{
 "metadata": {
  "name": "lab0_gprs13"
 }, 
 "name": "lab0_gprs13", 
 "nbformat": 2, 
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": "import sys as sys\nimport numpy as np\nimport pylab as pb", 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 48
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": "# Loading in data: the 0:1 and 1:2 ensure we get column vectors\n# for x and y.\nolympics = np.genfromtxt('olympicMarathonTimes.csv', delimiter=',')\nx = olympics[:, 0:1]\ny = olympics[:, 1:2]", 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 49
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": "print(x)\nprint(y)", 
     "language": "python", 
     "outputs": [
      {
       "output_type": "stream", 
       "stream": "stdout", 
       "text": "[[ 1896.]\n [ 1900.]\n [ 1904.]\n [ 1908.]\n [ 1912.]\n [ 1920.]\n [ 1924.]\n [ 1928.]\n [ 1932.]\n [ 1936.]\n [ 1948.]\n [ 1952.]\n [ 1956.]\n [ 1960.]\n [ 1964.]\n [ 1968.]\n [ 1972.]\n [ 1976.]\n [ 1980.]\n [ 1984.]\n [ 1988.]\n [ 1992.]\n [ 1996.]\n [ 2000.]\n [ 2004.]\n [ 2008.]\n [ 2012.]]\n[[ 4.47083333]\n [ 4.46472926]\n [ 5.22208333]\n [ 4.15467867]\n [ 3.90331675]\n [ 3.56951267]\n [ 3.82454477]\n [ 3.62483707]\n [ 3.59284275]\n [ 3.53880792]\n [ 3.67010309]\n [ 3.39029111]\n [ 3.43642612]\n [ 3.20583007]\n [ 3.13275665]\n [ 3.32819844]\n [ 3.13583758]\n [ 3.0789588 ]\n [ 3.10581822]\n [ 3.06552909]\n [ 3.09357349]\n [ 3.16111704]\n [ 3.14255244]\n [ 3.08527867]\n [ 3.10265829]\n [ 2.99877553]\n [ 3.03392977]]"
      }
     ], 
     "prompt_number": 50
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": "pb.plot(x, y, 'rx')", 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 51, 
       "text": "[<matplotlib.lines.Line2D at 0x5205310>]"
      }, 
      {
       "output_type": "display_data", 
       "png": 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      }
     ], 
     "prompt_number": 51
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": "m = -0.4\nc = 80", 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 52
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": "# This is an iterative solution for \n# finding the gradient and bias. \n# Notice how slow it is!\nxTest = np.linspace(1890, 2020, 130)[:, None]\nfor i in arange(100000):\n    m = ((y - c)*x).sum()/(x*x).sum()\n    c = (y-m*x).sum()/y.shape[0]\npb.plot(xTest, m*xTest + c, 'b-')\npb.plot(x, y, 'rx')\n", 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 53, 
       "text": "[<matplotlib.lines.Line2D at 0x520d5d0>]"
      }, 
      {
       "output_type": "display_data", 
       "png": 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MmTNFROTChQsSGRkpX3/9tYiI3HDDDbJv3z4REZk8ebJs3ry5oyV5Xf+oUaNk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\nYOATEZnE/wd5wHVD1oNJ2QAAAABJRU5ErkJggg==\n"
      }
     ], 
     "prompt_number": 53
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": "print(m)\nprint(c)", 
     "language": "python", 
     "outputs": [
      {
       "output_type": "stream", 
       "stream": "stdout", 
       "text": "-0.0129806477465\n28.8952457368"
      }
     ], 
     "prompt_number": 54
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": "Phi = np.hstack([np.ones(x.shape), x, x**2])", 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 55
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": "#This is the multivariate linear regression solution. \nw = np.linalg.solve(np.dot(Phi.T, Phi), np.dot(Phi.T, y))\nprint(w)", 
     "language": "python", 
     "outputs": [
      {
       "output_type": "stream", 
       "stream": "stdout", 
       "text": "[[  6.43641952e+02]\n [ -6.42502986e-01]\n [  1.61109703e-04]]"
      }
     ], 
     "prompt_number": 61
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": "xTest = np.linspace(1890, 2020, 130)[:, None]\nPhiTest = np.hstack([np.ones(xTest.shape), xTest, xTest**2])", 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 57
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": "fTest = np.dot(PhiTest, w)", 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 58
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": "pb.plot(x, y, 'rx')\npb.plot(xTest, fTest, '-') ", 
     "language": "python", 
     "outputs": [
      {
       "output_type": "pyout", 
       "prompt_number": 59, 
       "text": "[<matplotlib.lines.Line2D at 0x501a190>]"
      }, 
      {
       "output_type": "display_data", 
       "png": 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      }
     ], 
     "prompt_number": 59
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": "", 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 59
    }
   ]
  }
 ]
}