{ "metadata": { "name": "", "signature": "sha256:6932c3cff5282730616d7d883891eee8b4903b37eef2183ce9e129bc30b33542" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Sebastian Raschka](http://sebastianraschka.com) \n", "\n", "- [Open in IPython nbviewer](http://nbviewer.ipython.org/github/rasbt/One-Python-benchmark-per-day/blob/master/ipython_nbs/day16_numpy_vectorization.ipynb) \n", "\n", "- [Link to this IPython notebook on Github](https://github.com/rasbt/One-Python-benchmark-per-day/blob/master/ipython_nbs/day16_numpy_vectorization.ipynb) \n", "\n", "- [Link to the GitHub Repository One-Python-benchmark-per-day](https://github.com/rasbt/One-Python-benchmark-per-day)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%load_ext watermark" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "%watermark -a 'Sebastian Raschka' -v -d" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Sebastian Raschka 03/07/2014 \n", "\n", "CPython 3.4.1\n", "IPython 2.0.0\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "[More information](http://nbviewer.ipython.org/github/rasbt/python_reference/blob/master/ipython_magic/watermark.ipynb) about the `watermark` magic command extension." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Day 16 - One Python Benchmark per Day" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Vectorizing a classic `for`-loop in NumPy for calculating Euclidean distances" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One of the biggest advantages of NumPy, besides its convenient usage, is the speed gain over classic Python loop structures via vectorized arithmetic operations for its `ndarray` objects.\n", "\n", "In general, \"vectorizing\" means that artithmetic operations on elments in a vector can be done in parallel as an 1-step process. \n", "In theory, if we forget about additional overheads, a vectorized arithmetic addition, e.g.,\n", "\n", "$\\begin{pmatrix} 1 \\\\ 2 \\\\ 3 \\\\ 4 \\end{pmatrix} + 1 = \\begin{pmatrix} 1+1 \\\\ 2+1 \\\\ 3+1 \\\\ 4+1 \\end{pmatrix} = \\begin{pmatrix} 2 \\\\ 3 \\\\ 4 \\\\ 5\\end{pmatrix}$\n", "\n", "could be 4 times faster than adding the constant 1 to every number in sequential order.\n", "\n", "In NumPy, some operations that are using the architecture's \"BLAS\" (Basic Linear Algebra Subroutines) can also take advantage of CPUs with multiple cores and run multiple processes in parallel, for example, the matrix dot product (`numpy.np(A,B)` or `A.dot(B)`).\n", "Other array operations.\n", "\n", "Other arithmetic operations in NumPy, e.g, arithmetic addition, don't make use of BLAS in the current implementation of NumPy. However, those are still overcoming Python's GIL (Global Interpreter Lock) to allow multi-threading (not to be confused with multi-processing), which can still result in a significant speed boost. \n", "(Source: http://wiki.scipy.org/ParallelProgramming)" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Euclidean Distance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the following benchmarks, we will use a simple Euclidean distance calculation with the following equation \n", "\n", "\n", "\\begin{equation} d = \\sqrt{(X_1 - Y_1)^2 + (X_2 - Y_2)^2 + (X_3 - Y_3)^2 + ... (X_d - Y_d)}\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But before we skip to the actual benchmark, let us visualize it for a set of 2 3D coordinates:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from mpl_toolkits.mplot3d import proj3d\n", " \n", "\n", "coords1 = [1, 2, 3]\n", "coords2 = [4, 5, 6]\n", "\n", "fig = plt.figure(figsize=(7,7))\n", "ax = fig.add_subplot(111, projection='3d')\n", "\n", "ax.scatter((coords1[0], coords2[0]), \n", " (coords1[1], coords2[1]),\n", " (coords1[2], coords2[2]),\n", " color=\"k\", s=150)\n", "\n", "ax.plot((coords1[0], coords2[0]), \n", " (coords1[1], coords2[1]),\n", " (coords1[2], coords2[2]),\n", " color=\"r\")\n", "\n", "ax.set_xlabel('X')\n", "ax.set_ylabel('Y')\n", "ax.set_zlabel('Z')\n", "\n", "ax.text(x=2.5, y=3.5, z=4.0, s='d = 5.19')\n", " \n", "\n", "plt.title('Euclidean distance between 2 3D-coordinates')\n", "\n", "plt.show() " ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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gfaG977778NlnnyEajeKmm27CeeedB4/Hg7PPPhsvv/wy1qxZg3Q6jd/+9rcIBoM47rjj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\nNjYi8Q8jKW9ANnbv3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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Python and NumPy Implementations" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Small sample data of 3D coordinates\n", "\n", "coords1 = [1, 2, 3]\n", "coords2 = [4, 5, 6]\n", "np_c1 = np.array(coords1)\n", "np_c2 = np.array(coords2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# Classic For-loop\n", "\n", "def eucldist_forloop(coords1, coords2):\n", " \"\"\" Calculates the euclidean distance between 2 lists of coordinates. \"\"\"\n", " dist = 0\n", " for (x, y) in zip(coords1, coords2):\n", " dist += (x - y)**2\n", " return dist**0.5" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "# Generator expression\n", "\n", "def eucldist_generator(coords1, coords2):\n", " \"\"\" Calculates the euclidean distance between 2 lists of coordinates. \"\"\"\n", " return sum((x - y)**2 for x, y in zip(coords1, coords2))**0.5" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "# Vectorized version using NumPy\n", "\n", "def eucldist_vectorized(coords1, coords2):\n", " \"\"\" Calculates the euclidean distance between 2 lists of coordinates. \"\"\"\n", " return np.sqrt(np.sum((coords1 - coords2)**2))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "# Using an in-built NumPy function\n", "\n", "np.linalg.norm(np_c1 - np_c2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "5.196152422706632" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "print(eucldist_forloop(coords1, coords2))\n", "print(eucldist_generator(coords1, coords2))\n", "print(eucldist_vectorized(np_c1, np_c2))\n", "print(np.linalg.norm(np_c1 - np_c2))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "5.196152422706632\n", "5.196152422706632\n", "5.19615242271\n", "5.19615242271\n" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "`timeit` benchmarks" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import timeit\n", "import random\n", "random.seed(123)\n", "\n", "from numpy.linalg import norm as np_linalg_norm\n", "\n", "funcs = ('eucldist_forloop', 'eucldist_generator', 'eucldist_vectorized', 'np_linalg_norm')\n", "times = {f:[] for f in funcs}\n", "orders_n = [10**i for i in range(1, 8)]\n", "for n in orders_n:\n", " \n", " c1 = [random.randint(0,100) for _ in range(n)]\n", " c2 = [random.randint(0,100) for _ in range(n)]\n", " np_c1 = np.array(c1)\n", " np_c2 = np.array(c2)\n", " \n", " assert(eucldist_forloop(c1, c2) \n", " == eucldist_generator(c1, c2)\n", " == eucldist_vectorized(np_c1, np_c2)\n", " == np_linalg_norm(np_c1 - np_c2)\n", " )\n", " \n", " times['eucldist_forloop'].append(min(timeit.Timer('eucldist_forloop(c1, c2)', \n", " 'from __main__ import c1, c2, eucldist_forloop').repeat(repeat=50, number=1)))\n", " times['eucldist_generator'].append(min(timeit.Timer('eucldist_generator(c1, c2)', \n", " 'from __main__ import c1, c2, eucldist_generator').repeat(repeat=50, number=1)))\n", " times['eucldist_vectorized'].append(min(timeit.Timer('eucldist_vectorized(np_c1, np_c2)', \n", " 'from __main__ import np_c1, np_c2, eucldist_vectorized').repeat(repeat=50, number=1))) \n", " times['np_linalg_norm'].append(min(timeit.Timer('np_linalg_norm(np_c1 - np_c2)', \n", " 'from __main__ import np_c1, np_c2, np_linalg_norm').repeat(repeat=50, number=1))) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "labels = {'eucldist_forloop': 'for-loop',\n", " 'eucldist_generator': 'generator expression (comprehension equiv.)',\n", " 'eucldist_vectorized': 'NumPy vectorization',\n", " 'np_linalg_norm': 'numpy.linalg.norm'\n", " }\n", "\n", "def plot(times, orders_n, labels):\n", "\n", " colors = ('cyan', '#7DE786', 'black', 'blue') \n", " linestyles = ('-', '-', '--', '--')\n", " fig = plt.figure(figsize=(11,10))\n", " for lb,c,l in zip(labels.keys(), colors, linestyles):\n", " plt.plot(orders_n, times[lb], alpha=1, label=labels[lb], \n", " lw=3, color=c, linestyle=l)\n", " plt.xlabel('sample size n (items in the list)', fontsize=14)\n", " plt.ylabel('time per computation in seconds', fontsize=14)\n", " plt.xlim([min(orders_n) / 10, max(orders_n)* 10])\n", " plt.legend(loc=2, fontsize=14)\n", " plt.grid()\n", " plt.xticks(fontsize=16)\n", " plt.yticks(fontsize=16)\n", " plt.xscale('log')\n", " plt.yscale('log')\n", " plt.title('Python for-loop/generator expr. vs. NumPy vectorized code', fontsize=18)\n", " plt.show()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 45 }, { "cell_type": "code", "collapsed": false, "input": [ "plot(times, orders_n, labels)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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FISK6f/8+9enThwwMDEhfX5969+6d7wWionR0i8ve3p7q16+v6jCYYihqR/zD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FAAAg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\nxcWoV68ejh8/Xmq7F3exkGVjY4O4uDgkJSUhLi4OkZGRWLBgA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"text": [ "" ] } ], "prompt_number": 46 }, { "cell_type": "code", "collapsed": false, "input": [ "%watermark -m -v -d -t -z -p numpy" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "03/07/2014 14:00:21 EDT\n", "\n", "CPython 3.4.1\n", "IPython 2.0.0\n", "\n", "numpy 1.8.1\n", "\n", "compiler : GCC 4.2.1 (Apple Inc. build 5577)\n", "system : Darwin\n", "release : 13.2.0\n", "machine : x86_64\n", "processor : i386\n", "CPU cores : 4\n", "interpreter: 64bit\n" ] } ], "prompt_number": 47 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see in the plot, the vectorized code runs a lot faster than our classic Python `for`-loop (note that this graph is plotted on logarithmic scale)." ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }