import numpy as np

class NeuralNetwork:
    def __init__(self, x, y):
        self.input = x
        self.weights1 = np.random.rand(self.input.shape[1], 4)
        self.weights2 = np.random.rand(4, 1)
        self.y = y
        self.output = np.zeros(self.y.shape)

    def feedforward(self):
        self.layer1 = sigmoid(np.dot(self.input, self.weights1))
        self.output = sigmoid(np.dot(self.layer1, self.weights2))

    def backprop(self):
        d_weights2 = np.dot(self.layer1.T, (2*(self.y - self.output) * sigmoid_derivative(self.output)))
        d_weights1 = np.dot(self.input.T, (np.dot(2*(self.y - self.output) *
                                                 sigmoid_derivative(self.output), self.weights2.T) *
                                          sigmoid_derivative(self.layer1)))

        self.weights1 += learning_rate*d_weights1
        self.weights2 += learning_rate*d_weights2

    def train(self):
        self.output = self.feedforward()
        self.backprop()

def sigmoid(t): return 1/(1+np.exp(-t))
def sigmoid_derivative(p): return p*(1-p)

def loss(y, y_out):
    return np.mean(np.square(y - y_out))