gistfile1.txt

{
 "metadata": {
  "name": ""
 },
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "%matplotlib inline\n",
      "import numpy\n",
      "from matplotlib import pyplot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create an array x = [-3.00, -2.99, -2.98, \u2026, 2.98, 2.99, 3.00], and corresponding values of the standard Gaussian function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dx = 0.01\n",
      "x = numpy.arange(-3.0, 3.0+dx/2, dx)\n",
      "y = 1/sqrt(2*pi) * numpy.exp(-x**2 / 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Check the result is unit normalised."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(y.sum()*dx)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.997344300831\n"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "_This is not quite one as we have chopped the tails ( $>3 \\sigma$ ) off the distribution._"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For convenience, put x and y together in a recarray and save to a file."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xy = numpy.rec.array((x, y), names=('x', 'y'))\n",
      "numpy.savetxt('xy.txt', xy)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create samples of one hundred Gaussian random numbers."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "z1 = numpy.random.normal(size=100)\n",
      "z2 = numpy.random.normal(size=100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot your Gaussian curve, x versus y, with axis labels"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pyplot.plot(x, y)\n",
      "pyplot.xlabel('x')\n",
      "pyplot.ylabel(r'$y = \\frac{1}{\\sqrt{2}}\\ \\exp\\left(\\frac{x^2}{2}\\right)$')\n",
      "pyplot.hist(z1, normed=True, histtype='stepfilled', alpha=0.5)\n",
      "pyplot.hist(z2, normed=True, histtype='stepfilled', alpha=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "(array([ 0.12326755,  0.14381214,  0.30816887,  0.34925805,  0.36980264,\n",
        "        0.41089182,  0.18490132,  0.10272296,  0.04108918,  0.02054459]),\n",
        " array([-2.21097456, -1.72422844, -1.23748232, -0.7507362 , -0.26399008,\n",
        "        0.22275604,  0.70950216,  1.19624828,  1.6829944 ,  2.16974052,\n",
        "        2.65648664]),\n",
        " <a list of 1 Patch objects>)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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WRkxMDA4ODvTt27f0HM1/5OXlMXv2bHx9fdm1axeTJ09m7165Y9kYLfv4Y2qnpWGlNfwF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\nprPaUUQV6Hxoq3X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       "text": [
        "<matplotlib.figure.Figure at 0x111d9ea90>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}