{ "metadata": { "name": "vector_dot" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Vector Dot Products" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This tutorial is intended to explain properties of vector dot products.\n", "\n", "The dot product of two vecotrs is related to the angle betweeen the\n", "vectors. When the vectors are orthogonal, the dot product is equal to\n", "zero. The following code will demonstrate this." ] }, { "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": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "import seaborn\n", "seaborn.set()\n", "colors = seaborn.color_palette()\n", "import utils" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# For 3D plotting we need to import some extra stuff\n", "from mpl_toolkits.mplot3d import Axes3D" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# First create two random vectors in 3 dimensional space\n", "v1 = rand(3, 1)\n", "v2 = rand(3, 1)\n", "\n", "# And scale them to unit length\n", "v1 = v1 / norm(v1)\n", "v2 = v2 / norm(v2) " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot the vectors\n", "o = zeros(3) # origin\n", "\n", "# We'll use the object oriented plotting interface\n", "f = figure(figsize=(8, 8))\n", "ax = f.add_subplot(111, projection=\"3d\", axisbg=\"white\")\n", "ax.plot(*[[o[i], v1[i]] for i in range(3)], linewidth=3, label=\"vector1\")\n", "ax.plot(*[[o[i], v2[i]] for i in range(3)], linewidth=3, label=\"vector2\")\n", "for axisl in [\"x\", \"y\", \"z\"]:\n", " getattr(ax, \"set_%slabel\" % axisl)(axisl) # Here's a fun trick\n", "legend();" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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bvzmw+KZGVATsu76rxC6hULuMIx+ytTFT88KlFyqNRwGgvW9lOhwOh5zkYcR4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\nlZWFjIwMZn6vrq4Oq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} ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The vectors define a subspace. The subspace defined by these vectors is\n", "all the points that can be obtained from weighted sums of the two\n", "vectors. In this case the subspace will be the plane containing the two\n", "vectors. Lets visualize this by adding a bunch of points to our graph\n", "that are obtained from linear combinations (weighted sums) of our two\n", "vectors. If we think of the two vectors as regressors that we are\n", "putting into a linear model then the subspace defined by the vectors\n", "represents all the possible linear models." ] }, { "cell_type": "code", "collapsed": false, "input": [ "f = figure(figsize=(8, 8))\n", "ax = f.add_subplot(111, projection=\"3d\", axisbg=\"white\")\n", "ax.plot(*[[o[i], v1[i]] for i in range(3)], linewidth=3, label=\"vector1\")\n", "ax.plot(*[[o[i], v2[i]] for i in range(3)], linewidth=3, label=\"vector2\")\n", "for axisl in [\"x\", \"y\", \"z\"]:\n", " getattr(ax, \"set_%slabel\" % axisl)(axisl) # Here's a fun trick\n", "legend()\n", "\n", "for i in range(100):\n", " # generate a point that is a weighted sum of the 2 vectors\n", " w1 = randn(1)\n", " w2 = randn(1)\n", " point = w1 * v1 + w2 * v2\n", " ax.plot(*point, marker=\".\", color=\"k\")\n", "\n", "# We can find a vector that is orthogonal to the plane defined by v1 and v2\n", "# by taking the vector cross product. See the wikipedia page for a\n", "# definition of cross product\n", "v3 = cross(v1.reshape(1, 3), v2.reshape(1, 3)).squeeze() # Must be right shape for cross()\n", "ax.plot(*[[o[i], v3[i]] for i in range(3)], linewidth=3, label=\"orthogonal vector\")\n", "legend();" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "display_data", "png": 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69OnYt2+fpuM1CuphZglyaiulPJz8Js9ywpt6ZskKi8qVjtGsJKoXDIfDcR5o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\n" } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now explore the relationship between the dot product and the angle\n", "between these vectors. The dot product of two unit length vectors, v1\n", "and v2 is equal to the cosine of the angle between them (in radians)\n", "$\\cos(\\frac{\\pi}{2}) = 0$. Therefor the dot product of two vectors that are\n", "orthogonal must also be equal to 0." ] }, { "cell_type": "code", "collapsed": false, "input": [ "print v3[0] * v1[0] + v3[1] * v1[1] + v3[2] * v1[2]" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ -5.55111512e-17]\n" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also do this with ``dot``" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print dot(v3, v1)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ -5.55111512e-17]\n" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "A side note is that the angle, theta, between two unit vectors can be\n", "calculated using arccosine: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "theta = arccos(dot(v2.T, v1)).squeeze()\n", "# and radians can be converted to degrees\n", "theta_deg = theta * (180 / pi)\n", "print theta, theta_deg" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.468989585711 26.8711238968\n" ] } ], "prompt_number": 16 } ], "metadata": {} } ] }