clenshaw_vs_gauss.jl

using Plots, FastGaussQuadrature, FastTransforms
fejer1(N) = FastTransforms.fejernodes1(Float64, N), FastTransforms.fejerweights1(FastTransforms.FastTransforms.chebyshevmoments1(Float64, N))
fejer2(N) = FastTransforms.fejernodes2(Float64, N), FastTransforms.fejerweights2(FastTransforms.FastTransforms.chebyshevmoments2(Float64, N))
clenshawcurtis(N) = FastTransforms.clenshawcurtisnodes(Float64, N), FastTransforms.clenshawcurtisweights(FastTransforms.FastTransforms.chebyshevmoments1(Float64, N))
x = range(-1.2, stop = 1.2, length = 1000)
y = range(-0.4, stop = 0.4, length = 1000÷3)
r(z, x, w) = sum(k->w[k]/(z - x[k]), eachindex(x))
ϕ(z) = log((z+1)/(z-1))
quadrature_contour(xs, w; kwargs...) = contour(x, y, (x, y) -> abs(r(x + y*im, xs, w) - ϕ(x + y*im)); levels=map(i->1/10^i, 0:10), aspect_ratio=1, colorbar=false, xlimits=(-1.5, 1.5), ylimits=(-0.5, 0.5), kwargs...)
plts = [quadrature_contour(clenshawcurtis(64)...; title="Clenshaw-Curtis"),
        quadrature_contour(gausslegendre(64)...; title="Gauss-Legendre"),
        quadrature_contour(fejer1(64)...; title="Fejér 1"),
        quadrature_contour(fejer2(64)...; title="Fejér 2"),]
plot(plts..., layout=(2, 2), dpi=400, titlefontsize=10)