import numpy as np
import matplotlib.pyplot as plt
from numpy import linalg as la
from scipy.sparse import spdiags
import scipy.io as sio


# EX1 Part.A

def sigmoid(X,W):
    return 1 / (1 + np.exp(-1 * np.matmul(X.T, W)))

def cost(X,C,W):
    return (-1/len(X)) * (np.dot(C.T, np.log(sigmoid(X, W))) + np.dot((1-C).T, np.log(1-sigmoid(X, W))))

def gradient(X,C,W):
    ans = 1/X.shape[1] * np.dot(X ,(sigmoid(X,W) - C))
    return ans/np.linalg.norm(ans)

def hessian(X,C,W):
    D = np.diag((sigmoid(X,W) * (1-sigmoid(X,W))).reshape(-1))
    return 1/X.shape[1] * np.matmul(X, np.matmul(D,X.T))

# part 2 - tests