from pylab import plot, semilogy
from numpy import loadtxt, pi
D = loadtxt("conv.txt")
N = D[:, 0]
E = D[:, 1]
E_exact = 3*pi/8

figure(figsize=(8, 6), dpi=80)
semilogy(N, abs(E-E_exact), "k-")
grid()
title("Convergence of an FFT Poisson solver (semilogy)")
xlabel("N (number of PW in each direction)")
ylabel("E  -  E_exact  [a.u.]")
savefig("fft_convergence_semilogy.png")

figure(figsize=(8, 6), dpi=80)
calculated = abs(E-E_exact)
loglog(N, calculated, "ko", label="calculated")
predicted = 1/N
predicted = predicted * (calculated[-1] /  predicted[-1])
loglog(N, predicted, "g-", label="$1/N$")
grid()
title("Convergence of an FFT Poisson solver (loglog)")
xlabel("N (number of PW in each direction)")
ylabel("E  -  E_exact  [a.u.]")
legend()
savefig("fft_convergence_loglog.png")