compute_sigma_jets_trs#

t3toolbox.backend.sampling_derivatives.compute_sigma_jets_trs(var_tt_cores, right_tt_cores, down_tt_cores, xi_jets, dxi_jets, mu_jets, trs)#
def compute_sigma_jets_trs(
        var_tt_cores:   typ.Sequence[NDArray],  # dG. len=d, elm_shape=K+C+(rLi,nUi,rR(i+1))
        right_tt_cores: typ.Sequence[NDArray],  # Q.  len=d, elm_shape=C+(rRi,nUi,rR(i+1))
        down_tt_cores:  typ.Sequence[NDArray],  # O.  len=d, elm_shape=C+(rLi,nOi,rR(i+1))
        xi_jets:        typ.Sequence[NDArray],  # frame input jets, len=d, elm_shape=(2,)+W+C+(nUi,)
        dxi_jets:       typ.Sequence[NDArray],  # var  input jets, len=d, elm_shape=(2,)+W+K+C+(nOi,)
        mu_jets:        typ.Sequence[NDArray],  # frame left jets,  len=d, elm_shape=(order+1,)+W+C+(rLi,)
        trs:            NDArray,                # binomial tensor, shape=(order+1,order+1,order+1)
) -> typ.Tuple[NDArray, ...]:                   # sigma_jets. len=d, elm_shape=(order+1,)+W+K+C+(rR(i+1),)

Variation-leftward edge-variable jets sigma (the jet-ified Algorithm-7 sigma recursion).

sigma_i = sigma_{i-1} Q_i(xi_i) + mu_{i-1} dG_i(xi_i) + mu_{i-1} O_i(dxi_i) – three pushthroughs ('trs,rWCa,Caib,sWCi->tWCb'): the carried sigma jet through Q, and the frame mu jet through the variation core dG and the down frame O. Boundary sigma_0 = 0 (all orders).

Parameters:

  • var_tt_cores (t3toolbox.backend.common.typ.Sequence[NDArray])

  • right_tt_cores (t3toolbox.backend.common.typ.Sequence[NDArray])

  • down_tt_cores (t3toolbox.backend.common.typ.Sequence[NDArray])

  • xi_jets (t3toolbox.backend.common.typ.Sequence[NDArray])

  • dxi_jets (t3toolbox.backend.common.typ.Sequence[NDArray])

  • mu_jets (t3toolbox.backend.common.typ.Sequence[NDArray])

  • trs (NDArray)

Return type:

t3toolbox.backend.common.typ.Tuple[NDArray, Ellipsis]