ex2.py

#!/usr/local/Cellar/python/2.7.6/bin/python
# -*- coding: utf-8 -*-

import sys
import scipy.optimize, scipy.special
from numpy import *
from matplotlib import pyplot, cm
from mpl_toolkits.mplot3d import Axes3D

def plot( data ):
	positives  = data[data[:,2] == 1]
	negatives  = data[data[:,2] == 0]
	
	pyplot.xlabel("Exam 1 score")
	pyplot.ylabel("Exam 2 score")
	pyplot.xlim([25, 115])
	pyplot.ylim([25, 115])

	pyplot.scatter( negatives[:, 0], negatives[:, 1], c='y', marker='o', s=40, linewidths=1, label="Not admitted" )
	pyplot.scatter( positives[:, 0], positives[:, 1], c='b', marker='+', s=40, linewidths=2, label="Admitted" )
	pyplot.legend()
	
def plotBoundary( data, X, theta ):
	plot( data )
	plot_x = array( [min(X[:,1]), max(X[:,1])] )
	plot_y = (-1./ theta[2]) * (theta[1] * plot_x + theta[0])
	pyplot.plot( plot_x, plot_y )
	
def sigmoid( z ):
	return scipy.special.expit(z)
	# return 1.0 / (1.0 + exp( -z ))

def computeCost( theta, X, y ):
	m = shape( X )[0]
	hypo = sigmoid(X.dot( theta ))
	term1 = log( hypo ).T.dot( -y )
	term2 = log( 1.0 - hypo ).T.dot( 1-y )
	return ((term1 - term2) / m).flatten()

def gradientCost( theta, X, y ):
	m = shape(X)[0]
	return ( X.T.dot(sigmoid( X.dot( theta ) ) - y)  ) / m

def costFunction( theta, X, y ):
	cost 	 = computeCost( theta, X, y )
	gradient = gradientCost( theta, X, y )
	# m 	  	 = shape( X )[0]
	# hypo  	 = sigmoid( X.dot( theta ) )
	# term1 	 = log( hypo ).transpose().dot( -y )
	# term2 	 = log( 1.0 - hypo ).transpose().dot( 1 - y )
	# cost  	 = ((term1 - term2) / m)
	# gradient = (X.transpose().dot( hypo - y) ) / m
	return cost

def findMinTheta( theta, X, y ):
	result = scipy.optimize.fmin( costFunction, x0=theta, args=(X, y), maxiter=500, full_output=True )
	return result[0], result[1]

def predict( theta, X, binary=True ):
	prob = sigmoid( theta.dot( X ))
	if binary :
		return 1 if prob > 0.5 else 0
	else:
		return prob


def part1_1():
	data = genfromtxt( "/Users/saburookita/Downloads/mlclass-ex2-004/mlclass-ex2/ex2data1.txt", delimiter = ',' )
	m, n = shape( data )[0], shape(data)[1] - 1
	X 	 = c_[ ones((m, 1)), data[:, :n] ]
	y 	 = data[:, n:n+1]
	
	plot( data )
	pyplot.show()
	
def part1_2():
	data  = genfromtxt( "/Users/saburookita/Downloads/mlclass-ex2-004/mlclass-ex2/ex2data1.txt", delimiter = ',' )
	m, n  = shape( data )[0], shape(data)[1] - 1
	X 	  = c_[ ones((m, 1)), data[:, :n] ]
	y 	  = data[:, n:n+1]
	theta = zeros( (n+1, 1) ) 

	print computeCost(theta, X, y)
	theta, cost = findMinTheta( theta, X, y )	
	plotBoundary( data, X, theta )
	pyplot.show()

	test = array([1, 45, 85])
	print predict( test, theta )

def main():
	set_printoptions(precision=6, linewidth=200)
	part1_1()
	part1_2()
	

if __name__ == '__main__':
	main()