T3Weights.has_shared_tucker_weights

t3toolbox.tucker_tensor_train.T3Weights.has_shared_tucker_weights(sharing, rtol=1e-09)

def has_shared_tucker_weights(
        self,
        sharing:    typ.Sequence,   # len=d; one hashable group label per mode
        rtol:       float = 1e-9,   # relative tolerance on the Tucker-weight deviation
) -> NDArray:  # bool array, shape = stack_shape (scalar/0-d when unstacked)

True (per stack element) if the Tucker weights are equal within every sharing group – i.e. these weights are COMPATIBLE with the sharing partition: absorbing them into a tied T3 keeps it tied (Tucker weights scale the factors; equal group weights scale a shared factor identically). TT-bond weights are unconstrained (they never touch the factors).

Non-enforcing checker (see t3_tucker_weights_sharing_residual()): absorbing group-unequal weights is legitimate – it just unties the result. Weights built from the grouped T3-SVD (from_t3svd(x, sharing=...)) are group-equal by construction, and reciprocal/sqrt/concatenate/kronecker preserve group-equality.

Examples

>>> import numpy as np
>>> import t3toolbox.tucker_tensor_train as t3
>>> np.random.seed(0)
>>> x = t3.TuckerTensorTrain.randn((6, 6, 5), (3, 3, 2), (1, 3, 2, 1))
>>> tk, tt = x.data
>>> xs = t3.TuckerTensorTrain((tk[0], tk[0], tk[2]), tt)         # a tied point
>>> W = t3.T3Weights.from_t3svd(xs, sharing=(0, 0, 1))           # the grouped spectra
>>> print(bool(W.has_shared_tucker_weights((0, 0, 1))))
True
>>> W2 = t3.T3Weights.from_t3svd(xs)                             # per-mode spectra: unequal
>>> print(bool(W2.has_shared_tucker_weights((0, 0, 1))))
False
>>> xa = t3.t3_absorb_weights(xs, W.reciprocal())                # compatible weights ...
>>> print(bool(np.all(xa.has_shared_tucker_factors((0, 0, 1))))) # ... keep the T3 tied
True

Parameters:

• sharing (Sequence)

• rtol (float)

Return type:

NDArray