pyriemann.utils.distance.distance_thompson

pyriemann.utils.distance.distance_thompson(A, B, squared=False)

Thompson distance between SPD/HPD matrices.

The Thompson distance between two SPD/HPD matrices \(\mathbf{A}\) and \(\mathbf{B}\) is [1]:

\[d(\mathbf{A},\mathbf{B}) = \Vert \log(\mathbf{B}^{-1/2} \mathbf{A} \mathbf{B}^{-1/2}) \Vert_2 = \max_i | \log(\lambda_i) |\]

where \(\lambda_i\) are the joint eigenvalues of \(\mathbf{A}\) and \(\mathbf{B}\).

Parameters:

Andarray, shape (…, n, n)

First SPD/HPD matrices, at least 2D ndarray.

Bndarray, shape (…, n, n)

Second SPD/HPD matrices, same dimensions as A.

squaredbool, default=False

Return squared distance.

Returns:

dfloat or ndarray, shape (…,)

Thompson distance between A and B.

See also

distance

Notes

Added in version 0.10.

References

[1]

On certain contraction mappings in a partially ordered vector space A.C.Thompson. Proceedings of the American Mathematical Society, 1963.