NumCosmoXcorKernelClosure

Representation of $W_\ell(k)$ after sampling. Selected by NcXcor:closure-type for all kernels in a computation.

NC_XCOR_KERNEL_CLOSURE_SPLINE discovers its grid: it bisects until the fit meets a tolerance, so the sample count grows as $\epsilon^{-1/4}$ and the resulting spacing is uneven.

NC_XCOR_KERNEL_CLOSURE_CHEBYSHEV prescribes its grid. $W_\ell(k)$ is an integral of a compactly supported window against $j_\ell(k\chi)$, which is entire in $k$, so $W_\ell$ is entire in $k$ for any window and a Chebyshev series converges geometrically on it. The order follows from the total phase $k_\mathrm{max}\chi_\mathrm{max}$ rather than being discovered: below the order that resolves that phase the expansion carries nothing, and above it accuracy is nearly free. Under Limber $W_\ell(k)$ is zero outside the multipole’s band in $k$; the Chebyshev closure places a panel cut at every band edge of the block, so every panel is again smooth.