Numpy_Quickstart_Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.array([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "print(type(a))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 1)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[-1], a[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a[0] = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 2, 3])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "b = np.array([[1,2,3],[4,5,6]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]]\n"
     ]
    }
   ],
   "source": [
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.zeros((2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.],\n",
       "       [ 0.,  0.]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = np.ones((1,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c = np.full((2,2), 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7, 7],\n",
       "       [7, 7]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d = np.eye(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.,  0.],\n",
       "       [ 0.,  1.]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d #identity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "e = np.random.random((2,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.44777667,  0.57611561],\n",
       "       [ 0.39240514,  0.87228255]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.arange(1,13).reshape(3,4) #amazing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8],\n",
       "       [ 9, 10, 11, 12]])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = a[:2, 1:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [6, 7]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b #first two rows and columns 1 and 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.arange(1,13).reshape(3,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8],\n",
       "       [ 9, 10, 11, 12]])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "row_r1 = a[1, :] #when using integer indexing, we get a lower rank"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 6, 7, 8])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_r1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_r1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "row_r2 = a[1:2, :] # when using slicing, we get same rank as original!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 6, 7, 8]])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 4)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_r2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the subtle differences above. Same applied for column indexing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.arange(1,7).reshape(3,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 4 5]\n"
     ]
    }
   ],
   "source": [
    "print(a[[0, 1, 2], [0, 1, 0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 4, 5])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[[0,1,2], [0,1,0]] # interesting indexing - play with it to see"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.arange(1,13).reshape(4,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b = np.array([0,2,0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 0, 1])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  6  7 11]\n"
     ]
    }
   ],
   "source": [
    "print(a[np.arange(4), b]) #cute, you can create indexing!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above allows us do cute mutating! See below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a[np.arange(4), b] += 10 #this is very very cool!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[11,  2,  3],\n",
       "       [ 4,  5, 16],\n",
       "       [17,  8,  9],\n",
       "       [10, 21, 12]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "a = np.arange(1,7).reshape(3,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4],\n",
       "       [5, 6]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bool_idx = (a > 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False, False],\n",
       "       [ True,  True],\n",
       "       [ True,  True]], dtype=bool)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bool_idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4, 5, 6])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[bool_idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4, 5, 6])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[a>2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hideCode": true
   },
   "source": [
    "Every numpy array is a grid of elements of the same type. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "int64\n",
      "[1 2]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1,2])\n",
    "print(x.dtype)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float64\n",
      "[ 1.  2.]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1.0,2.0])\n",
    "print(x.dtype)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float64\n",
      "[ 1.  2.]\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1,2], dtype=np.float64)\n",
    "print(x.dtype)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Elementwise operations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.arange(1,5).reshape(2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = np.arange(5,9).reshape(2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 6],\n",
       "       [7, 8]])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6,  8],\n",
       "       [10, 12]])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x+y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6,  8],\n",
       "       [10, 12]])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4, -4],\n",
       "       [-4, -4]])"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x-y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4, -4],\n",
       "       [-4, -4]])"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.subtract(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5, 12],\n",
       "       [21, 32]])"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x*y #elementwise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5, 12],\n",
       "       [21, 32]])"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.multiply(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2       ,  0.33333333],\n",
       "       [ 0.42857143,  0.5       ]])"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x/y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2       ,  0.33333333],\n",
       "       [ 0.42857143,  0.5       ]])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.divide(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  1.41421356],\n",
       "       [ 1.73205081,  2.        ]])"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(x) #each element in x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 6],\n",
       "       [7, 8]])"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v = np.array([9,10])\n",
    "w = np.array([11,12])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For matrix multiplication we use np.dot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "219"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "219"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(v,w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([29, 67])"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dot(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([29, 67])"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x,v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[19, 22],\n",
       "       [43, 50]])"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[19, 22],\n",
       "       [43, 50]])"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.dot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(1,5).reshape(2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(x) #sum of all elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 6])"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(x, axis=0) #sum of each column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 7])"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(x, axis=1) #sum of each row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 3],\n",
       "       [2, 4]])"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T #transposes X, not inplace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.arange(1,13).reshape(4,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "v = np.array([1,0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1])"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = np.empty_like(x) #makes an empty array with same dimensions as x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0],\n",
       "       [0, 0, 0],\n",
       "       [0, 0, 0],\n",
       "       [0, 0, 0]])"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for i in range(4):\n",
    "    y[i, :] = x[i, :] + v # adding to each row of y, X + a constant vector v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  2,  4],\n",
       "       [ 5,  5,  7],\n",
       "       [ 8,  8, 10],\n",
       "       [11, 11, 13]])"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that when $x$ is large, an explicit loop can be very slow. Also, realise that adding the vector $v$ to each row of the matrix $x$ is equivalent to forming a matrix $vv$ by stacking multiple copies of $v$ vertically, and then performing elementwise summation of $x$ and $v$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(1,13).reshape(4,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v= np.array([1,0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1])"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vv = np.tile(v, (4,1)) #the 1 makes it a column stack"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 1],\n",
       "       [1, 0, 1],\n",
       "       [1, 0, 1],\n",
       "       [1, 0, 1]])"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 1, 1, 0, 1],\n",
       "       [1, 0, 1, 1, 0, 1],\n",
       "       [1, 0, 1, 1, 0, 1],\n",
       "       [1, 0, 1, 1, 0, 1]])"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tile(v, (4,2)) #2 column stacks side by side!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = x + vv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  2,  4],\n",
       "       [ 5,  5,  7],\n",
       "       [ 8,  8, 10],\n",
       "       [11, 11, 13]])"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y # this is the same result but we didnt use a for loop this time!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, broadcasting abstracts all of this thought for us! See below!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(1,13).reshape(4,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v = np.array([1,0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 7,  8,  9],\n",
       "       [10, 11, 12]])"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1])"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = x + v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  2,  4],\n",
       "       [ 5,  5,  7],\n",
       "       [ 8,  8, 10],\n",
       "       [11, 11, 13]])"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y # WOOOAAAHHHHH!!! # same as using for loop and stacking"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$y = x + v$ works even though $x$ has shape $(4,3)$ and $v$ has shape $(3,)$ due to broadcasting!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uses of broadcasting below!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Outer product calculation!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "v = np.array([1,2,3])\n",
    "w = np.array([4,5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 216,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1],\n",
       "       [2],\n",
       "       [3]])"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.reshape(v, (3,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4,  5],\n",
       "       [ 8, 10],\n",
       "       [12, 15]])"
      ]
     },
     "execution_count": 215,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.reshape(v, (3,1))*w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(1,7).reshape(2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 4, 6],\n",
       "       [5, 7, 9]])"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + v # adding v to each row of x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 5])"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4],\n",
       "       [2, 5],\n",
       "       [3, 6]])"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  9],\n",
       "       [ 6, 10],\n",
       "       [ 7, 11]])"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T + w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5,  6,  7],\n",
       "       [ 9, 10, 11]])"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(x.T + w).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  4,  6],\n",
       "       [ 8, 10, 12]])"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x*2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(0,4*np.pi, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = np.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10fef5e80>"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9OHC6kWO1zVwXIc1dADExwnWTc1lzqMpyLIpYQQmxl/b5TumvnRQ5BQVg2aRhtHZ0sf5w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\nMSYo/n8D3Edb3ZujjAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fe9bc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)\n",
    "plt.xlabel(\"X values\")\n",
    "plt.ylabel(\"Y values (Radians)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = np.cos(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1100246a0>"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xUTbnaYB2n/b20UXal5a+Ntj6T+Bx4H3AiyLyL8BrwDagMPDhmZ7ExURxzXir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\njDHG+MX/B/ajZRj1CirGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ffb8048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)\n",
    "plt.xlabel(\"X values\")\n",
    "plt.ylabel(\"Y values (Radians)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = np.tan(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10ffc52b0>"
      ]
     },
     "execution_count": 257,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bJlKRspe7v+DuLxb7fDM7Bpjh7k+4uwO3AZeVLUARkSLFosZQA5dEqrECb2lY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\nkZIpiYiISMmUREREpGRKIiIiUrL/DzSFr/pr3jLZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1101e4390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)\n",
    "plt.xlabel(\"X values\")\n",
    "plt.ylabel(\"Y values (Radians)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(0, 3 * np.pi, 0.1)\n",
    "y_sin = np.sin(x)\n",
    "y_cos = np.cos(x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x110fc79b0>"
      ]
     },
     "execution_count": 275,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k/AEgVSmVDTwFrLnaEyilnlVKTVZKTY6Li3O5QEfYXFBFU7uVlZOdbHCUvRIs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\nIbAWvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f5a0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_sin)\n",
    "plt.plot(x, y_cos)\n",
    "plt.xlabel('x axis label')\n",
    "plt.ylabel('y axis label')\n",
    "plt.title('Sine, Cosine')\n",
    "plt.legend(['Sine', 'Cosine'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EWIA353UJtzqGUg7htOVjjLnIFkGUUkq5Dh1Go5RSyubOdrTbtcA/gXCgANho\njLm0Ef8vFzh4xk9cLww4fpaP4ex0G/023T6np9vo9HQb/Ud7Y0yjjj1bcpFpcxCRtMaOqnBVuo1+\nm26f09NtdHq6jc6MHnZTSillc1o+SimlbM6Ry2ea1QEcgG6j36bb5/R0G52ebqMz4LDnfJRSSjku\nR97zUUop5aC0fJRSStmcw5WPiAwTkZ0iskdEHrM6j70RkRgRWSEi20Vkm4jca3UmeyUi7iKyQUQ+\ntTqLvRGRIBFZLCIZIrJDRAZZncneiMj9DX9jW0XkPRHxsTqTI3Go8hERd+BN4DIgAbhZRBKsTWV3\naoAHjTEJwEDgLt1Gp3QvsMPqEHbqdWCZMaYb0AfdTr8gIlHAPUCSMaYn4A6MtDaVY3Go8gFSgD3G\nmH3GmCrgfWC4xZnsijHmqDFmfcPXxdS/aURZm8r+iEg0cAUww+os9kZEAoHzgJkAxpgqY0yBtans\nkgfgKyIegB9wxOI8DsXRyicKOHzS95noG+spiUgc0A9YY20Su/Qa8Aj1iyGqX4oHcoHZDYclZ4iI\nv9Wh7IkxJgt4BTgEHAUKjTFfWpvKsTha+ahGEpEA4EPgPmNMkdV57ImIXAnkGGPSrc5ipzyA/sDb\nxph+QCmg51dPIiLB1B91iQciAX8RGW1tKsfiaOWTBcSc9H10w23qJCLiSX3xzDfGfGR1Hjs0BLha\nRA5Qf+j2dyIyz9pIdiUTyDTG/HuPeTH1ZaT+4yJgvzEm1xhTDXwEDLY4k0NxtPJZB3QWkXgR8aL+\nBN/HFmeyKyIi1B+r32GM+ZvVeeyRMeYPxphoY0wc9a+hb40x+qm1gTEmGzgsIl0bbhoKbLcwkj06\nBAwUEb+Gv7mh6KCMJrHZMtrNwRhTIyJ3A8upH10yyxizzeJY9mYIMAbYIiIbG2573BjzuYWZlOP5\nPTC/4UPePmCCxXnsijFmjYgsBtZTP8J0AzrNTpPo9DpKKaVsztEOuymllHICWj5KKaVsTstHKaWU\nzWn5KKWUsjktH6WUUjan5aOUUsrmtHyUUkrZnJaPUkopm9PyUUopZXNaPkoppWxOy0cppZTNafko\npZSyOS0fpWxERLaJyAVW51DKHmj5KHUKIjJKRNJEpEREjorIFyJyzpk+njGmhzFmZTNGVMphafko\n9StE5AHgNeAFIAKIBd4ErrYyl1LOQstHqf8iIoHAM8BdxpiPjDGlxphqY8ynxphHRMRbRF4TkSMN\n/14TEe9SSAHnAAAfHElEQVSG/xsmIp+KSIGI5InIDyLi1vCzAyJyUcPXfxaRhSLyrogUNxySSzop\nQ6SIfCgiuSKyX0TusWJbKNVStHyU+l+DAB9gySl+/kdgINAX6AOkAH9q+NmDQCYQTv0e0+PAqVZs\nvBp4Hwiifjn4NwAayuoTYBMQRf0SzfeJyKVn80spZU+0fJT6X6HAcWNMzSl+fgvwjDEmxxiTCzxN\n/dLlANVAO6B9w97SD+bUywX/aIz53BhTC8ylvsgAkoFwY8wzxpgqY8w+YDowshl+N6XsgpaPUv/r\nBBAmIh6n+HkkcPCk7w823AbwMrAH+FJE9onIY7/xPNknfV0G+DQ8Z3sgsuHQXYGIFFC/BxVxBr+L\nUnZJy0ep//UzUAlcc4qfH6G+IP4ttuE2jDHFxpgHjTEdqD+s9oCIDG3i8x8G9htjgk7618oYc3kT\nH0cpu6Xlo9R/McYUAk8Cb4rINSLiJyKeInKZiLwEvAf8SUTCRSSs4b7zAETkShHpJCICFAK1QF0T\nI6wFikXkURHxFRF3EekpIsnN9ksqZbFTHVZQyqUZY14VkWzqBxLMB4qBdOB5YD3QGtjccPdFwHMN\nX3emfuBAOJAPvGWMWdHE564VkSuBV4H9gDewk/8MalDK4cmpz4UqpZRSLUMPuymllLI5LR+llFI2\np+WjlFLK5rR8lFJK2Zwlo93CwsJMXFycFU+tlFKqhaSnpx83xoQ35r7NUj4iMgu4EsgxxvQ83f3j\n4uJIS0trjqdWSillJ0Tk4OnvVa+5DrulAsOa6bGUUko5uWbZ8zHGfC8icc3xWI3x+ZajHC+ppLWP\nJ618PGjt60lcqD/hrbxtFUEpl1VWVcO+3FKOFJRTXl1LRXUt5VW1+Hq5E+znRWiAF2EB3sQE++Hm\nJlbHVXbKZud8RGQKMAUgNjb2rB7r3Z8PsHpf3v/cHurvRbd2regZGcj5XcJJigvBy0PHVCh1purq\nDDuyi/hh93FW7zvB7mMlZBWUN+r/+nu5kxDZmp5RgSS2D+b8LuG08vFs4cTKUTTbDAcNez6fNuac\nT1JSkjmbcz6VNbUUV9RQXFFDUXk1BeXV7M0pISO7iJ3Zxew4WkxVbR0B3h6c2zmMy3u149IebbWI\nlGoEYwzpB/NZmHaYbzNyOF5SBUCXiAAS2rWmY3gAndoEEBXsi5+XB75e7vh4uFFeXUt+aTV5ZVUc\nK6xg25FCth4pYvuRIsqra/F0FwZ3DOOSHhFc2SuSQD8tImcjIunGmKTT39NBy+d0yqpq+GnPCb7N\nyGFFRg7ZRRWEBXgxIimGUSmxxIT4tdhzK+WoCsqqWJh2mA/WHWZvbin+Xu4M7R7BeV3CObdzGBGt\nfc7ocWtq69hwuIAvt2WzfNsxDuWV4ePpxjV9oxg3OI7u7Vo382+irOLy5XOyujrD97tzmb/mEN/s\nOIYBru4TyX0XdSE+zN8mGZSyZwVlVcz4YT+pqw5QUllDYvtgbkqK4Yre7fD3bt4j88YYth0pYt7q\ng/xrYxYV1XUMiA/hgYu7MKBDaLM+l7I9m5ePiLwHXACEAceAp4wxM091f1uWz8mOFpaTuuoAc1Yd\noLrWcEP/aH4/tBPRwbonpFxPaWUN73y3l9k/1ZfO5b3acveFnUmItM2eyL/3tGb+uJ9jRZX8rlsb\nHr60q+4JOTBL9nyawqry+bec4greXrmX+asPIQL3DO3Mred20HNCyiUYY/h8SzbPfrqd7KIKrujV\njt8P7US3tta86ZdX1ZK66gBvr9xDcWUNN/SP5vHLuxPs72VJHnXmtHwa6UhBOc99tp3Pt2TTqU0A\nz13Tk4G666+c2L7cEp76eBs/7D5OQrvWPHtNTxLbB1sdC4DCsmreWrmHmT/uJ9DXkyevSuDqPpHU\nr8unHIGWTxOtyMjhiaVbycwvZ9SAWJ64IgFfL3erYynVbIwxzFt9kOc/34GnuxsPXdKVWwbE4uFu\nf3v7O44W8diHm9mUWcgFXcN58bretA08s8EOyra0fM5AeVUtf/tqJ9N/2E/HcH/+cXM/ekQGWh1L\nqbOWU1zBI4s3s3JnLud1CeflG3qf8cg1W6mtM8xZdYCXl+/Ex9ONV0b0YWj3CKtjqdPQ8jkLP+4+\nzgMLN1JQVs0jw7oy6Zx43e1XDuu7Xbnc/8FGSitrePzy7owd1N6hXs97c0v4/YINbD9axMQh8Tx6\nWVe8PfSohL3S8jlLeaVVPPrhZr7afowrerXj5RG98fOyZAJwpc6IMYa3Vu7llS930jWiFW+M6ken\nNq2sjnVGKqprefGLDFJXHaBXVCDvjEkkKsjX6ljqV2j5NANjDNN/2MeLX2TQJaIV08cm6cWpyiGU\nVNbw0MJNLNuWzdV9Innx+l5O8eHpy23ZPLhwE96ebkwdk0hi+xCrI6n/0pTysb+zjXZCRJhyXkdm\nT0jhSEE5V7/xI6v2Hrc6llK/6XBeGde++RNf7TjGn67ozusj+zpF8QBc0qMtS+4aTIC3BzdPW8Oi\ntMNWR1JnQcvnNM7vEs7Hd59DWIA3Y2euZcmGTKsjKfWrtmYVct3bqzhWVMHciSlMPreDQ53faYxO\nbVrxr7uGkBIfwsOLN/OXz3dQV2f7ozfq7Gn5NEJcmD8f3jmY5LgQ7v9gE+98txcrDlcqdSorduZw\n49Sf8XJ348M7BjO4U5jVkVpMkJ8XqROSGTOwPVO/38eDizZRXVtndSzVRFo+jdTax5PUiclc1SeS\nF7/I4OlPtlOrn7iUHViYdpjJc9KID/NnyZ2D6RzhmAMLmsLD3Y1nhvfgoUu6sGRDFpPnpFFaWWN1\nLNUEWj5N4O3hzus39WXyOfGkrjrA/R9s1E9cylKzf9rPI4s3M7hjKAtvG0QbO79+pzmJCHf/rjMv\nXteLH3bnMmr6avJLq6yOpRpJy6eJ3NyEP12ZwKPDuvHxpiPcvWA9VTVaQMr23lyxh6c/2c6lPSKY\nMS6p2WegdhQjU2KZOiaJHdnF3Dx9NcdLKq2OpBpBy+cM3XFBR566KoHl245x29w0KqprrY6kXIQx\nhpeWZfDy8p1c2y+KN0f1d/kLLy9OiGDWuGQOnCjl5mmrySmusDqSOg0tn7MwYUg8L1zbi5W7cpk0\nZx3lVVpAqmUZY3jxiwzeWrmXm1NieXVEH7ucn80K53QOY/b4FLIKyhk5dTXZhVpA9kxftWdp1IBY\nXrmhD6v2nmCK7gGpFmSM4ZUvdzL1+32MHhjLC9f2xM3NuYZSn61BHUN5d2IKOcWVjJz2M8eKtIDs\nlZZPM7g+MZq/Xt+bH3Yf5875eg5ItYzXvt7Nmyv2cnNKDM9c3dPpruFpLklxIcyZmEJucSW3zFjD\nCT0HZJe0fJrJjUkxPH9tT77NyOH3763XUXCqWb3x7W5e/2Y3IxKjef6aXrrHcxqJ7YOZOT6ZzPwy\nRs9cS0GZjoKzN1o+zeiWAe3/fxDCgws36ZXXqlmk/rSfV77cxbX9onjx+t5aPI00sEMo08YksTen\nhHGz1lJcUW11JHUSLZ9mNmFI/P8Pw37q4206E4I6Kx+tz+TPn2zn4oQIXr6hN+5aPE1yXpdw3rql\nP9uOFDF5jp6TtSdaPi3gjgs6ctt5HZi7+iB//3q31XGUg/pq+zEebriA9J8399NRbWfoooQIXr2x\nD2sP5PH79zZQo4fE7YK+mlvIY5d146akGP7xzW5m/7Tf6jjKwfy89wR3LVhPz8jWTBubhI+na1/H\nc7aG943iqSsT+Gr7MR5fskWPSNgB17wk2gZEhOev7UlBeRVPf7KdEH8vhveNsjqWcgAZ2UVMeTeN\n2BA/UiekEOCiMxc0t/FD4skrreIf3+4h2N+LP1zW3epILk33fFqQh7sbr4/sx4D4EB5atImf9uh6\nQOq3ZRWUM27WWvy9PZgzMYVgfy+rIzmV+y/uwuiBsUz9bh+zftQjElbS8mlhPp7uTBubRHyYP7fN\nTWf7kSKrIyk7VVBWxbhZaymrrCV1YrIuFd0CRISnr+7JpT0iePaz7Xyx5ajVkVyWlo8NBPp6Mmdi\nCq18PJiQupasgnKrIyk7U1Fdy63vpnHoRBnTxibRrW1rqyM5LXc34fWR/egXE8S9H2wk7UCe1ZFc\nkpaPjbQL9CV1QgplVbWMm7WWwjK95kDVq6szPLhoE+sO5PPqjX0Y1DHU6khOz8fTnRnjkokO8mXy\nu2nsySmxOpLL0fKxoa5tWzFtTBIHT5Ry+7x0nYZHAfDS8p18tvkoj1/ejav6RFodx2WE+HuROiEF\nDzdh/Oy15BbrNDy2pOVjY4M6hvLidb35ed8J/vCRDvl0dfPXHOSd7/YyemAst57bweo4Lic21I+Z\n45I5XlLJre/qRai2pOVjgesTo7l3aGc+XJ/JP7/dY3UcZZEVO3N4cuk2Luwazp+v6qEThVqkT0wQ\nr93Uj02ZBdz/wUadFstGtHwsct9FnbmuXxR/+2oX/9qQZXUcZWM7jhZx9/z1dGvbijdG9dfZCyw2\nrGdb/nh5d77Yms1fl2dYHccl6NVrFhERXry+N1kF5TyyeDNRwb4kx4VYHUvZQE5xBZNS1xHg48HM\ncckuu/y1vZl0TjwHT5Qx9bt9tA/xZ9SAWKsjOTX9uGUhLw83po5JJCrYl9vmpnPwRKnVkVQLK6+q\n5dY5aeSXVTNzXDJtA32sjqQaiAhPXZXA+V3CeWLpVn7crReFtyQtH4sF+Xkxa3wydcYwMXUdheU6\nBNtZ1dUZHli4kc1Zhfzj5n70jAq0OpL6Lx7ubrwxqh+dwgO4Y346e3KKrY7ktLR87EB8mD/vjE7k\nUF4Zd85P14XonNQrX+7ki63Z/PHy7lycEGF1HHUKrXw8mTk+CW8PNyamppFXqgvRtYRmKR8RGSYi\nO0Vkj4g81hyP6WoGdgjlhWt78dOeEzy5VNcBcjaL0zN5a+Vebk6JZdI58VbHUacRHezHtLFJZBdV\ncNvcNCprdAh2czvr8hERd+BN4DIgAbhZRBLO9nFd0YikGO64oCPvrT3ErJ8OWB1HNZO1+/P4w0f1\n6/I8M1yHVDuK/rHBvDqiD+sO5Os1eS2gOfZ8UoA9xph9xpgq4H1geDM8rkt6+JKuXNojguc+2843\nO45ZHUedpYMnSrltbhoxwX68fUsinjqk2qFc1SeS+y/qwkfrs3hr5V6r4ziV5vhLiAIOn/R9ZsNt\nvyAiU0QkTUTScnNzm+FpnZObm/D3m/rSI7I197y3gR1HdRZsR1VYXs3E1HUYYNb4ZAL9PK2OpM7A\nPUM7cXWfSF5evlNnwW5GNvsYZoyZZoxJMsYkhYeH2+ppHZKflwczxiYT4OPB5Dlp5BRXWB1JNVF1\nbR13L1jPobwy3hmdSFyYv9WR1BkSEV66oTf9Y4O4f+FGNmcWWB3JKTRH+WQBMSd9H91wmzoLbQN9\nmDkumbzSKqa8m65zTjkQYwx//ngbP+w+zvPX9mJgB52l2tH5eLozdUwSof7eTJ6TxtFCXRblbDVH\n+awDOotIvIh4ASOBj5vhcV1ez6hAXhvZl02ZBTy4aJPOOeUgZv90gPlrDnH7+R25MSnm9P9BOYTw\nVt7MGp9MWVUtk1LTKK2ssTqSQzvr8jHG1AB3A8uBHcBCY8y2s31cVe/SHm15dFg3Ptt8lNe+3mV1\nHHUa32Yc47nPtnNJQgSPXNrV6jiqmXVt24o3RvUjI7uIe9/fSK1+IDxjzXLOxxjzuTGmizGmozHm\n+eZ4TPUft53XgRuTovnHt3tYsiHT6jjqFLYfKeL3CzbQvV1rXhvZFzc3HVLtjC7o2oanrurB1zuO\n8eIXO6yO47B0RkMHICI8d00vDuWV8ejiLUQF+ZESr5OQ2pNjRRVMmrOu/ur4ccn4eemfljMbNziO\nfbklTP9hP/FhAToJ6RnQiw4chJeHG++MTiQ62Jcpc9PYf1wnIbUXZVU1TJpTPy/fzPFJOlmoi3ji\nygQu6Fo/Cen3u/TykabS8nEgQX5ezJ6QjJsIE1PXka9zTlmuts5w7/sb2X6kiDdG9aNHpE4W6irq\nJyHtT+c2Adw5fz07s3US0qbQ8nEw7UP9mTYmkaz8cm6bm65zTlnshc938NX2Yzx5ZQK/66aThbqa\nAG8PZk9Ixt/bnYmp68gp0mvyGkvLxwElxYXw8ojerD2Qx8OLNusQbIvM/mk/M3/cz4QhcYwfopOF\nuqp2gb7MHJdMflkVk+boEOzG0vJxUMP7RvHIsK58vOkIL3+50+o4Lmf5tmye+XQ7l/aI4E9X6Dy6\nrq5nVCD/vLkf244UcveC9dTosiinpeXjwO44vyOjBsTy9sq9zFt90Oo4LmPDoXzueW8DfaKDeO2m\nfrjrkGoFDO0ewbPX9GTFzlyeWLpVZ8E+DR0P6sBEhGeu7sGxwgqeXLqVtq19uEgXKWtR+4+XMnlO\nGhGtfZgxLglfL3erIyk7csuA9hwpKOfNFXuJCvLl7t91tjqS3dI9Hwfn4e7GP0fVL8l893vrST+Y\nb3Ukp5VTXMHYWWswQOqEZMICvK2OpOzQQ5d05dp+Ubzy5S4Wp+tF4aei5eME/Lw8mDU+mbatfZiY\nuo7dx3TIZ3Mrrqhm/Kx1nCipYvb4ZDqEB1gdSdkpEeGv1/fmnE5hPPrhZr7N0HW5fo2Wj5MIC/Bm\n7qQBeHm4MXbWWo4U6Ky7zaWyppbb5qaz61gxb93Snz4xQVZHUnbOy8ONd8YkktCuNXfOX0/agTyr\nI9kdLR8nEhPix5wJKZRU1DB21loKyvQi1LNVU1vH/R9sZNXeE7x0Q28u6NrG6kjKQQR4e5A6IZnI\nQF8mpq7Ti1D/i5aPk0mIbM30cUkcyitj3Ox1FFdUWx3JYdXVGf7w0RY+35LNn67oznX9o62OpBxM\naIA3cyam4OvlzpiZazh0oszqSHZDy8cJDewQyluj+rMtq5BJc9Ior9JZEJrKGMOzn21nUXom9wzt\nzORzO1gdSTmomBA/3p04gMqaOkbNWK0L0TXQ8nFSFyVE8Leb+rLuQB63z9NpeJrq71/vZvZPB5gw\nJI77L9LhsursdG3birmTUigsq+aW6WvILa60OpLltHyc2NV9Innxul58tyuXe97bQLVedd0ob67Y\nwz++2c2IxGieuCIBEb2IVJ293tFBzJ6QzNHCCkbPWOPyEwNr+Ti5m5JjeeqqBJZvO6YF1AhvrdzD\ny8t3MrxvJC9e31sXhFPNKikuhBnjkth/opQxs9a49KAgLR8XMGFIPE9cmcAXW7O5e8F6qmq0gH7N\nWyv38NKy+uL52419ddoc1SKGdApj6phEdh0rYdT0NeS56B6Qlo+LmHROPE9eWb8HpAX0v/5dPFf3\nieTVEX20eFSLurBrG6aPTWJvbgmjpq/meInrnQPS8nEhE8+J589XJfDl9mPcPi+dimodhGCM4aVl\nGf9fPH+7sQ8e7vpnoVre+V3CmTkumQMnSrl52mpyil1rLSD9K3Mx44fE89w1PVmxM4exM9dSWO66\n1wHV1RmeWLqVt1bu5eaUWP5+U18tHmVT53QOY/b4FDLzyxnxzs8cPFFqdSSb0b80FzR6YHv+MbIf\nGw7nM9IFP3EBVNfWcf/CjcxbfYjbzu/AC9f21ENtyhKDOoay4NYBFJVXc/3bP7M1q9DqSDah5eOi\nruoTyYxxyRw4Xupyn7iKK6qZNCeNpRuP8Miwrvzhsu46nFpZql9sMItuH4yXuzBy2mpW7T1udaQW\np+Xjws7vEs78WwdQWF7NNW/+xJp9J6yO1OIy88u44e2fWbXnOH+9vhd3XtDJ6khKAdCpTQAf3jmY\ndoE+jJ+1jg+dfDkGLR8X1z82mH/dOYRgfy9Gz1zj1OuPbDpcwDVvruJIYTlzJqZwU3Ks1ZGU+oV2\ngb4sun0QSXHBPLhoE3/5Yge1dc65IqqWjyIuzJ8ldwwhJT6EhxZt4sUvMpzuBf9heiY3TfsZH083\nPrpjMEM6hVkdSalfFeTnxZyJKdwyIJap3+3jtrlplFTWWB2r2Wn5KAAC/TxJnVD/gn/nu72MnrHG\nKQYiVFTX8viSLTy4aBN9Y4JYcucQOke0sjqWUr/J092N56/txbPDe7BiZy7D3/iRjOwiq2M1Ky0f\n9f/+/YJ/ZUQfNhzO5/LXf2TVHsc98Xk4r4wbp/7MgjWHuP38jsybNIDwVrr0tXIcYwbFMXdSCkUV\nNQx/4ycWrDmEMc5xVEKs+EWSkpJMWlqazZ9XNd7O7GLunJ/O/uOl3HFBR+4Z2hlvD3erYzWKMYZF\naZk8++l2EPjbjX25OCHC6lhKnbHc4koeWLiRH3Yf54re7Xjh2l4E+npaHet/iEi6MSapUffV8lGn\nUlpZw1Mfb2NxeiZdIgJ4ZUQfekfb9xLSOUUVPPbRFr7NyGFAfAivjOhDTIif1bGUOmt1dYZ3vt/L\nq1/uItTfi2eG92RYz7ZWx/oFLR/VrL7NOMbjH20lp7iCKed15J6hnfDz8rA61i/U1hk+WHeYvy7L\noKK6lkeHdWP84DidlVo5nS2ZhTzy4WZ2HC3isp5teXp4D9q08rE6FqDlo1pAYXk1L3y2gw/SDhPR\n2puHLunK9f2j7eLNfc2+Ezz9yXa2Hy0iJS6Ev1zfi47hAVbHUqrFVNfWMe37fbz+zW683d24/YKO\nTBwSj6+XtYfGtXxUi0k7kMezn+1g0+ECEtq15rHLunFu5zBLZgjYdqSQN77dwxdbs4kK8uUPl3fj\nil7tdLYC5TL25pbwl8938PWOHNq29uH+iztzff9oy+Yo1PJRLaquzvDJ5iO8tGwnWQXlJLRrza3n\nxXNl70g8W/hFb4xh7f483v5uLyt35hLg7cGt53ZgynkdLP/Up5RV1uw7wYvLMthwqICYEF/GDYrj\nxuQYWvvYdlCCzcpHREYAfwa6AynGmEY1ipaPc6isqWXphiNM+2Efe3JKaBfoww2J0VzVJ5IuzXwt\nTU5RBUs3HmHJhiy2Hy0i1N+LiefEM3pge7sc9aOUrRlj+HL7MWb8sI91B/Lx93Ln+sRohveNol9M\nkE0OkduyfLoDdcBU4CEtH9dUV2f4blcus37az097jlNnoEtEAJf1bMeADiH0iQ7C37tpAxRqauvY\neqSINftO8MPu46zaW/+4faIDuSExmhsSY3RPR6lT2JpVyKyf9vPppqNU1dbRtrUPl/aI4HfdI+gT\nHUiQn1eLPK/ND7uJyEq0fBT11yMs23qUTzYdZd3BPIwBN4Hu7VrTtW0r2gX60DbQl4hW3ri7CXWm\nfqRaaWUNmfnlHM4v43BeGVuzCimtql/srmO4P1f0asfwflE6kECpJigsr2ZFRg7LtmazclcOFdX1\nKxjHhvjROzqQ2BA/wgK8CQ3wIjzAm76xQWc1klXLR9mFwrJqNhzOZ/3BfNIP5bMvt5Sc4srfnDcu\norU3McF+dG/XmgEdQkiJD7GbYaRKObKyqho2HCpgc2YhmzML2JJVyNHCil/8PX79wPl0anPmH/Ca\nUj6nrTgR+Rr4tSuZ/miMWdqEUFOAKQCxsTqbsCsI9PPkgq5tuKBrm/+/rbbOcLykkpyiSuqMwU0E\nNzfw9XQnMsgXH089lKZUS/Dz8mBIp7BfTKpbV2coLK/meEkluSWVRAf72iyP7vkopZRqFk3Z89GJ\nRZVSStncWZWPiFwrIpnAIOAzEVnePLGUUko5M0suMhWRXODgWT5MGOC48/3bhm6j36bb5/R0G52e\nbqP/aG+MCW/MHS0pn+YgImmNPbboqnQb/TbdPqen2+j0dBudGT3no5RSyua0fJRSStmcI5fPNKsD\nOADdRr9Nt8/p6TY6Pd1GZ8Bhz/kopZRyXI6856OUUspBafkopZSyOYcrHxEZJiI7RWSPiDxmdR57\nIyIxIrJCRLaLyDYRudfqTPZKRNxFZIOIfGp1FnsjIkEislhEMkRkh4gMsjqTvRGR+xv+xraKyHsi\nojPgNoFDlY+IuANvApcBCcDNIpJgbSq7UwM8aIxJAAYCd+k2OqV7gR1Wh7BTrwPLjDHdgD7odvoF\nEYkC7gGSjDE9AXdgpLWpHItDlQ+QAuwxxuwzxlQB7wPDLc5kV4wxR40x6xu+Lqb+TSPK2lT2R0Si\ngSuAGVZnsTciEgicB8wEMMZUGWMKrE1llzwAXxHxAPyAIxbncSiOVj5RwOGTvs9E31hPSUTigH7A\nGmuT2KXXgEeoX4lX/VI8kAvMbjgsOUNE/K0OZU+MMVnAK8Ah4ChQaIz50tpUjsXRykc1kogEAB8C\n9xljiqzOY09E5EogxxiTbnUWO+UB9AfeNsb0A0oBPb96EhEJpv6oSzwQCfiLyGhrUzkWRyufLCDm\npO+jG25TJxERT+qLZ74x5iOr89ihIcDVInKA+kO3vxORedZGsiuZQKYx5t97zIupLyP1HxcB+40x\nucaYauAjYLDFmRyKo5XPOqCziMSLiBf1J/g+tjiTXRERof5Y/Q5jzN+szmOPjDF/MMZEG2PiqH8N\nfWuM0U+tDYwx2cBhEenacNNQYLuFkezRIWCgiPg1/M0NRQdlNMlpl9G2J8aYGhG5G1hO/eiSWcaY\nbRbHsjdDgDHAFhHZ2HDb48aYzy3MpBzP74H5DR/y9gETLM5jV4wxa0RkMbCe+hGmG9BpdppEp9dR\nSillc4522E0ppZQT0PJRSillc1o+SimlbE7LRymllM1p+SillLI5LR+llFI2p+WjlFLK5v4PoWxo\nsbuMIo0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111b02f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the x and y coordinates for points on sine and cosine curves\n",
    "x = np.arange(0, 3 * np.pi, 0.1)\n",
    "y_sin = np.sin(x)\n",
    "y_cos = np.cos(x)\n",
    "\n",
    "# Set up a subplot grid that has height 2 and width 1,\n",
    "# and set the first such subplot as active.\n",
    "plt.subplot(2, 1, 1)\n",
    "\n",
    "# Make the first plot\n",
    "plt.plot(x, y_sin)\n",
    "plt.title('Sine')\n",
    "plt.tight_layout()\n",
    "\n",
    "# Set the second subplot as active, and make the second plot.\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(x, y_cos)\n",
    "plt.title('Cosine')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}