spd_learn.functional.innerproduct#

spd_learn.functional.innerproduct(X, Y, Cref, metric='riemann')[source]#

Inner product according to a specified metric.

It calculates the inner product between matrices in the tangent space \(\mathbf{X}\) and \(\mathbf{Y}\) at \(\mathbf{C}_\text{ref}\), according to a specified metric.

Parameters:

  • X (ndarray, shape (..., n, n)) – First matrices in tangent space at Cref.

  • Y (ndarray, shape (..., n, n) | None) – Second matrices in tangent space at Cref. If None, Y is set to X, giving the squared norm of X.

  • Cref (ndarray, shape (n, n) | None) – Reference matrix.

  • metric (string | callable, default="riemann") – Metric used for inner product, can be: “euclid”, “logchol”, “logeuclid”, “riemann”, or a callable function.

Returns:

G – Inner product between X and Y.

Return type:

float or ndarray, shape (…,)

Notes

Added in version 0.11.

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

See also

innerproduct_euclid, innerproduct_logchol, innerproduct_logeuclid, innerproduct_riemann