def test_mat_from_diag_triu_tril(self):
diag = gs.array([9., 9., 9.])
triu = gs.array([1., 2., 3.])
tril = -1 * triu
mat = gs.mat_from_diag_triu_tril(diag, triu, tril)
expected = gs.array([[9., 1., 2.], [
-1.,
9.,
3.,
], [-2., -3., 9.]])
result = mat
batch_diag = gs.eye(3)
batch_triu = gs.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]])
batch_tril = -1 * batch_triu
batch_mat = gs.mat_from_diag_triu_tril(batch_diag, batch_triu,
batch_tril)
batch_expected = gs.array([[[1., 1., 2.], [-1., 0., 3.],
[-2., -3., 0.]],
[[0., 4., 5.], [-4., 1., 6.],
[-5., -6., 0.]],
[[0., 7., 8.], [-7., 0., 9.],
[-8., -9., 1.]]])
batch_result = batch_mat
self.assertAllClose(expected, result)
self.assertAllClose(batch_expected, batch_result)
def test_mat_from_diag_triu_tril(self):
diag = gs.array([9.0, 9.0, 9.0])
triu = gs.array([1.0, 2.0, 3.0])
tril = -1 * triu
mat = gs.mat_from_diag_triu_tril(diag, triu, tril)
expected = gs.array([
[9.0, 1.0, 2.0],
[
-1.0,
9.0,
3.0,
],
[-2.0, -3.0, 9.0],
])
result = mat
batch_diag = gs.eye(3)
batch_triu = gs.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0],
[7.0, 8.0, 9.0]])
batch_tril = -1 * batch_triu
batch_mat = gs.mat_from_diag_triu_tril(batch_diag, batch_triu,
batch_tril)
batch_expected = gs.array([
[[1.0, 1.0, 2.0], [-1.0, 0.0, 3.0], [-2.0, -3.0, 0.0]],
[[0.0, 4.0, 5.0], [-4.0, 1.0, 6.0], [-5.0, -6.0, 0.0]],
[[0.0, 7.0, 8.0], [-7.0, 0.0, 9.0], [-8.0, -9.0, 1.0]],
])
batch_result = batch_mat
self.assertAllClose(expected, result)
self.assertAllClose(batch_expected, batch_result)
def samples_sym(self, mean_vec, cov, n_samples):
"""Generate symmetric matrices."""
n = self.mean.shape[-1]
samples_euclidean = gs.random.multivariate_normal(mean_vec, cov, (n_samples,))
diag = samples_euclidean[:, :n]
off_diag = samples_euclidean[:, n:] / gs.sqrt(2.0)
samples_sym = gs.mat_from_diag_triu_tril(
diag=diag, tri_upp=off_diag, tri_low=off_diag
)
return samples_sym
def __sample_spd(self, samples):
n = self.mean.shape[-1]
sym_matrix = self.manifold.logm(self.mean)
mean_euclidean = gs.hstack(
(gs.diagonal(sym_matrix)[None, :],
gs.sqrt(2.0) * gs.triu_to_vec(sym_matrix, k=1)[None, :]))[0]
samples_euclidean = gs.random.multivariate_normal(
mean_euclidean, self.cov, (samples, ))
diag = samples_euclidean[:, :n]
off_diag = samples_euclidean[:, n:] / gs.sqrt(2.0)
samples_sym = gs.mat_from_diag_triu_tril(diag=diag,
tri_upp=off_diag,
tri_low=off_diag)
samples_spd = self.manifold.expm(samples_sym)
return samples_spd