C-----------------------------------------------------------------------
SUBROUTINE SPTRUND(IROMB,MAXWV,IDRTI,IMAXI,JMAXI,
& IDRTO,IMAXO,JMAXO,KMAX,
& IPRIME,ISKIPI,JSKIPI,KSKIPI,
& ISKIPO,JSKIPO,KSKIPO,JCPU,GRID,
& GRIDMN,GRIDX,GRIDY)
C$$$ SUBPROGRAM DOCUMENTATION BLOCK
C
C SUBPROGRAM: SPTRUND SPECTRALLY TRUNCATE TO GRADIENTS
C PRGMMR: IREDELL ORG: W/NMC23 DATE: 96-02-29
C
C ABSTRACT: THIS SUBPROGRAM SPECTRALLY TRUNCATES SCALAR FIELDS
C ON A GLOBAL CYLINDRICAL GRID, RETURNING THEIR MEANS AND
C GRADIENTS TO A POSSIBLY DIFFERENT GLOBAL CYLINDRICAL GRID.
C THE WAVE-SPACE CAN BE EITHER TRIANGULAR OR RHOMBOIDAL.
C EITHER GRID-SPACE CAN BE EITHER AN EQUALLY-SPACED GRID
C (WITH OR WITHOUT POLE POINTS) OR A GAUSSIAN GRID.
C THE GRID FIELDS MAY HAVE GENERAL INDEXING.
C THE TRANSFORMS ARE ALL 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
C USAGE: CALL SPTRUND(IROMB,MAXWV,IDRTI,IMAXI,JMAXI,
C & IDRTO,IMAXO,JMAXO,KMAX,
C & IPRIME,ISKIPI,JSKIPI,KSKIPI,
C & ISKIPO,JSKIPO,KSKIPO,JCPU,GRID,
C & GRIDMN,GRIDX,GRIDY)
C INPUT ARGUMENTS:
C IROMB - INTEGER SPECTRAL DOMAIN SHAPE
C (0 FOR TRIANGULAR, 1 FOR RHOMBOIDAL)
C MAXWV - INTEGER SPECTRAL TRUNCATION
C IDRTI - INTEGER INPUT GRID IDENTIFIER
C (IDRTI=4 FOR GAUSSIAN GRID,
C IDRTI=0 FOR EQUALLY-SPACED GRID INCLUDING POLES,
C IDRTI=256 FOR EQUALLY-SPACED GRID EXCLUDING POLES)
C IMAXI - INTEGER EVEN NUMBER OF INPUT LONGITUDES.
C JMAXI - INTEGER NUMBER OF INPUT LATITUDES.
C IDRTO - INTEGER OUTPUT GRID IDENTIFIER
C (IDRTO=4 FOR GAUSSIAN GRID,
C IDRTO=0 FOR EQUALLY-SPACED GRID INCLUDING POLES,
C IDRTO=256 FOR EQUALLY-SPACED GRID EXCLUDING POLES)
C IMAXO - INTEGER EVEN NUMBER OF OUTPUT LONGITUDES.
C JMAXO - INTEGER NUMBER OF OUTPUT LATITUDES.
C KMAX - INTEGER NUMBER OF FIELDS TO TRANSFORM.
C IPRIME - INTEGER INPUT LONGITUDE INDEX FOR THE PRIME MERIDIAN.
C (DEFAULTS TO 1 IF IPRIME=0)
C (OUTPUT LONGITUDE INDEX FOR PRIME MERIDIAN ASSUMED 1.)
C ISKIPI - INTEGER SKIP NUMBER BETWEEN INPUT LONGITUDES
C (DEFAULTS TO 1 IF ISKIPI=0)
C JSKIPI - INTEGER SKIP NUMBER BETWEEN INPUT LATITUDES FROM SOUTH
C (DEFAULTS TO -IMAXI IF JSKIPI=0)
C KSKIPI - INTEGER SKIP NUMBER BETWEEN INPUT GRID FIELDS
C (DEFAULTS TO IMAXI*JMAXI IF KSKIPI=0)
C ISKIPO - INTEGER SKIP NUMBER BETWEEN OUTPUT LONGITUDES
C (DEFAULTS TO 1 IF ISKIPO=0)
C JSKIPO - INTEGER SKIP NUMBER BETWEEN OUTPUT LATITUDES FROM SOUTH
C (DEFAULTS TO -IMAXO IF JSKIPO=0)
C KSKIPO - INTEGER SKIP NUMBER BETWEEN OUTPUT GRID FIELDS
C (DEFAULTS TO IMAXO*JMAXO IF KSKIPO=0)
C JCPU - INTEGER NUMBER OF CPUS OVER WHICH TO MULTIPROCESS
C (DEFAULTS TO ENVIRONMENT NCPUS IF JCPU=0)
C GRID - REAL (*) INPUT GRID FIELDS
C OUTPUT ARGUMENTS:
C GRIDMN - REAL (KMAX) OUTPUT GLOBAL MEANS
C GRIDX - REAL (*) OUTPUT X-GRADIENTS
C GRIDY - REAL (*) OUTPUT Y-GRADIENTS
C
C SUBPROGRAMS CALLED:
C SPTRAN PERFORM A SCALAR SPHERICAL TRANSFORM
C SPTRAND PERFORM A GRADIENT SPHERICAL TRANSFORM
C NCPUS GETS ENVIRONMENT NUMBER OF CPUS
C
C REMARKS: 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 ----------------------- --------- -------------
C
C ATTRIBUTES:
C LANGUAGE: FORTRAN 77
C
C$$$
REAL GRID(*),GRIDX(*),GRIDY(*)
REAL W((MAXWV+1)*((IROMB+1)*MAXWV+2)/2*2+1,KMAX)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C TRANSFORM INPUT GRID TO WAVE
JC=JCPU
IF(JC.EQ.0) JC=NCPUS()
MX=(MAXWV+1)*((IROMB+1)*MAXWV+2)/2
MDIM=2*MX+1
JN=-JSKIPI
IF(JN.EQ.0) JN=IMAXI
JS=-JN
INP=(JMAXI-1)*MAX(0,-JN)+1
ISP=(JMAXI-1)*MAX(0,-JS)+1
CALL SPTRAN(IROMB,MAXWV,IDRTI,IMAXI,JMAXI,KMAX,
& IPRIME,ISKIPI,JN,JS,MDIM,KSKIPI,0,0,JC,
& W,GRID(INP),GRID(ISP),-1)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C TRANSFORM WAVE TO OUTPUT GRADIENTS
JN=-JSKIPO
IF(JN.EQ.0) JN=IMAXO
JS=-JN
INP=(JMAXO-1)*MAX(0,-JN)+1
ISP=(JMAXO-1)*MAX(0,-JS)+1
CALL SPTRAND(IROMB,MAXWV,IDRTO,IMAXO,JMAXO,KMAX,
& 0,ISKIPO,JN,JS,MDIM,KSKIPO,0,0,JC,
& W,GRIDMN,
& GRIDX(INP),GRIDX(ISP),GRIDY(INP),GRIDY(ISP),1)
C - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
END