sptran.f

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C> @file
C>
C> Perform a scalar spherical transform
C> @author IREDELL @date 96-02-29
 
C> This subprogram performs a spherical transform between spectral
C> coefficients of scalar quantities and fields on a global
C> cylindrical grid.  The wave-space can be either triangular or
C> rhomboidal.  The grid-space can be either an equally-spaced grid
C> (with or without pole points) or a gaussian grid.
C> The wave and grid fields may have general indexing,
C> but each wave field is in sequential 'ibm order',
C> i.e. with zonal wavenumber as the slower index.
C> Transforms are done in latitude pairs for efficiency;
C> thus grid arrays for each hemisphere must be passed.
C> If so requested, just a subset of the latitude pairs
C> may be transformed in each invocation of the subprogram.
C> The transforms are all multiprocessed over latitude except
C> the transform from fourier to spectral is multiprocessed
C> over zonal wavenumber to ensure reproducibility.
C> Transform several fields at a time to improve vectorization.
C> Subprogram can be called from a multiprocessing environment.
C>
C> PROGRAM HISTORY LOG:
C> -  96-02-29  IREDELL
C> - 1998-12-15  IREDELL  GENERIC FFT USED, OPENMP DIRECTIVES INSERTED
C>
C> @param IROMB    - INTEGER SPECTRAL DOMAIN SHAPE
C>                (0 FOR TRIANGULAR, 1 FOR RHOMBOIDAL)
C> @param MAXWV    - INTEGER SPECTRAL TRUNCATION
C> @param IDRT     - INTEGER GRID IDENTIFIER
C>                (IDRT=4 FOR GAUSSIAN GRID,
C>                 IDRT=0 FOR EQUALLY-SPACED GRID INCLUDING POLES,
C>                 IDRT=256 FOR EQUALLY-SPACED GRID EXCLUDING POLES)
C> @param IMAX     - INTEGER EVEN NUMBER OF LONGITUDES.
C> @param JMAX     - INTEGER NUMBER OF LATITUDES.
C> @param KMAX     - INTEGER NUMBER OF FIELDS TO TRANSFORM.
C> @param IPRIME   - INTEGER LONGITUDE INDEX FOR THE PRIME MERIDIAN.
C>                (DEFAULTS TO 1 IF IPRIME=0)
C> @param ISKIP    - INTEGER SKIP NUMBER BETWEEN LONGITUDES
C>                (DEFAULTS TO 1 IF ISKIP=0)
C> @param JNSKIP   - INTEGER SKIP NUMBER BETWEEN N.H. LATITUDES FROM NORTH
C>                (DEFAULTS TO IMAX IF JNSKIP=0)
C> @param JSSKIP   - INTEGER SKIP NUMBER BETWEEN S.H. LATITUDES FROM SOUTH
C>                (DEFAULTS TO -IMAX IF JSSKIP=0)
C> @param KWSKIP   - INTEGER SKIP NUMBER BETWEEN WAVE FIELDS
C>                (DEFAULTS TO (MAXWV+1)*((IROMB+1)*MAXWV+2) IF KWSKIP=0)
C> @param KGSKIP   - INTEGER SKIP NUMBER BETWEEN GRID FIELDS
C>                (DEFAULTS TO IMAX*JMAX IF KGSKIP=0)
C> @param JBEG     - INTEGER LATITUDE INDEX (FROM POLE) TO BEGIN TRANSFORM
C>                (DEFAULTS TO 1 IF JBEG=0)
C>                (IF JBEG=0 AND IDIR<0, WAVE IS ZEROED BEFORE TRANSFORM)
C> @param JEND     - INTEGER LATITUDE INDEX (FROM POLE) TO END TRANSFORM
C>                (DEFAULTS TO (JMAX+1)/2 IF JEND=0)
C> @param JCPU     - INTEGER NUMBER OF CPUS OVER WHICH TO MULTIPROCESS
C> @param[out] WAVE     - REAL (*) WAVE FIELDS IF IDIR>0
C> @param[out] GRIDN    - REAL (*) N.H. GRID FIELDS (STARTING AT JBEG) IF IDIR<0
C> @param[out] GRIDS    - REAL (*) S.H. GRID FIELDS (STARTING AT JBEG) IF IDIR<0
C> @param IDIR     - INTEGER TRANSFORM FLAG
C>                (IDIR>0 FOR WAVE TO GRID, IDIR<0 FOR GRID TO WAVE)
C>
C> SUBPROGRAMS CALLED:
C>  - sptranf()      Perform a scalar spherical transform
C>
C> Minimum grid dimensions for unaliased transforms to spectral:
C>   DIMENSION                    |LINEAR              |QUADRATIC
C>   -----------------------      |---------           |-------------
C>   IMAX                         | 2*MAXWV+2          | 3*MAXWV/2*2+2
C>   JMAX (IDRT=4,IROMB=0)        | 1*MAXWV+1          | 3*MAXWV/2+1
C>   JMAX (IDRT=4,IROMB=1)        | 2*MAXWV+1          | 5*MAXWV/2+1
C>   JMAX (IDRT=0,IROMB=0)        | 2*MAXWV+3          | 3*MAXWV/2*2+3
C>   JMAX (IDRT=0,IROMB=1)        | 4*MAXWV+3          | 5*MAXWV/2*2+3
C>   JMAX (IDRT=256,IROMB=0)      | 2*MAXWV+1          | 3*MAXWV/2*2+1
C>   JMAX (IDRT=256,IROMB=1)      | 4*MAXWV+1          | 5*MAXWV/2*2+1
C>      
      SUBROUTINE sptran(IROMB,MAXWV,IDRT,IMAX,JMAX,KMAX,
     &                  IPRIME,ISKIP,JNSKIP,JSSKIP,KWSKIP,KGSKIP,
     &                  JBEG,JEND,JCPU,
     &                  WAVE,GRIDN,GRIDS,IDIR)
 
      REAL WAVE(*),GRIDN(*),GRIDS(*)
!==EM==        integer JC, JCPU
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!==EM==
!        print *, "jjjjjjjcccccccccc  from SPTRAN- before NCPUS", JC
      mx=(maxwv+1)*((iromb+1)*maxwv+2)/2
      ip=iprime
      is=iskip
      jn=jnskip
      js=jsskip
      kw=kwskip
      kg=kgskip
      jb=jbeg
      je=jend
      jc=jcpu
      IF(ip.EQ.0) ip=1
      IF(is.EQ.0) is=1
      IF(jn.EQ.0) jn=imax
      IF(js.EQ.0) js=-jn
      IF(kw.EQ.0) kw=2*mx
      IF(kg.EQ.0) kg=imax*jmax
      IF(jb.EQ.0) jb=1
      IF(je.EQ.0) je=(jmax+1)/2
      IF(jc.EQ.0) jc=ncpus()
!   JC=NCPUS()
!==EM== 
!        print *, "jjjjjjjjjjjjjjjjjjjjcccccccccc  from SPTRAN", JC        
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      IF(idir.LT.0.AND.jbeg.EQ.0) THEN
        DO k=1,kmax
          kws=(k-1)*kw
          wave(kws+1:kws+2*mx)=0
        ENDDO
      ENDIF
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
!==EM==
!        print *, "jjjjjjjcccccccccc  from SPTRANF- before NCPUS", JC
      CALL sptranf(iromb,maxwv,idrt,imax,jmax,kmax,
     &             ip,is,jn,js,kw,kg,jb,je,jc,
     &             wave,gridn,grids,idir)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      END