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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 +} |