Vectorization demo_Ng.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4]\n"
     ]
    }
   ],
   "source": [
    "a = np.array ([1,2,3,4])\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vectorized Version:26.958227157592773ms\n"
     ]
    }
   ],
   "source": [
    "a = np.random.rand(1000000)\n",
    "b = np.random.rand(1000000)\n",
    "\n",
    "tic = time.time()\n",
    "c = np.dot(a,b)\n",
    "toc = time.time()\n",
    "\n",
    "print(\"Vectorized Version:\" + str(1000*(toc-tic)) + \"ms\")\n",
    "\n",
    "#much quicker"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "249903.23380749376\n",
      "For loop:874.1638660430908ms\n"
     ]
    }
   ],
   "source": [
    "c = 0\n",
    "tic = time.time()\n",
    "for i in range (1000000):\n",
    "    c += a[i]*b[i]\n",
    "toc = time.time()\n",
    "\n",
    "print(c)\n",
    "print(\"For loop:\" + str(1000*(toc-tic)) + \"ms\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whenever possible avoid explicit for-loops.\n",
    "Vectorizatin of u = Av\n",
    "\n",
    "u = np.dot(A, v)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Broadcasting operation demo in python. calculating percentages for each column of the matrix\n",
    "If you have an (m,n) matrix and you add or subtract or multiply or divide with a (1,n) matrix, then this will copy it n times into an (m,n) matrix. And then apply the addition, subtraction, and multiplication of division element wise.\n",
    "\n",
    "If conversely, you were to take the (m,n) matrix and add, subtract, multiply, divide by an (m,1) matrix, then also this would copy it now n times. And turn that into an (m,n) matrix and then apply the operation element wise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 56.    0.    4.4  68. ]\n",
      " [  1.2 104.   52.    8. ]\n",
      " [  1.8 135.   99.    0.9]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[56.0, 0.0, 4.4, 68.0],\n",
    "            [1.2, 104.0, 52.0, 8.0],\n",
    "            [1.8, 135.0, 99.0, 0.9]])\n",
    "\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 59.  239.  155.4  76.9]\n"
     ]
    }
   ],
   "source": [
    "sum_col = A.sum(axis=0) #sum vertically, axis=1, is horizontally\n",
    "print(sum_col)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[94.91525424  0.          2.83140283 88.42652796]\n",
      " [ 2.03389831 43.51464435 33.46203346 10.40312094]\n",
      " [ 3.05084746 56.48535565 63.70656371  1.17035111]]\n"
     ]
    }
   ],
   "source": [
    "percentage = 100 * A/sum_col.reshape(1,4)\n",
    "print(percentage)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[94.91525424  0.          2.83140283 88.42652796]\n",
      " [ 2.03389831 43.51464435 33.46203346 10.40312094]\n",
      " [ 3.05084746 56.48535565 63.70656371  1.17035111]]\n"
     ]
    }
   ],
   "source": [
    "#same as above\n",
    "perc = 100 * A/sum_col\n",
    "print(perc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "ename": "AssertionError",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-15-9b51e726c951>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mperc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mAssertionError\u001b[0m: "
     ]
    }
   ],
   "source": [
    "##did not work. assert(perc.shape == (3,3))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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