def ComputeGradients(X, Y, P, W, _lambda):
    grad_W = np.zeros([K,d]);
    grad_b = np.zeros([K,1]);
    n = X.shape[1];

    for i in range(n):
        g = np.reshape(-Y[:, i] + P[:, i], (10, 1));
        grad_W += g.dot(np.reshape(X[:, i], (1, d)));
        grad_b += g;

    grad_W /= n;
    grad_b /= n;
    grad_W += 2 * _lambda * W;

    return grad_W, grad_b;


def ComputeCost(X, Y, W, b, _lambda):
    n = X.shape[1];
    crossLoss = 0;
    regLoss = 0;

    regLoss = _lambda * np.sum(W * W);

    for i in range(n):
        crossLoss -= np.log(Y.T[i].dot(forwardRun(X[:, i], W, np.reshape(b, (K,)).T)));
    crossLoss /= float(n);

    return (crossLoss + regLoss);