spd_learn.modules.SymmetricPositiveDefinite#

class spd_learn.modules.SymmetricPositiveDefinite(mapping='exp', device=None, dtype=None)[source]#

Bases: Module

Symmetric Positive Definite Manifold parametrization.

This module projects a matrix onto the SPD manifold by first ensuring it is symmetric and then applying either the matrix exponential or the matrix softplus function.

Parameters:

  • mapping (str, optional) – Mapping from symmetric matrices to SPD matrices. Default is “exp”. Options are: “exp” and “softplus”

  • device (torch.device, optional) – Device for the module. Default is None. Note: This parametrization class has no parameters or buffers, so device is accepted for API consistency but not used.

  • dtype (torch.dtype, optional) – Data type for the module. Default is None. Note: This parametrization class has no parameters or buffers, so dtype is accepted for API consistency but not used.

Examples

>>> import torch
>>> from spd_learn.modules import SymmetricPositiveDefinite
>>> # Using matrix exponential (default)
>>> spd_exp = SymmetricPositiveDefinite(mapping="exp")
>>> X = torch.randn(2, 3, 3)
>>> S = spd_exp(X)  # Projects to SPD manifold
>>> # Using softplus mapping
>>> spd_softplus = SymmetricPositiveDefinite(mapping="softplus")
>>> S = spd_softplus(X)
forward(X)[source]#

Forward pass projecting input onto the SPD manifold.

Parameters:

X (torch.Tensor) – Input matrix of shape (…, n, n).

Returns:

The projected SPD matrix of shape (…, n, n).

Return type:

torch.Tensor

right_inverse(X)[source]#

Map from the SPD manifold onto the tangent space at identity.

This is useful for initializing parameters from SPD matrices when using this module as a parametrization.

Parameters:

X (torch.Tensor) – Input SPD matrix of shape (…, n, n).

Returns:

The corresponding tangent symmetric matrix.

Return type:

torch.Tensor