{ "metadata": { "name": "", "signature": "sha256:baaa271f2377baba713579ccea7caa79f3e69cc9dd08a44bfc5b304424770bf0" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Sebastian Raschka](http://www.sebastianraschka.com) \n", "\n", "- [Link to the containing GitHub Repository](https://github.com/rasbt/algorithms_in_ipython_notebooks)\n", "- [Link to this IPython Notebook on GitHub](https://github.com/rasbt/algorithms_in_ipython_notebooks/blob/master/ipython_nbs/geometry/points_in_hybercube.ipynb)\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%load_ext watermark" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "%watermark" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "30/06/2014 21:28:32\n", "\n", "CPython 3.4.1\n", "IPython 2.1.0\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 : 2\n", "interpreter: 64bit\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": [ "Counting points inside a hypercube" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given a vector of coordinates, we want to determine how many points lie inside a hypercube (a hypercube is the more general concept of a 3-dimensional cube in $d$ dimensions):\n", "\n", "\\begin{equation} \\begin{pmatrix} x_i\\\\ x_{i+1} \\\\ ... \\\\ x_{d} \\end{pmatrix} \\end{equation}\n", "\n", "E.g., in a 3-dimensional case in a kartesian coordinate system:\n", "\n", "\\begin{equation} \\begin{pmatrix} x\\\\ y\\\\ z \\end{pmatrix} \\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To approach this problem more mathematically, we would use the following equation to count the samples $k_n$ within this hypercube, where $\\phi$ is our so-called *window function*:\n", "\n", "$\\phi(\\pmb u) = \\Bigg[ \\begin{array}{ll} 1 & \\quad |u_j| \\leq 1/2 \\; ;\\quad \\quad j = 1, ..., d \\\\\n", "0 & \\quad otherwise \\end{array}$\n", "\n", "\n", "for a hypercube of unit length 1 centered at the coordinate system's origin. What this function basically does is assigning a value 1 to a sample point if it lies within 1/2 of the edges of the hypercube, and 0 if lies outside (note that the evaluation is done for all dimensions of the sample point).\n", "\n", "\n", "If we extend on this concept, we can define a more general equation that applies to hypercubes of any length $h_n$ that are centered at $\\pmb x$: \n", "\n", "$k_n = \\sum\\limits_{i=1}^{n} \\phi \\bigg( \\frac{\\pmb x - \\pmb x_i}{h_n} \\bigg)$ \n", "\n", "where $\\pmb u = \\bigg( \\frac{\\pmb x - \\pmb x_i}{h_n} \\bigg)$ \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Implementation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def inside_hypercube(x_vec, unit_len=1):\n", " \"\"\" Function to check if a point lies inside a hypercube.\"\"\"\n", " for ele in x_vec:\n", " if abs(ele) > (unit_len/2):\n", " return False\n", " return True" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "
" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3D-hypercubes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So let us visualize such an simple example: a typical 3-dimensional unit hypercube ($h_1 = 1$) and 10 sample points, where 3 of them lie within the hypercube (red triangles), and the other 7 outside (black dots)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "samples_3d = [\n", " [0, 0, 0], [0.2, 0.2, 0.2], [0.1, -0.1, -0.3],\n", " [-1.2,0.3,-0.3], [0.8,-0.82,-0.9], [1, 0.6, -0.7],\n", " [0.8,0.7,0.2], [0.7,-0.8,-0.45], [-0.3, 0.6, 0.9],\n", " [0.7,-0.6,-0.8]\n", " ]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "inside = []\n", "outside = []\n", "for vec in samples_3d:\n", " if inside_hypercube(vec, unit_len=1):\n", " inside.append(vec)\n", " else:\n", " outside.append(vec)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "from mpl_toolkits.mplot3d import Axes3D\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from itertools import product, combinations\n", "fig = plt.figure(figsize=(7,7))\n", "ax = fig.gca(projection='3d')\n", "ax.set_aspect(\"equal\")\n", "\n", "\n", "for row in inside:\n", " ax.scatter(row[0], row[1], row[2], color=\"r\", s=50, marker='^')\n", "\n", "for row in outside: \n", " ax.scatter(row[0], row[1], row[2], color=\"k\", s=50)\n", "\n", "# Plot Cube centered at the coordinate origin X=0, Y=0, Z=0\n", "h = [-0.5, 0.5]\n", "for s, e in combinations(np.array(list(product(h,h,h))), 2):\n", " if np.sum(np.abs(s-e)) == h[1]-h[0]:\n", " ax.plot3D(*zip(s,e), color=\"g\")\n", " \n", "ax.set_xlim(-1.5, 1.5)\n", "ax.set_ylim(-1.5, 1.5)\n", "ax.set_zlim(-1.5, 1.5)\n", "\n", "plt.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ihlQ2q334Wi4WYr246T1q7agPB3rxFzv6xpk5T94JqKDooK7biMVirnG/EEhK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\nU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