def dweighted_wiener(x,k,s=1.,t=0.,shift=0.,scale=1.):
from numpy import sqrt, array
from spyctral.fourier.eval import fseries as genfourier
from spyctral.fourier.eval import dfseries as dgenfourier
from spyctral.wiener.maps import dtheta_dx
from spyctral.wiener.maps import x_to_theta as x2theta
from spyctral.wiener.weights import sqrt_weight_bias as wx_sqrt
from spyctral.wiener.weights import dsqrt_weight_bias as dwx_sqrt
# Preprocessing and setup
x = array(x)
x = x.ravel()
k = array(k,dtype=int)
k = k.ravel()
theta = x2theta(x,shift=shift,scale=scale)
# First term: wx_sqrt * d/dx Phi
psi = (dtheta_dx(x,shift=shift,scale=scale)*dgenfourier(theta,k,s-1.,t).T).T
psi = (wx_sqrt(x,s,t,shift=shift,scale=scale)*(psi.T)).T
# Second term: d/dx wx_sqrt * Phi
psi += (dwx_sqrt(x,s,t,shift=shift,scale=scale)*genfourier(theta,k,s-1.,t).T).T
return psi/sqrt(scale)
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 weighted_wiener(x,k,s=1.,t=0.,shift=0.,scale=1.):
from numpy import sqrt, array
from spyctral.fourier.eval import fseries as genfourier
from spyctral.wiener.maps import x_to_theta as x2theta
from spyctral.wiener.weights import sqrt_weight_bias as wx_sqrt
# Preprocessing and setup
x = array(x)
x = x.ravel()
k = array(k,dtype=int)
k = k.ravel()
theta = x2theta(x,shift=shift,scale=scale)
psi = genfourier(theta,k,s-1.,t)
psi = (wx_sqrt((x-shift)/scale,s,t)*(psi.T)).T
return psi/sqrt(scale)
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
def xiw(x,n,s=1.,t=0.,shift=0.,scale=1.):
from numpy import sqrt, array
from spyctral.fourier.eval import fseries as genfourier
from spyctral.wiener.weights import sqrt_weight_bias as wx_sqrt
from spyctral.wiener.maps import x_to_theta as x2theta
# Preprocessing and setup
x = array(x)
x = x.ravel()
n = array(n,dtype=int)
n = n.ravel()
theta = x2theta(x,shift=shift,scale=scale)
psi = genfourier(theta,n,s-1.,t).real
psi = (wx_sqrt((x-shift)/scale,s,t)*(psi.T)).T
psi[:,n==0] *= sqrt(2)
psi[:,n!=0] *= 2
return psi/sqrt(scale)