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|
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#include "CPP_OPTIONS.h" |
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|
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c ================================================================== |
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c |
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c shpere.F: Routines that handle the projection onto sherical |
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c harmonics. |
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c |
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c Routines: |
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c |
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c o adfsc4dat - Adjoint routine of fsc4dat. |
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c o shc2grid - Evaluate a spherical harmonics model on a |
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c regular grid. |
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c o shc4grid - Evaluate a spherical harmonics model on a |
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c regular grid. |
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c |
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c o shcrotate - s/r used for the sph analysis ... |
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c o shc2zone - s/r used for the sph analysis ... |
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c o shc4zone - s/r used for the sph analysis ... |
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c o fsc2dat - s/r used for the sph analysis ... |
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c o frsbase - s/r used for the sph analysis ... |
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c o helmholtz - s/r used for the sph analysis ... |
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c o recur_z - s/r used for the sph analysis ... |
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c |
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c o shcError - Print error message and stop program (see below). |
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c |
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c IMSL Routines: |
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c |
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c o fftrb - Compute the real periodic sequence from its Fourier |
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c coefficients. |
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c --> replace by NAGLIB routine. C06... |
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c |
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c Platform-specific: |
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c |
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c M abort - FORTRAN intrinsic on SUN and, presumably, on CRAY to |
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c exit the program if an error condition is met. |
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c |
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c --> Replaced ABORT by shcError ( Christian Eckert MIT 22-Mar-2000 ) |
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c |
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c Note: |
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c ===== |
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c |
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c Where code is written in lower case letters, changes were |
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c introduced. The changes are mainly related to F90 syntax. |
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c Additionally, I replaced the call to the intrinsic *AMOD* |
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c by its generic name *MOD*. ( Ch.E. 25-May-1999 ) |
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c |
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c |
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c Documentation: |
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c |
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c |
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c ================================================================== |
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|
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SUBROUTINE FSC4DAT(N,FSC) |
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|
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IMPLICIT NONE |
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|
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INTEGER N |
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REAL FSC(N) |
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REAL SCALE |
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integer i |
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|
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#ifdef USE_SPH_PROJECTION |
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CALL FFTRF(N,FSC,FSC) |
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#else |
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do i=1,n |
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fsc(i) = 0.0 |
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enddo |
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#endif |
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|
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SCALE = 2.0/FLOAT(N) |
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FSC(1) = FSC(1)/FLOAT(N) |
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|
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CE FSC(2:N-1:2) = FSC(2:N-1:2)*SCALE |
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CE FSC(3:N :2) =-FSC(3:N: 2)*SCALE ! change sign of SINE coeffs. |
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|
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do i = 2,n-1,2 |
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fsc( i ) = fsc( i )*scale |
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enddo |
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do i = 3,n,2 |
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fsc( i ) = -fsc( i )*scale ! change sign of sine coeffs. |
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enddo |
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|
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IF (MOD(N,2).EQ.0) THEN |
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FSC(N) = FSC(N)/FLOAT(N) |
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ENDIF |
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|
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RETURN |
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END |
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|
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c ================================================================== |
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|
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subroutine adfsc4dat(n,adfsc) |
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|
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implicit none |
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|
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integer n |
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real adfsc(n) |
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|
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integer i |
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|
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#ifdef USE_SPH_PROJECTION |
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call fftrb(n,adfsc,adfsc) |
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#else |
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do i=1,n |
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adfsc(i) = 0.0 |
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enddo |
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#endif |
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|
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do i=1,n |
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adfsc(i) = adfsc(i)/float(n) |
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enddo |
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|
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end |
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|
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c ================================================================== |
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|
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SUBROUTINE SHC2GRID( LMAX, SHC, NLON, NLAT, GRID, P ) |
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C |
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C --- Evaluate a spherical harmonics model on a regular grid. |
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C |
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C SHC ! spherical harmonic coefficients in the order of |
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C ! |
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C ! C00 : SHC(1) |
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C ! S11 C10 C11 : SHC(2) SHC(3) SHC(4) |
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C ! S22 S21 C20 C21 C22 : SHC(5) SHC(6) SHC(7) SHC(8) SHC(9) |
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C ! |
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C ! i.e., C(L,M) = SHC(L*L+L+1+M) |
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C ! S(L,M) = SHC(L*L+L+1-M) |
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C NLAT ! number of latitude (zonal) lines. |
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C NLON ! number of longitude (meridional) lines. |
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C ! |
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C GRID ! grid values in the order of |
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C ! ((west to east),south to north) |
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C ! ((LON=1,NLON),LAT=1,NLAT) |
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C ! grid values are defined on the "centers" |
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C ! of geographically regular equi-angular blocks. |
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C |
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C --- Coded by Dr. Myung-Chan Kim, Center for Space Research, 1997 |
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C University of Texas at Austin, Austin, Texas, 78712 |
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C |
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IMPLICIT NONE |
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|
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INTEGER LMAX ! INPUT max. degree |
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REAL SHC((1+LMAX)*(1+LMAX)) ! INPUT spherical harmonics |
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INTEGER NLAT ! INPUT number of latitude lines. |
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INTEGER NLON ! INPUT number of longitude lines. |
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REAL GRID(NLON,NLAT) ! OUTPUT grid values |
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REAL P((LMAX+1)*(LMAX+2)/2) ! work space |
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|
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INTEGER NLONLMT |
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PARAMETER (NLONLMT=10000) |
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REAL HS (NLONLMT) |
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REAL HN (NLONLMT) |
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|
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REAL DLAT, ANGLE, XLAT1, XLAT2 |
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INTEGER LATS, LATN |
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|
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ce integer js, jn |
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|
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integer i |
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|
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ce IF(NLON.GT.NLONLMT) CALL ABORT('NLON.GT.NLONLMT') |
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ce IF(NLON.LT.LMAX*2 ) CALL ABORT('NLON.LT.LMAX*2 ') |
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IF(NLON.GT.NLONLMT) CALL shcError('NLON.GT.NLONLMT',1) |
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IF(NLON.LT.LMAX*2 ) CALL shcError('NLON.LT.LMAX*2 ',1) |
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|
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DLAT = 180.0/FLOAT(NLAT) |
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ANGLE = 180.0/FLOAT(NLON) |
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|
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CALL SHCROTATE(LMAX,SHC,ANGLE) |
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DO LATS = 1,(NLAT+1)/2 |
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LATN = NLAT-(LATS-1) |
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XLAT2 =-90.0 + FLOAT(LATS)*DLAT |
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XLAT1 = XLAT2-DLAT |
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do i=1,nlon |
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hs(i) = 0.0 |
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hn(i) = 0.0 |
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enddo |
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CALL SHC2ZONE( LMAX, SHC, XLAT1, XLAT2, HS, HN, P ) |
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CALL FSC2DAT( NLON, HS ) |
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CALL FSC2DAT( NLON, HN ) |
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do i=1,nlon |
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grid(i,lats) = hs(i) |
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grid(i,latn) = hn(i) |
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enddo |
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ENDDO |
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CALL SHCROTATE(LMAX,SHC,-ANGLE) |
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RETURN |
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END |
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|
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c ================================================================== |
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|
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SUBROUTINE SHC4GRID( LMAX, SHC, NLON, NLAT, GRID, P ) |
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|
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IMPLICIT NONE |
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|
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INTEGER LMAX ! INPUT max. degree |
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REAL SHC((1+LMAX)*(1+LMAX)) ! OUTPUT spherical harmonics |
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INTEGER NLAT ! INPUT number of latitude lines. |
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INTEGER NLON ! INPUT number of longitude lines. |
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REAL GRID(NLON,NLAT) ! INPUT grid values |
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REAL P((LMAX+1)*(LMAX+2)/2) ! work space |
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|
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INTEGER NLONLMT |
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PARAMETER (NLONLMT=10000) |
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REAL HS (NLONLMT) |
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REAL HN (NLONLMT) |
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|
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REAL DLAT, ANGLE, XLAT1, XLAT2 |
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INTEGER LATS, LATN |
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|
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ce integer js, jn |
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|
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integer i |
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|
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IF(NLON.GT.NLONLMT) THEN |
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PRINT *, 'NLON = ', NLON |
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PRINT *, 'NLONLMT = ', NLONLMT |
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ce CALL ABORT('NLON.GT.NLONLMT') |
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CALL shcError('NLON.GT.NLONLMT',1) |
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END IF |
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|
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IF(NLON.LT.LMAX*2 ) THEN |
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PRINT *, 'NLON = ', NLON |
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PRINT *, 'LMAX = ', LMAX |
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ce CALL ABORT('NLON.LT.LMAX*2') |
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CALL shcError('NLON.LT.LMAX*2',1) |
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END IF |
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|
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DLAT = 180.0/FLOAT(NLAT) |
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ANGLE = 180.0/FLOAT(NLON) |
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DO LATS = 1,(NLAT+1)/2 |
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LATN = NLAT-(LATS-1) |
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do i = 1,nlon |
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hs(i) = grid(i,lats) |
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hn(i) = grid(i,latn) |
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enddo |
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CALL FSC4DAT(NLON,HS) |
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CALL FSC4DAT(NLON,HN) |
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XLAT2 =-90.0 + FLOAT(LATS)*DLAT |
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XLAT1 = XLAT2-DLAT |
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CALL SHC4ZONE(LMAX,SHC,XLAT1,XLAT2,HS,HN,P) |
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ENDDO |
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CALL SHCROTATE(LMAX,SHC,-ANGLE) |
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|
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RETURN |
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END |
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|
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c ================================================================== |
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|
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SUBROUTINE SHCROTATE(LMAX,SHC,ANGLE) |
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|
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IMPLICIT NONE |
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|
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INTEGER LMAX ! max. degree of spherical harmonics. |
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REAL SHC((1+LMAX)*(1+LMAX)) ! spherical harmonic coeffs. |
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REAL ANGLE ! in degree. |
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|
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INTEGER LMAXLMT |
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PARAMETER (LMAXLMT=10000) |
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|
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REAL H(LMAXLMT*2+1) |
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INTEGER K, L, M |
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REAL SINA, COSA, C, S |
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|
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if (mod(angle,360.0) .ne. 0.0) then |
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|
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CALL FRSBASE(ANGLE,H,1,1+LMAX+LMAX) |
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|
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DO M = 0,LMAX |
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IF(M.EQ.0) THEN |
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SINA = 0.0 |
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COSA = 1.0 |
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ELSE |
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COSA = H(M+M) |
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SINA = H(M+M+1) |
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ENDIF |
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DO L = M,LMAX |
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K = L*L+L+1 |
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C = SHC(K+M) |
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S = SHC(K-M) |
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SHC(K+M) = COSA*C + SINA*S |
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SHC(K-M) =-SINA*C + COSA*S |
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ENDDO |
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ENDDO |
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|
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ENDIF |
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|
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RETURN |
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END |
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|
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c ================================================================== |
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|
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SUBROUTINE SHC2ZONE(LMAX,SHC,XLAT1,XLAT2,HS,HN,P) |
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|
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IMPLICIT NONE |
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|
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INTEGER LMAX ! INPUT max. degree of spher. harmonics. |
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REAL SHC((1+LMAX)*(1+LMAX)) ! INPUT spherical harmonic coeffs. |
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REAL XLAT1 ! INPUT latitude. |
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REAL XLAT2 ! INPUT latitude. |
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REAL HS(1+LMAX+LMAX) ! OUTPUT |
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REAL HN(1+LMAX+LMAX) ! OUTPUT |
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REAL P((LMAX+1)*(LMAX+2)/2) ! INPUT |
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|
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INTEGER LMAXLMT |
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PARAMETER (LMAXLMT=5000) |
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|
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REAL FACT(0:LMAXLMT) ! |
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INTEGER LMAX1, J, K, L, M |
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REAL DEG2RAD, SLAT |
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REAL A, B, E, F, Q, DA, DB, XLAT |
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|
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ce IF (LMAX.GT.LMAXLMT) CALL ABORT('LMAX.GT.LMAXLMT') |
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cph IF (LMAX.GT.LMAXLMT) CALL shcError('LMAX.GT.LMAXLMT',1) |
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|
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DEG2RAD = ACOS(-1.0)/180.0 |
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XLAT = 0.5*(XLAT1+XLAT2) |
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do k = 1,lmax |
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fact(k) = 1.0 |
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enddo |
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SLAT = SIN(XLAT*DEG2RAD) |
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|
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CALL HELMHOLTZ(LMAX,SLAT,P) |
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LMAX1 = LMAX+1 |
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K = 0 |
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DO M = 0,LMAX |
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A = 0.0 |
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B = 0.0 |
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E = 0.0 |
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F = 0.0 |
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DO L = M,LMAX-1,2 |
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K = K+1 |
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J = L*L+L+1 |
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Q = FACT(L)*P(K) |
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DA = Q*SHC(J+M) |
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DB = Q*SHC(J-M) |
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A = A+DA |
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B = B+DB |
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E = E+DA |
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F = F+DB |
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K = K+1 |
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J = J+L+L+2 |
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Q = FACT(L+1)*P(K) |
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DA = Q*SHC(J+M) |
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DB = Q*SHC(J-M) |
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A = A+DA |
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B = B+DB |
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E = E-DA |
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F = F-DB |
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ENDDO |
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IF(MOD(LMAX-L,2).EQ.0) THEN |
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K = K+1 |
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J = LMAX*LMAX+LMAX+1 |
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Q = FACT(LMAX)*P(K) |
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DA = Q*SHC(J+M) |
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DB = Q*SHC(J-M) |
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A = A+DA |
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B = B+DB |
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E = E+DA |
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F = F+DB |
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ENDIF |
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IF(M.EQ.0) THEN |
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HS(1) = A |
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HN(1) = E |
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ELSE |
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HS(M+M ) = A |
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HS(M+M+1) = B |
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HN(M+M ) = E |
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HN(M+M+1) = F |
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ENDIF |
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ENDDO |
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|
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RETURN |
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END |
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|
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c ================================================================== |
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|
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SUBROUTINE SHC4ZONE(LMAX,SHC,XLAT1,XLAT2,HS,HN,P) |
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|
| 382 |
IMPLICIT NONE |
| 383 |
|
| 384 |
INTEGER LMAX |
| 385 |
REAL SHC((1+LMAX)*(1+LMAX)) ! spherical harmonic coeffs. |
| 386 |
REAL XLAT1 ! latitude. |
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REAL XLAT2 ! latitude. |
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REAL P((LMAX+1)*(LMAX+2)/2) |
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C |
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C - output - |
| 391 |
C |
| 392 |
REAL HS(1+LMAX+LMAX) |
| 393 |
REAL HN(1+LMAX+LMAX) |
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C |
| 395 |
C - work space - |
| 396 |
C |
| 397 |
INTEGER LMAXLMT |
| 398 |
PARAMETER (LMAXLMT=5000) |
| 399 |
|
| 400 |
REAL XLAT, SIN0, SIN1, SIN2, SCALE |
| 401 |
REAL DEG2RAD, CE, CO, SE, SO |
| 402 |
INTEGER I, J, K, L, M |
| 403 |
INTEGER JP, I1, I2 |
| 404 |
|
| 405 |
ce IF(LMAX.GT.LMAXLMT) CALL ABORT('LMAX.GT.LMAXLMT') |
| 406 |
cph IF(LMAX.GT.LMAXLMT) CALL shcError('LMAX.GT.LMAXLMT',1) |
| 407 |
|
| 408 |
IF(XLAT1 .LT. -90.0+1.E-10) THEN |
| 409 |
do i = 1,(1+lmax)*(1+lmax) |
| 410 |
shc(i) = 0.0 |
| 411 |
enddo |
| 412 |
ENDIF |
| 413 |
|
| 414 |
XLAT = 0.5*(XLAT1+XLAT2) |
| 415 |
DEG2RAD = ACOS(-1.0)/180.0 |
| 416 |
SIN0 = SIN(XLAT *DEG2RAD) |
| 417 |
SIN1 = SIN(AMAX1(-90.0,XLAT1)*DEG2RAD) |
| 418 |
SIN2 = SIN(AMIN1( 0.0,XLAT2)*DEG2RAD) |
| 419 |
SCALE = (SIN2 - SIN1)*0.25 |
| 420 |
do i = 1,lmax+lmax+1 |
| 421 |
hs(i) = hs(i)*scale |
| 422 |
hn(i) = hn(i)*scale |
| 423 |
enddo |
| 424 |
|
| 425 |
CALL HELMHOLTZ(LMAX,SIN0,P) |
| 426 |
I = 0 |
| 427 |
cadj loop = parallel |
| 428 |
DO M = 0,LMAX |
| 429 |
IF (M .EQ. 0) THEN |
| 430 |
J = 1 |
| 431 |
JP = 1 |
| 432 |
ELSE |
| 433 |
J = 2*M |
| 434 |
JP = J+1 |
| 435 |
ENDIF |
| 436 |
CE = HS(J)+HN(J) |
| 437 |
CO = HS(J)-HN(J) |
| 438 |
SE = HS(J)+HN(JP) |
| 439 |
SO = HS(J)-HN(JP) |
| 440 |
I1 = I+1 |
| 441 |
I2 = I+2 |
| 442 |
cadj loop = parallel |
| 443 |
DO L = M,LMAX-1,2 |
| 444 |
K = L*L+L+1 |
| 445 |
SHC(K+M) = SHC(K+M) + P(I1) * CE |
| 446 |
SHC(K-M) = SHC(K-M) + P(I1) * SE |
| 447 |
K = K+L+L+2 |
| 448 |
SHC(K+M) = SHC(K+M) + P(I2) * CO |
| 449 |
SHC(K-M) = SHC(K-M) + P(I2) * SO |
| 450 |
ENDDO |
| 451 |
I = I + 2 |
| 452 |
IF(MOD(LMAX-M,2).NE.1) THEN |
| 453 |
I = I+1 |
| 454 |
K = LMAX*LMAX+LMAX+1 |
| 455 |
SHC(K+M) = SHC(K+M) + P(I) * CE |
| 456 |
SHC(K-M) = SHC(K-M) + P(I) * SE |
| 457 |
ENDIF |
| 458 |
ENDDO |
| 459 |
RETURN |
| 460 |
END |
| 461 |
|
| 462 |
c ================================================================== |
| 463 |
|
| 464 |
subroutine fsc2dat(n,fsc) |
| 465 |
c |
| 466 |
c --- this routine are coded to clarify the imsl's fftrf/fftrb. |
| 467 |
c |
| 468 |
implicit none |
| 469 |
|
| 470 |
integer n |
| 471 |
real fsc(n) |
| 472 |
|
| 473 |
integer i |
| 474 |
|
| 475 |
do i = 2,n-1,2 |
| 476 |
fsc(i ) = fsc(i )*0.5 |
| 477 |
fsc(i+1) = -fsc(i+1)*0.5 ! change sign of sine coeffs. |
| 478 |
enddo |
| 479 |
|
| 480 |
#ifdef USE_SPH_PROJECTION |
| 481 |
call fftrb(n,fsc,fsc) |
| 482 |
#else |
| 483 |
do i = 1,n |
| 484 |
fsc( i ) = 0.0 |
| 485 |
enddo |
| 486 |
#endif |
| 487 |
|
| 488 |
return |
| 489 |
end |
| 490 |
|
| 491 |
c ================================================================== |
| 492 |
|
| 493 |
SUBROUTINE FRSBASE(A,H,I,J) |
| 494 |
C |
| 495 |
C --- Given A (in degree), return H(I:J) = 1,COS(A),SIN(A)..... |
| 496 |
C |
| 497 |
IMPLICIT NONE |
| 498 |
|
| 499 |
REAL A |
| 500 |
REAL H(1) |
| 501 |
INTEGER I, J |
| 502 |
|
| 503 |
REAL DEG2RAD, T, ARG |
| 504 |
INTEGER N, L |
| 505 |
|
| 506 |
DEG2RAD = ACOS(-1.0)/180.0 |
| 507 |
|
| 508 |
N = J-I+1 |
| 509 |
IF(N.LE.0) RETURN |
| 510 |
H(I) = 1.0 |
| 511 |
IF(N.EQ.1) RETURN |
| 512 |
ARG = A * DEG2RAD |
| 513 |
H(I+1) = COS(ARG) |
| 514 |
IF(N.EQ.2) RETURN |
| 515 |
H(I+2) = SIN(ARG) |
| 516 |
IF(N.EQ.3) RETURN |
| 517 |
T = H(I+1)+H(I+1) |
| 518 |
H(I+3) = T*H(I+1) - 1.0 |
| 519 |
IF(N.EQ.4) RETURN |
| 520 |
H(I+4) = T*H(I+2) |
| 521 |
IF(N.EQ.5) RETURN |
| 522 |
DO L = I+5,J |
| 523 |
H(L) = T*H(L-2)-H(L-4) |
| 524 |
END DO |
| 525 |
|
| 526 |
RETURN |
| 527 |
END |
| 528 |
|
| 529 |
c ================================================================== |
| 530 |
|
| 531 |
SUBROUTINE HELMHOLTZ(LMAX,S,P) |
| 532 |
C |
| 533 |
C --- compute the fully normalized associated legendre polynomials. |
| 534 |
C |
| 535 |
IMPLICIT NONE |
| 536 |
|
| 537 |
INTEGER LMAX ! INPUT max. degree. |
| 538 |
REAL S ! INPUT sin(latitude). |
| 539 |
REAL P(1) ! OUTPUT assoc. legendre polynomials. |
| 540 |
|
| 541 |
INTEGER LMAXLMT |
| 542 |
PARAMETER(LMAXLMT=10800) |
| 543 |
|
| 544 |
REAL A(0:LMAXLMT) |
| 545 |
REAL ISECT(0:LMAXLMT) |
| 546 |
REAL X(LMAXLMT) |
| 547 |
REAL Y(LMAXLMT+LMAXLMT) |
| 548 |
REAL Z(LMAXLMT) |
| 549 |
|
| 550 |
INTEGER LMAXOLD |
| 551 |
DATA LMAXOLD/-1/ |
| 552 |
SAVE LMAXOLD, ISECT, X, Y, Z |
| 553 |
|
| 554 |
REAL C, CM, AK |
| 555 |
INTEGER K, L, N, M |
| 556 |
|
| 557 |
IF(LMAX.NE.LMAXOLD) THEN |
| 558 |
ISECT(0) = 1 |
| 559 |
DO L = 1,LMAX |
| 560 |
X(L) = SNGL(1.0D0/DSQRT(DBLE(FLOAT(4*L*L-1)))) |
| 561 |
Y(L) = SNGL(DSQRT(DBLE(FLOAT(L)))) |
| 562 |
Y(L+LMAX) = SNGL(DSQRT(DBLE(FLOAT(L+LMAX)))) |
| 563 |
ISECT(L) = L*LMAX-L*(L-3)/2+1 |
| 564 |
ENDDO |
| 565 |
CALL RECUR_Z(Z,LMAX) |
| 566 |
LMAXOLD = LMAX |
| 567 |
ENDIF |
| 568 |
|
| 569 |
C = SNGL(DSQRT(1.0D0-DBLE(S)*DBLE(S))) |
| 570 |
CM = 1.0 |
| 571 |
P(1) = 1.0 |
| 572 |
DO M = 1,LMAX |
| 573 |
K = ISECT(M) |
| 574 |
CM = C * CM |
| 575 |
P(K) = Z(M) * CM |
| 576 |
ENDDO |
| 577 |
N = 1 |
| 578 |
DO M = 0,LMAX-N |
| 579 |
K = ISECT(M)+N |
| 580 |
L = N+M |
| 581 |
AK = X(L)*Y(L+M)*Y(N) |
| 582 |
P(K) = S*P(K-1)/AK |
| 583 |
A(M) = AK |
| 584 |
ENDDO |
| 585 |
DO N = 2,LMAX |
| 586 |
DO M = 0,LMAX-N |
| 587 |
K = ISECT(M)+N |
| 588 |
L = N+M |
| 589 |
AK = X(L)*Y(L+M)*Y(N) |
| 590 |
P(K) =(S*P(K-1)-P(K-2)*A(M))/AK |
| 591 |
A(M) = AK |
| 592 |
ENDDO |
| 593 |
ENDDO |
| 594 |
RETURN |
| 595 |
END |
| 596 |
|
| 597 |
c ================================================================== |
| 598 |
|
| 599 |
SUBROUTINE RECUR_Z(Z,LMAX) |
| 600 |
C |
| 601 |
C --- Coefficients for fully normalized sectorial Legendre polynomials. |
| 602 |
C |
| 603 |
IMPLICIT NONE |
| 604 |
|
| 605 |
INTEGER LMAX |
| 606 |
REAL Z(LMAX) |
| 607 |
|
| 608 |
DOUBLE PRECISION ZZ |
| 609 |
INTEGER L |
| 610 |
|
| 611 |
ZZ = 2.0D0 |
| 612 |
DO L = 1,LMAX |
| 613 |
ZZ = ZZ * DBLE(FLOAT(L+L+1))/DBLE(FLOAT(L+L)) |
| 614 |
Z(L) = SNGL(DSQRT(ZZ)) |
| 615 |
ENDDO |
| 616 |
|
| 617 |
RETURN |
| 618 |
END |
| 619 |
|
| 620 |
c ================================================================== |
| 621 |
|
| 622 |
subroutine shcError( errstring, ierr ) |
| 623 |
c |
| 624 |
c --- Print an error message and exit. Written in order to replace |
| 625 |
c the machine specific routine ABORT. |
| 626 |
c ( Christian Eckert MIT 22-Mar-2000 ) |
| 627 |
c |
| 628 |
implicit none |
| 629 |
|
| 630 |
integer ierr |
| 631 |
character*(*) errstring |
| 632 |
|
| 633 |
if ( ierr .ne. 0 ) then |
| 634 |
print* |
| 635 |
print*,' sphere: ',errstring |
| 636 |
print* |
| 637 |
stop ' ... program stopped.' |
| 638 |
endif |
| 639 |
|
| 640 |
return |
| 641 |
end |
| 642 |
|
| 643 |
c ================================================================== |
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