{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Numpy provides us with multi-dimensional array objects which is useful for scientific computing. In numpy, rank refers to the number of dimensions of the array. The shape is a tuple of integers providing the size of the array in each dimension.\n",
    "\n",
    "[1,2,3] is a numpy object of rank 1 and shape 3\n",
    "\n",
    "[[1,2],\n",
    " [4,5],\n",
    " [7,8]] is a numpy object of rank 3 and shape 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a numpy object\n",
    "\n",
    "The following provides different ways of creating numpy objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3]\n",
      "(3,)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "a = np.array([1,2,3])\n",
    "print(a)\n",
    "print(a.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3  4]\n",
      " [ 5  6  7  8]\n",
      " [ 9 10 11 12]]\n",
      "(3, 4)\n"
     ]
    }
   ],
   "source": [
    "b = np.array([[1,2,3,4],[5,6,7,8],[9,10,11,12]])\n",
    "print(b)\n",
    "print(b.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a[1]= 2\n",
      "b[2,3]= 12\n"
     ]
    }
   ],
   "source": [
    "print(\"a[1]=\", a[1])\n",
    "print(\"b[2,3]=\", b[2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n"
     ]
    }
   ],
   "source": [
    "c = np.zeros((2,3))\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  1.  1.]\n",
      " [ 1.  1.  1.]]\n"
     ]
    }
   ],
   "source": [
    "d = np.ones((2,3))\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.]\n",
      " [ 0.  1.  0.]\n",
      " [ 0.  0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "e = np.eye(3)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n"
     ]
    }
   ],
   "source": [
    "f = np.arange(20).reshape(4,5)\n",
    "print(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accessing rows and columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 6 7 8 9]\n"
     ]
    }
   ],
   "source": [
    "print(f[1,:])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  6 11 16]\n"
     ]
    }
   ],
   "source": [
    "print(f[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5  6  7  8  9]\n",
      " [10 11 12 13 14]]\n"
     ]
    }
   ],
   "source": [
    "print(f[1:3,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mathematical Operations "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that in numpy, the traditional mathematical operations happen element wise and are not matrix operations like in matlab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "g = np.array([[1,2,3],[4,5,6],[7,8,9]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "h = np.array([[21,22,23],[24,25,26],[27,28,29]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[22, 24, 26],\n",
       "       [28, 30, 32],\n",
       "       [34, 36, 38]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h+g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20, 20, 20],\n",
       "       [20, 20, 20],\n",
       "       [20, 20, 20]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h-g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 21,  44,  69],\n",
       "       [ 96, 125, 156],\n",
       "       [189, 224, 261]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h*g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 21.        ,  11.        ,   7.66666667],\n",
       "       [  6.        ,   5.        ,   4.33333333],\n",
       "       [  3.85714286,   3.5       ,   3.22222222]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h/g"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note the difference between dot product and multiplication."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  2.  3.]\n",
      " [ 1.  2.  3.]\n",
      " [ 1.  2.  3.]]\n"
     ]
    }
   ],
   "source": [
    "i = np.ones((3,3))\n",
    "j = np.array([1,2,3])\n",
    "print(i*j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 6.  6.  6.]\n"
     ]
    }
   ],
   "source": [
    "print(i.dot(j))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[21 22 23]\n",
      " [24 25 26]\n",
      " [27 28 29]]\n"
     ]
    }
   ],
   "source": [
    "print(h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "225\n"
     ]
    }
   ],
   "source": [
    "print(np.sum(h))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[72 75 78]\n"
     ]
    }
   ],
   "source": [
    "print(np.sum(h, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[21 24 27]\n",
      " [22 25 28]\n",
      " [23 26 29]]\n"
     ]
    }
   ],
   "source": [
    "print(h.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For more on numpy, refer to the official numpy tutorial [here](https://docs.scipy.org/doc/numpy-dev/user/quickstart.html#the-ix-function)"
   ]
  }
 ],
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