Source code for geomstats.distributions.lognormal

"""LogNormal Distribution."""

import geomstats.backend as gs
from geomstats.geometry.euclidean import Euclidean, EuclideanMetric
from geomstats.geometry.hermitian_matrices import expmh, powermh
from geomstats.geometry.matrices import Matrices, MatricesMetric
from geomstats.geometry.spd_matrices import (

[docs] class LogNormalSPD: """LogNormal Distribution on manifold of SPD Matrices.""" def __init__(self, space, mean, cov): self._check_metric(space) = space self.mean = mean self.cov = cov @staticmethod def _check_metric(space): if not isinstance(space.metric, SPDLogEuclideanMetric) and not isinstance( space.metric, SPDAffineMetric ): raise ValueError( "Invalid Metric, " "Should be of type SPDLogEuclideanMetric" "or SPDAffineMetric" )
[docs] 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
[docs] def sample(self, n_samples): """Generate samples for SPD manifold.""" if isinstance(, SPDLogEuclideanMetric): sym_matrix = logmh(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.cov, n_samples ) mean_half = powermh(self.mean, 0.5) _samples = Matrices.mul(mean_half, samples_sym, mean_half) return expmh(_samples)
[docs] class LogNormalEuclidean: """LogNormal Distribution on Euclidean Space.""" def __init__(self, space, mean, cov): self._check_metric(space) = space self.mean = mean self.cov = cov @staticmethod def _check_metric(space): if type(space.metric) not in (EuclideanMetric, MatricesMetric): raise ValueError( "Invalid Metric, " "Should be of type EuclideanMetric or MatricesMetric" )
[docs] def sample(self, n_samples): """Generate samples for Euclidean Manifold.""" _samples = gs.random.multivariate_normal(self.mean, self.cov, (n_samples,)) return gs.exp(_samples)
[docs] class LogNormal: """LogNormal Distribution on manifold of SPD Matrices and Euclidean Spaces. (1) For Euclidean Spaces, if X is distributed as Normal(mean, cov), then exp(X) is distributed as LogNormal(mean, cov). (2) For SPDMatrices, there are different distributions based on metric a)LogEuclidean Metric : With this metric, LogNormal distribution is defined by transforming the mean -- an SPD matrix -- into a symmetric matrix through the Matrix logarithm, which gives the element "log-mean" that now belongs to a vector space. This log-mean and given cov are used to parametrize a Normal Distribution. b)AffineInvariant Metric : X is distributed as LogNormal(mean, cov) if exp(mean^{1/2}.X.mean^{1/2}) is distributed as Normal(0, cov) Parameters ---------- space : Manifold obj, {Euclidean(n), SPDMatrices(n)} Manifold to sample over. Manifold should be instance of Euclidean or SPDMatrices. mean : array-like, shape=[dim] if space is Euclidean Space shape=[n, n] if space is SPD Manifold Mean of the distribution. cov : array-like, shape=[dim, dim] if space is Euclidean Space shape=[n*(n+1)/2, n*(n+1)/2] if space is SPD Manifold Covariance of the distribution. Example -------- >>> import geomstats.backend as gs >>> from geomstats.geometry.spd_matrices import SPDMatrices >>> from geomstats.distributions.lognormal import LogNormal >>> mean = 2 * gs.eye(3) >>> cov = gs.eye(6) >>> SPDManifold = SPDMatrices(3, metric=SPDAffineMetric(3)) >>> LogNormalSampler = LogNormal(SPDManifold, mean, cov) >>> data = LogNormalSampler.sample(5) References ---------- .. [LNGASPD2016] A. Schwartzman, "LogNormal distributions and" "Geometric Averages of Symmetric Positive Definite Matrices.", International Statistical Review 84.3 (2016): 456-486. """ def __new__(cls, space, mean, cov=None): """Dispatch based on space.""" if not isinstance(space, SPDMatrices) and not isinstance(space, Euclidean): raise ValueError( "Invalid Manifold object. Should be of type SPDMatrices or Euclidean" ) if not space.belongs(mean): raise ValueError( "Invalid Value in mean, doesn't belong to ", type(space).__name__ ) if cov is not None: valid_cov_shape = (space.dim, space.dim) if cov.ndim != 2 or (cov.shape[0], cov.shape[1]) != valid_cov_shape: raise ValueError( "Invalid Shape, cov should have shape", valid_cov_shape ) else: cov = gs.eye(space.dim) if isinstance(space, Euclidean): return LogNormalEuclidean(space, mean, cov) return LogNormalSPD(space, mean, cov)