! scddns -- Copyright 2022 Paolo Luchini and Maurizio Quadrio
! http://CPLcode.net/Applications/FluidMechanics/Spectral-CD-DNS

!( Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE. !)

USE fft
have00=YES
totnproc=1
nprocy=1
myiproc=0
#define MPI_Barrier(MPI_COMM_WORLD)
VELOCITY=STRUCTURED ARRAY(u,v,w) OF COMPLEX
MOMFLUX=STRUCTURED ARRAY(uu,uv,vv,vw,ww,uw) OF COMPLEX
VELOCITY V(0..nx,-ny..ny,-1..nz+1)=0
MOMFLUX VV(0..nx,-ny..ny,-2..2)
INTEGER VVstart
INTEGER nxd=3∗nx DIV 2 -1; DO INC nxd UNTIL FFTfit(nxd)
INTEGER nyd=3∗ny -1; DO INC nyd UNTIL FFTfit(nyd)
ARRAY(0..nxd-1,0..nyd-1) OF VELOCITY Vd
ARRAY(0..nxd-1,0..nyd-1) OF MOMFLUX VVd

SUBROUTINE convolutions(INTEGER iz)
  Vd=0; LOOP FOR ix=0 TO nx
    DO Vd(ix,iy)=V(ix,iy,iz) FOR iy=0 TO ny
    DO Vd(ix,nyd+iy)=V(ix,iy,iz) FOR iy=-ny TO -1
    WITH Vd(ix,∗): IFTU(u); IFTU(v); IFTU(w)
  REPEAT LOOP
  DO WITH Vd(∗,iy): RFTU(u); RFTU(v); RFTU(w); FOR ALL iy
  DO WITH Vd(ix,iy), VVd(ix,iy)
    uu.REAL=u.REAL∗u.REAL; uu.IMAG=u.IMAG∗u.IMAG 
    uv.REAL=u.REAL∗v.REAL; uv.IMAG=u.IMAG∗v.IMAG 
    vv.REAL=v.REAL∗v.REAL; vv.IMAG=v.IMAG∗v.IMAG 
    vw.REAL=v.REAL∗w.REAL; vw.IMAG=v.IMAG∗w.IMAG 
    ww.REAL=w.REAL∗w.REAL; ww.IMAG=w.IMAG∗w.IMAG 
    uw.REAL=u.REAL∗w.REAL; uw.IMAG=u.IMAG∗w.IMAG 
  FOR ALL ix,iy
  DO WITH VVd(∗,iy): HFTU(uu); HFTU(uv); HFTU(vv); HFTU(vw); HFTU(ww); HFTU(uw) FOR ALL iy
  LOOP FOR ix=0 TO nx
    WITH VVd(ix,∗): FFTU(uu); FFTU(uv); FFTU(vv); FFTU(vw); FFTU(ww); FFTU(uw)
    DO VV(ix,iy,iz-VVstart)=VVd(ix,iy) FOR iy=0 TO ny
    DO VV(ix,iy,iz-VVstart)=VVd(ix,nyd+iy) FOR iy=-ny TO -1
  REPEAT LOOP
END convolutions