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spectral_transforms.F90
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!>@brief The module 'spectral_transforms' contains the subroutines spec_to_four and four_to_grid
module spectral_transforms
use kinddef
use mpi_wrapper, only : mp_alltoall,mype,npes
use stochy_internal_state_mod, only : stochy_internal_state
use stochy_namelist_def
private
public :: spec_to_four, four_to_grid,dozeuv_stochy,dezouv_stochy
public :: initialize_spectral,stochy_la2ga
integer, public :: ls_dim, &
ls_max_node, &
len_trie_ls, &
len_trio_ls, &
jcap,latg,latg2, &
skeblevs,levs,lnt, &
lonf,lonfx
!
integer, public, allocatable :: lat1s_a(:), lon_dims_a(:)
real(kind_dbl_prec), public, allocatable, dimension(:) :: colrad_a, wgt_a, rcs2_a, &
sinlat_a, coslat_a
contains
!>@brief The subrountine 'spec_to_four' converts the spherical harmonics to fourier coefficients
!>@details This code is taken from the legacy spectral GFS
subroutine spec_to_four(flnev,flnod,plnev,plnod, &
ls_node, &
workdim,four_gr, &
ls_nodes,max_ls_nodes, &
lats_nodes,global_lats, &
lats_node,ipt_lats_node, &
nvars )
!
implicit none
!
external esmf_dgemm
!
integer, intent(in) :: nvars
real(kind=kind_dbl_prec) flnev(len_trie_ls,2*nvars)
real(kind=kind_dbl_prec) flnod(len_trio_ls,2*nvars)
!
real(kind=kind_dbl_prec) plnev(len_trie_ls,latg2)
real(kind=kind_dbl_prec) plnod(len_trio_ls,latg2)
!
integer ls_node(ls_dim,3)
!
!cmr ls_node(1,1) ... ls_node(ls_max_node,1) : values of L
!cmr ls_node(1,2) ... ls_node(ls_max_node,2) : values of jbasev
!cmr ls_node(1,3) ... ls_node(ls_max_node,3) : values of jbasod
!
! local scalars
! -------------
!
integer j, l, lat, lat1, n, kn, n2,indev,indod
!
! local arrays
! ------------
!
real(kind=kind_dbl_prec), dimension(nvars*2,latg2) :: apev, apod
! xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
!
integer workdim, lats_node, ipt_lats_node
!
real(kind=kind_dbl_prec) four_gr(lonf+2,nvars,workdim)
!
integer ls_nodes(ls_dim,npes)
integer, dimension(npes) :: max_ls_nodes, lats_nodes
integer, dimension(latg) :: global_lats
real(kind=4),target,dimension(2,nvars,ls_dim*workdim,npes):: workr,works
real(kind=4),pointer:: work1dr(:),work1ds(:)
integer, dimension(npes) :: kpts, kptr, sendcounts, recvcounts, sdispls
!
integer ilat,ipt_ls, lmax,lval,jj,nv
integer node,arrsz,my_pe,nvar
integer ilat_list(npes) ! for OMP buffer copy
!
! statement functions
! -------------------
!
integer indlsev, jbasev, indlsod, jbasod
!
include 'function_indlsev'
include 'function_indlsod'
!
real(kind=kind_dbl_prec), parameter :: cons0=0.0d0, cons1=1.0d0
!
! xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
!
n2=2*nvars
arrsz=n2*ls_dim*workdim*npes
kpts = 0
!
do j = 1, ls_max_node ! start of do j loop #####################
!
l = ls_node(j,1)
jbasev = ls_node(j,2)
jbasod = ls_node(j,3)
indev = indlsev(l,l)
indod = indlsod(l+1,l)
!
lat1 = lat1s_a(l)
! compute the even and odd components of the fourier coefficients
!
! compute the sum of the even real terms for each level
! compute the sum of the even imaginary terms for each level
!
call esmf_dgemm('t', 'n', n2, latg2-lat1+1, (jcap+3-l)/2, &
cons1, flnev(indev,1), len_trie_ls, plnev(indev,lat1), &
len_trie_ls, cons0, apev(1,lat1), n2 )
!
! compute the sum of the odd real terms for each level
! compute the sum of the odd imaginary terms for each level
!
call esmf_dgemm('t', 'n', n2, latg2-lat1+1, (jcap+2-l)/2, &
cons1, flnod(indod,1), len_trio_ls, plnod(indod,lat1), &
len_trio_ls, cons0, apod(1,lat1), n2 )
!
!cxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
!
! compute the fourier coefficients for each level
! -----------------------------------------------
!
ilat_list(1) = 0
do node = 1, npes - 1
ilat_list(node+1) = ilat_list(node) + lats_nodes(node)
end do
!$omp parallel do private(node,jj,ilat,lat,ipt_ls,nvar,kn,n2)
do node=1,npes
do jj=1,lats_nodes(node)
ilat = ilat_list(node) + jj
lat = global_lats(ilat)
ipt_ls = min(lat,latg-lat+1)
if ( ipt_ls >= lat1s_a(ls_nodes(j,mype+1)) ) then
kpts(node) = kpts(node) + 1
kn = kpts(node)
!
if ( lat <= latg2 ) then
! northern hemisphere
do nvar=1,nvars
n2 = nvar + nvar
works(1,nvar,kn,node) = apev(n2-1,ipt_ls) + apod(n2-1,ipt_ls)
works(2,nvar,kn,node) = apev(n2,ipt_ls) + apod(n2,ipt_ls)
enddo
else
! southern hemisphere
do nvar=1,nvars
n2 = nvar + nvar
works(1,nvar,kn,node) = apev(n2-1,ipt_ls) - apod(n2-1,ipt_ls)
works(2,nvar,kn,node) = apev(n2,ipt_ls) - apod(n2,ipt_ls)
enddo
endif
endif
enddo
enddo
!
enddo ! end of do j loop #######################################
!
kptr = 0
do node=1,npes
do l=1,max_ls_nodes(node)
lval = ls_nodes(l,node)+1
do j=1,lats_node
lat = global_lats(ipt_lats_node-1+j)
if ( min(lat,latg-lat+1) >= lat1s_a(lval-1) ) then
kptr(node) = kptr(node) + 1
endif
enddo
enddo
enddo
!
!
!$omp parallel do private(node)
do node=1,npes
sendcounts(node) = kpts(node) * n2
recvcounts(node) = kptr(node) * n2
sdispls(node) = (node-1) * n2 * ls_dim * workdim
end do
work1dr(1:arrsz)=>workr
work1ds(1:arrsz)=>works
call mp_alltoall(work1ds, sendcounts, sdispls, &
work1dr,recvcounts,sdispls)
nullify(work1dr)
nullify(work1ds)
!$omp parallel do private(j,lat,lmax,nvar,lval,nv)
do j=1,lats_node
lmax = min(jcap,lonf/2)
n2 = lmax + lmax + 3
if ( n2 <= lonf+2 ) then
do nv=1,nvars
do lval = n2, lonf+2
four_gr(lval,nv,j) = cons0
enddo
enddo
endif
enddo
!
kptr = 0
!!
!$omp parallel do private(node,l,lval,j,lat,nvar,kn,n2)
do node=1,npes
do l=1,max_ls_nodes(node)
lval = ls_nodes(l,node)+1
n2 = lval + lval
do j=1,lats_node
lat = global_lats(ipt_lats_node-1+j)
if ( min(lat,latg-lat+1) >= lat1s_a(lval-1) ) then
kptr(node) = kptr(node) + 1
kn = kptr(node)
do nv=1,nvars
four_gr(n2-1,nv,j) = workr(1,nv,kn,node)
four_gr(n2, nv,j) = workr(2,nv,kn,node)
enddo
endif
enddo
enddo
enddo
!
return
end subroutine spec_to_four
!>@brief The subroutine 'four_to_grid' calculate real values form fourrier coefficients
!>@details This code is taken from the legacy spectral GFS
subroutine four_to_grid(syn_gr_a_1,syn_gr_a_2, lon_dim_coef,nvars)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
implicit none
!!
integer, intent(in) :: nvars
real(kind=kind_dbl_prec) syn_gr_a_1(lon_dim_coef,nvars)
real(kind=kind_dbl_prec) syn_gr_a_2(lonf,nvars)
integer lon_dim_coef
!________________________________________________________
real(kind=kind_dbl_prec) aux1crs(44002)
integer init
!________________________________________________________
init = 1
call dcrft_stochy(init, &
syn_gr_a_1(:,:) ,lon_dim_coef, &
syn_gr_a_2(:,:) ,lonf, &
lonf, nvars, &
aux1crs,22000, &
aux1crs(22001),20000)
init = 0
call dcrft_stochy(init, &
syn_gr_a_1(:,:) ,lon_dim_coef, &
syn_gr_a_2(:,:) ,lonf, &
lonf, nvars, &
aux1crs,22000, &
aux1crs(22001),20000)
return
end
SUBROUTINE dcrft_stochy(init,x,ldx,y,ldy,n,nvars, table,n1,wrk,n2)
implicit none
integer ,intent(in) :: ldx,ldy,n,nvars
integer init,n1,n2,i,j
real(kind_dbl_prec) x(ldx,nvars),y(ldy,nvars),table(44002),wrk
IF (init.ne.0) THEN
CALL rffti_stochy(n,table)
ELSE
DO j=1,nvars
y(1,j)=x(1,j)
DO i=2,n
y(i,j)=x(i+1,j)
ENDDO
CALL rfftb_stochy(n,y(:,j),table)
ENDDO
ENDIF
RETURN
END
! ******************************************************************
! ******************************************************************
! ****** ******
! ****** FFTPACK ******
! ****** ******
! ******************************************************************
! ******************************************************************
!
SUBROUTINE RFFTB_STOCHY (N,R,WSAVE)
implicit none
real(kind_dbl_prec), intent(inout) :: R(:)
real(kind_dbl_prec), intent(inout) :: WSAVE(44002)
integer :: N
IF (N .EQ. 1) RETURN
CALL RFFTB1_STOCHY (N,R,WSAVE,WSAVE(N+1:),WSAVE(2*N+1:))
RETURN
END
SUBROUTINE RFFTI_STOCHY (N,WSAVE)
implicit none
REAL(kind_dbl_prec), intent(inout) :: WSAVE(44002)
integer :: N
IF (N .EQ. 1) RETURN
CALL RFFTI1_STOCHY (N,WSAVE(N+1:),WSAVE(2*N+1:))
RETURN
END
SUBROUTINE RFFTB1_STOCHY (N,C,CH,WA,RFAC)
implicit none
integer, intent(in) :: N
real(kind_dbl_prec), intent(inout) :: CH(44002)
real(kind_dbl_prec), intent(inout) :: C(:)
real(kind_dbl_prec), intent(inout) :: WA(:)
real(kind_dbl_prec), intent(inout) :: RFAC(:)
integer :: NF,NA,L1,IW,IP,L2,IDO,IDL1,IX2,IX3,IX4
integer :: K1,I
NF = INT(RFAC(2))
NA = 0
L1 = 1
IW = 1
DO 116 K1=1,NF
IP = INT(RFAC(K1+2))
L2 = IP*L1
IDO = N/L2
IDL1 = IDO*L1
IF (IP .NE. 4) GO TO 103
IX2 = IW+IDO
IX3 = IX2+IDO
IF (NA .NE. 0) GO TO 101
CALL RADB4_STOCHY (IDO,L1,C(1:4*IDO*L1),CH(1:4*IDO*L1),WA(IW:),WA(IX2:),WA(IX3:))
GO TO 102
101 CALL RADB4_STOCHY (IDO,L1,CH(1:4*IDO*L1),C(1:4*IDO*L1),WA(IW:),WA(IX2:),WA(IX3:))
102 NA = 1-NA
GO TO 115
103 IF (IP .NE. 2) GO TO 106
IF (NA .NE. 0) GO TO 104
CALL RADB2_STOCHY (IDO,L1,C,CH,WA(IW:))
GO TO 105
104 CALL RADB2_STOCHY (IDO,L1,CH,C,WA(IW:))
105 NA = 1-NA
GO TO 115
106 IF (IP .NE. 3) GO TO 109
IX2 = IW+IDO
IF (NA .NE. 0) GO TO 107
CALL RADB3_STOCHY (IDO,L1,C,CH,WA(IW:),WA(IX2:))
GO TO 108
107 CALL RADB3_STOCHY (IDO,L1,CH,C,WA(IW:),WA(IX2:))
108 NA = 1-NA
GO TO 115
109 IF (IP .NE. 5) GO TO 112
IX2 = IW+IDO
IX3 = IX2+IDO
IX4 = IX3+IDO
IF (NA .NE. 0) GO TO 110
CALL RADB5_STOCHY (IDO,L1,C,CH,WA(IW:),WA(IX2:),WA(IX3:),WA(IX4:))
GO TO 111
110 CALL RADB5_STOCHY (IDO,L1,CH,C,WA(IW:),WA(IX2:),WA(IX3:),WA(IX4:))
111 NA = 1-NA
GO TO 115
112 IF (NA .NE. 0) GO TO 113
CALL RADBG_STOCHY (IDO,IP,L1,IDL1,C,C,C,CH,CH,WA(IW:))
GO TO 114
113 CALL RADBG_STOCHY (IDO,IP,L1,IDL1,CH,CH,CH,C,C,WA(IW:))
114 IF (IDO .EQ. 1) NA = 1-NA
115 L1 = L2
IW = IW+(IP-1)*IDO
116 CONTINUE
IF (NA .EQ. 0) RETURN
DO 117 I=1,N
C(I) = CH(I)
117 CONTINUE
RETURN
END
SUBROUTINE RFFTI1_STOCHY (N,WA,RFAC)
implicit none
integer, intent(in) :: N
REAL(kind_dbl_prec), intent(inout) :: WA(:)
REAL(kind_dbl_prec), intent(inout) :: RFAC(:)
integer :: NTRYH(4)
integer :: NL,NF, I, J, NQ,NR,LD,FI,IS,ID,L1,L2,IP
integer :: NTRY, NFM1, K1,II, IB, IDO, IPM, IC
REAL(kind_dbl_prec), parameter :: TPI=6.28318530717959
real(kind_dbl_prec) :: ARG,ARGLD,ARGH, TI2,TI4
DATA NTRYH(:) /4,2,3,5/
NL = N
NF = 0
J = 0
101 J = J+1
IF ( (J-4) .LE. 0) THEN
GOTO 102
ELSE
GOTO 103
ENDIF
102 NTRY = NTRYH(J)
GO TO 104
103 NTRY = NTRY+2
104 NQ = NL/NTRY
NR = NL-NTRY*NQ
IF (NR.EQ.0) THEN
GO TO 105
ELSE
GO TO 101
ENDIF
105 NF = NF+1
RFAC(NF+2) = FLOAT(NTRY)
NL = NQ
IF (NTRY .NE. 2) GO TO 107
IF (NF .EQ. 1) GO TO 107
DO 106 I=2,NF
IB = NF-I+2
RFAC(IB+2) = RFAC(IB+1)
106 CONTINUE
RFAC(3) = 2.
107 IF (NL .NE. 1) GO TO 104
RFAC(1) = FLOAT(N)
RFAC(2) = FLOAT(NF)
ARGH = TPI/FLOAT(N)
IS = 0
NFM1 = NF-1
L1 = 1
IF (NFM1 .EQ. 0) RETURN
!OCL NOVREC
DO 110 K1=1,NFM1
IP = INT(RFAC(K1+2))
LD = 0
L2 = L1*IP
IDO = N/L2
IPM = IP-1
DO 109 J=1,IPM
LD = LD+L1
I = IS
ARGLD = FLOAT(LD)*ARGH
FI = 0
!OCL SCALAR
DO 108 II=3,IDO,2
I = I+2
FI = FI+1
ARG = FI*ARGLD
WA(I-1) = COS(ARG)
WA(I) = SIN(ARG)
108 CONTINUE
IS = IS+IDO
109 CONTINUE
L1 = L2
110 CONTINUE
RETURN
END
SUBROUTINE RADB2_STOCHY (IDO,L1,CC,CH,WA1)
implicit none
integer, intent(in) :: IDO
integer, intent(in) :: L1
real(kind_dbl_prec), intent(inout) :: CC(IDO,2,L1)
real(kind_dbl_prec), intent(inout) :: CH(IDO,L1,2)
real(kind_dbl_prec), intent(inout) :: WA1(:)
integer :: K,I,IC,IDP2
real(kind_dbl_prec) :: TR2,TI2
DO 101 K=1,L1
CH(1,K,1) = CC(1,1,K)+CC(IDO,2,K)
CH(1,K,2) = CC(1,1,K)-CC(IDO,2,K)
101 CONTINUE
IF ( (IDO-2) .LT. 0) THEN
GO TO 107
ELSE IF (( IDO-2).EQ. 0)THEN
GO TO 105
ELSE
GO TO 102
ENDIF
102 IDP2 = IDO+2
!OCL NOVREC
DO 104 K=1,L1
DO 103 I=3,IDO,2
IC = IDP2-I
CH(I-1,K,1) = CC(I-1,1,K)+CC(IC-1,2,K)
TR2 = CC(I-1,1,K)-CC(IC-1,2,K)
CH(I,K,1) = CC(I,1,K)-CC(IC,2,K)
TI2 = CC(I,1,K)+CC(IC,2,K)
CH(I-1,K,2) = WA1(I-2)*TR2-WA1(I-1)*TI2
CH(I,K,2) = WA1(I-2)*TI2+WA1(I-1)*TR2
103 CONTINUE
104 CONTINUE
IF (MOD(IDO,2) .EQ. 1) RETURN
105 DO 106 K=1,L1
CH(IDO,K,1) = CC(IDO,1,K)+CC(IDO,1,K)
CH(IDO,K,2) = -(CC(1,2,K)+CC(1,2,K))
106 CONTINUE
107 RETURN
END
SUBROUTINE RADB3_STOCHY (IDO,L1,CC,CH,WA1,WA2)
implicit none
integer, intent(in) :: IDO,L1
real(kind_dbl_prec), intent(inout) :: CC(IDO,3,L1)
real(kind_dbl_prec), intent(inout) :: CH(IDO,L1,3)
real(kind_dbl_prec), intent(inout) :: WA1(:)
real(kind_dbl_prec), intent(inout) :: WA2(:)
REAL(kind_dbl_prec), parameter :: TAUR= -.5
REAL(kind_dbl_prec), parameter :: TAUI=.866025403784439
integer :: I,K,IDP2,IC
real(kind_dbl_prec) :: TR2,CR2,TI1,CI2,CR3,CI3,DR2,DR3,DI2,DI3
real(kind_dbl_prec) :: TI2,TI4
DO 101 K=1,L1
TR2 = CC(IDO,2,K)+CC(IDO,2,K)
CR2 = CC(1,1,K)+TAUR*TR2
CH(1,K,1) = CC(1,1,K)+TR2
CI3 = TAUI*(CC(1,3,K)+CC(1,3,K))
CH(1,K,2) = CR2-CI3
CH(1,K,3) = CR2+CI3
101 CONTINUE
IF (IDO .EQ. 1) RETURN
IDP2 = IDO+2
!OCL NOVREC
DO 103 K=1,L1
DO 102 I=3,IDO,2
IC = IDP2-I
TR2 = CC(I-1,3,K)+CC(IC-1,2,K)
CR2 = CC(I-1,1,K)+TAUR*TR2
CH(I-1,K,1) = CC(I-1,1,K)+TR2
TI2 = CC(I,3,K)-CC(IC,2,K)
CI2 = CC(I,1,K)+TAUR*TI2
CH(I,K,1) = CC(I,1,K)+TI2
CR3 = TAUI*(CC(I-1,3,K)-CC(IC-1,2,K))
CI3 = TAUI*(CC(I,3,K)+CC(IC,2,K))
DR2 = CR2-CI3
DR3 = CR2+CI3
DI2 = CI2+CR3
DI3 = CI2-CR3
CH(I-1,K,2) = WA1(I-2)*DR2-WA1(I-1)*DI2
CH(I,K,2) = WA1(I-2)*DI2+WA1(I-1)*DR2
CH(I-1,K,3) = WA2(I-2)*DR3-WA2(I-1)*DI3
CH(I,K,3) = WA2(I-2)*DI3+WA2(I-1)*DR3
102 CONTINUE
103 CONTINUE
RETURN
END
SUBROUTINE RADB4_STOCHY (IDO,L1,CC,CH,WA1,WA2,WA3)
implicit none
integer, intent(in) :: IDO,L1
real(kind_dbl_prec), intent(inout) :: CC(IDO,4,L1)
real(kind_dbl_prec), intent(inout) :: CH(IDO,L1,4)
real(kind_dbl_prec), intent(inout) :: WA1(:)
real(kind_dbl_prec), intent(inout) :: WA2(:)
real(kind_dbl_prec), intent(inout) :: WA3(:)
REAL(kind_dbl_prec), parameter :: SQRT2=1.414213562373095
integer :: I,K,IDP2,IC
real(kind_dbl_prec) :: TR1,TR2,TR3,TR4,TI1,TI2,TI3,TI4
real(kind_dbl_prec) :: CI2,CI3,CI4,CR2,CR3,CR4
DO 101 K=1,L1
TR1 = CC(1,1,K)-CC(IDO,4,K)
TR2 = CC(1,1,K)+CC(IDO,4,K)
TR3 = CC(IDO,2,K)+CC(IDO,2,K)
TR4 = CC(1,3,K)+CC(1,3,K)
CH(1,K,1) = TR2+TR3
CH(1,K,2) = TR1-TR4
CH(1,K,3) = TR2-TR3
CH(1,K,4) = TR1+TR4
101 CONTINUE
IF ( (IDO-2) .LT.0 ) THEN
GO TO 107
ELSE IF ( (IDO-2) .EQ.0 ) THEN
GO TO 105
ELSE
GO TO 102
ENDIF
102 IDP2 = IDO+2
!OCL NOVREC
DO 104 K=1,L1
DO 103 I=3,IDO,2
IC = IDP2-I
TI1 = CC(I,1,K)+CC(IC,4,K)
TI2 = CC(I,1,K)-CC(IC,4,K)
TI3 = CC(I,3,K)-CC(IC,2,K)
TR4 = CC(I,3,K)+CC(IC,2,K)
TR1 = CC(I-1,1,K)-CC(IC-1,4,K)
TR2 = CC(I-1,1,K)+CC(IC-1,4,K)
TI4 = CC(I-1,3,K)-CC(IC-1,2,K)
TR3 = CC(I-1,3,K)+CC(IC-1,2,K)
CH(I-1,K,1) = TR2+TR3
CR3 = TR2-TR3
CH(I,K,1) = TI2+TI3
CI3 = TI2-TI3
CR2 = TR1-TR4
CR4 = TR1+TR4
CI2 = TI1+TI4
CI4 = TI1-TI4
CH(I-1,K,2) = WA1(I-2)*CR2-WA1(I-1)*CI2
CH(I,K,2) = WA1(I-2)*CI2+WA1(I-1)*CR2
CH(I-1,K,3) = WA2(I-2)*CR3-WA2(I-1)*CI3
CH(I,K,3) = WA2(I-2)*CI3+WA2(I-1)*CR3
CH(I-1,K,4) = WA3(I-2)*CR4-WA3(I-1)*CI4
CH(I,K,4) = WA3(I-2)*CI4+WA3(I-1)*CR4
103 CONTINUE
104 CONTINUE
IF (MOD(IDO,2) .EQ. 1) RETURN
105 CONTINUE
DO 106 K=1,L1
TI1 = CC(1,2,K)+CC(1,4,K)
TI2 = CC(1,4,K)-CC(1,2,K)
TR1 = CC(IDO,1,K)-CC(IDO,3,K)
TR2 = CC(IDO,1,K)+CC(IDO,3,K)
CH(IDO,K,1) = TR2+TR2
CH(IDO,K,2) = SQRT2*(TR1-TI1)
CH(IDO,K,3) = TI2+TI2
CH(IDO,K,4) = -SQRT2*(TR1+TI1)
106 CONTINUE
107 RETURN
END
SUBROUTINE RADB5_STOCHY (IDO,L1,CC,CH,WA1,WA2,WA3,WA4)
implicit none
integer, intent(in) :: L1, IDO
REAL(kind_dbl_prec) :: CC(IDO,5,L1), CH(IDO,L1,5), WA1(*), WA2(*), WA3(*), WA4(*)
REAL(kind_dbl_prec), parameter :: TR11=0.309016994374947
REAL(kind_dbl_prec), parameter :: TI11= 0.951056516295154
REAL(kind_dbl_prec), parameter :: TR12=-0.809016994374947
REAL(kind_dbl_prec), parameter :: TI12=0.587785252292473
integer :: k,IDP2,I,IC
real(kind_dbl_prec) :: &
TI5,TI4,TR2,TR3,CR2,CR3,CI5,CI4, &
TI2,TI3,TR5,TR4, &
CI2,CI3,CR5,CR4, &
DR3,DR4,DI3,DI4,DR5,DR2,DI5,DI2
DO 101 K=1,L1
TI5 = CC(1,3,K)+CC(1,3,K)
TI4 = CC(1,5,K)+CC(1,5,K)
TR2 = CC(IDO,2,K)+CC(IDO,2,K)
TR3 = CC(IDO,4,K)+CC(IDO,4,K)
CH(1,K,1) = CC(1,1,K)+TR2+TR3
CR2 = CC(1,1,K)+TR11*TR2+TR12*TR3
CR3 = CC(1,1,K)+TR12*TR2+TR11*TR3
CI5 = TI11*TI5+TI12*TI4
CI4 = TI12*TI5-TI11*TI4
CH(1,K,2) = CR2-CI5
CH(1,K,3) = CR3-CI4
CH(1,K,4) = CR3+CI4
CH(1,K,5) = CR2+CI5
101 CONTINUE
IF (IDO .EQ. 1) RETURN
IDP2 = IDO+2
DO 103 K=1,L1
DO 102 I=3,IDO,2
IC = IDP2-I
TI5 = CC(I,3,K)+CC(IC,2,K)
TI2 = CC(I,3,K)-CC(IC,2,K)
TI4 = CC(I,5,K)+CC(IC,4,K)
TI3 = CC(I,5,K)-CC(IC,4,K)
TR5 = CC(I-1,3,K)-CC(IC-1,2,K)
TR2 = CC(I-1,3,K)+CC(IC-1,2,K)
TR4 = CC(I-1,5,K)-CC(IC-1,4,K)
TR3 = CC(I-1,5,K)+CC(IC-1,4,K)
CH(I-1,K,1) = CC(I-1,1,K)+TR2+TR3
CH(I,K,1) = CC(I,1,K)+TI2+TI3
CR2 = CC(I-1,1,K)+TR11*TR2+TR12*TR3
CI2 = CC(I,1,K)+TR11*TI2+TR12*TI3
CR3 = CC(I-1,1,K)+TR12*TR2+TR11*TR3
CI3 = CC(I,1,K)+TR12*TI2+TR11*TI3
CR5 = TI11*TR5+TI12*TR4
CI5 = TI11*TI5+TI12*TI4
CR4 = TI12*TR5-TI11*TR4
CI4 = TI12*TI5-TI11*TI4
DR3 = CR3-CI4
DR4 = CR3+CI4
DI3 = CI3+CR4
DI4 = CI3-CR4
DR5 = CR2+CI5
DR2 = CR2-CI5
DI5 = CI2-CR5
DI2 = CI2+CR5
CH(I-1,K,2) = WA1(I-2)*DR2-WA1(I-1)*DI2
CH(I,K,2) = WA1(I-2)*DI2+WA1(I-1)*DR2
CH(I-1,K,3) = WA2(I-2)*DR3-WA2(I-1)*DI3
CH(I,K,3) = WA2(I-2)*DI3+WA2(I-1)*DR3
CH(I-1,K,4) = WA3(I-2)*DR4-WA3(I-1)*DI4
CH(I,K,4) = WA3(I-2)*DI4+WA3(I-1)*DR4
CH(I-1,K,5) = WA4(I-2)*DR5-WA4(I-1)*DI5
CH(I,K,5) = WA4(I-2)*DI5+WA4(I-1)*DR5
102 CONTINUE
103 CONTINUE
RETURN
END
SUBROUTINE RADBG_STOCHY (IDO,IP,L1,IDL1,CC,C1,C2,CH,CH2,WA)
implicit real(kind=kind_dbl_prec) (A-H)
implicit real(kind=kind_dbl_prec) (O-Z)
REAL(kind_dbl_prec) :: CH(IDO,L1,IP), CC(IDO,IP,L1), C1(IDO,L1,IP), C2(IDL1,IP), &
CH2(IDL1,IP) , WA(*)
REAL(kind_dbl_prec), parameter :: TPI=6.28318530717959
ARG = TPI/FLOAT(IP)
DCP = COS(ARG)
DSP = SIN(ARG)
IDP2 = IDO+2
NBD = (IDO-1)/2
IPP2 = IP+2
IPPH = (IP+1)/2
IF (IDO .LT. L1) GO TO 103
DO K=1,L1
DO I=1,IDO
CH(I,K,1) = CC(I,1,K)
ENDDO
ENDDO
GO TO 106
103 DO 105 I=1,IDO
DO 104 K=1,L1
CH(I,K,1) = CC(I,1,K)
104 CONTINUE
105 CONTINUE
!OCL NOVREC
106 DO 108 J=2,IPPH
JC = IPP2-J
J2 = J+J
DO 107 K=1,L1
CH(1,K,J) = CC(IDO,J2-2,K)+CC(IDO,J2-2,K)
CH(1,K,JC) = CC(1,J2-1,K)+CC(1,J2-1,K)
107 CONTINUE
108 CONTINUE
IF (IDO .EQ. 1) GO TO 116
IF (NBD .LT. L1) GO TO 112
!OCL NOVREC
DO 111 J=2,IPPH
JC = IPP2-J
DO 110 K=1,L1
DO 109 I=3,IDO,2
IC = IDP2-I
CH(I-1,K,J) = CC(I-1,2*J-1,K)+CC(IC-1,2*J-2,K)
CH(I-1,K,JC) = CC(I-1,2*J-1,K)-CC(IC-1,2*J-2,K)
CH(I,K,J) = CC(I,2*J-1,K)-CC(IC,2*J-2,K)
CH(I,K,JC) = CC(I,2*J-1,K)+CC(IC,2*J-2,K)
109 CONTINUE
110 CONTINUE
111 CONTINUE
GO TO 116
112 DO 115 J=2,IPPH
JC = IPP2-J
DO 114 I=3,IDO,2
IC = IDP2-I
DO 113 K=1,L1
CH(I-1,K,J) = CC(I-1,2*J-1,K)+CC(IC-1,2*J-2,K)
CH(I-1,K,JC) = CC(I-1,2*J-1,K)-CC(IC-1,2*J-2,K)
CH(I,K,J) = CC(I,2*J-1,K)-CC(IC,2*J-2,K)
CH(I,K,JC) = CC(I,2*J-1,K)+CC(IC,2*J-2,K)
113 CONTINUE
114 CONTINUE
115 CONTINUE
116 AR1 = 1.
AI1 = 0.
!OCL NOVREC
DO 120 L=2,IPPH
LC = IPP2-L
AR1H = DCP*AR1-DSP*AI1
AI1 = DCP*AI1+DSP*AR1
AR1 = AR1H
DO 117 IK=1,IDL1
C2(IK,L) = CH2(IK,1)+AR1*CH2(IK,2)
C2(IK,LC) = AI1*CH2(IK,IP)
117 CONTINUE
DC2 = AR1
DS2 = AI1
AR2 = AR1
AI2 = AI1
!OCL NOVREC
DO 119 J=3,IPPH
JC = IPP2-J
AR2H = DC2*AR2-DS2*AI2
AI2 = DC2*AI2+DS2*AR2
AR2 = AR2H
DO 118 IK=1,IDL1
C2(IK,L) = C2(IK,L)+AR2*CH2(IK,J)
C2(IK,LC) = C2(IK,LC)+AI2*CH2(IK,JC)
118 CONTINUE
119 CONTINUE
120 CONTINUE
!OCL NOVREC
DO 122 J=2,IPPH
DO 121 IK=1,IDL1
CH2(IK,1) = CH2(IK,1)+CH2(IK,J)
121 CONTINUE
122 CONTINUE
!OCL NOVREC
DO 124 J=2,IPPH
JC = IPP2-J
DO 123 K=1,L1
CH(1,K,J) = C1(1,K,J)-C1(1,K,JC)
CH(1,K,JC) = C1(1,K,J)+C1(1,K,JC)
123 CONTINUE
124 CONTINUE
IF (IDO .EQ. 1) GO TO 132
IF (NBD .LT. L1) GO TO 128
!OCL NOVREC
DO 127 J=2,IPPH
JC = IPP2-J
DO 126 K=1,L1
DO 125 I=3,IDO,2
CH(I-1,K,J) = C1(I-1,K,J)-C1(I,K,JC)
CH(I-1,K,JC) = C1(I-1,K,J)+C1(I,K,JC)
CH(I,K,J) = C1(I,K,J)+C1(I-1,K,JC)
CH(I,K,JC) = C1(I,K,J)-C1(I-1,K,JC)
125 CONTINUE
126 CONTINUE
127 CONTINUE
GO TO 132
128 DO 131 J=2,IPPH
JC = IPP2-J
DO 130 I=3,IDO,2
DO 129 K=1,L1
CH(I-1,K,J) = C1(I-1,K,J)-C1(I,K,JC)
CH(I-1,K,JC) = C1(I-1,K,J)+C1(I,K,JC)
CH(I,K,J) = C1(I,K,J)+C1(I-1,K,JC)
CH(I,K,JC) = C1(I,K,J)-C1(I-1,K,JC)
129 CONTINUE
130 CONTINUE
131 CONTINUE
132 CONTINUE
IF (IDO .EQ. 1) RETURN
DO 133 IK=1,IDL1
C2(IK,1) = CH2(IK,1)
133 CONTINUE
DO 135 J=2,IP
DO 134 K=1,L1
C1(1,K,J) = CH(1,K,J)
134 CONTINUE
135 CONTINUE
IF (NBD .GT. L1) GO TO 139
IS = -IDO
DO 138 J=2,IP
IS = IS+IDO
IDIJ = IS
DO 137 I=3,IDO,2
IDIJ = IDIJ+2
DO 136 K=1,L1
C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)-WA(IDIJ)*CH(I,K,J)
C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)+WA(IDIJ)*CH(I-1,K,J)
136 CONTINUE
137 CONTINUE
138 CONTINUE
GO TO 143
139 IS = -IDO
!OCL NOVREC
DO 142 J=2,IP
IS = IS+IDO
DO 141 K=1,L1
IDIJ = IS
DO 140 I=3,IDO,2
IDIJ = IDIJ+2
C1(I-1,K,J) = WA(IDIJ-1)*CH(I-1,K,J)-WA(IDIJ)*CH(I,K,J)
C1(I,K,J) = WA(IDIJ-1)*CH(I,K,J)+WA(IDIJ)*CH(I-1,K,J)
140 CONTINUE
141 CONTINUE
142 CONTINUE
143 RETURN
END
!>@brief The subroutine 'dozeuv_stochy' caculates odd u and even v winds harmonics from the odd harmonics
! of divergence and even harmonics of vorticty
!>@details This code is taken from the legacy spectral GFS
subroutine dozeuv_stochy(dod,zev,uod,vev,epsedn,epsodn, snnp1ev,snnp1od,ls_node)
implicit none
real(kind_dbl_prec), intent(in) :: dod(len_trio_ls,2)
real(kind_dbl_prec), intent(in) :: zev(len_trie_ls,2)
real(kind_dbl_prec), intent(out) :: uod(len_trio_ls,2)
real(kind_dbl_prec), intent(out) :: vev(len_trie_ls,2)
real(kind_dbl_prec), intent(in) :: epsedn(len_trie_ls)
real(kind_dbl_prec), intent(in) :: epsodn(len_trio_ls)
real(kind_dbl_prec), intent(in) :: snnp1ev(len_trie_ls)
real(kind_dbl_prec), intent(in) :: snnp1od(len_trio_ls)
integer, intent(in) :: ls_node(ls_dim,3)
!cmr ls_node(1,1) ... ls_node(ls_max_node,1) : values of L
!cmr ls_node(1,2) ... ls_node(ls_max_node,2) : values of jbasev
!cmr ls_node(1,3) ... ls_node(ls_max_node,3) : values of jbasod
! locaals
integer l,locl,n
integer indev,indev1,indev2
integer indod,indod1,indod2
integer inddif
real(kind_dbl_prec) rl
real(kind_dbl_prec) cons0 !constant
integer indlsev,jbasev
integer indlsod,jbasod
real(kind_dbl_prec) rerth
include 'function2'
!......................................................................
cons0 = 0.d0 !constant
rerth =6.3712e+6 ! radius of earth (m)
do locl=1,ls_max_node
l=ls_node(locl,1)
jbasev=ls_node(locl,2)
vev(indlsev(l,l),1) = cons0 !constant
vev(indlsev(l,l),2) = cons0 !constant
enddo
!......................................................................
do locl=1,ls_max_node
l=ls_node(locl,1)
jbasev=ls_node(locl,2)
jbasod=ls_node(locl,3)
indev1 = indlsev(L,L)
if (mod(L,2).eq.mod(jcap+1,2)) then
indev2 = indlsev(jcap-1,L)
else
indev2 = indlsev(jcap ,L)
endif
indod1 = indlsod(l+1,l)
inddif = indev1 - indod1
do indev = indev1 , indev2
uod(indev-inddif,1) = -epsodn(indev-inddif) * zev(indev,1)
uod(indev-inddif,2) = -epsodn(indev-inddif) * zev(indev,2)
enddo
enddo
!......................................................................
do locl=1,ls_max_node
l=ls_node(locl,1)
jbasev=ls_node(locl,2)
jbasod=ls_node(locl,3)
indev1 = indlsev(L,L) + 1
if (mod(L,2).eq.mod(jcap+1,2)) then
indev2 = indlsev(jcap+1,L)
else
indev2 = indlsev(jcap ,L)
endif
indod1 = indlsod(l+1,l)
inddif = indev1 - indod1
do indev = indev1 , indev2
vev(indev,1) = epsedn(indev) * dod(indev-inddif,1)
vev(indev,2) = epsedn(indev) * dod(indev-inddif,2)
enddo
enddo
!......................................................................
do locl=1,ls_max_node
l=ls_node(locl,1)
jbasod=ls_node(locl,3)
indod1 = indlsod(L+1,L)
if (mod(L,2).eq.mod(jcap+1,2)) then
indod2 = indlsod(jcap ,L)
else
indod2 = indlsod(jcap+1,L) - 1
endif
if ( l .ge. 1 ) then
rl = l
do indod = indod1 , indod2
! u(l,n)=-i*l*d(l,n)/(n*(n+1))
uod(indod,1) = uod(indod,1) + rl * dod(indod,2) / snnp1od(indod)
uod(indod,2) = uod(indod,2) - rl * dod(indod,1) / snnp1od(indod)
enddo
endif
enddo
!......................................................................
do locl=1,ls_max_node
l=ls_node(locl,1)
jbasev=ls_node(locl,2)
indev1 = indlsev(L,L)
if (mod(L,2).eq.mod(jcap+1,2)) then