ex1 ipython notebook with mandatory problems completed, will do optio…

…nal problems and tidy up the code next

ex1/ex1.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Programming Exercise 1: Linear Regression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### 2 Linear regression with one variable"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "datafile = 'data/ex1data1.txt'\n",
+    "x,y = np.loadtxt(datafile,delimiter=',',usecols=(0,1),unpack=True) #Read in comma separated data\n",
+    "m = y.size # number of training examples"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### 2.1 Plotting the Data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "#Plot the data to see what it looks like\n",
+    "plt.figure(figsize=(10,6))\n",
+    "plt.plot(x,y,'rx',markersize=10)\n",
+    "plt.grid(True) #Always plot.grid true!\n",
+    "plt.ylabel('Profit in $10,000s')\n",
+    "plt.xlabel('Population of City in 10,000s')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### 2.2 Gradient Descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "X = np.insert([x],0,np.ones(m),axis=0) #Add a column of ones to x (x0=1)\n",
+    "iterations = 1500\n",
+    "alpha = 0.01"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def h(theta,xvec): #Linear hypothesis function\n",
+    "    return np.sum(theta*xvec)\n",
+    "\n",
+    "#Todo: Rewrite this without the sum over i and multiply matrices like a boss\n",
+    "def computeCost(theta,X): #Cost function\n",
+    "    j = 0\n",
+    "    for i in xrange(m):\n",
+    "        j += (h(theta, X[:,i])-y[i])**2\n",
+    "    return (1./(2*m)) * j\n",
+    "\n",
+    "#Test that running computeCost with 0's as theta returns 32.07:\n",
+    "print computeCost(np.zeros(2),X)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "#Actual gradient descent minimizing routine\n",
+    "jvec = [] #Used to plot cost as function of iteration\n",
+    "theta = np.zeros(2)\n",
+    "for meaninglessvariable in xrange(iterations):\n",
+    "    tmptheta = theta\n",
+    "    for i in xrange(len(tmptheta)):\n",
+    "        tmptheta[i] = theta[i] - (alpha/m)*sum([ (h(theta,X[:,k]) - y[k])*X[i][k] for k in xrange(m)])\n",
+    "    theta = tmptheta\n",
+    "    jvec.append(computeCost(theta,X))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "plt.plot(range(len(jvec)),jvec,'bo')\n",
+    "plt.grid(True)\n",
+    "plt.title(\"Convergence of Cost Function\")\n",
+    "plt.xlabel(\"Iteration number\")\n",
+    "plt.ylabel(\"Cost function\")\n",
+    "dummy = plt.xlim([-50,1600])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "#Plot the line on top of the data to ensure it looks correct\n",
+    "def myfit(xval):\n",
+    "    return theta[0] + theta[1]*xval\n",
+    "plt.figure(figsize=(10,6))\n",
+    "plt.plot(x,y,'rx',markersize=10,label='Training Data')\n",
+    "plt.plot(x,myfit(x),'b-',label = 'Hypothesis: h(x) = %0.2f + %0.2fx'%(theta[0],theta[1]))\n",
+    "plt.grid(True) #Always plot.grid true!\n",
+    "plt.ylabel('Profit in $10,000s')\n",
+    "plt.xlabel('Population of City in 10,000s')\n",
+    "plt.legend()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### 2.4 Visualizing _J($\\theta$)_"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}