def dweighted_fseries(theta,ks,gamma=0.,delta=0.,shift=0.,scale=1.):
from numpy import sqrt
from weights import sqrt_weight_bias as wsqrt_bias
from weights import dsqrt_weight_bias as dwsqrt_bias
w = wsqrt_bias(theta,gamma=gamma,delta=delta,scale=scale,shift=shift)
dw = dwsqrt_bias(theta,gamma=gamma,delta=delta,scale=scale,shift=shift)
Psi = fseries(theta,ks,gamma=gamma,delta=delta,scale=scale,shift=shift)
dPsi = dfseries(theta,ks,gamma=gamma,delta=delta,scale=scale,shift=shift)
# yay product rule
return (dw*Psi.T + w*dPsi.T).T/sqrt(scale)
def weighted_fseries(theta,k,gamma=0.,delta=0.,shift=0.,scale=1.):
from spyctral.common.maps import standard_scaleshift as sss
from spyctral.common.maps import physical_scaleshift as pss
from numpy import sqrt, array
from weights import sqrt_weight_bias as wsqrt_bias
theta = array(theta)
theta = theta.ravel()
sss(theta,shift=shift,scale=scale)
psi = fseries(theta,k,gamma=gamma,delta=delta,shift=0.,scale=1.)
phi = (wsqrt_bias(theta,gamma=gamma,delta=delta,shift=0.,scale=1.)*psi.T).T
pss(theta,shift=shift,scale=scale)
# Scaling:
return phi/sqrt(scale)
