def test_regularize_cov(lorenz_dataset):
_, _, X, _, _ = lorenz_dataset
X = X[:, :3]
calc_cross_cov_mats_from_data(X,
5,
regularization='kron',
reg_ops={'num_folds': 3})
def test_T_too_large():
"""Test that an error is raised when T is too large.
"""
X = np.random.randn(100, 5)
T = 99
calc_cross_cov_mats_from_data(X, T)
T = 100
with pytest.raises(ValueError):
calc_cross_cov_mats_from_data(X, T)
def test_cross_cov_mats_from_data_chunks_2d():
"""Test whether chunking the lagged matrix gives the same cross covariance matrices
with 2d inputs."""
np.random.seed(0)
cov = np.random.randn(10, 10)
cov = cov.T.dot(cov) + np.eye(10)
X = np.random.multivariate_normal(np.zeros(10), cov, size=10000)
ccms = calc_cross_cov_mats_from_data(X, 3, chunks=10)
ccms2 = calc_cross_cov_mats_from_data(X, 3)
assert_allclose(ccms, ccms2, rtol=1e-2)
def test_projected_cov_calc(lorenz_dataset):
"""Test the project_cross_cov_mats function by also directly projecting
the data."""
rng = np.random.RandomState(20200226)
T, d, X, _, _ = lorenz_dataset
X = X[:, :3]
N = 3
d = 2
T = 6
V = init_coef(N, d, rng, 'random_ortho')
tV = torch.tensor(V)
ccms = calc_cross_cov_mats_from_data(X, T)
tccms = torch.tensor(ccms)
pccms = project_cross_cov_mats(ccms, V)
cov = calc_cov_from_cross_cov_mats(pccms)
XL = form_lag_matrix(X, T)
big_V = np.zeros((T * N, T * d))
for ii in range(T):
big_V[ii * N:(ii + 1) * N, ii * d:(ii + 1) * d] = V
Xp = XL.dot(big_V)
cov2 = np.cov(Xp, rowvar=False)
cov2 = toeplitzify(cov2, T, d)
assert_allclose(cov, cov2)
tpccms = project_cross_cov_mats(tccms, tV)
tcov = calc_cov_from_cross_cov_mats(tpccms)
assert torch.allclose(tcov, torch.tensor(cov2))
assert_allclose(tcov.numpy(), cov2)
def lorenz_dataset():
rng = np.random.RandomState(20200129)
T, d = 20, 31
X = rng.randn(10000, d)
XL = gen_lorenz_data(10000)
X[:, :3] += XL
ccms = calc_cross_cov_mats_from_data(X, T=T)
ccov = calc_cov_from_cross_cov_mats(ccms)
return T, d, X, ccms, ccov