{
 "metadata": {
  "name": "Numpy+Matplotlib"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Numpy and Matplotlib"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Here I have included the code from the Python Boot Camp 2012 lecture on numpy and matplotlib.  You can follow along with the material on the slides without having to manually type the code itself.  The lecture was designed to provide an introduction to the numpy module (how python handles data arrays) and the matplotlib module (a python plotting module)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First we want to import the appropriate modules into our name space (note this is done automatically with the \"--pylab\" flag."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The primary building block of the numpy module is the class \"ndarray\".  A ndarray object represents a multidimensional, homogeneous array of fixed-sized items.  An associated date-type object describes the format of each element in the array.  An ndarray object is (almost) never instantiated directly, but instead using a method that returns an instance of the class."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([1, 2, 3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "array([1, 2, 3])"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The \"ones\" and \"zeros\" methods return an array object of the requested shape and type."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = np.ones((3,2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([[ 1.,  1.],\n",
        "       [ 1.,  1.],\n",
        "       [ 1.,  1.]])"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "(3, 2)"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c = np.zeros((1,3), int)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "array([[0, 0, 0]])"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "type(c)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "numpy.ndarray"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c.dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "dtype('int64')"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\"linspace\" creates a one-dimensional array running from arg1 to arg2 (with length arg3)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d = np.linspace(1,5,11)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "d"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "array([ 1. ,  1.4,  1.8,  2.2,  2.6,  3. ,  3.4,  3.8,  4.2,  4.6,  5. ])"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "numpy provides a variety of methods to read and write data to disk (binary, ascii, fits, csv, etc.).  These include \"loadtxt\" and \"tofile\".  I haven't included these because of limitations with the Notebook."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "ndarray objects can be indexed, sliced, and iterated over much like lists.  The format for slicing is still \"x1:x2:dx\"."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.arange(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[2:5]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "array([2, 3, 4])"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[:6:2] = -1000"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([-1000,     1, -1000,     3, -1000,     5,     6,     7,     8,     9])"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[::-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([    9,     8,     7,     6,     5, -1000,     3, -1000,     1, -1000])"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[2:-2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "array([-1000,     3, -1000,     5,     6,     7])"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Arrays can hold (almost) any type of data, as long as each individual element is identical (i.e., requires the same amount of memory).  The format of the ndarray can be specified with the \"dtype\" attribute.  Individual elements may be \"named\" in a structured array."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.zeros((2,),dtype=('i4,f4,a10'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "array([(0, 0.0, ''), (0, 0.0, '')], \n",
        "      dtype=[('f0', '<i4'), ('f1', '<f4'), ('f2', '|S10')])"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x['f1']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "array([ 0.,  0.], dtype=float32)"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that the same issues of references and copies that apply to other variables also apply to array objects."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = x['f1']"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "array([ 0.,  0.], dtype=float32)"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y += np.array([1.0, 1.0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "array([ 1.,  1.], dtype=float32)"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "array([(0, 1.0, ''), (0, 1.0, '')], \n",
        "      dtype=[('f0', '<i4'), ('f1', '<f4'), ('f2', '|S10')])"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A universal function (or \"ufunc\" for short) is a function that operates on ndarrays in an element-by-element fashion, supporting array broadcasting, type casting, and several other standard features. That is, a ufunc is a \u201cvectorized\u201d wrapper for a function that takes a fixed number of scalar inputs and produces a fixed number of scalar outputs.  Examples include add, subtract, multiply, exp, log, and power."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Most array operations thus occur on an element-by-element basis:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([[1, 2], [3, 4]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = np.array([[2, 3], [4, 5]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a + b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
        "array([[3, 5],\n",
        "       [7, 9]])"
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.multiply(a, b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "array([[ 2,  6],\n",
        "       [12, 20]])"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a ** b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 43,
       "text": [
        "array([[   1,    8],\n",
        "       [  81, 1024]])"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Standard linear algebra (i.e., matrix) operations are also available.  Many are stored in the linalg module."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.dot(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 44,
       "text": [
        "array([[10, 13],\n",
        "       [22, 29]])"
       ]
      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Universal functions run *much* faster than for loops, which should be avoided whenever possible."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.random.random((500,500))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = np.random.random((500,500))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mult1(a,b):\n",
      "    return a * b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mult2(a,b):\n",
      "    c = np.empty(a.shape)\n",
      "    for i in range(a.shape[0]):\n",
      "        for j in range(a.shape[1]):\n",
      "            c[i,j] = a[i,j] * b[i,j]\n",
      "    return c"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit mult1(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "100 loops, best of 3: 2.12 ms per loop"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "timeit mult2(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1 loops, best of 3: 328 ms per loop\n"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "numpy will (usually) intelligently deal with arrays of different sizes.  The smaller array is *broadcast* across the larger array so that they have compatible shapes.  Note that the rules for broadcasting are not always intuitive, so be careful!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a=np.array([1,2,3.])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a + 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "array([ 3.,  4.,  5.])"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b=np.array([10,20,30.,40])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a * b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "array([[  10.,   20.,   30.,   40.],\n",
        "       [  20.,   40.,   60.,   80.],\n",
        "       [  30.,   60.,   90.,  120.]])"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = a.reshape(3,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "array([[ 1.],\n",
        "       [ 2.],\n",
        "       [ 3.]])"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a * b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "array([[  10.,   20.,   30.,   40.],\n",
        "       [  20.,   40.,   60.,   80.],\n",
        "       [  30.,   60.,   90.,  120.]])"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Universal functions make it nearly trivial to compare arrays on an element-by-element basis."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([1, 3, 0], float)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = np.array([0, 3, 2], float)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a > b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "array([ True, False, False], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a == b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 64,
       "text": [
        "array([False,  True, False], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c = a <= b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 66,
       "text": [
        "array([False,  True,  True], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.logical_and(a > 0, a < 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 67,
       "text": [
        "array([ True, False, False], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.logical_or(a,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 68,
       "text": [
        "array([ True,  True,  True], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The *where* method provides a fast way to search (and extract) individual elements of an array.  When called with a single (conditional) argument, the method returns an array of indicies where the conditional is met.  If two additional arguments are added, more complex returns are possible."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([1, 3, 0, -5, 0], float)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.where(a != 0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 70,
       "text": [
        "(array([0, 1, 3]),)"
       ]
      }
     ],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[a != 0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 71,
       "text": [
        "array([ 1.,  3., -5.])"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.where(a != 0.0, 1 / a, a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 73,
       "text": [
        "array([ 1.        ,  0.33333333,  0.        , -0.2       ,  0.        ])"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.arange(9.).reshape(3, 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "array([[ 0.,  1.,  2.],\n",
        "       [ 3.,  4.,  5.],\n",
        "       [ 6.,  7.,  8.]])"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.where( x > 5 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 76,
       "text": [
        "(array([2, 2, 2]), array([0, 1, 2]))"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "ndarray objects provide basic statistical methods (mean, median, standard deviation, etc.)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.array([[1, 2], [3, 4]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 78,
       "text": [
        "2.5"
       ]
      }
     ],
     "prompt_number": 78
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(a, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 79,
       "text": [
        "array([ 2.,  3.])"
       ]
      }
     ],
     "prompt_number": 79
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(a, axis=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 80,
       "text": [
        "array([ 1.5,  3.5])"
       ]
      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.std(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 81,
       "text": [
        "1.1180339887498949"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.average(range(1,11), weights=range(10,0,-1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 82,
       "text": [
        "4.0"
       ]
      }
     ],
     "prompt_number": 82
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The *random* module contains basic random number generation, as well as a few common probability distribution functions.  Many more (complex) pdfs are available within scipy."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.rand(5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 83,
       "text": [
        "array([ 0.30690353,  0.30895097,  0.21526229,  0.3493788 ,  0.16837581])"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.randint(5, 10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 84,
       "text": [
        "9"
       ]
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.random.normal(1.5, 4.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 85,
       "text": [
        "3.0703190817944908"
       ]
      }
     ],
     "prompt_number": 85
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plotting is done with the *matplotlib* module.  If you have used MATLAB before, the syntax should look very familiar."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pylab as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 86
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The simplest (but still quite powerful) method is *plot*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([1,2,3])\n",
      "y = x**2\n",
      "plt.plot(x, y, \"ro\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 87,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10523ba90>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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z9e2332rmzJk6duxYX4/Vr128eFHl5eWqrKxUVlZWr+e5PqMT6nxyfUYnLS1Nhw4d0vnz\n51VWVibbtmVZVo9jork+E/JOOz8/X42Njd2/bmpqUn5+fiKWHpCGDh3a/VeqqVOnqqOjQ+fOnevj\nqfqvjo4OzZo1S08++aRmzpzZ63muz+iEO59cn7HJzs7W9OnTdeDAgR7fj/b6TEi0H3vsMa1fv16S\nVFtbq5ycHOXl5SVi6QHpzJkz3X/y7t+/X47j9NoHw/84jqOnn35abrdbixYtCnoM12fkIjmfXJ+R\nO3v2rJqbmyVJly5dUk1Njbxeb49jor0+I9oemT17tnbt2qWzZ8+qoKBAy5YtU0dHhyTp+eef17Rp\n07Rt2zbdfffdGjJkCJ/lDiPc+dy8ebNWr16tjIwMZWZmatOmTX08cf+1b98+ffrppxo1alT3b4a3\n335bJ06ckMT1Ga1IzifXZ+ROnTqliooKBQIBBQIBzZs3TxMnTtQnn3wiKbbrM6KfPQIA6B/4b+wA\nYBCiDQAGIdoAYBCiDQAGIdoAYBCiDQAG+S9SYVcuWVfujQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Another basic example."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(0, 2*np.pi, 300)\n",
      "y = np.sin(x)\n",
      "plt.plot(x, y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 88,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1057620d0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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E06HifftCVhZ88IHW5QNBSzciHpabCykp5mDxl14Kj5uz48fDuHHm4JUSJWyn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\nyQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here's a more realistic plot, including how to modify axis labels, create a legend, etc."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(0, 2*np.pi, 300)\n",
      "y = np.sin(x)\n",
      "y2 = np.sin(x**2)\n",
      "plt.plot(x, y, label=r'$\\sin(x)$')\n",
      "plt.plot(x, y2, label=r'$\\sin(x^2)$')\n",
      "plt.title('Some functions')\n",
      "plt.xlabel('x')\n",
      "plt.ylabel('y')\n",
      "plt.grid()\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 91,
       "text": [
        "<matplotlib.legend.Legend at 0x105938bd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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w+rTndZXNlegY3pHRHvGh8ajSVDG6litoaQ5KNeoMAkUOHiqVAHKyLV+aQ5Ox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\nTkSuQmCC\n"
      }
     ],
     "prompt_number": 91
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "numpy also provides capabilities for (least squares) polynomial fitting."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.array([0.0, 1.0, 2.0, 3.0,  4.0,  5.0])\n",
      "y = np.array([0.0, 0.8, 0.9, 0.1, -0.8, -1.0])\n",
      "z = np.polyfit(x, y, 3)\n",
      "p = np.poly1d(z)\n",
      "p30 = np.poly1d(np.polyfit(x, y, 30))\n",
      "xp = np.linspace(-2, 6, 100)\n",
      "plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--')\n",
      "plt.ylim(-2,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/numpy/lib/polynomial.py:560: RankWarning: Polyfit may be poorly conditioned\n",
        "  warnings.warn(msg, RankWarning)\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 92,
       "text": [
        "(-2, 2)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ll14ybz9loNCHJoTyZ/afTPGbYvAxpR7RL1iwgKCgIE6dOsUjjzzCggULimyn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\ncVLohRDCxkmhF0IIGyeFXgghbNz/A+A7DkgYNK89AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 92
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here's an example of the histogram plotting method (as well as the random number generation)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu, sigma = 0, 0.1\n",
      "s = np.random.normal(mu, sigma, 1000)\n",
      "count, bins, ignored = plt.hist(s, 30, normed=True)\n",
      "plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ), color='r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 93,
       "text": [
        "[<matplotlib.lines.Line2D at 0x105900c50>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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M1DuK0JmM3L3g/Mj9GnJ5lzvpyk5+4WJ7lRhpFCh1vjdyB4igmM3EE8tRfgzQ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\n"
      }
     ],
     "prompt_number": 93
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Probably the best way to learn about making new plots is looking at the \n",
      "<a href=\"http://matplotlib.sourceforge.net/gallery.html\">Matplotlib Gallery</a>."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}