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), reversed(k)(x2, x1).T)
# 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_fixed_delta():
noises = B.rand(3)
k = FixedDelta(noises)
# Verify that the kernel has the right properties.
assert k.stationary
assert k.var == 1
assert k.length_scale == 0
assert k.period == np.inf
assert str(k) == 'FixedDelta()'
# Check equality.
assert FixedDelta(noises) == FixedDelta(noises)
assert FixedDelta(noises) != FixedDelta(2 * noises)
assert FixedDelta(noises) != EQ()
# Standard tests:
standard_kernel_tests(k)
# Check correctness.
x1 = B.randn(5)
x2 = B.randn(5)
allclose(k(x1), B.zeros(5, 5))
allclose(k.elwise(x1), B.zeros(5, 1))
allclose(k(x1, x2), B.zeros(5, 5))
allclose(k.elwise(x1, x2), B.zeros(5, 1))
x1 = B.randn(3)
x2 = B.randn(3)
allclose(k(x1), B.diag(noises))
allclose(k.elwise(x1), B.uprank(noises))
allclose(k(x1, x2), B.zeros(3, 3))
allclose(k.elwise(x1, x2), B.zeros(3, 1))
def test_fixed_delta():
noises = B.rand(3)
k = FixedDelta(noises)
# Verify that the kernel has the right properties.
assert k.stationary
assert str(k) == "FixedDelta()"
# Check equality.
assert FixedDelta(noises) == FixedDelta(noises)
assert FixedDelta(noises) != FixedDelta(2 * noises)
assert FixedDelta(noises) != EQ()
# Standard tests:
standard_kernel_tests(k)
# Check correctness.
x1 = B.randn(5)
x2 = B.randn(5)
approx(k(x1), B.zeros(5, 5))
approx(k.elwise(x1), B.zeros(5, 1))
approx(k(x1, x2), B.zeros(5, 5))
approx(k.elwise(x1, x2), B.zeros(5, 1))
x1 = B.randn(3)
x2 = B.randn(3)
approx(k(x1), B.diag(noises))
approx(k.elwise(x1), B.uprank(noises))
approx(k(x1, x2), B.zeros(3, 3))
approx(k.elwise(x1, x2), B.zeros(3, 1))
