from numpy import *


def sigmoid(t):
    return 1/(1+exp(-t))

def forward(x, W1, b1, W2, b2):
    h = sigmoid(b1+dot(W1.T, x))    
    print("h=", h)
    out = sigmoid(b2+dot(W2.T, h))
    print("out=", out)
    return out

    
def cost(out, y):
    return (out-y)**2


x = array([1, -2])
W1 = array([[1,  -3],
            [-2, -2]])
b1 = array([-7, .5])        

W2 = array([[-2], [5]])
b2 = array([[-4]])

dx = array([0, 0.001])

dW2 = array([[0], [0.001]])
dW2 = array([[0.001], [0]])

dW1 = array([[0, 0],
             [0, 0.001]])


#Estimate the derivative w.r.t x2
print(  (cost(forward (x+dx, W1, b1, W2, b2),1)-
         cost(forward (x, W1, b1, W2,     b2),1))/0.001)