tv_gauge_residual#

t3toolbox.backend.tv_operations.tv_gauge_residual(frame, variations)#
def tv_gauge_residual(
        frame: typ.Tuple[
            typ.Sequence[NDArray],  # up_tucker_cores
            typ.Sequence[NDArray],  # down_tt_cores
            typ.Sequence[NDArray],  # left_tt_cores
            typ.Sequence[NDArray],  # right_tt_cores
        ],
        variations: typ.Tuple[
            typ.Sequence[NDArray],  # tucker_variations
            typ.Sequence[NDArray],  # tt_variations
        ],
) -> NDArray:  # shape = variation stack_shape (K+C); per stack element (scalar/0-d when unstacked)

Max violation of the gauge conditions for a tangent vector, per stack element.

The gauged tangent space requires each tucker variation orthogonal to its up-core, and each left-interior tt variation orthogonal to its left-core (see tv_orthogonal_gauge_projection()). Returns the max absolute gauge inner product reduced over the non-stack axes (shape = the variation stack K+C); a caller thresholds it (<= atol).

Parameters:

  • frame (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

  • variations (t3toolbox.backend.common.typ.Tuple[t3toolbox.backend.common.typ.Sequence[NDArray], t3toolbox.backend.common.typ.Sequence[NDArray]])

Return type:

NDArray