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def sigmoid(X):
    '''Compute the sigmoid function '''
    #d = zeros(shape=(X.shape))

    den = 1.0 + e ** (-1.0 * X)

    d = 1.0 / den

    return d

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def map_feature(x1, x2):
    '''
    Maps the two input features to quadratic features.

    Returns a new feature array with more features, comprising of
    X1, X2, X1 ** 2, X2 ** 2, X1*X2, X1*X2 ** 2, etc...

    Inputs X1, X2 must be the same size
    '''
    x1.shape = (x1.size, 1)

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from numpy import loadtxt, where, zeros, e, array, log, ones, append, linspace
from pylab import scatter, show, legend, xlabel, ylabel, contour, title
from scipy.optimize import fmin_bfgs


def sigmoid(X):
    '''Compute the sigmoid function '''
    #d = zeros(shape=(X.shape))

    den = 1.0 + e ** (-1.0 * X)

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#Plot Boundary
u = linspace(-1, 1.5, 50)
v = linspace(-1, 1.5, 50)
z = zeros(shape=(len(u), len(v)))
for i in range(len(u)):
    for j in range(len(v)):
        z[i, j] = (map_feature(array(u[i]), array(v[j])).dot(array(theta)))

z = z.T
contour(u, v, z)

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def predict(theta, X):
    '''Predict whether the label
    is 0 or 1 using learned logistic
    regression parameters '''
    m, n = X.shape
    p = zeros(shape=(m, 1))

    h = sigmoid(X.dot(theta.T))

    for it in range(0, h.shape[0]):

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from numpy import loadtxt, zeros, ones, array, linspace, logspace, mean, std, arange
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from pylab import plot, show, xlabel, ylabel

#Evaluate the linear regression

def feature_normalize(X):
    '''
    Returns a normalized version of X where

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def feature_normalize(X):
    '''
    Returns a normalized version of X where
    the mean value of each feature is 0 and the standard deviation
    is 1. This is often a good preprocessing step to do when
    working with learning algorithms.
    '''
    mean_r = []
    std_r = []

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from numpy import loadtxt, zeros, ones, array, linspace, logspace
from pylab import scatter, show, title, xlabel, ylabel, plot, contour


#Evaluate the linear regression
def compute_cost(X, y, theta):
    '''
    Comput cost for linear regression
    '''
    #Number of training samples

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from numpy import loadtxt, zeros, ones, array, linspace, logspace
from pylab import scatter, show, title, xlabel, ylabel, plot, contour



#Load the dataset
data = loadtxt('ex1data1.txt', delimiter=',')

#Plot the data