spd_learn.functional.vec_to_sym#

spd_learn.functional.vec_to_sym(x_vec, preserve_norm=True, upper=True)[source]#

Reconstructs symmetric matrices from vectorization.

This function is the inverse of sym_to_upper(). It reconstructs symmetric matrices from their vectorized triangular representation.

When preserve_norm=True, the inverse \(1/\sqrt{2}\) scaling is applied to off-diagonal elements to recover the original matrix values from a norm-preserving vectorization.

When preserve_norm=False, no scaling is applied (inverse of raw vech).

Parameters:

  • x_vec (torch.Tensor) – Vectorized triangular matrices with shape (…, n(n+1)/2).

  • preserve_norm (bool, default=True) – If True, applies inverse sqrt(2) scaling to off-diagonal elements. If False, uses raw values without scaling.

  • upper (bool, default=True) – If True, reconstructs from upper triangular representation. If False, reconstructs from lower triangular representation.

Returns:

Symmetric matrices with shape (…, n, n).

Return type:

torch.Tensor

See also

sym_to_upper()

Forward operation, vectorizes symmetric matrices.

ExpEig

Maps tangent vectors back to SPD manifold.

Examples

>>> import torch
>>> from spd_learn.functional import sym_to_upper, vec_to_sym
>>> X = torch.tensor([[1., 2.], [2., 3.]])
>>> v = sym_to_upper(X)
>>> X_reconstructed = vec_to_sym(v)
>>> torch.allclose(X, X_reconstructed)
True