pyriemann.geometry.tangentspace.innerproduct_wasserstein¶

pyriemann.geometry.tangentspace.innerproduct_wasserstein(X, Y, Cref)[source]¶

Wasserstein inner product.

Wasserstein inner product \(\mathbf{g}\) between symmetric/Hermitian matrices in tangent space \(\mathbf{X}\) and \(\mathbf{Y}\) at \(\mathbf{C}_\text{ref}\) is given in Eq.(7) of [1]. See also [2].

Parameters:

Xndarray, shape (…, n, n): First symmetric/Hermitian matrices in tangent space at Cref.
Yndarray, shape (…, n, n) | None: Second symmetric/Hermitian matrices in tangent space at Cref. If None, Y is set to X, giving the squared norm of X.
Crefndarray, shape (n, n): Reference SPD/HPD matrix.

Returns:

Gfloat or ndarray, shape (…,): Wasserstein inner product between X and Y.