import numpy as np
import random

# m denotes the number of examples
# x = x values
# y = y values
# theta = our solution
# alpha = step size
# numIterations = how many times we're going to loop
def gradientDescent(x, y, theta, alpha, m, numIterations):
    return theta


def genData(numPoints, bias, variance):
    x = np.zeros(shape=(numPoints, 2))
    y = np.zeros(shape=numPoints)
    # basically a straight line
    for i in range(0, numPoints):
        # bias feature
        x[i][0] = 1
        x[i][1] = i
        # our target variable
        y[i] = (i + bias) + random.uniform(0, 1) * variance
    return x, y

# gen 100 points with a bias of 25 and 10 variance as a bit of noise
x, y = genData(100, 25, 10)

#fix  for higher dimensions.
#here, m = 100, n = 2
m, n = np.shape(x) 

numIterations= 100000
alpha = 0.0005
theta = np.ones(n) #answer: #[offset, slope]
theta = gradientDescent(x, y, theta, alpha, m, numIterations)


print "Our solution line has a y-intercept of ", theta[0], "and a slope of", theta[1]
print "The data we're trying to fit is as follows"
for i in range (0, 100):
  print x[i][1], y[i]