mean_harm_spd#
- hypercoil.functional.semidefinite.mean_harm_spd(input: Tensor, axis: int | Sequence[int] = 0, require_nonsingular: bool = True) Tensor[source]#
The harmonic mean is computed as the matrix inverse of the Euclidean mean of matrix inverses:
\(\bar{X} = \left(\frac{1}{N}\sum_{i=1}^N X_{i}^{-1}\right)^{-1}\)
- Dimension:
- Input : \((N, *, D, D)\)
N denotes batch size,
*denotes any number of intervening dimensions, D denotes matrix row and column dimension.- Output : \((*, D, D)\)
As above.
- Parameters:
- inputTensor
Batch of matrices over which the Euclidean mean is to be computed.
- axisint
Axis or axes over which the mean is computed.
- require_nonsingularbool (default True)
Indicates that the input matrix must be nonsingular. If this is False, then the Moore-Penrose pseudoinverse is computed instead of the inverse.
- Returns:
- outputTensor
Log-Euclidean mean of the input batch.