notebooks/unit04/unit04_01.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was prepared by Cayetano Benavent, 2016."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NumPy 01 - Handling arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importing library (convention):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Array creation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([1,2,3,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Number of dimensions and size:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.ndim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Array shape:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reshape an array (1 Dimension to 2 Dimensions):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a2 = a.reshape((2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Array creation from range:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = np.arange(54)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
       "       34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,\n",
       "       51, 52, 53])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(54,)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create an array with evenly spaced numbers over a specified interval:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-20. , -19.6, -19.2, -18.8, -18.4, -18. , -17.6, -17.2, -16.8,\n",
       "       -16.4, -16. , -15.6, -15.2, -14.8, -14.4, -14. , -13.6, -13.2,\n",
       "       -12.8, -12.4, -12. , -11.6, -11.2, -10.8, -10.4, -10. ,  -9.6,\n",
       "        -9.2,  -8.8,  -8.4,  -8. ,  -7.6,  -7.2,  -6.8,  -6.4,  -6. ,\n",
       "        -5.6,  -5.2,  -4.8,  -4.4,  -4. ,  -3.6,  -3.2,  -2.8,  -2.4,\n",
       "        -2. ,  -1.6,  -1.2,  -0.8,  -0.4,   0. ,   0.4,   0.8,   1.2,\n",
       "         1.6,   2. ,   2.4,   2.8,   3.2,   3.6,   4. ,   4.4,   4.8,\n",
       "         5.2,   5.6,   6. ,   6.4,   6.8,   7.2,   7.6,   8. ,   8.4,\n",
       "         8.8,   9.2,   9.6,  10. ,  10.4,  10.8,  11.2,  11.6,  12. ,\n",
       "        12.4,  12.8,  13.2,  13.6,  14. ,  14.4,  14.8,  15.2,  15.6,\n",
       "        16. ,  16.4,  16.8,  17.2,  17.6,  18. ,  18.4,  18.8,  19.2,\n",
       "        19.6,  20. ])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linspace(-20, 20, 101)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reshape an array (1 Dimension to 4 Dimensions):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "b2 = b.reshape((2,3,3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[[ 0,  1,  2],\n",
       "         [ 3,  4,  5],\n",
       "         [ 6,  7,  8]],\n",
       "\n",
       "        [[ 9, 10, 11],\n",
       "         [12, 13, 14],\n",
       "         [15, 16, 17]],\n",
       "\n",
       "        [[18, 19, 20],\n",
       "         [21, 22, 23],\n",
       "         [24, 25, 26]]],\n",
       "\n",
       "\n",
       "       [[[27, 28, 29],\n",
       "         [30, 31, 32],\n",
       "         [33, 34, 35]],\n",
       "\n",
       "        [[36, 37, 38],\n",
       "         [39, 40, 41],\n",
       "         [42, 43, 44]],\n",
       "\n",
       "        [[45, 46, 47],\n",
       "         [48, 49, 50],\n",
       "         [51, 52, 53]]]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b2.ndim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reshape an array (N Dimensions to 1 Dimension):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,\n",
       "       34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,\n",
       "       51, 52, 53])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b2.ravel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating arrays of zeros:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating arrays of ones:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((3,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating array of random numbers (PRNG):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.12960929,  0.53675698,  0.41250439],\n",
       "       [ 0.72031705,  0.28929958,  0.54191109],\n",
       "       [ 0.50970017,  0.62802048,  0.21905545]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(111)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.61217018,  0.16906975,  0.43605902],\n",
       "       [ 0.76926247,  0.2953253 ,  0.14916296],\n",
       "       [ 0.02247832,  0.42022449,  0.23868214]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(111)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.61217018,  0.16906975,  0.43605902],\n",
       "       [ 0.76926247,  0.2953253 ,  0.14916296],\n",
       "       [ 0.02247832,  0.42022449,  0.23868214]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.rand(3,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating a sample (or samples) from a normal distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.18384316, -0.11512978,  1.08784319],\n",
       "       [ 1.52172568, -0.26208059, -1.75151683],\n",
       "       [ 0.09137849,  0.12458097,  0.37108135]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randn(3,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creating a sample (or samples) from a normal distribution\n",
    "defining mean, standard deviation and size:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "np.random.normal?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 52.00469631,  50.12063831,  50.7664686 ,  48.39489809,\n",
       "        56.4007917 ,  49.78019896,  47.73528502,  52.93444712,\n",
       "        58.88746287,  51.59213941,  45.00685284,  37.31608354,\n",
       "        48.00155432,  45.44966872,  55.85141283,  41.75928902,\n",
       "        45.47279955,  49.57454697,  56.96722487,  49.59600674,\n",
       "        52.27132622,  51.21754229,  42.41397875,  47.80533921,\n",
       "        47.80041833,  52.24410888,  45.70355354,  57.79712649,\n",
       "        49.09917571,  46.66731106,  59.57921481,  45.30017734,\n",
       "        61.67196829,  49.97683462,  54.54131908,  58.407208  ,\n",
       "        54.21131987,  51.22234972,  48.91888187,  46.1506765 ,\n",
       "        49.83990531,  43.03146011,  43.19383667,  43.3850918 ,\n",
       "        49.42343635,  45.57786318,  51.88613717,  51.87154546,\n",
       "        54.01013239,  55.23107712,  45.47600697,  43.65952864,\n",
       "        52.59181742,  45.00235787,  46.72479554,  46.29169618,\n",
       "        51.70042133,  53.8844131 ,  51.2513835 ,  56.22971067,\n",
       "        43.46866115,  49.01539828,  53.32188097,  51.65867771,\n",
       "        51.13615797,  44.78980439,  51.79443882,  57.34212037,\n",
       "        43.23946902,  59.30499713,  38.18646533,  56.69824263,\n",
       "        43.811018  ,  36.58560152,  43.06411929,  48.84015634,\n",
       "        45.02813522,  45.65662491,  43.56951559,  52.55074364,\n",
       "        54.24233054,  50.4387304 ,  52.22644453,  53.54667178,\n",
       "        45.42717588,  49.62230294,  47.82034   ,  47.17613004,\n",
       "        48.4310274 ,  55.87347427,  48.72979399,  53.86606174,\n",
       "        45.34304171,  47.02671058,  51.13294532,  44.64673922,\n",
       "        54.49996752,  56.0194491 ,  48.10618715,  50.52604352])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.normal(loc=50,scale=5,size=100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Slicing arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "c = np.arange(16).reshape((4,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 4,  5,  6,  7],\n",
       "       [ 8,  9, 10, 11],\n",
       "       [12, 13, 14, 15]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[1,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[2,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[2,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  4,  8, 12])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  5,  9, 13])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[0,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 11],\n",
       "       [14, 15]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[2:,2:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  1,  2,  3],\n",
       "       [ 8,  9, 10, 11]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[::2,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  2],\n",
       "       [ 4,  6],\n",
       "       [ 8, 10],\n",
       "       [12, 14]])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[:,::2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Copies and views\n",
    "\n",
    "d array is a view and e array is a copy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d = c[2:,2:]\n",
    "e = c[2:,2:].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 11],\n",
       "       [14, 15]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c[-1,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c[-1,-1] = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  0,   1,   2,   3],\n",
       "       [  4,   5,   6,   7],\n",
       "       [  8,   9,  10,  11],\n",
       "       [ 12,  13,  14, 500]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 10,  11],\n",
       "       [ 14, 500]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 11],\n",
       "       [14, 15]])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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