import random
import numpy as np
from numpy import arange
import matplotlib.pyplot as plt

random.seed(0)

def line_w_gauss_noise(inter,slope,noise,numPoints):
    x = np.zeros(shape=(numPoints, 2))
    y = np.zeros(shape=numPoints)
    for i in range(0, numPoints):
        x[i][0] = i
        x[i][1] = 1
        y[i] = (i + inter) + random.uniform(0, noise) * slope
    return x, y


def MSE(x,y,weights):
    N,D = np.shape(x)
    x_T = x.transpose()
    y_hat = np.dot(weights,x_T)
    return np.sum((y - y_hat)**2) / N


def dMSE(x,y,weights):
    N = len(x)
    inter = np.sum(np.dot(np.dot(x[:,1],weights[1]) - y,x[:,1])) * (2/N)
    slope = np.sum(np.dot(x[:,0],weights[0]) - y,) * (2/N)
    new_weight = np.array([slope,inter])
    return new_weight

def gradient_desscent(x,y,alpha,weights,iter):
    losses = list()
    costs = list()
    for n in range(iter):
        cost = MSE(x,y,weights)
        loss = np.sum(y - np.dot(x,weights))
        losses.append(loss)
        costs.append(cost)
        print(cost)
        print(loss)
        print(n)
        if np.abs(losses[n]) > np.abs(losses[n-1]):
            break

        weights = weights - (alpha * dMSE(x,y,weights))
    return weights,costs,losses

if __name__ == '__main__':
    x,y = line_w_gauss_noise(1,2,5,100)
    num_var = len(x.transpose())
    w = np.ones(num_var)

    result,cost,loss = gradient_desscent(x,y,0.001,w,80)
    print(result)
    y_hat = []
    for i in x[:,0]:
        y_hat.append(result[1]+(result[0]*i))

    plt.scatter(x[:,0],y)
    plt.plot(x[:,0],y_hat)
    plt.show()

    #plt.plot(cost)
    #plt.plot(loss)
    #plt.show()