gd2.py

gd2.py

def func(xlist):
    return 2*(xlist[0]-2.3)**2+3*(xlist[0]-4.1)*(xlist[1]-6.5)+5*(xlist[1]-8.0)**2

# functions
def partial_derivative(f, x_list, odr, epsilon = 1e-6, **kargs):
    h_list = x_list.copy()
    
    h_list[odr] = x_list[odr] + epsilon
    fx = f(x_list, **kargs)
    fh = f(h_list, **kargs)
    
    return (fh - fx) / epsilon 

def gradient(f, x_list, **kargs):
    grd = [partial_derivative(f, x_list, odr, **kargs) for odr in range(len(x_list))]
    return grd

def g_d(W, f, epochs, lr):
    loss_container = np.zeros((epochs+1, 1))
    W_container = np.zeros((epochs+1, W.shape[0]))
    loss_container[0] = f(W)
    W_container[0] = W
    
    for i in range(epochs):
        '''calculate the gradient'''
        grd = np.array(gradient(f, x_list=W))
        '''updated the weight'''
        W = W - lr*grd
        
#         pass value to container
        loss_container[i+1] = f(W)
        W_container[i+1] = W.reshape(-1)
            
    return loss_container, W_container

def show(W, e, l):
    loss_container, W_container = g_d(W, f=func, epochs=e, lr=l)

    fig = plt.figure(figsize=(12,3))
    cx0 = fig.add_subplot(121)
    cx2 = plt.subplot(122)

    cx0.plot(loss_container, label='Loss', color='C3')
    cx0.set_xlabel('epochs', fontsize=12)
    cx0.set_ylabel('loss', fontsize=12)
    cx0.legend()

    cx2.plot(W_container[:,0], label='W0')
    cx2.plot(W_container[:,1], label='W1')
    cx2.set_xlabel('epochs', fontsize=12)
    cx2.set_ylabel('w', fontsize=12)
    cx2.legend()

    plt.show()

    print(f'ini_loss = {loss_container[0]}, ini_w = {W_container[0]}')
    print(f'finl_loss = {loss_container[-1]}, finl_w = {W_container[-1]}')
    
    return loss_container, W_container