binomial_combine_tensor

t3toolbox.backend.sampling_derivatives.binomial_combine_tensor(order)

def binomial_combine_tensor(
        order:  int,        # highest derivative order K
) -> NDArray:               # trs. shape=(order+1,order+1,order+1). trs[t,r,s] = C(t,r) if r+s==t else 0

Binomial tensor driving every jet convolution.

trs[t,r,s] = C(t,r) when r+s==t and 0 otherwise, so contracting it against the outer product of two jets reproduces sum_{r+s=t} C(t,r) (.)^(r) (.)^(s) – the product rule on Taylor jets. Used by both the pushthrough (input jet, s in {0,1} -> slice [:, :, :2]) and the combine (full s). Pure structure (exact integer binomials), so always numpy – it folds into the compiled program as a device constant on the jax path, like the uniform masks.

Parameters:

order (int)

Return type:

NDArray