{
 "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)"
   ]
  }
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