fv_variation_shapes

t3toolbox.backend.fv_operations.fv_variation_shapes(frame)

def fv_variation_shapes(
        frame:  typ.Tuple,   # (U, O, P, Q) frame data; len=d each, elm_shape=stack_shape+(...)
) -> VariationShapes:        # (tucker_variation_shapes, tt_variation_shapes); WITHOUT the stack

The variation shapes of a frame: (nD_i, N_i) per Tucker variation and (rL_i, nU_i, rR_i) per TT variation, read off the frame cores.

The backend twin of the frontend T3Frame.variation_shapes – and the ONE place the frame-to-variation axis convention is written down for the ragged layer. Frame bookkeeping is non-obvious (the TT variation takes its left bond from the core itself but its right bond from the core’s own trailing axis, which is the NEXT bond – the gauge shift left[:-1] / right[1:] in mask form), so open-coding these indices is how they drift. Feed the result to fv_variations_zeros() / fv_variations_randn().

Parameters:

frame (t3toolbox.backend.common.typ.Tuple)

Return type:

VariationShapes