def standard_kernel_tests(k, shapes=None, dtype=np.float64):
if shapes is None:
shapes = [((10, 2), (5, 2)), ((10, 1), (5, 1)), ((10, ), (5, )),
((10, ), ()), ((), (5, )), ((), ())]
# Check various shapes of arguments.
for shape1, shape2 in shapes:
x1 = B.randn(dtype, *shape1)
x2 = B.randn(dtype, *shape2)
# Check that the kernel computes consistently.
allclose(k(x1, x2), B.transpose(reversed(k)(x2, x1)))
# Check `elwise`.
x2 = B.randn(dtype, *shape1)
allclose(k.elwise(x1, x2)[:, 0], B.diag(k(x1, x2)))
allclose(k.elwise(x1, x2), Kernel.elwise(k, x1, x2))
# The element-wise computation is more accurate, which is why we allow
# a discrepancy a bit larger than the square root of the machine
# epsilon.
allclose(k.elwise(x1)[:, 0],
B.diag(k(x1)),
desc='',
atol=1e-6,
rtol=1e-6)
allclose(k.elwise(x1), Kernel.elwise(k, x1))
def test_derivative_linear():
# Test derivative of kernel `Linear()`.
k = Linear()
x1 = B.randn(tf.float64, 10, 1)
x2 = B.randn(tf.float64, 5, 1)
# Test derivative with respect to first input.
allclose(k.diff(0, None)(x1, x2),
B.ones(tf.float64, 10, 5) * B.transpose(x2))
allclose(k.diff(0, None)(x1),
B.ones(tf.float64, 10, 10) * B.transpose(x1))
# Test derivative with respect to second input.
allclose(k.diff(None, 0)(x1, x2), B.ones(tf.float64, 10, 5) * x1)
allclose(k.diff(None, 0)(x1), B.ones(tf.float64, 10, 10) * x1)
# Test derivative with respect to both inputs.
ref = B.ones(tf.float64, 10, 5)
allclose(k.diff(0, 0)(x1, x2), ref)
allclose(k.diff(0)(x1, x2), ref)
ref = B.ones(tf.float64, 10, 10)
allclose(k.diff(0, 0)(x1), ref)
allclose(k.diff(0)(x1), ref)
def test_derivative_eq():
# Test derivative of kernel `EQ()`.
k = EQ()
x1 = B.randn(tf.float64, 10, 1)
x2 = B.randn(tf.float64, 5, 1)
# Test derivative with respect to first input.
allclose(k.diff(0, None)(x1, x2), -k(x1, x2) * (x1 - B.transpose(x2)))
allclose(k.diff(0, None)(x1), -k(x1) * (x1 - B.transpose(x1)))
# Test derivative with respect to second input.
allclose(k.diff(None, 0)(x1, x2), -k(x1, x2) * (B.transpose(x2) - x1))
allclose(k.diff(None, 0)(x1), -k(x1) * (B.transpose(x1) - x1))
# Test derivative with respect to both inputs.
ref = k(x1, x2) * (1 - (x1 - B.transpose(x2)) ** 2)
allclose(k.diff(0, 0)(x1, x2), ref)
allclose(k.diff(0)(x1, x2), ref)
ref = k(x1) * (1 - (x1 - B.transpose(x1)) ** 2)
allclose(k.diff(0, 0)(x1), ref)
allclose(k.diff(0)(x1), ref)
