{
 "metadata": {
  "name": "An-Introduction-to-NumPy-Basics"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# This function appears to be written for scalar values only.\n",
      "\n",
      "def f(x):\n",
      "    return 3 * x * x - 1\n",
      "\n",
      "print f(-1.0)\n",
      "print f(0.0)\n",
      "print f(1.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# But thanks to NumPy it can operate on arrays as well!\n",
      "\n",
      "import numpy as np\n",
      "\n",
      "x = np.array([-3.0, -2.0, -1.0, 0.0, 1.0, 2.0, 3.0])\n",
      "print f(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Graphing the result.\n",
      "\n",
      "import pylab as pl\n",
      "plot = pl.figure().add_subplot(111)\n",
      "plot.plot(x, f(x))\n",
      "plot.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Use linspace() to make lots of x values for a smoother plot.\n",
      "\n",
      "x = linspace(-3.0, 3.0, 200)\n",
      "\n",
      "plot = pl.figure().add_subplot(111)\n",
      "plot.plot(x, f(x))\n",
      "plot.grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# What if we start with data and want the parabola?\n",
      "# We can use optimize() to fit a curve to noisy data.\n",
      "\n",
      "x = numpy.array([-3.0, -2.0, -1.0, 0.0, 1.0, 2.0, 3.0])\n",
      "y = numpy.array([10.3, 5.1, 0.9, 3.6, 8.4, 16.3, 32.7])\n",
      "\n",
      "def parabola(x, a, b, c):\n",
      "    return a*x*x + b*x + c\n",
      "\n",
      "from scipy.optimize import curve_fit\n",
      "(a, b, c), pcov = curve_fit(parabola, x, y)\n",
      "\n",
      "print a, b, c"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Here is the curve that optimize() figured out,\n",
      "# plotted next to the points we used for input.\n",
      "\n",
      "plot = pl.figure().add_subplot(111)\n",
      "plot.scatter(x, y)\n",
      "plot.plot(x, parabola(x, a, b, c))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}