def test_periodic():
k = EQ().stretch(2).periodic(3)
yield eq, k.stationary, True
yield eq, k.length_scale, 2
yield eq, k.period, 3
yield eq, k.var, 1
# Test equality.
yield eq, EQ().periodic(2), EQ().periodic(2)
yield neq, EQ().periodic(2), EQ().periodic(3)
yield neq, Matern12().periodic(2), EQ().periodic(2)
# Standard tests:
for x in kernel_generator(k):
yield x
k = 5 * k.stretch(5)
yield eq, k.stationary, True
yield eq, k.length_scale, 10
yield eq, k.period, 15
yield eq, k.var, 5
# Check passing in a list.
k = EQ().periodic([1, 2])
yield k, np.random.randn(10, 2)
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_input_transform():
k = Linear().transform(lambda x: x - 5)
assert not k.stationary
with pytest.raises(RuntimeError):
k.length_scale
with pytest.raises(RuntimeError):
k.var
with pytest.raises(RuntimeError):
k.period
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 = np.random.randn(10, 2), np.random.randn(10, 2)
k2 = k.transform(lambda x: x ** 2)
k3 = k.transform(lambda x: x ** 2, lambda x: x - 5)
allclose(k(x1 ** 2, x2 ** 2), k2(x1, x2))
allclose(k(x1 ** 2, x2 - 5), k3(x1, x2))
def test_stretched():
k = EQ().stretch(2)
yield eq, k.stationary, True
yield eq, k.length_scale, 2
yield eq, k.period, np.inf
yield eq, k.var, 1
# Test equality.
yield eq, EQ().stretch(2), EQ().stretch(2)
yield neq, EQ().stretch(2), EQ().stretch(3)
yield neq, EQ().stretch(2), Matern12().stretch(2)
# Standard tests:
for x in kernel_generator(k):
yield x
k = EQ().stretch(1, 2)
yield eq, k.stationary, False
yield raises, RuntimeError, lambda: k.length_scale
yield raises, RuntimeError, lambda: k.period
yield eq, k.var, 1
# Check passing in a list.
k = EQ().stretch([1, 2])
yield k, np.random.randn(10, 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_exp():
k = Matern12()
# Verify that the kernel has the right properties.
assert k.stationary
assert k.var == 1
assert k.length_scale == 1
assert k.period == np.inf
assert str(k) == 'Exp()'
# Test equality.
assert Matern12() == Matern12()
assert Matern12() != Linear()
# Standard tests:
standard_kernel_tests(k)
def test_periodic():
k = EQ().stretch(2).periodic(3)
assert k.stationary
assert k.length_scale == 2
assert k.period == 3
assert k.var == 1
# 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)
assert k.stationary
assert k.length_scale == 10
assert k.period == 15
assert k.var == 5
# Check passing in a list.
k = EQ().periodic(np.array([1, 2]))
k(np.random.randn(10, 2))
def test_stretched():
k = EQ().stretch(2)
assert k.stationary
assert k.length_scale == 2
assert k.period == np.inf
assert k.var == 1
# 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)
assert not k.stationary
with pytest.raises(RuntimeError):
k.length_scale
with pytest.raises(RuntimeError):
k.period
assert k.var == 1
# Check passing in a list.
k = EQ().stretch(np.array([1, 2]))
k(np.random.randn(10, 2))
def test_basic_arithmetic():
k1 = EQ()
k2 = RQ(1e-1)
k3 = Matern12()
k4 = Matern32()
k5 = Matern52()
k6 = Delta()
k7 = Linear()
xs1 = np.random.randn(10, 2), np.random.randn(20, 2)
xs2 = np.random.randn(), np.random.randn()
yield ok, allclose(k6(xs1[0]), k6(xs1[0], xs1[0])), 'dispatch'
yield ok, allclose((k1 * k2)(*xs1), k1(*xs1) * k2(*xs1)), 'prod'
yield ok, allclose((k1 * k2)(*xs2), k1(*xs2) * k2(*xs2)), 'prod 2'
yield ok, allclose((k3 + k4)(*xs1), k3(*xs1) + k4(*xs1)), 'sum'
yield ok, allclose((k3 + k4)(*xs2), k3(*xs2) + k4(*xs2)), 'sum 2'
yield ok, allclose((5. * k5)(*xs1), 5. * k5(*xs1)), 'prod 3'
yield ok, allclose((5. * k5)(*xs2), 5. * k5(*xs2)), 'prod 4'
yield ok, allclose((5. + k7)(*xs1), 5. + k7(*xs1)), 'sum 3'
yield ok, allclose((5. + k7)(*xs2), 5. + k7(*xs2)), 'sum 4'
yield ok, allclose(k1.stretch(2.)(*xs1), k1(xs1[0] / 2.,
xs1[1] / 2.)), 'stretch'
yield ok, allclose(k1.stretch(2.)(*xs2), k1(xs2[0] / 2.,
xs2[1] / 2.)), 'stretch 2'
yield ok, allclose(
k1.periodic(1.)(*xs1),
k1.periodic(1.)(xs1[0], xs1[1] + 5.)), 'periodic'
yield ok, allclose(
k1.periodic(1.)(*xs2),
k1.periodic(1.)(xs2[0], xs2[1] + 5.)), 'periodic 2'
def test_input_transform():
k = Linear().transform(lambda x, c: x - 5)
yield eq, k.stationary, False
yield raises, RuntimeError, lambda: k.length_scale
yield raises, RuntimeError, lambda: k.var
yield raises, RuntimeError, lambda: k.period
def f1(x):
return x
def f2(x):
return x**2
# Test equality.
yield eq, EQ().transform(f1), EQ().transform(f1)
yield neq, EQ().transform(f1), EQ().transform(f2)
yield neq, EQ().transform(f1), Matern12().transform(f1)
# Standard tests:
for x in kernel_generator(k):
yield x
# Test computation of the kernel.
k = Linear()
x1, x2 = np.random.randn(10, 2), np.random.randn(10, 2)
k2 = k.transform(lambda x, c: x**2)
k3 = k.transform(lambda x, c: x**2, lambda x, c: x - 5)
yield assert_allclose, k(x1**2, x2**2), k2(x1, x2)
yield assert_allclose, k(x1**2, x2 - 5), k3(x1, x2)
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_derivative():
# First, check properties.
k = EQ().diff(0)
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 EQ().diff(0) == EQ().diff(0)
assert EQ().diff(0) != EQ().diff(1)
assert Matern12().diff(0) != EQ().diff(0)
# Standard tests:
for k in [EQ().diff(0), EQ().diff(None, 0), EQ().diff(0, None)]:
standard_kernel_tests(k, dtype=tf.float64)
# Check that a derivative must be specified.
with pytest.raises(RuntimeError):
EQ().diff(None, None)(np.array([1.0]))
with pytest.raises(RuntimeError):
EQ().diff(None, None).elwise(np.array([1.0]))
def test_selection():
k = (2 * EQ().stretch(5)).select(0)
assert k.stationary
assert k.length_scale == 5
assert k.period == np.inf
assert k.var == 2
# 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)
k = (2 * EQ().stretch(5)).select([2, 3])
assert k.stationary
assert k.length_scale == 5
assert k.period == np.inf
assert k.var == 2
k = (2 * EQ().stretch(np.array([1, 2, 3]))).select([0, 2])
assert k.stationary
allclose(k.length_scale, [1, 3])
allclose(k.period, [np.inf, np.inf])
assert k.var == 2
k = (2 * EQ().periodic(np.array([1, 2, 3]))).select([1, 2])
assert k.stationary
allclose(k.length_scale, [1, 1])
allclose(k.period, [2, 3])
assert k.var == 2
k = (2 * EQ().stretch(np.array([1, 2, 3]))).select([0, 2], [1, 2])
assert not k.stationary
with pytest.raises(RuntimeError):
k.length_scale
with pytest.raises(RuntimeError):
k.period
assert k.var == 2
k = (2 * EQ().periodic(np.array([1, 2, 3]))).select([0, 2], [1, 2])
assert not k.stationary
assert k.length_scale == 1
with pytest.raises(RuntimeError):
k.period
assert k.var == 2
# Test that computation is valid.
k1 = EQ().select([1, 2])
k2 = EQ()
x = np.random.randn(10, 3)
allclose(k1(x), k2(x[:, [1, 2]]))
def test_exp():
k = Matern12()
# Verify that the kernel has the right properties.
yield eq, k.stationary, True
yield eq, k.var, 1
yield eq, k.length_scale, 1
yield eq, k.period, np.inf
yield eq, str(k), 'Exp()'
# Test equality.
yield eq, Matern12(), Matern12()
yield neq, Matern12(), Linear()
# Standard tests:
for x in kernel_generator(k):
yield x
def test_selection():
k = (2 * EQ().stretch(5)).select(0)
yield eq, k.stationary, True
yield eq, k.length_scale, 5
yield eq, k.period, np.inf
yield eq, k.var, 2
# Test equality.
yield eq, EQ().select(0), EQ().select(0)
yield neq, EQ().select(0), EQ().select(1)
yield neq, EQ().select(0), Matern12().select(0)
# Standard tests:
for x in kernel_generator(k):
yield x
k = (2 * EQ().stretch(5)).select([2, 3])
yield eq, k.stationary, True
yield eq, k.length_scale, 5
yield eq, k.period, np.inf
yield eq, k.var, 2
k = (2 * EQ().stretch([1, 2, 3])).select([0, 2])
yield eq, k.stationary, True
yield assert_allclose, k.length_scale, [1, 3]
yield assert_allclose, k.period, [np.inf, np.inf]
yield eq, k.var, 2
k = (2 * EQ().periodic([1, 2, 3])).select([1, 2])
yield eq, k.stationary, True
yield assert_allclose, k.length_scale, [1, 1]
yield assert_allclose, k.period, [2, 3]
yield eq, k.var, 2
k = (2 * EQ().stretch([1, 2, 3])).select([0, 2], [1, 2])
yield eq, k.stationary, False
yield raises, RuntimeError, lambda: k.length_scale
yield raises, RuntimeError, lambda: k.period
yield eq, k.var, 2
k = (2 * EQ().periodic([1, 2, 3])).select([0, 2], [1, 2])
yield eq, k.stationary, False
yield eq, k.length_scale, 1
yield raises, RuntimeError, lambda: k.period
yield eq, k.var, 2
# Test that computation is valid.
k1 = EQ().select([1, 2])
k2 = EQ()
x = np.random.randn(10, 3)
yield assert_allclose, k1(x), k2(x[:, [1, 2]])
def test_scaled():
k = 2 * EQ()
assert k.stationary
# Test equality.
assert 2 * EQ() == 2 * EQ()
assert 2 * EQ() != 3 * EQ()
assert 2 * EQ() != 2 * Matern12()
# Standard tests:
standard_kernel_tests(k)
def test_scaled():
k = 2 * EQ()
# Verify that the kernel has the right properties.
assert k.stationary
# Test equality.
assert 2 * EQ() == 2 * EQ()
assert 2 * EQ() != 3 * EQ()
assert 2 * EQ() != 2 * Matern12()
# Standard tests:
standard_kernel_tests(k)
def test_scaled():
k = 2 * EQ()
assert k.stationary
assert k.length_scale == 1
assert k.period == np.inf
assert k.var == 2
# Test equality.
assert 2 * EQ() == 2 * EQ()
assert 2 * EQ() != 3 * EQ()
assert 2 * EQ() != 2 * Matern12()
# Standard tests:
standard_kernel_tests(k)
def test_scaled():
k = 2 * EQ()
yield eq, k.stationary, True
yield eq, k.length_scale, 1
yield eq, k.period, np.inf
yield eq, k.var, 2
# Test equality.
yield eq, 2 * EQ(), 2 * EQ()
yield neq, 2 * EQ(), 3 * EQ()
yield neq, 2 * EQ(), 2 * Matern12()
# Standard tests:
for x in kernel_generator(k):
yield x
def test_periodic():
k = EQ().stretch(2).periodic(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)
assert k.stationary
# Check passing in a list.
k = EQ().periodic(np.array([1, 2]))
k(np.random.randn(10, 2))
def test_stretched():
k = EQ().stretch(2)
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)
assert not k.stationary
# Check passing in a list.
k = EQ().stretch(np.array([1, 2]))
k(np.random.randn(10, 2))
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_selection():
k = (2 * EQ().stretch(5)).select(0)
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)
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 that computation is valid.
k1 = EQ().select([1, 2])
k2 = EQ()
x = np.random.randn(10, 3)
allclose(k1(x), k2(x[:, [1, 2]]))
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():
# First, check properties.
k = EQ().diff(0)
yield eq, k.stationary, False
yield raises, RuntimeError, lambda: k.length_scale
yield raises, RuntimeError, lambda: k.var
yield raises, RuntimeError, lambda: k.period
# Test equality.
yield eq, EQ().diff(0), EQ().diff(0)
yield neq, EQ().diff(0), EQ().diff(1)
yield neq, Matern12().diff(0), EQ().diff(0)
yield raises, RuntimeError, lambda: EQ().diff(None, None)(1)
# Third, check computation.
B.backend_to_tf()
s = B.Session()
# Test derivative of kernel EQ.
k = EQ()
x1 = B.array(np.random.randn(10, 1))
x2 = B.array(np.random.randn(5, 1))
# Test derivative with respect to first input.
ref = s.run(-dense(k(x1, x2)) * (x1 - B.transpose(x2)))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1, x2))), ref
ref = s.run(-dense(k(x1)) * (x1 - B.transpose(x1)))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1))), ref
# Test derivative with respect to second input.
ref = s.run(-dense(k(x1, x2)) * (B.transpose(x2) - x1))
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1, x2))), ref
ref = s.run(-dense(k(x1)) * (B.transpose(x1) - x1))
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1))), ref
# Test derivative with respect to both inputs.
ref = s.run(dense(k(x1, x2)) * (1 - (x1 - B.transpose(x2))**2))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1, x2))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1, x2))), ref
ref = s.run(dense(k(x1)) * (1 - (x1 - B.transpose(x1))**2))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1))), ref
# Test derivative of kernel Linear.
k = Linear()
x1 = B.array(np.random.randn(10, 1))
x2 = B.array(np.random.randn(5, 1))
# Test derivative with respect to first input.
ref = s.run(B.ones((10, 5), dtype=np.float64) * B.transpose(x2))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64) * B.transpose(x1))
yield assert_allclose, s.run(dense(k.diff(0, None)(x1))), ref
# Test derivative with respect to second input.
ref = s.run(B.ones((10, 5), dtype=np.float64) * x1)
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64) * x1)
yield assert_allclose, s.run(dense(k.diff(None, 0)(x1))), ref
# Test derivative with respect to both inputs.
ref = s.run(B.ones((10, 5), dtype=np.float64))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1, x2))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1, x2))), ref
ref = s.run(B.ones((10, 10), dtype=np.float64))
yield assert_allclose, s.run(dense(k.diff(0, 0)(x1))), ref
yield assert_allclose, s.run(dense(k.diff(0)(x1))), ref
s.close()
B.backend_to_np()