def test_convolve2d(self):
np.random.seed(1234)
img = np.random.randn(1, 5, 5, 1)
kernel = np.random.randn(3, 3, 1, 1)
output = bn.convolve2d(img, kernel)
self.assertTrue(
np.allclose(
output.value[0, ..., 0],
correlate(img[0, ..., 0], kernel[..., 0, 0])[1:-1, 1:-1]
)
)
p = bn.Parameter(kernel)
output = bn.convolve2d(img, p, 2, 1)
loss = bn.sum(bn.square(output))
loss.backward()
grad_backprop = p.grad
grad_numerical = np.zeros_like(grad_backprop)
eps = 1e-8
for i, j in itertools.product(range(3), repeat=2):
e = np.zeros_like(kernel)
e[i, j] += eps
loss_p = bn.sum(bn.square(bn.convolve2d(img, kernel + e, 2, 1))).value
loss_m = bn.sum(bn.square(bn.convolve2d(img, kernel - e, 2, 1))).value
grad_numerical[i, j] = (loss_p - loss_m) / (2 * eps)
self.assertTrue(np.allclose(grad_backprop, grad_numerical))
def test_abs(self):
np.random.seed(1234)
x = bn.Parameter(np.random.randn(5, 7))
sign = np.sign(x.value)
y = bn.abs(x)
self.assertTrue((y.value == np.abs(x.value)).all())
for _ in range(10000):
x.cleargrad()
y = bn.abs(x)
bn.square(y - 0.01).sum().backward()
x.value -= x.grad * 0.001
self.assertTrue(np.allclose(x.value, 0.01 * sign))
def test_logdet(self):
A = np.array([[2., 1.], [1., 3.]])
logdetA = np.linalg.slogdet(A)[1]
self.assertTrue((logdetA == bn.linalg.logdet(A).value).all())
A = bn.Parameter(A)
for _ in range(100):
A.cleargrad()
logdetA = bn.linalg.logdet(A)
loss = bn.square(logdetA - 1)
loss.backward()
A.value -= 0.1 * A.grad
self.assertAlmostEqual(logdetA.value, 1)
def test_trace(self):
arrays = [np.random.normal(size=(2, 2)), np.random.normal(size=(3, 4))]
for arr in arrays:
arr = bn.Parameter(arr)
tr_arr = bn.linalg.trace(arr)
self.assertEqual(tr_arr.value, np.trace(arr.value))
a = np.array([[1.5, 0], [-0.1, 1.1]])
a = bn.Parameter(a)
for _ in range(100):
a.cleargrad()
loss = bn.square(bn.linalg.trace(a) - 2)
loss.backward()
a.value -= 0.1 * a.grad
self.assertEqual(bn.linalg.trace(a).value, 2)
def test_cholesky(self):
A = np.array([[2., -1], [-1., 5.]])
L = np.linalg.cholesky(A)
Ap = bn.Parameter(A)
L_test = bn.linalg.cholesky(Ap)
self.assertTrue((L == L_test.value).all())
T = np.array([[1., 0.], [-1., 2.]])
for _ in range(1000):
Ap.cleargrad()
L_ = bn.linalg.cholesky(Ap)
loss = bn.square(T - L_).sum()
loss.backward()
Ap.value -= 0.1 * Ap.grad
self.assertTrue(np.allclose(Ap.value, T @ T.T))
def test_solve(self):
A = np.array([
[2., 1.],
[1., 3.]
])
B = np.array([1., 2.])[:, None]
AinvB = np.linalg.solve(A, B)
self.assertTrue((AinvB == bn.linalg.solve(A, B).value).all())
A = bn.Parameter(A)
B = bn.Parameter(B)
for _ in range(100):
A.cleargrad()
B.cleargrad()
AinvB = bn.linalg.solve(A, B)
loss = bn.square(AinvB - 1).sum()
loss.backward()
A.value -= A.grad
B.value -= B.grad
self.assertTrue(np.allclose(AinvB.value, 1))
def test_inverse(self):
A = np.array([
[2., 1.],
[1., 3.]
])
Ainv = np.linalg.inv(A)
self.assertTrue((Ainv == bn.linalg.inv(A).value).all())
B = np.array([
[-1., 1.],
[1., 0.5]
])
A = bn.Parameter(np.array([
[-0.4, 0.7],
[0.7, 0.7]
]))
for _ in range(100):
A.cleargrad()
Ainv = bn.linalg.inv(A)
loss = bn.square(Ainv - B).sum()
loss.backward()
A.value -= 0.1 * A.grad
self.assertTrue(np.allclose(A.value, np.linalg.inv(B)))
def test_sqrt(self):
x = bn.Parameter(2.)
y = bn.square(x)
self.assertEqual(y.value, 4)
y.backward()
self.assertEqual(x.grad, 4)