def test_exp_op():
x1_val = 2 * np.ones(3)
x1 = Tensor(x1_val)
y = x1.exp()
assert np.array_equal(y.data, np.exp(x1_val))
y.backward()
assert np.array_equal(x1.grad, np.exp(x1_val))
def test_log_op():
x1_val = 2 * np.ones(3)
x1 = Tensor(x1_val)
y = x1.log()
assert np.array_equal(y.data, np.log(x1_val))
y.backward()
assert np.array_equal(x1.grad, 1 / x1_val)
def test_mean():
x1_val = np.array([1, 2, 3, 4])
x = Tensor(x1_val)
y = x.mean()
assert np.array_equal(y.data, np.mean(x1_val))
y.backward()
assert np.array_equal(x.grad, np.ones(x1_val.shape) / 4)
def test_reduce_sum():
x1_val = 2 * np.ones(3)
x1 = Tensor(x1_val)
y = x1.sum()
assert np.array_equal(y.data, np.sum(x1_val))
y.backward()
assert np.array_equal(x1.grad, np.ones_like(x1_val))
def test_mix_all():
x1_val = 2 * np.ones(3)
x1 = Tensor(x1_val)
y = 1 / (1 + (-x1.sum()).exp())
expected_y_val = 1 / (1 + np.exp(-np.sum(x1_val)))
expected_y_grad = expected_y_val * (1 - expected_y_val) * np.ones_like(x1_val)
assert np.array_equal(y.data, expected_y_val)
y.backward()
assert np.sum(np.abs(x1.grad - expected_y_grad)) < 1E-10
def test_mul_two_vars():
x1_val = 2 * np.ones(3)
x2_val = 3 * np.ones(3)
x1 = Tensor(x1_val)
x2 = Tensor(x2_val)
y = x1 * x2
assert np.array_equal(y.data, x1_val * x2_val)
y.backward()
assert np.array_equal(x1.grad, x2_val)
assert np.array_equal(x2.grad, x1_val)
def test_div_two_vars():
x1_val = 2 * np.ones(3)
x2_val = 5 * np.ones(3)
x1 = Tensor(x1_val)
x2 = Tensor(x2_val)
y = x1 / x2
assert np.array_equal(y.data, x1_val / x2_val)
y.backward()
assert np.array_equal(x1.grad, np.ones_like(x1_val) / x2_val)
assert np.array_equal(x2.grad, -x1_val / (x2_val * x2_val))
def test_neg():
x2_val = 2 * np.ones(3)
x1_val = 3 * np.ones(3)
x1 = Tensor(x1_val)
x2 = Tensor(x2_val)
y = -x2 + x1
assert np.array_equal(y.data, -x2_val + x1_val)
y.backward()
assert np.array_equal(x2.grad, -np.ones_like(x2_val))
assert np.array_equal(x1.grad, np.ones_like(x1_val))
def test_add_two_vars():
x1_val = 2 * np.ones(3)
x2_val = 3 * np.ones(3)
x1 = Tensor(x1_val)
x2 = Tensor(x2_val)
y = x1 + x2
assert np.array_equal(y.data, x1_val + x2_val)
y.backward()
assert np.array_equal(x1.grad, np.ones_like(x1_val))
assert np.array_equal(x2.grad, np.ones_like(x2_val))
def test_exp_mix_op():
x1_val = 2 * np.ones(3)
x2_val = 4 * np.ones(3)
x1 = Tensor(x1_val)
x2 = Tensor(x2_val)
y = ((x1 * x2).log() + 1).exp()
assert np.array_equal(y.data, np.exp(np.log(x1_val * x2_val) + 1))
y.backward()
assert np.array_equal(x1.grad, y.data * x2_val / (x1_val * x2_val))
assert np.array_equal(x2.grad, y.data * x1_val / (x1_val * x2_val))
def test_logistic():
x1_val = 3 * np.ones(3)
w_val = 3 * np.zeros(3)
x1 = Tensor(x1_val)
w = Tensor(w_val)
y = 1 / (1 + (-(w * x1).sum()).exp())
expected_y_val = 1 / (1 + np.exp(-np.sum(w_val * x1_val)))
expected_y_grad = expected_y_val * (1 - expected_y_val) * x1_val
assert np.array_equal(y.data, expected_y_val)
y.backward()
assert np.sum(np.abs(w.grad - expected_y_grad)) < 1E-7
def test_log_two_vars():
x1_val = 2 * np.ones(3)
x2_val = 3 * np.ones(3)
x1 = Tensor(x1_val)
x2 = Tensor(x2_val)
y = (x1 * x2).log()
assert np.array_equal(y.data, np.log(x1_val * x2_val))
y.backward()
assert np.array_equal(x1.grad, x2_val / (x1_val * x2_val))
assert np.array_equal(x2.grad, x1_val / (x1_val * x2_val))
def test_add_mul_mix_1():
x1_val = 1 * np.ones(3)
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
x1 = Tensor(x1_val)
x2 = Tensor(x2_val)
x3 = Tensor(x3_val)
y = x1 + x2 * x3 * x1
assert np.array_equal(y.data, x1_val + x2_val * x3_val)
y.backward()
assert np.array_equal(x1.grad, np.ones_like(x1_val) + x2_val * x3_val)
assert np.array_equal(x2.grad, x3_val * x1_val)
assert np.array_equal(x3.grad, x2_val * x1_val)
def test_matmul_two_vars():
x2_val = np.array([[1, 2], [3, 4], [5, 6]]) # 3x2
x3_val = np.array([[7, 8, 9], [10, 11, 12]]) # 2x3
x2 = Tensor(x2_val)
x3 = Tensor(x3_val)
y = x2.matmul(x3)
expected_yval = np.matmul(x2_val, x3_val)
expected_grad_x2_val = np.matmul(np.ones_like(expected_yval), np.transpose(x3_val))
expected_grad_x3_val = np.matmul(np.transpose(x2_val), np.ones_like(expected_yval))
assert np.array_equal(y.data, expected_yval)
y.backward()
assert np.array_equal(x2.grad, expected_grad_x2_val)
assert np.array_equal(x3.grad, expected_grad_x3_val)
def test_logistic_loss():
y_val = 0
x_val = np.array([2, 3, 4])
w_val = np.random.random(3)
x = Tensor(x_val)
w = Tensor(w_val)
y = Tensor(y_val)
h = 1 / (1 + (-(w * x).sum()).exp())
l = y * h.log() + (1 - y) * (1 - h).log()
logistic = 1 / (1 + np.exp(-np.sum(w_val * x_val)))
expected_L_val = y_val * np.log(logistic) + (1 - y_val) * np.log(1 - logistic)
expected_w_grad = (y_val - logistic) * x_val
assert expected_L_val == l.data
l.backward()
assert np.sum(np.abs(expected_w_grad - w.grad)) < 1E-9
def test_div_by_const():
x2_val = 2 * np.ones(3)
x2 = Tensor(x2_val)
y = 5 / x2
assert np.array_equal(y.data, 5 / x2_val)
y.backward()
assert np.array_equal(x2.grad, -5 / (x2_val * x2_val))
def test_mul_by_const():
x2_val = 2 * np.ones(3)
x2 = Tensor(x2_val)
y = 5 * x2
assert np.array_equal(y.data, x2_val * 5)
y.backward()
assert np.array_equal(x2.grad, np.ones_like(x2_val) * 5)
def test_identity():
x2_val = 2 * np.ones(3)
x2 = Tensor(x2_val)
y = x2
assert np.array_equal(y.data, x2_val)
y.backward()
assert np.array_equal(x2.grad, np.ones_like(x2_val))
def test_sub_by_const():
x2_val = 2 * np.ones(3)
x2 = Tensor(x2_val)
y = np.ones(3) - x2
assert np.array_equal(y.data, np.ones(3) - x2_val)
y.backward()
assert np.array_equal(x2.grad, -np.ones_like(x2_val))
def test_add_mul_mix_3():
x2_val = 2 * np.ones(3)
x3_val = 3 * np.ones(3)
x2 = Tensor(x2_val)
x3 = Tensor(x3_val)
z = x2 * x2 + x2 + x3 + 3
y = z * z + x3
z_val = x2_val * x2_val + x2_val + x3_val + 3
expected_yval = z_val * z_val + x3_val
expected_grad_x2_val = 2 * (x2_val * x2_val + x2_val + x3_val + 3) * (2 * x2_val + 1)
expected_grad_x3_val = 2 * (x2_val * x2_val + x2_val + x3_val + 3) + 1
assert np.array_equal(y.data, expected_yval)
y.backward()
assert np.array_equal(x2.grad, expected_grad_x2_val)
assert np.array_equal(x3.grad, expected_grad_x3_val)
def auto_diff_lr():
# 注意，以下实现某些情况会有很大的数值误差，
# 所以一般真实系统实现会提供高阶算子，从而减少数值误差
N = 100
X_val, Y_val = gen_2d_data(N)
w_val = np.ones(3)
w = Tensor(w_val)
plot(N, X_val, Y_val, w_val)
test_accuracy(w_val, X_val, Y_val)
alpha = 0.01
max_iters = 300
for iteration in range(max_iters):
acc_L_val = 0
for i in range(N):
w.zero_gard()
x_val = X_val[i]
y_val = np.array(Y_val[i])
x = Tensor(x_val)
y = Tensor(y_val)
h = 1 / (1 + (-(w * x).sum()).exp())
l = y * h.log() + (1 - y) * (1 - h).log()
l.backward()
w.data += alpha * w.grad
acc_L_val += l.data
print("iter = %d, likelihood = %s, w = %s" %
(iteration, acc_L_val, w_val))
test_accuracy(w_val, X_val, Y_val)
plot(N, X_val, Y_val, w_val, True)
def test_reduce_sum_mix():
x1_val = 2 * np.ones(3)
x1 = Tensor(x1_val)
y = x1.sum().exp()
expected_y_val = np.exp(np.sum(x1_val))
assert np.array_equal(y.data, expected_y_val)
y.backward()
assert np.array_equal(x1.grad, expected_y_val * np.ones_like(x1_val))
x1.zero_gard()
y2 = x1.sum().log()
expected_y2_val = np.log(np.sum(x1_val))
assert np.array_equal(y2.data, expected_y2_val)
y2.backward()
assert np.array_equal(x1.grad, (1 / np.sum(x1_val)) * np.ones_like(x1_val))
from autodiff import Tensor
import numpy as np
x = Tensor(np.ones((2, 2)))
y = x + 2
z = y * y * 3
out = z.mean()
print(x)
print(y)
print(z)
print(out)
out.backward()
print(x.grad)
x = Tensor(np.random.randn(3))
y = x * 2
while np.linalg.norm(y.item) < 1000:
y = y * 2
print(x)
print(y)
gradients = Tensor([0.1, 1.0, 0.0001])
y.backward(gradients)
print(x.grad)
x = Tensor(2)