teoliphant/using_numba.ipynb

## using_numba.ipynb
{
 "metadata": {
  "name": "Using Numba"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I always enjoy showing people how much easier Numba makes it to speed up their NumPy-based technical codes.   With Numba, you usually can just write the code with loops and then add a decorator to your function and get speed-ups equivalent to having written the code in another compiled language (like C or Fortran).  \n",
      "\n",
      "Tonight when I saw this question on Stack Exchange: http://scicomp.stackexchange.com/questions/5473/how-to-express-this-complicated-expression-using-numpy-slices it looked like a perfect opportunity to test Numba again.\n",
      "\n",
      "So, I copied the looped_ver code from Nat Wilson (modified it slightly to make x[0] = 0) and then decorated it to let Numba compile the code.  The result continues to impress me about the code that Mark Florisson, Jon Riehl, and Siu Kwan Lam have put together.  Here is the equation that is being solved:\n",
      "\n",
      "$$\\displaystyle x_i = \\sum_{j=0}^{i-1} k_{i-j} a_{i-j} a_{j}$$\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from numba import jit, autojit\n",
      "\n",
      "def looped_ver(k, a):\n",
      "    x = np.empty_like(a)\n",
      "    x[0] = 0.0\n",
      "    for i in range(1, x.size):\n",
      "        sm = 0.0\n",
      "        for j in range(0, i):\n",
      "            sm += k[i-j,j] * a[i-j] * a[j]\n",
      "        x[i] = sm\n",
      "    return x\n",
      "\n",
      "typed_ver = jit('f8[:](f8[:,:],f8[:])')(looped_ver)\n",
      "auto_ver = autojit(looped_ver)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import time\n",
      "import numpy as np\n",
      "repeat = 3\n",
      "\n",
      "def getbest(func, *args):\n",
      "    import time\n",
      "    best = 1e12\n",
      "    for i in range(repeat):\n",
      "        start = time.time()\n",
      "        func(*args)\n",
      "        current = time.time() - start\n",
      "        if current < best:\n",
      "            best = current\n",
      "    return best\n",
      "    \n",
      "\n",
      "def timeit(N):\n",
      "    res = {'looped':[], 'auto':[], 'typed':[]}\n",
      "    for n in N:\n",
      "        k = np.random.rand(n,n)\n",
      "        a = np.random.rand(n)\n",
      "        for version in ['looped', 'auto', 'typed']:\n",
      "            func = eval('%s_ver' % version)\n",
      "            res[version].append(getbest(func, k, a))\n",
      "    return res"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = [100,200,500,1000,5000]\n",
      "res = timeit(N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(N, log10(res['typed']), N, log10(res['auto']), N, log10(res['looped']))\n",
      "legend(['Typed', 'Autojit', 'Python'], loc='upper left')\n",
      "ylabel(r'$\\log_{10}$(time) in seconds')\n",
      "xlabel('Size (N)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.text.Text at 0x1099c0bd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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o2rYdHdrXRq+H4GCoLrv2COdk957GsGHDaNiwIR07dqS2Mw+Mnj8PK1bA7NmO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\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "[res['looped'][i]/res['auto'][i] for i in range(len(N))]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "[1127.4761904761904,\n",
        " 1435.7611940298507,\n",
        " 1317.400260756193,\n",
        " 256.7791019225705,\n",
        " 137.61178578348566]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numba import _version\n",
      "print _version.version_version"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.7.0\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This was run on a Macbook Air.   Running `sysctl -n machdep.cpu.brand_string` resulted in:\n",
      "\n",
      "   Intel(R) Core(TM) i7-2677M CPU @ 1.80GHz"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}