utv_corewise_inner#

t3toolbox.backend.utv_operations.utv_corewise_inner(variations_a, variations_b, n_stack)#
def utv_corewise_inner(
        variations_a:  typ.Tuple,  # UT3Variations .data: (tkv, ttv, shape, masks), supercore stack = K + C
        variations_b:  typ.Tuple,  # UT3Variations .data: same structure as variations_a
        n_stack:       int,        # number of leading stack axes (K + C) to keep; 0 -> a single scalar
) -> NDArray:                      # coordinate inner product, shape = stack_shape[:n_stack] (scalar if n_stack==0)

The raw coordinate (corewise) inner product of two uniform tangents’ variations – mask-applied and stack-keeping; not the Hilbert-Schmidt metric.

The raw-tuple backend twin of corewise_inner() (which delegates here). Masks both variation supercores once (ufv_apply_variations_masks – so the garbage padding is zeroed, never summed into the dot), then sums the elementwise product over the leading mode index d and the trailing core axes, keeping the first n_stack stack axes (one dot per stacked tangent). Pass n_stack = len(stack_shape) to keep the whole K + C stack, or n_stack = 0 to collapse to a single scalar – the unstacked optimizer’s coordinate ⟨·,·⟩, the check-free twin the geometries’ inner binds (it equals Hilbert-Schmidt only on an orthonormal, gauged frame). Masking makes it robust to garbage padding, so the reduction needs no clean-padding precondition.

Parameters:

  • variations_a (t3toolbox.backend.common.typ.Tuple)

  • variations_b (t3toolbox.backend.common.typ.Tuple)

  • n_stack (int)

Return type:

NDArray