import numpy as np
import matplotlib.pyplot as plt

list_to_vec = lambda x: np.reshape(x, (len(x), 1))

def h(x, theta):
    return x @ theta

def error(x, y, theta):
    return h(x, theta) - list_to_vec(y)

def cost(x, y, theta):
    diff = error(x, y, theta)
    return np.sum(diff.T @ diff) / 2

class LearningAlgorithms:
    alpha       = 0.01
    threshold   = 1e-4

    @staticmethod
    def analytic_solution(x, y):
        return list_to_vec(np.linalg.inv(x.T @ x) @ x.T @ y)

    @staticmethod
    def batch_gradient_descent(x, y, theta):
        while True:
            for j in range(theta.shape[0]):
                summand     = -error(x, y, theta).T @ list_to_vec(x[:, j])
                diff        = LearningAlgorithms.alpha * np.sum(summand)
                theta[j]    += diff
            if diff < LearningAlgorithms.threshold:
                return theta

    @staticmethod
    def stochastic_gradient_descent(x, y, theta):
        while True:
            for i in range(x.shape[0]):
                for j in range(theta.shape[0]):
                    diff = LearningAlgorithms.alpha * (y[i] - h(x[i], theta))*x[i][j]
                    theta[j] += LearningAlgorithms.alpha * diff
            if diff < LearningAlgorithms.threshold:
                return theta


# load the data from a text file
# imagine data as a m x n matrix (m examples, n columns)
data    = np.loadtxt('data.txt')

# in every row, the input variables are the first n - 1 columns
x       = data[:,:-1]

# we're going to need an intercept/bias term for a complete linear parameterization, independent of x
# we call that x0 identically equal to unity
x0      = np.ones((x.shape[0],1))
x       = np.hstack((x0, x))

# in every row, the output variable is the last column
y       = data[:,-1]

# theta are the weights/parameters
theta   = np.ones((x.shape[1], 1))
print("Initial Cost: {}".format(cost(x, y, theta)))
theta = LearningAlgorithms.stochastic_gradient_descent(x, y, theta)
print("Cost after learning: {}".format(cost(x, y, theta)))


plt.scatter(x[:,1:], y)
plt.plot(x[:,1:], h(x, theta))
plt.show()