Timings and errors between hierarchical, Toeplitz-dot-Hankel, and asymptotic methods for converting Legendre expansions to Chebyshev expansions

ThreeMethodsComparison.jl

using FastTransforms, PyPlot

N = 40

t = Matrix{Float64}(N,6)
err = Matrix{Float64}(N,3)

for i in 1:N
    n = round(Int64, 10.0^(1 + 5*((i-1)/(N-1))))
    v = rand(n)
    println("n = ",n)

    leg2cheb(v);
    FastTransforms.th_leg2cheb(v);
    cjt(v,0.,0.);

    t[i,1] = @elapsed c1 = leg2cheb(v);
    t[i,2] = @elapsed c2 = FastTransforms.th_leg2cheb(v);
    t[i,3] = @elapsed c3 = cjt(v,0.,0.);

    p = plan_leg2cheb(v);
    p*v;
    t[i,4] = @elapsed p*v;
    p = FastTransforms.th_leg2chebplan(eltype(v),length(v));
    p*v;
    t[i,5] = @elapsed p*v;
    p = plan_cjt(v,0.,0.);
    p*v;
    t[i,6] = @elapsed p*v;

    gc()
    err[i,1] = norm(c1-c2,Inf)
    err[i,2] = norm(c1-c3,Inf)
    err[i,3] = norm(c2-c3,Inf)
end

NN = round.(Int,logspace(1,6,N))

clf();
loglog(NN,t[:,1],"^r",NN,t[:,2],"sg",NN,t[:,3],"pb")
loglog(NN,t[:,4],"vr",NN,t[:,5],"og",NN,t[:,6],"hb")
legend(["HODLR Total","T.*H Total","ASY Total","HODLR Execution","T.*H Execution","ASY Execution"],loc="upper left")
xlabel("\$N\$");ylabel("Execution Time (s)");grid(true)
savefig("Timings.png";bbox_inches="tight",dpi=300)

clf();
loglog(NN,err[:,1],"^r",NN,err[:,2],"sg",NN,err[:,3],"pb")
legend(["\$\|\|\$HODLR-T.*H\$\|\|_{\\infty}\$","\$\|\|\$HODLR-ASY\$\|\|_{\\infty}\$","\$\|\|\$T.*H-ASY\$\|\|_{\\infty}\$"],loc="upper left")
xlabel("\$N\$");ylabel("Maximum Absolute Error");grid(true)
savefig("Error.png";bbox_inches="tight",dpi=300)

Is it already known how transforms based on Potts, Steidl and Tasche (https://doi.org/10.1090/S0025-5718-98-00975-2) will fare in a comparison like this?