def int_connection(modes,gamma=0.,delta=0.,G=0,D=0):
"""
Implements the connection coefficient relation, taking the modes from
Szego-Fourier class (g,d) to Szego-Fourier class (g+G,d+D), and casts G and D
as integers so that the connection relation is sparse.
The convention assumed for an even number of modes is that they are centered
around the zero frequency, and that there is one more negative mode than
positive modes. Assumes G,D>0. (See int_connection_backward for inverse)
"""
from numpy import append
from scipy import conj
from spyctral.jacobi.jfft import rmatrix_apply_seq as jconnection
G = int(G)
D = int(D)
if (G+D)>0:
N = modes.shape[0]
[cmodes,smodes] = sc_collapse(modes,N)
cmodes = jconnection(cmodes,delta-1/2.,gamma-1/2.,D,G)
smodes = jconnection(smodes,delta+1/2.,gamma+1/2.,D,G)
return sc_expand(cmodes,smodes,N)
else:
return modes.copy()
from spyctral.jacobi.jfft import rmatrix_invert as jconnection_inv
from spyctral.jacobi.jfft import rmatrix_apply_seq as jconnection
from spyctral.fourier.connection import sc_collapse, sc_expand
from numpy import append
from scipy import conj
G = gamma; D = delta; delta = 0; gamma=0;
NEven = (N%2)==0
ucopy = u.copy()
if NEven:
N += 1
ucopy[0] /= 2.
ucopy = append(ucopy,conj(ucopy[0]))
[cmodes,smodes] = sc_collapse(ucopy,N)
cmodes = jconnection(cmodes,delta-1/2.,gamma-1/2.,D,G)
smodes = jconnection(smodes,delta+1/2.,gamma+1/2.,D,G)
utemp = sc_expand(cmodes,smodes,N)
if NEven:
utemp[0] += conj(utemp[-1])
utemp = utemp[:-1]
cmodes3 = jconnection_inv(cmodes,delta-1/2.,gamma-1/2.,D,G)
smodes3 = jconnection_inv(smodes,delta+1/2.,gamma+1/2.,D,G)
u2 = sc_expand(cmodes3,smodes3,N)
utemp2 = int_connection(u,gamma=0.,delta=0.,G=G,D=D)
u3 = int_connection_backward(utemp2,gamma=0.,delta=0.,G=G,D=D)