Exploration of a parallel implementation of a nested for-loop using IPython's machinery.

parallel_tweaking.ipynb

{
 "metadata": {
  "name": "parallel_tweaking"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Parallel Inner Products"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mat = numpy.random.random_sample((600, 600))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mat = numpy.asfortranarray(mat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.parallel import Client, require, interactive"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rc = Client()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dv = rc.direct_view()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lv = rc.load_balanced_view()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@require(\"numpy\")\n",
      "@interactive\n",
      "def simple_inner(i):\n",
      "    column = mat[:, i]\n",
      "    # have to use a list comprehension to prevent closure\n",
      "    return sum([numpy.inner(column, mat[:, j]) for j in xrange(i + 1, mat.shape[1])])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Local, serial performance."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit sum(simple_inner(i) for i in xrange(mat.shape[1] - 1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 720 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dv.push(dict(mat=mat), block=True);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Parallel implementation using a `DirectView`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit sum(dv.map(simple_inner, range(mat.shape[1] - 1), block=False))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 1.52 s per loop\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Parallel implementation using a `LoadBalancedView` with a large `chunksize` and unordered results."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit sum(lv.map(simple_inner, range(mat.shape[1] - 1), ordered=False, chunksize=(mat.shape[1] - 1) // len(lv), block=False))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 1.2 s per loop\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using two indices takes even more time due to additional communication."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@require(\"numpy\")\n",
      "@interactive\n",
      "def inner(i, j):\n",
      "    return numpy.inner(mat[:, i], mat[:, j])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "first = [i for i in xrange(mat.shape[1] - 1) for j in xrange(i + 1, mat.shape[1])]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "second = [j for i in xrange(mat.shape[1] - 1) for j in xrange(i + 1, mat.shape[1])]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit sum(dv.map(inner, first, second, block=False))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 2.79 s per loop\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit sum(lv.map(inner, first, second, unordered=True, chunksize=len(first) // len(lv), block=False))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 2.74 s per loop\n"
       ]
      }
     ],
     "prompt_number": 16
    }
   ],
   "metadata": {}
  }
 ]
}