p18: Chebyshev differentiation via FFT

We repeat p11 but using FFT.

%config InlineBackend.figure_format = 'svg'
from chebfftPy import chebfft
from numpy import pi,linspace,sin,cos,exp,round,zeros,arange,real,flipud
from numpy.fft import fft,ifft
from matplotlib.pyplot import figure,subplot,plot,grid,title,axis

figure(figsize=(10,12))
plot_count = 1

for N in [10,20]:
    xx = linspace(-1.0,1.0,100)
    ff = exp(xx)*sin(5*xx)
    x = cos(arange(0,N+1)*pi/N)
    f = exp(x)*sin(5*x)
    error = chebfft(f) - exp(x)*(sin(5*x)+5*cos(5*x))
    subplot(3,2,plot_count); plot_count +=1
    plot(xx,ff,'-',x,f,'o')
    grid(True)
    axis([-1, 1, -4,2])
    title('f(x), N='+str(N))
    subplot(3,2,plot_count); plot_count +=1
    plot(x,error,'-o')
    title('error in f\'(x), N='+str(N))
    grid(True)