{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Vectorized Code\n", "\n", "Always prefer builtin functions and operators to for loops. They are **much more efficient**." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.7979159 0.96836573 0.20664445 0.62135717 0.87544718 0.60766259\n", " 0.27853697 0.08548639 0.86701681 0.77239239 0.29827174 0.65149195\n", " 0.1794432 0.27125414 0.50458605 0.0865881 0.93080258 0.07003178\n", " 0.13422815 0.39212578]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "theta0 = 1\n", "theta1 = 2\n", "\n", "n = 20\n", "\n", "x = np.random.rand(n)\n", "y = theta0 + theta1*x + 0.1*np.random.randn(n)\n", "\n", "plt.scatter(x,y)\n", "\n", "print(x)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.13544506967538034\n", "0.1354450696753803\n" ] } ], "source": [ "# Compute the cost\n", "pred = theta0 + theta1*x\n", "\n", "residual = y - pred\n", "cost = np.sum(residual**2)\n", "\n", "cost2 = np.dot(residual, residual)\n", "\n", "print (cost)\n", "print (cost2)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.22467306247087163\n" ] } ], "source": [ "print(np.sum( (theta0 + theta1*x - y)**2 )) # one liner" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Takeaway: do not use for loops if possible\n", "\n", "* There are many functions / operators available for elementwise and summary operations on arrays. Find them and use them!\n", "\n", "* Sometimes you can use linear algebra to compute what you want!" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2 3]\n", " [4 5 6]\n", " [7 8 9]]\n", "45\n" ] } ], "source": [ "# Example\n", "A = np.array([[1, 2, 3], [4, 5, 6], [7,8, 9]])\n", "\n", "print(A)\n", "print(np.sum(A))" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2 3]\n", " [4 5 6]\n", " [7 8 9]]\n", "[12 15 18]\n" ] } ], "source": [ "print(A)\n", "print(np.sum(A, axis=0))" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2 3]\n", " [4 5 6]\n", " [7 8 9]]\n", "[ 6 15 24]\n" ] } ], "source": [ "print(A)\n", "print(np.sum(A, axis=1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Array slicing" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[1 2 3]\n", " [4 5 6]\n", " [7 8 9]]\n" ] } ], "source": [ "A = np.array([[1, 2, 3], [4, 5, 6], [7,8, 9]])\n", "print(A)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 2 3]\n" ] } ], "source": [ "# Get first row of A\n", "print(A[0, :])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2 5 8]\n" ] } ], "source": [ "# Get second column of A\n", "print(A[:, 1])" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1 2 3]\n", " [ 4 5 6]\n", " [10 11 12]]\n" ] } ], "source": [ "# Assign to third row of A\n", "A[2,:] = [10, 11, 12]\n", "print(A)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 5 6]\n", " [11 12]]\n" ] } ], "source": [ "# Get lower right block of A\n", "print(A[1:3, 1:3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Logical indexing" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[False False False True True True True True False False False]\n" ] } ], "source": [ "x = np.array([1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1])\n", "\n", "i = x >= 4 # elementwise comparison\n", "\n", "print(i)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 2 3 4 5 6 5 4 3 2 1]\n", "[False False False True True True True True False False False]\n", "[4 5 6 5 4]\n" ] } ], "source": [ "print(x)\n", "print(i)\n", "print(x[i]) # select entries of x for which i is true" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[4 5 6 5 4]\n" ] } ], "source": [ "print(x[x>=4]) # one-liner" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[3 4 5]\n" ] } ], "source": [ "a = np.array([1, 2, 3, 4, 5])\n", "b = np.array([5, 4, 3, 2, 1])\n", "print(a[ a >= b ]) # What does this print?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" } }, "nbformat": 4, "nbformat_minor": 1 }