compute_mu_jets

t3toolbox.backend.sampling_derivatives.compute_mu_jets(tt_cores, xi_jets, trs)

def compute_mu_jets(
        tt_cores:   typ.Sequence[NDArray],  # len=d, elm_shape=C+(rLi,nUi,rR(i+1))
        xi_jets:    typ.Sequence[NDArray],  # input jets,  len=d, elm_shape=(2,)+W+C+(nUi,)
        trs:        NDArray,                # binomial tensor -- ONLY its shape (order) is read here
) -> typ.Tuple[NDArray, ...]:               # mu_jets. len=d, elm_shape=(order+1,)+W+C+(rLi,). mu_jets[i][t]=mu_{i-1}^(t)

Left derivative-pushthrough jets (standard fused-recurrence form).

mu_jets[i] is the left edge variable entering core i (mu_{i-1}), stacked over derivative orders. The affine input jet (xi nonzero only at orders s in {0,1}) collapses each binomial pushthrough to a two-term recurrence mu_i^(t) = mu^(t).G.xi^(0) + t * mu^(t-1).G.xi^(1) – no dense trs tensor, no (order+1)^2 work. The two terms are folded into ONE contraction per core: stack [mu^(t), t * mu^(t-1)] on a jet-pair axis s and contract it together with the bond a against [G.xi^(0), G.xi^(1)] ('stWCa,sWCab->tWCb') – one larger GEMM for XLA to schedule turns the two-einsum form’s ~parity with the dense trs into a win. Equal to the dense compute_mu_jets_trs() to tolerance; see it for the binomial-tensor reference form.

Parameters:

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

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

• trs (NDArray)

Return type:

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