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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#III-[NumPy](http://www.numpy.org/) - Numerical Python \n",
      "\n",
      "Lecturer:*Jos\u00e9 Pedro Silva*<sup>[1](http://www-num.math.uni-wuppertal.de/en/amna/people/jose-pedro-silva.html)</sup> - [silva_at_math.uni-wuppertal.de](mailto:silva_at_math.uni-wuppertal.de)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "NumPy provides the backbone to all scientific computing in Python. It provides all the high-dimensional structures (arrays), operations and interfaces to C and Fortran"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Usually it is imported as np"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For ease of writing in these tutorials we will populate the entire namespace with numpy"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\"NumPy's main object is the homogeneous multidimensional array. It is a table of elements (usually numbers), all of the same type, indexed by a tuple of positive integers. In Numpy dimensions are called axes. The number of axes is rank.\"\n",
      "\n",
      "Let's create an array then"
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Create array from list"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "v = [1,2,3,4]\n",
      "av = np.array(v)\n",
      "av"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "array([1, 2, 3, 4])"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Create matrix from list (of lists)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m = [[1,2],[3,4]]\n",
      "am = array(m)\n",
      "am"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([[1, 2],\n",
        "       [3, 4]])"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Arrays have different methods and attributes"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "am.size #total number of elements"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "4"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "am.shape   #array shape (equivalent to Matlab's size)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(2, 2)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "am.size"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "4"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "am.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "(2, 2)"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "am.ndim"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "2"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In total, a lot of attributes and methods are available by default"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(dir(am))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "163"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One important attribute is dtype. NumPy arrays are statically typed and contain always the same type of data. (For the next generation of array containers, see [Blaze](http://blaze.pydata.org/docs/latest/index.html) ) Therefore, if not specified, it is infered from the data when the array is created"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "am.dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "dtype('int64')"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "array([1,2,3]).dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "dtype('int64')"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "array([1.1,2.2,3.4]).dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "dtype('float64')"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "array([1+2j,2+4j,3]).dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "dtype('complex128')"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "array([True,False]).dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "dtype('bool')"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There is an extensive list of available dtypes"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sctypes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "{'complex': [numpy.complex64, numpy.complex128, numpy.complex256],\n",
        " 'float': [numpy.float16, numpy.float32, numpy.float64, numpy.float128],\n",
        " 'int': [numpy.int8, numpy.int16, numpy.int32, numpy.int64],\n",
        " 'others': [bool, object, str, unicode, numpy.void],\n",
        " 'uint': [numpy.uint8, numpy.uint16, numpy.uint32, numpy.uint64]}"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Array generating funtions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "arange(0,10,2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([0, 2, 4, 6, 8])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "arange(-1,1,0.1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "array([ -1.00000000e+00,  -9.00000000e-01,  -8.00000000e-01,\n",
        "        -7.00000000e-01,  -6.00000000e-01,  -5.00000000e-01,\n",
        "        -4.00000000e-01,  -3.00000000e-01,  -2.00000000e-01,\n",
        "        -1.00000000e-01,  -2.22044605e-16,   1.00000000e-01,\n",
        "         2.00000000e-01,   3.00000000e-01,   4.00000000e-01,\n",
        "         5.00000000e-01,   6.00000000e-01,   7.00000000e-01,\n",
        "         8.00000000e-01,   9.00000000e-01])"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "linspace(0,10,6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "array([  0.,   2.,   4.,   6.,   8.,  10.])"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_.dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "dtype('float64')"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "linspace(0,10,6,dtype='uint32')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "array([ 0,  2,  4,  6,  8, 10], dtype=uint32)"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_.dtype"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "dtype('uint32')"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "linspace(-1,10,6,dtype='uint32')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "array([4294967295,          1,          3,          5,          7,\n",
        "               10], dtype=uint32)"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "finfo('float64')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "finfo(resolution=1e-15, min=-1.7976931348623157e+308, max=1.7976931348623157e+308, dtype=float64)"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "iinfo(np.int8), iinfo('uint8')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "(iinfo(min=-128, max=127, dtype=int8), iinfo(min=0, max=255, dtype=uint8))"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "logspace(0,1,10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([  1.        ,   1.29154967,   1.66810054,   2.15443469,\n",
        "         2.7825594 ,   3.59381366,   4.64158883,   5.9948425 ,\n",
        "         7.74263683,  10.        ])"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x,y = mgrid[0:5,0:5]\n",
      "x, y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "(array([[0, 0, 0, 0, 0],\n",
        "        [1, 1, 1, 1, 1],\n",
        "        [2, 2, 2, 2, 2],\n",
        "        [3, 3, 3, 3, 3],\n",
        "        [4, 4, 4, 4, 4]]), array([[0, 1, 2, 3, 4],\n",
        "        [0, 1, 2, 3, 4],\n",
        "        [0, 1, 2, 3, 4],\n",
        "        [0, 1, 2, 3, 4],\n",
        "        [0, 1, 2, 3, 4]]))"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When we already have each of the axis we call meshgrid"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(0,1,10)\n",
      "y = linspace(-1,1,5)\n",
      "meshgrid(x,y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "[array([[ 0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,\n",
        "          0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ],\n",
        "        [ 0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,\n",
        "          0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ],\n",
        "        [ 0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,\n",
        "          0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ],\n",
        "        [ 0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,\n",
        "          0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ],\n",
        "        [ 0.        ,  0.11111111,  0.22222222,  0.33333333,  0.44444444,\n",
        "          0.55555556,  0.66666667,  0.77777778,  0.88888889,  1.        ]]),\n",
        " array([[-1. , -1. , -1. , -1. , -1. , -1. , -1. , -1. , -1. , -1. ],\n",
        "        [-0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5],\n",
        "        [ 0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ,  0. ],\n",
        "        [ 0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5],\n",
        "        [ 1. ,  1. ,  1. ,  1. ,  1. ,  1. ,  1. ,  1. ,  1. ,  1. ]])]"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "A lot of times we will want to generate random data to test our implementations"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import random"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random.normal(0,1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "0.6633650258161853"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random.normal(-1,0.001)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "-1.0001122377014229"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random.normal(0,1,[2,3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "array([[-0.0965079 ,  0.61404973, -0.64773592],\n",
        "       [ 0.71630596,  0.76143585, -0.46887797]])"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random.poisson()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "0"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random.rand(5,5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "array([[ 0.87390908,  0.24764657,  0.99397698,  0.38955504,  0.48710422],\n",
        "       [ 0.73542102,  0.87108142,  0.27943569,  0.04596862,  0.93223845],\n",
        "       [ 0.12292627,  0.03837154,  0.94424234,  0.54406483,  0.25399445],\n",
        "       [ 0.04583676,  0.09379588,  0.91877364,  0.51265172,  0.36080634],\n",
        "       [ 0.56637395,  0.39093857,  0.52816819,  0.65556558,  0.94067937]])"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Indexing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Unlike Matlab, where parenthesis is used for indexing, in NumPy it is done using square brackets\n",
      "\n",
      "**Note:**Check with your colleagues if you both have the same array *a* in the next step. It is very important to have the same values at this point"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = random.rand(5,5)\n",
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 46,
       "text": [
        "array([[ 0.75916444,  0.94064948,  0.35674098,  0.76391983,  0.02329327],\n",
        "       [ 0.26212745,  0.55539317,  0.71104502,  0.31895431,  0.56786133],\n",
        "       [ 0.43040634,  0.2584529 ,  0.34181508,  0.24693744,  0.71610839],\n",
        "       [ 0.78713362,  0.21469213,  0.00365139,  0.21454292,  0.94248957],\n",
        "       [ 0.53490537,  0.61891915,  0.73147886,  0.72756939,  0.26000907]])"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[0,0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 47,
       "text": [
        "0.75916443575824311"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "array([ 0.75916444,  0.94064948,  0.35674098,  0.76391983,  0.02329327])"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[:,0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 49,
       "text": [
        "array([ 0.75916444,  0.26212745,  0.43040634,  0.78713362,  0.53490537])"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Very important: Slicing and indexing return views of the original array. Can you see any difference?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "aview1 = a[[0],:]\n",
      "aview1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 50,
       "text": [
        "array([[ 0.75916444,  0.94064948,  0.35674098,  0.76391983,  0.02329327]])"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "aview2 = a[0]\n",
      "aview2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 51,
       "text": [
        "array([ 0.75916444,  0.94064948,  0.35674098,  0.76391983,  0.02329327])"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "aview3 = a[[0]]\n",
      "aview3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 52,
       "text": [
        "array([[ 0.75916444,  0.94064948,  0.35674098,  0.76391983,  0.02329327]])"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print aview1.shape, aview2.shape, aview3.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(1, 5) (5,) (1, 5)\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Slicing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import YouTubeVideo\n",
      "YouTubeVideo('q_2TBbfMLzs',start=15)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "        <iframe\n",
        "            width=\"400\"\n",
        "            height=300\"\n",
        "            src=\"https://www.youtube.com/embed/q_2TBbfMLzs?start=15\"\n",
        "            frameborder=\"0\"\n",
        "            allowfullscreen\n",
        "        ></iframe>\n",
        "        "
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 56,
       "text": [
        "<IPython.lib.display.YouTubeVideo at 0x7f21ecc46490>"
       ]
      }
     ],
     "prompt_number": 56
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "array([[ 0.75916444,  0.94064948,  0.35674098,  0.76391983,  0.02329327],\n",
        "       [ 0.26212745,  0.55539317,  0.71104502,  0.31895431,  0.56786133],\n",
        "       [ 0.43040634,  0.2584529 ,  0.34181508,  0.24693744,  0.71610839],\n",
        "       [ 0.78713362,  0.21469213,  0.00365139,  0.21454292,  0.94248957],\n",
        "       [ 0.53490537,  0.61891915,  0.73147886,  0.72756939,  0.26000907]])"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[:,:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "array([[ 0.75916444,  0.94064948,  0.35674098,  0.76391983,  0.02329327],\n",
        "       [ 0.26212745,  0.55539317,  0.71104502,  0.31895431,  0.56786133],\n",
        "       [ 0.43040634,  0.2584529 ,  0.34181508,  0.24693744,  0.71610839],\n",
        "       [ 0.78713362,  0.21469213,  0.00365139,  0.21454292,  0.94248957],\n",
        "       [ 0.53490537,  0.61891915,  0.73147886,  0.72756939,  0.26000907]])"
       ]
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[0:2,1:3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 59,
       "text": [
        "array([[ 0.94064948,  0.35674098],\n",
        "       [ 0.55539317,  0.71104502]])"
       ]
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = arange(10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[1:6:3]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "array([1, 4])"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[::2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 62,
       "text": [
        "array([0, 2, 4, 6, 8])"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[::-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 63,
       "text": [
        "array([9, 8, 7, 6, 5, 4, 3, 2, 1, 0])"
       ]
      }
     ],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit \n",
      "a[::-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000000 loops, best of 3: 222 ns per loop\n"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%timeit\n",
      "reversed(a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000000 loops, best of 3: 182 ns per loop\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print a[5:], a[:4], a[-2:], a[:-4]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[5 6 7 8 9] [0 1 2 3] [8 9] [0 1 2 3 4 5]\n"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = random.rand(5,5)\n",
      "a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 67,
       "text": [
        "array([[ 0.63611189,  0.45387041,  0.84324789,  0.41564385,  0.8736876 ],\n",
        "       [ 0.15186863,  0.75865389,  0.11447856,  0.03593258,  0.35814001],\n",
        "       [ 0.76592388,  0.7361502 ,  0.36358767,  0.25983878,  0.94569104],\n",
        "       [ 0.43403234,  0.23080921,  0.64767593,  0.50096602,  0.27094573],\n",
        "       [ 0.79041938,  0.41486588,  0.4061916 ,  0.33896987,  0.68529799]])"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 68,
       "text": [
        "array([ 0.63611189,  0.45387041,  0.84324789,  0.41564385,  0.8736876 ])"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rows = [1,3]\n",
      "cols = [0,2]\n",
      "a[rows], a[:,cols], a[rows,cols]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 69,
       "text": [
        "(array([[ 0.15186863,  0.75865389,  0.11447856,  0.03593258,  0.35814001],\n",
        "        [ 0.43403234,  0.23080921,  0.64767593,  0.50096602,  0.27094573]]),\n",
        " array([[ 0.63611189,  0.84324789],\n",
        "        [ 0.15186863,  0.11447856],\n",
        "        [ 0.76592388,  0.36358767],\n",
        "        [ 0.43403234,  0.64767593],\n",
        "        [ 0.79041938,  0.4061916 ]]),\n",
        " array([ 0.15186863,  0.64767593]))"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Vorsicht! Round vs np.round"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mask = np.around(a)\n",
      "mask = mask.astype('bool')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 70
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a[mask]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 71,
       "text": [
        "array([ 0.63611189,  0.84324789,  0.8736876 ,  0.75865389,  0.76592388,\n",
        "        0.7361502 ,  0.94569104,  0.64767593,  0.50096602,  0.79041938,\n",
        "        0.68529799])"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mask = a > 1.0\n",
      "a[mask]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 72,
       "text": [
        "array([], dtype=float64)"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mask = a < 1.0\n",
      "a[mask]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 73,
       "text": [
        "array([ 0.63611189,  0.45387041,  0.84324789,  0.41564385,  0.8736876 ,\n",
        "        0.15186863,  0.75865389,  0.11447856,  0.03593258,  0.35814001,\n",
        "        0.76592388,  0.7361502 ,  0.36358767,  0.25983878,  0.94569104,\n",
        "        0.43403234,  0.23080921,  0.64767593,  0.50096602,  0.27094573,\n",
        "        0.79041938,  0.41486588,  0.4061916 ,  0.33896987,  0.68529799])"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mask = a > 0.7\n",
      "a[mask]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "array([ 0.84324789,  0.8736876 ,  0.75865389,  0.76592388,  0.7361502 ,\n",
        "        0.94569104,  0.79041938])"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "where(mask)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "(array([0, 0, 1, 2, 2, 2, 4]), array([2, 4, 1, 0, 1, 4, 0]))"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Linear Algebra"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy.linalg import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 76
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = arange(10)\n",
      "b = random.rand(10,1)\n",
      "A = random.randn(10,10)\n",
      "print x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0 1 2 3 4 5 6 7 8 9]\n"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x*2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 78,
       "text": [
        "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18])"
       ]
      }
     ],
     "prompt_number": 78
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x+5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 79,
       "text": [
        "array([ 5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
       ]
      }
     ],
     "prompt_number": 79
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x**2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 80,
       "text": [
        "array([ 0,  1,  4,  9, 16, 25, 36, 49, 64, 81])"
       ]
      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x*x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 81,
       "text": [
        "array([ 0,  1,  4,  9, 16, 25, 36, 49, 64, 81])"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "And one of the best features: broadcasting"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image\n",
      "Image('https://scipy-lectures.github.io/_images/numpy_broadcasting.png',width=800)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": 800
        }
       },
       "output_type": "pyout",
       "png": 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LZg1Ay40bNywsLMLDw5l+KBKJIiIiLC0t79y5w3IlFRUVI0eOpHKGIZFIRo8e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7v7VyeTkpIE94KamZmBBQVaE0OH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PBg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\n6rd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mzZoFqdAcsCjL/2zcuPH777/38fHx9va+cOECLTHs2bMnPj4+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\nmZubOzg4tLgPQRB5eXkcDsfGxgYyBgAA1MjNza2srEQ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CQklJicVi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\n",
       "prompt_number": 82,
       "text": [
        "<IPython.core.display.Image at 0x7f21ecbcb810>"
       ]
      }
     ],
     "prompt_number": 82
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x.shape, b.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 83,
       "text": [
        "((10,), (10, 1))"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x+b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 84,
       "text": [
        "array([[ 0.62627322,  1.62627322,  2.62627322,  3.62627322,  4.62627322,\n",
        "         5.62627322,  6.62627322,  7.62627322,  8.62627322,  9.62627322],\n",
        "       [ 0.01516076,  1.01516076,  2.01516076,  3.01516076,  4.01516076,\n",
        "         5.01516076,  6.01516076,  7.01516076,  8.01516076,  9.01516076],\n",
        "       [ 0.28310379,  1.28310379,  2.28310379,  3.28310379,  4.28310379,\n",
        "         5.28310379,  6.28310379,  7.28310379,  8.28310379,  9.28310379],\n",
        "       [ 0.79613997,  1.79613997,  2.79613997,  3.79613997,  4.79613997,\n",
        "         5.79613997,  6.79613997,  7.79613997,  8.79613997,  9.79613997],\n",
        "       [ 0.6313566 ,  1.6313566 ,  2.6313566 ,  3.6313566 ,  4.6313566 ,\n",
        "         5.6313566 ,  6.6313566 ,  7.6313566 ,  8.6313566 ,  9.6313566 ],\n",
        "       [ 0.29106039,  1.29106039,  2.29106039,  3.29106039,  4.29106039,\n",
        "         5.29106039,  6.29106039,  7.29106039,  8.29106039,  9.29106039],\n",
        "       [ 0.6707564 ,  1.6707564 ,  2.6707564 ,  3.6707564 ,  4.6707564 ,\n",
        "         5.6707564 ,  6.6707564 ,  7.6707564 ,  8.6707564 ,  9.6707564 ],\n",
        "       [ 0.67791273,  1.67791273,  2.67791273,  3.67791273,  4.67791273,\n",
        "         5.67791273,  6.67791273,  7.67791273,  8.67791273,  9.67791273],\n",
        "       [ 0.25119872,  1.25119872,  2.25119872,  3.25119872,  4.25119872,\n",
        "         5.25119872,  6.25119872,  7.25119872,  8.25119872,  9.25119872],\n",
        "       [ 0.39701644,  1.39701644,  2.39701644,  3.39701644,  4.39701644,\n",
        "         5.39701644,  6.39701644,  7.39701644,  8.39701644,  9.39701644]])"
       ]
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x2 = solve(A,b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 85
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A*x2-b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 86,
       "text": [
        "array([[ -3.95409374e-01,   4.13685767e-01,   2.14409468e-01,\n",
        "         -6.11842916e-01,   9.99325848e-02,  -1.80705335e-01,\n",
        "          4.60119301e-01,   1.85241297e-02,   1.83146509e-01,\n",
        "         -5.73630120e-01],\n",
        "       [ -6.88983026e-01,  -9.55154870e-01,   2.54459630e-01,\n",
        "          2.43030937e-01,  -2.06568041e-01,  -4.28551990e-01,\n",
        "          6.72499735e-01,  -4.51001736e-01,   1.46594431e-02,\n",
        "         -4.69708206e-01],\n",
        "       [ -3.46408297e-01,  -1.19438477e-01,  -3.27836245e-01,\n",
        "         -1.09431832e-01,  -3.93504767e-01,  -1.93695090e-01,\n",
        "         -2.53422338e-01,  -4.14724995e-01,  -2.97374203e-01,\n",
        "         -3.93128055e-01],\n",
        "       [ -7.78827743e-01,  -9.17404612e-01,  -7.45494711e-01,\n",
        "         -9.22583512e-01,  -9.41219026e-01,  -7.53176435e-01,\n",
        "         -8.45786322e-01,  -6.66898316e-01,  -7.99559214e-01,\n",
        "         -8.22526185e-01],\n",
        "       [ -1.03200940e+00,  -6.94543850e-01,  -1.15150462e+00,\n",
        "         -2.35762676e-01,  -5.29343164e-01,  -4.93288471e-01,\n",
        "         -5.16766367e-01,  -1.07569529e+00,  -8.58115139e-02,\n",
        "         -1.35220025e+00],\n",
        "       [ -7.80664600e-01,   2.68440722e-01,  -2.41399829e-01,\n",
        "         -3.06844995e-01,   3.31572377e-01,   9.34426675e-01,\n",
        "         -5.17301177e-01,   5.37634677e-01,   2.54035523e-04,\n",
        "          1.01212903e-01],\n",
        "       [ -1.72659782e+00,  -1.61006484e+00,  -1.73012235e-01,\n",
        "         -1.22882031e+00,  -1.87884725e+00,  -1.00480080e+00,\n",
        "         -2.72855063e-01,   7.06177709e-01,  -1.02047558e+00,\n",
        "         -1.53621766e+00],\n",
        "       [ -4.25488959e-01,  -9.28754504e-01,  -1.09543169e+00,\n",
        "         -8.60858296e-01,  -4.05409203e-01,  -5.91867877e-01,\n",
        "         -8.29765544e-01,  -6.12709584e-01,  -4.15395974e-01,\n",
        "         -6.09868912e-01],\n",
        "       [ -2.50242819e-01,  -2.87483231e-01,  -2.42666143e-01,\n",
        "         -2.39819874e-01,  -2.31899871e-01,  -2.65062491e-01,\n",
        "         -2.44599600e-01,  -2.49597843e-01,  -2.76084286e-01,\n",
        "         -2.74808172e-01],\n",
        "       [ -2.44695529e-01,  -2.42136197e-01,  -2.85091549e-01,\n",
        "         -2.06551965e-01,  -2.18391036e-01,  -2.75058884e-01,\n",
        "         -4.99375982e-01,  -3.36798199e-01,  -2.14202261e-01,\n",
        "         -2.67609670e-01]])"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A.dot(x2)-b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 87,
       "text": [
        "array([[  0.00000000e+00],\n",
        "       [ -4.16333634e-17],\n",
        "       [  2.22044605e-16],\n",
        "       [ -1.11022302e-16],\n",
        "       [  0.00000000e+00],\n",
        "       [ -6.66133815e-16],\n",
        "       [ -1.11022302e-16],\n",
        "       [  4.44089210e-16],\n",
        "       [ -5.55111512e-17],\n",
        "       [  0.00000000e+00]])"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.allclose(A.dot(x2),b)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 88,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "invA = inv(A)\n",
      "np.allclose(invA.dot(A),identity(shape(A)[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 89,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A.transpose()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 90,
       "text": [
        "array([[ 0.37271708,  1.46971809,  0.57517022,  0.11021651,  1.27367445,\n",
        "        -0.80129291, -2.09517358,  0.80999239,  0.05558992,  1.3773463 ],\n",
        "       [ 1.67895704,  2.05028301, -1.48702545, -0.77201885,  0.20087213,\n",
        "         0.91568713, -1.86392975, -0.80491598, -2.11011398,  1.40048879],\n",
        "       [ 1.35723633, -0.58808677,  0.40642882,  0.32242783,  1.65354952,\n",
        "         0.08127515,  0.98770556, -1.33975964,  0.49620902,  1.0120694 ],\n",
        "       [ 0.02329694, -0.56315889, -1.57794353, -0.80498979, -1.2575923 ,\n",
        "        -0.0258333 , -1.10740186, -0.58704659,  0.66173285,  1.72225559],\n",
        "       [ 1.17241964,  0.41749102,  1.00307793, -0.92363086, -0.32430052,\n",
        "         1.01900926, -2.39729186,  0.8744255 ,  1.12231799,  1.615202  ],\n",
        "       [ 0.71934504,  0.90167482, -0.81234691,  0.27352293, -0.43891831,\n",
        "         2.00564881, -0.66286563,  0.27610583, -0.80624321,  1.10278876],\n",
        "       [ 1.75392144, -1.49990155, -0.26967886, -0.31606838, -0.36428213,\n",
        "        -0.37026875,  0.78958106, -0.48727433,  0.38376945, -0.92557577],\n",
        "       [ 1.04099014,  0.95064144,  1.19588005,  0.82280369,  1.4125518 ,\n",
        "         1.35625362,  2.73233834,  0.20922773,  0.09309828,  0.54451729],\n",
        "       [ 1.30676399, -0.0650428 ,  0.1296577 , -0.02176826, -1.73428674,\n",
        "         0.47676915, -0.6939701 ,  0.84237936, -1.44721209,  1.65307857],\n",
        "       [ 0.08498941,  0.99144335,  0.99965521, -0.16798512,  2.2915605 ,\n",
        "         0.64199981, -1.71739006,  0.21834304, -1.37300009,  1.17014751]])"
       ]
      }
     ],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "A.sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 91,
       "text": [
        "22.004705986670082"
       ]
      }
     ],
     "prompt_number": 91
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 92,
       "text": [
        "22.004705986670082"
       ]
      }
     ],
     "prompt_number": 92
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sum(A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 93,
       "text": [
        "22.004705986670082"
       ]
      }
     ],
     "prompt_number": 93
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sum is np.sum"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 94,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[Numpy for Matlab Users](http://wiki.scipy.org/NumPy_for_Matlab_Users)\n",
      "\n",
      "[Other syntax conversions between languages](http://mathesaurus.sourceforge.net/)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "def css_styling():\n",
      "    styles = open(\"./styles/custom.css\", \"r\").read()\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<link href='http://fonts.googleapis.com/css?family=Fenix' rel='stylesheet' type='text/css'>\n",
        "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
        "<link href='http://fonts.googleapis.com/css?family=Source+Code+Pro:300,400' rel='stylesheet' type='text/css'>\n",
        "<style>\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
        "    }\n",
        "    div.cell{\n",
        "        width:1000px;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    h1 {\n",
        "        font-family: 'Alegreya Sans', sans-serif;\n",
        "    }\n",
        "    h2 {\n",
        "        font-family: 'Fenix', serif;\n",
        "    }\n",
        "    h3{\n",
        "\tfont-family: 'Fenix', serif;\n",
        "        margin-top:12px;\n",
        "        margin-bottom: 3px;\n",
        "       }\n",
        "    h4{\n",
        "\tfont-family: 'Fenix', serif;\n",
        "       }\n",
        "    h5 {\n",
        "        font-family: 'Alegreya Sans', sans-serif;\n",
        "    }\t   \n",
        "    div.text_cell_render{\n",
        "        font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
        "        line-height: 140%;\n",
        "        font-size: 130%;\n",
        "        width:1000px;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    .CodeMirror{\n",
        "\tfont-size: 120%;\n",
        "\tfont-family: 'Monaco', sans-serif;\n",
        "    }\n",
        "/*      .prompt{\n",
        "        display: None;\n",
        "    }*/\n",
        "    .text_cell_render h1 {\n",
        "        font-weight: 200;\n",
        "        font-size: 50pt;\n",
        "\t\tline-height: 100%;\n",
        "        color:#CD2305;\n",
        "        margin-bottom: 0.5em;\n",
        "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "    }\t\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 300;\n",
        "        font-size: 16pt;\n",
        "        color: #CD2305;\n",
        "        font-style: italic;\n",
        "        margin-bottom: .5em;\n",
        "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "    }\n",
        "    \n",
        "    .warning{\n",
        "        color: rgb( 240, 20, 20 )\n",
        "        }  \n",
        "</style>\n",
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
        "                           extensions: [\"AMSmath.js\"]\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
        "                }\n",
        "        });\n",
        "</script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "<IPython.core.display.HTML at 0x7f5e10322510>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}