def scale_nodes(L,N,delta=0.5,s=1.,t=0.):
from spyctral.wiener.quad import gq
from spyctral.common.scaling import scale_factor
[x,w] = gq(N,s=s,t=t)
return scale_factor(L,x,delta=delta)
def fft_collocation_overhead(N,s=1.,t=0.,shift=0.,scale=1.):
from numpy import sqrt
from spyctral.fourier.fft import fft_overhead
from spyctral.wiener.weights import sqrt_weight_bias as wx_sqrt
from spyctral.wiener.quad import gq
overhead = fft_overhead(N,gamma=s-1.,delta=t)
x = gq(N,s=1.,t=0.,shift=shift,scale=scale)[0]
premult = sqrt(scale)/wx_sqrt(x,s=s,t=t,shift=shift,scale=scale)
return [premult,overhead]
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 ifft_collocation(F,s=1.,t=0.,shift=0.,scale=1.):
from spyctral.fourier.fft import ifft as ifft_Psi
from spyctral.wiener.weights import sqrt_weight_bias as wx_sqrt
from spyctral.wiener.quad import gq
from numpy import sqrt
from spyctral.fourier.fft import fft_overhead, ifft_online
N = F.size
#overhead = fft_overhead(N,g=s-1.,d=t)
#fx = ifft_online(f,overhead)
fx = ifft_Psi(F,gamma=s-1.,delta=t)
x = gq(N,s=1.,t=0.,shift=shift,scale=scale)[0]
fx *= wx_sqrt(x,s=s,t=t,shift=shift,scale=scale)/float(sqrt(scale))
#print "hi"
return fx