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   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Development II: Testing breakout\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Exercise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Maclaurin series for $\\sin(x)$ is\n",
      "\n",
      "$\\sum^{\\infty}_{n=0} \\frac{(-1)^n}{(2n+1)!} x^{2n+1} = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\cdots\\quad\\text{ for all } x\\!$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import factorial\n",
      "from math import sin as builtin_sin\n",
      "import numpy as np\n",
      "\n",
      "def mysin(x,n):\n",
      "    sin = 0\n",
      "    for i in range(n):\n",
      "        sign = (-1)**i\n",
      "        sin += ((x**(2.0*i+1))/factorial(2*i+1))*sign\n",
      "    return sin\n",
      "\n",
      "\n",
      "def mysin3(x):\n",
      "    return x - (x**3)/factorial(3) + (x**5)/factorial(5)\n",
      "\n",
      "def mysin4(x):\n",
      "    return x - (x**3)/factorial(3) + (x**5)/factorial(5) - (x**7)/factorial(7)\n",
      "\n",
      "def test():\n",
      "    np.testing.assert_almost_equal(mysin(0.0,8),builtin_sin(0.0))\n",
      "    assert mysin3(0.5) == mysin(0.5, 3)\n",
      "    assert mysin4(0.5) == mysin(0.5, 4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "test()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "AssertionError",
       "evalue": "\nArrays are not almost equal to 7 decimals\n ACTUAL: -1.0\n DESIRED: 0.0",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-51-ea594c21b25d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mtest\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[1;32m<ipython-input-50-8d5c1c355a20>\u001b[0m in \u001b[0;36mtest\u001b[1;34m()\u001b[0m\n\u001b[0;32m     18\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     19\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mtest\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 20\u001b[1;33m     \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtesting\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0massert_almost_equal\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmysin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m8\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mbuiltin_sin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.0\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     21\u001b[0m     \u001b[1;32massert\u001b[0m \u001b[0mmysin3\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mmysin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     22\u001b[0m     \u001b[1;32massert\u001b[0m \u001b[0mmysin4\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mmysin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32m/usr/lib64/python2.7/site-packages/numpy/testing/utils.pyc\u001b[0m in \u001b[0;36massert_almost_equal\u001b[1;34m(actual, desired, decimal, err_msg, verbose)\u001b[0m\n\u001b[0;32m    466\u001b[0m         \u001b[1;32mpass\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    467\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mround\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdesired\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mactual\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mdecimal\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 468\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mAssertionError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    469\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    470\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mAssertionError\u001b[0m: \nArrays are not almost equal to 7 decimals\n ACTUAL: -1.0\n DESIRED: 0.0"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%debug"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "> \u001b[1;32m<ipython-input-1-482d5b34fc7c>\u001b[0m(18)\u001b[0;36mtest\u001b[1;34m()\u001b[0m\n",
        "\u001b[1;32m     17 \u001b[1;33m\u001b[1;32mdef\u001b[0m \u001b[0mtest\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[0m\u001b[1;32m---> 18 \u001b[1;33m    \u001b[1;32massert\u001b[0m \u001b[0mmysin3\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mmysin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[0m\u001b[1;32m     19 \u001b[1;33m    \u001b[1;32massert\u001b[0m \u001b[0mmysin4\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mmysin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m4\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[0m\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ipdb> mysin3(0.5)\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.47942708333333334\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ipdb> \n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.47942708333333334\n"
       ]
      },
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "ipdb> q\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "builtin_sin(0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "0.479425538604203"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "1. Fix the test.\n",
      "1. The Maclaurin series for $\\sin(x)$ is only valid in some neighborhood of values of x \"near\" 0.  Decide what values of x you will accept for the `mysin` functions and then modify each function to only "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.ge"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}