", + " numpy-universal\n", + " numpy-fft\n", + " numpy-linalg\n", + " scipy-linalg\n", + " scipy-optimize\n", + " scipy-signal\n", + " scipy-special\n", + " ulab-utils\n", + " ulab-tricks\n", + " ulab-programming\n", + "\n", + "Indices and tables\n", + "==================\n", + "\n", + "* :ref:`genindex`\n", + "* :ref:`modindex`\n", + "* :ref:`search`" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Notebook conversion" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:24:27.671415Z", + "start_time": "2022-01-07T18:24:24.933205Z" + } + }, + "outputs": [], + "source": [ + "import nbformat as nb\n", + "import nbformat.v4.nbbase as nb4\n", + "from nbconvert import RSTExporter\n", + "\n", + "from jinja2 import FileSystemLoader\n", + "rstexporter = RSTExporter(\n", + " extra_loaders=[FileSystemLoader('./templates')],\n", + " template_file = './templates/manual.tpl'\n", + ")\n", + "\n", + "def convert_notebook(fn):\n", + " source = nb.read(fn+'.ipynb', nb.NO_CONVERT)\n", + " notebook = nb4.new_notebook()\n", + " notebook.cells = []\n", + " append_cell = False\n", + " for cell in source['cells']:\n", + " if append_cell:\n", + " notebook.cells.append(cell)\n", + " else:\n", + " if cell.cell_type == 'markdown':\n", + " if cell.source == '__END_OF_DEFS__':\n", + " append_cell = True\n", + " \n", + " (rst, resources) = rstexporter.from_notebook_node(notebook)\n", + " with open('./manual/source/' + fn + '.rst', 'w') as fout:\n", + " # it's a bit odd, but even an emtpy notebook is converted into a \"None\" string\n", + " rst = rst.lstrip('None')\n", + " fout.write(rst)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:52:29.910335Z", + "start_time": "2022-01-07T19:52:28.432391Z" + } + }, + "outputs": [], + "source": [ + "files = ['ulab-intro',\n", + " 'ulab-ndarray',\n", + " 'numpy-functions', \n", + " 'numpy-universal',\n", + " 'numpy-fft',\n", + " 'numpy-linalg',\n", + " 'scipy-linalg',\n", + " 'scipy-optimize',\n", + " 'scipy-signal',\n", + " 'scipy-special',\n", + " 'ulab-utils',\n", + " 'ulab-tricks',\n", + " 'ulab-programming']\n", + "\n", + "for file in files:\n", + " convert_notebook(file)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Template" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-30T19:04:50.295563Z", + "start_time": "2020-10-30T19:04:50.227535Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Overwriting ./templates/manual.tpl\n" + ] + } + ], + "source": [ + "%%writefile ./templates/manual.tpl\n", + "\n", + "{%- extends 'display_priority.tpl' -%}\n", + "\n", + "\n", + "{% block in_prompt %}\n", + "{% endblock in_prompt %}\n", + "\n", + "{% block output_prompt %}\n", + "{% endblock output_prompt %}\n", + "\n", + "{% block input scoped%}\n", + "\n", + "{%- if cell.source.split('\\n')[0].startswith('%%micropython') -%}\n", + ".. code::\n", + " \n", + "{{ '\\n'.join(['# code to be run in micropython'] + cell.source.strip().split('\\n')[1:]) | indent}}\n", + "\n", + "{%- else -%}\n", + ".. code::\n", + "\n", + "{{ '\\n'.join(['# code to be run in CPython\\n'] + cell.source.strip().split('\\n')) | indent}}\n", + "{%- endif -%}\n", + "{% endblock input %}\n", + "\n", + "{% block error %}\n", + "::\n", + "\n", + "{{ super() }}\n", + "{% endblock error %}\n", + "\n", + "{% block traceback_line %}\n", + "{{ line | indent | strip_ansi }}\n", + "{% endblock traceback_line %}\n", + "\n", + "{% block execute_result %}\n", + "{% block data_priority scoped %}\n", + "{{ super() }}\n", + "{% endblock %}\n", + "{% endblock execute_result %}\n", + "\n", + "{% block stream %}\n", + ".. parsed-literal::\n", + "\n", + "{{ output.text | indent }}\n", + "{% endblock stream %}\n", + "\n", + "{% block data_svg %}\n", + ".. image:: {{ output.metadata.filenames['image/svg+xml'] | urlencode }}\n", + "{% endblock data_svg %}\n", + "\n", + "{% block data_png %}\n", + ".. image:: {{ output.metadata.filenames['image/png'] | urlencode }}\n", + "{%- set width=output | get_metadata('width', 'image/png') -%}\n", + "{%- if width is not none %}\n", + " :width: {{ width }}px\n", + "{%- endif %}\n", + "{%- set height=output | get_metadata('height', 'image/png') -%}\n", + "{%- if height is not none %}\n", + " :height: {{ height }}px\n", + "{%- endif %}\n", + "{% endblock data_png %}\n", + "\n", + "{% block data_jpg %}\n", + ".. image:: {{ output.metadata.filenames['image/jpeg'] | urlencode }}\n", + "{%- set width=output | get_metadata('width', 'image/jpeg') -%}\n", + "{%- if width is not none %}\n", + " :width: {{ width }}px\n", + "{%- endif %}\n", + "{%- set height=output | get_metadata('height', 'image/jpeg') -%}\n", + "{%- if height is not none %}\n", + " :height: {{ height }}px\n", + "{%- endif %}\n", + "{% endblock data_jpg %}\n", + "\n", + "{% block data_markdown %}\n", + "{{ output.data['text/markdown'] | convert_pandoc(\"markdown\", \"rst\") }}\n", + "{% endblock data_markdown %}\n", + "\n", + "{% block data_latex %}\n", + ".. math::\n", + "\n", + "{{ output.data['text/latex'] | strip_dollars | indent }}\n", + "{% endblock data_latex %}\n", + "\n", + "{% block data_text scoped %}\n", + ".. parsed-literal::\n", + "\n", + "{{ output.data['text/plain'] | indent }}\n", + "{% endblock data_text %}\n", + "\n", + "{% block data_html scoped %}\n", + ".. raw:: html\n", + "\n", + "{{ output.data['text/html'] | indent }}\n", + "{% endblock data_html %}\n", + "\n", + "{% block markdowncell scoped %}\n", + "{{ cell.source | convert_pandoc(\"markdown\", \"rst\") }}\n", + "{% endblock markdowncell %}\n", + "\n", + "{%- block rawcell scoped -%}\n", + "{%- if cell.metadata.get('raw_mimetype', '').lower() in resources.get('raw_mimetypes', ['']) %}\n", + "{{cell.source}}\n", + "{% endif -%}\n", + "{%- endblock rawcell -%}\n", + "\n", + "{% block headingcell scoped %}\n", + "{{ (\"#\" * cell.level + cell.source) | replace('\\n', ' ') | convert_pandoc(\"markdown\", \"rst\") }}\n", + "{% endblock headingcell %}\n", + "\n", + "{% block unknowncell scoped %}\n", + "unknown type {{cell.type}}\n", + "{% endblock unknowncell %}\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "interpreter": { + "hash": "ce9a02f9f7db620716422019cafa4bc1786ca85daa298b819f6da075e7993842" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/ulab-intro.ipynb b/circuitpython/extmod/ulab/docs/ulab-intro.ipynb new file mode 100644 index 0000000..67d6b60 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-intro.ipynb @@ -0,0 +1,897 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:07:55.382930Z", + "start_time": "2021-01-08T12:07:46.895325Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Matplotlib is building the font cache; this may take a moment.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:13:14.590799Z", + "start_time": "2022-01-07T18:13:14.585845Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:20:56.550047Z", + "start_time": "2022-01-07T18:20:56.527475Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../micropython/ports/unix/micropython-2\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "from ulab import numpy as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Enter ulab\n", + "\n", + "`ulab` is a `numpy`-like module for `micropython` and its derivatives, meant to simplify and speed up common mathematical operations on arrays. `ulab` implements a small subset of `numpy` and `scipy`. The functions were chosen such that they might be useful in the context of a microcontroller. However, the project is a living one, and suggestions for new features are always welcome. \n", + "\n", + "This document discusses how you can use the library, starting from building your own firmware, through questions like what affects the firmware size, what are the trade-offs, and what are the most important differences to `numpy` and `scipy`, respectively. The document is organised as follows:\n", + "\n", + "The chapter after this one helps you with firmware customisation.\n", + "\n", + "The third chapter gives a very concise summary of the `ulab` functions and array methods. This chapter can be used as a quick reference.\n", + "\n", + "The chapters after that are an in-depth review of most functions. Here you can find usage examples, benchmarks, as well as a thorough discussion of such concepts as broadcasting, and views versus copies. \n", + "\n", + "The final chapter of this book can be regarded as the programming manual. The inner working of `ulab` is dissected here, and you will also find hints as to how to implement your own `numpy`-compatible functions.\n", + "\n", + "\n", + "## Purpose\n", + "\n", + "Of course, the first question that one has to answer is, why on Earth one would need a fast math library on a microcontroller. After all, it is not expected that heavy number crunching is going to take place on bare metal. It is not meant to. On a PC, the main reason for writing fast code is the sheer amount of data that one wants to process. On a microcontroller, the data volume is probably small, but it might lead to catastrophic system failure, if these data are not processed in time, because the microcontroller is supposed to interact with the outside world in a timely fashion. In fact, this latter objective was the initiator of this project: I needed the Fourier transform of a signal coming from the ADC of the `pyboard`, and all available options were simply too slow. \n", + "\n", + "In addition to speed, another issue that one has to keep in mind when working with embedded systems is the amount of available RAM: I believe, everything here could be implemented in pure `python` with relatively little effort (in fact, there are a couple of `python`-only implementations of `numpy` functions out there), but the price we would have to pay for that is not only speed, but RAM, too. `python` code, if is not frozen, and compiled into the firmware, has to be compiled at runtime, which is not exactly a cheap process. On top of that, if numbers are stored in a list or tuple, which would be the high-level container, then they occupy 8 bytes, no matter, whether they are all smaller than 100, or larger than one hundred million. This is obviously a waste of resources in an environment, where resources are scarce. \n", + "\n", + "Finally, there is a reason for using `micropython` in the first place. Namely, that a microcontroller can be programmed in a very elegant, and *pythonic* way. But if it is so, why should we not extend this idea to other tasks and concepts that might come up in this context? If there was no other reason than this *elegance*, I would find that convincing enough.\n", + "\n", + "Based on the above-mentioned considerations, all functions in `ulab` are implemented in a way that \n", + "\n", + "1. conforms to `numpy` as much as possible\n", + "2. is so frugal with RAM as possible,\n", + "3. and yet, fast. Much faster than pure python. Think of speed-ups of 30-50!\n", + "\n", + "The main points of `ulab` are \n", + "\n", + "- compact, iterable and slicable containers of numerical data in one to four dimensions. These containers support all the relevant unary and binary operators (e.g., `len`, ==, +, *, etc.)\n", + "- vectorised computations on `micropython` iterables and numerical arrays (in `numpy`-speak, universal functions)\n", + "- computing statistical properties (mean, standard deviation etc.) on arrays\n", + "- basic linear algebra routines (matrix inversion, multiplication, reshaping, transposition, determinant, and eigenvalues, Cholesky decomposition and so on)\n", + "- polynomial fits to numerical data, and evaluation of polynomials\n", + "- fast Fourier transforms\n", + "- filtering of data (convolution and second-order filters)\n", + "- function minimisation, fitting, and numerical approximation routines\n", + "- interfacing between numerical data and peripheral hardware devices\n", + "\n", + "`ulab` implements close to a hundred functions and array methods. At the time of writing this manual (for version 4.0.0), the library adds approximately 120 kB of extra compiled code to the `micropython` (pyboard.v.1.17) firmware. However, if you are tight with flash space, you can easily shave tens of kB off the firmware. In fact, if only a small sub-set of functions are needed, you can get away with less than 10 kB of flash space. See the section on [customising ulab](#Customising-the-firmware).\n", + "\n", + "## Resources and legal matters\n", + "\n", + "The source code of the module can be found under https://github.com/v923z/micropython-ulab/tree/master/code. while the source of this user manual is under https://github.com/v923z/micropython-ulab/tree/master/docs.\n", + "\n", + "The MIT licence applies to all material. \n", + "\n", + "## Friendly request\n", + "\n", + "If you use `ulab`, and bump into a bug, or think that a particular function is missing, or its behaviour does not conform to `numpy`, please, raise a [ulab issue](#https://github.com/v923z/micropython-ulab/issues) on github, so that the community can profit from your experiences. \n", + "\n", + "Even better, if you find the project to be useful, and think that it could be made better, faster, tighter, and shinier, please, consider contributing, and issue a pull request with the implementation of your improvements and new features. `ulab` can only become successful, if it offers what the community needs.\n", + "\n", + "These last comments apply to the documentation, too. If, in your opinion, the documentation is obscure, misleading, or not detailed enough, please, let us know, so that *we* can fix it.\n", + "\n", + "## Differences between micropython-ulab and circuitpython-ulab\n", + "\n", + "`ulab` has originally been developed for `micropython`, but has since been integrated into a number of its flavours. Most of these are simply forks of `micropython` itself, with some additional functionality. One of the notable exceptions is `circuitpython`, which has slightly diverged at the core level, and this has some minor consequences. Some of these concern the C implementation details only, which all have been sorted out with the generous and enthusiastic support of Jeff Epler from [Adafruit Industries](http://www.adafruit.com).\n", + "\n", + "There are, however, a couple of instances, where the two environments differ at the python level in how the class properties can be accessed. We will point out the differences and possible workarounds at the relevant places in this document." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Customising the firmware\n", + "\n", + "\n", + "As mentioned above, `ulab` has considerably grown since its conception, which also means that it might no longer fit on the microcontroller of your choice. There are, however, a couple of ways of customising the firmware, and thereby reducing its size. \n", + "\n", + "All `ulab` options are listed in a single header file, [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h), which contains pre-processor flags for each feature that can be fine-tuned. The first couple of lines of the file look like this\n", + "\n", + "```c\n", + "// The pre-processor constants in this file determine how ulab behaves:\n", + "//\n", + "// - how many dimensions ulab can handle\n", + "// - which functions are included in the compiled firmware\n", + "// - whether the python syntax is numpy-like, or modular\n", + "// - whether arrays can be sliced and iterated over\n", + "// - which binary/unary operators are supported\n", + "//\n", + "// A considerable amount of flash space can be saved by removing (setting\n", + "// the corresponding constants to 0) the unnecessary functions and features.\n", + "\n", + "// Values defined here can be overridden by your own config file as\n", + "// make -DULAB_CONFIG_FILE=\"my_ulab_config.h\"\n", + "#if defined(ULAB_CONFIG_FILE)\n", + "#include ULAB_CONFIG_FILE\n", + "#endif\n", + "\n", + "// Adds support for complex ndarrays\n", + "#ifndef ULAB_SUPPORTS_COMPLEX\n", + "#define ULAB_SUPPORTS_COMPLEX (1)\n", + "#endif\n", + "\n", + "// Determines, whether scipy is defined in ulab. The sub-modules and functions\n", + "// of scipy have to be defined separately\n", + "#define ULAB_HAS_SCIPY (1)\n", + "\n", + "// The maximum number of dimensions the firmware should be able to support\n", + "// Possible values lie between 1, and 4, inclusive\n", + "#define ULAB_MAX_DIMS 2\n", + "\n", + "// By setting this constant to 1, iteration over array dimensions will be implemented\n", + "// as a function (ndarray_rewind_array), instead of writing out the loops in macros\n", + "// This reduces firmware size at the expense of speed\n", + "#define ULAB_HAS_FUNCTION_ITERATOR (0)\n", + "\n", + "// If NDARRAY_IS_ITERABLE is 1, the ndarray object defines its own iterator function\n", + "// This option saves approx. 250 bytes of flash space\n", + "#define NDARRAY_IS_ITERABLE (1)\n", + "\n", + "// Slicing can be switched off by setting this variable to 0\n", + "#define NDARRAY_IS_SLICEABLE (1)\n", + "\n", + "// The default threshold for pretty printing. These variables can be overwritten\n", + "// at run-time via the set_printoptions() function\n", + "#define ULAB_HAS_PRINTOPTIONS (1)\n", + "#define NDARRAY_PRINT_THRESHOLD 10\n", + "#define NDARRAY_PRINT_EDGEITEMS 3\n", + "\n", + "// determines, whether the dtype is an object, or simply a character\n", + "// the object implementation is numpythonic, but requires more space\n", + "#define ULAB_HAS_DTYPE_OBJECT (0)\n", + "\n", + "// the ndarray binary operators\n", + "#define NDARRAY_HAS_BINARY_OPS (1)\n", + "\n", + "// Firmware size can be reduced at the expense of speed by using function\n", + "// pointers in iterations. For each operator, he function pointer saves around\n", + "// 2 kB in the two-dimensional case, and around 4 kB in the four-dimensional case.\n", + "\n", + "#define NDARRAY_BINARY_USES_FUN_POINTER (0)\n", + "\n", + "#define NDARRAY_HAS_BINARY_OP_ADD (1)\n", + "#define NDARRAY_HAS_BINARY_OP_EQUAL (1)\n", + "#define NDARRAY_HAS_BINARY_OP_LESS (1)\n", + "#define NDARRAY_HAS_BINARY_OP_LESS_EQUAL (1)\n", + "#define NDARRAY_HAS_BINARY_OP_MORE (1)\n", + "#define NDARRAY_HAS_BINARY_OP_MORE_EQUAL (1)\n", + "#define NDARRAY_HAS_BINARY_OP_MULTIPLY (1)\n", + "#define NDARRAY_HAS_BINARY_OP_NOT_EQUAL (1)\n", + "#define NDARRAY_HAS_BINARY_OP_POWER (1)\n", + "#define NDARRAY_HAS_BINARY_OP_SUBTRACT (1)\n", + "#define NDARRAY_HAS_BINARY_OP_TRUE_DIVIDE (1)\n", + "... \n", + "```\n", + "\n", + "The meaning of flags with names `_HAS_` should be obvious, so we will just explain the other options. \n", + "\n", + "To see how much you can gain by un-setting the functions that you do not need, here are some pointers. In four dimensions, including all functions adds around 120 kB to the `micropython` firmware. On the other hand, if you are interested in Fourier transforms only, and strip everything else, you get away with less than 5 kB extra. \n", + "\n", + "## Compatibility with numpy\n", + "\n", + "The functions implemented in `ulab` are organised in four sub-modules at the C level, namely, `numpy`, `scipy`, `utils`, and `user`. This modularity is elevated to `python`, meaning that in order to use functions that are part of `numpy`, you have to import `numpy` as\n", + "\n", + "```python\n", + "from ulab import numpy as np\n", + "\n", + "x = np.array([4, 5, 6])\n", + "p = np.array([1, 2, 3])\n", + "np.polyval(p, x)\n", + "```\n", + "\n", + "There are a couple of exceptions to this rule, namely `fft`, and `linalg`, which are sub-modules even in `numpy`, thus you have to write them out as \n", + "\n", + "```python\n", + "from ulab import numpy as np\n", + "\n", + "A = np.array([1, 2, 3, 4]).reshape()\n", + "np.linalg.trace(A)\n", + "```\n", + "\n", + "Some of the functions in `ulab` are re-implementations of `scipy` functions, and they are to be imported as \n", + "\n", + "```python\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "\n", + "x = np.array([1, 2, 3])\n", + "spy.special.erf(x)\n", + "```\n", + "\n", + "`numpy`-compatibility has an enormous benefit : namely, by `try`ing to `import`, we can guarantee that the same, unmodified code runs in `CPython`, as in `micropython`. The following snippet is platform-independent, thus, the `python` code can be tested and debugged on a computer before loading it onto the microcontroller.\n", + "\n", + "```python\n", + "\n", + "try:\n", + " from ulab import numpy as np\n", + " from ulab import scipy as spy\n", + "except ImportError:\n", + " import numpy as np\n", + " import scipy as spy\n", + " \n", + "x = np.array([1, 2, 3])\n", + "spy.special.erf(x) \n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The impact of dimensionality\n", + "\n", + "### Reducing the number of dimensions\n", + "\n", + "`ulab` supports tensors of rank four, but this is expensive in terms of flash: with all available functions and options, the library adds around 100 kB to the firmware. However, if such high dimensions are not required, significant reductions in size can be gotten by changing the value of \n", + "\n", + "```c\n", + "#define ULAB_MAX_DIMS 2\n", + "```\n", + "\n", + "Two dimensions cost a bit more than half of four, while you can get away with around 20 kB of flash in one dimension, because all those functions that don't make sense (e.g., matrix inversion, eigenvalues etc.) are automatically stripped from the firmware.\n", + "\n", + "### Using the function iterator\n", + "\n", + "In higher dimensions, the firmware size increases, because each dimension (axis) adds another level of nested loops. An example of this is the macro of the binary operator in three dimensions\n", + "\n", + "```c\n", + "#define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\n", + " type_out *array = (type_out *)results->array;\n", + " size_t j = 0;\n", + " do {\n", + " size_t k = 0;\n", + " do {\n", + " size_t l = 0;\n", + " do {\n", + " *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\n", + " (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\n", + " (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\n", + " l++;\n", + " } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\n", + " (larray) -= (lstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\n", + " (larray) += (lstrides)[ULAB_MAX_DIMS - 2];\n", + " (rarray) -= (rstrides)[ULAB_MAX_DIMS - 1] * (results)->shape[ULAB_MAX_DIMS-1];\n", + " (rarray) += (rstrides)[ULAB_MAX_DIMS - 2];\n", + " k++;\n", + " } while(k < (results)->shape[ULAB_MAX_DIMS - 2]);\n", + " (larray) -= (lstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\n", + " (larray) += (lstrides)[ULAB_MAX_DIMS - 3];\n", + " (rarray) -= (rstrides)[ULAB_MAX_DIMS - 2] * results->shape[ULAB_MAX_DIMS-2];\n", + " (rarray) += (rstrides)[ULAB_MAX_DIMS - 3];\n", + " j++;\n", + " } while(j < (results)->shape[ULAB_MAX_DIMS - 3]);\n", + "```\n", + "\n", + "In order to reduce firmware size, it *might* make sense in higher dimensions to make use of the function iterator by setting the \n", + "\n", + "```c\n", + "#define ULAB_HAS_FUNCTION_ITERATOR (1)\n", + "```\n", + "\n", + "constant to 1. This allows the compiler to call the `ndarray_rewind_array` function, so that it doesn't have to unwrap the loops for `k`, and `j`. Instead of the macro above, we now have \n", + "\n", + "```c\n", + "#define BINARY_LOOP(results, type_out, type_left, type_right, larray, lstrides, rarray, rstrides, OPERATOR)\n", + " type_out *array = (type_out *)(results)->array;\n", + " size_t *lcoords = ndarray_new_coords((results)->ndim);\n", + " size_t *rcoords = ndarray_new_coords((results)->ndim);\n", + " for(size_t i=0; i < (results)->len/(results)->shape[ULAB_MAX_DIMS -1]; i++) {\n", + " size_t l = 0;\n", + " do {\n", + " *array++ = *((type_left *)(larray)) OPERATOR *((type_right *)(rarray));\n", + " (larray) += (lstrides)[ULAB_MAX_DIMS - 1];\n", + " (rarray) += (rstrides)[ULAB_MAX_DIMS - 1];\n", + " l++;\n", + " } while(l < (results)->shape[ULAB_MAX_DIMS - 1]);\n", + " ndarray_rewind_array((results)->ndim, larray, (results)->shape, lstrides, lcoords);\n", + " ndarray_rewind_array((results)->ndim, rarray, (results)->shape, rstrides, rcoords);\n", + " } while(0)\n", + "```\n", + "\n", + "Since the `ndarray_rewind_array` function is implemented only once, a lot of space can be saved. Obviously, function calls cost time, thus such trade-offs must be evaluated for each application. The gain also depends on which functions and features you include. Operators and functions that involve two arrays are expensive, because at the C level, the number of cases that must be handled scales with the squares of the number of data types. As an example, the innocent-looking expression\n", + "\n", + "```python\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3])\n", + "b = np.array([4, 5, 6])\n", + "\n", + "c = a + b\n", + "```\n", + "requires 25 loops in C, because the `dtypes` of both `a`, and `b` can assume 5 different values, and the addition has to be resolved for all possible cases. Hint: each binary operator costs between 3 and 4 kB in two dimensions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The ulab version string\n", + "\n", + "As is customary with `python` packages, information on the package version can be found be querying the `__version__` string. " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T06:25:27.328061Z", + "start_time": "2021-01-12T06:25:27.308199Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "you are running ulab version 2.1.0-2D\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab\n", + "\n", + "print('you are running ulab version', ulab.__version__)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The first three numbers indicate the major, minor, and sub-minor versions of `ulab` (defined by the `ULAB_VERSION` constant in [ulab.c](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.c)). We usually change the minor version, whenever a new function is added to the code, and the sub-minor version will be incremented, if a bug fix is implemented. \n", + "\n", + "`2D` tells us that the particular firmware supports tensors of rank 2 (defined by `ULAB_MAX_DIMS` in [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h)). \n", + "\n", + "If you find a bug, please, include the version string in your report!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Should you need the numerical value of `ULAB_MAX_DIMS`, you can get it from the version string in the following way:" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:00:00.616473Z", + "start_time": "2021-01-13T06:00:00.602787Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "version string: 2.1.0-2D\n", + "version dimensions: 2D\n", + "numerical value of dimensions: 2\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab\n", + "\n", + "version = ulab.__version__\n", + "version_dims = version.split('-')[1]\n", + "version_num = int(version_dims.replace('D', ''))\n", + "\n", + "print('version string: ', version)\n", + "print('version dimensions: ', version_dims)\n", + "print('numerical value of dimensions: ', version_num)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ulab with complex arrays\n", + "\n", + "If the firmware supports complex arrays, `-c` is appended to the version string as can be seen below." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:21:04.079894Z", + "start_time": "2022-01-07T18:21:04.058855Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "version string: 4.0.0-2D-c\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab\n", + "\n", + "version = ulab.__version__\n", + "\n", + "print('version string: ', version)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Finding out what your firmware supports\n", + "\n", + "`ulab` implements a number of array operators and functions, but this does not mean that all of these functions and methods are actually compiled into the firmware. You can fine-tune your firmware by setting/unsetting any of the `_HAS_` constants in [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h). \n", + "\n", + "### Functions included in the firmware\n", + "\n", + "The version string will not tell you everything about your firmware, because the supported functions and sub-modules can still arbitrarily be included or excluded. One way of finding out what is compiled into the firmware is calling `dir` with `ulab` as its argument." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:47:37.963507Z", + "start_time": "2021-01-08T12:47:37.936641Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "===== constants, functions, and modules of numpy =====\n", + "\n", + " ['__class__', '__name__', 'bool', 'sort', 'sum', 'acos', 'acosh', 'arange', 'arctan2', 'argmax', 'argmin', 'argsort', 'around', 'array', 'asin', 'asinh', 'atan', 'atanh', 'ceil', 'clip', 'concatenate', 'convolve', 'cos', 'cosh', 'cross', 'degrees', 'diag', 'diff', 'e', 'equal', 'exp', 'expm1', 'eye', 'fft', 'flip', 'float', 'floor', 'frombuffer', 'full', 'get_printoptions', 'inf', 'int16', 'int8', 'interp', 'linalg', 'linspace', 'log', 'log10', 'log2', 'logspace', 'max', 'maximum', 'mean', 'median', 'min', 'minimum', 'nan', 'ndinfo', 'not_equal', 'ones', 'pi', 'polyfit', 'polyval', 'radians', 'roll', 'set_printoptions', 'sin', 'sinh', 'sqrt', 'std', 'tan', 'tanh', 'trapz', 'uint16', 'uint8', 'vectorize', 'zeros']\n", + "\n", + "functions included in the fft module:\n", + " ['__class__', '__name__', 'fft', 'ifft']\n", + "\n", + "functions included in the linalg module:\n", + " ['__class__', '__name__', 'cholesky', 'det', 'dot', 'eig', 'inv', 'norm', 'trace']\n", + "\n", + "\n", + "===== modules of scipy =====\n", + "\n", + " ['__class__', '__name__', 'optimize', 'signal', 'special']\n", + "\n", + "functions included in the optimize module:\n", + " ['__class__', '__name__', 'bisect', 'fmin', 'newton']\n", + "\n", + "functions included in the signal module:\n", + " ['__class__', '__name__', 'sosfilt', 'spectrogram']\n", + "\n", + "functions included in the special module:\n", + " ['__class__', '__name__', 'erf', 'erfc', 'gamma', 'gammaln']\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import scipy as spy\n", + "\n", + "\n", + "print('===== constants, functions, and modules of numpy =====\\n\\n', dir(np))\n", + "\n", + "# since fft and linalg are sub-modules, print them separately\n", + "print('\\nfunctions included in the fft module:\\n', dir(np.fft))\n", + "print('\\nfunctions included in the linalg module:\\n', dir(np.linalg))\n", + "\n", + "print('\\n\\n===== modules of scipy =====\\n\\n', dir(spy))\n", + "print('\\nfunctions included in the optimize module:\\n', dir(spy.optimize))\n", + "print('\\nfunctions included in the signal module:\\n', dir(spy.signal))\n", + "print('\\nfunctions included in the special module:\\n', dir(spy.special))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Methods included in the firmware\n", + "\n", + "The `dir` function applied to the module or its sub-modules gives information on what the module and sub-modules include, but is not enough to find out which methods the `ndarray` class supports. We can list the methods by calling `dir` with the `array` object itself:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:48:17.927709Z", + "start_time": "2021-01-08T12:48:17.903132Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['__class__', '__name__', 'copy', 'sort', '__bases__', '__dict__', 'dtype', 'flatten', 'itemsize', 'reshape', 'shape', 'size', 'strides', 'tobytes', 'transpose']\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "print(dir(np.array))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Operators included in the firmware\n", + "\n", + "A list of operators cannot be generated as shown above. If you really need to find out, whether, e.g., the `**` operator is supported by the firmware, you have to `try` it:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-08T12:49:59.902054Z", + "start_time": "2021-01-08T12:49:59.875760Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "operator is not supported: unsupported types for __pow__: 'ndarray', 'ndarray'\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3])\n", + "b = np.array([4, 5, 6])\n", + "\n", + "try:\n", + " print(a ** b)\n", + "except Exception as e:\n", + " print('operator is not supported: ', e)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The exception above would be raised, if the firmware was compiled with the \n", + "\n", + "```c\n", + "#define NDARRAY_HAS_BINARY_OP_POWER (0)\n", + "```\n", + "\n", + "definition." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/ulab-ndarray.ipynb b/circuitpython/extmod/ulab/docs/ulab-ndarray.ipynb new file mode 100644 index 0000000..7524e35 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-ndarray.ipynb @@ -0,0 +1,3754 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:20:20.064769Z", + "start_time": "2021-01-12T16:20:19.787429Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:46:22.666663Z", + "start_time": "2022-01-07T18:46:22.663583Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T18:46:29.198681Z", + "start_time": "2022-01-07T18:46:29.177654Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../micropython/ports/unix/micropython-2\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# ndarray, the base class\n", + "\n", + "The `ndarray` is the underlying container of numerical data. It can be thought of as micropython's own `array` object, but has a great number of extra features starting with how it can be initialised, which operations can be done on it, and which functions can accept it as an argument. One important property of an `ndarray` is that it is also a proper `micropython` iterable.\n", + "\n", + "The `ndarray` consists of a short header, and a pointer that holds the data. The pointer always points to a contiguous segment in memory (`numpy` is more flexible in this regard), and the header tells the interpreter, how the data from this segment is to be read out, and what the bytes mean. Some operations, e.g., `reshape`, are fast, because they do not operate on the data, they work on the header, and therefore, only a couple of bytes are manipulated, even if there are a million data entries. A more detailed exposition of how operators are implemented can be found in the section titled [Programming ulab](#Programming_ula).\n", + "\n", + "Since the `ndarray` is a binary container, it is also compact, meaning that it takes only a couple of bytes of extra RAM in addition to what is required for storing the numbers themselves. `ndarray`s are also type-aware, i.e., one can save RAM by specifying a data type, and using the smallest reasonable one. Five such types are defined, namely `uint8`, `int8`, which occupy a single byte of memory per datum, `uint16`, and `int16`, which occupy two bytes per datum, and `float`, which occupies four or eight bytes per datum. The precision/size of the `float` type depends on the definition of `mp_float_t`. Some platforms, e.g., the PYBD, implement `double`s, but some, e.g., the pyboard.v.11, do not. You can find out, what type of float your particular platform implements by looking at the output of the [.itemsize](#.itemsize) class property, or looking at the exact `dtype`, when you print out an array.\n", + "\n", + "In addition to the five above-mentioned numerical types, it is also possible to define Boolean arrays, which can be used in the indexing of data. However, Boolean arrays are really nothing but arrays of type `uint8` with an extra flag. \n", + "\n", + "On the following pages, we will see how one can work with `ndarray`s. Those familiar with `numpy` should find that the nomenclature and naming conventions of `numpy` are adhered to as closely as possible. We will point out the few differences, where necessary.\n", + "\n", + "For the sake of comparison, in addition to the `ulab` code snippets, sometimes the equivalent `numpy` code is also presented. You can find out, where the snippet is supposed to run by looking at its first line, the header of the code block." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The ndinfo function\n", + "\n", + "A concise summary of a couple of the properties of an `ndarray` can be printed out by calling the `ndinfo` \n", + "function. In addition to finding out what the *shape* and *strides* of the array array, we also get the `itemsize`, as well as the type. An interesting piece of information is the *data pointer*, which tells us, what the address of the data segment of the `ndarray` is. We will see the significance of this in the section [Slicing and indexing](#Slicing-and-indexing).\n", + "\n", + "Note that this function simply prints some information, but does not return anything. If you need to get a handle of the data contained in the printout, you should call the dedicated `shape`, `strides`, or `itemsize` functions directly." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:24:08.710325Z", + "start_time": "2021-01-12T16:24:08.699287Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "class: ndarray\n", + "shape: (5,)\n", + "strides: (8,)\n", + "itemsize: 8\n", + "data pointer: 0x7f8f6fa2e240\n", + "type: float\n", + "\n", + "\n", + "class: ndarray\n", + "shape: (5, 5)\n", + "strides: (5, 1)\n", + "itemsize: 1\n", + "data pointer: 0x7f8f6fa2e2e0\n", + "type: uint8\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(5), dtype=np.float)\n", + "b = np.array(range(25), dtype=np.uint8).reshape((5, 5))\n", + "np.ndinfo(a)\n", + "print('\\n')\n", + "np.ndinfo(b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Initialising an array\n", + "\n", + "A new array can be created by passing either a standard micropython iterable, or another `ndarray` into the constructor." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Initialising by passing iterables\n", + "\n", + "If the iterable is one-dimensional, i.e., one whose elements are numbers, then a row vector will be created and returned. If the iterable is two-dimensional, i.e., one whose elements are again iterables, a matrix will be created. If the lengths of the iterables are not consistent, a `ValueError` will be raised. Iterables of different types can be mixed in the initialisation function. \n", + "\n", + "If the `dtype` keyword with the possible `uint8/int8/uint16/int16/float` values is supplied, the new `ndarray` will have that type, otherwise, it assumes `float` as default. In addition, if `ULAB_SUPPORTS_COMPLEX` is set to 1 in [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h), the `dtype` can also take on the value of `complex`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:24:21.952689Z", + "start_time": "2021-01-12T16:24:21.938231Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t [1, 2, 3, 4, 5, 6, 7, 8]\n", + "b:\t array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "\n", + "c:\t array([[0, 1, 2, 3, 4],\n", + " [20, 21, 22, 23, 24],\n", + " [44, 55, 66, 77, 88]], dtype=uint8)\n", + "\n", + "Traceback (most recent call last):\n", + " File \"/dev/shm/micropython.py\", line 15, in <module>\n", + "ValueError: iterables are not of the same length\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = [1, 2, 3, 4, 5, 6, 7, 8]\n", + "b = np.array(a)\n", + "\n", + "print(\"a:\\t\", a)\n", + "print(\"b:\\t\", b)\n", + "\n", + "# a two-dimensional array with mixed-type initialisers\n", + "c = np.array([range(5), range(20, 25, 1), [44, 55, 66, 77, 88]], dtype=np.uint8)\n", + "print(\"\\nc:\\t\", c)\n", + "\n", + "# and now we throw an exception\n", + "d = np.array([range(5), range(10), [44, 55, 66, 77, 88]], dtype=np.uint8)\n", + "print(\"\\nd:\\t\", d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Initialising by passing arrays\n", + "\n", + "An `ndarray` can be initialised by supplying another array. This statement is almost trivial, since `ndarray`s are iterables themselves, though it should be pointed out that initialising through arrays is a bit faster. This statement is especially true, if the `dtype`s of the source and output arrays are the same, because then the contents can simply be copied without further ado. While type conversion is also possible, it will always be slower than straight copying." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:24:33.050654Z", + "start_time": "2021-01-12T16:24:33.039754Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t [1, 2, 3, 4, 5, 6, 7, 8]\n", + "\n", + "b:\t array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "\n", + "c:\t array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)\n", + "\n", + "d:\t array([1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = [1, 2, 3, 4, 5, 6, 7, 8]\n", + "b = np.array(a)\n", + "c = np.array(b)\n", + "d = np.array(b, dtype=np.uint8)\n", + "\n", + "print(\"a:\\t\", a)\n", + "print(\"\\nb:\\t\", b)\n", + "print(\"\\nc:\\t\", c)\n", + "print(\"\\nd:\\t\", d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the default type of the `ndarray` is `float`. Hence, if the array is initialised from another array, type conversion will always take place, except, when the output type is specifically supplied. I.e., " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:24:39.722844Z", + "start_time": "2021-01-12T16:24:39.709963Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([0, 1, 2, 3, 4], dtype=uint8)\n", + "\n", + "b:\t array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(5), dtype=np.uint8)\n", + "b = np.array(a)\n", + "print(\"a:\\t\", a)\n", + "print(\"\\nb:\\t\", b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "will iterate over the elements in `a`, since in the assignment `b = np.array(a)`, no output type was given, therefore, `float` was assumed. On the other hand, " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:25:06.597051Z", + "start_time": "2021-01-12T16:25:06.585511Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([0, 1, 2, 3, 4], dtype=uint8)\n", + "\n", + "b:\t array([0, 1, 2, 3, 4], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(5), dtype=np.uint8)\n", + "b = np.array(a, dtype=np.uint8)\n", + "print(\"a:\\t\", a)\n", + "print(\"\\nb:\\t\", b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "will simply copy the content of `a` into `b` without any iteration, and will, therefore, be faster. Keep this in mind, whenever the output type, or performance is important." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Array initialisation functions\n", + "\n", + "There are nine functions that can be used for initialising an array. Starred functions accept `complex` as the value of the `dtype`, if the firmware was compiled with complex support.\n", + "\n", + "1. [numpy.arange](#arange)\n", + "1. [numpy.concatenate](#concatenate)\n", + "1. [numpy.diag*](#diag)\n", + "1. [numpy.empty*](#empty)\n", + "1. [numpy.eye*](#eye)\n", + "1. [numpy.frombuffer](#frombuffer)\n", + "1. [numpy.full*](#full)\n", + "1. [numpy.linspace*](#linspace)\n", + "1. [numpy.logspace](#logspace)\n", + "1. [numpy.ones*](#ones)\n", + "1. [numpy.zeros*](#zeros)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### arange\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.arange.html\n", + "\n", + "The function returns a one-dimensional array with evenly spaced values. Takes 3 positional arguments (two are optional), and the `dtype` keyword argument. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:26:03.795728Z", + "start_time": "2021-01-12T16:26:03.782352Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int16)\n", + "array([2, 3, 4, 5, 6, 7, 8, 9], dtype=int16)\n", + "array([2, 5, 8], dtype=int16)\n", + "array([2.0, 5.0, 8.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "print(np.arange(10))\n", + "print(np.arange(2, 10))\n", + "print(np.arange(2, 10, 3))\n", + "print(np.arange(2, 10, 3, dtype=np.float))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### concatenate\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.concatenate.html\n", + "\n", + "The function joins a sequence of arrays, if they are compatible in shape, i.e., if all shapes except the one along the joining axis are equal. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:26:37.145965Z", + "start_time": "2021-01-12T16:26:37.134350Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([[0, 1, 2, 3, 4],\n", + " [5, 6, 7, 8, 9],\n", + " [10, 11, 12, 13, 14],\n", + " [15, 16, 17, 18, 19],\n", + " [20, 21, 22, 23, 24],\n", + " [0, 1, 2, 3, 4],\n", + " [5, 6, 7, 8, 9],\n", + " [10, 11, 12, 13, 14]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(25), dtype=np.uint8).reshape((5, 5))\n", + "b = np.array(range(15), dtype=np.uint8).reshape((3, 5))\n", + "\n", + "c = np.concatenate((a, b), axis=0)\n", + "print(c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**WARNING**: `numpy` accepts arbitrary `dtype`s in the sequence of arrays, in `ulab` the `dtype`s must be identical. If you want to concatenate different types, you have to convert all arrays to the same type first. Here `b` is of `float` type, so it cannot directly be concatenated to `a`. However, if we cast the `dtype` of `b`, the concatenation works:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:26:56.120820Z", + "start_time": "2021-01-12T16:26:56.102365Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([[0, 1, 2, 3, 4],\n", + " [5, 6, 7, 8, 9],\n", + " [10, 11, 12, 13, 14],\n", + " [15, 16, 17, 18, 19],\n", + " [20, 21, 22, 23, 24]], dtype=uint8)\n", + "====================\n", + "d: array([[1, 2, 3],\n", + " [4, 5, 6],\n", + " [7, 8, 9],\n", + " [10, 11, 12],\n", + " [13, 14, 15]], dtype=uint8)\n", + "====================\n", + "c: array([[1, 2, 3, 0, 1, 2, 3, 4],\n", + " [4, 5, 6, 5, 6, 7, 8, 9],\n", + " [7, 8, 9, 10, 11, 12, 13, 14],\n", + " [10, 11, 12, 15, 16, 17, 18, 19],\n", + " [13, 14, 15, 20, 21, 22, 23, 24]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(25), dtype=np.uint8).reshape((5, 5))\n", + "b = np.array(range(15), dtype=np.float).reshape((5, 3))\n", + "d = np.array(b+1, dtype=np.uint8)\n", + "print('a: ', a)\n", + "print('='*20 + '\\nd: ', d)\n", + "c = np.concatenate((d, a), axis=1)\n", + "print('='*20 + '\\nc: ', c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## diag\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.diag.html\n", + "\n", + "Extract a diagonal, or construct a diagonal array.\n", + "\n", + "The function takes two arguments, an `ndarray`, and a shift. If the first argument is a two-dimensional array, the function returns a one-dimensional array containing the diagonal entries. The diagonal can be shifted by an amount given in the second argument.\n", + "\n", + "If the first argument is a one-dimensional array, the function returns a two-dimensional tensor with its diagonal elements given by the first argument.\n", + "\n", + "The `diag` function can accept a complex array, if the firmware was compiled with complex support." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([[1.0, 0.0, 0.0, 0.0],\n", + " [0.0, 2.0, 0.0, 0.0],\n", + " [0.0, 0.0, 3.0, 0.0],\n", + " [0.0, 0.0, 0.0, 4.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4])\n", + "print(np.diag(a))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([[0.0, 1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0, 7.0],\n", + " [8.0, 9.0, 10.0, 11.0],\n", + " [12.0, 13.0, 14.0, 15.0]], dtype=float64)\n", + "\n", + "diagonal of a: array([0.0, 5.0, 10.0, 15.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(16)).reshape((4, 4))\n", + "print('a: ', a)\n", + "print()\n", + "print('diagonal of a: ', np.diag(a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## empty\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.empty.html\n", + "\n", + "`empty` is simply an alias for `zeros`, i.e., as opposed to `numpy`, the entries of the tensor will be initialised to zero. \n", + "\n", + "The `empty` function can accept complex as the value of the dtype, if the firmware was compiled with complex support." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### eye\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.eye.html\n", + "\n", + "Another special array method is the `eye` function, whose call signature is \n", + "\n", + "```python\n", + "eye(N, M, k=0, dtype=float)\n", + "```\n", + "where `N` (`M`) specify the dimensions of the matrix (if only `N` is supplied, then we get a square matrix, otherwise one with `M` rows, and `N` columns), and `k` is the shift of the ones (the main diagonal corresponds to `k=0`). Here are a couple of examples.\n", + "\n", + "The `eye` function can accept `complex` as the value of the `dtype`, if the firmware was compiled with complex support." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### With a single argument" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:27:08.533394Z", + "start_time": "2021-01-12T16:27:08.518940Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([[1.0, 0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 1.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 1.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 1.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0, 1.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "print(np.eye(5))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Specifying the dimensions of the matrix" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:27:34.075468Z", + "start_time": "2021-01-12T16:27:34.064137Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([[0, 0, 0, 0, 0, 0],\n", + " [1, 0, 0, 0, 0, 0],\n", + " [0, 1, 0, 0, 0, 0],\n", + " [0, 0, 1, 0, 0, 0]], dtype=int16)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "print(np.eye(4, M=6, k=-1, dtype=np.int16))" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:27:42.492135Z", + "start_time": "2021-01-12T16:27:42.477684Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([[1, 0, 0, 0, 0, 0],\n", + " [0, 1, 0, 0, 0, 0],\n", + " [0, 0, 1, 0, 0, 0],\n", + " [0, 0, 0, 1, 0, 0]], dtype=int8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "print(np.eye(4, M=6, dtype=np.int8))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### frombuffer\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.frombuffer.html\n", + "\n", + "The function interprets a contiguous buffer as a one-dimensional array, and thus can be used for piping buffered data directly into an array. This method of analysing, e.g., ADC data is much more efficient than passing the ADC buffer into the `array` constructor, because `frombuffer` simply creates the `ndarray` header and blindly copies the memory segment, without inspecting the underlying data. \n", + "\n", + "The function takes a single positional argument, the buffer, and three keyword arguments. These are the `dtype` with a default value of `float`, the `offset`, with a default of 0, and the `count`, with a default of -1, meaning that all data are taken in." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-15T07:01:35.320458Z", + "start_time": "2021-01-15T07:01:35.307407Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "buffer: b'\\x01\\x02\\x03\\x04\\x05\\x06\\x07\\x08'\n", + "a, all data read: array([1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "b, all data with an offset: array([3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "c, only 3 items with an offset: array([3, 4, 5], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "buffer = b'\\x01\\x02\\x03\\x04\\x05\\x06\\x07\\x08'\n", + "print('buffer: ', buffer)\n", + "\n", + "a = np.frombuffer(buffer, dtype=np.uint8)\n", + "print('a, all data read: ', a)\n", + "\n", + "b = np.frombuffer(buffer, dtype=np.uint8, offset=2)\n", + "print('b, all data with an offset: ', b)\n", + "\n", + "c = np.frombuffer(buffer, dtype=np.uint8, offset=2, count=3)\n", + "print('c, only 3 items with an offset: ', c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### full\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.full.html\n", + "\n", + "The function returns an array of arbitrary dimension, whose elements are all equal to the second positional argument. The first argument is a tuple describing the shape of the tensor. The `dtype` keyword argument with a default value of `float` can also be supplied.\n", + "\n", + "The `full` function can accept a complex scalar, or `complex` as the value of `dtype`, if the firmware was compiled with complex support." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:29:11.931011Z", + "start_time": "2021-01-12T16:29:11.915195Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([[3.0, 3.0, 3.0, 3.0],\n", + " [3.0, 3.0, 3.0, 3.0]], dtype=float64)\n", + "\n", + "====================\n", + "\n", + "array([[3, 3, 3, 3],\n", + " [3, 3, 3, 3]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "# create an array with the default type\n", + "print(np.full((2, 4), 3))\n", + "\n", + "print('\\n' + '='*20 + '\\n')\n", + "# the array type is uint8 now\n", + "print(np.full((2, 4), 3, dtype=np.uint8))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### linspace\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html\n", + "\n", + "This function returns an array, whose elements are uniformly spaced between the `start`, and `stop` points. The number of intervals is determined by the `num` keyword argument, whose default value is 50. With the `endpoint` keyword argument (defaults to `True`) one can include `stop` in the sequence. In addition, the `dtype` keyword can be supplied to force type conversion of the output. The default is `float`. Note that, when `dtype` is of integer type, the sequence is not necessarily evenly spaced. This is not an error, rather a consequence of rounding. (This is also the `numpy` behaviour.)\n", + "\n", + "The `linspace` function can accept `complex` as the value of the `dtype`, if the firmware was compiled with complex support. The output `dtype` is automatically complex, if either of the endpoints is a complex scalar." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:29:45.897927Z", + "start_time": "2021-01-12T16:29:45.876325Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "default sequence:\t array([0.0, 0.2040816326530612, 0.4081632653061225, ..., 9.591836734693871, 9.795918367346932, 9.999999999999993], dtype=float64)\n", + "num=5:\t\t\t array([0.0, 2.5, 5.0, 7.5, 10.0], dtype=float64)\n", + "num=5:\t\t\t array([0.0, 2.0, 4.0, 6.0, 8.0], dtype=float64)\n", + "num=5:\t\t\t array([0, 0, 1, 2, 2, 3, 4], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "# generate a sequence with defaults\n", + "print('default sequence:\\t', np.linspace(0, 10))\n", + "\n", + "# num=5\n", + "print('num=5:\\t\\t\\t', np.linspace(0, 10, num=5))\n", + "\n", + "# num=5, endpoint=False\n", + "print('num=5:\\t\\t\\t', np.linspace(0, 10, num=5, endpoint=False))\n", + "\n", + "# num=5, endpoint=False, dtype=uint8\n", + "print('num=5:\\t\\t\\t', np.linspace(0, 5, num=7, endpoint=False, dtype=np.uint8))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### logspace\n", + "\n", + "`linspace`' equivalent for logarithmically spaced data is `logspace`. This function produces a sequence of numbers, in which the quotient of consecutive numbers is constant. This is a geometric sequence.\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.logspace.html\n", + "\n", + "This function returns an array, whose elements are uniformly spaced between the `start`, and `stop` points. The number of intervals is determined by the `num` keyword argument, whose default value is 50. With the `endpoint` keyword argument (defaults to `True`) one can include `stop` in the sequence. In addition, the `dtype` keyword can be supplied to force type conversion of the output. The default is `float`. Note that, exactly as in `linspace`, when `dtype` is of integer type, the sequence is not necessarily evenly spaced in log space.\n", + "\n", + "In addition to the keyword arguments found in `linspace`, `logspace` also accepts the `base` argument. The default value is 10. " + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:30:44.483893Z", + "start_time": "2021-01-12T16:30:44.466705Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "default sequence:\t array([1.0, 1.151395399326447, 1.325711365590109, ..., 754.3120063354646, 868.5113737513561, 1000.000000000004], dtype=float64)\n", + "num=5:\t\t\t array([10.0, 1778.279410038923, 316227.766016838, 56234132.5190349, 10000000000.0], dtype=float64)\n", + "num=5:\t\t\t array([10.0, 630.9573444801933, 39810.71705534974, 2511886.431509581, 158489319.2461114], dtype=float64)\n", + "num=5:\t\t\t array([2.0, 6.964404506368993, 24.25146506416637, 84.44850628946524, 294.066778879241], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "# generate a sequence with defaults\n", + "print('default sequence:\\t', np.logspace(0, 3))\n", + "\n", + "# num=5\n", + "print('num=5:\\t\\t\\t', np.logspace(1, 10, num=5))\n", + "\n", + "# num=5, endpoint=False\n", + "print('num=5:\\t\\t\\t', np.logspace(1, 10, num=5, endpoint=False))\n", + "\n", + "# num=5, endpoint=False\n", + "print('num=5:\\t\\t\\t', np.logspace(1, 10, num=5, endpoint=False, base=2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### ones, zeros\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.ones.html\n", + "\n", + "A couple of special arrays and matrices can easily be initialised by calling one of the `ones`, or `zeros` functions. `ones` and `zeros` follow the same pattern, and have the call signature\n", + "\n", + "```python\n", + "ones(shape, dtype=float)\n", + "zeros(shape, dtype=float)\n", + "```\n", + "where shape is either an integer, or a tuple specifying the shape.\n", + "\n", + "The `ones/zeros` functions can accept complex as the value of the dtype, if the firmware was compiled with complex support." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-12T16:32:05.422109Z", + "start_time": "2021-01-12T16:32:05.407921Z" + }, + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([1, 1, 1, 1, 1, 1], dtype=uint8)\n", + "array([[0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0],\n", + " [0.0, 0.0, 0.0, 0.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "print(np.ones(6, dtype=np.uint8))\n", + "\n", + "print(np.zeros((6, 4)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " When specifying the shape, make sure that the length of the tuple is not larger than the maximum dimension of your firmware." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:01:44.960353Z", + "start_time": "2021-01-13T06:01:44.944935Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "maximum number of dimensions: 2.1.0-2D\n", + "\n", + "Traceback (most recent call last):\n", + " File \"/dev/shm/micropython.py\", line 7, in <module>\n", + "TypeError: too many dimensions\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "import ulab\n", + "\n", + "print('maximum number of dimensions: ', ulab.__version__)\n", + "\n", + "print(np.zeros((2, 2, 2)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Customising array printouts" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`ndarray`s are pretty-printed, i.e., if the number of entries along the last axis is larger than 10 (default value), then only the first and last three entries will be printed. Also note that, as opposed to `numpy`, the printout always contains the `dtype`." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:02:20.162127Z", + "start_time": "2021-01-13T06:02:20.146219Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([0.0, 1.0, 2.0, ..., 197.0, 198.0, 199.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(200))\n", + "print(\"a:\\t\", a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### set_printoptions\n", + "\n", + "The default values can be overwritten by means of the `set_printoptions` function [numpy.set_printoptions](https://numpy.org/doc/1.18/reference/generated/numpy.set_printoptions.html), which accepts two keywords arguments, the `threshold`, and the `edgeitems`. The first of these arguments determines the length of the longest array that will be printed in full, while the second is the number of items that will be printed on the left and right hand side of the ellipsis, if the array is longer than `threshold`." + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:02:42.073823Z", + "start_time": "2021-01-13T06:02:42.057424Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a printed with defaults:\t array([0.0, 1.0, 2.0, ..., 17.0, 18.0, 19.0], dtype=float64)\n", + "\n", + "a printed in full:\t\t array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0], dtype=float64)\n", + "\n", + "a truncated with 2 edgeitems:\t array([0.0, 1.0, ..., 18.0, 19.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(20))\n", + "print(\"a printed with defaults:\\t\", a)\n", + "\n", + "np.set_printoptions(threshold=200)\n", + "print(\"\\na printed in full:\\t\\t\", a)\n", + "\n", + "np.set_printoptions(threshold=10, edgeitems=2)\n", + "print(\"\\na truncated with 2 edgeitems:\\t\", a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### get_printoptions\n", + "\n", + "The set value of the `threshold` and `edgeitems` can be retrieved by calling the `get_printoptions` function with no arguments. The function returns a *dictionary* with two keys." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:02:51.383653Z", + "start_time": "2021-01-13T06:02:51.372551Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'threshold': 100, 'edgeitems': 20}\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "np.set_printoptions(threshold=100, edgeitems=20)\n", + "print(np.get_printoptions())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Methods and properties of ndarrays\n", + "\n", + "Arrays have several *properties* that can queried, and some methods that can be called. With the exception of the flatten and transpose operators, properties return an object that describe some feature of the array, while the methods return a new array-like object. The `imag`, and `real` properties are included in the firmware only, when it was compiled with complex support.\n", + "\n", + "1. [.byteswap](#.byteswap)\n", + "1. [.copy](#.copy)\n", + "1. [.dtype](#.dtype)\n", + "1. [.flat](#.flat)\n", + "1. [.flatten](#.flatten)\n", + "1. [.imag*](#.imag)\n", + "1. [.itemsize](#.itemsize)\n", + "1. [.real*](#.real)\n", + "1. [.reshape](#.reshape)\n", + "1. [.shape](#.shape)\n", + "1. [.size](#.size)\n", + "1. [.T](#.transpose)\n", + "1. [.tobytes](#.tobytes)\n", + "1. [.tolist](#.tolist)\n", + "1. [.transpose](#.transpose)\n", + "1. [.sort](#.sort)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .byteswap\n", + "\n", + "`numpy` https://numpy.org/doc/stable/reference/generated/numpy.char.chararray.byteswap.html\n", + "\n", + "The method takes a single keyword argument, `inplace`, with values `True` or `False`, and swaps the bytes in the array. If `inplace = False`, a new `ndarray` is returned, otherwise the original values are overwritten.\n", + "\n", + "The `frombuffer` function is a convenient way of receiving data from peripheral devices that work with buffers. However, it is not guaranteed that the byte order (in other words, the _endianness_) of the peripheral device matches that of the microcontroller. The `.byteswap` method makes it possible to change the endianness of the incoming data stream.\n", + "\n", + "Obviously, byteswapping makes sense only for those cases, when a datum occupies more than one byte, i.e., for the `uint16`, `int16`, and `float` `dtype`s. When `dtype` is either `uint8`, or `int8`, the method simply returns a view or copy of self, depending upon the value of `inplace`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2021-02-15T16:06:20.409727Z", + "start_time": "2021-02-15T16:06:20.398057Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "buffer: b'\\x01\\x02\\x03\\x04\\x05\\x06\\x07\\x08'\n", + "a: array([513, 1027, 1541, 2055], dtype=uint16)\n", + "b: array([258, 772, 1286, 1800], dtype=uint16)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "buffer = b'\\x01\\x02\\x03\\x04\\x05\\x06\\x07\\x08'\n", + "print('buffer: ', buffer)\n", + "\n", + "a = np.frombuffer(buffer, dtype=np.uint16)\n", + "print('a: ', a)\n", + "b = a.byteswap()\n", + "print('b: ', b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .copy\n", + "\n", + "The `.copy` method creates a new *deep copy* of an array, i.e., the entries of the source array are *copied* into the target array." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:02:58.898485Z", + "start_time": "2021-01-13T06:02:58.878864Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([1, 2, 3, 4], dtype=int8)\n", + "====================\n", + "b: array([1, 2, 3, 4], dtype=int8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4], dtype=np.int8)\n", + "b = a.copy()\n", + "print('a: ', a)\n", + "print('='*20)\n", + "print('b: ', b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .dtype\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.dtype.htm\n", + "\n", + "The `.dtype` property is the `dtype` of an array. This can then be used for initialising another array with the matching type. `ulab` implements two versions of `dtype`; one that is `numpy`-like, i.e., one, which returns a `dtype` object, and one that is significantly cheaper in terms of flash space, but does not define a `dtype` object, and holds a single character (number) instead. " + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-11-02T17:16:12.818777Z", + "start_time": "2020-11-02T17:16:12.807147Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([1, 2, 3, 4], dtype=int8)\n", + "dtype of a: dtype('int8')\n", + "\n", + "b: array([5, 6, 7], dtype=int8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4], dtype=np.int8)\n", + "b = np.array([5, 6, 7], dtype=a.dtype)\n", + "print('a: ', a)\n", + "print('dtype of a: ', a.dtype)\n", + "print('\\nb: ', b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If the `ulab.h` header file sets the pre-processor constant `ULAB_HAS_DTYPE_OBJECT` to 0 as\n", + "\n", + "```c\n", + "#define ULAB_HAS_DTYPE_OBJECT (0)\n", + "```\n", + "then the output of the previous snippet will be" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "ExecuteTime": { + "end_time": "2020-11-02T20:36:23.099166Z", + "start_time": "2020-11-02T20:36:23.088586Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([1, 2, 3, 4], dtype=int8)\n", + "dtype of a: 98\n", + "\n", + "b: array([5, 6, 7], dtype=int8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4], dtype=np.int8)\n", + "b = np.array([5, 6, 7], dtype=a.dtype)\n", + "print('a: ', a)\n", + "print('dtype of a: ', a.dtype)\n", + "print('\\nb: ', b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here 98 is nothing but the ASCII value of the character `b`, which is the type code for signed 8-bit integers. The object definition adds around 600 bytes to the firmware." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .flat\n", + "\n", + "numpy: https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flat.htm\n", + "\n", + "`.flat` returns the array's flat iterator. For one-dimensional objects the flat iterator is equivalent to the standart iterator, while for higher dimensional tensors, it amounts to first flattening the array, and then iterating over it. Note, however, that the flat iterator does not consume RAM beyond what is required for holding the position of the iterator itself, while flattening produces a new copy." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n", + "2\n", + "3\n", + "4\n", + "a:\n", + " array([[1, 2, 3, 4],\n", + " [5, 6, 7, 8]], dtype=int8)\n", + "array([1, 2, 3, 4], dtype=int8)\n", + "array([5, 6, 7, 8], dtype=int8)\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n", + "6\n", + "7\n", + "8\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4], dtype=np.int8)\n", + "for _a in a:\n", + " print(_a)\n", + "\n", + "a = np.array([[1, 2, 3, 4], [5, 6, 7, 8]], dtype=np.int8)\n", + "print('a:\\n', a)\n", + "\n", + "for _a in a:\n", + " print(_a)\n", + "\n", + "for _a in a.flat:\n", + " print(_a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .flatten\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flatten.htm\n", + "\n", + "`.flatten` returns the flattened array. The array can be flattened in `C` style (i.e., moving along the last axis in the tensor), or in `fortran` style (i.e., moving along the first axis in the tensor)." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:07:16.735771Z", + "start_time": "2021-01-13T06:07:16.723514Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: \t\t array([1, 2, 3, 4], dtype=int8)\n", + "a flattened: \t array([1, 2, 3, 4], dtype=int8)\n", + "\n", + "b: array([[1, 2, 3],\n", + " [4, 5, 6]], dtype=int8)\n", + "b flattened (C): \t array([1, 2, 3, 4, 5, 6], dtype=int8)\n", + "b flattened (F): \t array([1, 4, 2, 5, 3, 6], dtype=int8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4], dtype=np.int8)\n", + "print(\"a: \\t\\t\", a)\n", + "print(\"a flattened: \\t\", a.flatten())\n", + "\n", + "b = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int8)\n", + "print(\"\\nb:\", b)\n", + "\n", + "print(\"b flattened (C): \\t\", b.flatten())\n", + "print(\"b flattened (F): \\t\", b.flatten(order='F'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .imag\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.imag.html\n", + "\n", + "The `.imag` property is defined only, if the firmware was compiled with complex support, and returns a copy with the imaginary part of an array. If the array is real, then the output is straight zeros with the `dtype` of the input. If the input is complex, the output `dtype` is always `float`, irrespective of the values." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:07:26.171208Z", + "start_time": "2022-01-07T19:07:26.152633Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([1, 2, 3], dtype=uint16)\n", + "a.imag:\t array([0, 0, 0], dtype=uint16)\n", + "\n", + "b:\t array([1.0+0.0j, 2.0+1.0j, 3.0-1.0j], dtype=complex)\n", + "b.imag:\t array([0.0, 1.0, -1.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3], dtype=np.uint16)\n", + "print(\"a:\\t\", a)\n", + "print(\"a.imag:\\t\", a.imag)\n", + "\n", + "b = np.array([1, 2+1j, 3-1j], dtype=np.complex)\n", + "print(\"\\nb:\\t\", b)\n", + "print(\"b.imag:\\t\", b.imag)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .itemsize\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.itemsize.html\n", + "\n", + "The `.itemsize` property is an integer with the size of elements in the array." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:07:49.080817Z", + "start_time": "2021-01-13T06:07:49.065749Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([1, 2, 3], dtype=int8)\n", + "itemsize of a: 1\n", + "\n", + "b:\n", + " array([[1.0, 2.0],\n", + " [3.0, 4.0]], dtype=float64)\n", + "itemsize of b: 8\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3], dtype=np.int8)\n", + "print(\"a:\\n\", a)\n", + "print(\"itemsize of a:\", a.itemsize)\n", + "\n", + "b= np.array([[1, 2], [3, 4]], dtype=np.float)\n", + "print(\"\\nb:\\n\", b)\n", + "print(\"itemsize of b:\", b.itemsize)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .real\n", + "\n", + "numpy: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.real.html\n", + "\n", + "The `.real` property is defined only, if the firmware was compiled with complex support, and returns a copy with the real part of an array." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:10:01.870921Z", + "start_time": "2022-01-07T19:10:01.860071Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([1, 2, 3], dtype=uint16)\n", + "a.real:\t array([1, 2, 3], dtype=uint16)\n", + "\n", + "b:\t array([1.0+0.0j, 2.0+1.0j, 3.0-1.0j], dtype=complex)\n", + "b.real:\t array([1.0, 2.0, 3.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3], dtype=np.uint16)\n", + "print(\"a:\\t\", a)\n", + "print(\"a.real:\\t\", a.real)\n", + "\n", + "b = np.array([1, 2+1j, 3-1j], dtype=np.complex)\n", + "print(\"\\nb:\\t\", b)\n", + "print(\"b.real:\\t\", b.real)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .reshape\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.reshape.html\n", + "\n", + "`reshape` re-writes the shape properties of an `ndarray`, but the array will not be modified in any other way. The function takes a single 2-tuple with two integers as its argument. The 2-tuple should specify the desired number of rows and columns. If the new shape is not consistent with the old, a `ValueError` exception will be raised." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:08:12.234490Z", + "start_time": "2021-01-13T06:08:12.217652Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a (4 by 4): array([[1, 2, 3, 4],\n", + " [5, 6, 7, 8],\n", + " [9, 10, 11, 12],\n", + " [13, 14, 15, 16]], dtype=uint8)\n", + "a (2 by 8): array([[1, 2, 3, 4, 5, 6, 7, 8],\n", + " [9, 10, 11, 12, 13, 14, 15, 16]], dtype=uint8)\n", + "a (1 by 16): array([[1, 2, 3, ..., 14, 15, 16]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]], dtype=np.uint8)\n", + "print('a (4 by 4):', a)\n", + "print('a (2 by 8):', a.reshape((2, 8)))\n", + "print('a (1 by 16):', a.reshape((1, 16)))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "Note that `ndarray.reshape()` can also be called by assigning to `ndarray.shape`. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .shape\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html\n", + "\n", + "The `.shape` property is a tuple whose elements are the length of the array along each axis. " + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:08:50.479850Z", + "start_time": "2021-01-13T06:08:50.464741Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([1, 2, 3, 4], dtype=int8)\n", + "shape of a: (4,)\n", + "\n", + "b:\n", + " array([[1, 2],\n", + " [3, 4]], dtype=int8)\n", + "shape of b: (2, 2)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4], dtype=np.int8)\n", + "print(\"a:\\n\", a)\n", + "print(\"shape of a:\", a.shape)\n", + "\n", + "b= np.array([[1, 2], [3, 4]], dtype=np.int8)\n", + "print(\"\\nb:\\n\", b)\n", + "print(\"shape of b:\", b.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By assigning a tuple to the `.shape` property, the array can be `reshape`d:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64)\n", + "\n", + "a:\n", + " array([[1.0, 2.0, 3.0],\n", + " [4.0, 5.0, 6.0],\n", + " [7.0, 8.0, 9.0]], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])\n", + "print('a:\\n', a)\n", + "\n", + "a.shape = (3, 3)\n", + "print('\\na:\\n', a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .size\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.size.html\n", + "\n", + "The `.size` property is an integer specifying the number of elements in the array. " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "ExecuteTime": { + "end_time": "2020-02-11T06:32:22.721112Z", + "start_time": "2020-02-11T06:32:22.713111Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([1, 2, 3], dtype=int8)\n", + "size of a: 3\n", + "\n", + "b:\n", + " array([[1, 2],\n", + "\t [3, 4]], dtype=int8)\n", + "size of b: 4\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3], dtype=np.int8)\n", + "print(\"a:\\n\", a)\n", + "print(\"size of a:\", a.size)\n", + "\n", + "b= np.array([[1, 2], [3, 4]], dtype=np.int8)\n", + "print(\"\\nb:\\n\", b)\n", + "print(\"size of b:\", b.size)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + ".T\n", + "\n", + "The `.T` property of the `ndarray` is equivalent to [.transpose](#.transpose)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .tobytes\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tobytes.html\n", + "\n", + "The `.tobytes` method can be used for acquiring a handle of the underlying data pointer of an array, and it returns a new `bytearray` that can be fed into any method that can accep a `bytearray`, e.g., ADC data can be buffered into this `bytearray`, or the `bytearray` can be fed into a DAC. Since the `bytearray` is really nothing but the bare data container of the array, any manipulation on the `bytearray` automatically modifies the array itself.\n", + "\n", + "Note that the method raises a `ValueError` exception, if the array is not dense (i.e., it has already been sliced)." + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:09:57.262071Z", + "start_time": "2021-01-13T06:09:57.250519Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint8)\n", + "b: bytearray(b'\\x00\\x01\\x02\\x03\\x04\\x05\\x06\\x07')\n", + "====================\n", + "b: bytearray(b'\\r\\x01\\x02\\x03\\x04\\x05\\x06\\x07')\n", + "a: array([13, 1, 2, 3, 4, 5, 6, 7], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(8), dtype=np.uint8)\n", + "print('a: ', a)\n", + "b = a.tobytes()\n", + "print('b: ', b)\n", + "\n", + "# modify b\n", + "b[0] = 13\n", + "\n", + "print('='*20)\n", + "print('b: ', b)\n", + "print('a: ', a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .tolist\n", + "\n", + "`numpy`: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tolist.html\n", + "\n", + "The `.tolist` method can be used for converting the numerical array into a (nested) `python` lists." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:01:28.671234Z", + "start_time": "2022-01-07T19:01:28.568786Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([0, 1, 2, 3], dtype=uint8)\n", + "b: [0, 1, 2, 3]\n", + "====================\n", + "c: array([[0, 1],\n", + " [2, 3]], dtype=uint8)\n", + "d: [[0, 1], [2, 3]]\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(4), dtype=np.uint8)\n", + "print('a: ', a)\n", + "b = a.tolist()\n", + "print('b: ', b)\n", + "\n", + "c = a.reshape((2, 2))\n", + "print('='*20)\n", + "print('c: ', c)\n", + "d = c.tolist()\n", + "print('d: ', d)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .transpose\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.transpose.html\n", + "\n", + "Returns the transposed array. Only defined, if the number of maximum dimensions is larger than 1." + ] + }, + { + "cell_type": "code", + "execution_count": 384, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-19T08:39:11.844987Z", + "start_time": "2019-10-19T08:39:11.828099Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[1, 2, 3],\n", + "\t [4, 5, 6],\n", + "\t [7, 8, 9],\n", + "\t [10, 11, 12]], dtype=uint8)\n", + "shape of a: (4, 3)\n", + "\n", + "transpose of a:\n", + " array([[1, 4, 7, 10],\n", + "\t [2, 5, 8, 11],\n", + "\t [3, 6, 9, 12]], dtype=uint8)\n", + "shape of a: (3, 4)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], dtype=np.uint8)\n", + "print('a:\\n', a)\n", + "print('shape of a:', a.shape)\n", + "a.transpose()\n", + "print('\\ntranspose of a:\\n', a)\n", + "print('shape of a:', a.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The transpose of the array can also be gotten through the `T` property:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[1, 2, 3],\n", + " [4, 5, 6],\n", + " [7, 8, 9]], dtype=uint8)\n", + "\n", + "transpose of a:\n", + " array([[1, 4, 7],\n", + " [2, 5, 8],\n", + " [3, 6, 9]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.uint8)\n", + "print('a:\\n', a)\n", + "print('\\ntranspose of a:\\n', a.T)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### .sort\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html\n", + "\n", + "In-place sorting of an `ndarray`. For a more detailed exposition, see [sort](#sort)." + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:11:20.989109Z", + "start_time": "2021-01-13T06:11:20.972842Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([[1, 12, 3, 0],\n", + " [5, 3, 4, 1],\n", + " [9, 11, 1, 8],\n", + " [7, 10, 0, 1]], dtype=uint8)\n", + "\n", + "a sorted along vertical axis:\n", + " array([[1, 3, 0, 0],\n", + " [5, 10, 1, 1],\n", + " [7, 11, 3, 1],\n", + " [9, 12, 4, 8]], dtype=uint8)\n", + "\n", + "a sorted along horizontal axis:\n", + " array([[0, 1, 3, 12],\n", + " [1, 3, 4, 5],\n", + " [1, 8, 9, 11],\n", + " [0, 1, 7, 10]], dtype=uint8)\n", + "\n", + "flattened a sorted:\n", + " array([0, 0, 1, ..., 10, 11, 12], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8)\n", + "print('\\na:\\n', a)\n", + "a.sort(axis=0)\n", + "print('\\na sorted along vertical axis:\\n', a)\n", + "\n", + "a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8)\n", + "a.sort(axis=1)\n", + "print('\\na sorted along horizontal axis:\\n', a)\n", + "\n", + "a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8)\n", + "a.sort(axis=None)\n", + "print('\\nflattened a sorted:\\n', a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unary operators\n", + "\n", + "With the exception of `len`, which returns a single number, all unary operators manipulate the underlying data element-wise. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### len\n", + "\n", + "This operator takes a single argument, the array, and returns either the length of the first axis." + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:11:49.266192Z", + "start_time": "2021-01-13T06:11:49.255493Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([1, 2, 3, 4, 5], dtype=uint8)\n", + "length of a: 5\n", + "shape of a: (5,)\n", + "\n", + "b:\t array([[0, 1, 2, 3, 4],\n", + " [0, 1, 2, 3, 4],\n", + " [0, 1, 2, 3, 4],\n", + " [0, 1, 2, 3, 4]], dtype=uint8)\n", + "length of b: 2\n", + "shape of b: (4, 5)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5], dtype=np.uint8)\n", + "b = np.array([range(5), range(5), range(5), range(5)], dtype=np.uint8)\n", + "\n", + "print(\"a:\\t\", a)\n", + "print(\"length of a: \", len(a))\n", + "print(\"shape of a: \", a.shape)\n", + "print(\"\\nb:\\t\", b)\n", + "print(\"length of b: \", len(b))\n", + "print(\"shape of b: \", b.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " The number returned by `len` is also the length of the iterations, when the array supplies the elements for an iteration (see later)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### invert\n", + "\n", + "The function is defined for integer data types (`uint8`, `int8`, `uint16`, and `int16`) only, takes a single argument, and returns the element-by-element, bit-wise inverse of the array. If a `float` is supplied, the function raises a `ValueError` exception.\n", + "\n", + "With signed integers (`int8`, and `int16`), the results might be unexpected, as in the example below:" + ] + }, + { + "cell_type": "code", + "execution_count": 98, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-11T13:16:16.754210Z", + "start_time": "2019-10-11T13:16:16.735618Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([0, -1, -100], dtype=int8)\n", + "inverse of a:\t array([-1, 0, 99], dtype=int8)\n", + "\n", + "a:\t\t array([0, 1, 254, 255], dtype=uint8)\n", + "inverse of a:\t array([255, 254, 1, 0], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([0, -1, -100], dtype=np.int8)\n", + "print(\"a:\\t\\t\", a)\n", + "print(\"inverse of a:\\t\", ~a)\n", + "\n", + "a = np.array([0, 1, 254, 255], dtype=np.uint8)\n", + "print(\"\\na:\\t\\t\", a)\n", + "print(\"inverse of a:\\t\", ~a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### abs\n", + "\n", + "This function takes a single argument, and returns the element-by-element absolute value of the array. When the data type is unsigned (`uint8`, or `uint16`), a copy of the array will be returned immediately, and no calculation takes place." + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-11T13:05:43.926821Z", + "start_time": "2019-10-11T13:05:43.912629Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t\t array([0, -1, -100], dtype=int8)\n", + "absolute value of a:\t array([0, 1, 100], dtype=int8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([0, -1, -100], dtype=np.int8)\n", + "print(\"a:\\t\\t\\t \", a)\n", + "print(\"absolute value of a:\\t \", abs(a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### neg\n", + "\n", + "This operator takes a single argument, and changes the sign of each element in the array. Unsigned values are wrapped. " + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-11T13:17:00.946009Z", + "start_time": "2019-10-11T13:17:00.927264Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([10, -1, 1], dtype=int8)\n", + "negative of a:\t array([-10, 1, -1], dtype=int8)\n", + "\n", + "b:\t\t array([0, 100, 200], dtype=uint8)\n", + "negative of b:\t array([0, 156, 56], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([10, -1, 1], dtype=np.int8)\n", + "print(\"a:\\t\\t\", a)\n", + "print(\"negative of a:\\t\", -a)\n", + "\n", + "b = np.array([0, 100, 200], dtype=np.uint8)\n", + "print(\"\\nb:\\t\\t\", b)\n", + "print(\"negative of b:\\t\", -b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### pos\n", + "\n", + "This function takes a single argument, and simply returns a copy of the array." + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-11T13:09:15.965662Z", + "start_time": "2019-10-11T13:09:15.945461Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t array([10, -1, 1], dtype=int8)\n", + "positive of a:\t array([10, -1, 1], dtype=int8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([10, -1, 1], dtype=np.int8)\n", + "print(\"a:\\t\\t\", a)\n", + "print(\"positive of a:\\t\", +a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Binary operators\n", + "\n", + "`ulab` implements the `+`, `-`, `*`, `/`, `**`, `<`, `>`, `<=`, `>=`, `==`, `!=`, `+=`, `-=`, `*=`, `/=`, `**=` binary operators that work element-wise. Broadcasting is available, meaning that the two operands do not even have to have the same shape. If the lengths along the respective axes are equal, or one of them is 1, or the axis is missing, the element-wise operation can still be carried out. \n", + "A thorough explanation of broadcasting can be found under https://numpy.org/doc/stable/user/basics.broadcasting.html. \n", + "\n", + "**WARNING**: note that relational operators (`<`, `>`, `<=`, `>=`, `==`, `!=`) should have the `ndarray` on their left hand side, when compared to scalars. This means that the following works" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:12:30.802935Z", + "start_time": "2021-01-13T06:12:30.786069Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([False, False, True], dtype=bool)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3])\n", + "print(a > 2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "while the equivalent statement, `2 < a`, will raise a `TypeError` exception:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:12:51.262197Z", + "start_time": "2021-01-13T06:12:51.244206Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Traceback (most recent call last):\n", + " File \"/dev/shm/micropython.py\", line 5, in <module>\n", + "TypeError: unsupported types for __lt__: 'int', 'ndarray'\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3])\n", + "print(2 < a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**WARNING:** `circuitpython` users should use the `equal`, and `not_equal` operators instead of `==`, and `!=`. See the section on [array comparison](#Comparison-of-arrays) for details." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Upcasting\n", + "\n", + "Binary operations require special attention, because two arrays with different typecodes can be the operands of an operation, in which case it is not trivial, what the typecode of the result is. This decision on the result's typecode is called upcasting. Since the number of typecodes in `ulab` is significantly smaller than in `numpy`, we have to define new upcasting rules. Where possible, I followed `numpy`'s conventions. \n", + "\n", + "`ulab` observes the following upcasting rules:\n", + "\n", + "1. Operations on two `ndarray`s of the same `dtype` preserve their `dtype`, even when the results overflow.\n", + "\n", + "2. if either of the operands is a float, the result is automatically a float\n", + "\n", + "3. When one of the operands is a scalar, it will internally be turned into a single-element `ndarray` with the *smallest* possible `dtype`. Thus, e.g., if the scalar is 123, it will be converted into an array of `dtype` `uint8`, while -1000 will be converted into `int16`. An `mp_obj_float`, will always be promoted to `dtype` `float`. Other micropython types (e.g., lists, tuples, etc.) raise a `TypeError` exception. \n", + "\n", + "4. \n", + " \n", + "| left hand side | right hand side | ulab result | numpy result |\n", + "|----------------|-----------------|-------------|--------------|\n", + "|`uint8` |`int8` |`int16` |`int16` |\n", + "|`uint8` |`int16` |`int16` |`int16` |\n", + "|`uint8` |`uint16` |`uint16` |`uint16` |\n", + "|`int8` |`int16` |`int16` |`int16` | \n", + "|`int8` |`uint16` |`uint16` |`int32` |\n", + "|`uint16` |`int16` |`float` |`int32` |\n", + " \n", + "Note that the last two operations are promoted to `int32` in `numpy`.\n", + " \n", + "**WARNING:** Due to the lower number of available data types, the upcasting rules of `ulab` are slightly different to those of `numpy`. Watch out for this, when porting code!\n", + "\n", + "Upcasting can be seen in action in the following snippet:" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:13:23.026904Z", + "start_time": "2021-01-13T06:13:23.009315Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([1, 2, 3, 4], dtype=uint8)\n", + "b:\t array([1, 2, 3, 4], dtype=int8)\n", + "a+b:\t array([2, 4, 6, 8], dtype=int16)\n", + "\n", + "a:\t array([1, 2, 3, 4], dtype=uint8)\n", + "c:\t array([1.0, 2.0, 3.0, 4.0], dtype=float64)\n", + "a*c:\t array([1.0, 4.0, 9.0, 16.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4], dtype=np.uint8)\n", + "b = np.array([1, 2, 3, 4], dtype=np.int8)\n", + "print(\"a:\\t\", a)\n", + "print(\"b:\\t\", b)\n", + "print(\"a+b:\\t\", a+b)\n", + "\n", + "c = np.array([1, 2, 3, 4], dtype=np.float)\n", + "print(\"\\na:\\t\", a)\n", + "print(\"c:\\t\", c)\n", + "print(\"a*c:\\t\", a*c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Benchmarks\n", + "\n", + "The following snippet compares the performance of binary operations to a possible implementation in python. For the time measurement, we will take the following snippet from the micropython manual:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T06:39:52.225256Z", + "start_time": "2020-05-07T06:39:52.194691Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "code", + "execution_count": 490, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-19T13:23:45.432395Z", + "start_time": "2019-10-19T13:23:45.344021Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "python add:\n", + "execution time: 10051 us\n", + "\n", + "python multiply:\n", + "execution time: 14175 us\n", + "\n", + "ulab add:\n", + "execution time: 222 us\n", + "\n", + "ulab multiply:\n", + "execution time: 213 us\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "@timeit\n", + "def py_add(a, b):\n", + " return [a[i]+b[i] for i in range(1000)]\n", + "\n", + "@timeit\n", + "def py_multiply(a, b):\n", + " return [a[i]*b[i] for i in range(1000)]\n", + "\n", + "@timeit\n", + "def ulab_add(a, b):\n", + " return a + b\n", + "\n", + "@timeit\n", + "def ulab_multiply(a, b):\n", + " return a * b\n", + "\n", + "a = [0.0]*1000\n", + "b = range(1000)\n", + "\n", + "print('python add:')\n", + "py_add(a, b)\n", + "\n", + "print('\\npython multiply:')\n", + "py_multiply(a, b)\n", + "\n", + "a = np.linspace(0, 10, num=1000)\n", + "b = np.ones(1000)\n", + "\n", + "print('\\nulab add:')\n", + "ulab_add(a, b)\n", + "\n", + "print('\\nulab multiply:')\n", + "ulab_multiply(a, b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The python implementation above is not perfect, and certainly, there is much room for improvement. However, the factor of 50 difference in execution time is very spectacular. This is nothing but a consequence of the fact that the `ulab` functions run `C` code, with very little python overhead. The factor of 50 appears to be quite universal: the FFT routine obeys similar scaling (see [Speed of FFTs](#Speed-of-FFTs)), and this number came up with font rendering, too: [fast font rendering on graphical displays](https://forum.micropython.org/viewtopic.php?f=15&t=5815&p=33362&hilit=ufont#p33383)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Comparison operators\n", + "\n", + "The smaller than, greater than, smaller or equal, and greater or equal operators return a vector of Booleans indicating the positions (`True`), where the condition is satisfied. " + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-17T15:08:38.673585Z", + "start_time": "2020-10-17T15:08:38.659225Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([True, True, True, True, False, False, False, False], dtype=bool)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5, 6, 7, 8], dtype=np.uint8)\n", + "print(a < 5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**WARNING**: at the moment, due to `micropython`'s implementation details, the `ndarray` must be on the left hand side of the relational operators.\n", + "\n", + "That is, while `a < 5` and `5 > a` have the same meaning, the following code will not work:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Traceback (most recent call last):\n", + " File \"/dev/shm/micropython.py\", line 5, in <module>\n", + "TypeError: unsupported types for __gt__: 'int', 'ndarray'\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5, 6, 7, 8], dtype=np.uint8)\n", + "print(5 > a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Iterating over arrays\n", + "\n", + "`ndarray`s are iterable, which means that their elements can also be accessed as can the elements of a list, tuple, etc. If the array is one-dimensional, the iterator returns scalars, otherwise a new reduced-dimensional *view* is created and returned." + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "ExecuteTime": { + "end_time": "2021-01-13T06:14:11.756254Z", + "start_time": "2021-01-13T06:14:11.742246Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([1, 2, 3, 4, 5], dtype=uint8)\n", + "element 0 in a: 1\n", + "element 1 in a: 2\n", + "element 2 in a: 3\n", + "element 3 in a: 4\n", + "element 4 in a: 5\n", + "\n", + "b:\t array([[0, 1, 2, 3, 4],\n", + " [10, 11, 12, 13, 14],\n", + " [20, 21, 22, 23, 24],\n", + " [30, 31, 32, 33, 34]], dtype=uint8)\n", + "element 0 in b: array([0, 1, 2, 3, 4], dtype=uint8)\n", + "element 1 in b: array([10, 11, 12, 13, 14], dtype=uint8)\n", + "element 2 in b: array([20, 21, 22, 23, 24], dtype=uint8)\n", + "element 3 in b: array([30, 31, 32, 33, 34], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5], dtype=np.uint8)\n", + "b = np.array([range(5), range(10, 15, 1), range(20, 25, 1), range(30, 35, 1)], dtype=np.uint8)\n", + "\n", + "print(\"a:\\t\", a)\n", + "\n", + "for i, _a in enumerate(a):\n", + " print(\"element %d in a:\"%i, _a)\n", + " \n", + "print(\"\\nb:\\t\", b)\n", + "\n", + "for i, _b in enumerate(b):\n", + " print(\"element %d in b:\"%i, _b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Slicing and indexing\n", + "\n", + "\n", + "### Views vs. copies\n", + "\n", + "`numpy` has a very important concept called *views*, which is a powerful extension of `python`'s own notion of slicing. Slices are special python objects of the form\n", + "\n", + "```python\n", + "slice = start:end:stop\n", + "```\n", + "\n", + "where `start`, `end`, and `stop` are (not necessarily non-negative) integers. Not all of these three numbers must be specified in an index, in fact, all three of them can be missing. The interpreter takes care of filling in the missing values. (Note that slices cannot be defined in this way, only there, where an index is expected.) For a good explanation on how slices work in python, you can read the stackoverflow question https://stackoverflow.com/questions/509211/understanding-slice-notation.\n", + "\n", + "In order to see what slicing does, let us take the string `a = '012345679'`! We can extract every second character by creating the slice `::2`, which is equivalent to `0:len(a):2`, i.e., increments the character pointer by 2 starting from 0, and traversing the string up to the very end." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T05:26:17.758735Z", + "start_time": "2020-10-12T05:26:17.748487Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "'02468'" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "string = '0123456789'\n", + "string[::2]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, we can do the same with numerical arrays." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T05:25:49.352435Z", + "start_time": "2020-10-12T05:25:49.339452Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8)\n", + "a[::2]:\t array([0, 2, 4, 6, 8], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(10), dtype=np.uint8)\n", + "print('a:\\t', a)\n", + "\n", + "print('a[::2]:\\t', a[::2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks similar to `string` above, but there is a very important difference that is not so obvious. Namely, `string[::2]` produces a partial copy of `string`, while `a[::2]` only produces a *view* of `a`. What this means is that `a`, and `a[::2]` share their data, and the only difference between the two is, how the data are read out. In other words, internally, `a[::2]` has the same data pointer as `a`. We can easily convince ourselves that this is indeed the case by calling the [ndinfo](#The_ndinfo_function) function: the *data pointer* entry is the same in the two printouts." + ] + }, + { + "cell_type": "code", + "execution_count": 73, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-16T18:43:07.480791Z", + "start_time": "2020-10-16T18:43:07.471473Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8) \n", + "\n", + "class: ndarray\n", + "shape: (10,)\n", + "strides: (1,)\n", + "itemsize: 1\n", + "data pointer: 0x7ff6c6193220\n", + "type: uint8\n", + "\n", + "====================\n", + "a[::2]: array([0, 2, 4, 6, 8], dtype=uint8) \n", + "\n", + "class: ndarray\n", + "shape: (5,)\n", + "strides: (2,)\n", + "itemsize: 1\n", + "data pointer: 0x7ff6c6193220\n", + "type: uint8\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(10), dtype=np.uint8)\n", + "print('a: ', a, '\\n')\n", + "np.ndinfo(a)\n", + "print('\\n' + '='*20)\n", + "print('a[::2]: ', a[::2], '\\n')\n", + "np.ndinfo(a[::2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you are still a bit confused about the meaning of *views*, the section [Slicing and assigning to slices](#Slicing-and-assigning-to-slices) should clarify the issue." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Indexing\n", + "\n", + "The simplest form of indexing is specifying a single integer between the square brackets as in " + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T18:31:45.485584Z", + "start_time": "2020-10-12T18:31:45.464551Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8)\n", + "the first, and last element of a:\n", + " 0 9\n", + "the second, and last but one element of a:\n", + " 1 8\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(10), dtype=np.uint8)\n", + "print(\"a: \", a)\n", + "print(\"the first, and last element of a:\\n\", a[0], a[-1])\n", + "print(\"the second, and last but one element of a:\\n\", a[1], a[-2])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Indexing can be applied to higher-dimensional tensors, too. When the length of the indexing sequences is smaller than the number of dimensions, a new *view* is returned, otherwise, we get a single number." + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T18:26:12.783883Z", + "start_time": "2020-10-12T18:26:12.770180Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[0, 1, 2],\n", + "\t[3, 4, 5],\n", + "\t[6, 7, 8]], dtype=uint8)\n", + "a[0]:\n", + " array([[0, 1, 2]], dtype=uint8)\n", + "a[1,1]: 4\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9), dtype=np.uint8).reshape((3, 3))\n", + "print(\"a:\\n\", a)\n", + "print(\"a[0]:\\n\", a[0])\n", + "print(\"a[1,1]: \", a[1,1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Indices can also be a list of Booleans. By using a Boolean list, we can select those elements of an array that satisfy a specific condition. At the moment, such indexing is defined for row vectors only; when the rank of the tensor is higher than 1, the function raises a `NotImplementedError` exception, though this will be rectified in a future version of `ulab`." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T17:34:34.105614Z", + "start_time": "2020-10-12T17:34:34.094017Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float)\n", + "a < 5:\t array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9), dtype=np.float)\n", + "print(\"a:\\t\", a)\n", + "print(\"a < 5:\\t\", a[a < 5])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Indexing with Boolean arrays can take more complicated expressions. This is a very concise way of comparing two vectors, e.g.:" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T18:03:38.846377Z", + "start_time": "2020-10-12T18:03:38.826689Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "\n", + "a**2:\t array([0, 1, 4, 9, 16, 25, 36, 49, 64], dtype=uint16)\n", + "\n", + "b:\t array([4, 4, 4, 3, 3, 3, 13, 13, 13], dtype=uint8)\n", + "\n", + "100*sin(b):\t array([-75.68024953079282, -75.68024953079282, -75.68024953079282, 14.11200080598672, 14.11200080598672, 14.11200080598672, 42.01670368266409, 42.01670368266409, 42.01670368266409], dtype=float)\n", + "\n", + "a[a*a > np.sin(b)*100.0]:\t array([0, 1, 2, 4, 5, 7, 8], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9), dtype=np.uint8)\n", + "b = np.array([4, 4, 4, 3, 3, 3, 13, 13, 13], dtype=np.uint8)\n", + "print(\"a:\\t\", a)\n", + "print(\"\\na**2:\\t\", a*a)\n", + "print(\"\\nb:\\t\", b)\n", + "print(\"\\n100*sin(b):\\t\", np.sin(b)*100.0)\n", + "print(\"\\na[a*a > np.sin(b)*100.0]:\\t\", a[a*a > np.sin(b)*100.0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Boolean indices can also be used in assignments, if the array is one-dimensional. The following example replaces the data in an array, wherever some condition is fulfilled." + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-13T16:14:21.055356Z", + "start_time": "2020-10-13T16:14:21.035329Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([0, 1, 2], dtype=uint8)\n", + "array([123, 123, 123, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9), dtype=np.uint8)\n", + "b = np.array(range(9)) + 12\n", + "\n", + "print(a[b < 15])\n", + "\n", + "a[b < 15] = 123\n", + "print(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "On the right hand side of the assignment we can even have another array." + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-13T16:14:10.054210Z", + "start_time": "2020-10-13T16:14:10.039523Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([0, 1, 2], dtype=uint8) array([12.0, 13.0, 14.0], dtype=float)\n", + "array([12, 13, 14, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array(range(9), dtype=np.uint8)\n", + "b = np.array(range(9)) + 12\n", + "\n", + "print(a[b < 15], b[b < 15])\n", + "\n", + "a[b < 15] = b[b < 15]\n", + "print(a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Slicing and assigning to slices\n", + "\n", + "You can also generate sub-arrays by specifying slices as the index of an array. Slices are special python objects of the form " + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T17:38:15.975404Z", + "start_time": "2020-10-12T17:38:15.955070Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[1, 2, 3],\n", + "\t[4, 5, 6],\n", + "\t[7, 8, 9]], dtype=uint8)\n", + "\n", + "a[0]:\n", + " array([[1, 2, 3]], dtype=uint8)\n", + "\n", + "a[0,:2]:\n", + " array([[1, 2]], dtype=uint8)\n", + "\n", + "a[:,0]:\n", + " array([[1],\n", + "\t[4],\n", + "\t[7]], dtype=uint8)\n", + "\n", + "a[-1]:\n", + " array([[7, 8, 9]], dtype=uint8)\n", + "\n", + "a[-1:-3:-1]:\n", + " array([[7, 8, 9],\n", + "\t[4, 5, 6]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.uint8)\n", + "print('a:\\n', a)\n", + "\n", + "# the first row\n", + "print('\\na[0]:\\n', a[0])\n", + "\n", + "# the first two elements of the first row\n", + "print('\\na[0,:2]:\\n', a[0,:2])\n", + "\n", + "# the zeroth element in each row (also known as the zeroth column)\n", + "print('\\na[:,0]:\\n', a[:,0])\n", + "\n", + "# the last row\n", + "print('\\na[-1]:\\n', a[-1])\n", + "\n", + "# the last two rows backwards\n", + "print('\\na[-1:-3:-1]:\\n', a[-1:-3:-1])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Assignment to slices can be done for the whole slice, per row, and per column. A couple of examples should make these statements clearer:" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T17:40:24.031254Z", + "start_time": "2020-10-12T17:40:24.011816Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[0, 0, 0],\n", + "\t[0, 0, 0],\n", + "\t[0, 0, 0]], dtype=uint8)\n", + "\n", + "a[0] = 1\n", + " array([[1, 1, 1],\n", + "\t[0, 0, 0],\n", + "\t[0, 0, 0]], dtype=uint8)\n", + "\n", + "a[:,0]:\n", + " array([[0, 0, 3],\n", + "\t[0, 0, 3],\n", + "\t[0, 0, 3]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.zeros((3, 3), dtype=np.uint8)\n", + "print('a:\\n', a)\n", + "\n", + "# assigning to the whole row\n", + "a[0] = 1\n", + "print('\\na[0] = 1\\n', a)\n", + "\n", + "a = np.zeros((3, 3), dtype=np.uint8)\n", + "\n", + "# assigning to a column\n", + "a[:,2] = 3.0\n", + "print('\\na[:,0]:\\n', a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, you should notice that we re-set the array `a` after the first assignment. Do you care to see what happens, if we do not do that? Well, here are the results:" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-12T17:44:09.180623Z", + "start_time": "2020-10-12T17:44:09.161578Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([[1, 1, 3],\n", + "\t[0, 0, 3],\n", + "\t[0, 0, 3]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.zeros((3, 3), dtype=np.uint8)\n", + "b = a[:,:]\n", + "# assign 1 to the first row\n", + "b[0] = 1\n", + "\n", + "# assigning to the last column\n", + "b[:,2] = 3\n", + "print('a: ', a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that both assignments involved `b`, and not `a`, yet, when we print out `a`, its entries are updated. This proves our earlier statement about the behaviour of *views*: in the statement `b = a[:,:]` we simply created a *view* of `a`, and not a *deep* copy of it, meaning that whenever we modify `b`, we actually modify `a`, because the underlying data container of `a` and `b` are shared between the two object. Having a single data container for two seemingly different objects provides an extremely powerful way of manipulating sub-sets of numerical data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to work on a *copy* of your data, you can use the `.copy` method of the `ndarray`. The following snippet should drive the point home:" + ] + }, + { + "cell_type": "code", + "execution_count": 90, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-17T13:06:20.223171Z", + "start_time": "2020-10-17T13:06:20.206422Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "class: ndarray\n", + "shape: (3, 3)\n", + "strides: (3, 1)\n", + "itemsize: 1\n", + "data pointer: 0x7ff737ea3220\n", + "type: uint8\n", + "\n", + "class: ndarray\n", + "shape: (3, 3)\n", + "strides: (3, 1)\n", + "itemsize: 1\n", + "data pointer: 0x7ff737ea3340\n", + "type: uint8\n", + "\n", + "a: array([[0, 0, 0],\n", + "\t[0, 0, 0],\n", + "\t[0, 0, 0]], dtype=uint8)\n", + "====================\n", + "b: array([[1, 1, 1],\n", + "\t[0, 0, 0],\n", + "\t[0, 0, 0]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.zeros((3, 3), dtype=np.uint8)\n", + "b = a.copy()\n", + "\n", + "# get the address of the underlying data pointer\n", + "\n", + "np.ndinfo(a)\n", + "print()\n", + "np.ndinfo(b)\n", + "\n", + "# assign 1 to the first row of b, and do not touch a\n", + "b[0] = 1\n", + "\n", + "print()\n", + "print('a: ', a)\n", + "print('='*20)\n", + "print('b: ', b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `.copy` method can also be applied to views: below, `a[0]` is a *view* of `a`, out of which we create a *deep copy* called `b`. This is a row vector now. We can then do whatever we want to with `b`, and that leaves `a` unchanged." + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-17T13:00:06.217232Z", + "start_time": "2020-10-17T13:00:06.207417Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "b: array([0, 0, 0], dtype=uint8)\n", + "====================\n", + "a: array([[0, 0, 0],\n", + "\t[0, 0, 0],\n", + "\t[0, 0, 0]], dtype=uint8)\n", + "====================\n", + "b: array([1, 0, 0], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "\n", + "a = np.zeros((3, 3), dtype=np.uint8)\n", + "b = a[0].copy()\n", + "print('b: ', b)\n", + "print('='*20)\n", + "# assign 1 to the first entry of b, and do not touch a\n", + "b[0] = 1\n", + "print('a: ', a)\n", + "print('='*20)\n", + "print('b: ', b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The fact that the underlying data of a view is the same as that of the original array has another important consequence, namely, that the creation of a view is cheap. Both in terms of RAM, and execution time. A view is really nothing but a short header with a data array that already exists, and is filled up. Hence, creating the view requires only the creation of its header. This operation is fast, and uses virtually no RAM." + ] + } + ], + "metadata": { + "interpreter": { + "hash": "ce9a02f9f7db620716422019cafa4bc1786ca85daa298b819f6da075e7993842" + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/ulab-numerical.ipynb b/circuitpython/extmod/ulab/docs/ulab-numerical.ipynb new file mode 100644 index 0000000..be54954 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-numerical.ipynb @@ -0,0 +1,1160 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2020-11-03T19:50:50.150235Z", + "start_time": "2020-11-03T19:50:48.888079Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:16:29.118001Z", + "start_time": "2022-01-07T19:16:29.114692Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2022-01-07T19:16:37.453883Z", + "start_time": "2022-01-07T19:16:37.422478Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../micropython/ports/unix/micropython-2\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Numerical\n", + "\n", + "Function in this section can be used for calculating statistical properties, or manipulating the arrangement of array elements." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## min, argmin, max, argmax\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.min.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.max.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html\n", + "\n", + "**WARNING:** Difference to `numpy`: the `out` keyword argument is not implemented.\n", + "\n", + "These functions follow the same pattern, and work with generic iterables, and `ndarray`s. `min`, and `max` return the minimum or maximum of a sequence. If the input array is two-dimensional, the `axis` keyword argument can be supplied, in which case the minimum/maximum along the given axis will be returned. If `axis=None` (this is also the default value), the minimum/maximum of the flattened array will be determined.\n", + "\n", + "`argmin/argmax` return the position (index) of the minimum/maximum in the sequence." + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-17T21:26:22.507996Z", + "start_time": "2020-10-17T21:26:22.492543Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([1.0, 2.0, 3.0], dtype=float)\n", + "array([], dtype=float)\n", + "[] 0\n", + "array([1.0, 2.0, 3.0], dtype=float)\n", + "array([], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "\n", + "a = np.array([1, 2, 3])\n", + "print(a)\n", + "print(a[-1:-1:-3])\n", + "try:\n", + " sa = list(a[-1:-1:-3])\n", + " la = len(sa)\n", + "except IndexError as e:\n", + " sa = str(e)\n", + " la = -1\n", + " \n", + "print(sa, la)\n", + "\n", + "a[-1:-1:-3] = np.ones(0)\n", + "print(a)\n", + "\n", + "b = np.ones(0) + 1\n", + "print(b)\n", + "# print('b', b.shape())" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-17T21:54:49.123748Z", + "start_time": "2020-10-17T21:54:49.093819Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0, 1, -3array([], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "a = np.array([1, 2, 3])\n", + "print(a[0:1:-3])" + ] + }, + { + "cell_type": "code", + "execution_count": 127, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-17T21:57:01.482277Z", + "start_time": "2020-10-17T21:57:01.477362Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0]" + ] + }, + "execution_count": 127, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "l = list(range(13))\n", + "\n", + "l[0:10:113]" + ] + }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-17T20:59:58.285134Z", + "start_time": "2020-10-17T20:59:58.263605Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(0,)" + ] + }, + "execution_count": 81, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "a = np.array([1, 2, 3])\n", + "np.ones(0, dtype=uint8) / np.zeros(0, dtype=uint16)\n", + "np.ones(0).shape" + ] + }, + { + "cell_type": "code", + "execution_count": 375, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-18T13:08:28.113525Z", + "start_time": "2019-10-18T13:08:28.093518Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: array([1.0, 2.0, 0.0, 1.0, 10.0], dtype=float)\n", + "min of a: 0.0\n", + "argmin of a: 2\n", + "\n", + "b:\n", + " array([[1.0, 2.0, 0.0],\n", + "\t [1.0, 10.0, -1.0]], dtype=float)\n", + "min of b (flattened): -1.0\n", + "min of b (axis=0): array([1.0, 2.0, -1.0], dtype=float)\n", + "min of b (axis=1): array([0.0, -1.0], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array([1, 2, 0, 1, 10])\n", + "print('a:', a)\n", + "print('min of a:', numerical.min(a))\n", + "print('argmin of a:', numerical.argmin(a))\n", + "\n", + "b = np.array([[1, 2, 0], [1, 10, -1]])\n", + "print('\\nb:\\n', b)\n", + "print('min of b (flattened):', numerical.min(b))\n", + "print('min of b (axis=0):', numerical.min(b, axis=0))\n", + "print('min of b (axis=1):', numerical.min(b, axis=1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## sum, std, mean\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.sum.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.mean.html\n", + "\n", + "These three functions follow the same pattern: if the axis keyword is not specified, it assumes the default value of `None`, and returns the result of the computation for the flattened array. Otherwise, the calculation is along the given axis." + ] + }, + { + "cell_type": "code", + "execution_count": 527, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-20T06:51:58.845076Z", + "start_time": "2019-10-20T06:51:58.798730Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: \n", + " array([[1.0, 2.0, 3.0],\n", + "\t [4.0, 5.0, 6.0],\n", + "\t [7.0, 8.0, 9.0]], dtype=float)\n", + "sum, flat array: 45.0\n", + "mean, horizontal: array([2.0, 5.0, 8.0], dtype=float)\n", + "std, vertical: array([2.44949, 2.44949, 2.44949], dtype=float)\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n", + "print('a: \\n', a)\n", + "\n", + "print('sum, flat array: ', numerical.sum(a))\n", + "\n", + "print('mean, horizontal: ', numerical.mean(a, axis=1))\n", + "\n", + "print('std, vertical: ', numerical.std(a, axis=0))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## roll\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.roll.html\n", + "\n", + "The roll function shifts the content of a vector by the positions given as the second argument. If the `axis` keyword is supplied, the shift is applied to the given axis." + ] + }, + { + "cell_type": "code", + "execution_count": 229, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-11T19:39:47.459395Z", + "start_time": "2019-10-11T19:39:47.443691Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\t\t\t array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float)\n", + "a rolled to the left:\t array([3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 1.0, 2.0], dtype=float)\n", + "a rolled to the right:\t array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n", + "print(\"a:\\t\\t\\t\", a)\n", + "\n", + "numerical.roll(a, 2)\n", + "print(\"a rolled to the left:\\t\", a)\n", + "\n", + "# this should be the original vector\n", + "numerical.roll(a, -2)\n", + "print(\"a rolled to the right:\\t\", a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Rolling works with matrices, too. If the `axis` keyword is 0, the matrix is rolled along its vertical axis, otherwise, horizontally. \n", + "\n", + "Horizontal rolls are faster, because they require fewer steps, and larger memory chunks are copied, however, they also require more RAM: basically the whole row must be stored internally. Most expensive are the `None` keyword values, because with `axis = None`, the array is flattened first, hence the row's length is the size of the whole matrix.\n", + "\n", + "Vertical rolls require two internal copies of single columns. " + ] + }, + { + "cell_type": "code", + "execution_count": 268, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-15T17:46:20.051069Z", + "start_time": "2019-10-15T17:46:20.033205Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[1.0, 2.0, 3.0, 4.0],\n", + "\t [5.0, 6.0, 7.0, 8.0]], dtype=float)\n", + "\n", + "a rolled to the left:\n", + " array([[3.0, 4.0, 5.0, 6.0],\n", + "\t [7.0, 8.0, 1.0, 2.0]], dtype=float)\n", + "\n", + "a rolled up:\n", + " array([[6.0, 3.0, 4.0, 5.0],\n", + "\t [2.0, 7.0, 8.0, 1.0]], dtype=float)\n", + "\n", + "a rolled with None:\n", + " array([[3.0, 4.0, 5.0, 2.0],\n", + "\t [7.0, 8.0, 1.0, 6.0]], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])\n", + "print(\"a:\\n\", a)\n", + "\n", + "numerical.roll(a, 2)\n", + "print(\"\\na rolled to the left:\\n\", a)\n", + "\n", + "numerical.roll(a, -1, axis=1)\n", + "print(\"\\na rolled up:\\n\", a)\n", + "\n", + "numerical.roll(a, 1, axis=None)\n", + "print(\"\\na rolled with None:\\n\", a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Simple running weighted average\n", + "\n", + "As a demonstration of the conciseness of `ulab/numpy` operations, we will calculate an exponentially weighted running average of a measurement vector in just a couple of lines. I chose this particular example, because I think that this can indeed be used in real-life applications." + ] + }, + { + "cell_type": "code", + "execution_count": 230, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-11T20:03:00.713235Z", + "start_time": "2019-10-11T20:03:00.696932Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "array([0.01165623031556606, 0.03168492019176483, 0.08612854033708572, 0.234121635556221, 0.6364086270332336], dtype=float)\n", + "0.2545634508132935\n", + "array([0.0, 0.0, 0.0, 0.0, 2.0], dtype=float)\n", + "0.3482121050357819\n", + "array([0.0, 0.0, 0.0, 2.0, 2.0], dtype=float)\n", + "0.3826635211706161\n", + "array([0.0, 0.0, 2.0, 2.0, 2.0], dtype=float)\n", + "0.3953374892473221\n", + "array([0.0, 2.0, 2.0, 2.0, 2.0], dtype=float)\n", + "0.3999999813735485\n", + "array([2.0, 2.0, 2.0, 2.0, 2.0], dtype=float)\n", + "0.3999999813735485\n", + "array([2.0, 2.0, 2.0, 2.0, 2.0], dtype=float)\n", + "0.3999999813735485\n", + "array([2.0, 2.0, 2.0, 2.0, 2.0], dtype=float)\n", + "0.3999999813735485\n", + "array([2.0, 2.0, 2.0, 2.0, 2.0], dtype=float)\n", + "0.3999999813735485\n", + "array([2.0, 2.0, 2.0, 2.0, 2.0], dtype=float)\n", + "0.3999999813735485\n", + "array([2.0, 2.0, 2.0, 2.0, 2.0], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "from ulab import vector\n", + "\n", + "def dummy_adc():\n", + " # dummy adc function, so that the results are reproducible\n", + " return 2\n", + " \n", + "n = 10\n", + "# These are the normalised weights; the last entry is the most dominant\n", + "weight = vector.exp([1, 2, 3, 4, 5])\n", + "weight = weight/numerical.sum(weight)\n", + "\n", + "print(weight)\n", + "# initial array of samples\n", + "samples = np.array([0]*n)\n", + "\n", + "for i in range(n):\n", + " # a new datum is inserted on the right hand side. This simply overwrites whatever was in the last slot\n", + " samples[-1] = dummy_adc()\n", + " print(numerical.mean(samples[-5:]*weight))\n", + " print(samples[-5:])\n", + " # the data are shifted by one position to the left\n", + " numerical.roll(samples, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## flip\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.flip.html\n", + "\n", + "The `flip` function takes one positional, an `ndarray`, and one keyword argument, `axis = None`, and reverses the order of elements along the given axis. If the keyword argument is `None`, the matrix' entries are flipped along all axes. `flip` returns a new copy of the array." + ] + }, + { + "cell_type": "code", + "execution_count": 275, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-16T06:35:52.163725Z", + "start_time": "2019-10-16T06:35:52.149231Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: \t array([1.0, 2.0, 3.0, 4.0, 5.0], dtype=float)\n", + "a flipped:\t array([5.0, 4.0, 3.0, 2.0, 1.0], dtype=float)\n", + "\n", + "a flipped horizontally\n", + " array([[3, 2, 1],\n", + "\t [6, 5, 4],\n", + "\t [9, 8, 7]], dtype=uint8)\n", + "\n", + "a flipped vertically\n", + " array([[7, 8, 9],\n", + "\t [4, 5, 6],\n", + "\t [1, 2, 3]], dtype=uint8)\n", + "\n", + "a flipped horizontally+vertically\n", + " array([[9, 8, 7],\n", + "\t [6, 5, 4],\n", + "\t [3, 2, 1]], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array([1, 2, 3, 4, 5])\n", + "print(\"a: \\t\", a)\n", + "print(\"a flipped:\\t\", np.flip(a))\n", + "\n", + "a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.uint8)\n", + "print(\"\\na flipped horizontally\\n\", numerical.flip(a, axis=1))\n", + "print(\"\\na flipped vertically\\n\", numerical.flip(a, axis=0))\n", + "print(\"\\na flipped horizontally+vertically\\n\", numerical.flip(a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## diff\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.diff.html\n", + "\n", + "The `diff` function returns the numerical derivative of the forward scheme, or more accurately, the differences of an `ndarray` along a given axis. The order of derivative can be stipulated with the `n` keyword argument, which should be between 0, and 9. Default is 1. If higher order derivatives are required, they can be gotten by repeated calls to the function. The `axis` keyword argument should be -1 (last axis, in `ulab` equivalent to the second axis, and this also happens to be the default value), 0, or 1. \n", + "\n", + "Beyond the output array, the function requires only a couple of bytes of extra RAM for the differentiation stencil. (The stencil is an `int8` array, one byte longer than `n`. This also explains, why the highest order is 9: the coefficients of a ninth-order stencil all fit in signed bytes, while 10 would require `int16`.) Note that as usual in numerical differentiation (and also in `numpy`), the length of the respective axis will be reduced by `n` after the operation. If `n` is larger than, or equal to the length of the axis, an empty array will be returned.\n", + "\n", + "**WARNING**: the `diff` function does not implement the `prepend` and `append` keywords that can be found in `numpy`. " + ] + }, + { + "cell_type": "code", + "execution_count": 169, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-31T11:51:02.854338Z", + "start_time": "2019-10-31T11:51:02.838000Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)\n", + "\n", + "first derivative:\n", + " array([1, 1, 1, 1, 1, 1, 1, 1], dtype=uint8)\n", + "\n", + "second derivative:\n", + " array([0, 0, 0, 0, 0, 0, 0], dtype=uint8)\n", + "\n", + "c:\n", + " array([[1.0, 2.0, 3.0, 4.0],\n", + "\t [4.0, 3.0, 2.0, 1.0],\n", + "\t [1.0, 4.0, 9.0, 16.0],\n", + "\t [0.0, 0.0, 0.0, 0.0]], dtype=float)\n", + "\n", + "first derivative, first axis:\n", + " array([[3.0, 1.0, -1.0, -3.0],\n", + "\t [-3.0, 1.0, 7.0, 15.0],\n", + "\t [-1.0, -4.0, -9.0, -16.0]], dtype=float)\n", + "\n", + "first derivative, second axis:\n", + " array([[1.0, 1.0, 1.0],\n", + "\t [-1.0, -1.0, -1.0],\n", + "\t [3.0, 5.0, 7.0],\n", + "\t [0.0, 0.0, 0.0]], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array(range(9), dtype=np.uint8)\n", + "print('a:\\n', a)\n", + "\n", + "print('\\nfirst derivative:\\n', numerical.diff(a, n=1))\n", + "print('\\nsecond derivative:\\n', numerical.diff(a, n=2))\n", + "\n", + "c = np.array([[1, 2, 3, 4], [4, 3, 2, 1], [1, 4, 9, 16], [0, 0, 0, 0]])\n", + "print('\\nc:\\n', c)\n", + "print('\\nfirst derivative, first axis:\\n', numerical.diff(c, axis=0))\n", + "print('\\nfirst derivative, second axis:\\n', numerical.diff(c, axis=1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## median\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.median.html\n", + "\n", + "The function computes the median along the specified axis, and returns the median of the array elements. If the `axis` keyword argument is `None`, the arrays is flattened first. The `dtype` of the results is always float." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2020-11-03T19:54:38.047790Z", + "start_time": "2020-11-03T19:54:38.029264Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a:\n", + " array([[0, 1, 2, 3],\n", + " [4, 5, 6, 7],\n", + " [8, 9, 10, 11]], dtype=int8)\n", + "\n", + "median of the flattened array: 5.5\n", + "\n", + "median along the vertical axis: array([4.0, 5.0, 6.0, 7.0], dtype=float)\n", + "\n", + "median along the horizontal axis: array([1.5, 5.5, 9.5], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "\n", + "a = np.array(range(12), dtype=np.int8).reshape((3, 4))\n", + "print('a:\\n', a)\n", + "print('\\nmedian of the flattened array: ', np.median(a))\n", + "print('\\nmedian along the vertical axis: ', np.median(a, axis=0))\n", + "print('\\nmedian along the horizontal axis: ', np.median(a, axis=1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## sort\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html\n", + "\n", + "The sort function takes an ndarray, and sorts its elements in ascending order along the specified axis using a heap sort algorithm. As opposed to the `.sort()` method discussed earlier, this function creates a copy of its input before sorting, and at the end, returns this copy. Sorting takes place in place, without auxiliary storage. The `axis` keyword argument takes on the possible values of -1 (the last axis, in `ulab` equivalent to the second axis, and this also happens to be the default value), 0, 1, or `None`. The first three cases are identical to those in [diff](#diff), while the last one flattens the array before sorting. \n", + "\n", + "If descending order is required, the result can simply be `flip`ped, see [flip](#flip).\n", + "\n", + "**WARNING:** `numpy` defines the `kind`, and `order` keyword arguments that are not implemented here. The function in `ulab` always uses heap sort, and since `ulab` does not have the concept of data fields, the `order` keyword argument would have no meaning." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "ExecuteTime": { + "end_time": "2019-11-05T16:06:27.536193Z", + "start_time": "2019-11-05T16:06:27.521792Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([[1.0, 12.0, 3.0, 0.0],\n", + "\t [5.0, 3.0, 4.0, 1.0],\n", + "\t [9.0, 11.0, 1.0, 8.0],\n", + "\t [7.0, 10.0, 0.0, 1.0]], dtype=float)\n", + "\n", + "a sorted along vertical axis:\n", + " array([[1.0, 3.0, 0.0, 0.0],\n", + "\t [5.0, 10.0, 1.0, 1.0],\n", + "\t [7.0, 11.0, 3.0, 1.0],\n", + "\t [9.0, 12.0, 4.0, 8.0]], dtype=float)\n", + "\n", + "a sorted along horizontal axis:\n", + " array([[0.0, 1.0, 3.0, 12.0],\n", + "\t [1.0, 3.0, 4.0, 5.0],\n", + "\t [1.0, 8.0, 9.0, 11.0],\n", + "\t [0.0, 1.0, 7.0, 10.0]], dtype=float)\n", + "\n", + "flattened a sorted:\n", + " array([0.0, 0.0, 1.0, ..., 10.0, 11.0, 12.0], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.float)\n", + "print('\\na:\\n', a)\n", + "b = numerical.sort(a, axis=0)\n", + "print('\\na sorted along vertical axis:\\n', b)\n", + "\n", + "c = numerical.sort(a, axis=1)\n", + "print('\\na sorted along horizontal axis:\\n', c)\n", + "\n", + "c = numerical.sort(a, axis=None)\n", + "print('\\nflattened a sorted:\\n', c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Heap sort requires $\\sim N\\log N$ operations, and notably, the worst case costs only 20% more time than the average. In order to get an order-of-magnitude estimate, we will take the sine of 1000 uniformly spaced numbers between 0, and two pi, and sort them:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import ulab as np\n", + "from ulab import vector\n", + "from ulab import numerical\n", + "\n", + "@timeit\n", + "def sort_time(array):\n", + " return numerical.sort(array)\n", + "\n", + "b = vector.sin(np.linspace(0, 6.28, num=1000))\n", + "print('b: ', b)\n", + "sort_time(b)\n", + "print('\\nb sorted:\\n', b)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## argsort\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.argsort.html\n", + "\n", + "Similarly to [sort](#sort), `argsort` takes a positional, and a keyword argument, and returns an unsigned short index array of type `ndarray` with the same dimensions as the input, or, if `axis=None`, as a row vector with length equal to the number of elements in the input (i.e., the flattened array). The indices in the output sort the input in ascending order. The routine in `argsort` is the same as in `sort`, therefore, the comments on computational expenses (time and RAM) also apply. In particular, since no copy of the original data is required, virtually no RAM beyond the output array is used. \n", + "\n", + "Since the underlying container of the output array is of type `uint16_t`, neither of the output dimensions should be larger than 65535. If that happens to be the case, the function will bail out with a `ValueError`." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "ExecuteTime": { + "end_time": "2019-11-06T06:28:45.719578Z", + "start_time": "2019-11-06T06:28:45.704072Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([[1.0, 12.0, 3.0, 0.0],\n", + "\t [5.0, 3.0, 4.0, 1.0],\n", + "\t [9.0, 11.0, 1.0, 8.0],\n", + "\t [7.0, 10.0, 0.0, 1.0]], dtype=float)\n", + "\n", + "a sorted along vertical axis:\n", + " array([[0, 1, 3, 0],\n", + "\t [1, 3, 2, 1],\n", + "\t [3, 2, 0, 3],\n", + "\t [2, 0, 1, 2]], dtype=uint16)\n", + "\n", + "a sorted along horizontal axis:\n", + " array([[3, 0, 2, 1],\n", + "\t [3, 1, 2, 0],\n", + "\t [2, 3, 0, 1],\n", + "\t [2, 3, 0, 1]], dtype=uint16)\n", + "\n", + "flattened a sorted:\n", + " array([3, 14, 0, ..., 13, 9, 1], dtype=uint16)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.float)\n", + "print('\\na:\\n', a)\n", + "b = numerical.argsort(a, axis=0)\n", + "print('\\na sorted along vertical axis:\\n', b)\n", + "\n", + "c = numerical.argsort(a, axis=1)\n", + "print('\\na sorted along horizontal axis:\\n', c)\n", + "\n", + "c = numerical.argsort(a, axis=None)\n", + "print('\\nflattened a sorted:\\n', c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since during the sorting, only the indices are shuffled, `argsort` does not modify the input array, as one can verify this by the following example:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "ExecuteTime": { + "end_time": "2019-11-06T16:04:31.653444Z", + "start_time": "2019-11-06T16:04:31.634995Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "a:\n", + " array([0, 5, 1, 3, 2, 4], dtype=uint8)\n", + "\n", + "sorting indices:\n", + " array([0, 2, 4, 3, 5, 1], dtype=uint16)\n", + "\n", + "the original array:\n", + " array([0, 5, 1, 3, 2, 4], dtype=uint8)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import numerical\n", + "\n", + "a = np.array([0, 5, 1, 3, 2, 4], dtype=np.uint8)\n", + "print('\\na:\\n', a)\n", + "b = numerical.argsort(a, axis=1)\n", + "print('\\nsorting indices:\\n', b)\n", + "print('\\nthe original array:\\n', a)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/ulab-poly.ipynb b/circuitpython/extmod/ulab/docs/ulab-poly.ipynb new file mode 100644 index 0000000..9cd7223 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-poly.ipynb @@ -0,0 +1,454 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-01T09:27:13.438054Z", + "start_time": "2020-05-01T09:27:13.191491Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2020-08-03T18:32:45.342280Z", + "start_time": "2020-08-03T18:32:45.338442Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2020-07-23T20:31:25.296014Z", + "start_time": "2020-07-23T20:31:25.265937Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Polynomials\n", + "\n", + "Functions in the polynomial sub-module can be invoked by importing the module first." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## polyval\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyval.html\n", + "\n", + "`polyval` takes two arguments, both arrays or other iterables." + ] + }, + { + "cell_type": "code", + "execution_count": 187, + "metadata": { + "ExecuteTime": { + "end_time": "2019-11-01T12:53:22.448303Z", + "start_time": "2019-11-01T12:53:22.435176Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "coefficients: [1, 1, 1, 0]\n", + "independent values: [0, 1, 2, 3, 4]\n", + "\n", + "values of p(x): array([0.0, 3.0, 14.0, 39.0, 84.0], dtype=float)\n", + "\n", + "ndarray (a): array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float)\n", + "value of p(a): array([0.0, 3.0, 14.0, 39.0, 84.0], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import poly\n", + "\n", + "p = [1, 1, 1, 0]\n", + "x = [0, 1, 2, 3, 4]\n", + "print('coefficients: ', p)\n", + "print('independent values: ', x)\n", + "print('\\nvalues of p(x): ', poly.polyval(p, x))\n", + "\n", + "# the same works with one-dimensional ndarrays\n", + "a = np.array(x)\n", + "print('\\nndarray (a): ', a)\n", + "print('value of p(a): ', poly.polyval(p, a))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## polyfit\n", + "\n", + "`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.polyfit.html\n", + "\n", + "polyfit takes two, or three arguments. The last one is the degree of the polynomial that will be fitted, the last but one is an array or iterable with the `y` (dependent) values, and the first one, an array or iterable with the `x` (independent) values, can be dropped. If that is the case, `x` will be generated in the function, assuming uniform sampling. \n", + "\n", + "If the length of `x`, and `y` are not the same, the function raises a `ValueError`." + ] + }, + { + "cell_type": "code", + "execution_count": 189, + "metadata": { + "ExecuteTime": { + "end_time": "2019-11-01T12:54:08.326802Z", + "start_time": "2019-11-01T12:54:08.311182Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "independent values:\t array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float)\n", + "dependent values:\t array([9.0, 4.0, 1.0, 0.0, 1.0, 4.0, 9.0], dtype=float)\n", + "fitted values:\t\t array([1.0, -6.0, 9.000000000000004], dtype=float)\n", + "\n", + "dependent values:\t array([9.0, 4.0, 1.0, 0.0, 1.0, 4.0, 9.0], dtype=float)\n", + "fitted values:\t\t array([1.0, -6.0, 9.000000000000004], dtype=float)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "import ulab as np\n", + "from ulab import poly\n", + "\n", + "x = np.array([0, 1, 2, 3, 4, 5, 6])\n", + "y = np.array([9, 4, 1, 0, 1, 4, 9])\n", + "print('independent values:\\t', x)\n", + "print('dependent values:\\t', y)\n", + "print('fitted values:\\t\\t', poly.polyfit(x, y, 2))\n", + "\n", + "# the same with missing x\n", + "print('\\ndependent values:\\t', y)\n", + "print('fitted values:\\t\\t', poly.polyfit(y, 2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Execution time\n", + "\n", + "`polyfit` is based on the inversion of a matrix (there is more on the background in https://en.wikipedia.org/wiki/Polynomial_regression), and it requires the intermediate storage of `2*N*(deg+1)` floats, where `N` is the number of entries in the input array, and `deg` is the fit's degree. The additional computation costs of the matrix inversion discussed in [inv](#inv) also apply. The example from above needs around 150 microseconds to return:" + ] + }, + { + "cell_type": "code", + "execution_count": 560, + "metadata": { + "ExecuteTime": { + "end_time": "2019-10-20T07:24:39.002243Z", + "start_time": "2019-10-20T07:24:38.978687Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "execution time: 153 us\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import ulab as np\n", + "from ulab import poly\n", + "\n", + "@timeit\n", + "def time_polyfit(x, y, n):\n", + " return poly.polyfit(x, y, n)\n", + "\n", + "x = np.array([0, 1, 2, 3, 4, 5, 6])\n", + "y = np.array([9, 4, 1, 0, 1, 4, 9])\n", + "\n", + "time_polyfit(x, y, 2)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/docs/ulab-programming.ipynb b/circuitpython/extmod/ulab/docs/ulab-programming.ipynb new file mode 100644 index 0000000..6eabf6d --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-programming.ipynb @@ -0,0 +1,798 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2020-10-25T21:25:53.804315Z", + "start_time": "2020-10-25T21:25:43.765649Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Programming ulab\n", + "\n", + "Earlier we have seen, how `ulab`'s functions and methods can be accessed in `micropython`. This last section of the book explains, how these functions are implemented. By the end of this chapter, not only would you be able to extend `ulab`, and write your own `numpy`-compatible functions, but through a deeper understanding of the inner workings of the functions, you would also be able to see what the trade-offs are at the `python` level.\n", + "\n", + "\n", + "## Code organisation\n", + "\n", + "As mentioned earlier, the `python` functions are organised into sub-modules at the C level. The C sub-modules can be found in `./ulab/code/`." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The `ndarray` object" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### General comments\n", + "\n", + "`ndarrays` are efficient containers of numerical data of the same type (i.e., signed/unsigned chars, signed/unsigned integers or `mp_float_t`s, which, depending on the platform, are either C `float`s, or C `double`s). Beyond storing the actual data in the void pointer `*array`, the type definition has eight additional members (on top of the `base` type). Namely, the `dtype`, which tells us, how the bytes are to be interpreted. Moreover, the `itemsize`, which stores the size of a single entry in the array, `boolean`, an unsigned integer, which determines, whether the arrays is to be treated as a set of Booleans, or as numerical data, `ndim`, the number of dimensions (`uint8_t`), `len`, the length of the array (the number of entries), the shape (`*size_t`), the strides (`*int32_t`). The length is simply the product of the numbers in `shape`.\n", + "\n", + "The type definition is as follows:\n", + "\n", + "```c\n", + "typedef struct _ndarray_obj_t {\n", + " mp_obj_base_t base;\n", + " uint8_t dtype;\n", + " uint8_t itemsize;\n", + " uint8_t boolean;\n", + " uint8_t ndim;\n", + " size_t len;\n", + " size_t shape[ULAB_MAX_DIMS];\n", + " int32_t strides[ULAB_MAX_DIMS];\n", + " void *array;\n", + "} ndarray_obj_t;\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Memory layout\n", + "\n", + "The values of an `ndarray` are stored in a contiguous segment in the RAM. The `ndarray` can be dense, meaning that all numbers in the linear memory segment belong to a linar combination of coordinates, and it can also be sparse, i.e., some elements of the linear storage space will be skipped, when the elements of the tensor are traversed. \n", + "\n", + "In the RAM, the position of the item $M(n_1, n_2, ..., n_{k-1}, n_k)$ in a dense tensor of rank $k$ is given by the linear combination \n", + "\n", + "\\begin{equation}\n", + "P(n_1, n_2, ..., n_{k-1}, n_k) = n_1 s_1 + n_2 s_2 + ... + n_{k-1}s_{k-1} + n_ks_k = \\sum_{i=1}^{k}n_is_i\n", + "\\end{equation}\n", + "where $s_i$ are the strides of the tensor, defined as \n", + "\n", + "\\begin{equation}\n", + "s_i = \\prod_{j=i+1}^k l_j\n", + "\\end{equation}\n", + "\n", + "where $l_j$ is length of the tensor along the $j$th axis. When the tensor is sparse (e.g., when the tensor is sliced), the strides along a particular axis will be multiplied by a non-zero integer. If this integer is different to $\\pm 1$, the linear combination above cannot access all elements in the RAM, i.e., some numbers will be skipped. Note that $|s_1| > |s_2| > ... > |s_{k-1}| > |s_k|$, even if the tensor is sparse. The statement is trivial for dense tensors, and it follows from the definition of $s_i$. For sparse tensors, a slice cannot have a step larger than the shape along that axis. But for dense tensors, $s_i/s_{i+1} = l_i$. \n", + "\n", + "When creating a *view*, we simply re-calculate the `strides`, and re-set the `*array` pointer.\n", + "\n", + "## Iterating over elements of a tensor\n", + "\n", + "The `shape` and `strides` members of the array tell us how we have to move our pointer, when we want to read out the numbers. For technical reasons that will become clear later, the numbers in `shape` and in `strides` are aligned to the right, and begin on the right hand side, i.e., if the number of possible dimensions is `ULAB_MAX_DIMS`, then `shape[ULAB_MAX_DIMS-1]` is the length of the last axis, `shape[ULAB_MAX_DIMS-2]` is the length of the last but one axis, and so on. If the number of actual dimensions, `ndim < ULAB_MAX_DIMS`, the first `ULAB_MAX_DIMS - ndim` entries in `shape` and `strides` will be equal to zero, but they could, in fact, be assigned any value, because these will never be accessed in an operation.\n", + "\n", + "With this definition of the strides, the linear combination in $P(n_1, n_2, ..., n_{k-1}, n_k)$ is a one-to-one mapping from the space of tensor coordinates, $(n_1, n_2, ..., n_{k-1}, n_k)$, and the coordinate in the linear array, $n_1s_1 + n_2s_2 + ... + n_{k-1}s_{k-1} + n_ks_k$, i.e., no two distinct sets of coordinates will result in the same position in the linear array. \n", + "\n", + "Since the `strides` are given in terms of bytes, when we iterate over an array, the void data pointer is usually cast to `uint8_t`, and the values are converted using the proper data type stored in `ndarray->dtype`. However, there might be cases, when it makes perfect sense to cast `*array` to a different type, in which case the `strides` have to be re-scaled by the value of `ndarray->itemsize`.\n", + "\n", + "### Iterating using the unwrapped loops\n", + "\n", + "The following macro definition is taken from [vector.h](https://github.com/v923z/micropython-ulab/blob/master/code/numpy/vector/vector.h), and demonstrates, how we can iterate over a single array in four dimensions. \n", + "\n", + "```c\n", + "#define ITERATE_VECTOR(type, array, source, sarray) do {\n", + " size_t i=0;\n", + " do {\n", + " size_t j = 0;\n", + " do {\n", + " size_t k = 0;\n", + " do {\n", + " size_t l = 0;\n", + " do {\n", + " *(array)++ = f(*((type *)(sarray)));\n", + " (sarray) += (source)->strides[ULAB_MAX_DIMS - 1];\n", + " l++;\n", + " } while(l < (source)->shape[ULAB_MAX_DIMS-1]);\n", + " (sarray) -= (source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1];\n", + " (sarray) += (source)->strides[ULAB_MAX_DIMS - 2];\n", + " k++;\n", + " } while(k < (source)->shape[ULAB_MAX_DIMS-2]);\n", + " (sarray) -= (source)->strides[ULAB_MAX_DIMS - 2] * (source)->shape[ULAB_MAX_DIMS-2];\n", + " (sarray) += (source)->strides[ULAB_MAX_DIMS - 3];\n", + " j++;\n", + " } while(j < (source)->shape[ULAB_MAX_DIMS-3]);\n", + " (sarray) -= (source)->strides[ULAB_MAX_DIMS - 3] * (source)->shape[ULAB_MAX_DIMS-3];\n", + " (sarray) += (source)->strides[ULAB_MAX_DIMS - 4];\n", + " i++;\n", + " } while(i < (source)->shape[ULAB_MAX_DIMS-4]);\n", + "} while(0)\n", + "```\n", + "\n", + "We start with the innermost loop, the one recursing `l`. `array` is already of type `mp_float_t`, while the source array, `sarray`, has been cast to `uint8_t` in the calling function. The numbers contained in `sarray` have to be read out in the proper type dictated by `ndarray->dtype`. This is what happens in the statement `*((type *)(sarray))`, and this number is then fed into the function `f`. Vectorised mathematical functions produce *dense* arrays, and for this reason, we can simply advance the `array` pointer. \n", + "\n", + "The advancing of the `sarray` pointer is a bit more involving: first, in the innermost loop, we simply move forward by the amount given by the last stride, which is `(source)->strides[ULAB_MAX_DIMS - 1]`, because the `shape` and the `strides` are aligned to the right. We move the pointer as many times as given by `(source)->shape[ULAB_MAX_DIMS-1]`, which is the length of the very last axis. Hence the the structure of the loop\n", + "\n", + "```c\n", + " size_t l = 0;\n", + " do {\n", + " ...\n", + " l++;\n", + " } while(l < (source)->shape[ULAB_MAX_DIMS-1]);\n", + "\n", + "```\n", + "Once we have exhausted the last axis, we have to re-wind the pointer, and advance it by an amount given by the last but one stride. Keep in mind that in the the innermost loop we moved our pointer `(source)->shape[ULAB_MAX_DIMS-1]` times by `(source)->strides[ULAB_MAX_DIMS - 1]`, i.e., we re-wind it by moving it backwards by `(source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1]`. In the next step, we move forward by `(source)->strides[ULAB_MAX_DIMS - 2]`, which is the last but one stride. \n", + "\n", + "\n", + "```c\n", + " (sarray) -= (source)->strides[ULAB_MAX_DIMS - 1] * (source)->shape[ULAB_MAX_DIMS-1];\n", + " (sarray) += (source)->strides[ULAB_MAX_DIMS - 2];\n", + "\n", + "```\n", + "\n", + "This pattern must be repeated for each axis of the array, and this is how we arrive at the four nested loops listed above." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Re-winding arrays by means of a function\n", + "\n", + "\n", + "In addition to un-wrapping the iteration loops by means of macros, there is another way of traversing all elements of a tensor: we note that, since $|s_1| > |s_2| > ... > |s_{k-1}| > |s_k|$, $P(n1, n2, ..., n_{k-1}, n_k)$ changes most slowly in the last coordinate. Hence, if we start from the very beginning, ($n_i = 0$ for all $i$), and walk along the linear RAM segment, we increment the value of $n_k$ as long as $n_k < l_k$. Once $n_k = l_k$, we have to reset $n_k$ to 0, and increment $n_{k-1}$ by one. After each such round, $n_{k-1}$ will be incremented by one, as long as $n_{k-1} < l_{k-1}$. Once $n_{k-1} = l_{k-1}$, we reset both $n_k$, and $n_{k-1}$ to 0, and increment $n_{k-2}$ by one. \n", + "\n", + "Rewinding the arrays in this way is implemented in the function `ndarray_rewind_array` in [ndarray.c](https://github.com/v923z/micropython-ulab/blob/master/code/ndarray.c). \n", + "\n", + "```c\n", + "void ndarray_rewind_array(uint8_t ndim, uint8_t *array, size_t *shape, int32_t *strides, size_t *coords) {\n", + " // resets the data pointer of a single array, whenever an axis is full\n", + " // since we always iterate over the very last axis, we have to keep track of\n", + " // the last ndim-2 axes only\n", + " array -= shape[ULAB_MAX_DIMS - 1] * strides[ULAB_MAX_DIMS - 1];\n", + " array += strides[ULAB_MAX_DIMS - 2];\n", + " for(uint8_t i=1; i < ndim-1; i++) {\n", + " coords[ULAB_MAX_DIMS - 1 - i] += 1;\n", + " if(coords[ULAB_MAX_DIMS - 1 - i] == shape[ULAB_MAX_DIMS - 1 - i]) { // we are at a dimension boundary\n", + " array -= shape[ULAB_MAX_DIMS - 1 - i] * strides[ULAB_MAX_DIMS - 1 - i];\n", + " array += strides[ULAB_MAX_DIMS - 2 - i];\n", + " coords[ULAB_MAX_DIMS - 1 - i] = 0;\n", + " coords[ULAB_MAX_DIMS - 2 - i] += 1;\n", + " } else { // coordinates can change only, if the last coordinate changes\n", + " return;\n", + " }\n", + " }\n", + "}\n", + "```\n", + "\n", + "and the function would be called as in the snippet below. Note that the innermost loop is factored out, so that we can save the `if(...)` statement for the last axis.\n", + "\n", + "```c\n", + " size_t *coords = ndarray_new_coords(results->ndim);\n", + " for(size_t i=0; i < results->len/results->shape[ULAB_MAX_DIMS -1]; i++) {\n", + " size_t l = 0;\n", + " do {\n", + " ...\n", + " l++;\n", + " } while(l < results->shape[ULAB_MAX_DIMS - 1]);\n", + " ndarray_rewind_array(results->ndim, array, results->shape, strides, coords);\n", + " } while(0)\n", + "\n", + "```\n", + "\n", + "The advantage of this method is that the implementation is independent of the number of dimensions: the iteration requires more or less the same flash space for 2 dimensions as for 22. However, the price we have to pay for this convenience is the extra function call." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Iterating over two ndarrays simultaneously: broadcasting\n", + "\n", + "Whenever we invoke a binary operator, call a function with two arguments of `ndarray` type, or assign something to an `ndarray`, we have to iterate over two views at the same time. The task is trivial, if the two `ndarray`s in question have the same shape (but not necessarily the same set of strides), because in this case, we can still iterate in the same loop. All that happens is that we move two data pointers in sync.\n", + "\n", + "The problem becomes a bit more involving, when the shapes of the two `ndarray`s are not identical. For such cases, `numpy` defines so-called broadcasting, which boils down to two rules. \n", + "\n", + "1. The shapes in the tensor with lower rank has to be prepended with axes of size 1 till the two ranks become equal.\n", + "2. Along all axes the two tensors should have the same size, or one of the sizes must be 1. \n", + "\n", + "If, after applying the first rule the second is not satisfied, the two `ndarray`s cannot be broadcast together. \n", + "\n", + "Now, let us suppose that we have two compatible `ndarray`s, i.e., after applying the first rule, the second is satisfied. How do we iterate over the elements in the tensors? \n", + "\n", + "We should recall, what exactly we do, when iterating over a single array: normally, we move the data pointer by the last stride, except, when we arrive at a dimension boundary (when the last axis is exhausted). At that point, we move the pointer by an amount dictated by the strides. And this is the key: *dictated by the strides*. Now, if we have two arrays that are originally not compatible, we define new strides for them, and use these in the iteration. With that, we are back to the case, where we had two compatible arrays. \n", + "\n", + "Now, let us look at the second broadcasting rule: if the two arrays have the same size, we take both `ndarray`s' strides along that axis. If, on the other hand, one of the `ndarray`s is of length 1 along one of its axes, we set the corresponding strides to 0. This will ensure that that data pointer is not moved, when we iterate over both `ndarray`s at the same time. \n", + "\n", + "Thus, in order to implement broadcasting, we first have to check, whether the two above-mentioned rules can be satisfied, and if so, we have to find the two new sets strides. \n", + "\n", + "The `ndarray_can_broadcast` function from [ndarray.c](https://github.com/v923z/micropython-ulab/blob/master/code/ndarray.c) takes two `ndarray`s, and returns `true`, if the two arrays can be broadcast together. At the same time, it also calculates new strides for the two arrays, so that they can be iterated over at the same time. \n", + "\n", + "```c\n", + "bool ndarray_can_broadcast(ndarray_obj_t *lhs, ndarray_obj_t *rhs, uint8_t *ndim, size_t *shape, int32_t *lstrides, int32_t *rstrides) {\n", + " // returns True or False, depending on, whether the two arrays can be broadcast together\n", + " // numpy's broadcasting rules are as follows:\n", + " //\n", + " // 1. the two shapes are either equal\n", + " // 2. one of the shapes is 1\n", + " memset(lstrides, 0, sizeof(size_t)*ULAB_MAX_DIMS);\n", + " memset(rstrides, 0, sizeof(size_t)*ULAB_MAX_DIMS);\n", + " lstrides[ULAB_MAX_DIMS - 1] = lhs->strides[ULAB_MAX_DIMS - 1];\n", + " rstrides[ULAB_MAX_DIMS - 1] = rhs->strides[ULAB_MAX_DIMS - 1];\n", + " for(uint8_t i=ULAB_MAX_DIMS; i > 0; i--) {\n", + " if((lhs->shape[i-1] == rhs->shape[i-1]) || (lhs->shape[i-1] == 0) || (lhs->shape[i-1] == 1) ||\n", + " (rhs->shape[i-1] == 0) || (rhs->shape[i-1] == 1)) {\n", + " shape[i-1] = MAX(lhs->shape[i-1], rhs->shape[i-1]);\n", + " if(shape[i-1] > 0) (*ndim)++;\n", + " if(lhs->shape[i-1] < 2) {\n", + " lstrides[i-1] = 0;\n", + " } else {\n", + " lstrides[i-1] = lhs->strides[i-1];\n", + " }\n", + " if(rhs->shape[i-1] < 2) {\n", + " rstrides[i-1] = 0;\n", + " } else {\n", + " rstrides[i-1] = rhs->strides[i-1];\n", + " }\n", + " } else {\n", + " return false;\n", + " }\n", + " }\n", + " return true;\n", + "}\n", + "```\n", + "\n", + "A good example of how the function would be called can be found in [vector.c](https://github.com/v923z/micropython-ulab/blob/master/code/numpy/vector/vector.c), in the `vector_arctan2` function:\n", + "\n", + "```c\n", + "mp_obj_t vector_arctan2(mp_obj_t y, mp_obj_t x) {\n", + " ...\n", + " uint8_t ndim = 0;\n", + " size_t *shape = m_new(size_t, ULAB_MAX_DIMS);\n", + " int32_t *xstrides = m_new(int32_t, ULAB_MAX_DIMS);\n", + " int32_t *ystrides = m_new(int32_t, ULAB_MAX_DIMS);\n", + " if(!ndarray_can_broadcast(ndarray_x, ndarray_y, &ndim, shape, xstrides, ystrides)) {\n", + " mp_raise_ValueError(translate(\"operands could not be broadcast together\"));\n", + " m_del(size_t, shape, ULAB_MAX_DIMS);\n", + " m_del(int32_t, xstrides, ULAB_MAX_DIMS);\n", + " m_del(int32_t, ystrides, ULAB_MAX_DIMS);\n", + " }\n", + "\n", + " uint8_t *xarray = (uint8_t *)ndarray_x->array;\n", + " uint8_t *yarray = (uint8_t *)ndarray_y->array;\n", + " \n", + " ndarray_obj_t *results = ndarray_new_dense_ndarray(ndim, shape, NDARRAY_FLOAT);\n", + " mp_float_t *rarray = (mp_float_t *)results->array;\n", + " ...\n", + "```\n", + "\n", + "After the new strides have been calculated, the iteration loop is identical to what we discussed in the previous section." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Contracting an `ndarray`\n", + "\n", + "\n", + "There are many operations that reduce the number of dimensions of an `ndarray` by 1, i.e., that remove an axis from the tensor. The drill is the same as before, with the exception that first we have to remove the `strides` and `shape` that corresponds to the axis along which we intend to contract. The `numerical_reduce_axes` function from [numerical.c](https://github.com/v923z/micropython-ulab/blob/master/code/numerical/numerical.c) does that. \n", + "\n", + "\n", + "```c\n", + "static void numerical_reduce_axes(ndarray_obj_t *ndarray, int8_t axis, size_t *shape, int32_t *strides) {\n", + " // removes the values corresponding to a single axis from the shape and strides array\n", + " uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + axis;\n", + " if((ndarray->ndim == 1) && (axis == 0)) {\n", + " index = 0;\n", + " shape[ULAB_MAX_DIMS - 1] = 0;\n", + " return;\n", + " }\n", + " for(uint8_t i = ULAB_MAX_DIMS - 1; i > 0; i--) {\n", + " if(i > index) {\n", + " shape[i] = ndarray->shape[i];\n", + " strides[i] = ndarray->strides[i];\n", + " } else {\n", + " shape[i] = ndarray->shape[i-1];\n", + " strides[i] = ndarray->strides[i-1];\n", + " }\n", + " }\n", + "}\n", + "```\n", + "\n", + "Once the reduced `strides` and `shape` are known, we place the axis in question in the innermost loop, and wrap it with the loops, whose coordinates are in the `strides`, and `shape` arrays. The `RUN_STD` macro from [numerical.h](https://github.com/v923z/micropython-ulab/blob/master/code/numpy/numerical/numerical.h) is a good example. The macro is expanded in the `numerical_sum_mean_std_ndarray` function. \n", + "\n", + "\n", + "```c\n", + "static mp_obj_t numerical_sum_mean_std_ndarray(ndarray_obj_t *ndarray, mp_obj_t axis, uint8_t optype, size_t ddof) {\n", + " uint8_t *array = (uint8_t *)ndarray->array;\n", + " size_t *shape = m_new(size_t, ULAB_MAX_DIMS);\n", + " memset(shape, 0, sizeof(size_t)*ULAB_MAX_DIMS);\n", + " int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);\n", + " memset(strides, 0, sizeof(uint32_t)*ULAB_MAX_DIMS);\n", + "\n", + " int8_t ax = mp_obj_get_int(axis);\n", + " if(ax < 0) ax += ndarray->ndim;\n", + " if((ax < 0) || (ax > ndarray->ndim - 1)) {\n", + " mp_raise_ValueError(translate(\"index out of range\"));\n", + " }\n", + " numerical_reduce_axes(ndarray, ax, shape, strides);\n", + " uint8_t index = ULAB_MAX_DIMS - ndarray->ndim + ax;\n", + " ndarray_obj_t *results = NULL;\n", + " uint8_t *rarray = NULL;\n", + " ...\n", + "\n", + "```\n", + "Here is the macro for the three-dimensional case: \n", + "\n", + "```c\n", + "#define RUN_STD(ndarray, type, array, results, r, shape, strides, index, div) do {\n", + " size_t k = 0;\n", + " do {\n", + " size_t l = 0;\n", + " do {\n", + " RUN_STD1((ndarray), type, (array), (results), (r), (index), (div));\n", + " (array) -= (ndarray)->strides[(index)] * (ndarray)->shape[(index)];\n", + " (array) += (strides)[ULAB_MAX_DIMS - 1];\n", + " l++;\n", + " } while(l < (shape)[ULAB_MAX_DIMS - 1]);\n", + " (array) -= (strides)[ULAB_MAX_DIMS - 2] * (shape)[ULAB_MAX_DIMS-2];\n", + " (array) += (strides)[ULAB_MAX_DIMS - 3];\n", + " k++;\n", + " } while(k < (shape)[ULAB_MAX_DIMS - 2]);\n", + "} while(0)\n", + "```\n", + "In `RUN_STD`, we simply move our pointers; the calculation itself happens in the `RUN_STD1` macro below. (Note that this is the implementation of the numerically stable Welford algorithm.)\n", + "\n", + "```c\n", + "#define RUN_STD1(ndarray, type, array, results, r, index, div)\n", + "({\n", + " mp_float_t M, m, S = 0.0, s = 0.0;\n", + " M = m = *(mp_float_t *)((type *)(array));\n", + " for(size_t i=1; i < (ndarray)->shape[(index)]; i++) {\n", + " (array) += (ndarray)->strides[(index)];\n", + " mp_float_t value = *(mp_float_t *)((type *)(array));\n", + " m = M + (value - M) / (mp_float_t)i;\n", + " s = S + (value - M) * (value - m);\n", + " M = m;\n", + " S = s;\n", + " }\n", + " (array) += (ndarray)->strides[(index)];\n", + " *(r)++ = MICROPY_FLOAT_C_FUN(sqrt)((ndarray)->shape[(index)] * s / (div));\n", + "})\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Upcasting\n", + "\n", + "When in an operation the `dtype`s of two arrays are different, the result's `dtype` will be decided by the following upcasting rules:\n", + "\n", + "1. Operations with two `ndarray`s of the same `dtype` preserve their `dtype`, even when the results overflow.\n", + "\n", + "2. if either of the operands is a float, the result automatically becomes a float\n", + "\n", + "3. otherwise\n", + "\n", + " - `uint8` + `int8` => `int16`, \n", + " - `uint8` + `int16` => `int16`\n", + " - `uint8` + `uint16` => `uint16`\n", + " \n", + " - `int8` + `int16` => `int16`\n", + " - `int8` + `uint16` => `uint16` (in numpy, the result is a `int32`)\n", + "\n", + " - `uint16` + `int16` => `float` (in numpy, the result is a `int32`)\n", + " \n", + "4. When one operand of a binary operation is a generic scalar `micropython` variable, i.e., `mp_obj_int`, or `mp_obj_float`, it will be converted to a linear array of length 1, and with the smallest `dtype` that can accommodate the variable in question. After that the broadcasting rules apply, as described in the section [Iterating over two ndarrays simultaneously: broadcasting](#Iterating_over_two_ndarrays_simultaneously:_broadcasting)\n", + "\n", + "Upcasting is resolved in place, wherever it is required. Notable examples can be found in [ndarray_operators.c](https://github.com/v923z/micropython-ulab/blob/master/code/ndarray_operators.c)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Slicing and indexing" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "An `ndarray` can be indexed with three types of objects: integer scalars, slices, and another `ndarray`, whose elements are either integer scalars, or Booleans. Since slice and integer indices can be thought of as modifications of the `strides`, these indices return a view of the `ndarray`. This statement does not hold for `ndarray` indices, and therefore, the return a copy of the array." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Extending ulab\n", + "\n", + "The `user` module is disabled by default, as can be seen from the last couple of lines of [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h)\n", + "\n", + "```c\n", + "// user-defined module\n", + "#ifndef ULAB_USER_MODULE\n", + "#define ULAB_USER_MODULE (0)\n", + "#endif\n", + "```\n", + "\n", + "The module contains a very simple function, `user_dummy`, and this function is bound to the module itself. In other words, even if the module is enabled, one has to `import`:\n", + "\n", + "```python\n", + "\n", + "import ulab\n", + "from ulab import user\n", + "\n", + "user.dummy_function(2.5)\n", + "```\n", + "which should just return 5.0. Even if `numpy`-compatibility is required (i.e., if most functions are bound at the top level to `ulab` directly), having to `import` the module has a great advantage. Namely, only the [user.h](https://github.com/v923z/micropython-ulab/blob/master/code/user/user.h) and [user.c](https://github.com/v923z/micropython-ulab/blob/master/code/user/user.c) files have to be modified, thus it should be relatively straightforward to update your local copy from [github](https://github.com/v923z/micropython-ulab/blob/master/). \n", + "\n", + "Now, let us see, how we can add a more meaningful function. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Creating a new ndarray\n", + "\n", + "In the [General comments](#General_comments) sections we have seen the type definition of an `ndarray`. This structure can be generated by means of a couple of functions listed in [ndarray.c](https://github.com/v923z/micropython-ulab/blob/master/code/ndarray.c). \n", + "\n", + "\n", + "### ndarray_new_ndarray\n", + "\n", + "The `ndarray_new_ndarray` functions is called by all other array-generating functions. It takes the number of dimensions, `ndim`, a `uint8_t`, the `shape`, a pointer to `size_t`, the `strides`, a pointer to `int32_t`, and `dtype`, another `uint8_t` as its arguments, and returns a new array with all entries initialised to 0. \n", + "\n", + "Assuming that `ULAB_MAX_DIMS > 2`, a new dense array of dimension 3, of `shape` (3, 4, 5), of `strides` (1000, 200, 10), and `dtype` `uint16_t` can be generated by the following instructions\n", + "\n", + "```c\n", + "size_t *shape = m_new(size_t, ULAB_MAX_DIMS);\n", + "shape[ULAB_MAX_DIMS - 1] = 5;\n", + "shape[ULAB_MAX_DIMS - 2] = 4;\n", + "shape[ULAB_MAX_DIMS - 3] = 3;\n", + "\n", + "int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);\n", + "strides[ULAB_MAX_DIMS - 1] = 10;\n", + "strides[ULAB_MAX_DIMS - 2] = 200;\n", + "strides[ULAB_MAX_DIMS - 3] = 1000;\n", + "\n", + "ndarray_obj_t *new_ndarray = ndarray_new_ndarray(3, shape, strides, NDARRAY_UINT16);\n", + "```\n", + "\n", + "### ndarray_new_dense_ndarray\n", + "\n", + "The functions simply calculates the `strides` from the `shape`, and calls `ndarray_new_ndarray`. Assuming that `ULAB_MAX_DIMS > 2`, a new dense array of dimension 3, of `shape` (3, 4, 5), and `dtype` `mp_float_t` can be generated by the following instructions\n", + "\n", + "```c\n", + "size_t *shape = m_new(size_t, ULAB_MAX_DIMS);\n", + "shape[ULAB_MAX_DIMS - 1] = 5;\n", + "shape[ULAB_MAX_DIMS - 2] = 4;\n", + "shape[ULAB_MAX_DIMS - 3] = 3;\n", + "\n", + "ndarray_obj_t *new_ndarray = ndarray_new_dense_ndarray(3, shape, NDARRAY_FLOAT);\n", + "```\n", + "\n", + "### ndarray_new_linear_array\n", + "\n", + "Since the dimensions of a linear array are known (1), the `ndarray_new_linear_array` takes the `length`, a `size_t`, and the `dtype`, an `uint8_t`. Internally, `ndarray_new_linear_array` generates the `shape` array, and calls `ndarray_new_dense_array` with `ndim = 1`.\n", + "\n", + "A linear array of length 100, and `dtype` `uint8` could be created by the function call\n", + "\n", + "```c\n", + "ndarray_obj_t *new_ndarray = ndarray_new_linear_array(100, NDARRAY_UINT8)\n", + "```\n", + "\n", + "### ndarray_new_ndarray_from_tuple\n", + "\n", + "This function takes a `tuple`, which should hold the lengths of the axes (in other words, the `shape`), and the `dtype`, and calls internally `ndarray_new_dense_array`. A new `ndarray` can be generated by calling \n", + "\n", + "```c\n", + "ndarray_obj_t *new_ndarray = ndarray_new_ndarray_from_tuple(shape, NDARRAY_FLOAT);\n", + "```\n", + "where `shape` is a tuple.\n", + "\n", + "\n", + "### ndarray_new_view\n", + "\n", + "This function crates a *view*, and takes the source, an `ndarray`, the number of dimensions, an `uint8_t`, the `shape`, a pointer to `size_t`, the `strides`, a pointer to `int32_t`, and the offset, an `int32_t` as arguments. The offset is the number of bytes by which the void `array` pointer is shifted. E.g., the `python` statement\n", + "\n", + "```python\n", + "a = np.array([0, 1, 2, 3, 4, 5], dtype=uint8)\n", + "b = a[1::2]\n", + "```\n", + "\n", + "produces the array\n", + "\n", + "```python\n", + "array([1, 3, 5], dtype=uint8)\n", + "```\n", + "which holds its data at position `x0 + 1`, if `a`'s pointer is at `x0`. In this particular case, the offset is 1. \n", + "\n", + "The array `b` from the example above could be generated as \n", + "\n", + "```c\n", + "size_t *shape = m_new(size_t, ULAB_MAX_DIMS);\n", + "shape[ULAB_MAX_DIMS - 1] = 3;\n", + "\n", + "int32_t *strides = m_new(int32_t, ULAB_MAX_DIMS);\n", + "strides[ULAB_MAX_DIMS - 1] = 2;\n", + "\n", + "int32_t offset = 1;\n", + "uint8_t ndim = 1;\n", + "\n", + "ndarray_obj_t *new_ndarray = ndarray_new_view(ndarray_a, ndim, shape, strides, offset);\n", + "```\n", + "\n", + "### ndarray_copy_array\n", + "\n", + "The `ndarray_copy_array` function can be used for copying the contents of an array. Note that the target array has to be created beforehand. E.g., a one-to-one copy can be gotten by \n", + "\n", + "```c\n", + "ndarray_obj_t *new_ndarray = ndarray_new_ndarray(source->ndim, source->shape, source->strides, source->dtype);\n", + "ndarray_copy_array(source, new_ndarray);\n", + "\n", + "```\n", + "Note that the function cannot be used for forcing type conversion, i.e., the input and output types must be identical, because the function simply calls the `memcpy` function. On the other hand, the input and output `strides` do not necessarily have to be equal.\n", + "\n", + "### ndarray_copy_view\n", + "\n", + "The `ndarray_obj_t *new_ndarray = ...` instruction can be saved by calling the `ndarray_copy_view` function with the single `source` argument. \n", + "\n", + "\n", + "## Accessing data in the ndarray\n", + "\n", + "Having seen, how arrays can be generated and copied, it is time to look at how the data in an `ndarray` can be accessed and modified. \n", + "\n", + "For starters, let us suppose that the object in question comes from the user (i.e., via the `micropython` interface), First, we have to acquire a pointer to the `ndarray` by calling \n", + "\n", + "```c\n", + "ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(object_in);\n", + "```\n", + "\n", + "If it is not clear, whether the object is an `ndarray` (e.g., if we want to write a function that can take `ndarray`s, and other iterables as its argument), we find this out by evaluating \n", + "\n", + "```c\n", + "mp_obj_is_type(object_in, &ulab_ndarray_type)\n", + "```\n", + "which should return `true`. Once the pointer is at our disposal, we can get a pointer to the underlying numerical array as discussed earlier, i.e., \n", + "\n", + "```c\n", + "uint8_t *array = (uint8_t *)ndarray->array;\n", + "```\n", + "\n", + "If you need to find out the `dtype` of the array, you can get it by accessing the `dtype` member of the `ndarray`, i.e., \n", + "\n", + "```c\n", + "ndarray->dtype\n", + "```\n", + "should be equal to `B`, `b`, `H`, `h`, or `f`. The size of a single item is stored in the `itemsize` member. This number should be equal to 1, if the `dtype` is `B`, or `b`, 2, if the `dtype` is `H`, or `h`, 4, if the `dtype` is `f`, and 8 for `d`. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Boilerplate\n", + "\n", + "In the next section, we will construct a function that generates the element-wise square of a dense array, otherwise, raises a `TypeError` exception. Dense arrays can easily be iterated over, since we do not have to care about the `shape` and the `strides`. If the array is sparse, the section [Iterating over elements of a tensor](#Iterating-over-elements-of-a-tensor) should contain hints as to how the iteration can be implemented.\n", + "\n", + "The function is listed under [user.c](https://github.com/v923z/micropython-ulab/tree/master/code/user/). The `user` module is bound to `ulab` in [ulab.c](https://github.com/v923z/micropython-ulab/tree/master/code/ulab.c) in the lines \n", + "\n", + "```c\n", + " #if ULAB_USER_MODULE\n", + " { MP_ROM_QSTR(MP_QSTR_user), MP_ROM_PTR(&ulab_user_module) },\n", + " #endif\n", + "```\n", + "which assumes that at the very end of [ulab.h](https://github.com/v923z/micropython-ulab/tree/master/code/ulab.h) the \n", + "\n", + "```c\n", + "// user-defined module\n", + "#ifndef ULAB_USER_MODULE\n", + "#define ULAB_USER_MODULE (1)\n", + "#endif\n", + "```\n", + "constant has been set to 1. After compilation, you can call a particular `user` function in `python` by importing the module first, i.e., \n", + "\n", + "```python\n", + "from ulab import numpy as np\n", + "from ulab import user\n", + "\n", + "user.some_function(...)\n", + "```\n", + "\n", + "This separation of user-defined functions from the rest of the code ensures that the integrity of the main module and all its functions are always preserved. Even in case of a catastrophic failure, you can exclude the `user` module, and start over.\n", + "\n", + "And now the function:\n", + "\n", + "\n", + "```c\n", + "static mp_obj_t user_square(mp_obj_t arg) {\n", + " // the function takes a single dense ndarray, and calculates the \n", + " // element-wise square of its entries\n", + " \n", + " // raise a TypeError exception, if the input is not an ndarray\n", + " if(!mp_obj_is_type(arg, &ulab_ndarray_type)) {\n", + " mp_raise_TypeError(translate(\"input must be an ndarray\"));\n", + " }\n", + " ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(arg);\n", + " \n", + " // make sure that the input is a dense array\n", + " if(!ndarray_is_dense(ndarray)) {\n", + " mp_raise_TypeError(translate(\"input must be a dense ndarray\"));\n", + " }\n", + " \n", + " // if the input is a dense array, create `results` with the same number of \n", + " // dimensions, shape, and dtype\n", + " ndarray_obj_t *results = ndarray_new_dense_ndarray(ndarray->ndim, ndarray->shape, ndarray->dtype);\n", + " \n", + " // since in a dense array the iteration over the elements is trivial, we \n", + " // can cast the data arrays ndarray->array and results->array to the actual type\n", + " if(ndarray->dtype == NDARRAY_UINT8) {\n", + " uint8_t *array = (uint8_t *)ndarray->array;\n", + " uint8_t *rarray = (uint8_t *)results->array;\n", + " for(size_t i=0; i < ndarray->len; i++, array++) {\n", + " *rarray++ = (*array) * (*array);\n", + " }\n", + " } else if(ndarray->dtype == NDARRAY_INT8) {\n", + " int8_t *array = (int8_t *)ndarray->array;\n", + " int8_t *rarray = (int8_t *)results->array;\n", + " for(size_t i=0; i < ndarray->len; i++, array++) {\n", + " *rarray++ = (*array) * (*array);\n", + " }\n", + " } else if(ndarray->dtype == NDARRAY_UINT16) {\n", + " uint16_t *array = (uint16_t *)ndarray->array;\n", + " uint16_t *rarray = (uint16_t *)results->array;\n", + " for(size_t i=0; i < ndarray->len; i++, array++) {\n", + " *rarray++ = (*array) * (*array);\n", + " }\n", + " } else if(ndarray->dtype == NDARRAY_INT16) {\n", + " int16_t *array = (int16_t *)ndarray->array;\n", + " int16_t *rarray = (int16_t *)results->array;\n", + " for(size_t i=0; i < ndarray->len; i++, array++) {\n", + " *rarray++ = (*array) * (*array);\n", + " }\n", + " } else { // if we end up here, the dtype is NDARRAY_FLOAT\n", + " mp_float_t *array = (mp_float_t *)ndarray->array;\n", + " mp_float_t *rarray = (mp_float_t *)results->array;\n", + " for(size_t i=0; i < ndarray->len; i++, array++) {\n", + " *rarray++ = (*array) * (*array);\n", + " } \n", + " }\n", + " // at the end, return a micropython object\n", + " return MP_OBJ_FROM_PTR(results);\n", + "}\n", + "\n", + "```\n", + "\n", + "To summarise, the steps for *implementing* a function are\n", + "\n", + "1. If necessary, inspect the type of the input object, which is always a `mp_obj_t` object\n", + "2. If the input is an `ndarray_obj_t`, acquire a pointer to it by calling `ndarray_obj_t *ndarray = MP_OBJ_TO_PTR(arg);`\n", + "3. Create a new array, or modify the existing one; get a pointer to the data by calling `uint8_t *array = (uint8_t *)ndarray->array;`, or something equivalent\n", + "4. Once the new data have been calculated, return a `micropython` object by calling `MP_OBJ_FROM_PTR(...)`.\n", + "\n", + "The listing above contains the implementation of the function, but as such, it cannot be called from `python`: \n", + "it still has to be bound to the name space. This we do by first defining a function object in \n", + "\n", + "```c\n", + "MP_DEFINE_CONST_FUN_OBJ_1(user_square_obj, user_square);\n", + "\n", + "```\n", + "\n", + "`micropython` defines a number of `MP_DEFINE_CONST_FUN_OBJ_N` macros in [obj.h](https://github.com/micropython/micropython/blob/master/py/obj.h). `N` is always the number of arguments the function takes. We had a function definition `static mp_obj_t user_square(mp_obj_t arg)`, i.e., we dealt with a single argument. \n", + "\n", + "Finally, we have to bind this function object in the globals table of the `user` module: \n", + "\n", + "```c\n", + "STATIC const mp_rom_map_elem_t ulab_user_globals_table[] = {\n", + " { MP_OBJ_NEW_QSTR(MP_QSTR___name__), MP_OBJ_NEW_QSTR(MP_QSTR_user) },\n", + " { MP_OBJ_NEW_QSTR(MP_QSTR_square), (mp_obj_t)&user_square_obj },\n", + "};\n", + "```\n", + "\n", + "Thus, the three steps required for the definition of a user-defined function are \n", + "\n", + "1. The low-level implementation of the function itself\n", + "2. The definition of a function object by calling MP_DEFINE_CONST_FUN_OBJ_N()\n", + "3. Binding this function object to the namespace in the `ulab_user_globals_table[]`" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": {}, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/circuitpython/extmod/ulab/docs/ulab-tricks.ipynb b/circuitpython/extmod/ulab/docs/ulab-tricks.ipynb new file mode 100644 index 0000000..ec67c8c --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-tricks.ipynb @@ -0,0 +1,582 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-01T09:27:13.438054Z", + "start_time": "2020-05-01T09:27:13.191491Z" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2020-08-03T18:32:45.342280Z", + "start_time": "2020-08-03T18:32:45.338442Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2020-07-23T20:31:25.296014Z", + "start_time": "2020-07-23T20:31:25.265937Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tricks\n", + "\n", + "This section of the book discusses a couple of tricks that can be exploited to either speed up computations, or save on RAM. However, there is probably no silver bullet, and you have to evaluate your code in terms of execution speed (if the execution is time critical), or RAM used. You should also keep in mind that, if a particular code snippet is optimised on some hardware, there is no guarantee that on another piece of hardware, you will get similar improvements. Hardware implementations are vastly different. Some microcontrollers do not even have an FPU, so you should not be surprised that you get significantly different benchmarks. Just to underline this statement, you can study the [collection of benchmarks](https://github.com/thiagofe/ulab_samples)." + ] + }, + { + "source": [ + "## Use an `ndarray`, if you can\n", + "\n", + "Many functions in `ulab` are implemented in a universal fashion, meaning that both generic `micropython` iterables, and `ndarray`s can be passed as an argument. E.g., both \n", + "\n", + "```python\n", + "from ulab import numpy as np\n", + "\n", + "np.sum([1, 2, 3, 4, 5])\n", + "```\n", + "and\n", + "\n", + "```python\n", + "from ulab import numpy as np\n", + "\n", + "a = np.array([1, 2, 3, 4, 5])\n", + "np.sum(a)\n", + "```\n", + "\n", + "will return the `micropython` variable 15 as the result. Still, `np.sum(a)` is evaluated significantly faster, because in `np.sum([1, 2, 3, 4, 5])`, the interpreter has to fetch 5 `micropython` variables, convert them to `float`, and sum the values, while the C type of `a` is known, thus the interpreter can invoke a single `for` loop for the evaluation of the `sum`. In the `for` loop, there are no function calls, the iteration simply walks through the pointer holding the values of `a`, and adds the values to an accumulator. If the array `a` is already available, then you can gain a factor of 3 in speed by calling `sum` on the array, instead of using the list. Compared to the python implementation of the same functionality, the speed-up is around 40 (again, this might depend on the hardware).\n", + "\n", + "On the other hand, if the array is not available, then there is not much point in converting the list to an `ndarray` and passing that to the function. In fact, you should expect a slow-down: the constructor has to iterate over the list elements, and has to convert them to a numerical type. On top of that, it also has to reserve RAM for the `ndarray`." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "## Use a reasonable `dtype`\n", + "\n", + "Just as in `numpy`, the default `dtype` is `float`. But this does not mean that that is the most suitable one in all scenarios. If data are streamed from an 8-bit ADC, and you only want to know the maximum, or the sum, then it is quite reasonable to use `uint8` for the `dtype`. Storing the same data in `float` array would cost 4 or 8 times as much RAM, with absolutely no gain. Do not rely on the default value of the constructor's keyword argument, and choose one that fits!" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "## Beware the axis!\n", + "\n", + "Whenever `ulab` iterates over multi-dimensional arrays, the outermost loop is the first axis, then the second axis, and so on. E.g., when the `sum` of \n", + "\n", + "```python\n", + "a = array([[1, 2, 3, 4],\n", + " [5, 6, 7, 8], \n", + " [9, 10, 11, 12]], dtype=uint8)\n", + "```\n", + "\n", + "is being calculated, first the data pointer walks along `[1, 2, 3, 4]` (innermost loop, last axis), then is moved back to the position, where 5 is stored (this is the nesting loop), and traverses `[5, 6, 7, 8]`, and so on. Moving the pointer back to 5 is more expensive, than moving it along an axis, because the position of 5 has to be calculated, whereas moving from 5 to 6 is simply an addition to the address. Thus, while the matrix\n", + "\n", + "```python\n", + "b = array([[1, 5, 9],\n", + " [2, 6, 10], \n", + " [3, 7, 11],\n", + " [4, 8, 12]], dtype=uint8)\n", + "```\n", + "\n", + "holds the same data as `a`, the summation over the entries in `b` is slower, because the pointer has to be re-wound three times, as opposed to twice in `a`. For small matrices the savings are not significant, but you would definitely notice the difference, if you had \n", + "\n", + "```\n", + "a = array(range(2000)).reshape((2, 1000))\n", + "b = array(range(2000)).reshape((1000, 2))\n", + "```\n", + "\n", + "The moral is that, in order to improve on the execution speed, whenever possible, you should try to make the last axis the longest. As a side note, `numpy` can re-arrange its loops, and puts the longest axis in the innermost loop. This is why the longest axis is sometimes referred to as the fast axis. In `ulab`, the order of the axes is fixed. " + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "## Reduce the number of artifacts\n", + "\n", + "Before showing a real-life example, let us suppose that we want to interpolate uniformly sampled data, and the absolute magnitude is not really important, we only care about the ratios between neighbouring value. One way of achieving this is calling the `interp` functions. However, we could just as well work with slices." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([ 0, 5, 10, 6, 2, 11, 20, 12, 4], dtype=uint8)" + ] + }, + "metadata": {}, + "execution_count": 18 + } + ], + "source": [ + "a = array([0, 10, 2, 20, 4], dtype=np.uint8)\n", + "b = np.zeros(9, dtype=np.uint8)\n", + "\n", + "b[::2] = 2 * a\n", + "b[1::2] = a[:-1] + a[1:]\n", + "\n", + "b //= 2\n", + "b" + ] + }, + { + "source": [ + "`b` now has values from `a` at every even position, and interpolates the values on every odd position. If only the relative magnitudes are important, then we can even save the division by 2, and we end up with " + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "a = array([0, 10, 2, 20, 4], dtype=np.uint8)\n", + "b = np.zeros(9, dtype=np.uint8)\n", + "\n", + "b[::2] = 2 * a\n", + "b[1::2] = a[:-1] + a[1:]\n", + "\n", + "b" + ], + "cell_type": "code", + "metadata": {}, + "execution_count": 16, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([ 0, 10, 20, 12, 4, 22, 40, 24, 8], dtype=uint8)" + ] + }, + "metadata": {}, + "execution_count": 16 + } + ] + }, + { + "source": [ + "Importantly, we managed to keep the results in the smaller `dtype`, `uint8`. Now, while the two assignments above are terse and pythonic, the code is not the most efficient: the right hand sides are compound statements, generating intermediate results. To store them, RAM has to be allocated. This takes time, and leads to memory fragmentation. Better is to write out the assignments in 4 instructions:" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([ 0, 10, 20, 12, 4, 22, 40, 24, 8], dtype=uint8)" + ] + }, + "metadata": {}, + "execution_count": 15 + } + ], + "source": [ + "b = np.zeros(9, dtype=np.uint8)\n", + "\n", + "b[::2] = a\n", + "b[::2] += a\n", + "b[1::2] = a[:-1]\n", + "b[1::2] += a[1:]\n", + "\n", + "b" + ] + }, + { + "source": [ + "The results are the same, but no extra RAM is allocated, except for the views `a[:-1]`, and `a[1:]`, but those had to be created even in the origin implementation." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "### Upscaling images\n", + "\n", + "And now the example: there are low-resolution thermal cameras out there. Low resolution might mean 8 by 8 pixels. Such a small number of pixels is just not reasonable to plot, no matter how small the display is. If you want to make the camera image a bit more pleasing, you can upscale (stretch) it in both dimensions. This can be done exactly as we up-scaled the linear array:" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "b = np.zeros((15, 15), dtype=np.uint8)\n", + "\n", + "b[1::2,::2] = a[:-1,:]\n", + "b[1::2,::2] += a[1:, :]\n", + "b[1::2,::2] //= 2\n", + "b[::,1::2] = a[::,:-1:2]\n", + "b[::,1::2] += a[::,2::2]\n", + "b[::,1::2] //= 2" + ] + }, + { + "source": [ + "Up-scaling by larger numbers can be done in a similar fashion, you simply have more assignments." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "There are cases, when one cannot do away with the intermediate results. Two prominent cases are the `where` function, and indexing by means of a Boolean array. E.g., in" + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([1, 2, 3])" + ] + }, + "metadata": {}, + "execution_count": 20 + } + ], + "source": [ + "a = array([1, 2, 3, 4, 5])\n", + "b = a[a < 4]\n", + "b" + ] + }, + { + "source": [ + "the expression `a < 4` produces the Boolean array, " + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "source": [ + "a < 4" + ], + "cell_type": "code", + "metadata": {}, + "execution_count": 22, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "array([ True, True, True, False, False])" + ] + }, + "metadata": {}, + "execution_count": 22 + } + ] + }, + { + "source": [ + "If you repeatedly have such conditions in a loop, you might have to peridically call the garbage collector to remove the Boolean arrays that are used only once." + ], + "cell_type": "markdown", + "metadata": {} + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/docs/ulab-utils.ipynb b/circuitpython/extmod/ulab/docs/ulab-utils.ipynb new file mode 100644 index 0000000..4fddc53 --- /dev/null +++ b/circuitpython/extmod/ulab/docs/ulab-utils.ipynb @@ -0,0 +1,471 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-04T18:21:22.822563Z", + "start_time": "2021-03-04T18:21:18.656643Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Populating the interactive namespace from numpy and matplotlib\n" + ] + } + ], + "source": [ + "%pylab inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Notebook magic" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-05T06:53:22.506665Z", + "start_time": "2021-03-05T06:53:22.499658Z" + } + }, + "outputs": [], + "source": [ + "from IPython.core.magic import Magics, magics_class, line_cell_magic\n", + "from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n", + "from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n", + "import subprocess\n", + "import os" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-05T06:53:23.127314Z", + "start_time": "2021-03-05T06:53:23.103181Z" + } + }, + "outputs": [], + "source": [ + "@magics_class\n", + "class PyboardMagic(Magics):\n", + " @cell_magic\n", + " @magic_arguments()\n", + " @argument('-skip')\n", + " @argument('-unix')\n", + " @argument('-pyboard')\n", + " @argument('-file')\n", + " @argument('-data')\n", + " @argument('-time')\n", + " @argument('-memory')\n", + " def micropython(self, line='', cell=None):\n", + " args = parse_argstring(self.micropython, line)\n", + " if args.skip: # doesn't care about the cell's content\n", + " print('skipped execution')\n", + " return None # do not parse the rest\n", + " if args.unix: # tests the code on the unix port. Note that this works on unix only\n", + " with open('/dev/shm/micropython.py', 'w') as fout:\n", + " fout.write(cell)\n", + " proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n", + " stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n", + " print(proc.stdout.read().decode(\"utf-8\"))\n", + " print(proc.stderr.read().decode(\"utf-8\"))\n", + " return None\n", + " if args.file: # can be used to copy the cell content onto the pyboard's flash\n", + " spaces = \" \"\n", + " try:\n", + " with open(args.file, 'w') as fout:\n", + " fout.write(cell.replace('\\t', spaces))\n", + " printf('written cell to {}'.format(args.file))\n", + " except:\n", + " print('Failed to write to disc!')\n", + " return None # do not parse the rest\n", + " if args.data: # can be used to load data from the pyboard directly into kernel space\n", + " message = pyb.exec(cell)\n", + " if len(message) == 0:\n", + " print('pyboard >>>')\n", + " else:\n", + " print(message.decode('utf-8'))\n", + " # register new variable in user namespace\n", + " self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n", + " \n", + " if args.time: # measures the time of executions\n", + " pyb.exec('import utime')\n", + " message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n", + " \"\\nprint('execution time: {:d} us'.format(delta))\")\n", + " print(message.decode('utf-8'))\n", + " \n", + " if args.memory: # prints out memory information \n", + " message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n", + " print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n", + " message = pyb.exec(cell)\n", + " print(\">>> \", message.decode('utf-8'))\n", + " message = pyb.exec('print(mem_info())')\n", + " print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n", + "\n", + " if args.pyboard:\n", + " message = pyb.exec(cell)\n", + " print(message.decode('utf-8'))\n", + "\n", + "ip = get_ipython()\n", + "ip.register_magics(PyboardMagic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## pyboard" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:35.126401Z", + "start_time": "2020-05-07T07:35:35.105824Z" + } + }, + "outputs": [], + "source": [ + "import pyboard\n", + "pyb = pyboard.Pyboard('/dev/ttyACM0')\n", + "pyb.enter_raw_repl()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-19T19:11:18.145548Z", + "start_time": "2020-05-19T19:11:18.137468Z" + } + }, + "outputs": [], + "source": [ + "pyb.exit_raw_repl()\n", + "pyb.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "ExecuteTime": { + "end_time": "2020-05-07T07:35:38.725924Z", + "start_time": "2020-05-07T07:35:38.645488Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "%%micropython -pyboard 1\n", + "\n", + "import utime\n", + "import ulab as np\n", + "\n", + "def timeit(n=1000):\n", + " def wrapper(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " run_times = np.zeros(n, dtype=np.uint16)\n", + " for i in range(n):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n", + " print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n", + " print('\\tbest: %d us'%np.min(run_times))\n", + " print('\\tworst: %d us'%np.max(run_times))\n", + " print('\\taverage: %d us'%np.mean(run_times))\n", + " print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n", + " return result\n", + " return new_func\n", + " return wrapper\n", + "\n", + "def timeit(f, *args, **kwargs):\n", + " func_name = str(f).split(' ')[1]\n", + " def new_func(*args, **kwargs):\n", + " t = utime.ticks_us()\n", + " result = f(*args, **kwargs)\n", + " print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n", + " return result\n", + " return new_func" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "__END_OF_DEFS__" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# ulab utilities\n", + "\n", + "\n", + "There might be cases, when the format of your data does not conform to `ulab`, i.e., there is no obvious way to map the data to any of the five supported `dtype`s. A trivial example is an ADC or microphone signal with 32-bit resolution. For such cases, `ulab` defines the `utils` module, which, at the moment, has four functions that are not `numpy` compatible, but which should ease interfacing `ndarray`s to peripheral devices. \n", + "\n", + "The `utils` module can be enabled by setting the `ULAB_HAS_UTILS_MODULE` constant to 1 in [ulab.h](https://github.com/v923z/micropython-ulab/blob/master/code/ulab.h):\n", + "\n", + "```c\n", + "#ifndef ULAB_HAS_UTILS_MODULE\n", + "#define ULAB_HAS_UTILS_MODULE (1)\n", + "#endif\n", + "```\n", + "\n", + "This still does not compile any functions into the firmware. You can add a function by setting the corresponding pre-processor constant to 1. E.g., \n", + "\n", + "```c\n", + "#ifndef ULAB_UTILS_HAS_FROM_INT16_BUFFER\n", + "#define ULAB_UTILS_HAS_FROM_INT16_BUFFER (1)\n", + "#endif\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## from_int32_buffer, from_uint32_buffer\n", + "\n", + "With the help of `utils.from_int32_buffer`, and `utils.from_uint32_buffer`, it is possible to convert 32-bit integer buffers to `ndarrays` of float type. These functions have a syntax similar to `numpy.frombuffer`; they support the `count=-1`, and `offset=0` keyword arguments. However, in addition, they also accept `out=None`, and `byteswap=False`. \n", + "\n", + "Here is an example without keyword arguments" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-05T06:53:26.256516Z", + "start_time": "2021-03-05T06:53:26.007070Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: bytearray(b'\\x01\\x01\\x00\\x00\\x00\\x00\\x00\\xff')\n", + "\n", + "unsigned integers: array([257.0, 4278190080.000001], dtype=float64)\n", + "\n", + "b: bytearray(b'\\x01\\x01\\x00\\x00\\x00\\x00\\x00\\xff')\n", + "\n", + "signed integers: array([257.0, -16777216.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import utils\n", + "\n", + "a = bytearray([1, 1, 0, 0, 0, 0, 0, 255])\n", + "print('a: ', a)\n", + "print()\n", + "print('unsigned integers: ', utils.from_uint32_buffer(a))\n", + "\n", + "b = bytearray([1, 1, 0, 0, 0, 0, 0, 255])\n", + "print('\\nb: ', b)\n", + "print()\n", + "print('signed integers: ', utils.from_int32_buffer(b))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The meaning of `count`, and `offset` is similar to that in `numpy.frombuffer`. `count` is the number of floats that will be converted, while `offset` would discard the first `offset` number of bytes from the buffer before the conversion.\n", + "\n", + "In the example above, repeated calls to either of the functions returns a new `ndarray`. You can save RAM by supplying the `out` keyword argument with a pre-defined `ndarray` of sufficient size, in which case the results will be inserted into the `ndarray`. If the `dtype` of `out` is not `float`, a `TypeError` exception will be raised." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-05T06:53:41.551440Z", + "start_time": "2021-03-05T06:53:41.534163Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "b: bytearray(b'\\x01\\x00\\x01\\x00\\x00\\x01\\x00\\x01')\n", + "a: array([65537.0, 16777472.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import utils\n", + "\n", + "a = np.array([1, 2], dtype=np.float)\n", + "b = bytearray([1, 0, 1, 0, 0, 1, 0, 1])\n", + "print('b: ', b)\n", + "utils.from_uint32_buffer(b, out=a)\n", + "print('a: ', a)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, since there is no guarantee that the endianness of a particular peripheral device supplying the buffer is the same as that of the microcontroller, `from_(u)intbuffer` allows a conversion via the `byteswap` keyword argument." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2021-03-05T06:53:52.242950Z", + "start_time": "2021-03-05T06:53:52.229160Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a: bytearray(b'\\x01\\x00\\x00\\x00\\x00\\x00\\x00\\x01')\n", + "buffer without byteswapping: array([1.0, 16777216.0], dtype=float64)\n", + "buffer with byteswapping: array([16777216.0, 1.0], dtype=float64)\n", + "\n", + "\n" + ] + } + ], + "source": [ + "%%micropython -unix 1\n", + "\n", + "from ulab import numpy as np\n", + "from ulab import utils\n", + "\n", + "a = bytearray([1, 0, 0, 0, 0, 0, 0, 1])\n", + "print('a: ', a)\n", + "print('buffer without byteswapping: ', utils.from_uint32_buffer(a))\n", + "print('buffer with byteswapping: ', utils.from_uint32_buffer(a, byteswap=True))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## from_int16_buffer, from_uint16_buffer\n", + "\n", + "These two functions are identical to `utils.from_int32_buffer`, and `utils.from_uint32_buffer`, with the exception that they convert 16-bit integers to floating point `ndarray`s. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "toc": { + "base_numbering": 1, + "nav_menu": {}, + "number_sections": true, + "sideBar": true, + "skip_h1_title": false, + "title_cell": "Table of Contents", + "title_sidebar": "Contents", + "toc_cell": false, + "toc_position": { + "height": "calc(100% - 180px)", + "left": "10px", + "top": "150px", + "width": "382.797px" + }, + "toc_section_display": true, + "toc_window_display": true + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/circuitpython/extmod/ulab/requirements.txt b/circuitpython/extmod/ulab/requirements.txt new file mode 100644 index 0000000..44a988d --- /dev/null +++ b/circuitpython/extmod/ulab/requirements.txt @@ -0,0 +1 @@ +sphinx-autoapi diff --git a/circuitpython/extmod/ulab/requirements_cp_dev.txt b/circuitpython/extmod/ulab/requirements_cp_dev.txt new file mode 100644 index 0000000..2b7114e --- /dev/null +++ b/circuitpython/extmod/ulab/requirements_cp_dev.txt @@ -0,0 +1,15 @@ +# for extract-pyi +isort +black + +# For docs +Sphinx<4 +sphinx-rtd-theme +myst-parser +sphinx-autoapi +sphinxcontrib-svg2pdfconverter +readthedocs-sphinx-search + +# for check-stubs +mypy + diff --git a/circuitpython/extmod/ulab/run-tests b/circuitpython/extmod/ulab/run-tests new file mode 100755 index 0000000..880b13f --- /dev/null +++ b/circuitpython/extmod/ulab/run-tests @@ -0,0 +1,570 @@ +#! /usr/bin/env python3 + +import os +import subprocess +import sys +import platform +import argparse +import re +import threading +import multiprocessing +from multiprocessing.pool import ThreadPool +from glob import glob + +if os.name == 'nt': + MICROPYTHON = os.getenv('MICROPY_MICROPYTHON', 'micropython/ports/windows/micropython.exe') +else: + MICROPYTHON = os.getenv('MICROPY_MICROPYTHON', 'micropython/ports/unix/micropython') + +# mpy-cross is only needed if --via-mpy command-line arg is passed +MPYCROSS = os.getenv('MICROPY_MPYCROSS', '../mpy-cross/mpy-cross') + +# Set PYTHONIOENCODING so that CPython will use utf-8 on systems which set another encoding in the locale +os.environ['PYTHONIOENCODING'] = 'utf-8' + +def rm_f(fname): + if os.path.exists(fname): + os.remove(fname) + + +# unescape wanted regex chars and escape unwanted ones +def convert_regex_escapes(line): + cs = [] + escape = False + for c in str(line, 'utf8'): + if escape: + escape = False + cs.append(c) + elif c == '\\': + escape = True + elif c in ('(', ')', '[', ']', '{', '}', '.', '*', '+', '^', '$'): + cs.append('\\' + c) + else: + cs.append(c) + # accept carriage-return(s) before final newline + if cs[-1] == '\n': + cs[-1] = '\r*\n' + return bytes(''.join(cs), 'utf8') + + +def run_micropython(pyb, args, test_file, is_special=False): + special_tests = ( + 'micropython/meminfo.py', 'basics/bytes_compare3.py', + 'basics/builtin_help.py', 'thread/thread_exc2.py', + ) + had_crash = False + if pyb is None: + # run on PC + if test_file.startswith(('cmdline/', 'feature_check/')) or test_file in special_tests: + # special handling for tests of the unix cmdline program + is_special = True + + if is_special: + # check for any cmdline options needed for this test + args = [MICROPYTHON] + with open(test_file, 'rb') as f: + line = f.readline() + if line.startswith(b'# cmdline:'): + # subprocess.check_output on Windows only accepts strings, not bytes + args += [str(c, 'utf-8') for c in line[10:].strip().split()] + + # run the test, possibly with redirected input + try: + if 'repl_' in test_file: + # Need to use a PTY to test command line editing + try: + import pty + except ImportError: + # in case pty module is not available, like on Windows + return b'SKIP\n' + import select + + def get(required=False): + rv = b'' + while True: + ready = select.select([emulator], [], [], 0.02) + if ready[0] == [emulator]: + rv += os.read(emulator, 1024) + else: + if not required or rv: + return rv + + def send_get(what): + os.write(emulator, what) + return get() + + with open(test_file, 'rb') as f: + # instead of: output_mupy = subprocess.check_output(args, stdin=f) + # openpty returns two read/write file descriptors. The first one is + # used by the program which provides the virtual + # terminal service, and the second one is used by the + # subprogram which requires a tty to work. + emulator, subterminal = pty.openpty() + p = subprocess.Popen(args, stdin=subterminal, stdout=subterminal, + stderr=subprocess.STDOUT, bufsize=0) + banner = get(True) + output_mupy = banner + b''.join(send_get(line) for line in f) + send_get(b'\x04') # exit the REPL, so coverage info is saved + p.kill() + os.close(emulator) + os.close(subterminal) + else: + output_mupy = subprocess.check_output(args + [test_file], stderr=subprocess.STDOUT) + except subprocess.CalledProcessError: + return b'CRASH' + + else: + # a standard test run on PC + + # create system command + cmdlist = [MICROPYTHON, '-X', 'emit=' + args.emit] + if args.heapsize is not None: + cmdlist.extend(['-X', 'heapsize=' + args.heapsize]) + + # if running via .mpy, first compile the .py file + if args.via_mpy: + subprocess.check_output([MPYCROSS, '-mcache-lookup-bc', '-o', 'mpytest.mpy', test_file]) + cmdlist.extend(['-m', 'mpytest']) + else: + cmdlist.append(test_file) + + # run the actual test + e = {"MICROPYPATH": os.getcwd() + ":", "LANG": "en_US.UTF-8"} + p = subprocess.Popen(cmdlist, env=e, stdout=subprocess.PIPE, stderr=subprocess.STDOUT) + output_mupy = b'' + while p.poll() is None: + output_mupy += p.stdout.read() + output_mupy += p.stdout.read() + if p.returncode != 0: + output_mupy = b'CRASH' + + # clean up if we had an intermediate .mpy file + if args.via_mpy: + rm_f('mpytest.mpy') + + else: + # run on pyboard + import pyboard + pyb.enter_raw_repl() + try: + output_mupy = pyb.execfile(test_file) + except pyboard.PyboardError: + had_crash = True + output_mupy = b'CRASH' + + # canonical form for all ports/platforms is to use \n for end-of-line + output_mupy = output_mupy.replace(b'\r\n', b'\n') + + # don't try to convert the output if we should skip this test + if had_crash or output_mupy in (b'SKIP\n', b'CRASH'): + return output_mupy + + if is_special or test_file in special_tests: + # convert parts of the output that are not stable across runs + with open(test_file + '.exp', 'rb') as f: + lines_exp = [] + for line in f.readlines(): + if line == b'########\n': + line = (line,) + else: + line = (line, re.compile(convert_regex_escapes(line))) + lines_exp.append(line) + lines_mupy = [line + b'\n' for line in output_mupy.split(b'\n')] + if output_mupy.endswith(b'\n'): + lines_mupy = lines_mupy[:-1] # remove erroneous last empty line + i_mupy = 0 + for i in range(len(lines_exp)): + if lines_exp[i][0] == b'########\n': + # 8x #'s means match 0 or more whole lines + line_exp = lines_exp[i + 1] + skip = 0 + while i_mupy + skip < len(lines_mupy) and not line_exp[1].match(lines_mupy[i_mupy + skip]): + skip += 1 + if i_mupy + skip >= len(lines_mupy): + lines_mupy[i_mupy] = b'######## FAIL\n' + break + del lines_mupy[i_mupy:i_mupy + skip] + lines_mupy.insert(i_mupy, b'########\n') + i_mupy += 1 + else: + # a regex + if lines_exp[i][1].match(lines_mupy[i_mupy]): + lines_mupy[i_mupy] = lines_exp[i][0] + else: + #print("don't match: %r %s" % (lines_exp[i][1], lines_mupy[i_mupy])) # DEBUG + pass + i_mupy += 1 + if i_mupy >= len(lines_mupy): + break + output_mupy = b''.join(lines_mupy) + + return output_mupy + + +def run_feature_check(pyb, args, base_path, test_file): + return run_micropython(pyb, args, base_path + "/feature_check/" + test_file, is_special=True) + +class ThreadSafeCounter: + def __init__(self, start=0): + self._value = start + self._lock = threading.Lock() + + def add(self, to_add): + with self._lock: self._value += to_add + + def append(self, arg): + self.add([arg]) + + @property + def value(self): + return self._value + +def run_tests(pyb, tests, args, base_path=".", num_threads=1): + test_count = ThreadSafeCounter() + testcase_count = ThreadSafeCounter() + passed_count = ThreadSafeCounter() + failed_tests = ThreadSafeCounter([]) + skipped_tests = ThreadSafeCounter([]) + + skip_tests = set() + skip_native = False + skip_int_big = False + skip_set_type = False + skip_async = False + skip_const = False + skip_revops = False + skip_endian = False + has_complex = True + has_coverage = False + + upy_float_precision = 32 + + # Some tests shouldn't be run under Travis CI + if os.getenv('TRAVIS') == 'true': + skip_tests.add('basics/memoryerror.py') + skip_tests.add('thread/thread_gc1.py') # has reliability issues + skip_tests.add('thread/thread_lock4.py') # has reliability issues + skip_tests.add('thread/stress_heap.py') # has reliability issues + skip_tests.add('thread/stress_recurse.py') # has reliability issues + + if upy_float_precision == 0: + skip_tests.add('extmod/ujson_dumps_float.py') + skip_tests.add('extmod/ujson_loads_float.py') + skip_tests.add('misc/rge_sm.py') + if upy_float_precision < 32: + skip_tests.add('float/float2int_intbig.py') # requires fp32, there's float2int_fp30_intbig.py instead + skip_tests.add('float/string_format.py') # requires fp32, there's string_format_fp30.py instead + skip_tests.add('float/bytes_construct.py') # requires fp32 + skip_tests.add('float/bytearray_construct.py') # requires fp32 + if upy_float_precision < 64: + skip_tests.add('float/float_divmod.py') # tested by float/float_divmod_relaxed.py instead + skip_tests.add('float/float2int_doubleprec_intbig.py') + skip_tests.add('float/float_parse_doubleprec.py') + + if not has_complex: + skip_tests.add('float/complex1.py') + skip_tests.add('float/complex1_intbig.py') + skip_tests.add('float/int_big_float.py') + skip_tests.add('float/true_value.py') + skip_tests.add('float/types.py') + + if not has_coverage: + skip_tests.add('cmdline/cmd_parsetree.py') + + # Some tests shouldn't be run on a PC + if args.target == 'unix': + # unix build does not have the GIL so can't run thread mutation tests + for t in tests: + if t.startswith('thread/mutate_'): + skip_tests.add(t) + + # Some tests shouldn't be run on pyboard + if args.target != 'unix': + skip_tests.add('basics/exception_chain.py') # warning is not printed + skip_tests.add('micropython/meminfo.py') # output is very different to PC output + skip_tests.add('extmod/machine_mem.py') # raw memory access not supported + + if args.target == 'wipy': + skip_tests.add('misc/print_exception.py') # requires error reporting full + skip_tests.update({'extmod/uctypes_%s.py' % t for t in 'bytearray le native_le ptr_le ptr_native_le sizeof sizeof_native array_assign_le array_assign_native_le'.split()}) # requires uctypes + skip_tests.add('extmod/zlibd_decompress.py') # requires zlib + skip_tests.add('extmod/uheapq1.py') # uheapq not supported by WiPy + skip_tests.add('extmod/urandom_basic.py') # requires urandom + skip_tests.add('extmod/urandom_extra.py') # requires urandom + elif args.target == 'esp8266': + skip_tests.add('misc/rge_sm.py') # too large + elif args.target == 'minimal': + skip_tests.add('basics/class_inplace_op.py') # all special methods not supported + skip_tests.add('basics/subclass_native_init.py')# native subclassing corner cases not support + skip_tests.add('misc/rge_sm.py') # too large + skip_tests.add('micropython/opt_level.py') # don't assume line numbers are stored + + # Some tests are known to fail on 64-bit machines + if pyb is None and platform.architecture()[0] == '64bit': + pass + + # Some tests use unsupported features on Windows + if os.name == 'nt': + skip_tests.add('import/import_file.py') # works but CPython prints forward slashes + + # Some tests are known to fail with native emitter + # Remove them from the below when they work + if args.emit == 'native': + skip_tests.update({'basics/%s.py' % t for t in 'gen_yield_from gen_yield_from_close gen_yield_from_ducktype gen_yield_from_exc gen_yield_from_executing gen_yield_from_iter gen_yield_from_send gen_yield_from_stopped gen_yield_from_throw gen_yield_from_throw2 gen_yield_from_throw3 generator1 generator2 generator_args generator_close generator_closure generator_exc generator_pend_throw generator_return generator_send'.split()}) # require yield + skip_tests.update({'basics/%s.py' % t for t in 'bytes_gen class_store_class globals_del string_join gen_stack_overflow'.split()}) # require yield + skip_tests.update({'basics/async_%s.py' % t for t in 'def await await2 for for2 with with2 coroutine'.split()}) # require yield + skip_tests.update({'basics/%s.py' % t for t in 'try_reraise try_reraise2'.split()}) # require raise_varargs + skip_tests.update({'basics/%s.py' % t for t in 'with_break with_continue with_return'.split()}) # require complete with support + skip_tests.add('basics/array_construct2.py') # requires generators + skip_tests.add('basics/bool1.py') # seems to randomly fail + skip_tests.add('basics/builtin_hash_gen.py') # requires yield + skip_tests.add('basics/class_bind_self.py') # requires yield + skip_tests.add('basics/del_deref.py') # requires checking for unbound local + skip_tests.add('basics/del_local.py') # requires checking for unbound local + skip_tests.add('basics/exception_chain.py') # raise from is not supported + skip_tests.add('basics/for_range.py') # requires yield_value + skip_tests.add('basics/try_finally_loops.py') # requires proper try finally code + skip_tests.add('basics/try_finally_return.py') # requires proper try finally code + skip_tests.add('basics/try_finally_return2.py') # requires proper try finally code + skip_tests.add('basics/unboundlocal.py') # requires checking for unbound local + skip_tests.add('import/gen_context.py') # requires yield_value + skip_tests.add('misc/features.py') # requires raise_varargs + skip_tests.add('misc/rge_sm.py') # requires yield + skip_tests.add('misc/print_exception.py') # because native doesn't have proper traceback info + skip_tests.add('misc/sys_exc_info.py') # sys.exc_info() is not supported for native + skip_tests.add('micropython/emg_exc.py') # because native doesn't have proper traceback info + skip_tests.add('micropython/heapalloc_traceback.py') # because native doesn't have proper traceback info + skip_tests.add('micropython/heapalloc_iter.py') # requires generators + skip_tests.add('micropython/schedule.py') # native code doesn't check pending events + skip_tests.add('stress/gc_trace.py') # requires yield + skip_tests.add('stress/recursive_gen.py') # requires yield + skip_tests.add('extmod/vfs_userfs.py') # because native doesn't properly handle globals across different modules + skip_tests.add('../extmod/ulab/tests/argminmax.py') # requires yield + + def run_one_test(test_file): + test_file = test_file.replace('\\', '/') + + if args.filters: + # Default verdict is the opposit of the first action + verdict = "include" if args.filters[0][0] == "exclude" else "exclude" + for action, pat in args.filters: + if pat.search(test_file): + verdict = action + if verdict == "exclude": + return + + test_basename = os.path.basename(test_file) + test_name = os.path.splitext(test_basename)[0] + is_native = test_name.startswith("native_") or test_name.startswith("viper_") + is_endian = test_name.endswith("_endian") + is_int_big = test_name.startswith("int_big") or test_name.endswith("_intbig") + is_set_type = test_name.startswith("set_") or test_name.startswith("frozenset") + is_async = test_name.startswith("async_") + is_const = test_name.startswith("const") + + skip_it = test_file in skip_tests + skip_it |= skip_native and is_native + skip_it |= skip_endian and is_endian + skip_it |= skip_int_big and is_int_big + skip_it |= skip_set_type and is_set_type + skip_it |= skip_async and is_async + skip_it |= skip_const and is_const + skip_it |= skip_revops and test_name.startswith("class_reverse_op") + + if args.list_tests: + if not skip_it: + print(test_file) + return + + if skip_it: + print("skip ", test_file) + skipped_tests.append(test_name) + return + + # get expected output + test_file_expected = test_file + '.exp' + if os.path.isfile(test_file_expected): + # expected output given by a file, so read that in + with open(test_file_expected, 'rb') as f: + output_expected = f.read() + else: + if not args.write_exp: + output_expected = b"NOEXP\n" + else: + # run CPython to work out expected output + e = {"PYTHONPATH": os.getcwd(), + "PATH": os.environ["PATH"], + "LANG": "en_US.UTF-8"} + p = subprocess.Popen([MICROPYTHON, test_file], env=e, stdout=subprocess.PIPE) + output_expected = b'' + while p.poll() is None: + output_expected += p.stdout.read() + output_expected += p.stdout.read() + with open(test_file_expected, 'wb') as f: + f.write(output_expected) + + # canonical form for all host platforms is to use \n for end-of-line + output_expected = output_expected.replace(b'\r\n', b'\n') + + if args.write_exp: + return + + # run MicroPython + output_mupy = run_micropython(pyb, args, test_file) + + if output_mupy == b'SKIP\n': + print("skip ", test_file) + skipped_tests.append(test_name) + return + + if output_expected == b'NOEXP\n': + print("noexp", test_file) + failed_tests.append(test_name) + return + + testcase_count.add(len(output_expected.splitlines())) + + filename_expected = test_basename + ".exp" + filename_mupy = test_basename + ".out" + + if output_expected == output_mupy: + print("pass ", test_file) + passed_count.add(1) + rm_f(filename_expected) + rm_f(filename_mupy) + else: + with open(filename_expected, "wb") as f: + f.write(output_expected) + with open(filename_mupy, "wb") as f: + f.write(output_mupy) + print("### Expected") + print(output_expected) + print("### Actual") + print(output_mupy) + print("FAIL ", test_file) + failed_tests.append(test_name) + + test_count.add(1) + + if args.list_tests: + return True + + if num_threads > 1: + pool = ThreadPool(num_threads) + pool.map(run_one_test, tests) + else: + for test in tests: + run_one_test(test) + + print("{} tests performed ({} individual testcases)".format(test_count.value, testcase_count.value)) + print("{} tests passed".format(passed_count.value)) + + if len(skipped_tests.value) > 0: + print("{} tests skipped: {}".format(len(skipped_tests.value), ' '.join(sorted(skipped_tests.value)))) + if len(failed_tests.value) > 0: + print("{} tests failed: {}".format(len(failed_tests.value), ' '.join(sorted(failed_tests.value)))) + return False + + # all tests succeeded + return True + + +class append_filter(argparse.Action): + + def __init__(self, option_strings, dest, **kwargs): + super().__init__(option_strings, dest, default=[], **kwargs) + + def __call__(self, parser, args, value, option): + if not hasattr(args, self.dest): + args.filters = [] + if option.startswith(("-e", "--e")): + option = "exclude" + else: + option = "include" + args.filters.append((option, re.compile(value))) + + +def main(): + cmd_parser = argparse.ArgumentParser( + formatter_class=argparse.RawDescriptionHelpFormatter, + description='Run and manage tests for MicroPython.', + epilog='''\ +Options -i and -e can be multiple and processed in the order given. Regex +"search" (vs "match") operation is used. An action (include/exclude) of +the last matching regex is used: + run-tests -i async - exclude all, then include tests containg "async" anywhere + run-tests -e '/big.+int' - include all, then exclude by regex + run-tests -e async -i async_foo - include all, exclude async, yet still include async_foo +''') + cmd_parser.add_argument('--target', default='unix', help='the target platform') + cmd_parser.add_argument('--device', default='/dev/ttyACM0', help='the serial device or the IP address of the pyboard') + cmd_parser.add_argument('-b', '--baudrate', default=115200, help='the baud rate of the serial device') + cmd_parser.add_argument('-u', '--user', default='micro', help='the telnet login username') + cmd_parser.add_argument('-p', '--password', default='python', help='the telnet login password') + cmd_parser.add_argument('-d', '--test-dirs', nargs='*', help='input test directories (if no files given)') + cmd_parser.add_argument('-e', '--exclude', action=append_filter, metavar='REGEX', dest='filters', help='exclude test by regex on path/name.py') + cmd_parser.add_argument('-i', '--include', action=append_filter, metavar='REGEX', dest='filters', help='include test by regex on path/name.py') + cmd_parser.add_argument('--write-exp', action='store_true', help='save .exp files to run tests w/o CPython') + cmd_parser.add_argument('--list-tests', action='store_true', help='list tests instead of running them') + cmd_parser.add_argument('--emit', default='bytecode', help='MicroPython emitter to use (bytecode or native)') + cmd_parser.add_argument('--heapsize', help='heapsize to use (use default if not specified)') + cmd_parser.add_argument('--via-mpy', action='store_true', help='compile .py files to .mpy first') + cmd_parser.add_argument('--keep-path', action='store_true', help='do not clear MICROPYPATH when running tests') + cmd_parser.add_argument('-j', '--jobs', default=1, metavar='N', type=int, help='Number of tests to run simultaneously') + cmd_parser.add_argument('--auto-jobs', action='store_const', dest='jobs', const=multiprocessing.cpu_count(), help='Set the -j values to the CPU (thread) count') + cmd_parser.add_argument('files', nargs='*', help='input test files') + args = cmd_parser.parse_args() + + EXTERNAL_TARGETS = ('pyboard', 'wipy', 'esp8266', 'esp32', 'minimal') + if args.target == 'unix' or args.list_tests: + pyb = None + elif args.target in EXTERNAL_TARGETS: + import pyboard + pyb = pyboard.Pyboard(args.device, args.baudrate, args.user, args.password) + pyb.enter_raw_repl() + else: + raise ValueError('target must be either %s or unix' % ", ".join(EXTERNAL_TARGETS)) + + if len(args.files) == 0: + if args.test_dirs is None: + if args.target == 'pyboard': + # run pyboard tests + test_dirs = ('basics', 'micropython', 'float', 'misc', 'stress', 'extmod', 'pyb', 'pybnative', 'inlineasm') + elif args.target in ('esp8266', 'esp32', 'minimal'): + test_dirs = ('basics', 'micropython', 'float', 'misc', 'extmod') + elif args.target == 'wipy': + # run WiPy tests + test_dirs = ('basics', 'micropython', 'misc', 'extmod', 'wipy') + else: + # run PC tests + test_dirs = ( + 'basics', 'micropython', 'float', 'import', 'io', 'misc', + 'stress', 'unicode', 'extmod', '../extmod/ulab/tests', 'unix', 'cmdline', + ) + else: + # run tests from these directories + test_dirs = args.test_dirs + tests = sorted(test_file for test_files in (glob('{}/*.py'.format(dir)) for dir in test_dirs) for test_file in test_files) + else: + # tests explicitly given + tests = args.files + + if not args.keep_path: + # clear search path to make sure tests use only builtin modules + os.environ['MICROPYPATH'] = '' + + # Even if we run completely different tests in a different directory, + # we need to access feature_check's from the same directory as the + # run-tests script itself. + base_path = os.path.dirname(sys.argv[0]) or "." + try: + res = run_tests(pyb, tests, args, base_path, args.jobs) + finally: + if pyb: + pyb.close() + + if not res: + sys.exit(1) + +if __name__ == "__main__": + main() diff --git a/circuitpython/extmod/ulab/snippets/rclass.py b/circuitpython/extmod/ulab/snippets/rclass.py new file mode 100644 index 0000000..cb95021 --- /dev/null +++ b/circuitpython/extmod/ulab/snippets/rclass.py @@ -0,0 +1,75 @@ +from typing import List, Tuple, Union # upip.install("pycopy-typing") +from ulab import numpy as np + +_DType = int +_RClassKeyType = Union[slice, int, float, list, tuple, np.ndarray] + +# this is a stripped down version of RClass (used by np.r_[...etc]) +# it doesn't include support for string arguments as the first index element +class RClass: + + def __getitem__(self, key: Union[_RClassKeyType, Tuple[_RClassKeyType, ...]]): + + if not isinstance(key, tuple): + key = (key,) + + objs: List[np.ndarray] = [] + scalars: List[int] = [] + arraytypes: List[_DType] = [] + scalartypes: List[_DType] = [] + + # these may get overridden in following loop + axis = 0 + + for idx, item in enumerate(key): + scalar = False + + try: + if isinstance(item, np.ndarray): + newobj = item + + elif isinstance(item, slice): + step = item.step + start = item.start + stop = item.stop + if start is None: + start = 0 + if step is None: + step = 1 + if isinstance(step, complex): + size = int(abs(step)) + newobj: np.ndarray = np.linspace(start, stop, num=size) + else: + newobj = np.arange(start, stop, step) + + # if is number + elif isinstance(item, (int, float, bool)): + newobj = np.array([item]) + scalars.append(len(objs)) + scalar = True + scalartypes.append(newobj.dtype()) + + else: + newobj = np.array(item) + + except TypeError: + raise Exception("index object %s of type %s is not supported by r_[]" % ( + str(item), type(item))) + + objs.append(newobj) + if not scalar and isinstance(newobj, np.ndarray): + arraytypes.append(newobj.dtype()) + + # Ensure that scalars won't up-cast unless warranted + final_dtype = min(arraytypes + scalartypes) + for idx, obj in enumerate(objs): + if obj.dtype != final_dtype: + objs[idx] = np.array(objs[idx], dtype=final_dtype) + + return np.concatenate(tuple(objs), axis=axis) + + # this seems weird - not sure what it's for + def __len__(self): + return 0 + +r_ = RClass() diff --git a/circuitpython/extmod/ulab/test-common.sh b/circuitpython/extmod/ulab/test-common.sh new file mode 100644 index 0000000..d4e4d1e --- /dev/null +++ b/circuitpython/extmod/ulab/test-common.sh @@ -0,0 +1,19 @@ +#!/bin/sh +set -e +dims="$1" +micropython="$2" +for level1 in $(printf "%dd " $(seq 1 ${dims})) +do + for level2 in numpy scipy utils complex; do + rm -f *.exp + if ! env MICROPY_MICROPYTHON="$micropython" ./run-tests -d tests/"$level1"/"$level2"; then + for exp in *.exp; do + testbase=$(basename $exp .exp); + echo -e "\nFAILURE $testbase"; + diff -u $testbase.exp $testbase.out; + done + exit 1 + fi + done +done + diff --git a/circuitpython/extmod/ulab/tests/1d/complex/complex_exp.py b/circuitpython/extmod/ulab/tests/1d/complex/complex_exp.py new file mode 100644 index 0000000..979b5b8 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/complex/complex_exp.py @@ -0,0 +1,17 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(4), dtype=dtype) + print('\narray:\n', a) + print('\nexponential:\n', np.exp(a)) + +b = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +print('\narray:\n', b) +print('\nexponential:\n', np.exp(b))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/1d/complex/complex_exp.py.exp b/circuitpython/extmod/ulab/tests/1d/complex/complex_exp.py.exp new file mode 100644 index 0000000..fb34d53 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/complex/complex_exp.py.exp @@ -0,0 +1,42 @@ + +array: + array([0, 1, 2, 3], dtype=uint8) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int8) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=uint16) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int16) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], dtype=complex) + +exponential: + array([1.0+0.0j, 2.718281828459045+0.0j, 7.38905609893065+0.0j, 20.08553692318767+0.0j], dtype=complex) + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +exponential: + array([1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/1d/complex/complex_sqrt.py b/circuitpython/extmod/ulab/tests/1d/complex/complex_sqrt.py new file mode 100644 index 0000000..aa709ae --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/complex/complex_sqrt.py @@ -0,0 +1,18 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(4), dtype=dtype) + outtype = np.float if dtype is not np.complex else np.complex + print('\narray:\n', a) + print('\nsquare root:\n', np.sqrt(a, dtype=outtype)) + +b = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +print('\narray:\n', b) +print('\nsquare root:\n', np.sqrt(b, dtype=np.complex))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/1d/complex/complex_sqrt.py.exp b/circuitpython/extmod/ulab/tests/1d/complex/complex_sqrt.py.exp new file mode 100644 index 0000000..30459fc --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/complex/complex_sqrt.py.exp @@ -0,0 +1,42 @@ + +array: + array([0, 1, 2, 3], dtype=uint8) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int8) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=uint16) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int16) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], dtype=complex) + +square root: + array([0.0+0.0j, 1.0+0.0j, 1.414213562373095+0.0j, 1.732050807568877+0.0j], dtype=complex) + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +square root: + array([0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/1d/complex/imag_real.py b/circuitpython/extmod/ulab/tests/1d/complex/imag_real.py new file mode 100644 index 0000000..e05783b --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/complex/imag_real.py @@ -0,0 +1,19 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(5), dtype=dtype) + print('real part: ', np.real(a)) + print('imaginary part: ', np.imag(a)) + + +b = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +print('real part: ', np.real(b)) +print('imaginary part: ', np.imag(b)) + diff --git a/circuitpython/extmod/ulab/tests/1d/complex/imag_real.py.exp b/circuitpython/extmod/ulab/tests/1d/complex/imag_real.py.exp new file mode 100644 index 0000000..977fb4a --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/complex/imag_real.py.exp @@ -0,0 +1,14 @@ +real part: array([0, 1, 2, 3, 4], dtype=uint8) +imaginary part: array([0, 0, 0, 0, 0], dtype=uint8) +real part: array([0, 1, 2, 3, 4], dtype=int8) +imaginary part: array([0, 0, 0, 0, 0], dtype=int8) +real part: array([0, 1, 2, 3, 4], dtype=uint16) +imaginary part: array([0, 0, 0, 0, 0], dtype=uint16) +real part: array([0, 1, 2, 3, 4], dtype=int16) +imaginary part: array([0, 0, 0, 0, 0], dtype=int16) +real part: array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) +imaginary part: array([0.0, 0.0, 0.0, 0.0, 0.0], dtype=float64) +real part: array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) +imaginary part: array([0.0, 0.0, 0.0, 0.0, 0.0], dtype=float64) +real part: array([0.0, 0.0, 2.0, 3.0], dtype=float64) +imaginary part: array([0.0, 1.0, 2.0, -3.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/00smoke.py b/circuitpython/extmod/ulab/tests/1d/numpy/00smoke.py new file mode 100644 index 0000000..c756273 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/00smoke.py @@ -0,0 +1,3 @@ +from ulab import numpy as np + +print(np.ones(3)) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/00smoke.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/00smoke.py.exp new file mode 100644 index 0000000..f4cff3b --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/00smoke.py.exp @@ -0,0 +1 @@ +array([1.0, 1.0, 1.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/argminmax.py b/circuitpython/extmod/ulab/tests/1d/numpy/argminmax.py new file mode 100644 index 0000000..e2aa0bc --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/argminmax.py @@ -0,0 +1,62 @@ +from ulab import numpy as np + +# Adapted from https://docs.python.org/3.8/library/itertools.html#itertools.permutations +def permutations(iterable, r=None): + # permutations('ABCD', 2) --> AB AC AD BA BC BD CA CB CD DA DB DC + # permutations(range(3)) --> 012 021 102 120 201 210 + pool = tuple(iterable) + n = len(pool) + r = n if r is None else r + if r > n: + return + indices = list(range(n)) + cycles = list(range(n, n-r, -1)) + yield tuple(pool[i] for i in indices[:r]) + while n: + for i in reversed(range(r)): + cycles[i] -= 1 + if cycles[i] == 0: + indices[i:] = indices[i+1:] + indices[i:i+1] + cycles[i] = n - i + else: + j = cycles[i] + indices[i], indices[-j] = indices[-j], indices[i] + yield tuple(pool[i] for i in indices[:r]) + break + else: + return + +# Combinations expected to throw +try: + print(np.argmin([])) +except ValueError: + print("ValueError") + +try: + print(np.argmax([])) +except ValueError: + print("ValueError") + +# Combinations expected to succeed +print(np.argmin([1])) +print(np.argmax([1])) +print(np.argmin(np.array([1]))) +print(np.argmax(np.array([1]))) + +print() +print("max tests") +for p in permutations((100,200,300)): + m1 = np.argmax(p) + m2 = np.argmax(np.array(p)) + print(p, m1, m2) + if m1 != m2 or p[m1] != max(p): + print("FAIL", p, m1, m2, max(p)) + +print() +print("min tests") +for p in permutations((100,200,300)): + m1 = np.argmin(p) + m2 = np.argmin(np.array(p)) + print(p, m1, m2) + if m1 != m2 or p[m1] != min(p): + print("FAIL", p, m1, m2, min(p)) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/argminmax.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/argminmax.py.exp new file mode 100644 index 0000000..d77e4c7 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/argminmax.py.exp @@ -0,0 +1,22 @@ +ValueError +ValueError +0 +0 +0 +0 + +max tests +(100, 200, 300) 2 2 +(100, 300, 200) 1 1 +(200, 100, 300) 2 2 +(200, 300, 100) 1 1 +(300, 100, 200) 0 0 +(300, 200, 100) 0 0 + +min tests +(100, 200, 300) 0 0 +(100, 300, 200) 0 0 +(200, 100, 300) 1 1 +(200, 300, 100) 2 2 +(300, 100, 200) 1 1 +(300, 200, 100) 2 2 diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/compare.py b/circuitpython/extmod/ulab/tests/1d/numpy/compare.py new file mode 100644 index 0000000..cd9fb98 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/compare.py @@ -0,0 +1,13 @@ +from ulab import numpy as np + +a = np.array([1, 2, 3, 4, 5], dtype=np.uint8) +b = np.array([5, 4, 3, 2, 1], dtype=np.float) +print(np.minimum(a, b)) +print(np.maximum(a, b)) +print(np.maximum(1, 5.5)) + +a = np.array(range(9), dtype=np.uint8) +print(np.clip(a, 3, 7)) + +b = 3 * np.ones(len(a), dtype=np.float) +print(np.clip(a, b, 7)) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/compare.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/compare.py.exp new file mode 100644 index 0000000..b9024e4 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/compare.py.exp @@ -0,0 +1,5 @@ +array([1.0, 2.0, 3.0, 2.0, 1.0], dtype=float64) +array([5.0, 4.0, 3.0, 4.0, 5.0], dtype=float64) +5.5 +array([3, 3, 3, 3, 4, 5, 6, 7, 7], dtype=uint8) +array([3.0, 3.0, 3.0, 3.0, 4.0, 5.0, 6.0, 7.0, 7.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/convolve.py b/circuitpython/extmod/ulab/tests/1d/numpy/convolve.py new file mode 100644 index 0000000..93aa23f --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/convolve.py @@ -0,0 +1,15 @@ +import math + +try: + from ulab import numpy as np +except ImportError: + import numpy as np + +x = np.array((1,2,3)) +y = np.array((1,10,100,1000)) +result = (np.convolve(x, y)) +ref_result = np.array([1, 12, 123, 1230, 2300, 3000],dtype=np.float) +cmp_result = [] +for p,q in zip(list(result), list(ref_result)): + cmp_result.append(math.isclose(p, q, rel_tol=1e-06, abs_tol=1e-06)) +print(cmp_result) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/convolve.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/convolve.py.exp new file mode 100644 index 0000000..63a3ac6 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/convolve.py.exp @@ -0,0 +1 @@ +[True, True, True, True, True, True] diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/fft.py b/circuitpython/extmod/ulab/tests/1d/numpy/fft.py new file mode 100644 index 0000000..1a1dee7 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/fft.py @@ -0,0 +1,37 @@ +import math +try: + from ulab import numpy as np + use_ulab = True +except ImportError: + import numpy as np + use_ulab = False + +x = np.linspace(-np.pi, np.pi, num=8) +y = np.sin(x) + +if use_ulab: + a, b = np.fft.fft(y) + c, d = np.fft.ifft(a, b) + # c should be equal to y + cmp_result = [] + for p,q in zip(list(y), list(c)): + cmp_result.append(math.isclose(p, q, rel_tol=1e-09, abs_tol=1e-09)) + print(cmp_result) + + z = np.zeros(len(x)) + a, b = np.fft.fft(y, z) + c, d = np.fft.ifft(a, b) + # c should be equal to y + cmp_result = [] + for p,q in zip(list(y), list(c)): + cmp_result.append(math.isclose(p, q, rel_tol=1e-09, abs_tol=1e-09)) + print(cmp_result) + +else: + a = np.fft.fft(y) + c = np.fft.ifft(a) + # c should be equal to y + cmp_result = [] + for p,q in zip(list(y), list(c.real)): + cmp_result.append(math.isclose(p, q, rel_tol=1e-09, abs_tol=1e-09)) + print(cmp_result) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/fft.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/fft.py.exp new file mode 100644 index 0000000..c9b2279 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/fft.py.exp @@ -0,0 +1,2 @@ +[True, True, True, True, True, True, True, True] +[True, True, True, True, True, True, True, True] diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/gc.py b/circuitpython/extmod/ulab/tests/1d/numpy/gc.py new file mode 100644 index 0000000..4dbf079 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/gc.py @@ -0,0 +1,11 @@ +from ulab import numpy as np +import gc + +data = np.ones(1000)[6:-6] +print(sum(data)) +print(data) + +gc.collect() + +print(sum(data)) +print(data)
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/gc.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/gc.py.exp new file mode 100644 index 0000000..f14e5c8 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/gc.py.exp @@ -0,0 +1,4 @@ +988.0000000000001 +array([1.0, 1.0, 1.0, ..., 1.0, 1.0, 1.0], dtype=float64) +988.0000000000001 +array([1.0, 1.0, 1.0, ..., 1.0, 1.0, 1.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/interp.py b/circuitpython/extmod/ulab/tests/1d/numpy/interp.py new file mode 100644 index 0000000..09d3dc3 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/interp.py @@ -0,0 +1,12 @@ +try: + from ulab import numpy as np +except ImportError: + import numpy as np + +x = np.array([1, 2, 3, 4, 5]) +xp = np.array([1, 2, 3, 4]) +fp = np.array([1, 2, 3, 4]) +print(np.interp(x, xp, fp)) +print(np.interp(x, xp, fp, left=0.0)) +print(np.interp(x, xp, fp, right=10.0)) +print(np.interp(x, xp, fp, left=0.0, right=10.0)) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/interp.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/interp.py.exp new file mode 100644 index 0000000..717a890 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/interp.py.exp @@ -0,0 +1,4 @@ +array([1.0, 2.0, 3.0, 4.0, 4.0], dtype=float64) +array([1.0, 2.0, 3.0, 4.0, 4.0], dtype=float64) +array([1.0, 2.0, 3.0, 4.0, 10.0], dtype=float64) +array([1.0, 2.0, 3.0, 4.0, 10.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/optimize.py b/circuitpython/extmod/ulab/tests/1d/numpy/optimize.py new file mode 100644 index 0000000..fce8672 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/optimize.py @@ -0,0 +1,28 @@ +import math + +try: + from ulab import scipy as spy +except ImportError: + import scipy as spy + +def f(x): + return x**2 - 2.0 + +ref_result = 1.4142135623715149 +result = (spy.optimize.bisect(f, 1.0, 3.0)) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +ref_result = -7.105427357601002e-15 +result = spy.optimize.fmin(f, 3.0, fatol=1e-15) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +ref_result = -7.105427357601002e-15 +result = spy.optimize.fmin(f, 3.0, xatol=1e-8, fatol=1e-15, maxiter=500) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +ref_result = 1.41421826342255 +result = (spy.optimize.newton(f, 3.0, tol=0.001, rtol=0.01)) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (spy.optimize.newton(f, 3.0, tol=0.001, rtol=0.01, maxiter=100)) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/optimize.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/optimize.py.exp new file mode 100644 index 0000000..2e883c5 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/optimize.py.exp @@ -0,0 +1,5 @@ +True +True +True +True +True diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/poly.py b/circuitpython/extmod/ulab/tests/1d/numpy/poly.py new file mode 100644 index 0000000..02ce7f5 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/poly.py @@ -0,0 +1,51 @@ +import math + +try: + from ulab import numpy as np +except ImportError: + import numpy as np + +p = [1, 1, 1, 0] +x = [0, 1, 2, 3, 4] +result = np.polyval(p, x) +ref_result = np.array([0, 3, 14, 39, 84]) +for i in range(len(x)): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) + +a = np.array(x) +result = np.polyval(p, a) +ref_result = np.array([0, 3, 14, 39, 84]) +for i in range(len(x)): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) + +# linear fit +x = np.linspace(-10, 10, 20) +y = 1.5*x + 3 +result = np.polyfit(x, y, 1) +ref_result = np.array([ 1.5, 3.0]) +for i in range(2): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) + +# 2nd degree fit +x = np.linspace(-10, 10, 20) +y = x*x*2.5 - x*0.5 + 1.2 +result = np.polyfit(x, y, 2) +ref_result = np.array([2.5, -0.5, 1.2]) +for i in range(3): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) + +# 3rd degree fit +x = np.linspace(-10, 10, 20) +y = x*x*x*1.255 + x*x*1.0 - x*0.75 + 0.0 +result = np.polyfit(x, y, 3) +ref_result = np.array([1.255, 1.0, -0.75, 0.0]) +for i in range(4): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) + +# 4th degree fit +x = np.linspace(-10, 10, 20) +y = x*x*x*x + x*x*x*1.255 + x*x*1.0 - x*0.75 + 0.0 +result = np.polyfit(x, y, 4) +ref_result = np.array([1.0, 1.255, 1.0, -0.75, 0.0]) +for i in range(5): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/poly.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/poly.py.exp new file mode 100644 index 0000000..9d0c61b --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/poly.py.exp @@ -0,0 +1,24 @@ +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/slicing.py b/circuitpython/extmod/ulab/tests/1d/numpy/slicing.py new file mode 100644 index 0000000..466c3b2 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/slicing.py @@ -0,0 +1,23 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +for num in range(1,4): + for start in range(-num, num+1): + for end in range(-num, num+1): + for stride in (-3, -2, -1, 1, 2, 3): + l = list(range(num)) + a = np.array(l, dtype=np.int8) + sl = l[start:end:stride] + ll = len(sl) + try: + sa = list(a[start:end:stride]) + except IndexError as e: + sa = str(e) + print("%2d [% d:% d:% d] %-24r %-24r%s" % ( + num, start, end, stride, sl, sa, " ***" if sa != sl else "")) + + a[start:end:stride] = np.ones(len(sl)) * -1 + print("%2d [% d:% d:% d] %r" % ( + num, start, end, stride, list(a))) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/slicing.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/slicing.py.exp new file mode 100644 index 0000000..9d7d892 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/slicing.py.exp @@ -0,0 +1,996 @@ + 1 [-1:-1:-3] [] [] + 1 [-1:-1:-3] [0] + 1 [-1:-1:-2] [] [] + 1 [-1:-1:-2] [0] + 1 [-1:-1:-1] [] [] + 1 [-1:-1:-1] [0] + 1 [-1:-1: 1] [] [] + 1 [-1:-1: 1] [0] + 1 [-1:-1: 2] [] [] + 1 [-1:-1: 2] [0] + 1 [-1:-1: 3] [] [] + 1 [-1:-1: 3] [0] + 1 [-1: 0:-3] [] [] + 1 [-1: 0:-3] [0] + 1 [-1: 0:-2] [] [] + 1 [-1: 0:-2] [0] + 1 [-1: 0:-1] [] [] + 1 [-1: 0:-1] [0] + 1 [-1: 0: 1] [] [] + 1 [-1: 0: 1] [0] + 1 [-1: 0: 2] [] [] + 1 [-1: 0: 2] [0] + 1 [-1: 0: 3] [] [] + 1 [-1: 0: 3] [0] + 1 [-1: 1:-3] [] [] + 1 [-1: 1:-3] [0] + 1 [-1: 1:-2] [] [] + 1 [-1: 1:-2] [0] + 1 [-1: 1:-1] [] [] + 1 [-1: 1:-1] [0] + 1 [-1: 1: 1] [0] [0] + 1 [-1: 1: 1] [-1] + 1 [-1: 1: 2] [0] [0] + 1 [-1: 1: 2] [-1] + 1 [-1: 1: 3] [0] [0] + 1 [-1: 1: 3] [-1] + 1 [ 0:-1:-3] [] [] + 1 [ 0:-1:-3] [0] + 1 [ 0:-1:-2] [] [] + 1 [ 0:-1:-2] [0] + 1 [ 0:-1:-1] [] [] + 1 [ 0:-1:-1] [0] + 1 [ 0:-1: 1] [] [] + 1 [ 0:-1: 1] [0] + 1 [ 0:-1: 2] [] [] + 1 [ 0:-1: 2] [0] + 1 [ 0:-1: 3] [] [] + 1 [ 0:-1: 3] [0] + 1 [ 0: 0:-3] [] [] + 1 [ 0: 0:-3] [0] + 1 [ 0: 0:-2] [] [] + 1 [ 0: 0:-2] [0] + 1 [ 0: 0:-1] [] [] + 1 [ 0: 0:-1] [0] + 1 [ 0: 0: 1] [] [] + 1 [ 0: 0: 1] [0] + 1 [ 0: 0: 2] [] [] + 1 [ 0: 0: 2] [0] + 1 [ 0: 0: 3] [] [] + 1 [ 0: 0: 3] [0] + 1 [ 0: 1:-3] [] [] + 1 [ 0: 1:-3] [0] + 1 [ 0: 1:-2] [] [] + 1 [ 0: 1:-2] [0] + 1 [ 0: 1:-1] [] [] + 1 [ 0: 1:-1] [0] + 1 [ 0: 1: 1] [0] [0] + 1 [ 0: 1: 1] [-1] + 1 [ 0: 1: 2] [0] [0] + 1 [ 0: 1: 2] [-1] + 1 [ 0: 1: 3] [0] [0] + 1 [ 0: 1: 3] [-1] + 1 [ 1:-1:-3] [] [] + 1 [ 1:-1:-3] [0] + 1 [ 1:-1:-2] [] [] + 1 [ 1:-1:-2] [0] + 1 [ 1:-1:-1] [] [] + 1 [ 1:-1:-1] [0] + 1 [ 1:-1: 1] [] [] + 1 [ 1:-1: 1] [0] + 1 [ 1:-1: 2] [] [] + 1 [ 1:-1: 2] [0] + 1 [ 1:-1: 3] [] [] + 1 [ 1:-1: 3] [0] + 1 [ 1: 0:-3] [] [] + 1 [ 1: 0:-3] [0] + 1 [ 1: 0:-2] [] [] + 1 [ 1: 0:-2] [0] + 1 [ 1: 0:-1] [] [] + 1 [ 1: 0:-1] [0] + 1 [ 1: 0: 1] [] [] + 1 [ 1: 0: 1] [0] + 1 [ 1: 0: 2] [] [] + 1 [ 1: 0: 2] [0] + 1 [ 1: 0: 3] [] [] + 1 [ 1: 0: 3] [0] + 1 [ 1: 1:-3] [] [] + 1 [ 1: 1:-3] [0] + 1 [ 1: 1:-2] [] [] + 1 [ 1: 1:-2] [0] + 1 [ 1: 1:-1] [] [] + 1 [ 1: 1:-1] [0] + 1 [ 1: 1: 1] [] [] + 1 [ 1: 1: 1] [0] + 1 [ 1: 1: 2] [] [] + 1 [ 1: 1: 2] [0] + 1 [ 1: 1: 3] [] [] + 1 [ 1: 1: 3] [0] + 2 [-2:-2:-3] [] [] + 2 [-2:-2:-3] [0, 1] + 2 [-2:-2:-2] [] [] + 2 [-2:-2:-2] [0, 1] + 2 [-2:-2:-1] [] [] + 2 [-2:-2:-1] [0, 1] + 2 [-2:-2: 1] [] [] + 2 [-2:-2: 1] [0, 1] + 2 [-2:-2: 2] [] [] + 2 [-2:-2: 2] [0, 1] + 2 [-2:-2: 3] [] [] + 2 [-2:-2: 3] [0, 1] + 2 [-2:-1:-3] [] [] + 2 [-2:-1:-3] [0, 1] + 2 [-2:-1:-2] [] [] + 2 [-2:-1:-2] [0, 1] + 2 [-2:-1:-1] [] [] + 2 [-2:-1:-1] [0, 1] + 2 [-2:-1: 1] [0] [0] + 2 [-2:-1: 1] [-1, 1] + 2 [-2:-1: 2] [0] [0] + 2 [-2:-1: 2] [-1, 1] + 2 [-2:-1: 3] [0] [0] + 2 [-2:-1: 3] [-1, 1] + 2 [-2: 0:-3] [] [] + 2 [-2: 0:-3] [0, 1] + 2 [-2: 0:-2] [] [] + 2 [-2: 0:-2] [0, 1] + 2 [-2: 0:-1] [] [] + 2 [-2: 0:-1] [0, 1] + 2 [-2: 0: 1] [] [] + 2 [-2: 0: 1] [0, 1] + 2 [-2: 0: 2] [] [] + 2 [-2: 0: 2] [0, 1] + 2 [-2: 0: 3] [] [] + 2 [-2: 0: 3] [0, 1] + 2 [-2: 1:-3] [] [] + 2 [-2: 1:-3] [0, 1] + 2 [-2: 1:-2] [] [] + 2 [-2: 1:-2] [0, 1] + 2 [-2: 1:-1] [] [] + 2 [-2: 1:-1] [0, 1] + 2 [-2: 1: 1] [0] [0] + 2 [-2: 1: 1] [-1, 1] + 2 [-2: 1: 2] [0] [0] + 2 [-2: 1: 2] [-1, 1] + 2 [-2: 1: 3] [0] [0] + 2 [-2: 1: 3] [-1, 1] + 2 [-2: 2:-3] [] [] + 2 [-2: 2:-3] [0, 1] + 2 [-2: 2:-2] [] [] + 2 [-2: 2:-2] [0, 1] + 2 [-2: 2:-1] [] [] + 2 [-2: 2:-1] [0, 1] + 2 [-2: 2: 1] [0, 1] [0, 1] + 2 [-2: 2: 1] [-1, -1] + 2 [-2: 2: 2] [0] [0] + 2 [-2: 2: 2] [-1, 1] + 2 [-2: 2: 3] [0] [0] + 2 [-2: 2: 3] [-1, 1] + 2 [-1:-2:-3] [1] [1] + 2 [-1:-2:-3] [0, -1] + 2 [-1:-2:-2] [1] [1] + 2 [-1:-2:-2] [0, -1] + 2 [-1:-2:-1] [1] [1] + 2 [-1:-2:-1] [0, -1] + 2 [-1:-2: 1] [] [] + 2 [-1:-2: 1] [0, 1] + 2 [-1:-2: 2] [] [] + 2 [-1:-2: 2] [0, 1] + 2 [-1:-2: 3] [] [] + 2 [-1:-2: 3] [0, 1] + 2 [-1:-1:-3] [] [] + 2 [-1:-1:-3] [0, 1] + 2 [-1:-1:-2] [] [] + 2 [-1:-1:-2] [0, 1] + 2 [-1:-1:-1] [] [] + 2 [-1:-1:-1] [0, 1] + 2 [-1:-1: 1] [] [] + 2 [-1:-1: 1] [0, 1] + 2 [-1:-1: 2] [] [] + 2 [-1:-1: 2] [0, 1] + 2 [-1:-1: 3] [] [] + 2 [-1:-1: 3] [0, 1] + 2 [-1: 0:-3] [1] [1] + 2 [-1: 0:-3] [0, -1] + 2 [-1: 0:-2] [1] [1] + 2 [-1: 0:-2] [0, -1] + 2 [-1: 0:-1] [1] [1] + 2 [-1: 0:-1] [0, -1] + 2 [-1: 0: 1] [] [] + 2 [-1: 0: 1] [0, 1] + 2 [-1: 0: 2] [] [] + 2 [-1: 0: 2] [0, 1] + 2 [-1: 0: 3] [] [] + 2 [-1: 0: 3] [0, 1] + 2 [-1: 1:-3] [] [] + 2 [-1: 1:-3] [0, 1] + 2 [-1: 1:-2] [] [] + 2 [-1: 1:-2] [0, 1] + 2 [-1: 1:-1] [] [] + 2 [-1: 1:-1] [0, 1] + 2 [-1: 1: 1] [] [] + 2 [-1: 1: 1] [0, 1] + 2 [-1: 1: 2] [] [] + 2 [-1: 1: 2] [0, 1] + 2 [-1: 1: 3] [] [] + 2 [-1: 1: 3] [0, 1] + 2 [-1: 2:-3] [] [] + 2 [-1: 2:-3] [0, 1] + 2 [-1: 2:-2] [] [] + 2 [-1: 2:-2] [0, 1] + 2 [-1: 2:-1] [] [] + 2 [-1: 2:-1] [0, 1] + 2 [-1: 2: 1] [1] [1] + 2 [-1: 2: 1] [0, -1] + 2 [-1: 2: 2] [1] [1] + 2 [-1: 2: 2] [0, -1] + 2 [-1: 2: 3] [1] [1] + 2 [-1: 2: 3] [0, -1] + 2 [ 0:-2:-3] [] [] + 2 [ 0:-2:-3] [0, 1] + 2 [ 0:-2:-2] [] [] + 2 [ 0:-2:-2] [0, 1] + 2 [ 0:-2:-1] [] [] + 2 [ 0:-2:-1] [0, 1] + 2 [ 0:-2: 1] [] [] + 2 [ 0:-2: 1] [0, 1] + 2 [ 0:-2: 2] [] [] + 2 [ 0:-2: 2] [0, 1] + 2 [ 0:-2: 3] [] [] + 2 [ 0:-2: 3] [0, 1] + 2 [ 0:-1:-3] [] [] + 2 [ 0:-1:-3] [0, 1] + 2 [ 0:-1:-2] [] [] + 2 [ 0:-1:-2] [0, 1] + 2 [ 0:-1:-1] [] [] + 2 [ 0:-1:-1] [0, 1] + 2 [ 0:-1: 1] [0] [0] + 2 [ 0:-1: 1] [-1, 1] + 2 [ 0:-1: 2] [0] [0] + 2 [ 0:-1: 2] [-1, 1] + 2 [ 0:-1: 3] [0] [0] + 2 [ 0:-1: 3] [-1, 1] + 2 [ 0: 0:-3] [] [] + 2 [ 0: 0:-3] [0, 1] + 2 [ 0: 0:-2] [] [] + 2 [ 0: 0:-2] [0, 1] + 2 [ 0: 0:-1] [] [] + 2 [ 0: 0:-1] [0, 1] + 2 [ 0: 0: 1] [] [] + 2 [ 0: 0: 1] [0, 1] + 2 [ 0: 0: 2] [] [] + 2 [ 0: 0: 2] [0, 1] + 2 [ 0: 0: 3] [] [] + 2 [ 0: 0: 3] [0, 1] + 2 [ 0: 1:-3] [] [] + 2 [ 0: 1:-3] [0, 1] + 2 [ 0: 1:-2] [] [] + 2 [ 0: 1:-2] [0, 1] + 2 [ 0: 1:-1] [] [] + 2 [ 0: 1:-1] [0, 1] + 2 [ 0: 1: 1] [0] [0] + 2 [ 0: 1: 1] [-1, 1] + 2 [ 0: 1: 2] [0] [0] + 2 [ 0: 1: 2] [-1, 1] + 2 [ 0: 1: 3] [0] [0] + 2 [ 0: 1: 3] [-1, 1] + 2 [ 0: 2:-3] [] [] + 2 [ 0: 2:-3] [0, 1] + 2 [ 0: 2:-2] [] [] + 2 [ 0: 2:-2] [0, 1] + 2 [ 0: 2:-1] [] [] + 2 [ 0: 2:-1] [0, 1] + 2 [ 0: 2: 1] [0, 1] [0, 1] + 2 [ 0: 2: 1] [-1, -1] + 2 [ 0: 2: 2] [0] [0] + 2 [ 0: 2: 2] [-1, 1] + 2 [ 0: 2: 3] [0] [0] + 2 [ 0: 2: 3] [-1, 1] + 2 [ 1:-2:-3] [1] [1] + 2 [ 1:-2:-3] [0, -1] + 2 [ 1:-2:-2] [1] [1] + 2 [ 1:-2:-2] [0, -1] + 2 [ 1:-2:-1] [1] [1] + 2 [ 1:-2:-1] [0, -1] + 2 [ 1:-2: 1] [] [] + 2 [ 1:-2: 1] [0, 1] + 2 [ 1:-2: 2] [] [] + 2 [ 1:-2: 2] [0, 1] + 2 [ 1:-2: 3] [] [] + 2 [ 1:-2: 3] [0, 1] + 2 [ 1:-1:-3] [] [] + 2 [ 1:-1:-3] [0, 1] + 2 [ 1:-1:-2] [] [] + 2 [ 1:-1:-2] [0, 1] + 2 [ 1:-1:-1] [] [] + 2 [ 1:-1:-1] [0, 1] + 2 [ 1:-1: 1] [] [] + 2 [ 1:-1: 1] [0, 1] + 2 [ 1:-1: 2] [] [] + 2 [ 1:-1: 2] [0, 1] + 2 [ 1:-1: 3] [] [] + 2 [ 1:-1: 3] [0, 1] + 2 [ 1: 0:-3] [1] [1] + 2 [ 1: 0:-3] [0, -1] + 2 [ 1: 0:-2] [1] [1] + 2 [ 1: 0:-2] [0, -1] + 2 [ 1: 0:-1] [1] [1] + 2 [ 1: 0:-1] [0, -1] + 2 [ 1: 0: 1] [] [] + 2 [ 1: 0: 1] [0, 1] + 2 [ 1: 0: 2] [] [] + 2 [ 1: 0: 2] [0, 1] + 2 [ 1: 0: 3] [] [] + 2 [ 1: 0: 3] [0, 1] + 2 [ 1: 1:-3] [] [] + 2 [ 1: 1:-3] [0, 1] + 2 [ 1: 1:-2] [] [] + 2 [ 1: 1:-2] [0, 1] + 2 [ 1: 1:-1] [] [] + 2 [ 1: 1:-1] [0, 1] + 2 [ 1: 1: 1] [] [] + 2 [ 1: 1: 1] [0, 1] + 2 [ 1: 1: 2] [] [] + 2 [ 1: 1: 2] [0, 1] + 2 [ 1: 1: 3] [] [] + 2 [ 1: 1: 3] [0, 1] + 2 [ 1: 2:-3] [] [] + 2 [ 1: 2:-3] [0, 1] + 2 [ 1: 2:-2] [] [] + 2 [ 1: 2:-2] [0, 1] + 2 [ 1: 2:-1] [] [] + 2 [ 1: 2:-1] [0, 1] + 2 [ 1: 2: 1] [1] [1] + 2 [ 1: 2: 1] [0, -1] + 2 [ 1: 2: 2] [1] [1] + 2 [ 1: 2: 2] [0, -1] + 2 [ 1: 2: 3] [1] [1] + 2 [ 1: 2: 3] [0, -1] + 2 [ 2:-2:-3] [1] [1] + 2 [ 2:-2:-3] [0, -1] + 2 [ 2:-2:-2] [1] [1] + 2 [ 2:-2:-2] [0, -1] + 2 [ 2:-2:-1] [1] [1] + 2 [ 2:-2:-1] [0, -1] + 2 [ 2:-2: 1] [] [] + 2 [ 2:-2: 1] [0, 1] + 2 [ 2:-2: 2] [] [] + 2 [ 2:-2: 2] [0, 1] + 2 [ 2:-2: 3] [] [] + 2 [ 2:-2: 3] [0, 1] + 2 [ 2:-1:-3] [] [] + 2 [ 2:-1:-3] [0, 1] + 2 [ 2:-1:-2] [] [] + 2 [ 2:-1:-2] [0, 1] + 2 [ 2:-1:-1] [] [] + 2 [ 2:-1:-1] [0, 1] + 2 [ 2:-1: 1] [] [] + 2 [ 2:-1: 1] [0, 1] + 2 [ 2:-1: 2] [] [] + 2 [ 2:-1: 2] [0, 1] + 2 [ 2:-1: 3] [] [] + 2 [ 2:-1: 3] [0, 1] + 2 [ 2: 0:-3] [1] [1] + 2 [ 2: 0:-3] [0, -1] + 2 [ 2: 0:-2] [1] [1] + 2 [ 2: 0:-2] [0, -1] + 2 [ 2: 0:-1] [1] [1] + 2 [ 2: 0:-1] [0, -1] + 2 [ 2: 0: 1] [] [] + 2 [ 2: 0: 1] [0, 1] + 2 [ 2: 0: 2] [] [] + 2 [ 2: 0: 2] [0, 1] + 2 [ 2: 0: 3] [] [] + 2 [ 2: 0: 3] [0, 1] + 2 [ 2: 1:-3] [] [] + 2 [ 2: 1:-3] [0, 1] + 2 [ 2: 1:-2] [] [] + 2 [ 2: 1:-2] [0, 1] + 2 [ 2: 1:-1] [] [] + 2 [ 2: 1:-1] [0, 1] + 2 [ 2: 1: 1] [] [] + 2 [ 2: 1: 1] [0, 1] + 2 [ 2: 1: 2] [] [] + 2 [ 2: 1: 2] [0, 1] + 2 [ 2: 1: 3] [] [] + 2 [ 2: 1: 3] [0, 1] + 2 [ 2: 2:-3] [] [] + 2 [ 2: 2:-3] [0, 1] + 2 [ 2: 2:-2] [] [] + 2 [ 2: 2:-2] [0, 1] + 2 [ 2: 2:-1] [] [] + 2 [ 2: 2:-1] [0, 1] + 2 [ 2: 2: 1] [] [] + 2 [ 2: 2: 1] [0, 1] + 2 [ 2: 2: 2] [] [] + 2 [ 2: 2: 2] [0, 1] + 2 [ 2: 2: 3] [] [] + 2 [ 2: 2: 3] [0, 1] + 3 [-3:-3:-3] [] [] + 3 [-3:-3:-3] [0, 1, 2] + 3 [-3:-3:-2] [] [] + 3 [-3:-3:-2] [0, 1, 2] + 3 [-3:-3:-1] [] [] + 3 [-3:-3:-1] [0, 1, 2] + 3 [-3:-3: 1] [] [] + 3 [-3:-3: 1] [0, 1, 2] + 3 [-3:-3: 2] [] [] + 3 [-3:-3: 2] [0, 1, 2] + 3 [-3:-3: 3] [] [] + 3 [-3:-3: 3] [0, 1, 2] + 3 [-3:-2:-3] [] [] + 3 [-3:-2:-3] [0, 1, 2] + 3 [-3:-2:-2] [] [] + 3 [-3:-2:-2] [0, 1, 2] + 3 [-3:-2:-1] [] [] + 3 [-3:-2:-1] [0, 1, 2] + 3 [-3:-2: 1] [0] [0] + 3 [-3:-2: 1] [-1, 1, 2] + 3 [-3:-2: 2] [0] [0] + 3 [-3:-2: 2] [-1, 1, 2] + 3 [-3:-2: 3] [0] [0] + 3 [-3:-2: 3] [-1, 1, 2] + 3 [-3:-1:-3] [] [] + 3 [-3:-1:-3] [0, 1, 2] + 3 [-3:-1:-2] [] [] + 3 [-3:-1:-2] [0, 1, 2] + 3 [-3:-1:-1] [] [] + 3 [-3:-1:-1] [0, 1, 2] + 3 [-3:-1: 1] [0, 1] [0, 1] + 3 [-3:-1: 1] [-1, -1, 2] + 3 [-3:-1: 2] [0] [0] + 3 [-3:-1: 2] [-1, 1, 2] + 3 [-3:-1: 3] [0] [0] + 3 [-3:-1: 3] [-1, 1, 2] + 3 [-3: 0:-3] [] [] + 3 [-3: 0:-3] [0, 1, 2] + 3 [-3: 0:-2] [] [] + 3 [-3: 0:-2] [0, 1, 2] + 3 [-3: 0:-1] [] [] + 3 [-3: 0:-1] [0, 1, 2] + 3 [-3: 0: 1] [] [] + 3 [-3: 0: 1] [0, 1, 2] + 3 [-3: 0: 2] [] [] + 3 [-3: 0: 2] [0, 1, 2] + 3 [-3: 0: 3] [] [] + 3 [-3: 0: 3] [0, 1, 2] + 3 [-3: 1:-3] [] [] + 3 [-3: 1:-3] [0, 1, 2] + 3 [-3: 1:-2] [] [] + 3 [-3: 1:-2] [0, 1, 2] + 3 [-3: 1:-1] [] [] + 3 [-3: 1:-1] [0, 1, 2] + 3 [-3: 1: 1] [0] [0] + 3 [-3: 1: 1] [-1, 1, 2] + 3 [-3: 1: 2] [0] [0] + 3 [-3: 1: 2] [-1, 1, 2] + 3 [-3: 1: 3] [0] [0] + 3 [-3: 1: 3] [-1, 1, 2] + 3 [-3: 2:-3] [] [] + 3 [-3: 2:-3] [0, 1, 2] + 3 [-3: 2:-2] [] [] + 3 [-3: 2:-2] [0, 1, 2] + 3 [-3: 2:-1] [] [] + 3 [-3: 2:-1] [0, 1, 2] + 3 [-3: 2: 1] [0, 1] [0, 1] + 3 [-3: 2: 1] [-1, -1, 2] + 3 [-3: 2: 2] [0] [0] + 3 [-3: 2: 2] [-1, 1, 2] + 3 [-3: 2: 3] [0] [0] + 3 [-3: 2: 3] [-1, 1, 2] + 3 [-3: 3:-3] [] [] + 3 [-3: 3:-3] [0, 1, 2] + 3 [-3: 3:-2] [] [] + 3 [-3: 3:-2] [0, 1, 2] + 3 [-3: 3:-1] [] [] + 3 [-3: 3:-1] [0, 1, 2] + 3 [-3: 3: 1] [0, 1, 2] [0, 1, 2] + 3 [-3: 3: 1] [-1, -1, -1] + 3 [-3: 3: 2] [0, 2] [0, 2] + 3 [-3: 3: 2] [-1, 1, -1] + 3 [-3: 3: 3] [0] [0] + 3 [-3: 3: 3] [-1, 1, 2] + 3 [-2:-3:-3] [1] [1] + 3 [-2:-3:-3] [0, -1, 2] + 3 [-2:-3:-2] [1] [1] + 3 [-2:-3:-2] [0, -1, 2] + 3 [-2:-3:-1] [1] [1] + 3 [-2:-3:-1] [0, -1, 2] + 3 [-2:-3: 1] [] [] + 3 [-2:-3: 1] [0, 1, 2] + 3 [-2:-3: 2] [] [] + 3 [-2:-3: 2] [0, 1, 2] + 3 [-2:-3: 3] [] [] + 3 [-2:-3: 3] [0, 1, 2] + 3 [-2:-2:-3] [] [] + 3 [-2:-2:-3] [0, 1, 2] + 3 [-2:-2:-2] [] [] + 3 [-2:-2:-2] [0, 1, 2] + 3 [-2:-2:-1] [] [] + 3 [-2:-2:-1] [0, 1, 2] + 3 [-2:-2: 1] [] [] + 3 [-2:-2: 1] [0, 1, 2] + 3 [-2:-2: 2] [] [] + 3 [-2:-2: 2] [0, 1, 2] + 3 [-2:-2: 3] [] [] + 3 [-2:-2: 3] [0, 1, 2] + 3 [-2:-1:-3] [] [] + 3 [-2:-1:-3] [0, 1, 2] + 3 [-2:-1:-2] [] [] + 3 [-2:-1:-2] [0, 1, 2] + 3 [-2:-1:-1] [] [] + 3 [-2:-1:-1] [0, 1, 2] + 3 [-2:-1: 1] [1] [1] + 3 [-2:-1: 1] [0, -1, 2] + 3 [-2:-1: 2] [1] [1] + 3 [-2:-1: 2] [0, -1, 2] + 3 [-2:-1: 3] [1] [1] + 3 [-2:-1: 3] [0, -1, 2] + 3 [-2: 0:-3] [1] [1] + 3 [-2: 0:-3] [0, -1, 2] + 3 [-2: 0:-2] [1] [1] + 3 [-2: 0:-2] [0, -1, 2] + 3 [-2: 0:-1] [1] [1] + 3 [-2: 0:-1] [0, -1, 2] + 3 [-2: 0: 1] [] [] + 3 [-2: 0: 1] [0, 1, 2] + 3 [-2: 0: 2] [] [] + 3 [-2: 0: 2] [0, 1, 2] + 3 [-2: 0: 3] [] [] + 3 [-2: 0: 3] [0, 1, 2] + 3 [-2: 1:-3] [] [] + 3 [-2: 1:-3] [0, 1, 2] + 3 [-2: 1:-2] [] [] + 3 [-2: 1:-2] [0, 1, 2] + 3 [-2: 1:-1] [] [] + 3 [-2: 1:-1] [0, 1, 2] + 3 [-2: 1: 1] [] [] + 3 [-2: 1: 1] [0, 1, 2] + 3 [-2: 1: 2] [] [] + 3 [-2: 1: 2] [0, 1, 2] + 3 [-2: 1: 3] [] [] + 3 [-2: 1: 3] [0, 1, 2] + 3 [-2: 2:-3] [] [] + 3 [-2: 2:-3] [0, 1, 2] + 3 [-2: 2:-2] [] [] + 3 [-2: 2:-2] [0, 1, 2] + 3 [-2: 2:-1] [] [] + 3 [-2: 2:-1] [0, 1, 2] + 3 [-2: 2: 1] [1] [1] + 3 [-2: 2: 1] [0, -1, 2] + 3 [-2: 2: 2] [1] [1] + 3 [-2: 2: 2] [0, -1, 2] + 3 [-2: 2: 3] [1] [1] + 3 [-2: 2: 3] [0, -1, 2] + 3 [-2: 3:-3] [] [] + 3 [-2: 3:-3] [0, 1, 2] + 3 [-2: 3:-2] [] [] + 3 [-2: 3:-2] [0, 1, 2] + 3 [-2: 3:-1] [] [] + 3 [-2: 3:-1] [0, 1, 2] + 3 [-2: 3: 1] [1, 2] [1, 2] + 3 [-2: 3: 1] [0, -1, -1] + 3 [-2: 3: 2] [1] [1] + 3 [-2: 3: 2] [0, -1, 2] + 3 [-2: 3: 3] [1] [1] + 3 [-2: 3: 3] [0, -1, 2] + 3 [-1:-3:-3] [2] [2] + 3 [-1:-3:-3] [0, 1, -1] + 3 [-1:-3:-2] [2] [2] + 3 [-1:-3:-2] [0, 1, -1] + 3 [-1:-3:-1] [2, 1] [2, 1] + 3 [-1:-3:-1] [0, -1, -1] + 3 [-1:-3: 1] [] [] + 3 [-1:-3: 1] [0, 1, 2] + 3 [-1:-3: 2] [] [] + 3 [-1:-3: 2] [0, 1, 2] + 3 [-1:-3: 3] [] [] + 3 [-1:-3: 3] [0, 1, 2] + 3 [-1:-2:-3] [2] [2] + 3 [-1:-2:-3] [0, 1, -1] + 3 [-1:-2:-2] [2] [2] + 3 [-1:-2:-2] [0, 1, -1] + 3 [-1:-2:-1] [2] [2] + 3 [-1:-2:-1] [0, 1, -1] + 3 [-1:-2: 1] [] [] + 3 [-1:-2: 1] [0, 1, 2] + 3 [-1:-2: 2] [] [] + 3 [-1:-2: 2] [0, 1, 2] + 3 [-1:-2: 3] [] [] + 3 [-1:-2: 3] [0, 1, 2] + 3 [-1:-1:-3] [] [] + 3 [-1:-1:-3] [0, 1, 2] + 3 [-1:-1:-2] [] [] + 3 [-1:-1:-2] [0, 1, 2] + 3 [-1:-1:-1] [] [] + 3 [-1:-1:-1] [0, 1, 2] + 3 [-1:-1: 1] [] [] + 3 [-1:-1: 1] [0, 1, 2] + 3 [-1:-1: 2] [] [] + 3 [-1:-1: 2] [0, 1, 2] + 3 [-1:-1: 3] [] [] + 3 [-1:-1: 3] [0, 1, 2] + 3 [-1: 0:-3] [2] [2] + 3 [-1: 0:-3] [0, 1, -1] + 3 [-1: 0:-2] [2] [2] + 3 [-1: 0:-2] [0, 1, -1] + 3 [-1: 0:-1] [2, 1] [2, 1] + 3 [-1: 0:-1] [0, -1, -1] + 3 [-1: 0: 1] [] [] + 3 [-1: 0: 1] [0, 1, 2] + 3 [-1: 0: 2] [] [] + 3 [-1: 0: 2] [0, 1, 2] + 3 [-1: 0: 3] [] [] + 3 [-1: 0: 3] [0, 1, 2] + 3 [-1: 1:-3] [2] [2] + 3 [-1: 1:-3] [0, 1, -1] + 3 [-1: 1:-2] [2] [2] + 3 [-1: 1:-2] [0, 1, -1] + 3 [-1: 1:-1] [2] [2] + 3 [-1: 1:-1] [0, 1, -1] + 3 [-1: 1: 1] [] [] + 3 [-1: 1: 1] [0, 1, 2] + 3 [-1: 1: 2] [] [] + 3 [-1: 1: 2] [0, 1, 2] + 3 [-1: 1: 3] [] [] + 3 [-1: 1: 3] [0, 1, 2] + 3 [-1: 2:-3] [] [] + 3 [-1: 2:-3] [0, 1, 2] + 3 [-1: 2:-2] [] [] + 3 [-1: 2:-2] [0, 1, 2] + 3 [-1: 2:-1] [] [] + 3 [-1: 2:-1] [0, 1, 2] + 3 [-1: 2: 1] [] [] + 3 [-1: 2: 1] [0, 1, 2] + 3 [-1: 2: 2] [] [] + 3 [-1: 2: 2] [0, 1, 2] + 3 [-1: 2: 3] [] [] + 3 [-1: 2: 3] [0, 1, 2] + 3 [-1: 3:-3] [] [] + 3 [-1: 3:-3] [0, 1, 2] + 3 [-1: 3:-2] [] [] + 3 [-1: 3:-2] [0, 1, 2] + 3 [-1: 3:-1] [] [] + 3 [-1: 3:-1] [0, 1, 2] + 3 [-1: 3: 1] [2] [2] + 3 [-1: 3: 1] [0, 1, -1] + 3 [-1: 3: 2] [2] [2] + 3 [-1: 3: 2] [0, 1, -1] + 3 [-1: 3: 3] [2] [2] + 3 [-1: 3: 3] [0, 1, -1] + 3 [ 0:-3:-3] [] [] + 3 [ 0:-3:-3] [0, 1, 2] + 3 [ 0:-3:-2] [] [] + 3 [ 0:-3:-2] [0, 1, 2] + 3 [ 0:-3:-1] [] [] + 3 [ 0:-3:-1] [0, 1, 2] + 3 [ 0:-3: 1] [] [] + 3 [ 0:-3: 1] [0, 1, 2] + 3 [ 0:-3: 2] [] [] + 3 [ 0:-3: 2] [0, 1, 2] + 3 [ 0:-3: 3] [] [] + 3 [ 0:-3: 3] [0, 1, 2] + 3 [ 0:-2:-3] [] [] + 3 [ 0:-2:-3] [0, 1, 2] + 3 [ 0:-2:-2] [] [] + 3 [ 0:-2:-2] [0, 1, 2] + 3 [ 0:-2:-1] [] [] + 3 [ 0:-2:-1] [0, 1, 2] + 3 [ 0:-2: 1] [0] [0] + 3 [ 0:-2: 1] [-1, 1, 2] + 3 [ 0:-2: 2] [0] [0] + 3 [ 0:-2: 2] [-1, 1, 2] + 3 [ 0:-2: 3] [0] [0] + 3 [ 0:-2: 3] [-1, 1, 2] + 3 [ 0:-1:-3] [] [] + 3 [ 0:-1:-3] [0, 1, 2] + 3 [ 0:-1:-2] [] [] + 3 [ 0:-1:-2] [0, 1, 2] + 3 [ 0:-1:-1] [] [] + 3 [ 0:-1:-1] [0, 1, 2] + 3 [ 0:-1: 1] [0, 1] [0, 1] + 3 [ 0:-1: 1] [-1, -1, 2] + 3 [ 0:-1: 2] [0] [0] + 3 [ 0:-1: 2] [-1, 1, 2] + 3 [ 0:-1: 3] [0] [0] + 3 [ 0:-1: 3] [-1, 1, 2] + 3 [ 0: 0:-3] [] [] + 3 [ 0: 0:-3] [0, 1, 2] + 3 [ 0: 0:-2] [] [] + 3 [ 0: 0:-2] [0, 1, 2] + 3 [ 0: 0:-1] [] [] + 3 [ 0: 0:-1] [0, 1, 2] + 3 [ 0: 0: 1] [] [] + 3 [ 0: 0: 1] [0, 1, 2] + 3 [ 0: 0: 2] [] [] + 3 [ 0: 0: 2] [0, 1, 2] + 3 [ 0: 0: 3] [] [] + 3 [ 0: 0: 3] [0, 1, 2] + 3 [ 0: 1:-3] [] [] + 3 [ 0: 1:-3] [0, 1, 2] + 3 [ 0: 1:-2] [] [] + 3 [ 0: 1:-2] [0, 1, 2] + 3 [ 0: 1:-1] [] [] + 3 [ 0: 1:-1] [0, 1, 2] + 3 [ 0: 1: 1] [0] [0] + 3 [ 0: 1: 1] [-1, 1, 2] + 3 [ 0: 1: 2] [0] [0] + 3 [ 0: 1: 2] [-1, 1, 2] + 3 [ 0: 1: 3] [0] [0] + 3 [ 0: 1: 3] [-1, 1, 2] + 3 [ 0: 2:-3] [] [] + 3 [ 0: 2:-3] [0, 1, 2] + 3 [ 0: 2:-2] [] [] + 3 [ 0: 2:-2] [0, 1, 2] + 3 [ 0: 2:-1] [] [] + 3 [ 0: 2:-1] [0, 1, 2] + 3 [ 0: 2: 1] [0, 1] [0, 1] + 3 [ 0: 2: 1] [-1, -1, 2] + 3 [ 0: 2: 2] [0] [0] + 3 [ 0: 2: 2] [-1, 1, 2] + 3 [ 0: 2: 3] [0] [0] + 3 [ 0: 2: 3] [-1, 1, 2] + 3 [ 0: 3:-3] [] [] + 3 [ 0: 3:-3] [0, 1, 2] + 3 [ 0: 3:-2] [] [] + 3 [ 0: 3:-2] [0, 1, 2] + 3 [ 0: 3:-1] [] [] + 3 [ 0: 3:-1] [0, 1, 2] + 3 [ 0: 3: 1] [0, 1, 2] [0, 1, 2] + 3 [ 0: 3: 1] [-1, -1, -1] + 3 [ 0: 3: 2] [0, 2] [0, 2] + 3 [ 0: 3: 2] [-1, 1, -1] + 3 [ 0: 3: 3] [0] [0] + 3 [ 0: 3: 3] [-1, 1, 2] + 3 [ 1:-3:-3] [1] [1] + 3 [ 1:-3:-3] [0, -1, 2] + 3 [ 1:-3:-2] [1] [1] + 3 [ 1:-3:-2] [0, -1, 2] + 3 [ 1:-3:-1] [1] [1] + 3 [ 1:-3:-1] [0, -1, 2] + 3 [ 1:-3: 1] [] [] + 3 [ 1:-3: 1] [0, 1, 2] + 3 [ 1:-3: 2] [] [] + 3 [ 1:-3: 2] [0, 1, 2] + 3 [ 1:-3: 3] [] [] + 3 [ 1:-3: 3] [0, 1, 2] + 3 [ 1:-2:-3] [] [] + 3 [ 1:-2:-3] [0, 1, 2] + 3 [ 1:-2:-2] [] [] + 3 [ 1:-2:-2] [0, 1, 2] + 3 [ 1:-2:-1] [] [] + 3 [ 1:-2:-1] [0, 1, 2] + 3 [ 1:-2: 1] [] [] + 3 [ 1:-2: 1] [0, 1, 2] + 3 [ 1:-2: 2] [] [] + 3 [ 1:-2: 2] [0, 1, 2] + 3 [ 1:-2: 3] [] [] + 3 [ 1:-2: 3] [0, 1, 2] + 3 [ 1:-1:-3] [] [] + 3 [ 1:-1:-3] [0, 1, 2] + 3 [ 1:-1:-2] [] [] + 3 [ 1:-1:-2] [0, 1, 2] + 3 [ 1:-1:-1] [] [] + 3 [ 1:-1:-1] [0, 1, 2] + 3 [ 1:-1: 1] [1] [1] + 3 [ 1:-1: 1] [0, -1, 2] + 3 [ 1:-1: 2] [1] [1] + 3 [ 1:-1: 2] [0, -1, 2] + 3 [ 1:-1: 3] [1] [1] + 3 [ 1:-1: 3] [0, -1, 2] + 3 [ 1: 0:-3] [1] [1] + 3 [ 1: 0:-3] [0, -1, 2] + 3 [ 1: 0:-2] [1] [1] + 3 [ 1: 0:-2] [0, -1, 2] + 3 [ 1: 0:-1] [1] [1] + 3 [ 1: 0:-1] [0, -1, 2] + 3 [ 1: 0: 1] [] [] + 3 [ 1: 0: 1] [0, 1, 2] + 3 [ 1: 0: 2] [] [] + 3 [ 1: 0: 2] [0, 1, 2] + 3 [ 1: 0: 3] [] [] + 3 [ 1: 0: 3] [0, 1, 2] + 3 [ 1: 1:-3] [] [] + 3 [ 1: 1:-3] [0, 1, 2] + 3 [ 1: 1:-2] [] [] + 3 [ 1: 1:-2] [0, 1, 2] + 3 [ 1: 1:-1] [] [] + 3 [ 1: 1:-1] [0, 1, 2] + 3 [ 1: 1: 1] [] [] + 3 [ 1: 1: 1] [0, 1, 2] + 3 [ 1: 1: 2] [] [] + 3 [ 1: 1: 2] [0, 1, 2] + 3 [ 1: 1: 3] [] [] + 3 [ 1: 1: 3] [0, 1, 2] + 3 [ 1: 2:-3] [] [] + 3 [ 1: 2:-3] [0, 1, 2] + 3 [ 1: 2:-2] [] [] + 3 [ 1: 2:-2] [0, 1, 2] + 3 [ 1: 2:-1] [] [] + 3 [ 1: 2:-1] [0, 1, 2] + 3 [ 1: 2: 1] [1] [1] + 3 [ 1: 2: 1] [0, -1, 2] + 3 [ 1: 2: 2] [1] [1] + 3 [ 1: 2: 2] [0, -1, 2] + 3 [ 1: 2: 3] [1] [1] + 3 [ 1: 2: 3] [0, -1, 2] + 3 [ 1: 3:-3] [] [] + 3 [ 1: 3:-3] [0, 1, 2] + 3 [ 1: 3:-2] [] [] + 3 [ 1: 3:-2] [0, 1, 2] + 3 [ 1: 3:-1] [] [] + 3 [ 1: 3:-1] [0, 1, 2] + 3 [ 1: 3: 1] [1, 2] [1, 2] + 3 [ 1: 3: 1] [0, -1, -1] + 3 [ 1: 3: 2] [1] [1] + 3 [ 1: 3: 2] [0, -1, 2] + 3 [ 1: 3: 3] [1] [1] + 3 [ 1: 3: 3] [0, -1, 2] + 3 [ 2:-3:-3] [2] [2] + 3 [ 2:-3:-3] [0, 1, -1] + 3 [ 2:-3:-2] [2] [2] + 3 [ 2:-3:-2] [0, 1, -1] + 3 [ 2:-3:-1] [2, 1] [2, 1] + 3 [ 2:-3:-1] [0, -1, -1] + 3 [ 2:-3: 1] [] [] + 3 [ 2:-3: 1] [0, 1, 2] + 3 [ 2:-3: 2] [] [] + 3 [ 2:-3: 2] [0, 1, 2] + 3 [ 2:-3: 3] [] [] + 3 [ 2:-3: 3] [0, 1, 2] + 3 [ 2:-2:-3] [2] [2] + 3 [ 2:-2:-3] [0, 1, -1] + 3 [ 2:-2:-2] [2] [2] + 3 [ 2:-2:-2] [0, 1, -1] + 3 [ 2:-2:-1] [2] [2] + 3 [ 2:-2:-1] [0, 1, -1] + 3 [ 2:-2: 1] [] [] + 3 [ 2:-2: 1] [0, 1, 2] + 3 [ 2:-2: 2] [] [] + 3 [ 2:-2: 2] [0, 1, 2] + 3 [ 2:-2: 3] [] [] + 3 [ 2:-2: 3] [0, 1, 2] + 3 [ 2:-1:-3] [] [] + 3 [ 2:-1:-3] [0, 1, 2] + 3 [ 2:-1:-2] [] [] + 3 [ 2:-1:-2] [0, 1, 2] + 3 [ 2:-1:-1] [] [] + 3 [ 2:-1:-1] [0, 1, 2] + 3 [ 2:-1: 1] [] [] + 3 [ 2:-1: 1] [0, 1, 2] + 3 [ 2:-1: 2] [] [] + 3 [ 2:-1: 2] [0, 1, 2] + 3 [ 2:-1: 3] [] [] + 3 [ 2:-1: 3] [0, 1, 2] + 3 [ 2: 0:-3] [2] [2] + 3 [ 2: 0:-3] [0, 1, -1] + 3 [ 2: 0:-2] [2] [2] + 3 [ 2: 0:-2] [0, 1, -1] + 3 [ 2: 0:-1] [2, 1] [2, 1] + 3 [ 2: 0:-1] [0, -1, -1] + 3 [ 2: 0: 1] [] [] + 3 [ 2: 0: 1] [0, 1, 2] + 3 [ 2: 0: 2] [] [] + 3 [ 2: 0: 2] [0, 1, 2] + 3 [ 2: 0: 3] [] [] + 3 [ 2: 0: 3] [0, 1, 2] + 3 [ 2: 1:-3] [2] [2] + 3 [ 2: 1:-3] [0, 1, -1] + 3 [ 2: 1:-2] [2] [2] + 3 [ 2: 1:-2] [0, 1, -1] + 3 [ 2: 1:-1] [2] [2] + 3 [ 2: 1:-1] [0, 1, -1] + 3 [ 2: 1: 1] [] [] + 3 [ 2: 1: 1] [0, 1, 2] + 3 [ 2: 1: 2] [] [] + 3 [ 2: 1: 2] [0, 1, 2] + 3 [ 2: 1: 3] [] [] + 3 [ 2: 1: 3] [0, 1, 2] + 3 [ 2: 2:-3] [] [] + 3 [ 2: 2:-3] [0, 1, 2] + 3 [ 2: 2:-2] [] [] + 3 [ 2: 2:-2] [0, 1, 2] + 3 [ 2: 2:-1] [] [] + 3 [ 2: 2:-1] [0, 1, 2] + 3 [ 2: 2: 1] [] [] + 3 [ 2: 2: 1] [0, 1, 2] + 3 [ 2: 2: 2] [] [] + 3 [ 2: 2: 2] [0, 1, 2] + 3 [ 2: 2: 3] [] [] + 3 [ 2: 2: 3] [0, 1, 2] + 3 [ 2: 3:-3] [] [] + 3 [ 2: 3:-3] [0, 1, 2] + 3 [ 2: 3:-2] [] [] + 3 [ 2: 3:-2] [0, 1, 2] + 3 [ 2: 3:-1] [] [] + 3 [ 2: 3:-1] [0, 1, 2] + 3 [ 2: 3: 1] [2] [2] + 3 [ 2: 3: 1] [0, 1, -1] + 3 [ 2: 3: 2] [2] [2] + 3 [ 2: 3: 2] [0, 1, -1] + 3 [ 2: 3: 3] [2] [2] + 3 [ 2: 3: 3] [0, 1, -1] + 3 [ 3:-3:-3] [2] [2] + 3 [ 3:-3:-3] [0, 1, -1] + 3 [ 3:-3:-2] [2] [2] + 3 [ 3:-3:-2] [0, 1, -1] + 3 [ 3:-3:-1] [2, 1] [2, 1] + 3 [ 3:-3:-1] [0, -1, -1] + 3 [ 3:-3: 1] [] [] + 3 [ 3:-3: 1] [0, 1, 2] + 3 [ 3:-3: 2] [] [] + 3 [ 3:-3: 2] [0, 1, 2] + 3 [ 3:-3: 3] [] [] + 3 [ 3:-3: 3] [0, 1, 2] + 3 [ 3:-2:-3] [2] [2] + 3 [ 3:-2:-3] [0, 1, -1] + 3 [ 3:-2:-2] [2] [2] + 3 [ 3:-2:-2] [0, 1, -1] + 3 [ 3:-2:-1] [2] [2] + 3 [ 3:-2:-1] [0, 1, -1] + 3 [ 3:-2: 1] [] [] + 3 [ 3:-2: 1] [0, 1, 2] + 3 [ 3:-2: 2] [] [] + 3 [ 3:-2: 2] [0, 1, 2] + 3 [ 3:-2: 3] [] [] + 3 [ 3:-2: 3] [0, 1, 2] + 3 [ 3:-1:-3] [] [] + 3 [ 3:-1:-3] [0, 1, 2] + 3 [ 3:-1:-2] [] [] + 3 [ 3:-1:-2] [0, 1, 2] + 3 [ 3:-1:-1] [] [] + 3 [ 3:-1:-1] [0, 1, 2] + 3 [ 3:-1: 1] [] [] + 3 [ 3:-1: 1] [0, 1, 2] + 3 [ 3:-1: 2] [] [] + 3 [ 3:-1: 2] [0, 1, 2] + 3 [ 3:-1: 3] [] [] + 3 [ 3:-1: 3] [0, 1, 2] + 3 [ 3: 0:-3] [2] [2] + 3 [ 3: 0:-3] [0, 1, -1] + 3 [ 3: 0:-2] [2] [2] + 3 [ 3: 0:-2] [0, 1, -1] + 3 [ 3: 0:-1] [2, 1] [2, 1] + 3 [ 3: 0:-1] [0, -1, -1] + 3 [ 3: 0: 1] [] [] + 3 [ 3: 0: 1] [0, 1, 2] + 3 [ 3: 0: 2] [] [] + 3 [ 3: 0: 2] [0, 1, 2] + 3 [ 3: 0: 3] [] [] + 3 [ 3: 0: 3] [0, 1, 2] + 3 [ 3: 1:-3] [2] [2] + 3 [ 3: 1:-3] [0, 1, -1] + 3 [ 3: 1:-2] [2] [2] + 3 [ 3: 1:-2] [0, 1, -1] + 3 [ 3: 1:-1] [2] [2] + 3 [ 3: 1:-1] [0, 1, -1] + 3 [ 3: 1: 1] [] [] + 3 [ 3: 1: 1] [0, 1, 2] + 3 [ 3: 1: 2] [] [] + 3 [ 3: 1: 2] [0, 1, 2] + 3 [ 3: 1: 3] [] [] + 3 [ 3: 1: 3] [0, 1, 2] + 3 [ 3: 2:-3] [] [] + 3 [ 3: 2:-3] [0, 1, 2] + 3 [ 3: 2:-2] [] [] + 3 [ 3: 2:-2] [0, 1, 2] + 3 [ 3: 2:-1] [] [] + 3 [ 3: 2:-1] [0, 1, 2] + 3 [ 3: 2: 1] [] [] + 3 [ 3: 2: 1] [0, 1, 2] + 3 [ 3: 2: 2] [] [] + 3 [ 3: 2: 2] [0, 1, 2] + 3 [ 3: 2: 3] [] [] + 3 [ 3: 2: 3] [0, 1, 2] + 3 [ 3: 3:-3] [] [] + 3 [ 3: 3:-3] [0, 1, 2] + 3 [ 3: 3:-2] [] [] + 3 [ 3: 3:-2] [0, 1, 2] + 3 [ 3: 3:-1] [] [] + 3 [ 3: 3:-1] [0, 1, 2] + 3 [ 3: 3: 1] [] [] + 3 [ 3: 3: 1] [0, 1, 2] + 3 [ 3: 3: 2] [] [] + 3 [ 3: 3: 2] [0, 1, 2] + 3 [ 3: 3: 3] [] [] + 3 [ 3: 3: 3] [0, 1, 2] diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/slicing2.py b/circuitpython/extmod/ulab/tests/1d/numpy/slicing2.py new file mode 100644 index 0000000..05b2d79 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/slicing2.py @@ -0,0 +1,8 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +a = np.array(range(9), dtype=np.float) +print("a:\t", list(a)) +print("a < 5:\t", list(a[a < 5])) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/slicing2.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/slicing2.py.exp new file mode 100644 index 0000000..2c94646 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/slicing2.py.exp @@ -0,0 +1,2 @@ +a: [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0] +a < 5: [0.0, 1.0, 2.0, 3.0, 4.0] diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/sum.py b/circuitpython/extmod/ulab/tests/1d/numpy/sum.py new file mode 100644 index 0000000..a029313 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/sum.py @@ -0,0 +1,21 @@ +from ulab import numpy as np + +r = range(15) + +a = np.array(r, dtype=np.uint8) +print(np.sum(a)) + +a = np.array(r, dtype=np.int8) +print(np.sum(a)) + +a = np.array(r, dtype=np.uint16) +print(np.sum(a)) + +a = np.array(r, dtype=np.int16) +print(np.sum(a)) + +a = np.array(r, dtype=np.float) +print(np.sum(a)) + +a = np.array([False] + [True]*15, dtype=np.bool) +print(np.sum(a)) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/sum.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/sum.py.exp new file mode 100644 index 0000000..7f1b801 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/sum.py.exp @@ -0,0 +1,6 @@ +105 +105 +105 +105 +105.0 +15 diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/trapz.py b/circuitpython/extmod/ulab/tests/1d/numpy/trapz.py new file mode 100644 index 0000000..7060c12 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/trapz.py @@ -0,0 +1,9 @@ +try: + from ulab import numpy as np +except ImportError: + import numpy as np + +x = np.linspace(0, 9, num=10) +y = x*x +print(np.trapz(y)) +print(np.trapz(y, x=x)) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/trapz.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/trapz.py.exp new file mode 100644 index 0000000..3084186 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/trapz.py.exp @@ -0,0 +1,2 @@ +244.5 +244.5 diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/universal_functions.py b/circuitpython/extmod/ulab/tests/1d/numpy/universal_functions.py new file mode 100644 index 0000000..1dc3b60 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/universal_functions.py @@ -0,0 +1,141 @@ +import math + +try: + from ulab import numpy as np + from ulab import scipy as spy +except ImportError: + import numpy as np + import scipy as spy + +result = (np.sin(np.pi/2)) +ref_result = 1.0 +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.cos(np.pi/2)) +ref_result = 0.0 +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.tan(np.pi/2)) +ref_result = 1.633123935319537e+16 +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.sinh(np.pi/2)) +ref_result = 2.3012989023072947 +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.cosh(np.pi/2)) +ref_result = 2.5091784786580567 +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.tanh(np.pi/2)) +ref_result = 0.9171523356672744 +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +ref_result = np.pi/2 +result = (np.asin(np.sin(np.pi/2))) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.acos(np.cos(np.pi/2))) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.atan(np.tan(np.pi/2))) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.cosh(np.acosh(np.pi/2))) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +result = (np.sinh(np.asinh(np.pi/2))) +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +print(np.degrees(np.pi)) +print(np.radians(np.degrees(np.pi))) +print(np.floor(np.pi)) +print(np.ceil(np.pi)) +print(np.sqrt(np.pi)) +print(np.exp(1)) +print(np.log(np.exp(1))) + +print(np.log2(2**1)) + +print(np.log10(10**1)) +print(np.exp(1) - np.expm1(1)) + +x = np.array([-1, +1, +1, -1]) +y = np.array([-1, -1, +1, +1]) +result = (np.arctan2(y, x) * 180 / np.pi) +ref_result = np.array([-135.0, -45.0, 45.0, 135.0], dtype=np.float) +cmp_result = [] +for i in range(len(x)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +x = np.linspace(-2*np.pi, 2*np.pi, 5) +result = np.sin(x) +ref_result = np.array([2.4492936e-16, -1.2246468e-16, 0.0000000e+00, 1.2246468e-16, -2.4492936e-16], dtype=np.float) +cmp_result = [] +for i in range(len(x)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +result = np.cos(x) +ref_result = np.array([1., -1., 1., -1., 1.], dtype=np.float) +cmp_result = [] +for i in range(len(x)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +result = np.tan(x) +ref_result = np.array([2.4492936e-16, 1.2246468e-16, 0.0000000e+00, -1.2246468e-16, -2.4492936e-16], dtype=np.float) +cmp_result = [] +for i in range(len(x)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +result = np.sinh(x) +ref_result = np.array([-267.74489404, -11.54873936, 0., 11.54873936, 267.74489404], dtype=np.float) +cmp_result = [] +for i in range(len(x)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +result = np.cosh(x) +ref_result = np.array([267.74676148, 11.59195328, 1.0, 11.59195328, 267.74676148], dtype=np.float) +cmp_result = [] +for i in range(len(x)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +result = np.tanh(x) +ref_result = np.array([-0.9999930253396107, -0.99627207622075, 0.0, 0.99627207622075, 0.9999930253396107], dtype=np.float) +cmp_result = [] +for i in range(len(x)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +result = (spy.special.erf(np.linspace(-3, 3, num=5))) +ref_result = np.array([-0.9999779095030014, -0.9661051464753108, 0.0, 0.9661051464753108, 0.9999779095030014], dtype=np.float) +cmp_result = [] +for i in range(len(ref_result)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +result = (spy.special.erfc(np.linspace(-3, 3, num=5))) +ref_result = np.array([1.99997791e+00, 1.96610515e+00, 1.00000000e+00, 3.38948535e-02, 2.20904970e-05], dtype=np.float) +cmp_result = [] +for i in range(len(ref_result)): + cmp_result.append(math.isclose(result[i], ref_result[i], rel_tol=1E-6, abs_tol=1E-6)) +print(cmp_result) + +result = (spy.special.gamma(np.array([0, 0.5, 1, 5]))) +ref_result = np.array([1.77245385, 1.0, 24.0]) +cmp_result = [] +cmp_result.append(math.isinf(result[0])) +for i in range(len(ref_result)): + cmp_result.append(math.isclose(result[i+1], ref_result[i], rel_tol=1E-9, abs_tol=1E-9)) +print(cmp_result) + +result = (spy.special.gammaln([0, -1, -2, -3, -4])) +cmp_result = [] +for i in range(len(ref_result)): + cmp_result.append(math.isinf(result[i])) +print(cmp_result) diff --git a/circuitpython/extmod/ulab/tests/1d/numpy/universal_functions.py.exp b/circuitpython/extmod/ulab/tests/1d/numpy/universal_functions.py.exp new file mode 100644 index 0000000..2931d6c --- /dev/null +++ b/circuitpython/extmod/ulab/tests/1d/numpy/universal_functions.py.exp @@ -0,0 +1,32 @@ +True +True +True +True +True +True +True +True +True +True +True +180.0 +3.141592653589793 +3.0 +4.0 +1.772453850905516 +2.718281828459045 +1.0 +1.0 +1.0 +1.0 +[True, True, True, True] +[True, True, True, True, True] +[True, True, True, True, True] +[True, True, True, True, True] +[True, True, True, True, True] +[True, True, True, True, True] +[True, True, True, True, True] +[True, True, True, True, True] +[True, True, True, True, True] +[True, True, True, True] +[True, True, True] diff --git a/circuitpython/extmod/ulab/tests/2d/complex/binary_op.py b/circuitpython/extmod/ulab/tests/2d/complex/binary_op.py new file mode 100644 index 0000000..36efa76 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/binary_op.py @@ -0,0 +1,26 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +n = 5 +a = np.array(range(n), dtype=np.complex) +c = np.array(range(n), dtype=np.complex) + +print(a == c) +print(a != c) +print() + +c = np.array(range(n), dtype=np.complex) * 1j +print(a == c) +print(a != c) +print() + +for dtype in dtypes: + b = np.array(range(n), dtype=dtype) + print(b == a) + print(b != a) + print() + diff --git a/circuitpython/extmod/ulab/tests/2d/complex/binary_op.py.exp b/circuitpython/extmod/ulab/tests/2d/complex/binary_op.py.exp new file mode 100644 index 0000000..ef92f16 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/binary_op.py.exp @@ -0,0 +1,21 @@ +array([True, True, True, True, True], dtype=bool) +array([False, False, False, False, False], dtype=bool) + +array([True, False, False, False, False], dtype=bool) +array([False, True, True, True, True], dtype=bool) + +array([True, True, True, True, True], dtype=bool) +array([False, False, False, False, False], dtype=bool) + +array([True, True, True, True, True], dtype=bool) +array([False, False, False, False, False], dtype=bool) + +array([True, True, True, True, True], dtype=bool) +array([False, False, False, False, False], dtype=bool) + +array([True, True, True, True, True], dtype=bool) +array([False, False, False, False, False], dtype=bool) + +array([True, True, True, True, True], dtype=bool) +array([False, False, False, False, False], dtype=bool) + diff --git a/circuitpython/extmod/ulab/tests/2d/complex/complex_exp.py b/circuitpython/extmod/ulab/tests/2d/complex/complex_exp.py new file mode 100644 index 0000000..90b3adf --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/complex_exp.py @@ -0,0 +1,24 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(4), dtype=dtype) + b = a.reshape((2, 2)) + print('\narray:\n', a) + print('\nexponential:\n', np.exp(a)) + print('\narray:\n', b) + print('\nexponential:\n', np.exp(b)) + +b = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +print('\narray:\n', b) +print('\nexponential:\n', np.exp(b)) + +b = np.array([[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]], dtype=np.complex) +print('\narray:\n', b) +print('\nexponential:\n', np.exp(b))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/complex/complex_exp.py.exp b/circuitpython/extmod/ulab/tests/2d/complex/complex_exp.py.exp new file mode 100644 index 0000000..3f7c0af --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/complex_exp.py.exp @@ -0,0 +1,98 @@ + +array: + array([0, 1, 2, 3], dtype=uint8) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=uint8) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int8) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=int8) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=uint16) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=uint16) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int16) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=int16) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0.0, 1.0], + [2.0, 3.0]], dtype=float64) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], dtype=complex) + +exponential: + array([1.0+0.0j, 2.718281828459045+0.0j, 7.38905609893065+0.0j, 20.08553692318767+0.0j], dtype=complex) + +array: + array([[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], dtype=complex) + +exponential: + array([[1.0+0.0j, 2.718281828459045+0.0j], + [7.38905609893065+0.0j, 20.08553692318767+0.0j]], dtype=complex) + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +exponential: + array([1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], dtype=complex) + +array: + array([[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], dtype=complex) + +exponential: + array([[1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], + [1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/2d/complex/complex_sqrt.py b/circuitpython/extmod/ulab/tests/2d/complex/complex_sqrt.py new file mode 100644 index 0000000..5baebb5 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/complex_sqrt.py @@ -0,0 +1,25 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(4), dtype=dtype) + b = a.reshape((2, 2)) + outtype = np.float if dtype is not np.complex else np.complex + print('\narray:\n', a) + print('\nsquare root:\n', np.sqrt(a, dtype=outtype)) + print('\narray:\n', b) + print('\nsquare root:\n', np.sqrt(b, dtype=outtype)) + +b = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +print('\narray:\n', b) +print('\nsquare root:\n', np.sqrt(b, dtype=np.complex)) + +b = np.array([[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]], dtype=np.complex) +print('\narray:\n', b) +print('\nsquare root:\n', np.sqrt(b, dtype=np.complex)) diff --git a/circuitpython/extmod/ulab/tests/2d/complex/complex_sqrt.py.exp b/circuitpython/extmod/ulab/tests/2d/complex/complex_sqrt.py.exp new file mode 100644 index 0000000..30cb5e5 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/complex_sqrt.py.exp @@ -0,0 +1,98 @@ + +array: + array([0, 1, 2, 3], dtype=uint8) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=uint8) + +square root: + array([[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int8) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=int8) + +square root: + array([[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=uint16) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=uint16) + +square root: + array([[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int16) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=int16) + +square root: + array([[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], dtype=float64) + +array: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877], dtype=float64) + +array: + array([[0.0, 1.0], + [2.0, 3.0]], dtype=float64) + +square root: + array([[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], dtype=float64) + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], dtype=complex) + +square root: + array([0.0+0.0j, 1.0+0.0j, 1.414213562373095+0.0j, 1.732050807568877+0.0j], dtype=complex) + +array: + array([[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], dtype=complex) + +square root: + array([[0.0+0.0j, 1.0+0.0j], + [1.414213562373095+0.0j, 1.732050807568877+0.0j]], dtype=complex) + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +square root: + array([0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j], dtype=complex) + +array: + array([[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], dtype=complex) + +square root: + array([[0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j], + [0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/2d/complex/conjugate.py b/circuitpython/extmod/ulab/tests/2d/complex/conjugate.py new file mode 100644 index 0000000..eafaf57 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/conjugate.py @@ -0,0 +1,12 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + print(np.conjugate(np.array(range(5), dtype=dtype))) + +a = np.array([1, 2+2j, 3-3j, 4j], dtype=np.complex) +print(np.conjugate(a))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/complex/conjugate.py.exp b/circuitpython/extmod/ulab/tests/2d/complex/conjugate.py.exp new file mode 100644 index 0000000..4f9a8bb --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/conjugate.py.exp @@ -0,0 +1,7 @@ +array([0, 1, 2, 3, 4], dtype=uint8) +array([0, 1, 2, 3, 4], dtype=int8) +array([0, 1, 2, 3, 4], dtype=uint16) +array([0, 1, 2, 3, 4], dtype=int16) +array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) +array([0.0+-0.0j, 1.0+-0.0j, 2.0+-0.0j, 3.0+-0.0j, 4.0+-0.0j], dtype=complex) +array([1.0+-0.0j, 2.0-2.0j, 3.0+3.0j, 0.0-4.0j], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/2d/complex/imag_real.py b/circuitpython/extmod/ulab/tests/2d/complex/imag_real.py new file mode 100644 index 0000000..536d729 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/imag_real.py @@ -0,0 +1,28 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(4), dtype=dtype) + b = a.reshape((2, 2)) + print('\narray:\n', a) + print('\nreal part:\n', np.real(a)) + print('\nimaginary part:\n', np.imag(a)) + print('\narray:\n', b) + print('\nreal part:\n', np.real(b)) + print('\nimaginary part:\n', np.imag(b), '\n') + + +b = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +print('\nreal part:\n', np.real(b)) +print('\nimaginary part:\n', np.imag(b)) + +b = np.array([[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]], dtype=np.complex) +print('\nreal part:\n', np.real(b)) +print('\nimaginary part:\n', np.imag(b)) + diff --git a/circuitpython/extmod/ulab/tests/2d/complex/imag_real.py.exp b/circuitpython/extmod/ulab/tests/2d/complex/imag_real.py.exp new file mode 100644 index 0000000..3df1561 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/imag_real.py.exp @@ -0,0 +1,146 @@ + +array: + array([0, 1, 2, 3], dtype=uint8) + +real part: + array([0, 1, 2, 3], dtype=uint8) + +imaginary part: + array([0, 0, 0, 0], dtype=uint8) + +array: + array([[0, 1], + [2, 3]], dtype=uint8) + +real part: + array([[0, 1], + [2, 3]], dtype=uint8) + +imaginary part: + array([[0, 0], + [0, 0]], dtype=uint8) + + +array: + array([0, 1, 2, 3], dtype=int8) + +real part: + array([0, 1, 2, 3], dtype=int8) + +imaginary part: + array([0, 0, 0, 0], dtype=int8) + +array: + array([[0, 1], + [2, 3]], dtype=int8) + +real part: + array([[0, 1], + [2, 3]], dtype=int8) + +imaginary part: + array([[0, 0], + [0, 0]], dtype=int8) + + +array: + array([0, 1, 2, 3], dtype=uint16) + +real part: + array([0, 1, 2, 3], dtype=uint16) + +imaginary part: + array([0, 0, 0, 0], dtype=uint16) + +array: + array([[0, 1], + [2, 3]], dtype=uint16) + +real part: + array([[0, 1], + [2, 3]], dtype=uint16) + +imaginary part: + array([[0, 0], + [0, 0]], dtype=uint16) + + +array: + array([0, 1, 2, 3], dtype=int16) + +real part: + array([0, 1, 2, 3], dtype=int16) + +imaginary part: + array([0, 0, 0, 0], dtype=int16) + +array: + array([[0, 1], + [2, 3]], dtype=int16) + +real part: + array([[0, 1], + [2, 3]], dtype=int16) + +imaginary part: + array([[0, 0], + [0, 0]], dtype=int16) + + +array: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +real part: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +imaginary part: + array([0.0, 0.0, 0.0, 0.0], dtype=float64) + +array: + array([[0.0, 1.0], + [2.0, 3.0]], dtype=float64) + +real part: + array([[0.0, 1.0], + [2.0, 3.0]], dtype=float64) + +imaginary part: + array([[0.0, 0.0], + [0.0, 0.0]], dtype=float64) + + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], dtype=complex) + +real part: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +imaginary part: + array([0.0, 0.0, 0.0, 0.0], dtype=float64) + +array: + array([[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], dtype=complex) + +real part: + array([[0.0, 1.0], + [2.0, 3.0]], dtype=float64) + +imaginary part: + array([[0.0, 0.0], + [0.0, 0.0]], dtype=float64) + + +real part: + array([0.0, 0.0, 2.0, 3.0], dtype=float64) + +imaginary part: + array([0.0, 1.0, 2.0, -3.0], dtype=float64) + +real part: + array([[0.0, 0.0, 2.0, 3.0], + [0.0, 0.0, 2.0, 3.0]], dtype=float64) + +imaginary part: + array([[0.0, 1.0, 2.0, -3.0], + [0.0, 1.0, 2.0, -3.0]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/complex/sort_complex.py b/circuitpython/extmod/ulab/tests/2d/complex/sort_complex.py new file mode 100644 index 0000000..1ac1edc --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/sort_complex.py @@ -0,0 +1,26 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + print(np.sort_complex(np.array(range(5, 0, -1), dtype=dtype))) + +print() +n = 6 +a = np.array(range(n, 0, -1)) * 1j +b = np.array([1] * n) +print(np.sort_complex(a + b)) + +a = np.array(range(n)) * 1j +b = np.array([1] * n) +print(np.sort_complex(a + b)) + +print() +a = np.array([0, -3j, 1+2j, 1-2j, 2j], dtype=np.complex) +print(np.sort_complex(a)) + +a = np.array([0, 3j, 1-2j, 1+2j, -2j], dtype=np.complex) +print(np.sort_complex(a)) diff --git a/circuitpython/extmod/ulab/tests/2d/complex/sort_complex.py.exp b/circuitpython/extmod/ulab/tests/2d/complex/sort_complex.py.exp new file mode 100644 index 0000000..9026e4a --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/complex/sort_complex.py.exp @@ -0,0 +1,12 @@ +array([1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j], dtype=complex) +array([1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j], dtype=complex) +array([1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j], dtype=complex) +array([1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j], dtype=complex) +array([1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j], dtype=complex) +array([1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j], dtype=complex) + +array([1.0+1.0j, 1.0+2.0j, 1.0+3.0j, 1.0+4.0j, 1.0+5.0j, 1.0+6.0j], dtype=complex) +array([1.0+0.0j, 1.0+1.0j, 1.0+2.0j, 1.0+3.0j, 1.0+4.0j, 1.0+5.0j], dtype=complex) + +array([-0.0-3.0j, 0.0+0.0j, 0.0+2.0j, 1.0-2.0j, 1.0+2.0j], dtype=complex) +array([-0.0-2.0j, 0.0+0.0j, 0.0+3.0j, 1.0-2.0j, 1.0+2.0j], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/00smoke.py b/circuitpython/extmod/ulab/tests/2d/numpy/00smoke.py new file mode 100644 index 0000000..bc7dcf8 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/00smoke.py @@ -0,0 +1,3 @@ +from ulab import numpy as np + +print(np.eye(3)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/00smoke.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/00smoke.py.exp new file mode 100644 index 0000000..dd49fad --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/00smoke.py.exp @@ -0,0 +1,3 @@ +array([[1.0, 0.0, 0.0], + [0.0, 1.0, 0.0], + [0.0, 0.0, 1.0]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/any_all.py b/circuitpython/extmod/ulab/tests/2d/numpy/any_all.py new file mode 100644 index 0000000..08788bc --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/any_all.py @@ -0,0 +1,11 @@ +from ulab import numpy as np + +a = np.array(range(12)).reshape((3, 4)) + +print(np.all(a)) +print(np.all(a, axis=0)) +print(np.all(a, axis=1)) + +print(np.any(a)) +print(np.any(a, axis=0)) +print(np.any(a, axis=1))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/any_all.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/any_all.py.exp new file mode 100644 index 0000000..be72280 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/any_all.py.exp @@ -0,0 +1,6 @@ +False +array([False, True, True, True], dtype=bool) +array([False, True, True], dtype=bool) +True +array([True, True, True, True], dtype=bool) +array([True, True, True], dtype=bool) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/arange.py b/circuitpython/extmod/ulab/tests/2d/numpy/arange.py new file mode 100644 index 0000000..91d21fe --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/arange.py @@ -0,0 +1,11 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +for dtype in dtypes: + print(np.arange(10, dtype=dtype)) + print(np.arange(2, 10, dtype=dtype)) + print(np.arange(2, 10, 3, dtype=dtype))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/arange.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/arange.py.exp new file mode 100644 index 0000000..894e008 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/arange.py.exp @@ -0,0 +1,15 @@ +array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8) +array([2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8) +array([2, 5, 8], dtype=uint8) +array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int8) +array([2, 3, 4, 5, 6, 7, 8, 9], dtype=int8) +array([2, 5, 8], dtype=int8) +array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint16) +array([2, 3, 4, 5, 6, 7, 8, 9], dtype=uint16) +array([2, 5, 8], dtype=uint16) +array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int16) +array([2, 3, 4, 5, 6, 7, 8, 9], dtype=int16) +array([2, 5, 8], dtype=int16) +array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64) +array([2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64) +array([2.0, 5.0, 8.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/buffer.py b/circuitpython/extmod/ulab/tests/2d/numpy/buffer.py new file mode 100644 index 0000000..5cce5b9 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/buffer.py @@ -0,0 +1,17 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +def print_as_buffer(a): + print(len(memoryview(a)), list(memoryview(a))) +print_as_buffer(np.ones(3)) +print_as_buffer(np.zeros(3)) +print_as_buffer(np.eye(4)) +print_as_buffer(np.ones(1, dtype=np.int8)) +print_as_buffer(np.ones(2, dtype=np.uint8)) +print_as_buffer(np.ones(3, dtype=np.int16)) +print_as_buffer(np.ones(4, dtype=np.uint16)) +print_as_buffer(np.ones(5, dtype=np.float)) +print_as_buffer(np.linspace(0, 1, 9)) + diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/buffer.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/buffer.py.exp new file mode 100644 index 0000000..f5fb3d4 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/buffer.py.exp @@ -0,0 +1,9 @@ +3 [1.0, 1.0, 1.0] +3 [0.0, 0.0, 0.0] +16 [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0] +1 [1] +2 [1, 1] +3 [1, 1, 1] +4 [1, 1, 1, 1] +5 [1.0, 1.0, 1.0, 1.0, 1.0] +9 [0.0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0] diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/cholesky.py b/circuitpython/extmod/ulab/tests/2d/numpy/cholesky.py new file mode 100644 index 0000000..beab3c1 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/cholesky.py @@ -0,0 +1,14 @@ +from ulab import numpy as np + +a = np.array([[1, 2], [2, 5]]) +print(np.linalg.cholesky(a)) + +b = a = np.array([[25, 15, -5], [15, 18, 0], [-5, 0, 11]]) +print(np.linalg.cholesky(b)) + +c = np.array([[18, 22, 54, 42], [22, 70, 86, 62], [54, 86, 174, 134], [42, 62, 134, 106]]) +print(np.linalg.cholesky(c)) + + + + diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/cholesky.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/cholesky.py.exp new file mode 100644 index 0000000..a8e88ef --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/cholesky.py.exp @@ -0,0 +1,9 @@ +array([[1.0, 0.0], + [2.0, 1.0]], dtype=float64) +array([[5.0, 0.0, 0.0], + [3.0, 3.0, 0.0], + [-1.0, 1.0, 3.0]], dtype=float64) +array([[4.242640687119285, 0.0, 0.0, 0.0], + [5.185449728701349, 6.565905201197403, 0.0, 0.0], + [12.72792206135786, 3.046038495400855, 1.649742247909068, 0.0], + [9.899494936611665, 1.624553864213789, 1.849711005231386, 1.392621247645583]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/concatenate.py b/circuitpython/extmod/ulab/tests/2d/numpy/concatenate.py new file mode 100644 index 0000000..bcae97a --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/concatenate.py @@ -0,0 +1,18 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +a = np.array([1,2,3], dtype=np.float) +b = np.array([4,5,6], dtype=np.float) + +print(np.concatenate((a,b))) +print(np.concatenate((a,b), axis=0)) + +a = np.array([[1,2,3],[4,5,6],[7,8,9]], dtype=np.float) +b = np.array([[1,2,3],[4,5,6],[7,8,9]], dtype=np.float) + +print(np.concatenate((a,b), axis=0)) +print(np.concatenate((a,b), axis=1)) +print(np.concatenate((b,a), axis=0)) +print(np.concatenate((b,a), axis=1)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/concatenate.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/concatenate.py.exp new file mode 100644 index 0000000..4310f35 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/concatenate.py.exp @@ -0,0 +1,20 @@ +array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float64) +array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float64) +array([[1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0], + [1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0]], dtype=float64) +array([[1.0, 2.0, 3.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 4.0, 5.0, 6.0], + [7.0, 8.0, 9.0, 7.0, 8.0, 9.0]], dtype=float64) +array([[1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0], + [1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0]], dtype=float64) +array([[1.0, 2.0, 3.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 4.0, 5.0, 6.0], + [7.0, 8.0, 9.0, 7.0, 8.0, 9.0]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/constructors.py b/circuitpython/extmod/ulab/tests/2d/numpy/constructors.py new file mode 100644 index 0000000..dad3db2 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/constructors.py @@ -0,0 +1,13 @@ +from ulab import numpy as np + +print(np.ones(3)) +print(np.ones((2,3))) +print(np.zeros(3)) +print(np.zeros((2,3))) +print(np.eye(3)) +print(np.ones(1, dtype=np.int8)) +print(np.ones(2, dtype=np.uint8)) +print(np.ones(3, dtype=np.int16)) +print(np.ones(4, dtype=np.uint16)) +print(np.ones(5, dtype=np.float)) +print(np.linspace(0, 1, 9)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/constructors.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/constructors.py.exp new file mode 100644 index 0000000..07dd7b0 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/constructors.py.exp @@ -0,0 +1,15 @@ +array([1.0, 1.0, 1.0], dtype=float64) +array([[1.0, 1.0, 1.0], + [1.0, 1.0, 1.0]], dtype=float64) +array([0.0, 0.0, 0.0], dtype=float64) +array([[0.0, 0.0, 0.0], + [0.0, 0.0, 0.0]], dtype=float64) +array([[1.0, 0.0, 0.0], + [0.0, 1.0, 0.0], + [0.0, 0.0, 1.0]], dtype=float64) +array([1], dtype=int8) +array([1, 1], dtype=uint8) +array([1, 1, 1], dtype=int16) +array([1, 1, 1, 1], dtype=uint16) +array([1.0, 1.0, 1.0, 1.0, 1.0], dtype=float64) +array([0.0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/eye.py b/circuitpython/extmod/ulab/tests/2d/numpy/eye.py new file mode 100644 index 0000000..630eed4 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/eye.py @@ -0,0 +1,30 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +print(np.ones(3)) +print(np.ones((3,3))) + +print(np.eye(3)) +print(np.eye(3, M=4)) +print(np.eye(3, M=4, k=0)) +print(np.eye(3, M=4, k=-1)) +print(np.eye(3, M=4, k=-2)) +print(np.eye(3, M=4, k=-3)) +print(np.eye(3, M=4, k=1)) +print(np.eye(3, M=4, k=2)) +print(np.eye(3, M=4, k=3)) +print(np.eye(4, M=4)) +print(np.eye(4, M=3, k=0)) +print(np.eye(4, M=3, k=-1)) +print(np.eye(4, M=3, k=-2)) +print(np.eye(4, M=3, k=-3)) +print(np.eye(4, M=3, k=1)) +print(np.eye(4, M=3, k=2)) +print(np.eye(4, M=3, k=3)) + +for dtype in dtypes: + print(np.eye(3, dtype=dtype))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/eye.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/eye.py.exp new file mode 100644 index 0000000..2591d42 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/eye.py.exp @@ -0,0 +1,78 @@ +array([1.0, 1.0, 1.0], dtype=float64) +array([[1.0, 1.0, 1.0], + [1.0, 1.0, 1.0], + [1.0, 1.0, 1.0]], dtype=float64) +array([[1.0, 0.0, 0.0], + [0.0, 1.0, 0.0], + [0.0, 0.0, 1.0]], dtype=float64) +array([[1.0, 0.0, 0.0, 0.0], + [0.0, 1.0, 0.0, 0.0], + [0.0, 0.0, 1.0, 0.0]], dtype=float64) +array([[1.0, 0.0, 0.0, 0.0], + [0.0, 1.0, 0.0, 0.0], + [0.0, 0.0, 1.0, 0.0]], dtype=float64) +array([[0.0, 0.0, 0.0, 0.0], + [1.0, 0.0, 0.0, 0.0], + [0.0, 1.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [1.0, 0.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 1.0, 0.0, 0.0], + [0.0, 0.0, 1.0, 0.0], + [0.0, 0.0, 0.0, 1.0]], dtype=float64) +array([[0.0, 0.0, 1.0, 0.0], + [0.0, 0.0, 0.0, 1.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 0.0, 0.0, 1.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) +array([[1.0, 0.0, 0.0, 0.0], + [0.0, 1.0, 0.0, 0.0], + [0.0, 0.0, 1.0, 0.0], + [0.0, 0.0, 0.0, 1.0]], dtype=float64) +array([[1.0, 0.0, 0.0], + [0.0, 1.0, 0.0], + [0.0, 0.0, 1.0], + [0.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 0.0, 0.0], + [1.0, 0.0, 0.0], + [0.0, 1.0, 0.0], + [0.0, 0.0, 1.0]], dtype=float64) +array([[0.0, 0.0, 0.0], + [0.0, 0.0, 0.0], + [1.0, 0.0, 0.0], + [0.0, 1.0, 0.0]], dtype=float64) +array([[0.0, 0.0, 0.0], + [0.0, 0.0, 0.0], + [0.0, 0.0, 0.0], + [1.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 1.0, 0.0], + [0.0, 0.0, 1.0], + [0.0, 0.0, 0.0], + [0.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 0.0, 1.0], + [0.0, 0.0, 0.0], + [0.0, 0.0, 0.0], + [0.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 0.0, 0.0], + [0.0, 0.0, 0.0], + [0.0, 0.0, 0.0], + [0.0, 0.0, 0.0]], dtype=float64) +array([[1, 0, 0], + [0, 1, 0], + [0, 0, 1]], dtype=uint8) +array([[1, 0, 0], + [0, 1, 0], + [0, 0, 1]], dtype=int8) +array([[1, 0, 0], + [0, 1, 0], + [0, 0, 1]], dtype=uint16) +array([[1, 0, 0], + [0, 1, 0], + [0, 0, 1]], dtype=int16) +array([[1.0, 0.0, 0.0], + [0.0, 1.0, 0.0], + [0.0, 0.0, 1.0]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/full.py b/circuitpython/extmod/ulab/tests/2d/numpy/full.py new file mode 100644 index 0000000..474f518 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/full.py @@ -0,0 +1,9 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +for dtype in dtypes: + print(np.full((2, 4), 3, dtype=dtype))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/full.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/full.py.exp new file mode 100644 index 0000000..0bf90a4 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/full.py.exp @@ -0,0 +1,10 @@ +array([[3, 3, 3, 3], + [3, 3, 3, 3]], dtype=uint8) +array([[3, 3, 3, 3], + [3, 3, 3, 3]], dtype=int8) +array([[3, 3, 3, 3], + [3, 3, 3, 3]], dtype=uint16) +array([[3, 3, 3, 3], + [3, 3, 3, 3]], dtype=int16) +array([[3.0, 3.0, 3.0, 3.0], + [3.0, 3.0, 3.0, 3.0]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/initialisation.py b/circuitpython/extmod/ulab/tests/2d/numpy/initialisation.py new file mode 100644 index 0000000..6136d51 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/initialisation.py @@ -0,0 +1,10 @@ +try: + from ulab import numpy as np +except ImportError: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +for dtype1 in dtypes: + for dtype2 in dtypes: + print(np.array(np.array(range(5), dtype=dtype1), dtype=dtype2))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/initialisation.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/initialisation.py.exp new file mode 100644 index 0000000..09312c4 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/initialisation.py.exp @@ -0,0 +1,25 @@ +array([0, 1, 2, 3, 4], dtype=uint8) +array([0, 1, 2, 3, 4], dtype=int8) +array([0, 1, 2, 3, 4], dtype=uint16) +array([0, 1, 2, 3, 4], dtype=int16) +array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) +array([0, 1, 2, 3, 4], dtype=uint8) +array([0, 1, 2, 3, 4], dtype=int8) +array([0, 1, 2, 3, 4], dtype=uint16) +array([0, 1, 2, 3, 4], dtype=int16) +array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) +array([0, 1, 2, 3, 4], dtype=uint8) +array([0, 1, 2, 3, 4], dtype=int8) +array([0, 1, 2, 3, 4], dtype=uint16) +array([0, 1, 2, 3, 4], dtype=int16) +array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) +array([0, 1, 2, 3, 4], dtype=uint8) +array([0, 1, 2, 3, 4], dtype=int8) +array([0, 1, 2, 3, 4], dtype=uint16) +array([0, 1, 2, 3, 4], dtype=int16) +array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) +array([0, 1, 2, 3, 4], dtype=uint8) +array([0, 1, 2, 3, 4], dtype=int8) +array([0, 1, 2, 3, 4], dtype=uint16) +array([0, 1, 2, 3, 4], dtype=int16) +array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/isinf.py b/circuitpython/extmod/ulab/tests/2d/numpy/isinf.py new file mode 100644 index 0000000..7beff9d --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/isinf.py @@ -0,0 +1,24 @@ + +from ulab import numpy as np + +print('isinf(0): ', np.isinf(0)) + +a = np.array([1, 2, np.nan]) +print('\n' + '='*20) +print('a:\n', a) +print('\nisinf(a):\n', np.isinf(a)) + +b = np.array([1, 2, np.inf]) +print('\n' + '='*20) +print('b:\n', b) +print('\nisinf(b):\n', np.isinf(b)) + +c = np.array([1, 2, 3], dtype=np.uint16) +print('\n' + '='*20) +print('c:\n', c) +print('\nisinf(c):\n', np.isinf(c)) + +d = np.eye(5) * 1e999 +print('\n' + '='*20) +print('d:\n', d) +print('\nisinf(d):\n', np.isinf(d))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/isinf.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/isinf.py.exp new file mode 100644 index 0000000..3e8a3d0 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/isinf.py.exp @@ -0,0 +1,37 @@ +isinf(0): False + +==================== +a: + array([1.0, 2.0, nan], dtype=float64) + +isinf(a): + array([False, False, False], dtype=bool) + +==================== +b: + array([1.0, 2.0, inf], dtype=float64) + +isinf(b): + array([False, False, True], dtype=bool) + +==================== +c: + array([1, 2, 3], dtype=uint16) + +isinf(c): + array([False, False, False], dtype=bool) + +==================== +d: + array([[inf, nan, nan, nan, nan], + [nan, inf, nan, nan, nan], + [nan, nan, inf, nan, nan], + [nan, nan, nan, inf, nan], + [nan, nan, nan, nan, inf]], dtype=float64) + +isinf(d): + array([[True, False, False, False, False], + [False, True, False, False, False], + [False, False, True, False, False], + [False, False, False, True, False], + [False, False, False, False, True]], dtype=bool) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/linalg.py b/circuitpython/extmod/ulab/tests/2d/numpy/linalg.py new file mode 100644 index 0000000..ead6f1f --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/linalg.py @@ -0,0 +1,95 @@ +import math + +try: + from ulab import numpy as np +except ImportError: + import numpy as np + +def matrix_is_close(A, B, n): + # primitive (i.e., independent of other functions) check of closeness of two square matrices + for i in range(n): + for j in range(n): + print(math.isclose(A[i][j], B[i][j], rel_tol=1E-9, abs_tol=1E-9)) + +a = np.array([1,2,3], dtype=np.int16) +b = np.array([4,5,6], dtype=np.int16) +ab = np.dot(a.transpose(), b) +print(math.isclose(ab, 32.0, rel_tol=1E-9, abs_tol=1E-9)) + +a = np.array([1,2,3], dtype=np.int16) +b = np.array([4,5,6], dtype=np.float) +ab = np.dot(a.transpose(), b) +print(math.isclose(ab, 32.0, rel_tol=1E-9, abs_tol=1E-9)) + +a = np.array([[1, 2], [3, 4]]) +b = np.array([[5, 6], [7, 8]]) + +c = np.array([[19, 22], [43, 50]]) +matrix_is_close(np.dot(a, b), c, 2) + +c = np.array([[26, 30], [38, 44]]) +matrix_is_close(np.dot(a.transpose(), b), c, 2) + +c = np.array([[17, 23], [39, 53]]) +matrix_is_close(np.dot(a, b.transpose()), c, 2) + +c = np.array([[23, 31], [34, 46]]) +matrix_is_close(np.dot(a.transpose(), b.transpose()), c, 2) + +a = np.array([[1., 2.], [3., 4.]]) +b = np.linalg.inv(a) +ab = np.dot(a, b) +c = np.eye(2) +matrix_is_close(ab, c, 2) + +a = np.array([[1, 2, 3, 4], [4, 5, 6, 4], [7, 8.6, 9, 4], [3, 4, 5, 6]]) +b = np.linalg.inv(a) +ab = np.dot(a, b) +c = np.eye(4) +matrix_is_close(ab, c, 4) + +a = np.array([[1, 2, 3, 4], [4, 5, 6, 4], [7, 8.6, 9, 4], [3, 4, 5, 6]]) +result = (np.linalg.det(a)) +ref_result = 7.199999999999995 +print(math.isclose(result, ref_result, rel_tol=1E-9, abs_tol=1E-9)) + +a = np.array([1, 2, 3]) +w, v = np.linalg.eig(np.diag(a)) +for i in range(3): + print(math.isclose(w[i], a[i], rel_tol=1E-9, abs_tol=1E-9)) +for i in range(3): + for j in range(3): + if i == j: + print(math.isclose(v[i][j], 1.0, rel_tol=1E-9, abs_tol=1E-9)) + else: + print(math.isclose(v[i][j], 0.0, rel_tol=1E-9, abs_tol=1E-9)) + + +a = np.array([[25, 15, -5], [15, 18, 0], [-5, 0, 11]]) +result = (np.linalg.cholesky(a)) +ref_result = np.array([[5., 0., 0.], [ 3., 3., 0.], [-1., 1., 3.]]) +for i in range(3): + for j in range(3): + print(math.isclose(result[i][j], ref_result[i][j], rel_tol=1E-9, abs_tol=1E-9)) + +a = np.array([1,2,3,4,5], dtype=np.float) +result = (np.linalg.norm(a)) +ref_result = 7.416198487095663 +print(math.isclose(result, ref_result, rel_tol=1E-9, abs_tol=1E-9)) + +a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) +result = (np.linalg.norm(a)) ## Here is a problem +ref_result = 16.881943016134134 +print(math.isclose(result, ref_result, rel_tol=1E-6, abs_tol=1E-6)) + +a = np.array([[0, 1, 2], [3, 4 ,5], [5, 4, 8], [4, 4, 8] ], dtype=np.int16) +result = (np.linalg.norm(a,axis=0)) # fails on low tolerance +ref_result = np.array([7.071068, 7.0, 12.52996]) +for i in range(3): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-6, abs_tol=1E-6)) + +a = np.array([[0, 1, 2], [3, 4 ,5], [5, 4, 8], [4, 4, 8] ], dtype=np.int16) +result = (np.linalg.norm(a,axis=1)) # fails on low tolerance +ref_result = np.array([2.236068, 7.071068, 10.24695, 9.797959]) +for i in range(4): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-6, abs_tol=1E-6)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/linalg.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/linalg.py.exp new file mode 100644 index 0000000..0b1a61c --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/linalg.py.exp @@ -0,0 +1,69 @@ +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True +True diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/linspace.py b/circuitpython/extmod/ulab/tests/2d/numpy/linspace.py new file mode 100644 index 0000000..c97199a --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/linspace.py @@ -0,0 +1,10 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +for dtype in dtypes: + print(np.linspace(0, 10, num=5, dtype=dtype)) + print(np.linspace(0, 10, num=5, endpoint=True, dtype=dtype)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/linspace.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/linspace.py.exp new file mode 100644 index 0000000..2b95990 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/linspace.py.exp @@ -0,0 +1,10 @@ +array([0, 2, 5, 7, 10], dtype=uint8) +array([0, 2, 5, 7, 10], dtype=uint8) +array([0, 2, 5, 7, 10], dtype=int8) +array([0, 2, 5, 7, 10], dtype=int8) +array([0, 2, 5, 7, 10], dtype=uint16) +array([0, 2, 5, 7, 10], dtype=uint16) +array([0, 2, 5, 7, 10], dtype=int16) +array([0, 2, 5, 7, 10], dtype=int16) +array([0.0, 2.5, 5.0, 7.5, 10.0], dtype=float64) +array([0.0, 2.5, 5.0, 7.5, 10.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/logspace.py b/circuitpython/extmod/ulab/tests/2d/numpy/logspace.py new file mode 100644 index 0000000..e6f2047 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/logspace.py @@ -0,0 +1,10 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +for dtype in dtypes: + print(np.logspace(0, 10, num=5, endpoint=False, dtype=dtype)) + print(np.logspace(0, 10, num=5, endpoint=True, dtype=dtype))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/logspace.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/logspace.py.exp new file mode 100644 index 0000000..1a09cef --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/logspace.py.exp @@ -0,0 +1,10 @@ +array([1, 100, 16, 64, 0], dtype=uint8) +array([1, 60, 160, 120, 0], dtype=uint8) +array([1, 100, 16, 64, 0], dtype=int8) +array([1, 60, -96, 120, 0], dtype=int8) +array([1, 100, 10000, 16960, 57600], dtype=uint16) +array([1, 316, 34464, 34424, 0], dtype=uint16) +array([1, 100, 10000, 16960, -7936], dtype=int16) +array([1, 316, -31072, -31112, 0], dtype=int16) +array([1.0, 100.0, 10000.0, 1000000.0, 100000000.0], dtype=float64) +array([1.0, 316.227766016838, 100000.0, 31622776.6016838, 10000000000.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/methods.py b/circuitpython/extmod/ulab/tests/2d/numpy/methods.py new file mode 100644 index 0000000..0fa7912 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/methods.py @@ -0,0 +1,51 @@ +try: + from ulab import numpy as np +except ImportError: + import numpy as np + +a = np.array([1, 2, 3, 4], dtype=np.int8) +b = a.copy() +print(b) +a = np.array([[1,2,3],[4,5,6],[7,8,9]], dtype=np.int16) +b = a.copy() +print(b) +a = np.array([[1,2,3],[4,5,6],[7,8,9]], dtype=np.float) +b = a.copy() +print(b) +print(a.dtype) +print(a.flatten()) +print(np.array([1,2,3], dtype=np.uint8).itemsize) +print(np.array([1,2,3], dtype=np.uint16).itemsize) +print(np.array([1,2,3], dtype=np.int8).itemsize) +print(np.array([1,2,3], dtype=np.int16).itemsize) +print(np.array([1,2,3], dtype=np.float).itemsize) +print(np.array([1,2,3], dtype=np.float).shape) +print(np.array([[1],[2],[3]], dtype=np.float).shape) +print(np.array([[1],[2],[3]], dtype=np.float).reshape((1,3))) +print(np.array([[1],[2],[3]]).size) +print(np.array([1,2,3], dtype=np.float).size) +print(np.array([1,2,3], dtype=np.uint8).tobytes()) +print(np.array([1,2,3], dtype=np.int8).tobytes()) +print(np.array([1,2,3], dtype=np.float).transpose().shape) +print(np.array([[1],[2],[3]], dtype=np.float).transpose().shape) +a = np.array([1, 2, 3, 4, 5, 6], dtype=np.uint8) +b = a.byteswap(inplace=False) +print(a) +print(b) +c = a.byteswap(inplace=True) +print(a) +print(c) +a = np.array([1, 2, 3, 4, 5, 6], dtype=np.uint16) +b = a.byteswap(inplace=False) +print(a) +print(b) +c = a.byteswap(inplace=True) +print(a) +print(c) +a = np.array([1, 2, 3, 4, 5, 6], dtype=np.float) +b = a.byteswap(inplace=False) +print(a) +print(b) +c = a.byteswap(inplace=True) +print(a) +print(c) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/methods.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/methods.py.exp new file mode 100644 index 0000000..fb035da --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/methods.py.exp @@ -0,0 +1,35 @@ +array([1, 2, 3, 4], dtype=int8) +array([[1, 2, 3], + [4, 5, 6], + [7, 8, 9]], dtype=int16) +array([[1.0, 2.0, 3.0], + [4.0, 5.0, 6.0], + [7.0, 8.0, 9.0]], dtype=float64) +100 +array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64) +1 +2 +1 +2 +8 +(3,) +(3, 1) +array([[1.0, 2.0, 3.0]], dtype=float64) +3 +3 +bytearray(b'\x01\x02\x03') +bytearray(b'\x01\x02\x03') +(3,) +(1, 3) +array([1, 2, 3, 4, 5, 6], dtype=uint8) +array([1, 2, 3, 4, 5, 6], dtype=uint8) +array([1, 2, 3, 4, 5, 6], dtype=uint8) +array([1, 2, 3, 4, 5, 6], dtype=uint8) +array([1, 2, 3, 4, 5, 6], dtype=uint16) +array([256, 512, 768, 1024, 1280, 1536], dtype=uint16) +array([256, 512, 768, 1024, 1280, 1536], dtype=uint16) +array([256, 512, 768, 1024, 1280, 1536], dtype=uint16) +array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float64) +array([3.038651941617419e-319, 3.162020133383978e-322, 1.043466644016713e-320, 2.055313086699586e-320, 2.561236308041022e-320, 3.067159529382458e-320], dtype=float64) +array([3.038651941617419e-319, 3.162020133383978e-322, 1.043466644016713e-320, 2.055313086699586e-320, 2.561236308041022e-320, 3.067159529382458e-320], dtype=float64) +array([3.038651941617419e-319, 3.162020133383978e-322, 1.043466644016713e-320, 2.055313086699586e-320, 2.561236308041022e-320, 3.067159529382458e-320], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/numericals.py b/circuitpython/extmod/ulab/tests/2d/numpy/numericals.py new file mode 100644 index 0000000..909929f --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/numericals.py @@ -0,0 +1,214 @@ +import math +try: + from ulab import numpy as np +except ImportError: + import numpy as np + +print("Testing np.min:") +print(np.min([1])) +print(np.min(np.array([1], dtype=np.float))) +a = np.array([[1,2,3],[4,5,6],[7,8,9]], dtype=np.uint8) +print(np.min(a)) +print(np.min(a, axis=0)) +print(np.min(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.uint8) +print(np.min(a)) +print(np.min(a, axis=0)) +print(np.min(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.int8) +print(np.min(a)) ## Problem here +print(np.min(a, axis=0)) +print(np.min(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.uint16) +print(np.min(a)) +print(np.min(a, axis=0)) +print(np.min(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.int16) +print(np.min(a)) +print(np.min(a, axis=0)) +print(np.min(a, axis=1)) +a = np.array([range(2**56-3, 2**56),range(2**16-3, 2**16),range(2**8-3, 2**8)], dtype=np.float) +print(np.min(a)) +print(np.min(a, axis=0)) +print(np.min(a, axis=1)) + +print("Testing np.max:") +print(np.max([1])) +print(np.max(np.array([1], dtype=np.float))) +a = np.array([[1,2,3],[4,5,6],[7,8,9]], dtype=np.uint8) +print(np.max(a)) +print(np.max(a, axis=0)) +print(np.max(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.uint8) +print(np.max(a)) +print(np.max(a, axis=0)) +print(np.max(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.int8) +print(np.max(a)) ## Problem here +print(np.max(a, axis=0)) +print(np.max(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.uint16) +print(np.max(a)) +print(np.max(a, axis=0)) +print(np.max(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.int16) +print(np.max(a)) +print(np.max(a, axis=0)) +print(np.max(a, axis=1)) +a = np.array([range(2**56-3, 2**56),range(2**16-3, 2**16),range(2**8-3, 2**8)], dtype=np.float) +print(np.max(a)) +print(np.max(a, axis=0)) +print(np.max(a, axis=1)) + +print("Testing np.argmin:") +print(np.argmin([1])) +print(np.argmin(np.array([1], dtype=np.float))) +a = np.array([[1,2,3],[4,5,6],[7,8,9]], dtype=np.uint8) +print(np.argmin(a)) +print(np.argmin(a, axis=0)) +print(np.argmin(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.uint8) +print(np.argmin(a)) +print(np.argmin(a, axis=0)) +print(np.argmin(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.int8) +print(np.argmin(a)) ## Problem here +print(np.argmin(a, axis=0)) +print(np.argmin(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.uint16) +print(np.argmin(a)) +print(np.argmin(a, axis=0)) +print(np.argmin(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.int16) +print(np.argmin(a)) +print(np.argmin(a, axis=0)) +print(np.argmin(a, axis=1)) +a = np.array([range(2**56-3, 2**56),range(2**16-3, 2**16),range(2**8-3, 2**8)], dtype=np.float) +print(np.argmin(a)) +print(np.argmin(a, axis=0)) +print(np.argmin(a, axis=1)) + +print("Testing np.argmax:") +print(np.argmax([1])) +print(np.argmax(np.array([1], dtype=np.float))) +a = np.array([[1,2,3],[4,5,6],[7,8,9]], dtype=np.uint8) +print(np.argmax(a)) +print(np.argmax(a, axis=0)) +print(np.argmax(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.uint8) +print(np.argmax(a)) +print(np.argmax(a, axis=0)) +print(np.argmax(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.int8) +print(np.argmax(a)) ## Problem here +print(np.argmax(a, axis=0)) +print(np.argmax(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.uint16) +print(np.argmax(a)) +print(np.argmax(a, axis=0)) +print(np.argmax(a, axis=1)) +a = np.array([range(255-5, 255),range(240-5, 240),range(250-5,250)], dtype=np.int16) +print(np.argmax(a)) +print(np.argmax(a, axis=0)) +print(np.argmax(a, axis=1)) +a = np.array([range(2**56-3, 2**56),range(2**16-3, 2**16),range(2**8-3, 2**8)], dtype=np.float) +print(np.argmax(a)) +print(np.argmax(a, axis=0)) +print(np.argmax(a, axis=1)) + +print("Testing np.minimum:") +print(np.minimum(10, 9)) +print(np.minimum(10.0, 9.0)) +a = np.array([range(255-3, 255),range(240-3, 240),range(250-3,250)], dtype=np.float) +b = np.array([range(2**56-3, 2**56),range(2**16-3, 2**16),range(2**8-3, 2**8)], dtype=np.float) +print(np.minimum(a, b)) + +print("Testing np.maximum:") +print(np.maximum(a, b)) +print(np.maximum(10, 9)) +print(np.maximum(10.0, 9.0)) +a = np.array([range(255-3, 255),range(240-3, 240),range(250-3,250)], dtype=np.float) +b = np.array([range(2**56-3, 2**56),range(2**16-3, 2**16),range(2**8-3, 2**8)], dtype=np.float) +print(np.maximum(a, b)) + +print("Testing np.sort:") +a = np.array([range(255-3, 255),range(240-3, 240),range(250-3,250)], dtype=np.uint8) +b = np.array([range(2**56-3, 2**56),range(2**16-3, 2**16),range(2**8-3, 2**8)], dtype=np.float) +print(np.sort(a, axis=None)) +print(np.sort(b, axis=None)) +print(np.sort(a, axis=0)) +print(np.sort(b, axis=0)) +print(np.sort(a, axis=1)) +print(np.sort(b, axis=1)) + +print("Testing np.sum:") +a = np.array([253, 254, 255], dtype=np.uint8) +print(np.sum(a)) +print(np.sum(a, axis=0)) +a = np.array([range(255-3, 255),range(240-3, 240),range(250-3,250)], dtype=np.float) +print(np.sum(a)) +print(np.sum(a, axis=0)) +print(np.sum(a, axis=1)) + +print("Testing np.mean:") +a = np.array([253, 254, 255], dtype=np.uint8) +print(np.mean(a)) +print(np.mean(a, axis=0)) +a = np.array([range(255-3, 255),range(240-3, 240),range(250-3,250)], dtype=np.float) +#print(np.mean(a)) +print(math.isclose(np.mean(a), 246.3333333333333, rel_tol=1e-06, abs_tol=1e-06)) +#print(np.mean(a, axis=0)) +result = np.mean(a, axis=0) +ref_result = [245.33333333, 246.33333333, 247.33333333] +for p, q in zip(list(result), ref_result): + print(math.isclose(p, q, rel_tol=1e-06, abs_tol=1e-06)) + +#print(np.mean(a, axis=1)) +result = np.mean(a, axis=1) +ref_result = [253., 238., 248.] +for p, q in zip(list(result), ref_result): + print(math.isclose(p, q, rel_tol=1e-06, abs_tol=1e-06)) + +print("Testing np.std:") +a = np.array([253, 254, 255], dtype=np.uint8) +#print(np.std(a)) +print(math.isclose(np.std(a), 0.816496580927726, rel_tol=1e-06, abs_tol=1e-06)) +print(math.isclose(np.std(a, axis=0), 0.816496580927726, rel_tol=1e-06, abs_tol=1e-06)) +a = np.array([range(255-3, 255),range(240-3, 240),range(250-3,250)], dtype=np.float) +#print(np.std(a)) +print(math.isclose(np.std(a), 6.289320754704403, rel_tol=1e-06, abs_tol=1e-06)) +#print(np.std(a, axis=0)) +result = np.std(a, axis=0) +ref_result = [6.23609564, 6.23609564, 6.23609564] +for p, q in zip(list(result), ref_result): + print(math.isclose(p, q, rel_tol=1e-06, abs_tol=1e-06)) + +#print(np.std(a, axis=1)) +result = np.std(a, axis=1) +ref_result = [0.81649658, 0.81649658, 0.81649658] +for p, q in zip(list(result), ref_result): + print(math.isclose(p, q, rel_tol=1e-06, abs_tol=1e-06)) + +print("Testing np.median:") +a = np.array([253, 254, 255], dtype=np.uint8) +print(np.median(a)) +print(np.median(a, axis=0)) +a = np.array([range(255-3, 255),range(240-3, 240),range(250-3,250)], dtype=np.float) +print(np.median(a)) +print(np.median(a, axis=0)) +print(np.median(a, axis=1)) +print("Testing np.roll:") ## Here is problem +print(np.arange(10)) +print(np.roll(np.arange(10), 2)) +print(np.roll(np.arange(10), -2)) +a = np.array([1, 2, 3, 4, 5, 6, 7, 8]) +print(np.roll(a, 2)) +print(np.roll(a, -2)) +print("Testing np.clip:") +print(np.clip(5, 3, 6)) ## Here is problem +print(np.clip(7, 3, 6)) +print(np.clip(1, 3, 6)) +a = np.array([1,2,3,4,5,6,7], dtype=np.int8) +print(np.clip(a, 3, 5)) +a = np.array([1,2,3,4,5,6,7], dtype=np.float) +print(np.clip(a, 3, 5)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/numericals.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/numericals.py.exp new file mode 100644 index 0000000..957b4ba --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/numericals.py.exp @@ -0,0 +1,158 @@ +Testing np.min: +1 +1.0 +1 +array([1, 2, 3], dtype=uint8) +array([1, 4, 7], dtype=uint8) +235 +array([235, 236, 237, 238, 239], dtype=uint8) +array([250, 235, 245], dtype=uint8) +-21 +array([-21, -20, -19, -18, -17], dtype=int8) +array([-6, -21, -11], dtype=int8) +235 +array([235, 236, 237, 238, 239], dtype=uint16) +array([250, 235, 245], dtype=uint16) +235 +array([235, 236, 237, 238, 239], dtype=int16) +array([250, 235, 245], dtype=int16) +253.0 +array([253.0, 254.0, 255.0], dtype=float64) +array([7.205759403792793e+16, 65533.0, 253.0], dtype=float64) +Testing np.max: +1 +1.0 +9 +array([7, 8, 9], dtype=uint8) +array([3, 6, 9], dtype=uint8) +254 +array([250, 251, 252, 253, 254], dtype=uint8) +array([254, 239, 249], dtype=uint8) +-2 +array([-6, -5, -4, -3, -2], dtype=int8) +array([-2, -17, -7], dtype=int8) +254 +array([250, 251, 252, 253, 254], dtype=uint16) +array([254, 239, 249], dtype=uint16) +254 +array([250, 251, 252, 253, 254], dtype=int16) +array([254, 239, 249], dtype=int16) +7.205759403792793e+16 +array([7.205759403792793e+16, 7.205759403792793e+16, 7.205759403792793e+16], dtype=float64) +array([7.205759403792793e+16, 65535.00000000001, 255.0], dtype=float64) +Testing np.argmin: +0 +0 +0 +array([0, 0, 0], dtype=int16) +array([0, 0, 0], dtype=int16) +5 +array([1, 1, 1, 1, 1], dtype=int16) +array([0, 0, 0], dtype=int16) +5 +array([1, 1, 1, 1, 1], dtype=int16) +array([0, 0, 0], dtype=int16) +5 +array([1, 1, 1, 1, 1], dtype=int16) +array([0, 0, 0], dtype=int16) +5 +array([1, 1, 1, 1, 1], dtype=int16) +array([0, 0, 0], dtype=int16) +6 +array([2, 2, 2], dtype=int16) +array([0, 0, 0], dtype=int16) +Testing np.argmax: +0 +0 +8 +array([2, 2, 2], dtype=int16) +array([2, 2, 2], dtype=int16) +4 +array([0, 0, 0, 0, 0], dtype=int16) +array([4, 4, 4], dtype=int16) +4 +array([0, 0, 0, 0, 0], dtype=int16) +array([4, 4, 4], dtype=int16) +4 +array([0, 0, 0, 0, 0], dtype=int16) +array([4, 4, 4], dtype=int16) +4 +array([0, 0, 0, 0, 0], dtype=int16) +array([4, 4, 4], dtype=int16) +0 +array([0, 0, 0], dtype=int16) +array([0, 2, 2], dtype=int16) +Testing np.minimum: +9 +9.0 +array([[252.0, 253.0, 254.0], + [237.0, 238.0, 239.0], + [247.0, 248.0, 249.0]], dtype=float64) +Testing np.maximum: +array([[7.205759403792793e+16, 7.205759403792793e+16, 7.205759403792793e+16], + [65533.0, 65534.0, 65535.00000000001], + [253.0, 254.0, 255.0]], dtype=float64) +10 +10.0 +array([[7.205759403792793e+16, 7.205759403792793e+16, 7.205759403792793e+16], + [65533.0, 65534.0, 65535.00000000001], + [253.0, 254.0, 255.0]], dtype=float64) +Testing np.sort: +array([237, 238, 239, 247, 248, 249, 252, 253, 254], dtype=uint8) +array([253.0, 254.0, 255.0, 65533.0, 65534.0, 65535.00000000001, 7.205759403792793e+16, 7.205759403792793e+16, 7.205759403792793e+16], dtype=float64) +array([[237, 238, 239], + [247, 248, 249], + [252, 253, 254]], dtype=uint8) +array([[253.0, 254.0, 255.0], + [65533.0, 65534.0, 65535.00000000001], + [7.205759403792793e+16, 7.205759403792793e+16, 7.205759403792793e+16]], dtype=float64) +array([[252, 253, 254], + [237, 238, 239], + [247, 248, 249]], dtype=uint8) +array([[7.205759403792793e+16, 7.205759403792793e+16, 7.205759403792793e+16], + [65533.0, 65534.0, 65535.00000000001], + [253.0, 254.0, 255.0]], dtype=float64) +Testing np.sum: +762 +250 +2217.0 +array([736.0, 739.0000000000001, 742.0], dtype=float64) +array([759.0, 714.0000000000001, 744.0], dtype=float64) +Testing np.mean: +254.0 +254.0 +True +True +True +True +True +True +True +Testing np.std: +True +True +True +True +True +True +True +True +True +Testing np.median: +254.0 +254.0 +248.0 +array([247.0, 248.0, 249.0], dtype=float64) +array([253.0, 238.0, 248.0], dtype=float64) +Testing np.roll: +array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int16) +array([8, 9, 0, 1, 2, 3, 4, 5, 6, 7], dtype=int16) +array([2, 3, 4, 5, 6, 7, 8, 9, 0, 1], dtype=int16) +array([7.0, 8.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0], dtype=float64) +array([3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 1.0, 2.0], dtype=float64) +Testing np.clip: +5 +6 +3 +array([3, 3, 3, 4, 5, 5, 5], dtype=int16) +array([3.0, 3.0, 3.0, 4.0, 5.0, 5.0, 5.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/ones.py b/circuitpython/extmod/ulab/tests/2d/numpy/ones.py new file mode 100644 index 0000000..f0aee86 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/ones.py @@ -0,0 +1,13 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +print(np.ones(3)) +print(np.ones((3,3))) + +for dtype in dtypes: + print(np.ones((3,3), dtype=dtype)) + print(np.ones((4,2), dtype=dtype)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/ones.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/ones.py.exp new file mode 100644 index 0000000..9e66f3c --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/ones.py.exp @@ -0,0 +1,39 @@ +array([1.0, 1.0, 1.0], dtype=float64) +array([[1.0, 1.0, 1.0], + [1.0, 1.0, 1.0], + [1.0, 1.0, 1.0]], dtype=float64) +array([[1, 1, 1], + [1, 1, 1], + [1, 1, 1]], dtype=uint8) +array([[1, 1], + [1, 1], + [1, 1], + [1, 1]], dtype=uint8) +array([[1, 1, 1], + [1, 1, 1], + [1, 1, 1]], dtype=int8) +array([[1, 1], + [1, 1], + [1, 1], + [1, 1]], dtype=int8) +array([[1, 1, 1], + [1, 1, 1], + [1, 1, 1]], dtype=uint16) +array([[1, 1], + [1, 1], + [1, 1], + [1, 1]], dtype=uint16) +array([[1, 1, 1], + [1, 1, 1], + [1, 1, 1]], dtype=int16) +array([[1, 1], + [1, 1], + [1, 1], + [1, 1]], dtype=int16) +array([[1.0, 1.0, 1.0], + [1.0, 1.0, 1.0], + [1.0, 1.0, 1.0]], dtype=float64) +array([[1.0, 1.0], + [1.0, 1.0], + [1.0, 1.0], + [1.0, 1.0]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/operators.py b/circuitpython/extmod/ulab/tests/2d/numpy/operators.py new file mode 100644 index 0000000..acc316b --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/operators.py @@ -0,0 +1,169 @@ +try: + from ulab import numpy as np +except ImportError: + import numpy as np + + +print(len(np.array([1, 2, 3, 4, 5], dtype=np.uint8))) +print(len(np.array([[1, 2, 3],[4, 5, 6]]))) + +print(~np.array([0, -1, -100], dtype=np.uint8)) +print(~np.array([0, -1, -100], dtype=np.uint16)) +print(~np.array([0, -1, -100], dtype=np.int8)) +print(~np.array([0, -1, -100], dtype=np.int16)) + +print(abs(np.array([0, -1, -100], dtype=np.uint8))) +print(abs(np.array([0, -1, -100], dtype=np.uint16))) +print(abs(np.array([0, -1, -100], dtype=np.int8))) +print(abs(np.array([0, -1, -100], dtype=np.int16))) +print(abs(np.array([0, -1, -100], dtype=np.float))) + +print(-(np.array([0, -1, -100], dtype=np.uint8))) +print(-(np.array([0, -1, -100], dtype=np.uint16))) +print(-(np.array([0, -1, -100], dtype=np.int8))) +print(-(np.array([0, -1, -100], dtype=np.int16))) +print(-(np.array([0, -1, -100], dtype=np.float))) + +print(+(np.array([0, -1, -100], dtype=np.uint8))) +print(+(np.array([0, -1, -100], dtype=np.uint16))) +print(+(np.array([0, -1, -100], dtype=np.int8))) +print(+(np.array([0, -1, -100], dtype=np.int16))) +print(+(np.array([0, -1, -100], dtype=np.float))) + +print(np.array([1,2,3], dtype=np.float) > np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) > np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) > np.array([4,5,6], dtype=np.int16)) +print(np.array([1,2,3], dtype=np.float) < np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) < np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) < np.array([4,5,6], dtype=np.int16)) + +print(np.array([1,2,3], dtype=np.float) >= np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) >= np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) >= np.array([4,5,6], dtype=np.int16)) +print(np.array([1,2,3], dtype=np.float) <= np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) <= np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) <= np.array([4,5,6], dtype=np.int16)) + +print(np.array([1,2,3], dtype=np.float) > 4) +print(np.array([1,2,3], dtype=np.float) > 4.0) +print(np.array([1,2,3], dtype=np.float) < 4) +print(np.array([1,2,3], dtype=np.float) < 4.0) + +print(np.array([1,2,3], dtype=np.float) == np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) == np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) == np.array([4,5,6], dtype=np.int16)) +print(np.array([1,2,3], dtype=np.float) != np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) != np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) != np.array([4,5,6], dtype=np.int16)) + +print(np.array([1,2,3], dtype=np.float) == 4) +print(np.array([1,2,3], dtype=np.float) == 4.0) +print(np.array([1,2,3], dtype=np.float) != 4) +print(np.array([1,2,3], dtype=np.float) != 4.0) + +print(np.array([1,2,3], dtype=np.float) - np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) - np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) - np.array([4,5,6], dtype=np.int16)) + +print(np.array([1,2,3], dtype=np.float) + np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) + np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) + np.array([4,5,6], dtype=np.int16)) + +print(np.array([1,2,3], dtype=np.float) * np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) * np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) * np.array([4,5,6], dtype=np.int16)) + +print(np.array([1,2,3], dtype=np.float) ** np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) ** np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) ** np.array([4,5,6], dtype=np.int16)) + +print(np.array([1,2,3], dtype=np.float) / np.array([4,5,6], dtype=np.float)) +print(np.array([1,2,3], dtype=np.float) / np.array([4,5,6], dtype=np.uint16)) +print(np.array([1,2,3], dtype=np.float) / np.array([4,5,6], dtype=np.int16)) + +print(np.array([1,2,3], dtype=np.float) - 4) +print(np.array([1,2,3], dtype=np.float) - 4.0) +print(np.array([1,2,3], dtype=np.float) + 4) +print(np.array([1,2,3], dtype=np.float) + 4.0) + +print(np.array([1,2,3], dtype=np.float) * 4) +print(np.array([1,2,3], dtype=np.float) * 4.0) +print(np.array([1,2,3], dtype=np.float) ** 4) +print(np.array([1,2,3], dtype=np.float) ** 4.0) + +print(np.array([1,2,3], dtype=np.float) / 4) +print(np.array([1,2,3], dtype=np.float) / 4.0) + +a = np.array([1,2,3], dtype=np.float) +a -= np.array([4,5,6], dtype=np.float) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a -= np.array([4,5,6], dtype=np.uint16) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a -= np.array([4,5,6], dtype=np.int16) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a += np.array([4,5,6], dtype=np.float) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a += np.array([4,5,6], dtype=np.uint16) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a += np.array([4,5,6], dtype=np.int16) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a *= np.array([4,5,6], dtype=np.float) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a *= np.array([4,5,6], dtype=np.uint16) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a *= np.array([4,5,6], dtype=np.int16) +print(a) + +a = np.array([1,2,3], dtype=np.float) +#a /= np.array([4,5,6]) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a **= np.array([4,5,6], dtype=np.float) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a **= np.array([4,5,6], dtype=np.uint16) +print(a) + +a = np.array([1,2,3], dtype=np.float) +a **= np.array([4,5,6], dtype=np.int16) +print(a) + +print(np.array([1,2,3],dtype=np.uint8) + np.array([4,5,6],dtype=np.uint8)) +print(np.array([1,2,3],dtype=np.uint8) + np.array([4,5,6],dtype=np.int8)) +print(np.array([1,2,3],dtype=np.int8) + np.array([4,5,6],dtype=np.int8)) +print(np.array([1,2,3],dtype=np.uint8) + np.array([4,5,6],dtype=np.uint16)) +print(np.array([1,2,3],dtype=np.int8) + np.array([4,5,6],dtype=np.uint16)) +print(np.array([1,2,3],dtype=np.uint8) + np.array([4,5,6],dtype=np.int16)) +print(np.array([1,2,3],dtype=np.int8) + np.array([4,5,6],dtype=np.int16)) +print(np.array([1,2,3],dtype=np.uint16) + np.array([4,5,6],dtype=np.uint16)) +print(np.array([1,2,3],dtype=np.int16) + np.array([4,5,6],dtype=np.int16)) +print(np.array([1,2,3],dtype=np.int16) + np.array([4,5,6],dtype=np.uint16)) + +print(np.array([1,2,3],dtype=np.uint8) + np.array([4,5,6],dtype=np.float)) +print(np.array([1,2,3],dtype=np.int8) + np.array([4,5,6],dtype=np.float)) +print(np.array([1,2,3],dtype=np.uint16) + np.array([4,5,6],dtype=np.float)) +print(np.array([1,2,3],dtype=np.int16) + np.array([4,5,6],dtype=np.float)) +print(np.array([1,2,3],dtype=np.int16) + np.array([4,5,6],dtype=np.float)) + +a = np.array([1, 2, 3, 4, 5], dtype=np.uint8) +for i, _a in enumerate(a): + print("element %d in a:"%i, _a) + diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/operators.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/operators.py.exp new file mode 100644 index 0000000..9749509 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/operators.py.exp @@ -0,0 +1,105 @@ +5 +2 +array([255, 0, 99], dtype=uint8) +array([65535, 0, 99], dtype=uint16) +array([-1, 0, 99], dtype=int8) +array([-1, 0, 99], dtype=int16) +array([0, 255, 156], dtype=uint8) +array([0, 65535, 65436], dtype=uint16) +array([0, 1, 100], dtype=int8) +array([0, 1, 100], dtype=int16) +array([0.0, 1.0, 100.0], dtype=float64) +array([0, 1, 100], dtype=uint8) +array([0, 1, 100], dtype=uint16) +array([0, 1, 100], dtype=int8) +array([0, 1, 100], dtype=int16) +array([-0.0, 1.0, 100.0], dtype=float64) +array([0, 255, 156], dtype=uint8) +array([0, 65535, 65436], dtype=uint16) +array([0, -1, -100], dtype=int8) +array([0, -1, -100], dtype=int16) +array([0.0, -1.0, -100.0], dtype=float64) +array([False, False, False], dtype=bool) +array([False, False, False], dtype=bool) +array([False, False, False], dtype=bool) +array([True, True, True], dtype=bool) +array([True, True, True], dtype=bool) +array([True, True, True], dtype=bool) +array([False, False, False], dtype=bool) +array([False, False, False], dtype=bool) +array([False, False, False], dtype=bool) +array([True, True, True], dtype=bool) +array([True, True, True], dtype=bool) +array([True, True, True], dtype=bool) +array([False, False, False], dtype=bool) +array([False, False, False], dtype=bool) +array([True, True, True], dtype=bool) +array([True, True, True], dtype=bool) +array([False, False, False], dtype=bool) +array([False, False, False], dtype=bool) +array([False, False, False], dtype=bool) +array([True, True, True], dtype=bool) +array([True, True, True], dtype=bool) +array([True, True, True], dtype=bool) +array([False, False, False], dtype=bool) +array([False, False, False], dtype=bool) +array([True, True, True], dtype=bool) +array([True, True, True], dtype=bool) +array([-3.0, -3.0, -3.0], dtype=float64) +array([-3.0, -3.0, -3.0], dtype=float64) +array([-3.0, -3.0, -3.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([4.0, 10.0, 18.0], dtype=float64) +array([4.0, 10.0, 18.0], dtype=float64) +array([4.0, 10.0, 18.0], dtype=float64) +array([1.0, 32.0, 729.0], dtype=float64) +array([1.0, 32.0, 729.0], dtype=float64) +array([1.0, 32.0, 729.0], dtype=float64) +array([0.25, 0.4, 0.5], dtype=float64) +array([0.25, 0.4, 0.5], dtype=float64) +array([0.25, 0.4, 0.5], dtype=float64) +array([-3.0, -2.0, -1.0], dtype=float64) +array([-3.0, -2.0, -1.0], dtype=float64) +array([5.0, 6.0, 7.0], dtype=float64) +array([5.0, 6.0, 7.0], dtype=float64) +array([4.0, 8.0, 12.0], dtype=float64) +array([4.0, 8.0, 12.0], dtype=float64) +array([1.0, 16.0, 81.0], dtype=float64) +array([1.0, 16.0, 81.0], dtype=float64) +array([0.25, 0.5, 0.75], dtype=float64) +array([0.25, 0.5, 0.75], dtype=float64) +array([-3.0, -3.0, -3.0], dtype=float64) +array([-3.0, -3.0, -3.0], dtype=float64) +array([-3.0, -3.0, -3.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([4.0, 10.0, 18.0], dtype=float64) +array([4.0, 10.0, 18.0], dtype=float64) +array([4.0, 10.0, 18.0], dtype=float64) +array([1.0, 2.0, 3.0], dtype=float64) +array([1.0, 32.0, 729.0], dtype=float64) +array([1.0, 32.0, 729.0], dtype=float64) +array([1.0, 32.0, 729.0], dtype=float64) +array([5, 7, 9], dtype=uint16) +array([5, 7, 9], dtype=int16) +array([5, 7, 9], dtype=int8) +array([5, 7, 9], dtype=uint16) +array([5, 7, 9], dtype=int16) +array([5, 7, 9], dtype=int16) +array([5, 7, 9], dtype=int16) +array([5, 7, 9], dtype=uint16) +array([5, 7, 9], dtype=int16) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +array([5.0, 7.0, 9.0], dtype=float64) +element 0 in a: 1 +element 1 in a: 2 +element 2 in a: 3 +element 3 in a: 4 +element 4 in a: 5 diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/signal.py b/circuitpython/extmod/ulab/tests/2d/numpy/signal.py new file mode 100644 index 0000000..d7a6412 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/signal.py @@ -0,0 +1,37 @@ +import math +try: + from ulab import numpy as np + from ulab import scipy as spy +except ImportError: + import numpy as np + import scipy as spy + +x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=np.float) +sos = np.array([[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]],dtype=np.float) +result = spy.signal.sosfilt(sos, x) + +ref_result = np.array([0.0000e+00, 1.0000e+00, -4.0000e+00, 2.4000e+01, -1.0400e+02, 4.4000e+02, -1.7280e+03, 6.5320e+03, -2.3848e+04, 8.4864e+04], dtype=np.float) +cmp_result = [] +for p,q in zip(list(result), list(ref_result)): + cmp_result.append(math.isclose(p, q, rel_tol=1e-06, abs_tol=1e-06)) +print(cmp_result) + +x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]) +sos = np.array([[1, 2, 3, 1, 5, 6], [1, 2, 3, 1, 5, 6]],dtype=np.float) +zi = np.array([[1, 2], [3, 4]],dtype=np.float) +y, zo = spy.signal.sosfilt(sos, x, zi=zi) + +y_ref = np.array([ 4.00000e+00, -1.60000e+01, 6.30000e+01, -2.27000e+02, 8.03000e+02, -2.75100e+03, 9.27100e+03, -3.07750e+04, 1.01067e+05, -3.28991e+05], dtype=np.float) +zo_ref = np.array([[37242.0, 74835.],[1026187.0, 1936542.0]], dtype=np.float) +cmp_result = [] +for p,q in zip(list(y), list(y_ref)): + cmp_result.append(math.isclose(p, q, rel_tol=1e-06, abs_tol=1e-06)) +print(cmp_result) + +cmp_result = [] +for i in range(2): + temp = [] + for j in range(2): + temp.append(math.isclose(zo[i][j], zo_ref[i][j], rel_tol=1E-9, abs_tol=1E-9)) + cmp_result.append(temp) +print(cmp_result) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/signal.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/signal.py.exp new file mode 100644 index 0000000..dd38a17 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/signal.py.exp @@ -0,0 +1,3 @@ +[True, True, True, True, True, True, True, True, True, True] +[True, True, True, True, True, True, True, True, True, True] +[[True, True], [True, True]] diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/where.py b/circuitpython/extmod/ulab/tests/2d/numpy/where.py new file mode 100644 index 0000000..18bf1cc --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/where.py @@ -0,0 +1,18 @@ +from ulab import numpy as np + + +a = np.array(range(8)) + +print(np.where(a < 4, 1, 0)) +print(np.where(a < 4, 2 * a, 0)) + +a = np.array(range(12)).reshape((3, 4)) +print(np.where(a < 6, a, -1)) + +b = np.array(range(4)) +print(np.where(a < 6, 10 + b, -1)) + +# test upcasting here +b = np.array(range(4), dtype=np.uint8) +c = np.array([25, 25, 25, 25], dtype=np.int16) +print(np.where(a < 6, b, c)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/where.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/where.py.exp new file mode 100644 index 0000000..b61090b --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/where.py.exp @@ -0,0 +1,11 @@ +array([1, 1, 1, 1, 0, 0, 0, 0], dtype=uint8) +array([0.0, 2.0, 4.0, 6.0, 0.0, 0.0, 0.0, 0.0], dtype=float64) +array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, -1.0, -1.0], + [-1.0, -1.0, -1.0, -1.0]], dtype=float64) +array([[10.0, 11.0, 12.0, 13.0], + [10.0, 11.0, -1.0, -1.0], + [-1.0, -1.0, -1.0, -1.0]], dtype=float64) +array([[0, 1, 2, 3], + [0, 1, 25, 25], + [25, 25, 25, 25]], dtype=int16) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/zeros.py b/circuitpython/extmod/ulab/tests/2d/numpy/zeros.py new file mode 100644 index 0000000..af9bd0f --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/zeros.py @@ -0,0 +1,13 @@ +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float) + +print(np.zeros(3)) +print(np.zeros((3,3))) + +for dtype in dtypes: + print(np.zeros((3,3), dtype=dtype)) + print(np.zeros((4,2), dtype=dtype)) diff --git a/circuitpython/extmod/ulab/tests/2d/numpy/zeros.py.exp b/circuitpython/extmod/ulab/tests/2d/numpy/zeros.py.exp new file mode 100644 index 0000000..ec61a9c --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/numpy/zeros.py.exp @@ -0,0 +1,39 @@ +array([0.0, 0.0, 0.0], dtype=float64) +array([[0.0, 0.0, 0.0], + [0.0, 0.0, 0.0], + [0.0, 0.0, 0.0]], dtype=float64) +array([[0, 0, 0], + [0, 0, 0], + [0, 0, 0]], dtype=uint8) +array([[0, 0], + [0, 0], + [0, 0], + [0, 0]], dtype=uint8) +array([[0, 0, 0], + [0, 0, 0], + [0, 0, 0]], dtype=int8) +array([[0, 0], + [0, 0], + [0, 0], + [0, 0]], dtype=int8) +array([[0, 0, 0], + [0, 0, 0], + [0, 0, 0]], dtype=uint16) +array([[0, 0], + [0, 0], + [0, 0], + [0, 0]], dtype=uint16) +array([[0, 0, 0], + [0, 0, 0], + [0, 0, 0]], dtype=int16) +array([[0, 0], + [0, 0], + [0, 0], + [0, 0]], dtype=int16) +array([[0.0, 0.0, 0.0], + [0.0, 0.0, 0.0], + [0.0, 0.0, 0.0]], dtype=float64) +array([[0.0, 0.0], + [0.0, 0.0], + [0.0, 0.0], + [0.0, 0.0]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/2d/scipy/cho_solve.py b/circuitpython/extmod/ulab/tests/2d/scipy/cho_solve.py new file mode 100644 index 0000000..57643c8 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/scipy/cho_solve.py @@ -0,0 +1,29 @@ +import math + +try: + from ulab import scipy, numpy as np +except ImportError: + import scipy + import numpy as np + +## test cholesky solve +L = np.array([[3, 0, 0, 0], [2, 1, 0, 0], [1, 0, 1, 0], [1, 2, 1, 8]]) +b = np.array([4, 2, 4, 2]) + +# L needs to be a lower triangular matrix +result = scipy.linalg.cho_solve(L, b) +ref_result = np.array([-0.01388888888888906, -0.6458333333333331, 2.677083333333333, -0.01041666666666667]) + +for i in range(4): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-6, abs_tol=1E-6)) + +## test cholesky and cho_solve together +C = np.array([[18, 22, 54, 42], [22, 70, 86, 62], [54, 86, 174, 134], [42, 62, 134, 106]]) +L = np.linalg.cholesky(C) + +# L is a lower triangular matrix obtained by performing cholesky of positive-definite linear system +result = scipy.linalg.cho_solve(L, b) +ref_result = np.array([6.5625, 1.1875, -2.9375, 0.4375]) + +for i in range(4): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-6, abs_tol=1E-6)) diff --git a/circuitpython/extmod/ulab/tests/2d/scipy/cho_solve.py.exp b/circuitpython/extmod/ulab/tests/2d/scipy/cho_solve.py.exp new file mode 100644 index 0000000..483b67e --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/scipy/cho_solve.py.exp @@ -0,0 +1,8 @@ +True +True +True +True +True +True +True +True diff --git a/circuitpython/extmod/ulab/tests/2d/scipy/solve_triangular.py b/circuitpython/extmod/ulab/tests/2d/scipy/solve_triangular.py new file mode 100644 index 0000000..fdb6743 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/scipy/solve_triangular.py @@ -0,0 +1,22 @@ +import math + +try: + from ulab import scipy, numpy as np +except ImportError: + import scipy + import numpy as np + +A = np.array([[3, 0, 2, 6], [2, 1, 0, 1], [1, 0, 1, 4], [1, 2, 1, 8]]) +b = np.array([4, 2, 4, 2]) + +# forward substitution +result = scipy.linalg.solve_triangular(A, b, lower=True) +ref_result = np.array([1.333333333, -0.666666666, 2.666666666, -0.083333333]) +for i in range(4): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-6, abs_tol=1E-6)) + +# backward substitution +result = scipy.linalg.solve_triangular(A, b, lower=False) +ref_result = np.array([-1.166666666, 1.75, 3.0, 0.25]) +for i in range(4): + print(math.isclose(result[i], ref_result[i], rel_tol=1E-6, abs_tol=1E-6)) diff --git a/circuitpython/extmod/ulab/tests/2d/scipy/solve_triangular.py.exp b/circuitpython/extmod/ulab/tests/2d/scipy/solve_triangular.py.exp new file mode 100644 index 0000000..483b67e --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/scipy/solve_triangular.py.exp @@ -0,0 +1,8 @@ +True +True +True +True +True +True +True +True diff --git a/circuitpython/extmod/ulab/tests/2d/utils/from_buffer.py b/circuitpython/extmod/ulab/tests/2d/utils/from_buffer.py new file mode 100644 index 0000000..64a9897 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/utils/from_buffer.py @@ -0,0 +1,22 @@ +from ulab import numpy as np +from ulab import utils + +a = bytearray([1, 0, 0, 1, 0, 255, 255, 255]) +print(utils.from_uint16_buffer(a)) +a = bytearray([1, 0, 0, 1, 0, 255, 255, 255]) +print(utils.from_int16_buffer(a)) + +a = bytearray([1, 0, 0, 1, 0, 255, 255, 255]) +print(utils.from_uint32_buffer(a)) +a = bytearray([1, 0, 0, 1, 0, 255, 255, 255]) +print(utils.from_int32_buffer(a)) + +a = bytearray([1, 0, 0, 1, 0, 0, 255, 255]) +print(utils.from_uint32_buffer(a)) +a = bytearray([1, 0, 0, 1, 0, 0, 255, 255]) +print(utils.from_int32_buffer(a)) + +a = bytearray([1, 0, 0, 0, 0, 0, 0, 1]) +print(utils.from_uint32_buffer(a)) +a = bytearray([1, 0, 0, 0, 0, 0, 0, 1]) +print(utils.from_int32_buffer(a)) diff --git a/circuitpython/extmod/ulab/tests/2d/utils/from_buffer.py.exp b/circuitpython/extmod/ulab/tests/2d/utils/from_buffer.py.exp new file mode 100644 index 0000000..de9f743 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/2d/utils/from_buffer.py.exp @@ -0,0 +1,8 @@ +array([1.0, 256.0, 65280.0, 65535.00000000001], dtype=float64) +array([1.0, 256.0, -256.0, -1.0], dtype=float64) +array([16777217.0, 4294967040.0], dtype=float64) +array([16777217.0, -256.0], dtype=float64) +array([16777217.0, 4294901760.0], dtype=float64) +array([16777217.0, -65536.0], dtype=float64) +array([1.0, 16777216.0], dtype=float64) +array([1.0, 16777216.0], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/3d/complex/complex_exp.py b/circuitpython/extmod/ulab/tests/3d/complex/complex_exp.py new file mode 100644 index 0000000..ef36e22 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/3d/complex/complex_exp.py @@ -0,0 +1,24 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(4), dtype=dtype) + b = a.reshape((2, 2)) + print('\narray:\n', a) + print('\nexponential:\n', np.exp(a)) + print('\narray:\n', b) + print('\nexponential:\n', np.exp(b)) + +a = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +b = np.array([[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]], dtype=np.complex) +c = np.array([[[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]], [[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]]], dtype=np.complex) + +for m in (a, b, c): + print('\n\narray:\n', m) + print('\nexponential:\n', np.exp(m)) diff --git a/circuitpython/extmod/ulab/tests/3d/complex/complex_exp.py.exp b/circuitpython/extmod/ulab/tests/3d/complex/complex_exp.py.exp new file mode 100644 index 0000000..0ebc9c8 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/3d/complex/complex_exp.py.exp @@ -0,0 +1,115 @@ + +array: + array([0, 1, 2, 3], dtype=uint8) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=uint8) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int8) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=int8) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=uint16) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=uint16) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int16) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=int16) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0.0, 1.0], + [2.0, 3.0]], dtype=float64) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], dtype=complex) + +exponential: + array([1.0+0.0j, 2.718281828459045+0.0j, 7.38905609893065+0.0j, 20.08553692318767+0.0j], dtype=complex) + +array: + array([[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], dtype=complex) + +exponential: + array([[1.0+0.0j, 2.718281828459045+0.0j], + [7.38905609893065+0.0j, 20.08553692318767+0.0j]], dtype=complex) + + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +exponential: + array([1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], dtype=complex) + + +array: + array([[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], dtype=complex) + +exponential: + array([[1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], + [1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]], dtype=complex) + + +array: + array([[[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]]], dtype=complex) + +exponential: + array([[[1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], + [1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]], + + [[1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], + [1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]]], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/3d/complex/complex_sqrt.py b/circuitpython/extmod/ulab/tests/3d/complex/complex_sqrt.py new file mode 100644 index 0000000..4bc9def --- /dev/null +++ b/circuitpython/extmod/ulab/tests/3d/complex/complex_sqrt.py @@ -0,0 +1,26 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(8), dtype=dtype) + b = a.reshape((2, 2, 2)) + outtype = np.float if dtype is not np.complex else np.complex + print('\narray:\n', a) + print('\nsquare root:\n', np.sqrt(a, dtype=outtype)) + print('\narray:\n', b) + print('\nsquare root:\n', np.sqrt(b, dtype=outtype)) + + +a = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +b = np.array([0, 1j, 2+2j, 3-3j] * 2, dtype=np.complex).reshape((2, 4)) +c = np.array([0, 1j, 2+2j, 3-3j] * 2, dtype=np.complex).reshape((2, 2, 2)) + +for m in (a, b, c): + print('\n\narray:\n', m) + print('\nsquare root:\n', np.sqrt(m, dtype=np.complex)) diff --git a/circuitpython/extmod/ulab/tests/3d/complex/complex_sqrt.py.exp b/circuitpython/extmod/ulab/tests/3d/complex/complex_sqrt.py.exp new file mode 100644 index 0000000..1744cc7 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/3d/complex/complex_sqrt.py.exp @@ -0,0 +1,151 @@ + +array: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint8) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877, 2.0, 2.23606797749979, 2.449489742783178, 2.645751311064591], dtype=float64) + +array: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=uint8) + +square root: + array([[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], dtype=float64) + +array: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=int8) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877, 2.0, 2.23606797749979, 2.449489742783178, 2.645751311064591], dtype=float64) + +array: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=int8) + +square root: + array([[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], dtype=float64) + +array: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint16) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877, 2.0, 2.23606797749979, 2.449489742783178, 2.645751311064591], dtype=float64) + +array: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=uint16) + +square root: + array([[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], dtype=float64) + +array: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=int16) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877, 2.0, 2.23606797749979, 2.449489742783178, 2.645751311064591], dtype=float64) + +array: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=int16) + +square root: + array([[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], dtype=float64) + +array: + array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0], dtype=float64) + +square root: + array([0.0, 1.0, 1.414213562373095, 1.732050807568877, 2.0, 2.23606797749979, 2.449489742783178, 2.645751311064591], dtype=float64) + +array: + array([[[0.0, 1.0], + [2.0, 3.0]], + + [[4.0, 5.0], + [6.0, 7.0]]], dtype=float64) + +square root: + array([[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], dtype=float64) + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j, 6.0+0.0j, 7.0+0.0j], dtype=complex) + +square root: + array([0.0+0.0j, 1.0+0.0j, 1.414213562373095+0.0j, 1.732050807568877+0.0j, 2.0+0.0j, 2.23606797749979+0.0j, 2.449489742783178+0.0j, 2.645751311064591+0.0j], dtype=complex) + +array: + array([[[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], + + [[4.0+0.0j, 5.0+0.0j], + [6.0+0.0j, 7.0+0.0j]]], dtype=complex) + +square root: + array([[[0.0+0.0j, 1.0+0.0j], + [1.414213562373095+0.0j, 1.732050807568877+0.0j]], + + [[2.0+0.0j, 2.23606797749979+0.0j], + [2.449489742783178+0.0j, 2.645751311064591+0.0j]]], dtype=complex) + + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +square root: + array([0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j], dtype=complex) + + +array: + array([[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], dtype=complex) + +square root: + array([[0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j], + [0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]], dtype=complex) + + +array: + array([[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]], dtype=complex) + +square root: + array([[[0.0+0.0j, 0.7071067811865476+0.7071067811865475j], + [1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]], + + [[0.0+0.0j, 0.7071067811865476+0.7071067811865475j], + [1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]]], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/3d/complex/imag_real.py b/circuitpython/extmod/ulab/tests/3d/complex/imag_real.py new file mode 100644 index 0000000..1e12a8d --- /dev/null +++ b/circuitpython/extmod/ulab/tests/3d/complex/imag_real.py @@ -0,0 +1,28 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(8), dtype=dtype) + print('\narray:\n', a) + print('\nreal part:\n', np.real(a)) + print('\nimaginary part:\n', np.imag(a)) + for m in (a.reshape((2, 4)), a.reshape((2, 2, 2))): + print('\narray:\n', m) + print('\nreal part:\n', np.real(m)) + print('\nimaginary part:\n', np.imag(m), '\n') + + +a = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +b = np.array([[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]], dtype=np.complex) +c = np.array([[[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]], [[0, 1j, 2+2j, 3-3j], [0, 1j, 2+2j, 3-3j]]], dtype=np.complex) + +for m in (a, b, c): + print('\n\narray:\n', m) + print('\nreal part:\n', np.real(m)) + print('\nimaginary part:\n', np.imag(m)) diff --git a/circuitpython/extmod/ulab/tests/3d/complex/imag_real.py.exp b/circuitpython/extmod/ulab/tests/3d/complex/imag_real.py.exp new file mode 100644 index 0000000..3eaf9d0 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/3d/complex/imag_real.py.exp @@ -0,0 +1,309 @@ + +array: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint8) + +real part: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint8) + +imaginary part: + array([0, 0, 0, 0, 0, 0, 0, 0], dtype=uint8) + +array: + array([[0, 1, 2, 3], + [4, 5, 6, 7]], dtype=uint8) + +real part: + array([[0, 1, 2, 3], + [4, 5, 6, 7]], dtype=uint8) + +imaginary part: + array([[0, 0, 0, 0], + [0, 0, 0, 0]], dtype=uint8) + + +array: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=uint8) + +real part: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=uint8) + +imaginary part: + array([[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]], dtype=uint8) + + +array: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=int8) + +real part: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=int8) + +imaginary part: + array([0, 0, 0, 0, 0, 0, 0, 0], dtype=int8) + +array: + array([[0, 1, 2, 3], + [4, 5, 6, 7]], dtype=int8) + +real part: + array([[0, 1, 2, 3], + [4, 5, 6, 7]], dtype=int8) + +imaginary part: + array([[0, 0, 0, 0], + [0, 0, 0, 0]], dtype=int8) + + +array: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=int8) + +real part: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=int8) + +imaginary part: + array([[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]], dtype=int8) + + +array: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint16) + +real part: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint16) + +imaginary part: + array([0, 0, 0, 0, 0, 0, 0, 0], dtype=uint16) + +array: + array([[0, 1, 2, 3], + [4, 5, 6, 7]], dtype=uint16) + +real part: + array([[0, 1, 2, 3], + [4, 5, 6, 7]], dtype=uint16) + +imaginary part: + array([[0, 0, 0, 0], + [0, 0, 0, 0]], dtype=uint16) + + +array: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=uint16) + +real part: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=uint16) + +imaginary part: + array([[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]], dtype=uint16) + + +array: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=int16) + +real part: + array([0, 1, 2, 3, 4, 5, 6, 7], dtype=int16) + +imaginary part: + array([0, 0, 0, 0, 0, 0, 0, 0], dtype=int16) + +array: + array([[0, 1, 2, 3], + [4, 5, 6, 7]], dtype=int16) + +real part: + array([[0, 1, 2, 3], + [4, 5, 6, 7]], dtype=int16) + +imaginary part: + array([[0, 0, 0, 0], + [0, 0, 0, 0]], dtype=int16) + + +array: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=int16) + +real part: + array([[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], dtype=int16) + +imaginary part: + array([[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]], dtype=int16) + + +array: + array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0], dtype=float64) + +real part: + array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0], dtype=float64) + +imaginary part: + array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], dtype=float64) + +array: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0]], dtype=float64) + +real part: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0]], dtype=float64) + +imaginary part: + array([[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) + + +array: + array([[[0.0, 1.0], + [2.0, 3.0]], + + [[4.0, 5.0], + [6.0, 7.0]]], dtype=float64) + +real part: + array([[[0.0, 1.0], + [2.0, 3.0]], + + [[4.0, 5.0], + [6.0, 7.0]]], dtype=float64) + +imaginary part: + array([[[0.0, 0.0], + [0.0, 0.0]], + + [[0.0, 0.0], + [0.0, 0.0]]], dtype=float64) + + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j, 4.0+0.0j, 5.0+0.0j, 6.0+0.0j, 7.0+0.0j], dtype=complex) + +real part: + array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0], dtype=float64) + +imaginary part: + array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], dtype=float64) + +array: + array([[0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], + [4.0+0.0j, 5.0+0.0j, 6.0+0.0j, 7.0+0.0j]], dtype=complex) + +real part: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0]], dtype=float64) + +imaginary part: + array([[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) + + +array: + array([[[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], + + [[4.0+0.0j, 5.0+0.0j], + [6.0+0.0j, 7.0+0.0j]]], dtype=complex) + +real part: + array([[[0.0, 1.0], + [2.0, 3.0]], + + [[4.0, 5.0], + [6.0, 7.0]]], dtype=float64) + +imaginary part: + array([[[0.0, 0.0], + [0.0, 0.0]], + + [[0.0, 0.0], + [0.0, 0.0]]], dtype=float64) + + + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +real part: + array([0.0, 0.0, 2.0, 3.0], dtype=float64) + +imaginary part: + array([0.0, 1.0, 2.0, -3.0], dtype=float64) + + +array: + array([[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], dtype=complex) + +real part: + array([[0.0, 0.0, 2.0, 3.0], + [0.0, 0.0, 2.0, 3.0]], dtype=float64) + +imaginary part: + array([[0.0, 1.0, 2.0, -3.0], + [0.0, 1.0, 2.0, -3.0]], dtype=float64) + + +array: + array([[[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]]], dtype=complex) + +real part: + array([[[0.0, 0.0, 2.0, 3.0], + [0.0, 0.0, 2.0, 3.0]], + + [[0.0, 0.0, 2.0, 3.0], + [0.0, 0.0, 2.0, 3.0]]], dtype=float64) + +imaginary part: + array([[[0.0, 1.0, 2.0, -3.0], + [0.0, 1.0, 2.0, -3.0]], + + [[0.0, 1.0, 2.0, -3.0], + [0.0, 1.0, 2.0, -3.0]]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/3d/numpy/create.py b/circuitpython/extmod/ulab/tests/3d/numpy/create.py new file mode 100644 index 0000000..a5c1fa1 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/3d/numpy/create.py @@ -0,0 +1,2 @@ +from ulab import numpy as np +print(sum(np.ones((3,2,4)))) diff --git a/circuitpython/extmod/ulab/tests/3d/numpy/create.py.exp b/circuitpython/extmod/ulab/tests/3d/numpy/create.py.exp new file mode 100644 index 0000000..099429b --- /dev/null +++ b/circuitpython/extmod/ulab/tests/3d/numpy/create.py.exp @@ -0,0 +1,2 @@ +array([[3.0, 3.0, 3.0, 3.0], + [3.0, 3.0, 3.0, 3.0]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/4d/complex/complex_exp.py b/circuitpython/extmod/ulab/tests/4d/complex/complex_exp.py new file mode 100644 index 0000000..63ed873 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/4d/complex/complex_exp.py @@ -0,0 +1,26 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(4), dtype=dtype) + b = a.reshape((2, 2)) + print('\narray:\n', a) + print('\nexponential:\n', np.exp(a)) + print('\narray:\n', b) + print('\nexponential:\n', np.exp(b)) + + +a = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +b = np.array([0, 1j, 2+2j, 3-3j] * 2, dtype=np.complex).reshape((2, 4)) +c = np.array([0, 1j, 2+2j, 3-3j] * 2, dtype=np.complex).reshape((2, 2, 2)) +d = np.array([0, 1j, 2+2j, 3-3j] * 4, dtype=np.complex).reshape((2, 2, 2, 2)) + +for m in (a, b, c, d): + print('\n\narray:\n', m) + print('\nexponential:\n', np.exp(m)) diff --git a/circuitpython/extmod/ulab/tests/4d/complex/complex_exp.py.exp b/circuitpython/extmod/ulab/tests/4d/complex/complex_exp.py.exp new file mode 100644 index 0000000..ebf135e --- /dev/null +++ b/circuitpython/extmod/ulab/tests/4d/complex/complex_exp.py.exp @@ -0,0 +1,142 @@ + +array: + array([0, 1, 2, 3], dtype=uint8) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=uint8) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int8) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=int8) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=uint16) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=uint16) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0, 1, 2, 3], dtype=int16) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0, 1], + [2, 3]], dtype=int16) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0.0, 1.0, 2.0, 3.0], dtype=float64) + +exponential: + array([1.0, 2.718281828459045, 7.38905609893065, 20.08553692318767], dtype=float64) + +array: + array([[0.0, 1.0], + [2.0, 3.0]], dtype=float64) + +exponential: + array([[1.0, 2.718281828459045], + [7.38905609893065, 20.08553692318767]], dtype=float64) + +array: + array([0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], dtype=complex) + +exponential: + array([1.0+0.0j, 2.718281828459045+0.0j, 7.38905609893065+0.0j, 20.08553692318767+0.0j], dtype=complex) + +array: + array([[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], dtype=complex) + +exponential: + array([[1.0+0.0j, 2.718281828459045+0.0j], + [7.38905609893065+0.0j, 20.08553692318767+0.0j]], dtype=complex) + + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +exponential: + array([1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], dtype=complex) + + +array: + array([[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], dtype=complex) + +exponential: + array([[1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j], + [1.0+0.0j, 0.5403023058681398+0.8414709848078965j, -3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]], dtype=complex) + + +array: + array([[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]], dtype=complex) + +exponential: + array([[[1.0+0.0j, 0.5403023058681398+0.8414709848078965j], + [-3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]], + + [[1.0+0.0j, 0.5403023058681398+0.8414709848078965j], + [-3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]]], dtype=complex) + + +array: + array([[[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]], + + [[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]]], dtype=complex) + +exponential: + array([[[[1.0+0.0j, 0.5403023058681398+0.8414709848078965j], + [-3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]], + + [[1.0+0.0j, 0.5403023058681398+0.8414709848078965j], + [-3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]]], + + [[[1.0+0.0j, 0.5403023058681398+0.8414709848078965j], + [-3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]], + + [[1.0+0.0j, 0.5403023058681398+0.8414709848078965j], + [-3.074932320639359+6.71884969742825j, -19.88453084414699-2.834471132487004j]]]], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/4d/complex/complex_sqrt.py b/circuitpython/extmod/ulab/tests/4d/complex/complex_sqrt.py new file mode 100644 index 0000000..052a07d --- /dev/null +++ b/circuitpython/extmod/ulab/tests/4d/complex/complex_sqrt.py @@ -0,0 +1,27 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(16), dtype=dtype) + b = a.reshape((2, 2, 2, 2)) + outtype = np.float if dtype is not np.complex else np.complex + print('\narray:\n', a) + print('\nsquare root:\n', np.sqrt(a, dtype=outtype)) + print('\narray:\n', b) + print('\nsquare root:\n', np.sqrt(b, dtype=outtype)) + + +a = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +b = np.array([0, 1j, 2+2j, 3-3j] * 2, dtype=np.complex).reshape((2, 4)) +c = np.array([0, 1j, 2+2j, 3-3j] * 2, dtype=np.complex).reshape((2, 2, 2)) +d = np.array([0, 1j, 2+2j, 3-3j] * 4, dtype=np.complex).reshape((2, 2, 2, 2)) + +for m in (a, b, c, d): + print('\n\narray:\n', m) + print('\nsquare root:\n', np.sqrt(m, dtype=np.complex)) diff --git a/circuitpython/extmod/ulab/tests/4d/complex/complex_sqrt.py.exp b/circuitpython/extmod/ulab/tests/4d/complex/complex_sqrt.py.exp new file mode 100644 index 0000000..44f87f0 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/4d/complex/complex_sqrt.py.exp @@ -0,0 +1,250 @@ + +array: + array([0, 1, 2, ..., 13, 14, 15], dtype=uint8) + +square root: + array([0.0, 1.0, 1.414213562373095, ..., 3.605551275463989, 3.741657386773941, 3.872983346207417], dtype=float64) + +array: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=uint8) + +square root: + array([[[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], + + [[[2.82842712474619, 3.0], + [3.16227766016838, 3.3166247903554]], + + [[3.464101615137754, 3.605551275463989], + [3.741657386773941, 3.872983346207417]]]], dtype=float64) + +array: + array([0, 1, 2, ..., 13, 14, 15], dtype=int8) + +square root: + array([0.0, 1.0, 1.414213562373095, ..., 3.605551275463989, 3.741657386773941, 3.872983346207417], dtype=float64) + +array: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=int8) + +square root: + array([[[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], + + [[[2.82842712474619, 3.0], + [3.16227766016838, 3.3166247903554]], + + [[3.464101615137754, 3.605551275463989], + [3.741657386773941, 3.872983346207417]]]], dtype=float64) + +array: + array([0, 1, 2, ..., 13, 14, 15], dtype=uint16) + +square root: + array([0.0, 1.0, 1.414213562373095, ..., 3.605551275463989, 3.741657386773941, 3.872983346207417], dtype=float64) + +array: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=uint16) + +square root: + array([[[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], + + [[[2.82842712474619, 3.0], + [3.16227766016838, 3.3166247903554]], + + [[3.464101615137754, 3.605551275463989], + [3.741657386773941, 3.872983346207417]]]], dtype=float64) + +array: + array([0, 1, 2, ..., 13, 14, 15], dtype=int16) + +square root: + array([0.0, 1.0, 1.414213562373095, ..., 3.605551275463989, 3.741657386773941, 3.872983346207417], dtype=float64) + +array: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=int16) + +square root: + array([[[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], + + [[[2.82842712474619, 3.0], + [3.16227766016838, 3.3166247903554]], + + [[3.464101615137754, 3.605551275463989], + [3.741657386773941, 3.872983346207417]]]], dtype=float64) + +array: + array([0.0, 1.0, 2.0, ..., 13.0, 14.0, 15.0], dtype=float64) + +square root: + array([0.0, 1.0, 1.414213562373095, ..., 3.605551275463989, 3.741657386773941, 3.872983346207417], dtype=float64) + +array: + array([[[[0.0, 1.0], + [2.0, 3.0]], + + [[4.0, 5.0], + [6.0, 7.0]]], + + [[[8.0, 9.0], + [10.0, 11.0]], + + [[12.0, 13.0], + [14.0, 15.0]]]], dtype=float64) + +square root: + array([[[[0.0, 1.0], + [1.414213562373095, 1.732050807568877]], + + [[2.0, 2.23606797749979], + [2.449489742783178, 2.645751311064591]]], + + [[[2.82842712474619, 3.0], + [3.16227766016838, 3.3166247903554]], + + [[3.464101615137754, 3.605551275463989], + [3.741657386773941, 3.872983346207417]]]], dtype=float64) + +array: + array([0j, 1.0+0.0j, 2.0+0.0j, ..., 13.0+0.0j, 14.0+0.0j, 15.0+0.0j], dtype=complex) + +square root: + array([0j, 1.0+0.0j, 1.414213562373095+0.0j, ..., 3.605551275463989+0.0j, 3.741657386773941+0.0j, 3.872983346207417+0.0j], dtype=complex) + +array: + array([[[[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], + + [[4.0+0.0j, 5.0+0.0j], + [6.0+0.0j, 7.0+0.0j]]], + + [[[8.0+0.0j, 9.0+0.0j], + [10.0+0.0j, 11.0+0.0j]], + + [[12.0+0.0j, 13.0+0.0j], + [14.0+0.0j, 15.0+0.0j]]]], dtype=complex) + +square root: + array([[[[0.0+0.0j, 1.0+0.0j], + [1.414213562373095+0.0j, 1.732050807568877+0.0j]], + + [[2.0+0.0j, 2.23606797749979+0.0j], + [2.449489742783178+0.0j, 2.645751311064591+0.0j]]], + + [[[2.82842712474619+0.0j, 3.0+0.0j], + [3.16227766016838+0.0j, 3.3166247903554+0.0j]], + + [[3.464101615137754+0.0j, 3.605551275463989+0.0j], + [3.741657386773941+0.0j, 3.872983346207417+0.0j]]]], dtype=complex) + + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +square root: + array([0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j], dtype=complex) + + +array: + array([[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], dtype=complex) + +square root: + array([[0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j], + [0.0+0.0j, 0.7071067811865476+0.7071067811865475j, 1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]], dtype=complex) + + +array: + array([[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]], dtype=complex) + +square root: + array([[[0.0+0.0j, 0.7071067811865476+0.7071067811865475j], + [1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]], + + [[0.0+0.0j, 0.7071067811865476+0.7071067811865475j], + [1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]]], dtype=complex) + + +array: + array([[[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]], + + [[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]]], dtype=complex) + +square root: + array([[[[0.0+0.0j, 0.7071067811865476+0.7071067811865475j], + [1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]], + + [[0.0+0.0j, 0.7071067811865476+0.7071067811865475j], + [1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]]], + + [[[0.0+0.0j, 0.7071067811865476+0.7071067811865475j], + [1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]], + + [[0.0+0.0j, 0.7071067811865476+0.7071067811865475j], + [1.553773974030037+0.6435942529055827j, 1.902976705995016-0.7882387605032136j]]]], dtype=complex) diff --git a/circuitpython/extmod/ulab/tests/4d/complex/imag_real.py b/circuitpython/extmod/ulab/tests/4d/complex/imag_real.py new file mode 100644 index 0000000..63b9da5 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/4d/complex/imag_real.py @@ -0,0 +1,29 @@ +# this test is meaningful only, when the firmware supports complex arrays + +try: + from ulab import numpy as np +except: + import numpy as np + +dtypes = (np.uint8, np.int8, np.uint16, np.int16, np.float, np.complex) + +for dtype in dtypes: + a = np.array(range(16), dtype=dtype) + print('\narray:\n', a) + print('\nreal part:\n', np.real(a)) + print('\nimaginary part:\n', np.imag(a)) + for m in (a.reshape((4, 4)), a.reshape((2, 2, 4)), a.reshape((2, 2, 2, 2))): + print('\narray:\n', m) + print('\nreal part:\n', np.real(m)) + print('\nimaginary part:\n', np.imag(m), '\n') + + +a = np.array([0, 1j, 2+2j, 3-3j], dtype=np.complex) +b = np.array([0, 1j, 2+2j, 3-3j] * 2, dtype=np.complex).reshape((2, 4)) +c = np.array([0, 1j, 2+2j, 3-3j] * 2, dtype=np.complex).reshape((2, 2, 2)) +d = np.array([0, 1j, 2+2j, 3-3j] * 4, dtype=np.complex).reshape((2, 2, 2, 2)) + +for m in (a, b, c, d): + print('\n\narray:\n', m) + print('\nreal part:\n', np.real(m)) + print('\nimaginary part:\n', np.imag(m))
\ No newline at end of file diff --git a/circuitpython/extmod/ulab/tests/4d/complex/imag_real.py.exp b/circuitpython/extmod/ulab/tests/4d/complex/imag_real.py.exp new file mode 100644 index 0000000..95c9ab2 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/4d/complex/imag_real.py.exp @@ -0,0 +1,625 @@ + +array: + array([0, 1, 2, ..., 13, 14, 15], dtype=uint8) + +real part: + array([0, 1, 2, ..., 13, 14, 15], dtype=uint8) + +imaginary part: + array([0, 0, 0, ..., 0, 0, 0], dtype=uint8) + +array: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11], + [12, 13, 14, 15]], dtype=uint8) + +real part: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11], + [12, 13, 14, 15]], dtype=uint8) + +imaginary part: + array([[0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]], dtype=uint8) + + +array: + array([[[0, 1, 2, 3], + [4, 5, 6, 7]], + + [[8, 9, 10, 11], + [12, 13, 14, 15]]], dtype=uint8) + +real part: + array([[[0, 1, 2, 3], + [4, 5, 6, 7]], + + [[8, 9, 10, 11], + [12, 13, 14, 15]]], dtype=uint8) + +imaginary part: + array([[[0, 0, 0, 0], + [0, 0, 0, 0]], + + [[0, 0, 0, 0], + [0, 0, 0, 0]]], dtype=uint8) + + +array: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=uint8) + +real part: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=uint8) + +imaginary part: + array([[[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]], + + [[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]]], dtype=uint8) + + +array: + array([0, 1, 2, ..., 13, 14, 15], dtype=int8) + +real part: + array([0, 1, 2, ..., 13, 14, 15], dtype=int8) + +imaginary part: + array([0, 0, 0, ..., 0, 0, 0], dtype=int8) + +array: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11], + [12, 13, 14, 15]], dtype=int8) + +real part: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11], + [12, 13, 14, 15]], dtype=int8) + +imaginary part: + array([[0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]], dtype=int8) + + +array: + array([[[0, 1, 2, 3], + [4, 5, 6, 7]], + + [[8, 9, 10, 11], + [12, 13, 14, 15]]], dtype=int8) + +real part: + array([[[0, 1, 2, 3], + [4, 5, 6, 7]], + + [[8, 9, 10, 11], + [12, 13, 14, 15]]], dtype=int8) + +imaginary part: + array([[[0, 0, 0, 0], + [0, 0, 0, 0]], + + [[0, 0, 0, 0], + [0, 0, 0, 0]]], dtype=int8) + + +array: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=int8) + +real part: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=int8) + +imaginary part: + array([[[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]], + + [[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]]], dtype=int8) + + +array: + array([0, 1, 2, ..., 13, 14, 15], dtype=uint16) + +real part: + array([0, 1, 2, ..., 13, 14, 15], dtype=uint16) + +imaginary part: + array([0, 0, 0, ..., 0, 0, 0], dtype=uint16) + +array: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11], + [12, 13, 14, 15]], dtype=uint16) + +real part: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11], + [12, 13, 14, 15]], dtype=uint16) + +imaginary part: + array([[0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]], dtype=uint16) + + +array: + array([[[0, 1, 2, 3], + [4, 5, 6, 7]], + + [[8, 9, 10, 11], + [12, 13, 14, 15]]], dtype=uint16) + +real part: + array([[[0, 1, 2, 3], + [4, 5, 6, 7]], + + [[8, 9, 10, 11], + [12, 13, 14, 15]]], dtype=uint16) + +imaginary part: + array([[[0, 0, 0, 0], + [0, 0, 0, 0]], + + [[0, 0, 0, 0], + [0, 0, 0, 0]]], dtype=uint16) + + +array: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=uint16) + +real part: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=uint16) + +imaginary part: + array([[[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]], + + [[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]]], dtype=uint16) + + +array: + array([0, 1, 2, ..., 13, 14, 15], dtype=int16) + +real part: + array([0, 1, 2, ..., 13, 14, 15], dtype=int16) + +imaginary part: + array([0, 0, 0, ..., 0, 0, 0], dtype=int16) + +array: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11], + [12, 13, 14, 15]], dtype=int16) + +real part: + array([[0, 1, 2, 3], + [4, 5, 6, 7], + [8, 9, 10, 11], + [12, 13, 14, 15]], dtype=int16) + +imaginary part: + array([[0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0], + [0, 0, 0, 0]], dtype=int16) + + +array: + array([[[0, 1, 2, 3], + [4, 5, 6, 7]], + + [[8, 9, 10, 11], + [12, 13, 14, 15]]], dtype=int16) + +real part: + array([[[0, 1, 2, 3], + [4, 5, 6, 7]], + + [[8, 9, 10, 11], + [12, 13, 14, 15]]], dtype=int16) + +imaginary part: + array([[[0, 0, 0, 0], + [0, 0, 0, 0]], + + [[0, 0, 0, 0], + [0, 0, 0, 0]]], dtype=int16) + + +array: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=int16) + +real part: + array([[[[0, 1], + [2, 3]], + + [[4, 5], + [6, 7]]], + + [[[8, 9], + [10, 11]], + + [[12, 13], + [14, 15]]]], dtype=int16) + +imaginary part: + array([[[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]], + + [[[0, 0], + [0, 0]], + + [[0, 0], + [0, 0]]]], dtype=int16) + + +array: + array([0.0, 1.0, 2.0, ..., 13.0, 14.0, 15.0], dtype=float64) + +real part: + array([0.0, 1.0, 2.0, ..., 13.0, 14.0, 15.0], dtype=float64) + +imaginary part: + array([0.0, 0.0, 0.0, ..., 0.0, 0.0, 0.0], dtype=float64) + +array: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0], + [12.0, 13.0, 14.0, 15.0]], dtype=float64) + +real part: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0], + [12.0, 13.0, 14.0, 15.0]], dtype=float64) + +imaginary part: + array([[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) + + +array: + array([[[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0]], + + [[8.0, 9.0, 10.0, 11.0], + [12.0, 13.0, 14.0, 15.0]]], dtype=float64) + +real part: + array([[[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0]], + + [[8.0, 9.0, 10.0, 11.0], + [12.0, 13.0, 14.0, 15.0]]], dtype=float64) + +imaginary part: + array([[[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], + + [[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]]], dtype=float64) + + +array: + array([[[[0.0, 1.0], + [2.0, 3.0]], + + [[4.0, 5.0], + [6.0, 7.0]]], + + [[[8.0, 9.0], + [10.0, 11.0]], + + [[12.0, 13.0], + [14.0, 15.0]]]], dtype=float64) + +real part: + array([[[[0.0, 1.0], + [2.0, 3.0]], + + [[4.0, 5.0], + [6.0, 7.0]]], + + [[[8.0, 9.0], + [10.0, 11.0]], + + [[12.0, 13.0], + [14.0, 15.0]]]], dtype=float64) + +imaginary part: + array([[[[0.0, 0.0], + [0.0, 0.0]], + + [[0.0, 0.0], + [0.0, 0.0]]], + + [[[0.0, 0.0], + [0.0, 0.0]], + + [[0.0, 0.0], + [0.0, 0.0]]]], dtype=float64) + + +array: + array([0j, 1.0+0.0j, 2.0+0.0j, ..., 13.0+0.0j, 14.0+0.0j, 15.0+0.0j], dtype=complex) + +real part: + array([0.0, 1.0, 2.0, ..., 13.0, 14.0, 15.0], dtype=float64) + +imaginary part: + array([0.0, 0.0, 0.0, ..., 0.0, 0.0, 0.0], dtype=float64) + +array: + array([[0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], + [4.0+0.0j, 5.0+0.0j, 6.0+0.0j, 7.0+0.0j], + [8.0+0.0j, 9.0+0.0j, 10.0+0.0j, 11.0+0.0j], + [12.0+0.0j, 13.0+0.0j, 14.0+0.0j, 15.0+0.0j]], dtype=complex) + +real part: + array([[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0], + [8.0, 9.0, 10.0, 11.0], + [12.0, 13.0, 14.0, 15.0]], dtype=float64) + +imaginary part: + array([[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], dtype=float64) + + +array: + array([[[0.0+0.0j, 1.0+0.0j, 2.0+0.0j, 3.0+0.0j], + [4.0+0.0j, 5.0+0.0j, 6.0+0.0j, 7.0+0.0j]], + + [[8.0+0.0j, 9.0+0.0j, 10.0+0.0j, 11.0+0.0j], + [12.0+0.0j, 13.0+0.0j, 14.0+0.0j, 15.0+0.0j]]], dtype=complex) + +real part: + array([[[0.0, 1.0, 2.0, 3.0], + [4.0, 5.0, 6.0, 7.0]], + + [[8.0, 9.0, 10.0, 11.0], + [12.0, 13.0, 14.0, 15.0]]], dtype=float64) + +imaginary part: + array([[[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]], + + [[0.0, 0.0, 0.0, 0.0], + [0.0, 0.0, 0.0, 0.0]]], dtype=float64) + + +array: + array([[[[0.0+0.0j, 1.0+0.0j], + [2.0+0.0j, 3.0+0.0j]], + + [[4.0+0.0j, 5.0+0.0j], + [6.0+0.0j, 7.0+0.0j]]], + + [[[8.0+0.0j, 9.0+0.0j], + [10.0+0.0j, 11.0+0.0j]], + + [[12.0+0.0j, 13.0+0.0j], + [14.0+0.0j, 15.0+0.0j]]]], dtype=complex) + +real part: + array([[[[0.0, 1.0], + [2.0, 3.0]], + + [[4.0, 5.0], + [6.0, 7.0]]], + + [[[8.0, 9.0], + [10.0, 11.0]], + + [[12.0, 13.0], + [14.0, 15.0]]]], dtype=float64) + +imaginary part: + array([[[[0.0, 0.0], + [0.0, 0.0]], + + [[0.0, 0.0], + [0.0, 0.0]]], + + [[[0.0, 0.0], + [0.0, 0.0]], + + [[0.0, 0.0], + [0.0, 0.0]]]], dtype=float64) + + + +array: + array([0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], dtype=complex) + +real part: + array([0.0, 0.0, 2.0, 3.0], dtype=float64) + +imaginary part: + array([0.0, 1.0, 2.0, -3.0], dtype=float64) + + +array: + array([[0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j], + [0.0+0.0j, 0.0+1.0j, 2.0+2.0j, 3.0-3.0j]], dtype=complex) + +real part: + array([[0.0, 0.0, 2.0, 3.0], + [0.0, 0.0, 2.0, 3.0]], dtype=float64) + +imaginary part: + array([[0.0, 1.0, 2.0, -3.0], + [0.0, 1.0, 2.0, -3.0]], dtype=float64) + + +array: + array([[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]], dtype=complex) + +real part: + array([[[0.0, 0.0], + [2.0, 3.0]], + + [[0.0, 0.0], + [2.0, 3.0]]], dtype=float64) + +imaginary part: + array([[[0.0, 1.0], + [2.0, -3.0]], + + [[0.0, 1.0], + [2.0, -3.0]]], dtype=float64) + + +array: + array([[[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]], + + [[[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]], + + [[0.0+0.0j, 0.0+1.0j], + [2.0+2.0j, 3.0-3.0j]]]], dtype=complex) + +real part: + array([[[[0.0, 0.0], + [2.0, 3.0]], + + [[0.0, 0.0], + [2.0, 3.0]]], + + [[[0.0, 0.0], + [2.0, 3.0]], + + [[0.0, 0.0], + [2.0, 3.0]]]], dtype=float64) + +imaginary part: + array([[[[0.0, 1.0], + [2.0, -3.0]], + + [[0.0, 1.0], + [2.0, -3.0]]], + + [[[0.0, 1.0], + [2.0, -3.0]], + + [[0.0, 1.0], + [2.0, -3.0]]]], dtype=float64) diff --git a/circuitpython/extmod/ulab/tests/4d/numpy/create.py b/circuitpython/extmod/ulab/tests/4d/numpy/create.py new file mode 100644 index 0000000..64c344c --- /dev/null +++ b/circuitpython/extmod/ulab/tests/4d/numpy/create.py @@ -0,0 +1,2 @@ +from ulab import numpy as np +print(sum(np.ones((3,4,2,5)))) diff --git a/circuitpython/extmod/ulab/tests/4d/numpy/create.py.exp b/circuitpython/extmod/ulab/tests/4d/numpy/create.py.exp new file mode 100644 index 0000000..9a28f75 --- /dev/null +++ b/circuitpython/extmod/ulab/tests/4d/numpy/create.py.exp @@ -0,0 +1,11 @@ +array([[[3.0, 3.0, 3.0, 3.0, 3.0], + [3.0, 3.0, 3.0, 3.0, 3.0]], + + [[3.0, 3.0, 3.0, 3.0, 3.0], + [3.0, 3.0, 3.0, 3.0, 3.0]], + + [[3.0, 3.0, 3.0, 3.0, 3.0], + [3.0, 3.0, 3.0, 3.0, 3.0]], + + [[3.0, 3.0, 3.0, 3.0, 3.0], + [3.0, 3.0, 3.0, 3.0, 3.0]]], dtype=float64) |