512 lines
15 KiB
Text
512 lines
15 KiB
Text
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-05-01T09:27:13.438054Z",
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"start_time": "2020-05-01T09:27:13.191491Z"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Populating the interactive namespace from numpy and matplotlib\n"
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]
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}
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],
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"source": [
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"%pylab inline"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Notebook magic"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-08-03T18:32:45.342280Z",
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"start_time": "2020-08-03T18:32:45.338442Z"
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}
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},
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"outputs": [],
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"source": [
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"from IPython.core.magic import Magics, magics_class, line_cell_magic\n",
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"from IPython.core.magic import cell_magic, register_cell_magic, register_line_magic\n",
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"from IPython.core.magic_arguments import argument, magic_arguments, parse_argstring\n",
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"import subprocess\n",
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"import os"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-07-23T20:31:25.296014Z",
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"start_time": "2020-07-23T20:31:25.265937Z"
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}
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},
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"outputs": [],
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"source": [
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"@magics_class\n",
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"class PyboardMagic(Magics):\n",
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" @cell_magic\n",
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" @magic_arguments()\n",
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" @argument('-skip')\n",
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" @argument('-unix')\n",
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" @argument('-pyboard')\n",
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" @argument('-file')\n",
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" @argument('-data')\n",
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" @argument('-time')\n",
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" @argument('-memory')\n",
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" def micropython(self, line='', cell=None):\n",
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" args = parse_argstring(self.micropython, line)\n",
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" if args.skip: # doesn't care about the cell's content\n",
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" print('skipped execution')\n",
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" return None # do not parse the rest\n",
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" if args.unix: # tests the code on the unix port. Note that this works on unix only\n",
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" with open('/dev/shm/micropython.py', 'w') as fout:\n",
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" fout.write(cell)\n",
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" proc = subprocess.Popen([\"../../micropython/ports/unix/micropython\", \"/dev/shm/micropython.py\"], \n",
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" stdout=subprocess.PIPE, stderr=subprocess.PIPE)\n",
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" print(proc.stdout.read().decode(\"utf-8\"))\n",
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" print(proc.stderr.read().decode(\"utf-8\"))\n",
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" return None\n",
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" if args.file: # can be used to copy the cell content onto the pyboard's flash\n",
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" spaces = \" \"\n",
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" try:\n",
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" with open(args.file, 'w') as fout:\n",
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" fout.write(cell.replace('\\t', spaces))\n",
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" printf('written cell to {}'.format(args.file))\n",
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" except:\n",
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" print('Failed to write to disc!')\n",
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" return None # do not parse the rest\n",
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" if args.data: # can be used to load data from the pyboard directly into kernel space\n",
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" message = pyb.exec(cell)\n",
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" if len(message) == 0:\n",
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" print('pyboard >>>')\n",
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" else:\n",
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" print(message.decode('utf-8'))\n",
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" # register new variable in user namespace\n",
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" self.shell.user_ns[args.data] = string_to_matrix(message.decode(\"utf-8\"))\n",
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" \n",
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" if args.time: # measures the time of executions\n",
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" pyb.exec('import utime')\n",
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" message = pyb.exec('t = utime.ticks_us()\\n' + cell + '\\ndelta = utime.ticks_diff(utime.ticks_us(), t)' + \n",
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" \"\\nprint('execution time: {:d} us'.format(delta))\")\n",
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" print(message.decode('utf-8'))\n",
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" \n",
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" if args.memory: # prints out memory information \n",
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" message = pyb.exec('from micropython import mem_info\\nprint(mem_info())\\n')\n",
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" print(\"memory before execution:\\n========================\\n\", message.decode('utf-8'))\n",
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" message = pyb.exec(cell)\n",
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" print(\">>> \", message.decode('utf-8'))\n",
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" message = pyb.exec('print(mem_info())')\n",
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" print(\"memory after execution:\\n========================\\n\", message.decode('utf-8'))\n",
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"\n",
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" if args.pyboard:\n",
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" message = pyb.exec(cell)\n",
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" print(message.decode('utf-8'))\n",
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"\n",
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"ip = get_ipython()\n",
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"ip.register_magics(PyboardMagic)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## pyboard"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 57,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-05-07T07:35:35.126401Z",
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"start_time": "2020-05-07T07:35:35.105824Z"
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}
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},
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"outputs": [],
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"source": [
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"import pyboard\n",
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"pyb = pyboard.Pyboard('/dev/ttyACM0')\n",
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"pyb.enter_raw_repl()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-05-19T19:11:18.145548Z",
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"start_time": "2020-05-19T19:11:18.137468Z"
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}
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},
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"outputs": [],
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"source": [
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"pyb.exit_raw_repl()\n",
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"pyb.close()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 58,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-05-07T07:35:38.725924Z",
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"start_time": "2020-05-07T07:35:38.645488Z"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n"
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]
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}
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],
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"source": [
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"%%micropython -pyboard 1\n",
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"\n",
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"import utime\n",
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"import ulab as np\n",
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"\n",
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"def timeit(n=1000):\n",
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" def wrapper(f, *args, **kwargs):\n",
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" func_name = str(f).split(' ')[1]\n",
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" def new_func(*args, **kwargs):\n",
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" run_times = np.zeros(n, dtype=np.uint16)\n",
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" for i in range(n):\n",
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" t = utime.ticks_us()\n",
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" result = f(*args, **kwargs)\n",
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" run_times[i] = utime.ticks_diff(utime.ticks_us(), t)\n",
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" print('{}() execution times based on {} cycles'.format(func_name, n, (delta2-delta1)/n))\n",
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" print('\\tbest: %d us'%np.min(run_times))\n",
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" print('\\tworst: %d us'%np.max(run_times))\n",
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" print('\\taverage: %d us'%np.mean(run_times))\n",
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" print('\\tdeviation: +/-%.3f us'%np.std(run_times)) \n",
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" return result\n",
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" return new_func\n",
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" return wrapper\n",
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"\n",
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"def timeit(f, *args, **kwargs):\n",
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" func_name = str(f).split(' ')[1]\n",
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" def new_func(*args, **kwargs):\n",
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" t = utime.ticks_us()\n",
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" result = f(*args, **kwargs)\n",
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" print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')\n",
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" return result\n",
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" return new_func"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"__END_OF_DEFS__"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Fourier transforms\n",
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"\n",
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"Functions related to Fourier transforms can be called by prepending them with `numpy.fft.`. The module defines the following two functions:\n",
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"\n",
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"1. [numpy.fft.fft](#fft)\n",
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"1. [numpy.fft.ifft](#ifft)\n",
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"\n",
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"`numpy`: https://docs.scipy.org/doc/numpy/reference/generated/numpy.fft.ifft.html\n",
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"\n",
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"## fft\n",
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"\n",
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"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:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 341,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2019-10-17T17:33:38.487729Z",
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"start_time": "2019-10-17T17:33:38.473515Z"
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}
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([20.+0.j, 0.+0.j, -4.+4.j, 0.+0.j, -4.+0.j, 0.+0.j, -4.-4.j,\n",
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" 0.+0.j])"
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]
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},
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"execution_count": 341,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"fft.fft([1, 2, 3, 4, 1, 2, 3, 4])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**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",
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"\n",
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"**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. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 114,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2020-02-16T18:38:07.294862Z",
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"start_time": "2020-02-16T18:38:07.233842Z"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"real part:\t array([5119.996, -5.004663, -5.004798, ..., -5.005482, -5.005643, -5.006577], dtype=float)\r\n",
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"\r\n",
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"imaginary part:\t array([0.0, 1631.333, 815.659, ..., -543.764, -815.6588, -1631.333], dtype=float)\r\n",
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"\r\n",
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"real part:\t array([5119.996, -5.004663, -5.004798, ..., -5.005482, -5.005643, -5.006577], dtype=float)\r\n",
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"\r\n",
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"imaginary part:\t array([0.0, 1631.333, 815.659, ..., -543.764, -815.6588, -1631.333], dtype=float)\r\n",
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"\n"
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]
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}
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],
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"source": [
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"%%micropython -pyboard 1\n",
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"\n",
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"from ulab import numpy as np\n",
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"\n",
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"x = np.linspace(0, 10, num=1024)\n",
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"y = np.sin(x)\n",
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"z = np.zeros(len(x))\n",
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"\n",
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"a, b = np.fft.fft(x)\n",
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"print('real part:\\t', a)\n",
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"print('\\nimaginary part:\\t', b)\n",
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"\n",
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"c, d = np.fft.fft(x, z)\n",
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"print('\\nreal part:\\t', c)\n",
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"print('\\nimaginary part:\\t', d)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## ifft\n",
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"\n",
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"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."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 459,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2019-10-19T13:08:17.647416Z",
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"start_time": "2019-10-19T13:08:17.597456Z"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"original vector:\t array([0.0, 0.009775016, 0.0195491, ..., -0.5275068, -0.5357859, -0.5440139], dtype=float)\n",
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"\n",
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"real part of inverse:\t array([-2.980232e-08, 0.0097754, 0.0195494, ..., -0.5275064, -0.5357857, -0.5440133], dtype=float)\n",
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"\n",
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"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",
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"\n"
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]
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}
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],
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"source": [
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"%%micropython -pyboard 1\n",
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"\n",
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"from ulab import numpy as np\n",
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"\n",
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"x = np.linspace(0, 10, num=1024)\n",
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"y = np.sin(x)\n",
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"\n",
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"a, b = np.fft.fft(y)\n",
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"\n",
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"print('original vector:\\t', y)\n",
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"\n",
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"y, z = np.fft.ifft(a, b)\n",
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"# the real part should be equal to y\n",
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"print('\\nreal part of inverse:\\t', y)\n",
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"# the imaginary part should be equal to zero\n",
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"print('\\nimaginary part of inverse:\\t', z)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Computation and storage costs"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### RAM\n",
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"\n",
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"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. "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Speed of FFTs\n",
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"\n",
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"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",
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"https://github.com/peterhinch/micropython-fourier/blob/master/README.md#8-performance. "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 494,
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"metadata": {
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"ExecuteTime": {
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"end_time": "2019-10-19T13:25:40.540913Z",
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"start_time": "2019-10-19T13:25:40.509598Z"
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}
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"execution time: 1985 us\n",
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"\n"
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]
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}
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],
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"source": [
|
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"%%micropython -pyboard 1\n",
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"\n",
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"from ulab import numpy as np\n",
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"\n",
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"x = np.linspace(0, 10, num=1024)\n",
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"y = np.sin(x)\n",
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"\n",
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"@timeit\n",
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"def np_fft(y):\n",
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" return np.fft.fft(y)\n",
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"\n",
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"a, b = np_fft(y)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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. "
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.5"
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},
|
|
"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
|
|
}
|