def get_kernel_cholesky(X_train,
hyps,
str_cov,
is_fixed_noise=constants.IS_FIXED_GP_NOISE,
is_gradient=False,
debug=False):
"""
This function computes a kernel inverse with Cholesky decomposition.
:param X_train: inputs. Shape: (n, d) or (n, m, d).
:type X_train: numpy.ndarray
:param hyps: dictionary of hyperparameters for Gaussian process.
:type hyps: dict.
:param str_cov: the name of covariance function.
:type str_cov: str.
:param is_fixed_noise: flag for fixing a noise.
:type is_fixed_noise: bool., optional
:param is_gradient: flag for computing and returning gradients of negative log marginal likelihood.
:type is_gradient: bool., optional
:param debug: flag for printing log messages.
:type debug: bool., optional
:returns: a tuple of kernel matrix over `X_train`, lower matrix computed by Cholesky decomposition, and gradients of kernel matrix. If `is_gradient` is False, gradients of kernel matrix would be None.
:rtype: tuple of (numpy.ndarray, numpy.ndarray, numpy.ndarray)
:raises: AssertionError
"""
assert isinstance(X_train, np.ndarray)
assert isinstance(hyps, dict)
assert isinstance(str_cov, str)
assert isinstance(is_fixed_noise, bool)
assert isinstance(is_gradient, bool)
assert isinstance(debug, bool)
utils_gp.check_str_cov('get_kernel_cholesky', str_cov, X_train.shape)
cov_X_X = covariance.cov_main(
str_cov, X_train, X_train, hyps,
True) + hyps['noise']**2 * np.eye(X_train.shape[0])
cov_X_X = (cov_X_X + cov_X_X.T) / 2.0
try:
lower = scipy.linalg.cholesky(cov_X_X, lower=True)
except np.linalg.LinAlgError: # pragma: no cover
cov_X_X += 1e-2 * np.eye(X_train.shape[0])
lower = scipy.linalg.cholesky(cov_X_X, lower=True)
if is_gradient:
grad_cov_X_X = covariance.grad_cov_main(str_cov,
X_train,
X_train,
hyps,
is_fixed_noise,
same_X_Xs=True)
else:
grad_cov_X_X = None
return cov_X_X, lower, grad_cov_X_X
def test_grad_cov_main():
cur_hyps = utils_covariance.get_hyps('se', 2)
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main(123, np.zeros((10, 2)), np.zeros((10, 2)),
cur_hyps, True)
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main('se', 123, np.zeros((10, 2)), cur_hyps, True)
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main('se', np.zeros((10, 2)), 123, cur_hyps, True)
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main('se', np.zeros((10, 2)), np.zeros((10, 2)),
123, True)
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main('se', np.zeros((10, 2)), np.zeros((10, 2)),
cur_hyps, 'abc')
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main('abc', np.zeros((10, 2)), np.zeros((10, 2)),
cur_hyps, True)
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main('se',
np.zeros((10, 2)),
np.zeros((10, 2)),
cur_hyps,
True,
same_X_Xs='abc')
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main('se',
np.zeros((10, 2)),
np.zeros((10, 2)),
cur_hyps,
True,
same_X_Xs=False)
with pytest.raises(AssertionError) as error:
covariance.grad_cov_main('se',
np.zeros((10, 2)),
np.zeros((10, 2)),
cur_hyps,
True,
jitter='abc')
grad_cov_ = covariance.grad_cov_main('se', np.ones((1, 2)), np.ones(
(1, 2)), cur_hyps, True)
print(grad_cov_)
truth_grad_cov_ = np.array([[[2.00002, 0.0, 0.0]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
grad_cov_ = covariance.grad_cov_main('se', np.ones((1, 2)), np.ones(
(1, 2)), cur_hyps, False)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.02, 2.00002, 0.0, 0.0]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
cur_hyps['lengthscales'] = 1.0
grad_cov_ = covariance.grad_cov_main('se', np.ones((1, 2)), np.zeros(
(1, 2)), cur_hyps, False)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.02, 0.73577888, 0.73577888]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
grad_cov_ = covariance.grad_cov_main('matern32', np.ones((1, 2)),
np.zeros((1, 2)), cur_hyps, False)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.02, 0.59566154, 0.51802578]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
grad_cov_ = covariance.grad_cov_main('matern32', np.ones((1, 2)),
np.zeros((1, 2)), cur_hyps, True)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.59566154, 0.51802578]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
grad_cov_ = covariance.grad_cov_main('matern52', np.ones((1, 2)),
np.zeros((1, 2)), cur_hyps, False)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.02, 0.63458673, 0.8305486]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
def test_grad_cov_main():
cur_hyps = utils_covariance.get_hyps('se', 2)
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main(123, np.zeros((10, 2)), np.zeros((10, 2)),
cur_hyps, True)
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main('se', 123, np.zeros((10, 2)), cur_hyps,
True)
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main('se', np.zeros((10, 2)), 123, cur_hyps,
True)
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main('se', np.zeros((10, 2)), np.zeros(
(10, 2)), 123, True)
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main('se', np.zeros((10, 2)), np.zeros(
(10, 2)), cur_hyps, 'abc')
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main('abc', np.zeros((10, 2)), np.zeros(
(10, 2)), cur_hyps, True)
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main('se',
np.zeros((10, 2)),
np.zeros((10, 2)),
cur_hyps,
True,
same_X_Xp='abc')
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main('se',
np.zeros((10, 2)),
np.zeros((10, 2)),
cur_hyps,
True,
same_X_Xp=False)
with pytest.raises(AssertionError) as error:
package_target.grad_cov_main('se',
np.zeros((10, 2)),
np.zeros((10, 2)),
cur_hyps,
True,
jitter='abc')
grad_cov_ = package_target.grad_cov_main('se', np.ones((1, 2)),
np.ones((1, 2)), cur_hyps, True)
print(grad_cov_)
truth_grad_cov_ = np.array([[[2.00002, 0.0, 0.0]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
grad_cov_ = package_target.grad_cov_main('se', np.ones((1, 2)),
np.ones((1, 2)), cur_hyps, False)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.02, 2.00002, 0.0, 0.0]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
cur_hyps['lengthscales'] = 1.0
grad_cov_ = package_target.grad_cov_main('se', np.ones((1, 2)),
np.zeros((1, 2)), cur_hyps, False)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.02, 0.73577888, 0.73577888]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
grad_cov_ = package_target.grad_cov_main('matern32', np.ones((1, 2)),
np.zeros((1, 2)), cur_hyps, False)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.02, 0.59566154, 0.51802578]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
grad_cov_ = package_target.grad_cov_main('matern32', np.ones((1, 2)),
np.zeros((1, 2)), cur_hyps, True)
print(grad_cov_)
truth_grad_cov_ = np.array([[[0.59566154, 0.51802578]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)
grad_cov_ = package_target.grad_cov_main('matern52', np.ones((1, 2)),
np.zeros((1, 2)), cur_hyps, False)
print(grad_cov_)
print(np.squeeze(grad_cov_)[0])
print(np.squeeze(grad_cov_)[1])
print(np.squeeze(grad_cov_)[2])
truth_grad_cov_ = np.array(
[[[0.02, 0.6345867279080876, 0.5872865507000906]]])
assert np.all(np.abs(grad_cov_ - truth_grad_cov_) < TEST_EPSILON)