filter_example/Filtering_example_Octave.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This other notebook use [Octave](https://www.gnu.org/software/octave/), a free clone of MATLAB."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans = 4.2.2\n"
     ]
    }
   ],
   "source": [
    "version"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Iterative computation example (signal filtering)\n",
    "\n",
    "This short Octave example is meant to show how Julia can be very fast with iterative computations (e.g. `for` loops), thanks to JIT compilation.\n",
    "\n",
    "Outline:\n",
    "\n",
    "1. An example of iterative computation: exponential smoothing\n",
    "2. How to measure the performance of a program using `tic`, `tac`\n",
    "\n",
    "## A simple iterative computation: Exponential smoothing\n",
    "\n",
    "[Exponential smoothing](https://en.wikipedia.org/wiki/Exponential_smoothing) (also known as \"exponentially weighted moving average\", \"1st order Autoregressive filter\", \"1st order IIR filter\" in signal processing) is a simple recursive filter which can smooth a times series $\\{u_k\\}_{k\\in\\mathbb{N}}$:\n",
    "\n",
    "$$ y_k = ay_{k-1} + (1-a) u_k, \\;\\;\\;\\; k\\in\\mathbb{N}^+, a\\in[0,1[$$\n",
    "\n",
    "Parameter $a$ tunes the smoothing, between none ($a=0$) and strong smoothing ($a\\to1^-$).\n",
    "\n",
    "This is a simple example of a computation that **cannot be vectorized**. Therefore, iteration in a `for` loop cannot be avoided."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example data\n",
    "\n",
    "a kind of random walk, 1000 pts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "randn(\"seed\", 0) % rng(0) in Matlab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "  -2.1539\n",
      "  -3.8406\n",
      "  -4.1771\n",
      "  -3.2734\n",
      "  -3.2200\n",
      "  -2.8456\n",
      "  -3.2280\n",
      "  -3.0542\n",
      "  -2.5635\n",
      "  -2.1738\n",
      "\n"
     ]
    }
   ],
   "source": [
    "u = cumsum(randn(1000,1));\n",
    "u(1:10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  1000\n"
     ]
    }
   ],
   "source": [
    "length(u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An Octave implemenation of the smoothing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "function y = smooth(u, a)\n",
    "    y = zeros(length(u),1);\n",
    "    \n",
    "    y(1) = (1-a)*u(1);\n",
    "    for k=2:length(u)\n",
    "        y(k) = a*y(k-1) + (1-a)*u(k);\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "  -0.21539\n",
      "  -0.57791\n",
      "  -0.93783\n",
      "  -1.17139\n",
      "  -1.37625\n",
      "  -1.52318\n",
      "  -1.69367\n",
      "  -1.82972\n",
      "  -1.90310\n",
      "  -1.93017\n",
      "\n"
     ]
    }
   ],
   "source": [
    "smooth(u, 0.9)(1:10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot, to check that things work properly"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a =  0.95000\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure();\n",
    "% Call function here\n",
    "\n",
    "a = 0.95\n",
    "hold on;\n",
    "plot(u);\n",
    "plot(smooth(u, a), 'linewidth',5);\n",
    "legend(\"original signal\", \"smoothed\");\n",
    "title(\"signal filter with Octave\")\n",
    "print -dpng signal_filtering_octave.png;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performance analysis\n",
    "\n",
    "With `tic()` and `toc()` like in Matlab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time is 0.0166769 seconds.\n"
     ]
    }
   ],
   "source": [
    "tic();\n",
    "smooth(u, 0.9);\n",
    "toc();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since this time is too short to be meaningful, let's use more points (10\n",
    "M):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "randn(\"seed\", 0);\n",
    "u = cumsum(randn(10^7, 1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed time is 92.661 seconds.\n"
     ]
    }
   ],
   "source": [
    "tic();\n",
    "smooth(u, 0.9);\n",
    "toc();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10 Mpts take **93 s** to compute (compared to **~70 ms** with Julia). Clearly, there is no JIT enabled here. It's even worse than a native Python loop (4.4 s). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Octave JIT Compiler\n",
    "\n",
    "There is a `--jit-compiler` [command line option](https://octave.org/doc/v4.2.2/Command-Line-Options.html) for Octave that should be tried. \n",
    "\n",
    "However, on my Debian Stretch system, with Octave 4.2.2 from backports, I get an startup error:\n",
    "\n",
    "```bash\n",
    "$ octave --jit-compiler\n",
    "octave exited with signal 11\n",
    "```"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "GNU Octave",
     "url": "https://www.gnu.org/software/octave/support.html"
    },
    {
     "text": "Octave Kernel",
     "url": "https://github.com/Calysto/octave_kernel"
    },
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "octave",
   "version": "4.2.2"
  },
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700"
   },
   "moveMenuLeft": true,
   "nav_menu": {
    "height": "161px",
    "width": "252px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": false,
   "threshold": 4,
   "toc_cell": false,
   "toc_position": {
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