#This function takes a value from X and two thetas that determine what side
#of the sigmoid curve x falls on, this returns either 1 or 0
def sigmoid( x, theta0, theta1):

    output = 1/ (1 + np.exp( -( theta0 + theta1 * x)))

    return output

def round( num):

    if num > .5:
        return 1
    else:
        return 0

# this is the sum of the sigmoid function for all of X
def sumofSigmoid( X, Y ,theta0, theta1):

    sum = 0

    for i in range( 0, len(X)):

            sum += ((sigmoid( X[i], theta0, theta1) - Y[i]) * X[i])

    return np.squeeze(sum)

#minimises theta0 and theta1 using one step of gradient descent method, sounds like decending grades :/
def gradient( X, Y, theta0, theta1, learning_rate):

    temp0 = theta0 - (learning_rate * sumofSigmoid( X, Y, theta0, theta1))
    temp1 = theta0 - (learning_rate * sumofSigmoid( X, Y, theta0, theta1))

    return temp0, temp1

#this function updates the gradient for n amount of iterations
def gradeDescent( X, Y, iterations, learning_rate):

    tempa = -4
    tempb = 1

    #normalize X
    X = (X - np.mean(X, axis=0)) / np.std(X, axis=0)

    for i in range( 1, iterations):

        tempa, tempb = gradient( X, Y, tempa, tempb, learning_rate)
        print cost(X, Y, tempa, tempb)

    return tempa, tempb

#returns the total cost of X and Y based on theta
def cost( X, Y, theta0, theta1):

    step1 = 0
    step2 = 0

    #for each X and Y in the dataset find cost for 1 and 0
    for i in range( 0, len(X)):

        temp = sigmoid( X[i], theta0, theta1)
        step1 += Y[i] * np.log(temp)
        step2 += (1-Y[i]) * np.log(1 - temp)

    #completes the algorithm for finging the cost and returns
    total = -step1 - step2
    return np.mean(total)