spd_learn.functional.mean_thompson#

spd_learn.functional.mean_thompson(X, *, tol=1e-06, maxiter=50, init=None, sample_weight=None)[source]#

Mean of SPD/HPD matrices according to the Thompson metric.

The Thompson mean of SPD/HPD matrices is described in [1].

Parameters:

  • X (ndarray, shape (..., n_matrices, n, n)) – Set of SPD/HPD matrices.

  • tol (float, default=1e-6) – Tolerance to stop the gradient descent.

  • maxiter (int, default=50) – Maximum number of iterations.

  • init (None | ndarray, shape (n, n), default=None) – A SPD/HPD matrix used to initialize the gradient descent. If None, the weighted Euclidean mean is used.

  • sample_weight (None) – Not used.

Returns:

M – Thompson mean.

Return type:

ndarray, shape (…, n, n)

Notes

Added in version 0.10.

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

See also

gmean

References

[1]

Differential geometry with extreme eigenvalues in the positive semidefinite cone C. Mostajeran, N. Da Costa, G. Van Goffrier and R. Sepulchre. SIAM Journal on Matrix Analysis and Applications, 2024