def basis_representation(self, matrix_representation):
"""Calculate the coefficients of given matrix in the basis.
Compute a 1d-array that corresponds to the input matrix in the basis
representation.
Parameters
----------
matrix_representation : array-like, shape=[..., n, n]
Matrix.
Returns
-------
basis_representation : array-like, shape=[..., dim]
Representation in the basis.
"""
if self.n == 2:
return matrix_representation[..., 1, 0][..., None]
if self.n == 3:
vec = gs.stack([
matrix_representation[..., 2, 1],
matrix_representation[..., 0, 2],
matrix_representation[..., 1, 0],
])
return gs.transpose(vec)
return gs.triu_to_vec(matrix_representation, k=1)
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
def sample(self, n_samples):
"""Generate samples for SPD manifold"""
if isinstance(self.manifold.metric, SPDMetricLogEuclidean):
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 = self.samples_sym(mean_euclidean, self.cov, n_samples)
else:
samples_sym = self.samples_sym(gs.zeros(self.manifold.dim),
self.cov, n_samples)
mean_half = self.manifold.powerm(self.mean, 0.5)
_samples = Matrices.mul(mean_half, samples_sym, mean_half)
return self.manifold.expm(_samples)
def to_vector(mat):
"""Convert a symmetric matrix into a vector.
Parameters
----------
mat : array-like, shape=[..., n, n]
Matrix.
Returns
-------
vec : array-like, shape=[..., n(n+1)/2]
Vector.
"""
if not gs.all(Matrices.is_symmetric(mat)):
logging.warning("non-symmetric matrix encountered.")
mat = Matrices.to_symmetric(mat)
return gs.triu_to_vec(mat)
