def test_input_transform():
k = Linear().transform(lambda x: x - 5)
# Verify that the kernel has the right properties.
assert not k.stationary
def f1(x):
return x
def f2(x):
return x**2
# Test equality.
assert EQ().transform(f1) == EQ().transform(f1)
assert EQ().transform(f1) != EQ().transform(f2)
assert EQ().transform(f1) != Matern12().transform(f1)
# Standard tests:
standard_kernel_tests(k)
# Test computation of the kernel.
k = Linear()
x1, x2 = B.randn(10, 2), B.randn(10, 2)
k2 = k.transform(lambda x: x**2)
k3 = k.transform(lambda x: x**2, lambda x: x - 5)
approx(k(x1**2, x2**2), k2(x1, x2))
approx(k(x1**2, x2 - 5), k3(x1, x2))
def test_shifted():
k = ShiftedKernel(2 * EQ(), 5)
# Verify that the kernel has the right properties.
assert k.stationary
# Test equality.
assert Linear().shift(2) == Linear().shift(2)
assert Linear().shift(2) != Linear().shift(3)
assert Linear().shift(2) != DecayingKernel(1, 1).shift(2)
# Standard tests:
standard_kernel_tests(k)
k = (2 * EQ()).shift(5, 6)
# Verify that the kernel has the right properties.
assert not k.stationary
# Check computation.
x1 = B.randn(10, 2)
x2 = B.randn(5, 2)
k = Linear()
approx(k.shift(5)(x1, x2), k(x1 - 5, x2 - 5))
# Check passing in a list.
k = Linear().shift(np.array([1, 2]))
k(B.randn(10, 2))
def test_construction(x1, x2):
k = EQ()
k(x1)
k(x1, x2)
k.elwise(x1)
k.elwise(x1, x2)
# Test `MultiInput` construction.
approx(
k(MultiInput(x1, x2)),
B.concat2d([k(x1, x1), k(x1, x2)], [k(x2, x1), k(x2, x2)]),
)
approx(k(x1, MultiInput(x1, x2)), B.concat(k(x1, x1), k(x1, x2), axis=1))
approx(k(MultiInput(x1, x2), x2), B.concat(k(x1, x2), k(x2, x2), axis=0))
approx(
k.elwise(MultiInput(x1, x2)),
B.concat(k.elwise(x1, x1), k.elwise(x2, x2), axis=0),
)
with pytest.raises(ValueError):
k.elwise(MultiInput(x1), MultiInput(x1, x2))
with pytest.raises(ValueError):
k.elwise(x1, MultiInput(x1, x2))
with pytest.raises(ValueError):
k.elwise(MultiInput(x1, x2), x2)
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_reversal():
x1 = B.randn(10, 2)
x2 = B.randn(5, 2)
x3 = B.randn()
# Test with a stationary and non-stationary kernel.
for k in [EQ(), Linear()]:
approx(k(x1), reversed(k)(x1))
approx(k(x3), reversed(k)(x3))
approx(k(x1, x2), reversed(k)(x1, x2))
approx(k(x1, x2), reversed(k)(x2, x1).T)
# Test double reversal does the right thing.
approx(k(x1), reversed(reversed(k))(x1))
approx(k(x3), reversed(reversed(k))(x3))
approx(k(x1, x2), reversed(reversed(k))(x1, x2))
approx(k(x1, x2), reversed(reversed(k))(x2, x1).T)
# Verify that the kernel has the right properties.
k = reversed(EQ())
assert k.stationary
k = reversed(Linear())
assert not k.stationary
assert str(k) == "Reversed(Linear())"
# Check equality.
assert reversed(Linear()) == reversed(Linear())
assert reversed(Linear()) != Linear()
assert reversed(Linear()) != reversed(EQ())
assert reversed(Linear()) != reversed(DecayingKernel(1, 1))
# Standard tests:
standard_kernel_tests(k)
def test_nested_derivatives(dtype):
x = B.randn(dtype, 10, 2)
res = EQ().diff(0, 0).diff(0, 0)(x)
assert ~B.isnan(res[0, 0])
res = EQ().diff(1, 1).diff(1, 1)(x)
assert ~B.isnan(res[0, 0])
def test_posterior_kernel():
k = PosteriorKernel(EQ(), EQ(), EQ(), B.randn(5, 2), EQ()(B.randn(5, 1)))
# Verify that the kernel has the right properties.
assert not k.stationary
assert str(k) == "PosteriorKernel()"
# Standard tests:
standard_kernel_tests(k, shapes=[((10, 2), (5, 2))])
def test_corrective_kernel():
a, b = B.randn(3, 3), B.randn(3, 3)
a, b = a.dot(a.T), b.dot(b.T)
z = B.randn(3, 2)
k = CorrectiveKernel(EQ(), EQ(), z, a, b)
# Verify that the kernel has the right properties.
assert not k.stationary
assert str(k) == "CorrectiveKernel()"
# Standard tests:
standard_kernel_tests(k, shapes=[((10, 2), (5, 2))])
def test_periodic():
k = EQ().stretch(2).periodic(3)
# Verify that the kernel has the right properties.
assert str(k) == "(EQ() > 2) per 3"
assert k.stationary
# Test equality.
assert EQ().periodic(2) == EQ().periodic(2)
assert EQ().periodic(2) != EQ().periodic(3)
assert Matern12().periodic(2) != EQ().periodic(2)
# Standard tests:
standard_kernel_tests(k)
k = 5 * k.stretch(5)
# Verify that the kernel has the right properties.
assert k.stationary
# Check passing in a list.
k = EQ().periodic(np.array([1, 2]))
k(B.randn(10, 2))
# Check periodication of a zero.
k = ZeroKernel()
assert k.periodic(3) is k
def test_selection():
k = (2 * EQ().stretch(5)).select(0)
# Verify that the kernel has the right properties.
assert k.stationary
# Test equality.
assert EQ().select(0) == EQ().select(0)
assert EQ().select(0) != EQ().select(1)
assert EQ().select(0) != Matern12().select(0)
# Standard tests:
standard_kernel_tests(k)
# Verify that the kernel has the right properties.
k = (2 * EQ().stretch(5)).select([2, 3])
assert k.stationary
k = (2 * EQ().stretch(np.array([1, 2, 3]))).select([0, 2])
assert k.stationary
k = (2 * EQ().periodic(np.array([1, 2, 3]))).select([1, 2])
assert k.stationary
k = (2 * EQ().stretch(np.array([1, 2, 3]))).select([0, 2], [1, 2])
assert not k.stationary
k = (2 * EQ().periodic(np.array([1, 2, 3]))).select([0, 2], [1, 2])
assert not k.stationary
# Test computation of the kernel.
k1 = EQ().select([1, 2])
k2 = EQ()
x = B.randn(10, 3)
approx(k1(x), k2(x[:, [1, 2]]))
def test_tensor_product():
k = TensorProductKernel(lambda x: B.sum(x ** 2, axis=1))
assert not k.stationary
with pytest.raises(RuntimeError):
k.length_scale
with pytest.raises(RuntimeError):
k.var
with pytest.raises(RuntimeError):
k.period
# Test equality.
assert k == k
assert k != TensorProductKernel(lambda x: x)
assert k != EQ()
# Standard tests:
standard_kernel_tests(k)
# Check computation of kernel.
k = TensorProductKernel(lambda x: x)
x1 = np.linspace(0, 1, 100)[:, None]
x2 = np.linspace(0, 1, 50)[:, None]
allclose(k(x1), x1 * x1.T)
allclose(k(x1, x2), x1 * x2.T)
k = TensorProductKernel(lambda x: x ** 2)
allclose(k(x1), x1 ** 2 * (x1 ** 2).T)
allclose(k(x1, x2), (x1 ** 2) * (x2 ** 2).T)
def test_zero():
k = ZeroKernel()
x1 = B.randn(10, 2)
x2 = B.randn(5, 2)
# Test that the kernel computes correctly.
approx(k(x1, x2), np.zeros((10, 5)))
# Verify that the kernel has the right properties.
assert k.stationary
assert str(k) == "0"
# Test equality.
assert ZeroKernel() == ZeroKernel()
assert ZeroKernel() != Linear()
# Standard tests:
standard_kernel_tests(k)
def test_delta_evaluations(x1, x2):
k = Delta()
n1 = B.shape(B.uprank(x1))[0]
n2 = B.shape(B.uprank(x2))[0]
# Check uniqueness checks.
allclose(k(x1), B.eye(n1))
allclose(k(x1, x2), B.zeros(n1, n2))
# Standard tests:
standard_kernel_tests(k)
# Test `Unique` inputs.
assert isinstance(k(Unique(x1), Unique(x1.copy())), Zero)
assert isinstance(k(Unique(x1), Unique(x1)), Diagonal)
assert isinstance(k(Unique(x1), x1), Zero)
assert isinstance(k(x1, Unique(x1)), Zero)
allclose(k.elwise(Unique(x1), Unique(x1.copy())), B.zeros(n1, 1))
allclose(k.elwise(Unique(x1), Unique(x1)), B.ones(n1, 1))
allclose(k.elwise(Unique(x1), x1), B.zeros(n1, 1))
allclose(k.elwise(x1, Unique(x1)), B.zeros(n1, 1))
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_delta_evaluations(x1, w1, x2, w2):
k = Delta()
n1 = num_elements(x1)
n2 = num_elements(x2)
# Check uniqueness checks.
approx(k(x1), B.eye(n1))
approx(k(x1, x2), B.zeros(n1, n2))
# Standard tests:
standard_kernel_tests(k)
# Test `Unique` inputs.
assert isinstance(k(Unique(x1), Unique(x1.copy())), Zero)
assert isinstance(k(Unique(x1), Unique(x1)), Diagonal)
assert isinstance(k(Unique(x1), x1), Zero)
assert isinstance(k(x1, Unique(x1)), Zero)
approx(k.elwise(Unique(x1), Unique(x1.copy())), B.zeros(n1, 1))
approx(k.elwise(Unique(x1), Unique(x1)), B.ones(n1, 1))
approx(k.elwise(Unique(x1), x1), B.zeros(n1, 1))
# Test `WeightedUnique` inputs.
assert isinstance(k(WeightedUnique(x1, w1), WeightedUnique(x1.copy(), w1)),
Zero)
assert isinstance(k(WeightedUnique(x1, w1), WeightedUnique(x1, w1)),
Diagonal)
assert isinstance(k(WeightedUnique(x1, w1), x1), Zero)
assert isinstance(k(x1, WeightedUnique(x1, w1)), Zero)
approx(k.elwise(WeightedUnique(x1, w1), WeightedUnique(x1.copy(), w1)),
B.zeros(n1, 1))
approx(k.elwise(WeightedUnique(x1, w1), WeightedUnique(x1, w1)),
B.ones(n1, 1))
approx(k.elwise(WeightedUnique(x1, w1), x1), B.zeros(n1, 1))
approx(k.elwise(x1, WeightedUnique(x1, w1)), B.zeros(n1, 1))
approx(k.elwise(x1, WeightedUnique(x1, w1)), B.zeros(n1, 1))
def test_basic_arithmetic():
k1 = EQ()
k2 = RQ(1e-1)
k3 = Matern12()
k4 = Matern32()
k5 = Matern52()
k6 = Delta()
k7 = Linear()
xs1 = B.randn(10, 2), B.randn(20, 2)
xs2 = B.randn(), B.randn()
approx(k6(xs1[0]), k6(xs1[0], xs1[0]))
approx((k1 * k2)(*xs1), k1(*xs1) * k2(*xs1))
approx((k1 * k2)(*xs2), k1(*xs2) * k2(*xs2))
approx((k3 + k4)(*xs1), k3(*xs1) + k4(*xs1))
approx((k3 + k4)(*xs2), k3(*xs2) + k4(*xs2))
approx((5.0 * k5)(*xs1), 5.0 * k5(*xs1))
approx((5.0 * k5)(*xs2), 5.0 * k5(*xs2))
approx((5.0 + k7)(*xs1), 5.0 + k7(*xs1))
approx((5.0 + k7)(*xs2), 5.0 + k7(*xs2))
approx(k1.stretch(2.0)(*xs1), k1(xs1[0] / 2.0, xs1[1] / 2.0))
approx(k1.stretch(2.0)(*xs2), k1(xs2[0] / 2.0, xs2[1] / 2.0))
approx(k1.periodic(1.0)(*xs1), k1.periodic(1.0)(xs1[0], xs1[1] + 5.0))
approx(k1.periodic(1.0)(*xs2), k1.periodic(1.0)(xs2[0], xs2[1] + 5.0))
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)
def test_stretched():
k = EQ().stretch(2)
# Verify that the kernel has the right properties.
assert k.stationary
# Test equality.
assert EQ().stretch(2) == EQ().stretch(2)
assert EQ().stretch(2) != EQ().stretch(3)
assert EQ().stretch(2) != Matern12().stretch(2)
# Standard tests:
standard_kernel_tests(k)
k = EQ().stretch(1, 2)
# Verify that the kernel has the right properties.
assert not k.stationary
# Check passing in a list.
k = EQ().stretch(np.array([1, 2]))
k(B.randn(10, 2))
def test_tensor_product():
k = TensorProductKernel(lambda x: B.sum(x**2, axis=1))
# Verify that the kernel has the right properties.
assert not k.stationary
# Test equality.
assert k == k
assert k != TensorProductKernel(lambda x: x)
assert k != EQ()
# Standard tests:
standard_kernel_tests(k)
# Test computation of the kernel.
k = TensorProductKernel(lambda x: x)
x1 = np.linspace(0, 1, 100)[:, None]
x2 = np.linspace(0, 1, 50)[:, None]
approx(k(x1), x1 * x1.T)
approx(k(x1, x2), x1 * x2.T)
k = TensorProductKernel(lambda x: x**2)
approx(k(x1), x1**2 * (x1**2).T)
approx(k(x1, x2), (x1**2) * (x2**2).T)
# Check againtst fallback brute force computation.
approx(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.
approx(k.elwise(x1)[:, 0], B.diag(k(x1)), atol=1e-6, rtol=1e-6)
approx(k.elwise(x1), Kernel.elwise(k, x1))
def test_corner_cases():
with pytest.raises(RuntimeError):
Kernel()(1.0)
@pytest.mark.parametrize(
"x1",
[B.randn(10), Input(B.randn(10)),
FDD(None, B.randn(10))])
@pytest.mark.parametrize(
"x2",
[B.randn(10), Input(B.randn(10)),
FDD(None, B.randn(10))])
def test_construction(x1, x2):
k = EQ()
k(x1)
k(x1, x2)
k.elwise(x1)
k.elwise(x1, x2)
# Test `MultiInput` construction.
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))
# 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) == 'Delta()'
# Check equality.
assert Delta() == Delta()
assert Delta() != Delta(epsilon=k.epsilon * 10)
assert Delta() != EQ()
@pytest.mark.parametrize('x1_x2', [(np.array(0), np.array(1)),
(B.randn(10), B.randn(5)),
(B.randn(10, 1), B.randn(5, 1)),
(B.randn(10, 2), B.randn(5, 2))])
def test_delta_evaluations(x1_x2):
k = Delta()
x1, x2 = x1_x2
n1 = B.shape(B.uprank(x1))[0]
n2 = B.shape(B.uprank(x2))[0]
# Check uniqueness checks.
allclose(k(x1), B.eye(n1))
allclose(k(x1, x2), B.zeros(n1, n2))
# Standard tests:
standard_kernel_tests(k)
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))
