def fft_collocation(f,s=1.,t=0.,shift=0.,scale=1.):
from spyctral.fourier.fft import fft as fft_Psi
from spyctral.wiener.weights import sqrt_weight_bias as wx_sqrt
from spyctral.wiener.quad import gq
from numpy import sqrt
# This stuff can all be overhead
N = f.size
x = gq(N,s=1.,t=0.,shift=shift,scale=scale)[0]
modes = f/wx_sqrt(x,s=s,t=t,shift=shift,scale=scale)
temp = fft_Psi(modes,gamma=s-1.,delta=t)*float(sqrt(scale))
temp[-s:] = 0
temp[:s] = 0
return temp
def fft_galerkin(f,s=1.,t=0.,shift=0.,scale=1.):
from spyctral.fourier.fft import fft as fft_Psi
from spyctral.fourier.connection import int_connection as connect
from numpy import sqrt,ones,abs,array
N = len(f)
modes = fft_Psi(f)
#eps = 1e-16
#modes[abs(modes)<eps] = 0
# Is there a better way to do this?
for ss in range(int(s)):
for count in range(N-1):
modes[N-count-2] -= modes[N-count-1]
modes *= 2**(s/2.)/(1j)**s
modes = connect(modes,0,0,int(s-1),int(t))
modes[:s] = 0
modes[-s:] = 0
return modes*sqrt(scale)
