pyriemann.utils.distance.distance_chol

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

Cholesky distance between SPD/HPD matrices.

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

\[d(\mathbf{A},\mathbf{B}) = \Vert \text{chol}(\mathbf{A}) - \text{chol}(\mathbf{B}) \Vert_F\]

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 (…,)

Cholesky distance between A and B.

See also

distance

Notes

Added in version 0.7.

References

[1]

Non-Euclidean statistics for covariance matrices, with applications to diffusion tensor imaging I.L. Dryden, A. Koloydenko, D. Zhou. Ann Appl Stat, 2009, 3(3), pp. 1102-1123.