Use relative tolerance when adaptively splining source functions for CMB spectra

Author: hersle

docs/src/comparison.md

@@ -409,7 +409,7 @@ l = 20:20:2000 # CLASS default is lmax = 2500
 Dl1 = Dl_class([:TT, :TE, :EE], l, pars)
 jl = SphericalBesselCache(l)
 Dl2 = Dl_symboltz([:TT, :TE, :EE], jl, pars)
-plot_compare(l, l, Dl1[:, 1], Dl2[:, 1], "l", "Dₗ(TT)"; tol = 1e-12)
+plot_compare(l, l, Dl1[:, 1], Dl2[:, 1], "l", "Dₗ(TT)"; tol = 9e-13)
 ```
 ```@example class
 plot_compare(l, l, Dl1[:, 2], Dl2[:, 2], "l", "Dₗ(TE)"; tol = 2e-14)

src/observables/angular.jl

@@ -181,12 +181,12 @@ function spectrum_cmb(ΘlAs::AbstractMatrix, ΘlBs::AbstractMatrix, P0s::Abstrac
 end
 
 """
-    spectrum_cmb(modes::AbstractVector, prob::CosmologyProblem, jl::SphericalBesselCache; normalization = :Cl, unit = nothing, kτ0s = 0.1*jl.l[begin]:2π/2:2*jl.l[end], u = (τ->tanh(τ)), u⁻¹ = (u->atanh(u)), Nlos = 768, integrator = TrapezoidalRule(), bgopts = (alg = Rodas4P(), reltol = 1e-9, abstol = 1e-9), ptopts = (alg = KenCarp4(), reltol = 1e-8, abstol = 1e-8), sourceopts = (atol = 1e0,), verbose = false, kwargs...)
+    spectrum_cmb(modes::AbstractVector, prob::CosmologyProblem, jl::SphericalBesselCache; normalization = :Cl, unit = nothing, kτ0s = 0.1*jl.l[begin]:2π/2:2*jl.l[end], u = (τ->tanh(τ)), u⁻¹ = (u->atanh(u)), Nlos = 768, integrator = TrapezoidalRule(), bgopts = (alg = Rodas4P(), reltol = 1e-9, abstol = 1e-9), ptopts = (alg = KenCarp4(), reltol = 1e-8, abstol = 1e-8), sourceopts = (rtol = 1e-2,), verbose = false, kwargs...)
 
 Compute the CMB power spectra `modes` (`:TT`, `:EE`, `:TE` or an array thereof) ``C_l^{AB}``'s at angular wavenumbers `ls` from the cosmological solution `sol`.
 If `unit` is `nothing` the spectra are of dimensionless temperature fluctuations relative to the present photon temperature; while if `unit` is a temperature unit the spectra are of dimensionful temperature fluctuations.
 """
-function spectrum_cmb(modes::AbstractVector, prob::CosmologyProblem, jl::SphericalBesselCache; normalization = :Cl, unit = nothing, kτ0s = 0.1*jl.l[begin]:2π/2:2*jl.l[end], u = (τ->tanh(τ)), u⁻¹ = (u->atanh(u)), Nlos = 768, integrator = TrapezoidalRule(), bgopts = (alg = Rodas4P(), reltol = 1e-9, abstol = 1e-9), ptopts = (alg = KenCarp4(), reltol = 1e-8, abstol = 1e-8), sourceopts = (atol = 1e0,), verbose = false, kwargs...)
+function spectrum_cmb(modes::AbstractVector, prob::CosmologyProblem, jl::SphericalBesselCache; normalization = :Cl, unit = nothing, kτ0s = 0.1*jl.l[begin]:2π/2:2*jl.l[end], u = (τ->tanh(τ)), u⁻¹ = (u->atanh(u)), Nlos = 768, integrator = TrapezoidalRule(), bgopts = (alg = Rodas4P(), reltol = 1e-9, abstol = 1e-9), ptopts = (alg = KenCarp4(), reltol = 1e-8, abstol = 1e-8), sourceopts = (rtol = 1e-2,), verbose = false, kwargs...)
     ls = jl.l
     sol = solve(prob; bgopts, verbose)
     τ0 = getsym(sol, prob.M.τ0)(sol)