| 1 |
jmc |
1.3 |
C $Header: $ |
| 2 |
|
|
C $Name: $ |
| 3 |
heimbach |
1.1 |
|
| 4 |
|
|
#include "CPP_OPTIONS.h" |
| 5 |
|
|
|
| 6 |
|
|
c ================================================================== |
| 7 |
|
|
c |
| 8 |
|
|
c shpere.F: Routines that handle the projection onto sherical |
| 9 |
|
|
c harmonics. |
| 10 |
|
|
c |
| 11 |
|
|
c Routines: |
| 12 |
|
|
c |
| 13 |
|
|
c o adfsc4dat - Adjoint routine of fsc4dat. |
| 14 |
|
|
c o shc2grid - Evaluate a spherical harmonics model on a |
| 15 |
|
|
c regular grid. |
| 16 |
|
|
c o shc4grid - Evaluate a spherical harmonics model on a |
| 17 |
|
|
c regular grid. |
| 18 |
|
|
c |
| 19 |
|
|
c o shcrotate - s/r used for the sph analysis ... |
| 20 |
|
|
c o shc2zone - s/r used for the sph analysis ... |
| 21 |
|
|
c o shc4zone - s/r used for the sph analysis ... |
| 22 |
|
|
c o fsc2dat - s/r used for the sph analysis ... |
| 23 |
|
|
c o frsbase - s/r used for the sph analysis ... |
| 24 |
|
|
c o helmholtz - s/r used for the sph analysis ... |
| 25 |
|
|
c o recur_z - s/r used for the sph analysis ... |
| 26 |
|
|
c |
| 27 |
|
|
c o shcError - Print error message and stop program (see below). |
| 28 |
|
|
c |
| 29 |
|
|
c IMSL Routines: |
| 30 |
|
|
c |
| 31 |
|
|
c o fftrb - Compute the real periodic sequence from its Fourier |
| 32 |
|
|
c coefficients. |
| 33 |
|
|
c --> replace by NAGLIB routine. C06... |
| 34 |
|
|
c |
| 35 |
|
|
c Platform-specific: |
| 36 |
|
|
c |
| 37 |
|
|
c M abort - FORTRAN intrinsic on SUN and, presumably, on CRAY to |
| 38 |
|
|
c exit the program if an error condition is met. |
| 39 |
|
|
c |
| 40 |
|
|
c --> Replaced ABORT by shcError ( Christian Eckert MIT 22-Mar-2000 ) |
| 41 |
|
|
c |
| 42 |
|
|
c Note: |
| 43 |
|
|
c ===== |
| 44 |
|
|
c |
| 45 |
|
|
c Where code is written in lower case letters, changes were |
| 46 |
|
|
c introduced. The changes are mainly related to F90 syntax. |
| 47 |
|
|
c Additionally, I replaced the call to the intrinsic *AMOD* |
| 48 |
|
|
c by its generic name *MOD*. ( Ch.E. 25-May-1999 ) |
| 49 |
|
|
c |
| 50 |
|
|
c |
| 51 |
|
|
c Documentation: |
| 52 |
|
|
c |
| 53 |
|
|
c |
| 54 |
|
|
c ================================================================== |
| 55 |
|
|
|
| 56 |
|
|
SUBROUTINE FSC4DAT(N,FSC) |
| 57 |
|
|
|
| 58 |
|
|
IMPLICIT NONE |
| 59 |
|
|
|
| 60 |
|
|
INTEGER N |
| 61 |
|
|
REAL FSC(N) |
| 62 |
|
|
REAL SCALE |
| 63 |
|
|
integer i |
| 64 |
|
|
|
| 65 |
|
|
#ifdef USE_SPH_PROJECTION |
| 66 |
|
|
CALL FFTRF(N,FSC,FSC) |
| 67 |
|
|
#else |
| 68 |
|
|
do i=1,n |
| 69 |
|
|
fsc(i) = 0.0 |
| 70 |
|
|
enddo |
| 71 |
|
|
#endif |
| 72 |
|
|
|
| 73 |
|
|
SCALE = 2.0/FLOAT(N) |
| 74 |
|
|
FSC(1) = FSC(1)/FLOAT(N) |
| 75 |
|
|
|
| 76 |
|
|
CE FSC(2:N-1:2) = FSC(2:N-1:2)*SCALE |
| 77 |
|
|
CE FSC(3:N :2) =-FSC(3:N: 2)*SCALE ! change sign of SINE coeffs. |
| 78 |
|
|
|
| 79 |
|
|
do i = 2,n-1,2 |
| 80 |
|
|
fsc( i ) = fsc( i )*scale |
| 81 |
|
|
enddo |
| 82 |
|
|
do i = 3,n,2 |
| 83 |
|
|
fsc( i ) = -fsc( i )*scale ! change sign of sine coeffs. |
| 84 |
|
|
enddo |
| 85 |
|
|
|
| 86 |
|
|
IF (MOD(N,2).EQ.0) THEN |
| 87 |
|
|
FSC(N) = FSC(N)/FLOAT(N) |
| 88 |
|
|
ENDIF |
| 89 |
|
|
|
| 90 |
|
|
RETURN |
| 91 |
|
|
END |
| 92 |
|
|
|
| 93 |
|
|
c ================================================================== |
| 94 |
|
|
|
| 95 |
|
|
subroutine adfsc4dat(n,adfsc) |
| 96 |
|
|
|
| 97 |
|
|
implicit none |
| 98 |
|
|
|
| 99 |
|
|
integer n |
| 100 |
|
|
real adfsc(n) |
| 101 |
|
|
|
| 102 |
|
|
integer i |
| 103 |
|
|
|
| 104 |
|
|
#ifdef USE_SPH_PROJECTION |
| 105 |
|
|
call fftrb(n,adfsc,adfsc) |
| 106 |
|
|
#else |
| 107 |
|
|
do i=1,n |
| 108 |
|
|
adfsc(i) = 0.0 |
| 109 |
|
|
enddo |
| 110 |
|
|
#endif |
| 111 |
|
|
|
| 112 |
|
|
do i=1,n |
| 113 |
|
|
adfsc(i) = adfsc(i)/float(n) |
| 114 |
|
|
enddo |
| 115 |
|
|
|
| 116 |
|
|
end |
| 117 |
|
|
|
| 118 |
|
|
c ================================================================== |
| 119 |
|
|
|
| 120 |
|
|
SUBROUTINE SHC2GRID( LMAX, SHC, NLON, NLAT, GRID, P ) |
| 121 |
|
|
C |
| 122 |
|
|
C --- Evaluate a spherical harmonics model on a regular grid. |
| 123 |
|
|
C |
| 124 |
|
|
C SHC ! spherical harmonic coefficients in the order of |
| 125 |
|
|
C ! |
| 126 |
|
|
C ! C00 : SHC(1) |
| 127 |
|
|
C ! S11 C10 C11 : SHC(2) SHC(3) SHC(4) |
| 128 |
|
|
C ! S22 S21 C20 C21 C22 : SHC(5) SHC(6) SHC(7) SHC(8) SHC(9) |
| 129 |
|
|
C ! |
| 130 |
|
|
C ! i.e., C(L,M) = SHC(L*L+L+1+M) |
| 131 |
|
|
C ! S(L,M) = SHC(L*L+L+1-M) |
| 132 |
|
|
C NLAT ! number of latitude (zonal) lines. |
| 133 |
|
|
C NLON ! number of longitude (meridional) lines. |
| 134 |
|
|
C ! |
| 135 |
|
|
C GRID ! grid values in the order of |
| 136 |
|
|
C ! ((west to east),south to north) |
| 137 |
|
|
C ! ((LON=1,NLON),LAT=1,NLAT) |
| 138 |
|
|
C ! grid values are defined on the "centers" |
| 139 |
|
|
C ! of geographically regular equi-angular blocks. |
| 140 |
|
|
C |
| 141 |
|
|
C --- Coded by Dr. Myung-Chan Kim, Center for Space Research, 1997 |
| 142 |
|
|
C University of Texas at Austin, Austin, Texas, 78712 |
| 143 |
|
|
C |
| 144 |
|
|
IMPLICIT NONE |
| 145 |
|
|
|
| 146 |
|
|
INTEGER LMAX ! INPUT max. degree |
| 147 |
|
|
REAL SHC((1+LMAX)*(1+LMAX)) ! INPUT spherical harmonics |
| 148 |
|
|
INTEGER NLAT ! INPUT number of latitude lines. |
| 149 |
|
|
INTEGER NLON ! INPUT number of longitude lines. |
| 150 |
|
|
REAL GRID(NLON,NLAT) ! OUTPUT grid values |
| 151 |
|
|
REAL P((LMAX+1)*(LMAX+2)/2) ! work space |
| 152 |
|
|
|
| 153 |
|
|
INTEGER NLONLMT |
| 154 |
|
|
PARAMETER (NLONLMT=10000) |
| 155 |
|
|
REAL HS (NLONLMT) |
| 156 |
|
|
REAL HN (NLONLMT) |
| 157 |
|
|
|
| 158 |
|
|
REAL DLAT, ANGLE, XLAT1, XLAT2 |
| 159 |
|
|
INTEGER LATS, LATN |
| 160 |
|
|
|
| 161 |
|
|
ce integer js, jn |
| 162 |
|
|
|
| 163 |
|
|
integer i |
| 164 |
|
|
|
| 165 |
|
|
ce IF(NLON.GT.NLONLMT) CALL ABORT('NLON.GT.NLONLMT') |
| 166 |
|
|
ce IF(NLON.LT.LMAX*2 ) CALL ABORT('NLON.LT.LMAX*2 ') |
| 167 |
|
|
IF(NLON.GT.NLONLMT) CALL shcError('NLON.GT.NLONLMT',1) |
| 168 |
|
|
IF(NLON.LT.LMAX*2 ) CALL shcError('NLON.LT.LMAX*2 ',1) |
| 169 |
|
|
|
| 170 |
|
|
DLAT = 180.0/FLOAT(NLAT) |
| 171 |
|
|
ANGLE = 180.0/FLOAT(NLON) |
| 172 |
|
|
|
| 173 |
|
|
CALL SHCROTATE(LMAX,SHC,ANGLE) |
| 174 |
|
|
DO LATS = 1,(NLAT+1)/2 |
| 175 |
|
|
LATN = NLAT-(LATS-1) |
| 176 |
|
|
XLAT2 =-90.0 + FLOAT(LATS)*DLAT |
| 177 |
|
|
XLAT1 = XLAT2-DLAT |
| 178 |
|
|
do i=1,nlon |
| 179 |
|
|
hs(i) = 0.0 |
| 180 |
|
|
hn(i) = 0.0 |
| 181 |
|
|
enddo |
| 182 |
|
|
CALL SHC2ZONE( LMAX, SHC, XLAT1, XLAT2, HS, HN, P ) |
| 183 |
|
|
CALL FSC2DAT( NLON, HS ) |
| 184 |
|
|
CALL FSC2DAT( NLON, HN ) |
| 185 |
|
|
do i=1,nlon |
| 186 |
|
|
grid(i,lats) = hs(i) |
| 187 |
|
|
grid(i,latn) = hn(i) |
| 188 |
|
|
enddo |
| 189 |
|
|
ENDDO |
| 190 |
|
|
CALL SHCROTATE(LMAX,SHC,-ANGLE) |
| 191 |
|
|
RETURN |
| 192 |
|
|
END |
| 193 |
|
|
|
| 194 |
|
|
c ================================================================== |
| 195 |
|
|
|
| 196 |
|
|
SUBROUTINE SHC4GRID( LMAX, SHC, NLON, NLAT, GRID, P ) |
| 197 |
|
|
|
| 198 |
|
|
IMPLICIT NONE |
| 199 |
|
|
|
| 200 |
|
|
INTEGER LMAX ! INPUT max. degree |
| 201 |
|
|
REAL SHC((1+LMAX)*(1+LMAX)) ! OUTPUT spherical harmonics |
| 202 |
|
|
INTEGER NLAT ! INPUT number of latitude lines. |
| 203 |
|
|
INTEGER NLON ! INPUT number of longitude lines. |
| 204 |
|
|
REAL GRID(NLON,NLAT) ! INPUT grid values |
| 205 |
|
|
REAL P((LMAX+1)*(LMAX+2)/2) ! work space |
| 206 |
|
|
|
| 207 |
|
|
INTEGER NLONLMT |
| 208 |
|
|
PARAMETER (NLONLMT=10000) |
| 209 |
|
|
REAL HS (NLONLMT) |
| 210 |
|
|
REAL HN (NLONLMT) |
| 211 |
|
|
|
| 212 |
|
|
REAL DLAT, ANGLE, XLAT1, XLAT2 |
| 213 |
|
|
INTEGER LATS, LATN |
| 214 |
|
|
|
| 215 |
|
|
ce integer js, jn |
| 216 |
|
|
|
| 217 |
|
|
integer i |
| 218 |
|
|
|
| 219 |
|
|
IF(NLON.GT.NLONLMT) THEN |
| 220 |
|
|
PRINT *, 'NLON = ', NLON |
| 221 |
|
|
PRINT *, 'NLONLMT = ', NLONLMT |
| 222 |
|
|
ce CALL ABORT('NLON.GT.NLONLMT') |
| 223 |
|
|
CALL shcError('NLON.GT.NLONLMT',1) |
| 224 |
|
|
END IF |
| 225 |
|
|
|
| 226 |
|
|
IF(NLON.LT.LMAX*2 ) THEN |
| 227 |
|
|
PRINT *, 'NLON = ', NLON |
| 228 |
|
|
PRINT *, 'LMAX = ', LMAX |
| 229 |
|
|
ce CALL ABORT('NLON.LT.LMAX*2') |
| 230 |
|
|
CALL shcError('NLON.LT.LMAX*2',1) |
| 231 |
|
|
END IF |
| 232 |
|
|
|
| 233 |
|
|
DLAT = 180.0/FLOAT(NLAT) |
| 234 |
|
|
ANGLE = 180.0/FLOAT(NLON) |
| 235 |
|
|
DO LATS = 1,(NLAT+1)/2 |
| 236 |
|
|
LATN = NLAT-(LATS-1) |
| 237 |
|
|
do i = 1,nlon |
| 238 |
|
|
hs(i) = grid(i,lats) |
| 239 |
|
|
hn(i) = grid(i,latn) |
| 240 |
|
|
enddo |
| 241 |
|
|
CALL FSC4DAT(NLON,HS) |
| 242 |
|
|
CALL FSC4DAT(NLON,HN) |
| 243 |
|
|
XLAT2 =-90.0 + FLOAT(LATS)*DLAT |
| 244 |
|
|
XLAT1 = XLAT2-DLAT |
| 245 |
|
|
CALL SHC4ZONE(LMAX,SHC,XLAT1,XLAT2,HS,HN,P) |
| 246 |
|
|
ENDDO |
| 247 |
|
|
CALL SHCROTATE(LMAX,SHC,-ANGLE) |
| 248 |
|
|
|
| 249 |
|
|
RETURN |
| 250 |
|
|
END |
| 251 |
|
|
|
| 252 |
|
|
c ================================================================== |
| 253 |
|
|
|
| 254 |
|
|
SUBROUTINE SHCROTATE(LMAX,SHC,ANGLE) |
| 255 |
|
|
|
| 256 |
|
|
IMPLICIT NONE |
| 257 |
|
|
|
| 258 |
|
|
INTEGER LMAX ! max. degree of spherical harmonics. |
| 259 |
|
|
REAL SHC((1+LMAX)*(1+LMAX)) ! spherical harmonic coeffs. |
| 260 |
|
|
REAL ANGLE ! in degree. |
| 261 |
|
|
|
| 262 |
|
|
INTEGER LMAXLMT |
| 263 |
|
|
PARAMETER (LMAXLMT=10000) |
| 264 |
|
|
|
| 265 |
|
|
REAL H(LMAXLMT*2+1) |
| 266 |
|
|
INTEGER K, L, M |
| 267 |
|
|
REAL SINA, COSA, C, S |
| 268 |
|
|
|
| 269 |
|
|
if (mod(angle,360.0) .ne. 0.0) then |
| 270 |
|
|
|
| 271 |
|
|
CALL FRSBASE(ANGLE,H,1,1+LMAX+LMAX) |
| 272 |
|
|
|
| 273 |
|
|
DO M = 0,LMAX |
| 274 |
|
|
IF(M.EQ.0) THEN |
| 275 |
|
|
SINA = 0.0 |
| 276 |
|
|
COSA = 1.0 |
| 277 |
|
|
ELSE |
| 278 |
|
|
COSA = H(M+M) |
| 279 |
|
|
SINA = H(M+M+1) |
| 280 |
|
|
ENDIF |
| 281 |
|
|
DO L = M,LMAX |
| 282 |
|
|
K = L*L+L+1 |
| 283 |
|
|
C = SHC(K+M) |
| 284 |
|
|
S = SHC(K-M) |
| 285 |
|
|
SHC(K+M) = COSA*C + SINA*S |
| 286 |
|
|
SHC(K-M) =-SINA*C + COSA*S |
| 287 |
|
|
ENDDO |
| 288 |
|
|
ENDDO |
| 289 |
|
|
|
| 290 |
|
|
ENDIF |
| 291 |
|
|
|
| 292 |
|
|
RETURN |
| 293 |
|
|
END |
| 294 |
|
|
|
| 295 |
|
|
c ================================================================== |
| 296 |
|
|
|
| 297 |
|
|
SUBROUTINE SHC2ZONE(LMAX,SHC,XLAT1,XLAT2,HS,HN,P) |
| 298 |
|
|
|
| 299 |
|
|
IMPLICIT NONE |
| 300 |
|
|
|
| 301 |
|
|
INTEGER LMAX ! INPUT max. degree of spher. harmonics. |
| 302 |
|
|
REAL SHC((1+LMAX)*(1+LMAX)) ! INPUT spherical harmonic coeffs. |
| 303 |
|
|
REAL XLAT1 ! INPUT latitude. |
| 304 |
|
|
REAL XLAT2 ! INPUT latitude. |
| 305 |
|
|
REAL HS(1+LMAX+LMAX) ! OUTPUT |
| 306 |
|
|
REAL HN(1+LMAX+LMAX) ! OUTPUT |
| 307 |
|
|
REAL P((LMAX+1)*(LMAX+2)/2) ! INPUT |
| 308 |
|
|
|
| 309 |
|
|
INTEGER LMAXLMT |
| 310 |
|
|
PARAMETER (LMAXLMT=5000) |
| 311 |
|
|
|
| 312 |
|
|
REAL FACT(0:LMAXLMT) ! |
| 313 |
|
|
INTEGER LMAX1, J, K, L, M |
| 314 |
|
|
REAL DEG2RAD, SLAT |
| 315 |
|
|
REAL A, B, E, F, Q, DA, DB, XLAT |
| 316 |
|
|
|
| 317 |
|
|
ce IF (LMAX.GT.LMAXLMT) CALL ABORT('LMAX.GT.LMAXLMT') |
| 318 |
heimbach |
1.2 |
cph IF (LMAX.GT.LMAXLMT) CALL shcError('LMAX.GT.LMAXLMT',1) |
| 319 |
heimbach |
1.1 |
|
| 320 |
|
|
DEG2RAD = ACOS(-1.0)/180.0 |
| 321 |
|
|
XLAT = 0.5*(XLAT1+XLAT2) |
| 322 |
|
|
do k = 1,lmax |
| 323 |
|
|
fact(k) = 1.0 |
| 324 |
|
|
enddo |
| 325 |
|
|
SLAT = SIN(XLAT*DEG2RAD) |
| 326 |
|
|
|
| 327 |
|
|
CALL HELMHOLTZ(LMAX,SLAT,P) |
| 328 |
|
|
LMAX1 = LMAX+1 |
| 329 |
|
|
K = 0 |
| 330 |
|
|
DO M = 0,LMAX |
| 331 |
|
|
A = 0.0 |
| 332 |
|
|
B = 0.0 |
| 333 |
|
|
E = 0.0 |
| 334 |
|
|
F = 0.0 |
| 335 |
|
|
DO L = M,LMAX-1,2 |
| 336 |
|
|
K = K+1 |
| 337 |
|
|
J = L*L+L+1 |
| 338 |
|
|
Q = FACT(L)*P(K) |
| 339 |
|
|
DA = Q*SHC(J+M) |
| 340 |
|
|
DB = Q*SHC(J-M) |
| 341 |
|
|
A = A+DA |
| 342 |
|
|
B = B+DB |
| 343 |
|
|
E = E+DA |
| 344 |
|
|
F = F+DB |
| 345 |
|
|
K = K+1 |
| 346 |
|
|
J = J+L+L+2 |
| 347 |
|
|
Q = FACT(L+1)*P(K) |
| 348 |
|
|
DA = Q*SHC(J+M) |
| 349 |
|
|
DB = Q*SHC(J-M) |
| 350 |
|
|
A = A+DA |
| 351 |
|
|
B = B+DB |
| 352 |
|
|
E = E-DA |
| 353 |
|
|
F = F-DB |
| 354 |
|
|
ENDDO |
| 355 |
|
|
IF(MOD(LMAX-L,2).EQ.0) THEN |
| 356 |
|
|
K = K+1 |
| 357 |
|
|
J = LMAX*LMAX+LMAX+1 |
| 358 |
|
|
Q = FACT(LMAX)*P(K) |
| 359 |
|
|
DA = Q*SHC(J+M) |
| 360 |
|
|
DB = Q*SHC(J-M) |
| 361 |
|
|
A = A+DA |
| 362 |
|
|
B = B+DB |
| 363 |
|
|
E = E+DA |
| 364 |
|
|
F = F+DB |
| 365 |
|
|
ENDIF |
| 366 |
|
|
IF(M.EQ.0) THEN |
| 367 |
|
|
HS(1) = A |
| 368 |
|
|
HN(1) = E |
| 369 |
|
|
ELSE |
| 370 |
|
|
HS(M+M ) = A |
| 371 |
|
|
HS(M+M+1) = B |
| 372 |
|
|
HN(M+M ) = E |
| 373 |
|
|
HN(M+M+1) = F |
| 374 |
|
|
ENDIF |
| 375 |
|
|
ENDDO |
| 376 |
|
|
|
| 377 |
|
|
RETURN |
| 378 |
|
|
END |
| 379 |
|
|
|
| 380 |
|
|
c ================================================================== |
| 381 |
|
|
|
| 382 |
|
|
SUBROUTINE SHC4ZONE(LMAX,SHC,XLAT1,XLAT2,HS,HN,P) |
| 383 |
|
|
|
| 384 |
|
|
IMPLICIT NONE |
| 385 |
|
|
|
| 386 |
|
|
INTEGER LMAX |
| 387 |
|
|
REAL SHC((1+LMAX)*(1+LMAX)) ! spherical harmonic coeffs. |
| 388 |
|
|
REAL XLAT1 ! latitude. |
| 389 |
|
|
REAL XLAT2 ! latitude. |
| 390 |
|
|
REAL P((LMAX+1)*(LMAX+2)/2) |
| 391 |
|
|
C |
| 392 |
|
|
C - output - |
| 393 |
|
|
C |
| 394 |
|
|
REAL HS(1+LMAX+LMAX) |
| 395 |
|
|
REAL HN(1+LMAX+LMAX) |
| 396 |
|
|
C |
| 397 |
|
|
C - work space - |
| 398 |
|
|
C |
| 399 |
|
|
INTEGER LMAXLMT |
| 400 |
|
|
PARAMETER (LMAXLMT=5000) |
| 401 |
|
|
|
| 402 |
|
|
REAL XLAT, SIN0, SIN1, SIN2, SCALE |
| 403 |
|
|
REAL DEG2RAD, CE, CO, SE, SO |
| 404 |
|
|
INTEGER I, J, K, L, M |
| 405 |
|
|
INTEGER JP, I1, I2 |
| 406 |
|
|
|
| 407 |
|
|
ce IF(LMAX.GT.LMAXLMT) CALL ABORT('LMAX.GT.LMAXLMT') |
| 408 |
heimbach |
1.2 |
cph IF(LMAX.GT.LMAXLMT) CALL shcError('LMAX.GT.LMAXLMT',1) |
| 409 |
heimbach |
1.1 |
|
| 410 |
|
|
IF(XLAT1 .LT. -90.0+1.E-10) THEN |
| 411 |
|
|
do i = 1,(1+lmax)*(1+lmax) |
| 412 |
|
|
shc(i) = 0.0 |
| 413 |
|
|
enddo |
| 414 |
|
|
ENDIF |
| 415 |
|
|
|
| 416 |
|
|
XLAT = 0.5*(XLAT1+XLAT2) |
| 417 |
|
|
DEG2RAD = ACOS(-1.0)/180.0 |
| 418 |
|
|
SIN0 = SIN(XLAT *DEG2RAD) |
| 419 |
|
|
SIN1 = SIN(AMAX1(-90.0,XLAT1)*DEG2RAD) |
| 420 |
|
|
SIN2 = SIN(AMIN1( 0.0,XLAT2)*DEG2RAD) |
| 421 |
|
|
SCALE = (SIN2 - SIN1)*0.25 |
| 422 |
|
|
do i = 1,lmax+lmax+1 |
| 423 |
|
|
hs(i) = hs(i)*scale |
| 424 |
|
|
hn(i) = hn(i)*scale |
| 425 |
|
|
enddo |
| 426 |
|
|
|
| 427 |
|
|
CALL HELMHOLTZ(LMAX,SIN0,P) |
| 428 |
|
|
I = 0 |
| 429 |
|
|
cadj loop = parallel |
| 430 |
|
|
DO M = 0,LMAX |
| 431 |
|
|
IF (M .EQ. 0) THEN |
| 432 |
|
|
J = 1 |
| 433 |
|
|
JP = 1 |
| 434 |
|
|
ELSE |
| 435 |
|
|
J = 2*M |
| 436 |
|
|
JP = J+1 |
| 437 |
|
|
ENDIF |
| 438 |
|
|
CE = HS(J)+HN(J) |
| 439 |
|
|
CO = HS(J)-HN(J) |
| 440 |
|
|
SE = HS(J)+HN(JP) |
| 441 |
|
|
SO = HS(J)-HN(JP) |
| 442 |
|
|
I1 = I+1 |
| 443 |
|
|
I2 = I+2 |
| 444 |
|
|
cadj loop = parallel |
| 445 |
|
|
DO L = M,LMAX-1,2 |
| 446 |
|
|
K = L*L+L+1 |
| 447 |
|
|
SHC(K+M) = SHC(K+M) + P(I1) * CE |
| 448 |
|
|
SHC(K-M) = SHC(K-M) + P(I1) * SE |
| 449 |
|
|
K = K+L+L+2 |
| 450 |
jmc |
1.3 |
SHC(K+M) = SHC(K+M) + P(I2) * CO |
| 451 |
heimbach |
1.1 |
SHC(K-M) = SHC(K-M) + P(I2) * SO |
| 452 |
|
|
ENDDO |
| 453 |
|
|
I = I + 2 |
| 454 |
|
|
IF(MOD(LMAX-M,2).NE.1) THEN |
| 455 |
|
|
I = I+1 |
| 456 |
|
|
K = LMAX*LMAX+LMAX+1 |
| 457 |
|
|
SHC(K+M) = SHC(K+M) + P(I) * CE |
| 458 |
|
|
SHC(K-M) = SHC(K-M) + P(I) * SE |
| 459 |
|
|
ENDIF |
| 460 |
|
|
ENDDO |
| 461 |
|
|
RETURN |
| 462 |
|
|
END |
| 463 |
|
|
|
| 464 |
|
|
c ================================================================== |
| 465 |
|
|
|
| 466 |
|
|
subroutine fsc2dat(n,fsc) |
| 467 |
|
|
c |
| 468 |
|
|
c --- this routine are coded to clarify the imsl's fftrf/fftrb. |
| 469 |
|
|
c |
| 470 |
|
|
implicit none |
| 471 |
|
|
|
| 472 |
|
|
integer n |
| 473 |
|
|
real fsc(n) |
| 474 |
|
|
|
| 475 |
|
|
integer i |
| 476 |
|
|
|
| 477 |
|
|
do i = 2,n-1,2 |
| 478 |
|
|
fsc(i ) = fsc(i )*0.5 |
| 479 |
|
|
fsc(i+1) = -fsc(i+1)*0.5 ! change sign of sine coeffs. |
| 480 |
|
|
enddo |
| 481 |
|
|
|
| 482 |
|
|
#ifdef USE_SPH_PROJECTION |
| 483 |
|
|
call fftrb(n,fsc,fsc) |
| 484 |
|
|
#else |
| 485 |
|
|
do i = 1,n |
| 486 |
|
|
fsc( i ) = 0.0 |
| 487 |
|
|
enddo |
| 488 |
|
|
#endif |
| 489 |
|
|
|
| 490 |
|
|
return |
| 491 |
|
|
end |
| 492 |
|
|
|
| 493 |
|
|
c ================================================================== |
| 494 |
|
|
|
| 495 |
|
|
SUBROUTINE FRSBASE(A,H,I,J) |
| 496 |
|
|
C |
| 497 |
|
|
C --- Given A (in degree), return H(I:J) = 1,COS(A),SIN(A)..... |
| 498 |
|
|
C |
| 499 |
|
|
IMPLICIT NONE |
| 500 |
|
|
|
| 501 |
|
|
REAL A |
| 502 |
|
|
REAL H(1) |
| 503 |
|
|
INTEGER I, J |
| 504 |
|
|
|
| 505 |
|
|
REAL DEG2RAD, T, ARG |
| 506 |
|
|
INTEGER N, L |
| 507 |
|
|
|
| 508 |
|
|
DEG2RAD = ACOS(-1.0)/180.0 |
| 509 |
|
|
|
| 510 |
|
|
N = J-I+1 |
| 511 |
|
|
IF(N.LE.0) RETURN |
| 512 |
|
|
H(I) = 1.0 |
| 513 |
|
|
IF(N.EQ.1) RETURN |
| 514 |
|
|
ARG = A * DEG2RAD |
| 515 |
|
|
H(I+1) = COS(ARG) |
| 516 |
|
|
IF(N.EQ.2) RETURN |
| 517 |
|
|
H(I+2) = SIN(ARG) |
| 518 |
|
|
IF(N.EQ.3) RETURN |
| 519 |
|
|
T = H(I+1)+H(I+1) |
| 520 |
|
|
H(I+3) = T*H(I+1) - 1.0 |
| 521 |
|
|
IF(N.EQ.4) RETURN |
| 522 |
|
|
H(I+4) = T*H(I+2) |
| 523 |
|
|
IF(N.EQ.5) RETURN |
| 524 |
|
|
DO L = I+5,J |
| 525 |
|
|
H(L) = T*H(L-2)-H(L-4) |
| 526 |
|
|
END DO |
| 527 |
|
|
|
| 528 |
|
|
RETURN |
| 529 |
jmc |
1.3 |
END |
| 530 |
heimbach |
1.1 |
|
| 531 |
|
|
c ================================================================== |
| 532 |
|
|
|
| 533 |
|
|
SUBROUTINE HELMHOLTZ(LMAX,S,P) |
| 534 |
|
|
C |
| 535 |
|
|
C --- compute the fully normalized associated legendre polynomials. |
| 536 |
|
|
C |
| 537 |
|
|
IMPLICIT NONE |
| 538 |
|
|
|
| 539 |
|
|
INTEGER LMAX ! INPUT max. degree. |
| 540 |
|
|
REAL S ! INPUT sin(latitude). |
| 541 |
|
|
REAL P(1) ! OUTPUT assoc. legendre polynomials. |
| 542 |
|
|
|
| 543 |
|
|
INTEGER LMAXLMT |
| 544 |
|
|
PARAMETER(LMAXLMT=10800) |
| 545 |
|
|
|
| 546 |
|
|
REAL A(0:LMAXLMT) |
| 547 |
|
|
REAL ISECT(0:LMAXLMT) |
| 548 |
|
|
REAL X(LMAXLMT) |
| 549 |
|
|
REAL Y(LMAXLMT+LMAXLMT) |
| 550 |
|
|
REAL Z(LMAXLMT) |
| 551 |
|
|
|
| 552 |
|
|
INTEGER LMAXOLD |
| 553 |
|
|
DATA LMAXOLD/-1/ |
| 554 |
|
|
SAVE LMAXOLD, ISECT, X, Y, Z |
| 555 |
|
|
|
| 556 |
|
|
REAL C, CM, AK |
| 557 |
|
|
INTEGER K, L, N, M |
| 558 |
|
|
|
| 559 |
|
|
IF(LMAX.NE.LMAXOLD) THEN |
| 560 |
|
|
ISECT(0) = 1 |
| 561 |
|
|
DO L = 1,LMAX |
| 562 |
|
|
X(L) = SNGL(1.0D0/DSQRT(DBLE(FLOAT(4*L*L-1)))) |
| 563 |
|
|
Y(L) = SNGL(DSQRT(DBLE(FLOAT(L)))) |
| 564 |
|
|
Y(L+LMAX) = SNGL(DSQRT(DBLE(FLOAT(L+LMAX)))) |
| 565 |
|
|
ISECT(L) = L*LMAX-L*(L-3)/2+1 |
| 566 |
|
|
ENDDO |
| 567 |
|
|
CALL RECUR_Z(Z,LMAX) |
| 568 |
|
|
LMAXOLD = LMAX |
| 569 |
|
|
ENDIF |
| 570 |
|
|
|
| 571 |
|
|
C = SNGL(DSQRT(1.0D0-DBLE(S)*DBLE(S))) |
| 572 |
|
|
CM = 1.0 |
| 573 |
|
|
P(1) = 1.0 |
| 574 |
|
|
DO M = 1,LMAX |
| 575 |
|
|
K = ISECT(M) |
| 576 |
|
|
CM = C * CM |
| 577 |
|
|
P(K) = Z(M) * CM |
| 578 |
|
|
ENDDO |
| 579 |
|
|
N = 1 |
| 580 |
|
|
DO M = 0,LMAX-N |
| 581 |
|
|
K = ISECT(M)+N |
| 582 |
|
|
L = N+M |
| 583 |
|
|
AK = X(L)*Y(L+M)*Y(N) |
| 584 |
|
|
P(K) = S*P(K-1)/AK |
| 585 |
|
|
A(M) = AK |
| 586 |
|
|
ENDDO |
| 587 |
|
|
DO N = 2,LMAX |
| 588 |
|
|
DO M = 0,LMAX-N |
| 589 |
|
|
K = ISECT(M)+N |
| 590 |
|
|
L = N+M |
| 591 |
|
|
AK = X(L)*Y(L+M)*Y(N) |
| 592 |
|
|
P(K) =(S*P(K-1)-P(K-2)*A(M))/AK |
| 593 |
|
|
A(M) = AK |
| 594 |
|
|
ENDDO |
| 595 |
|
|
ENDDO |
| 596 |
|
|
RETURN |
| 597 |
|
|
END |
| 598 |
|
|
|
| 599 |
|
|
c ================================================================== |
| 600 |
|
|
|
| 601 |
|
|
SUBROUTINE RECUR_Z(Z,LMAX) |
| 602 |
|
|
C |
| 603 |
|
|
C --- Coefficients for fully normalized sectorial Legendre polynomials. |
| 604 |
|
|
C |
| 605 |
|
|
IMPLICIT NONE |
| 606 |
|
|
|
| 607 |
|
|
INTEGER LMAX |
| 608 |
|
|
REAL Z(LMAX) |
| 609 |
|
|
|
| 610 |
|
|
DOUBLE PRECISION ZZ |
| 611 |
|
|
INTEGER L |
| 612 |
|
|
|
| 613 |
|
|
ZZ = 2.0D0 |
| 614 |
|
|
DO L = 1,LMAX |
| 615 |
|
|
ZZ = ZZ * DBLE(FLOAT(L+L+1))/DBLE(FLOAT(L+L)) |
| 616 |
|
|
Z(L) = SNGL(DSQRT(ZZ)) |
| 617 |
|
|
ENDDO |
| 618 |
|
|
|
| 619 |
|
|
RETURN |
| 620 |
|
|
END |
| 621 |
|
|
|
| 622 |
|
|
c ================================================================== |
| 623 |
|
|
|
| 624 |
|
|
subroutine shcError( errstring, ierr ) |
| 625 |
|
|
c |
| 626 |
|
|
c --- Print an error message and exit. Written in order to replace |
| 627 |
|
|
c the machine specific routine ABORT. |
| 628 |
|
|
c ( Christian Eckert MIT 22-Mar-2000 ) |
| 629 |
|
|
c |
| 630 |
|
|
implicit none |
| 631 |
|
|
|
| 632 |
|
|
integer ierr |
| 633 |
|
|
character*(*) errstring |
| 634 |
|
|
|
| 635 |
|
|
if ( ierr .ne. 0 ) then |
| 636 |
|
|
print* |
| 637 |
|
|
print*,' sphere: ',errstring |
| 638 |
|
|
print* |
| 639 |
|
|
stop ' ... program stopped.' |
| 640 |
|
|
endif |
| 641 |
|
|
|
| 642 |
|
|
return |
| 643 |
|
|
end |
| 644 |
|
|
|
| 645 |
|
|
c ================================================================== |
Parent Directory
| 
Revision Log
| 
Revision Graph