{
 "metadata": {
  "name": "02-MPL-NumPy-basics"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Matplotlib and NumPy basics"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Basic plotting"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dat = [3, -1, 0.5, 4, 2]\n",
      "plot(dat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "[<matplotlib.lines.Line2D at 0x106119510>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ffvghPXv2dDKPNW7+H/3HP8L778ORIyan2/efu3ksy1JOZymnO0T7+wvbtWvn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\nqIuIeIiKuoiIh/w/I954DQid4CwAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plotting points\n",
      "A = (0,1)\n",
      "B = (1,0)\n",
      "C = (2,1)\n",
      "\n",
      "# x = [A[0], B[0], C[0]]\n",
      "x = map(lambda i: i[0], [A,B,C])\n",
      "y = [i[1] for i in [A,B,C]]\n",
      "\n",
      "plot(x, y, 'bo-')\n",
      "axis([-0.1, 2.1, -0.1, 1.1]); # note ; at the end"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "[-0.1, 2.1, -0.1, 1.1]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Style and plot attributes"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "MATLAB like API"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = range(11)\n",
      "y1 = [i**2 for i in x]\n",
      "y2 = [i**2 for i in reversed(x)]\n",
      "\n",
      "plot(x, y1, 'ro-')\n",
      "plot(x, y2, 'gs--')\n",
      "xlabel('x')\n",
      "ylabel('y')\n",
      "title('$f(x) \\sim x^2$')\n",
      "grid()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ACn38MZEHDzK7aVMAwq9tfjEoiIipU5WFZQvkb8R0MspI2BWdlw5OVLHdGVy8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\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Lists vs arrays"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = range(5)\n",
      "y = x + 4"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "TypeError",
       "evalue": "can only concatenate list (not \"int\") to list",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-5-7c650f8da057>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;31mTypeError\u001b[0m: can only concatenate list (not \"int\") to list"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = 2 * x   # not what we expect for a math expression\n",
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "[0, 1, 2, 3, 4, 0, 1, 2, 3, 4]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = array(range(5)) # covert a list to array object\n",
      "y = 2*x + 1\n",
      "print(y)\n",
      "type(y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1 3 5 7 9]\n"
       ]
      },
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "numpy.ndarray"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = arange(11) # numpy built-in\n",
      "plot(x, x**2, 'ro-')\n",
      "plot(x, (10-x)**2, 'gs-')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1061e52d0>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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zadOmja0vL1KdE0zB1JamasRoNoW7xWJh+vTphISEMHv27Mrj0dHRJCYmApCY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\nAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = arange(-1, 1.1, 0.1) # arange works with floats\n",
      "plot(x, x**2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1061ef510>]"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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//ct2RMFH1bp4QpW7+Jyq+LpTtS5lVLlLwFIVX3uq1sVbVLmLX6mKr5qqdamM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\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(-pi, pi, 256) # nb of points instead of sampling\n",
      "plot(x, sin(x), label=r'$\\sin(x)$')\n",
      "plot(x, cos(x), label=r'$\\cos(x)$' )\n",
      "legend(loc='upper left')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.legend.Legend at 0x106481810>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ZxpS2mehYdrY6AjTlaZsnAr0C+enYTzzKeiQ6ilDmuqdeFnqp0NIy0lh/aj0D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\n"
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Note on pylab import\n",
      "\n",
      "\"`%pylan inline`\" does the following:\n",
      "\n",
      "    from numpy import *\n",
      "    from numpy.fft import *\n",
      "    from numpy.random import *\n",
      "    from numpy.linalg import *\n",
      "    from matplotlib.pyplot import *\n",
      "\n",
      "    # provide the recommended module abbrevs in the pylab namespace\n",
      "    # recommended for scripts\n",
      "    import matplotlib.pyplot as plt\n",
      "    import numpy as np\n",
      "    import numpy.ma as ma\n",
      "\n",
      "try `help(cos)`\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Efficiency"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import random\n",
      "\n",
      "def rand_gauss(N):\n",
      "    return [random.gauss(0,1) for _ in xrange(N)]\n",
      "\n",
      "sample_size = 500\n",
      "\n",
      "d1 = rand_gauss(sample_size)\n",
      "\n",
      "d2 = np.random.randn(sample_size)\n",
      "\n",
      "subplot(1,2,1)\n",
      "hist(d1, label='gauss')\n",
      "subplot(1,2,2)\n",
      "hist(d2, color='red')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "(array([  1,   6,  32,  68, 127, 118,  89,  45,  12,   2]),\n",
        " array([-3.36075237, -2.70074813, -2.04074388, -1.38073963, -0.72073539,\n",
        "       -0.06073114,  0.5992731 ,  1.25927735,  1.91928159,  2.57928584,\n",
        "        3.23929008]),\n",
        " <a list of 10 Patch objects>)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit rand_gauss(sample_size)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 loops, best of 3: 656 us per loop\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit np.random.randn(sample_size)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "10000 loops, best of 3: 20.2 us per loop\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "NumPy: N-dimentional array object"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_lst = range(10)  # regular list\n",
      "x_lst[0:-1:2]      # [start:stop:step]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[0, 2, 4, 6, 8]"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_arr = arange(10)\n",
      "x_arr[0:-1:2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "array([0, 2, 4, 6, 8])"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print x_lst\n",
      "x_lst[0] = 'hi'\n",
      "print x_lst"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
        "['hi', 1, 2, 3, 4, 5, 6, 7, 8, 9]\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_arr[0] = 'hi'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "ValueError",
       "evalue": "invalid literal for long() with base 10: 'hi'",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-17-862aa56c851a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx_arr\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'hi'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;31mValueError\u001b[0m: invalid literal for long() with base 10: 'hi'"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x_arr[0] = 10.5 # danger zone\n",
      "x_arr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "array([10,  1,  2,  3,  4,  5,  6,  7,  8,  9])"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Numpy arrays are **statically typed** and **homogeneous**. The type of the elements is determined when array is created!"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def a_info(arr):\n",
      "    print 'dtype:', arr.dtype   # data type\n",
      "    print 'nbytes:', arr.nbytes # nb of bytes\n",
      "    print 'ndim:', arr.ndim\n",
      "    print 'shape:', arr.shape\n",
      "    print 'size:', arr.size\n",
      "    \n",
      "a_info(x_arr)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dtype: int64\n",
        "nbytes: 80\n",
        "ndim: 1\n",
        "shape: (10,)\n",
        "size: 10\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(x_arr) == x_arr.size"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = arange(3, dtype='float')\n",
      "a_info(y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dtype: float64\n",
        "nbytes: 24\n",
        "ndim: 1\n",
        "shape: (3,)\n",
        "size: 3\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# type casting\n",
      "a_info(y.astype('complex'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dtype: complex128\n",
        "nbytes: 48\n",
        "ndim: 1\n",
        "shape: (3,)\n",
        "size: 3\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Multi-dimentional array and indexing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = array( [[2.0, 1, 3], [0.1, 0.2, 0.3]] )\n",
      "M"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([[ 2. ,  1. ,  3. ],\n",
        "       [ 0.1,  0.2,  0.3]])"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a_info(M)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "dtype: float64\n",
        "nbytes: 48\n",
        "ndim: 2\n",
        "shape: (2, 3)\n",
        "size: 6\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M[0,0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "2.0"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M[0] # select 1st row"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "array([ 2.,  1.,  3.])"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M[1,:] # select 2d row"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "array([ 0.1,  0.2,  0.3])"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M[:, -1] # select last column"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "array([ 3. ,  0.3])"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# assignment works the same way\n",
      "M[:,-1] = 100\n",
      "M"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([[   2. ,    1. ,  100. ],\n",
        "       [   0.1,    0.2,  100. ]])"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M[0:, 1:] # all rows, 2 last columns"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "array([[   1. ,  100. ],\n",
        "       [   0.2,  100. ]])"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Array generation functions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print arange(-1.0, 1.0, 0.2)  # low, high (excl), step"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ -1.00000000e+00  -8.00000000e-01  -6.00000000e-01  -4.00000000e-01\n",
        "  -2.00000000e-01  -2.22044605e-16   2.00000000e-01   4.00000000e-01\n",
        "   6.00000000e-01   8.00000000e-01]\n"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print linspace(-1.0, 1.0, 9)  # low, high (incl), nb_of_points"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-1.   -0.75 -0.5  -0.25  0.    0.25  0.5   0.75  1.  ]\n"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print zeros((3,3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.  0.  0.]\n",
        " [ 0.  0.  0.]\n",
        " [ 0.  0.  0.]]\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print diag((3.,2,1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 3.  0.  0.]\n",
        " [ 0.  2.  0.]\n",
        " [ 0.  0.  1.]]\n"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.random.rand(2, 4)  # random numbers from a uniform distribution between [0, 1["
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.66800989  0.96622993  0.43213735  0.33973   ]\n",
        " [ 0.79521694  0.76777532  0.24617852  0.78354752]]\n"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print np.random.randn(2, 4)  # randome numbers from a normal distribution (mu=0, sigma=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 1.00360327  2.09461226  1.1273358   0.51963957]\n",
        " [ 0.59788146 -0.17339674  0.8364903   1.04364158]]\n"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Fancy indexing"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = linspace(-1, 1, 5)\n",
      "print 'x:', x\n",
      "\n",
      "c = (x >= 0)\n",
      "print 'c:', c\n",
      "print c.dtype\n",
      "\n",
      "print 'x[c]:', x[c]\n",
      "\n",
      "y = exp(x)\n",
      "print 'y[c]', y[c]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "x: [-1.  -0.5  0.   0.5  1. ]\n",
        "c: [False False  True  True  True]\n",
        "bool"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "x[c]: [ 0.   0.5  1. ]\n",
        "y[c]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " [ 1.          1.64872127  2.71828183]\n"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "c = (x >= -0.5) * ( x <= 0.5)\n",
      "x[c]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "array([-0.5,  0. ,  0.5])"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Array methods"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def a_meth(arr):\n",
      "    print 'min:', arr.min()\n",
      "    print 'max:', arr.max()\n",
      "    print 'mean:', arr.mean()\n",
      "    print 'std:', arr.std()\n",
      "\n",
      "x = randn(100)*2.3 + 1.7\n",
      "a_meth(x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "min: -3.009859938\n",
        "max: 7.72678056926\n",
        "mean: 1.65085133248\n",
        "std: 2.27740367094\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Array operations"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "v = arange(6)\n",
      "print 2 * v - 5 # linear transform"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[-5 -3 -1  1  3  5]\n"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "v2 = v[::-1]\n",
      "print v + v2    # element-wise sum"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[5 5 5 5 5 5]\n"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print (1 - np.exp(v))  # vectorized function"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[   0.           -1.71828183   -6.3890561   -19.08553692  -53.59815003\n",
        " -147.4131591 ]\n"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = (rand(4,3) * 10).astype('int')\n",
      "print 2*M"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[12  2 18]\n",
        " [18 16 12]\n",
        " [ 6 10 16]\n",
        " [18 18 10]]\n"
       ]
      }
     ],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "v = array([0,1,2])\n",
      "print M * v       # multiply every row by vector"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0  1 18]\n",
        " [ 0  8 12]\n",
        " [ 0  5 16]\n",
        " [ 0  9 10]]\n"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "File I/O"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = randn(10, 3)\n",
      "save('data/M.npy', M)  # dump an array into a binary file (similar to MATLAB's .mat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = load('data/M.npy')\n",
      "(N - M).sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 71,
       "text": [
        "0.0"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "savetxt('data/M.csv', M, fmt='%.3f', delimiter='\\t')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 76
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "!head data/M.csv"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.036\t1.617\t-0.977\r\n",
        "0.600\t-1.656\t1.417\r\n",
        "-1.850\t0.007\t0.246\r\n",
        "1.088\t-0.170\t0.941\r\n",
        "1.316\t-1.822\t0.389\r\n",
        "-0.447\t1.119\t0.179\r\n",
        "-0.393\t-0.904\t-1.427\r\n",
        "1.363\t-0.968\t1.443\r\n",
        "1.425\t-0.509\t-0.882\r\n",
        "-0.031\t0.431\t0.011\r\n"
       ]
      }
     ],
     "prompt_number": 77
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = genfromtxt('data/M.csv')\n",
      "N"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 81,
       "text": [
        "array([[ 1.036,  1.617, -0.977],\n",
        "       [ 0.6  , -1.656,  1.417],\n",
        "       [-1.85 ,  0.007,  0.246],\n",
        "       [ 1.088, -0.17 ,  0.941],\n",
        "       [ 1.316, -1.822,  0.389],\n",
        "       [-0.447,  1.119,  0.179],\n",
        "       [-0.393, -0.904, -1.427],\n",
        "       [ 1.363, -0.968,  1.443],\n",
        "       [ 1.425, -0.509, -0.882],\n",
        "       [-0.031,  0.431,  0.011]])"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(N-M).sum()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 80,
       "text": [
        "0.0028902802726487797"
       ]
      }
     ],
     "prompt_number": 80
    }
   ],
   "metadata": {}
  }
 ]
}