spd_learn.functional.exp_map_euclid

spd_learn.functional.exp_map_euclid(X, Cref, **kwargs)

Project matrices back to manifold by Euclidean exponential map.

The projection of a matrix \(\mathbf{X}\) from tangent space to manifold with Euclidean exponential map according to a reference matrix \(\mathbf{C}_\text{ref}\) is:

\[\mathbf{X}_\text{original} = \mathbf{X} + \mathbf{C}_\text{ref}\]

Parameters:

• X (ndarray, shape (..., n, m)) – Matrices in tangent space.

• Cref (ndarray, shape (n, m)) – Reference matrix.

Returns:

X_original – Matrices in manifold.

Return type:

ndarray, shape (…, n, m)

Notes

Added in version 0.4.

Changed in version 0.12: Add support for NumPy and PyTorch.