import numpy as np
import matplotlib.pyplot as plt

def scaling(X):
    """mean normalzation"""
    l = []
    for k in range(X.shape[1]):
        x = X[:,k]
        def f(e):
            tmp0 = sum(x) / len(x)
            tmp1 = max(x) - min(x)
            return (e - tmp0) / tmp1
        m =  list(map(float, (list(map(f, x[:, 0])))))
        l.append(m)
    return np.matrix(l).transpose()


l_cost_function = [] # lists to record data for debugging
l_iterations = [] 

def m_g_d(A, y, alfa):
    """computes gradient descent"""
    l = len(A)
    X = np.c_[np.ones(l), T1]
    tmp = np.matrix([0] * X.shape[1], dtype=np.float64)
    theta = np.matrix([0] * X.shape[1], dtype=np.float64)
    cnt = 0
    m = len(X)
    ma = alfa * (1 / m)
    delta = J_m(X, y, theta)
    print(delta)
    while delta > 0.00001:
        beg = J_m(X, y, theta)
        for j in range(X.shape[1]):
            tmp[:,j] = theta[:,j] - ma * ((((X * theta.transpose()) - y.transpose()).transpose()) * X[:,j])
        theta = tmp
        end = J_m(X, y, theta)
        l_cost_function.append(end)
        l_iterations.append(cnt)
        delta = abs(end - beg)
        cnt += 1
    return (theta, cnt, end)



def J_m(A, y, theta):
    """computes cost function """
    n = len(A)
    return (1 / (2 * n)) * float(sum([x * x for x in A * theta.transpose() - y.transpose()]))