pyriemann.geometry.tangentspace.innerproduct_logchol¶

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

Log-Cholesky inner product.

Log-Cholesky inner product \(\mathbf{g}\) between symmetric matrices in tangent space \(\mathbf{X}\) and \(\mathbf{Y}\) at \(\mathbf{C}_\text{ref}\) is given in [1].

Parameters:

Xndarray, shape (…, n, n): First symmetric matrices in tangent space at Cref.
Yndarray, shape (…, n, n) | None: Second symmetric 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 matrix.

Returns:

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