pquadrature for oscillating integrals

[mzaffalon]

I get wrong results when I use pquadrature to compute the Fourier transform of a Gaussian, but only when abstol is set to a value other than the default value.

The commented out lines (changing the integration limits, leaving abstol to its default value and using quadgk) all give the correct result.

using PyPlot
using Cubature

function test_numerical_integration_FT()
    t_c, σ = 0.05, .7
    freq = linspace(-.2, .2, 21)
    y_imag = zeros(freq)
    for i = 1:length(freq)
        f_red = 2π * freq[i]
        y_imag[i] = -pquadrature(t -> exp(-(t - t_c)^2 / 2σ^2) * sin(f_red * t), -5., 5., abstol=1e-10)[1]
        #y_imag[i] = -pquadrature(t -> exp(-(t - t_c)^2 / 2σ^2) * sin(f_red * t), -5., 5.1, abstol=1e-10)[1]
        #y_imag[i] = -pquadrature(t -> exp(-(t - t_c)^2 / 2σ^2) * sin(f_red * t), -5., 5.)[1]
        #y_imag[i] = -quadgk(t -> exp(-(t - t_c)^2 / 2σ^2) * sin(f_red * t), -5., 5., abstol=1e-3, reltol=1e-3)[1]
    end
    # analytical FT
    y = sqrt(2π)σ * exp(-2π * freq .* (π * freq * σ^2 + 1im * t_c))
    figure(); grid(true)
    plot(freq, y_imag, label="numerical, imag")
    plot(freq, imag(y), label="analytical, imag")
    legend(frameon=false)
end