Basics of Numpy

gistfile1.txt

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To know about Numpy check my [blog](http://www.bigdataexaminer.com/5-amazingly-powerful-python-libraries-for-data-science/)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#N- Dimensional array\n",
      "\n",
      "Arrays allows you to perform mathematical operations on whole blocks of data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# easiest way to create an array is by using an array function\n",
      "import numpy as np # I am importing numpy as np\n",
      "\n",
      "scores = [89,56.34, 76,89, 98]\n",
      "first_arr =np.array(scores)\n",
      "print first_arr\n",
      "print first_arr.dtype  # .dtype return the data type of the array object"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 89.    56.34  76.    89.    98.  ]\n",
        "float64\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Nested lists with equal length, will be converted into a multidimensional array\n",
      "scores_1 = [[34,56,23,89], [11,45,76,34]]\n",
      "second_arr = np.array(scores_1)\n",
      "print second_arr\n",
      "print second_arr.ndim  #.ndim gives you the dimensions of an array.\n",
      "print second_arr.shape #(number of rows, number of columns)\n",
      "print second_arr.dtype "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[34 56 23 89]\n",
        " [11 45 76 34]]\n",
        "2\n",
        "(2L, 4L)\n",
        "int32\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.zeros(10) # returns a array of zeros, the same applies for np.ones(10)\n",
      "x"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.zeros((4,3)) # you can also mention the shape of the array"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "array([[ 0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.]])"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.arange(15)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14])"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.eye(6) # Create a square N x N identity matrix (1\u2019s on the diagonal and 0\u2019s elsewhere)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "array([[ 1.,  0.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  1.,  0.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  1.,  0.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  1.,  0.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  1.,  0.],\n",
        "       [ 0.,  0.,  0.,  0.,  0.,  1.]])"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Batch operations on data can be performed without using for loops, this is called vectorization\n",
      "scores = [89,56.34, 76,89, 98]\n",
      "first_arr =np.array(scores)\n",
      "print first_arr\n",
      "print first_arr * first_arr\n",
      "print first_arr - first_arr\n",
      "print 1/(first_arr)\n",
      "print first_arr ** 0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 89.    56.34  76.    89.    98.  ]\n",
        "[ 7921.      3174.1956  5776.      7921.      9604.    ]\n",
        "[ 0.  0.  0.  0.  0.]\n",
        "[ 0.01123596  0.01774938  0.01315789  0.01123596  0.01020408]\n",
        "[ 9.43398113  7.5059976   8.71779789  9.43398113  9.89949494]\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Indexing and Slicing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# you may want to select a subset of your data, for which Numpy array indexing is really useful\n",
      "new_arr = np.arange(12)\n",
      "print new_arr\n",
      "print new_arr[5]\n",
      "print new_arr[4:9]\n",
      "new_arr[4:9] = 99 #assign sequence of values from 4 to 9 as 99\n",
      "print new_arr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0  1  2  3  4  5  6  7  8  9 10 11]\n",
        "5\n",
        "[4 5 6 7 8]\n",
        "[ 0  1  2  3 99 99 99 99 99  9 10 11]\n"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# A major diffence between lists and array is that, array slices are views on the original array. This means that\n",
      "# the data is not copied, and any modifications to the view will be reflected in the source\n",
      "#  array. \n",
      "modi_arr = new_arr[4:9] \n",
      "modi_arr[1] = 123456\n",
      "print new_arr                  # you can see the changes are refelected in main array. \n",
      "modi_arr[:]                  # the sliced variable\n",
      "            "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[     0      1      2      3     99 123456     99     99     99      9\n",
        "     10     11]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "array([    99, 123456,     99,     99,     99])"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# arrays can be treated like matrices\n",
      "matrix_arr =np.array([[3,4,5],[6,7,8],[9,5,1]])\n",
      "print matrix_arr\n",
      "print matrix_arr[1]\n",
      "print matrix_arr[0][2] #first row and third column\n",
      "print matrix_arr[0,2] # This is same as the above operation\n",
      "\n",
      "from IPython.display import Image  # importing a image from my computer.\n",
      "i = Image(filename='Capture.png')\n",
      "i # Blue print of a matrix "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[3 4 5]\n",
        " [6 7 8]\n",
        " [9 5 1]]\n",
        "[6 7 8]\n",
        "5\n",
        "5\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 9,
       "text": [
        "<IPython.core.display.Image at 0x4e41290>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cd C:\\Users\\tk\\Desktop\\pics # changing my directory"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "C:\\Users\\tk\\Desktop\\pics\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# 3d arrays -> this is a 2x2x3 array\n",
      "three_d_arr = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
      "print three_d_arr\n",
      "print \"returns the second list inside first list {}\".format(three_d_arr[0,1])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[[ 1  2  3]\n",
        "  [ 4  5  6]]\n",
        "\n",
        " [[ 7  8  9]\n",
        "  [10 11 12]]]\n",
        "returns the second list inside first list [4 5 6]\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "three_d_arr = np.array([[[1, 2, 3], [4, 5, 6]], [[7, 8, 9], [10, 11, 12]]])\n",
      "print three_d_arr[0]\n",
      "#if you omit later indices, the returned object will be a lowerdimensional\n",
      "# ndarray consisting of all the data along the higher dimensions"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[1 2 3]\n",
        " [4 5 6]]\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I have used [format](https://docs.python.org/2/tutorial/inputoutput.html) function in the below cell."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "copied_values = three_d_arr[0].copy() # copy arr[0] value to copied_values\n",
      "three_d_arr[0]= 99  # change all values of arr[0] to 99 \n",
      "print \"New value of three_d_arr: {}\".format(three_d_arr)  # check the new value of three_d_arr \n",
      "three_d_arr[0] = copied_values # assign copied values back to three_d_arr[0]\n",
      "print\" three_d_arr again: {}\".format(three_d_arr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "New value of three_d_arr: [[[99 99 99]\n",
        "  [99 99 99]]\n",
        "\n",
        " [[ 7  8  9]\n",
        "  [10 11 12]]]\n",
        " three_d_arr again: [[[99 99 99]\n",
        "  [99 99 99]]\n",
        "\n",
        " [[ 7  8  9]\n",
        "  [10 11 12]]]\n"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "matrix_arr =np.array([[3,4,5],[6,7,8],[9,5,1]])\n",
      "print \"The original matrix {}:\".format(matrix_arr)\n",
      "print \"slices the first two rows:{}\".format(matrix_arr[:2]) # similar to list slicing. returns first two rows of the array\n",
      "print \"Slices the first two rows and two columns:{}\".format(matrix_arr[:2, 1:])\n",
      "print \"returns 6 and 7: {}\".format(matrix_arr[1,:2])\n",
      "print \"Returns first column: {}\".format(matrix_arr[:,:1]) #Note that a colon by itself means to take the entire axis"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The original matrix [[3 4 5]\n",
        " [6 7 8]\n",
        " [9 5 1]]:\n",
        "slices the first two rows:[[3 4 5]\n",
        " [6 7 8]]\n",
        "Slices the first two rows and two columns:[[4 5]\n",
        " [7 8]]\n",
        "returns 6 and 7: [6 7]\n",
        "Returns first column: [[3]\n",
        " [6]\n",
        " [9]]\n"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image  # importing a image from my computer.\n",
      "j = Image(filename='Expre.png')\n",
      "j # diagrammatic explanation of matrix array slicing works."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 80,
       "text": [
        "<IPython.core.display.Image at 0x3ab2ba8>"
       ]
      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Import random module from Numpy \n",
      "personals = np.array(['Manu', 'Jeevan', 'Prakash', 'Manu', 'Prakash', 'Jeevan', 'Prakash'])\n",
      "print personals == 'Manu' #checks for the string 'Manu' in personals. If present it returns true; else false#"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ True False False  True False False False]\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import random \n",
      "random_no = random.randn(7,4)\n",
      "print random_no\n",
      "random_no[personals =='Manu'] #The function returns the rows for which the value of manu is true\n",
      "# Check the image displayed in the cell below. "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[-0.129557    0.3684001  -0.15747451 -0.1196816 ]\n",
        " [-0.35946571 -1.23477985  1.08186057 -0.61596683]\n",
        " [ 1.67096505  1.11183755 -0.39640455  0.22848279]\n",
        " [-0.27989438 -1.51275966 -0.48825407  1.32425359]\n",
        " [-0.04493194 -1.10371501 -0.52742166 -1.06265549]\n",
        " [ 1.16938298 -0.60478133  1.40615125 -1.35350336]\n",
        " [ 0.86325448  1.97577081  0.05339779  0.71515521]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "array([[-0.129557  ,  0.3684001 , -0.15747451, -0.1196816 ],\n",
        "       [-0.27989438, -1.51275966, -0.48825407,  1.32425359]])"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cd C:\\Users\\Manu\\Desktop \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "C:\\Users\\Manu\\Desktop\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image\n",
      "k = Image(filename='Matrix.png')\n",
      "k"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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x+TFiEDJWP6o8+x0vesYkvg/ct+rP5T3u6F6mikEGIYIg1hV0/qkgZBAiCGK9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\nQmCC\n",
       "prompt_number": 11,
       "text": [
        "<IPython.core.display.Image at 0x3a034e0>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random_no[personals == 'Manu', 2:] #First two columns and first two rows."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "array([[-0.15747451, -0.1196816 ],\n",
        "       [-0.48825407,  1.32425359]])"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# To select everything except 'Manu', you can != or negate the condition using -:\n",
      "print personals != 'Manu'\n",
      "random_no[-(personals == 'Manu')] #get everything except 1st and 4th rows"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[False  True  True False  True  True  True]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "array([[-0.35946571, -1.23477985,  1.08186057, -0.61596683],\n",
        "       [ 1.67096505,  1.11183755, -0.39640455,  0.22848279],\n",
        "       [-0.04493194, -1.10371501, -0.52742166, -1.06265549],\n",
        "       [ 1.16938298, -0.60478133,  1.40615125, -1.35350336],\n",
        "       [ 0.86325448,  1.97577081,  0.05339779,  0.71515521]])"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# you can use boolean operator &(and), |(or)\n",
      "new_variable = (personals == 'Manu') | (personals == 'Jeevan')\n",
      "print new_variable\n",
      "random_no[new_variable] "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ True  True False  True False  True False]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "array([[-0.129557  ,  0.3684001 , -0.15747451, -0.1196816 ],\n",
        "       [-0.35946571, -1.23477985,  1.08186057, -0.61596683],\n",
        "       [-0.27989438, -1.51275966, -0.48825407,  1.32425359],\n",
        "       [ 1.16938298, -0.60478133,  1.40615125, -1.35350336]])"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random_no[random_no < 0] =0 \n",
      "random_no # This will set all negative values to zero"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "array([[ 0.        ,  0.3684001 ,  0.        ,  0.        ],\n",
        "       [ 0.        ,  0.        ,  1.08186057,  0.        ],\n",
        "       [ 1.67096505,  1.11183755,  0.        ,  0.22848279],\n",
        "       [ 0.        ,  0.        ,  0.        ,  1.32425359],\n",
        "       [ 0.        ,  0.        ,  0.        ,  0.        ],\n",
        "       [ 1.16938298,  0.        ,  1.40615125,  0.        ],\n",
        "       [ 0.86325448,  1.97577081,  0.05339779,  0.71515521]])"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "random_no[ personals != 'Manu'] = 9 # This will set all rows except 1 and 4 to 9. \n",
      "random_no"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": [
        "array([[ 0.        ,  0.3684001 ,  0.        ,  0.        ],\n",
        "       [ 9.        ,  9.        ,  9.        ,  9.        ],\n",
        "       [ 9.        ,  9.        ,  9.        ,  9.        ],\n",
        "       [ 0.        ,  0.        ,  0.        ,  1.32425359],\n",
        "       [ 9.        ,  9.        ,  9.        ,  9.        ],\n",
        "       [ 9.        ,  9.        ,  9.        ,  9.        ],\n",
        "       [ 9.        ,  9.        ,  9.        ,  9.        ]])"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Fancy Indexing(Indexing using integer arrays)\n",
      "Fancy indexing copies data into a new array\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from numpy import random\n",
      "algebra = random.randn(7,4) # empty will return a matrix of size 7,4\n",
      "for j in range(7):\n",
      "    algebra[j] = j\n",
      "algebra"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([[ 0.,  0.,  0.,  0.],\n",
        "       [ 1.,  1.,  1.,  1.],\n",
        "       [ 2.,  2.,  2.,  2.],\n",
        "       [ 3.,  3.,  3.,  3.],\n",
        "       [ 4.,  4.,  4.,  4.],\n",
        "       [ 5.,  5.,  5.,  5.],\n",
        "       [ 6.,  6.,  6.,  6.]])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# To select a subset of rows in particular order, you can simply pass a list.\n",
      "algebra[[4,5,1]] #returns a subset of rows"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([[ 4.,  4.,  4.,  4.],\n",
        "       [ 5.,  5.,  5.,  5.],\n",
        "       [ 1.,  1.,  1.,  1.]])"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fancy = np.arange(36).reshape(9,4) #reshape is to reshape an array\n",
      "print fancy\n",
      "fancy[[1,4,3,2],[3,2,1,0]] #the position of the output array are[(1,3),(4,2),(3,1),(2,0)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0  1  2  3]\n",
        " [ 4  5  6  7]\n",
        " [ 8  9 10 11]\n",
        " [12 13 14 15]\n",
        " [16 17 18 19]\n",
        " [20 21 22 23]\n",
        " [24 25 26 27]\n",
        " [28 29 30 31]\n",
        " [32 33 34 35]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "array([ 7, 18, 13,  8])"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fancy[[1, 4, 8, 2]][:, [0, 3, 1, 2]] # entire first row is selected, but the elements are interchanged, same goes for 4th, 8th and 2 nd row."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "array([[ 4,  7,  5,  6],\n",
        "       [16, 19, 17, 18],\n",
        "       [32, 35, 33, 34],\n",
        "       [ 8, 11,  9, 10]])"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# another way to do the above operation is by using np.ix_ function.\n",
      "fancy[np.ix_([1,4,8,2],[0,3,1,2])]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 42,
       "text": [
        "array([[ 4,  7,  5,  6],\n",
        "       [16, 19, 17, 18],\n",
        "       [32, 35, 33, 34],\n",
        "       [ 8, 11,  9, 10]])"
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Transposing Arrays"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "transpose= np.arange(12).reshape(3,4) \n",
      "transpose.T # the shape has changed to 4,3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 47,
       "text": [
        "array([[ 0,  4,  8],\n",
        "       [ 1,  5,  9],\n",
        "       [ 2,  6, 10],\n",
        "       [ 3,  7, 11]])"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#you can use np.dot function to perform matrix computations. You can calculate X transpose X as follows:\n",
      "np.dot(transpose.T, transpose)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "array([[ 80,  92, 104, 116],\n",
        "       [ 92, 107, 122, 137],\n",
        "       [104, 122, 140, 158],\n",
        "       [116, 137, 158, 179]])"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#universal functions\n",
      "They perform element wise operations on data in arrays."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "funky =np.arange(8)\n",
      "print np.sqrt(funky)\n",
      "print np.exp(funky) #exponent of the array\n",
      "# these are called as unary functions"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.          1.          1.41421356  1.73205081  2.          2.23606798\n",
        "  2.44948974  2.64575131]\n",
        "[  1.00000000e+00   2.71828183e+00   7.38905610e+00   2.00855369e+01\n",
        "   5.45981500e+01   1.48413159e+02   4.03428793e+02   1.09663316e+03]\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Binary functions take two value, Others such as maximum, add\n",
      "x = random.randn(10)\n",
      "y = random.randn(10)\n",
      "print x\n",
      "print y\n",
      "print np.maximum(x,y)# element wise operation\n",
      "print np.modf(x)# function modf returns the fractional and integral parts of a floating point arrays"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-0.47538326 -0.32308133  1.45505923 -0.53196376 -1.34427866 -2.14409558\n",
        " -0.96296558  0.14068437 -0.29208196 -1.17537313]\n",
        "[-1.68868842 -0.53788536 -1.01887225 -0.02972594 -1.04607062 -2.08636169\n",
        "  0.34398903 -0.64183089  1.55401001  0.73270627]\n",
        "[-0.47538326 -0.32308133  1.45505923 -0.02972594 -1.04607062 -2.08636169\n",
        "  0.34398903  0.14068437  1.55401001  0.73270627]\n",
        "(array([-0.47538326, -0.32308133,  0.45505923, -0.53196376, -0.34427866,\n",
        "       -0.14409558, -0.96296558,  0.14068437, -0.29208196, -0.17537313]), array([-0., -0.,  1., -0., -1., -2., -0.,  0., -0., -1.]))\n"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# List of unary functions avaliable\n",
      "from IPython.display import Image  \n",
      "l = Image(filename='unary functions.png')\n",
      "l"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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A1NE21+mb64cHBHVAf7Sp7/jAGktW4zj7A9Z1bZJsW31k9Oa6pmyOh6zGJdtf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       "prompt_number": 67,
       "text": [
        "<IPython.core.display.Image at 0x4eaf690>"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#List of binary functions available\n",
      "from IPython.display import Image  \n",
      "l = Image(filename='binary functions.png')\n",
      "l\n",
      "#logical operators , and  greater, greater_equal,less, less_equal, equal, not_equal operations can also be performed"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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hTlZjt+9n+NZbctiynWZCHQzQeQZlPk4J6DIRDJIyYiacCUEPB0YmT5wAbFKH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\nUw9d3lRNl+flu5VdoIOko8w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KKaW8mm+//T9Dwd0Esm0K9wAAAABJRU5ErkJggg==\n",
       "prompt_number": 69,
       "text": [
        "<IPython.core.display.Image at 0x4eafb50>"
       ]
      }
     ],
     "prompt_number": 69
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Data processing using Arrays"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mtrices =np.arange(-5,5,1)\n",
      "x, y = np.meshgrid(mtrices, mtrices) #mesh grid function takes two 1 d arrays and produces two 2d arrays\n",
      "print \"Matrix values of y: {}\".format(y)\n",
      "print \"Matrix values of x: {}\".format(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Matrix values of y: [[-5 -5 -5 -5 -5 -5 -5 -5 -5 -5]\n",
        " [-4 -4 -4 -4 -4 -4 -4 -4 -4 -4]\n",
        " [-3 -3 -3 -3 -3 -3 -3 -3 -3 -3]\n",
        " [-2 -2 -2 -2 -2 -2 -2 -2 -2 -2]\n",
        " [-1 -1 -1 -1 -1 -1 -1 -1 -1 -1]\n",
        " [ 0  0  0  0  0  0  0  0  0  0]\n",
        " [ 1  1  1  1  1  1  1  1  1  1]\n",
        " [ 2  2  2  2  2  2  2  2  2  2]\n",
        " [ 3  3  3  3  3  3  3  3  3  3]\n",
        " [ 4  4  4  4  4  4  4  4  4  4]]\n",
        "Matrix values of x: [[-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]\n",
        " [-5 -4 -3 -2 -1  0  1  2  3  4]]\n"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[zip](http://stackoverflow.com/questions/13704860/zip-lists-in-python) function is clearly explained here."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x1= np.array([1,2,3,4,5])\n",
      "y1 = np.array([6,7,8,9,10])\n",
      "cond =[True, False, True, True, False]\n",
      "#If you want to take a value from x1 whenever the corresponding value in cond is true, otherwise take value from y.\n",
      "z1 = [(x,y,z) for x,y,z in zip(x1, y1, cond)] # I have used zip function To illustrate the concept\n",
      "print z1\n",
      "np.where(cond, x1, y1) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[(1, 6, True), (2, 7, False), (3, 8, True), (4, 9, True), (5, 10, False)]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 124,
       "text": [
        "array([ 1,  7,  3,  4, 10])"
       ]
      }
     ],
     "prompt_number": 124
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ra = np.random.randn(5,5)\n",
      "# If you want to replace negative values in ra with -1 and positive values with 1. You can do it using where function\n",
      "print ra\n",
      "print np.where(ra>0, 1, -1) # If values in ra are greater than zero, replace it with 1, else replace it with -1.\n",
      "# to set only positive values\n",
      "np.where(ra >0, 1, ra) # same implies to negative values"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[-0.91593384  0.38253326 -0.13340929 -0.12353528 -0.90849552]\n",
        " [ 2.23109011 -0.7980066   0.13600282 -0.2447923   1.32865533]\n",
        " [-0.65568719 -1.48154609  0.8033841  -0.84157511 -0.19588005]\n",
        " [ 1.42527047  0.63082249 -0.80092209 -0.69935209  0.20470869]\n",
        " [ 0.18245815 -0.99953295  0.05586992  0.38031972  0.60522581]]\n",
        "[[-1  1 -1 -1 -1]\n",
        " [ 1 -1  1 -1  1]\n",
        " [-1 -1  1 -1 -1]\n",
        " [ 1  1 -1 -1  1]\n",
        " [ 1 -1  1  1  1]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 132,
       "text": [
        "array([[-0.91593384,  1.        , -0.13340929, -0.12353528, -0.90849552],\n",
        "       [ 1.        , -0.7980066 ,  1.        , -0.2447923 ,  1.        ],\n",
        "       [-0.65568719, -1.48154609,  1.        , -0.84157511, -0.19588005],\n",
        "       [ 1.        ,  1.        , -0.80092209, -0.69935209,  1.        ],\n",
        "       [ 1.        , -0.99953295,  1.        ,  1.        ,  1.        ]])"
       ]
      }
     ],
     "prompt_number": 132
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Statistical methods"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "thie = np.random.randn(5,5)\n",
      "print thie.mean() # calculates the mean of thie\n",
      "print np.mean(thie) # alternate method to calculate mean\n",
      "print thie.sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.286291297223\n",
        "0.286291297223\n",
        "7.15728243058\n"
       ]
      }
     ],
     "prompt_number": 136
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "jp =np.arange(12).reshape(4,3)\n",
      "print\"The arrays are: {}\".format(jp)\n",
      "print \"The sum of rows are :{}\".format(np.sum(jp, axis =0)) #axis =0, gives you sum of the columns. axis =1 , gives sum of rows.\n",
      "# remember this zero is for columns and one is for rows."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The arrays are: [[ 0  1  2]\n",
        " [ 3  4  5]\n",
        " [ 6  7  8]\n",
        " [ 9 10 11]]\n",
        "The sum of rows are :[18 22 26]\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print jp.sum(1)#returns sum of rows"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 3 12 21 30]\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "jp.cumsum(0)  #cumulative sum of columns, try the same for jp.cumprod(0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "array([[ 0,  1,  2],\n",
        "       [ 3,  5,  7],\n",
        "       [ 9, 12, 15],\n",
        "       [18, 22, 26]])"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "jp.cumsum(1)#cumulative sum of rows"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "array([[ 0,  1,  3],\n",
        "       [ 3,  7, 12],\n",
        "       [ 6, 13, 21],\n",
        "       [ 9, 19, 30]])"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xp =np.random.randn(100)\n",
      "print(xp > 0).sum() # sum of all positive values\n",
      "print (xp < 0).sum()\n",
      "tandf =np.array([True,False,True,False,True,False])\n",
      "print tandf.any()#checks if any of the values are true\n",
      "print tandf.all() #returns false even if a single value is false\n",
      "#These methods also work with non-boolean arrays, where non-zero elements evaluate to True."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "45\n",
        "55\n",
        "True\n",
        "False\n"
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b>Other array functions are:<br> </b>\n",
      "std, var -> standard deviation and variance <br>\n",
      "min, max -> Minimum and Maximum <br>\n",
      "argmin, argmax -> Indices of minimum and maximum elements"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Sorting"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lp = np.random.randn(8)\n",
      "print lp\n",
      "lp.sort()\n",
      "lp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-0.38465299 -0.84381465 -1.78393531 -0.80242681 -2.54136215 -0.47354742\n",
        " -1.17517075  0.23759082]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 55,
       "text": [
        "array([-2.54136215, -1.78393531, -1.17517075, -0.84381465, -0.80242681,\n",
        "       -0.47354742, -0.38465299,  0.23759082])"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tp = np.random.randn(4,4)\n",
      "tp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 57,
       "text": [
        "array([[ 0.4968525 , -0.65497365, -0.43687651,  0.51706412],\n",
        "       [-1.39148137, -0.0166924 , -0.82572908,  2.20839298],\n",
        "       [-0.5400157 , -0.8311936 , -1.92611011,  0.04556166],\n",
        "       [ 0.41679611, -1.1659837 , -1.7181857 ,  0.15529182]])"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tp.sort(1) #check the rows are sorted\n",
      "tp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "array([[-0.65497365, -0.43687651,  0.4968525 ,  0.51706412],\n",
        "       [-1.39148137, -0.82572908, -0.0166924 ,  2.20839298],\n",
        "       [-1.92611011, -0.8311936 , -0.5400157 ,  0.04556166],\n",
        "       [-1.7181857 , -1.1659837 ,  0.15529182,  0.41679611]])"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "personals = np.array(['Manu', 'Jeevan', 'Prakash', 'Manu', 'Prakash', 'Jeevan', 'Prakash'])\n",
      "np.unique(personals)# returns the unique elements in the array"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "array(['Jeevan', 'Manu', 'Prakash'], \n",
        "      dtype='|S7')"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "set(personals) # set is an alternative to unique function"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 65,
       "text": [
        "{'Jeevan', 'Manu', 'Prakash'}"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.in1d(personals, ['Manu']) #in1d function checks for the value 'Manu' and returns True, other wise returns False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 67,
       "text": [
        "array([ True, False, False,  True, False, False, False], dtype=bool)"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b> Other Functions are :<br> </b>\n",
      "intersect1d(x, y)-> Compute the sorted, common elements in x and y <br>\n",
      "union1d(x,y) -> compute the sorted union of elements <br>\n",
      "setdiff1d(x,y) -> set difference, elements in x that are not in y <br>\n",
      "setxor1d(x, y) -> Set symmetric differences; elements that are in either of the arrays, but not both <br>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Linear Algebra"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cp = np.array([[1,2,3],[4,5,6]])\n",
      "dp = np.array([[7,8],[9,10],[11,12]])\n",
      "print \"CP array :{}\".format(cp)\n",
      "print \"DP array :{}\".format(dp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CP array :[[1 2 3]\n",
        " [4 5 6]]\n",
        "DP array :[[ 7  8]\n",
        " [ 9 10]\n",
        " [11 12]]\n"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# element wise multiplication\n",
      "cp.dot(dp) # this is equivalent to np.dot(x,y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 73,
       "text": [
        "array([[ 58,  64],\n",
        "       [139, 154]])"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.dot(cp, np.ones(3)) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 77,
       "text": [
        "array([  6.,  15.])"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# numpy.linalg has standard matrix operations like determinants and inverse.\n",
      "from numpy.linalg import inv, qr\n",
      "cp = np.array([[1,2,3],[4,5,6]])\n",
      "new_mat = cp.T.dot(cp) # multiply cp inverse and cp, this is element wise multiplication\n",
      "print new_mat"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[17 22 27]\n",
        " [22 29 36]\n",
        " [27 36 45]]\n"
       ]
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sp = np.random.randn(5,5)\n",
      "print inv(sp)\n",
      "rt = inv(sp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[  8.42073934  -3.99404791  -1.02750024  -9.15141449 -11.83177632]\n",
        " [  0.99455489   0.12614541   0.97324631   0.13731371   1.83602625]\n",
        " [  7.22433965  -3.9236319   -1.72053933  -8.26352406 -11.80445805]\n",
        " [  4.35711911  -2.62701594  -0.75752399  -4.80133342  -6.89057351]\n",
        " [  4.97536913  -1.66709125   0.42132364  -4.00769704  -4.45711904]]\n"
       ]
      }
     ],
     "prompt_number": 90
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# to calculate the product of a matrix and its inverse\n",
      "sp.dot(rt)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 91,
       "text": [
        "array([[  1.00000000e+00,  -6.66133815e-16,  -3.88578059e-16,\n",
        "         -4.44089210e-16,  -5.77315973e-15],\n",
        "       [ -8.88178420e-16,   1.00000000e+00,   1.11022302e-16,\n",
        "          4.44089210e-16,   8.88178420e-16],\n",
        "       [ -2.66453526e-15,   2.22044605e-16,   1.00000000e+00,\n",
        "         -3.55271368e-15,   2.22044605e-15],\n",
        "       [  8.88178420e-16,   0.00000000e+00,  -1.11022302e-16,\n",
        "          1.00000000e+00,  -8.88178420e-16],\n",
        "       [  0.00000000e+00,  -6.66133815e-16,   1.66533454e-16,\n",
        "          8.88178420e-16,   1.00000000e+00]])"
       ]
      }
     ],
     "prompt_number": 91
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "q,r = qr(sp)\n",
      "print q\n",
      "r"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[-0.50510571  0.0181599   0.07531349  0.59150958 -0.62368481]\n",
        " [ 0.13921471 -0.40513763  0.84451738  0.24413444  0.20897736]\n",
        " [ 0.53635022 -0.51829708 -0.46188958  0.47703793 -0.05281481]\n",
        " [-0.66103319 -0.49468555 -0.25644088  0.01307464  0.50238278]\n",
        " [ 0.02917284  0.56761612 -0.04488163  0.6023111   0.55871984]]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 95,
       "text": [
        "array([[ 2.90927288, -0.76452754, -3.08539037,  0.77536573, -1.07156322],\n",
        "       [-0.        ,  2.28961296,  1.31005059, -0.44393071, -1.96748764],\n",
        "       [-0.        ,  0.        ,  1.48340931, -2.65558951,  0.18679631],\n",
        "       [ 0.        ,  0.        ,  0.        , -0.37900614,  0.4507976 ],\n",
        "       [-0.        , -0.        , -0.        , -0.        , -0.12535448]])"
       ]
      }
     ],
     "prompt_number": 95
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b>Other Matrix Functions</b> <br>\n",
      "<li>diag : Return the diagonal (or off-diagonal) elements of a square matrix as a 1D array, or convert a 1D array into a square<br>\n",
      "matrix with zeros on the off-diagonal\n",
      "<li> trace: Compute the sum of the diagonal elements\n",
      "<li> det: Compute the matrix determinant\n",
      "<li> eig: Compute the eigenvalues and eigenvectors of a square matrix\n",
      "<li> pinv: Compute the pseudo-inverse of a square matrix\n",
      "<li> svd: Compute the singular value decomposition (SVD)\n",
      "<li> solve: Solve the linear system Ax = b for x, where A is a square matrix\n",
      "<li> lstsq: Compute the least-squares solution to y = Xb"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}