T3Weights.from_t3svd

classmethod t3toolbox.tucker_tensor_train.T3Weights.from_t3svd(x, **kwargs)

def from_t3svd(cls, x: 'TuckerTensorTrain', **kwargs) -> 'T3Weights':

The singular values of x as a weight object – the canonical (unmodified) σ’s, so from_t3svd(x).reciprocal() is the inverse-σ (Grasedyck-Kramer) weighting. **kwargs pass to t3svd(); the weights are shape-consistent with the t3svd result (with x itself when x has minimal ranks, the usual case).

The σ’s are per-coordinate in the T3-SVD gauge. As a tangent metric (T3FrameWeights.from_t3weights) they pair with a frame whose Tucker basis is the singular basis – build it with t3svd_orthogonal_representations() (one SVD, gauge-preserving), not with the default t3_orthogonal_representations(x), whose re-orthogonalization rotates the basis arbitrarily.

Parameters:

x (TuckerTensorTrain)

Return type:

T3Weights