| 1 |
jmc |
1.1 |
C $Header: /u/gcmpack/MITgcm/model/src/solve_tridiagonal.F,v 1.10 2012/03/15 15:25:18 jmc Exp $ |
| 2 |
|
|
C $Name: $ |
| 3 |
|
|
|
| 4 |
|
|
#include "CPP_OPTIONS.h" |
| 5 |
|
|
|
| 6 |
|
|
CBOP |
| 7 |
|
|
C !ROUTINE: SOLVE_UV_TRIDIAGO |
| 8 |
|
|
C !INTERFACE: |
| 9 |
|
|
SUBROUTINE SOLVE_UV_TRIDIAGO( |
| 10 |
|
|
I kSize, ols, solve4u, solve4v, |
| 11 |
|
|
I aU, bU, cU, rhsU, |
| 12 |
|
|
I aV, bV, cV, rhsV, |
| 13 |
|
|
O uFld, vFld, |
| 14 |
|
|
O errCode, |
| 15 |
|
|
I subIter, myIter, myThid ) |
| 16 |
|
|
C !DESCRIPTION: \bv |
| 17 |
|
|
C *==========================================================* |
| 18 |
|
|
C | S/R SOLVE_UV_TRIDIAGO |
| 19 |
|
|
C | o Solve a pair of tri-diagonal system along X and Y lines |
| 20 |
|
|
C | (in X-dir for uFld and in Y-dir for vFld) |
| 21 |
|
|
C *==========================================================* |
| 22 |
|
|
C | o Used, e.g., in linear part of seaice LSR solver |
| 23 |
|
|
C *==========================================================* |
| 24 |
|
|
C \ev |
| 25 |
|
|
|
| 26 |
|
|
C !USES: |
| 27 |
|
|
IMPLICIT NONE |
| 28 |
|
|
C == Global data == |
| 29 |
|
|
#include "SIZE.h" |
| 30 |
|
|
#include "EEPARAMS.h" |
| 31 |
|
|
|
| 32 |
|
|
C !INPUT/OUTPUT PARAMETERS: |
| 33 |
|
|
C == Routine Arguments == |
| 34 |
|
|
C kSize :: size in 3rd dimension |
| 35 |
|
|
C ols :: size of overlap (of input arg array) |
| 36 |
|
|
C solve4u :: logical flag, do solve for u-component if true |
| 37 |
|
|
C solve4v :: logical flag, do solve for v-component if true |
| 38 |
|
|
C aU,bU,cU :: u-matrix (lower diagonal, main diagonal & upper diagonal) |
| 39 |
|
|
C rhsU :: RHS vector (u-component) |
| 40 |
|
|
C aV,bV,cV :: v-matrix (lower diagonal, main diagonal & upper diagonal) |
| 41 |
|
|
C rhsV :: RHS vector (v-component) |
| 42 |
|
|
C uFld :: X = solution of: A_u * X = rhsU |
| 43 |
|
|
C vFld :: X = solution of: A_v * X = rhsV |
| 44 |
|
|
C errCode :: > 0 if singular matrix |
| 45 |
|
|
C subIter :: current sub-iteration number |
| 46 |
|
|
C myIter :: current iteration number |
| 47 |
|
|
C myThid :: my Thread Id number |
| 48 |
|
|
INTEGER kSize, ols |
| 49 |
|
|
LOGICAL solve4u, solve4v |
| 50 |
|
|
_RL aU (1-ols:sNx+ols,1-ols:sNy+ols,kSize,nSx,nSy) |
| 51 |
|
|
_RL bU (1-ols:sNx+ols,1-ols:sNy+ols,kSize,nSx,nSy) |
| 52 |
|
|
_RL cU (1-ols:sNx+ols,1-ols:sNy+ols,kSize,nSx,nSy) |
| 53 |
|
|
_RL rhsU(1-ols:sNx+ols,1-ols:sNy+ols,kSize,nSx,nSy) |
| 54 |
|
|
_RL aV (1-ols:sNx+ols,1-ols:sNy+ols,kSize,nSx,nSy) |
| 55 |
|
|
_RL bV (1-ols:sNx+ols,1-ols:sNy+ols,kSize,nSx,nSy) |
| 56 |
|
|
_RL cV (1-ols:sNx+ols,1-ols:sNy+ols,kSize,nSx,nSy) |
| 57 |
|
|
_RL rhsV(1-ols:sNx+ols,1-ols:sNy+ols,kSize,nSx,nSy) |
| 58 |
|
|
_RL uFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,kSize,nSx,nSy) |
| 59 |
|
|
_RL vFld(1-OLx:sNx+OLx,1-OLy:sNy+OLy,kSize,nSx,nSy) |
| 60 |
|
|
INTEGER errCode |
| 61 |
|
|
INTEGER subIter, myIter, myThid |
| 62 |
|
|
|
| 63 |
|
|
C !SHARED LOCAL VARIABLES: |
| 64 |
|
|
C aTu, cTu, yTu :: tile edges coeff and RHS for u-component |
| 65 |
|
|
C aTv, cTv, yTv :: tile edges coeff and RHS for v-component |
| 66 |
|
|
COMMON /SOLVE_UV_3DIAG_LOCAL/ |
| 67 |
|
|
& aTu, cTu, yTu, aTv, cTv, yTv |
| 68 |
|
|
_RL aTu(2,1:sNy,nSx,nSy) |
| 69 |
|
|
_RL cTu(2,1:sNy,nSx,nSy) |
| 70 |
|
|
_RL yTu(2,1:sNy,nSx,nSy) |
| 71 |
|
|
_RL aTv(2,1:sNx,nSx,nSy) |
| 72 |
|
|
_RL cTv(2,1:sNx,nSx,nSy) |
| 73 |
|
|
_RL yTv(2,1:sNx,nSx,nSy) |
| 74 |
|
|
|
| 75 |
|
|
C !LOCAL VARIABLES: |
| 76 |
|
|
C == Local variables == |
| 77 |
|
|
INTEGER bi, bj, bm, bp |
| 78 |
|
|
INTEGER i,j,k |
| 79 |
|
|
INTEGER ii, im, ip |
| 80 |
|
|
INTEGER jj, jm, jp |
| 81 |
|
|
_RL tmpVar |
| 82 |
|
|
_RL uTmp1, uTmp2, vTmp1, vTmp2 |
| 83 |
|
|
_RL alpU(1:sNx,1:sNy,nSx,nSy) |
| 84 |
|
|
_RL gamU(1:sNx,1:sNy,nSx,nSy) |
| 85 |
|
|
_RL yy_U(1:sNx,1:sNy,nSx,nSy) |
| 86 |
|
|
_RL alpV(1:sNx,1:sNy,nSx,nSy) |
| 87 |
|
|
_RL gamV(1:sNx,1:sNy,nSx,nSy) |
| 88 |
|
|
_RL yy_V(1:sNx,1:sNy,nSx,nSy) |
| 89 |
|
|
CEOP |
| 90 |
|
|
|
| 91 |
|
|
errCode = 0 |
| 92 |
|
|
IF ( .NOT.solve4u .AND. .NOT.solve4v ) RETURN |
| 93 |
|
|
|
| 94 |
|
|
C-- outside loop on level number k |
| 95 |
|
|
DO k = 1,kSize |
| 96 |
|
|
|
| 97 |
|
|
IF ( solve4u ) THEN |
| 98 |
|
|
DO bj=myByLo(myThid),myByHi(myThid) |
| 99 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 100 |
|
|
|
| 101 |
|
|
C-- work on local copy: |
| 102 |
|
|
DO j= 1,sNy |
| 103 |
|
|
DO i= 1,sNx |
| 104 |
|
|
alpU(i,j,bi,bj) = aU(i,j,k,bi,bj) |
| 105 |
|
|
gamU(i,j,bi,bj) = cU(i,j,k,bi,bj) |
| 106 |
|
|
yy_U(i,j,bi,bj) = rhsU(i,j,k,bi,bj) |
| 107 |
|
|
ENDDO |
| 108 |
|
|
ENDDO |
| 109 |
|
|
|
| 110 |
|
|
C-- Beginning of forward sweep (i=1) |
| 111 |
|
|
i = 1 |
| 112 |
|
|
DO j= 1,sNy |
| 113 |
|
|
C- normalise row [1] ( 1 on main diagonal) |
| 114 |
|
|
tmpVar = bU(i,j,k,bi,bj) |
| 115 |
|
|
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 116 |
|
|
tmpVar = 1. _d 0 / tmpVar |
| 117 |
|
|
ELSE |
| 118 |
|
|
tmpVar = 0. _d 0 |
| 119 |
|
|
errCode = 1 |
| 120 |
|
|
ENDIF |
| 121 |
|
|
gamU(i,j,bi,bj) = gamU(i,j,bi,bj)*tmpVar |
| 122 |
|
|
alpU(i,j,bi,bj) = alpU(i,j,bi,bj)*tmpVar |
| 123 |
|
|
yy_U(i,j,bi,bj) = yy_U(i,j,bi,bj)*tmpVar |
| 124 |
|
|
ENDDO |
| 125 |
|
|
|
| 126 |
|
|
C-- Middle of forward sweep (i=2:sNx) |
| 127 |
|
|
DO j= 1,sNy |
| 128 |
|
|
DO i= 2,sNx |
| 129 |
|
|
im = i-1 |
| 130 |
|
|
C- update row [i] <-- [i] - alp_i * [i-1] and normalise (main diagonal = 1) |
| 131 |
|
|
tmpVar = bU(i,j,k,bi,bj) - alpU(i,j,bi,bj)*gamU(im,j,bi,bj) |
| 132 |
|
|
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 133 |
|
|
tmpVar = 1. _d 0 / tmpVar |
| 134 |
|
|
ELSE |
| 135 |
|
|
tmpVar = 0. _d 0 |
| 136 |
|
|
errCode = 1 |
| 137 |
|
|
ENDIF |
| 138 |
|
|
yy_U(i,j,bi,bj) = ( yy_U(i,j,bi,bj) |
| 139 |
|
|
& - alpU(i,j,bi,bj)*yy_U(im,j,bi,bj) |
| 140 |
|
|
& )*tmpVar |
| 141 |
|
|
gamU(i,j,bi,bj) = gamU(i,j,bi,bj)*tmpVar |
| 142 |
|
|
alpU(i,j,bi,bj) = - alpU(i,j,bi,bj)*alpU(im,j,bi,bj)*tmpVar |
| 143 |
|
|
ENDDO |
| 144 |
|
|
ENDDO |
| 145 |
|
|
|
| 146 |
|
|
C-- Backward sweep (i=sNx-1:-1:1) |
| 147 |
|
|
DO j= 1,sNy |
| 148 |
|
|
DO ii= 1,sNx-1 |
| 149 |
|
|
i = sNx - ii |
| 150 |
|
|
ip = i+1 |
| 151 |
|
|
C- update row [i] <-- [i] - gam_i * [i+1] |
| 152 |
|
|
yy_U(i,j,bi,bj) = yy_U(i,j,bi,bj) |
| 153 |
|
|
& - gamU(i,j,bi,bj)*yy_U(ip,j,bi,bj) |
| 154 |
|
|
alpU(i,j,bi,bj) = alpU(i,j,bi,bj) |
| 155 |
|
|
& - gamU(i,j,bi,bj)*alpU(ip,j,bi,bj) |
| 156 |
|
|
gamU(i,j,bi,bj) = -gamU(i,j,bi,bj)*gamU(ip,j,bi,bj) |
| 157 |
|
|
ENDDO |
| 158 |
|
|
ENDDO |
| 159 |
|
|
|
| 160 |
|
|
C-- At this stage, the 3-diagonal system is reduced to Identity with two |
| 161 |
|
|
C more columns (alp & gam) corresponding to unknow X(i=0) and X(i=sNx+1): |
| 162 |
|
|
C X_0 |
| 163 |
|
|
C alp 1 0 ... 0 0 gam X_1 Y_1 |
| 164 |
|
|
C alp 0 1 ... 0 0 gam X_2 Y_2 |
| 165 |
|
|
C |
| 166 |
|
|
C . . . ... . . . . . |
| 167 |
|
|
C ( . . . ... . . . )( . ) = ( . ) |
| 168 |
|
|
C . . . ... . . . . . |
| 169 |
|
|
C |
| 170 |
|
|
C alp 0 0 ... 1 0 gam X_n-1 Y_n-1 |
| 171 |
|
|
C alp 0 0 ... 0 1 gam X_n Y_n |
| 172 |
|
|
C X_n+1 |
| 173 |
|
|
C----- |
| 174 |
|
|
|
| 175 |
|
|
C-- Store tile edges coeff: (1) <--> i=1 ; (2) <--> i=sNx |
| 176 |
|
|
DO j= 1,sNy |
| 177 |
|
|
aTu(1,j,bi,bj) = alpU( 1, j,bi,bj) |
| 178 |
|
|
cTu(1,j,bi,bj) = gamU( 1, j,bi,bj) |
| 179 |
|
|
yTu(1,j,bi,bj) = yy_U( 1, j,bi,bj) |
| 180 |
|
|
aTu(2,j,bi,bj) = alpU(sNx,j,bi,bj) |
| 181 |
|
|
cTu(2,j,bi,bj) = gamU(sNx,j,bi,bj) |
| 182 |
|
|
yTu(2,j,bi,bj) = yy_U(sNx,j,bi,bj) |
| 183 |
|
|
ENDDO |
| 184 |
|
|
|
| 185 |
|
|
C end bi,bj-loops |
| 186 |
|
|
ENDDO |
| 187 |
|
|
ENDDO |
| 188 |
|
|
|
| 189 |
|
|
C-- Solve for tile edges values |
| 190 |
|
|
IF ( nPx*nPy.GT.1 .OR. useCubedSphereExchange ) THEN |
| 191 |
|
|
STOP 'ABNORMAL END: S/R SOLVE_UV_TRIDIAGO: missing code' |
| 192 |
|
|
ENDIF |
| 193 |
|
|
_BARRIER |
| 194 |
|
|
_BEGIN_MASTER(myThid) |
| 195 |
|
|
DO bj=1,nSy |
| 196 |
|
|
DO j=1,sNy |
| 197 |
|
|
|
| 198 |
|
|
DO bi=2,nSx |
| 199 |
|
|
bm = bi-1 |
| 200 |
|
|
C- update row [1,bi] <- [1,bi] - a(1,bi)*[2,bi-1] (& normalise diag) |
| 201 |
|
|
tmpVar = oneRL - aTu(1,j,bi,bj)*cTu(2,j,bm,bj) |
| 202 |
|
|
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 203 |
|
|
tmpVar = 1. _d 0 / tmpVar |
| 204 |
|
|
ELSE |
| 205 |
|
|
tmpVar = 0. _d 0 |
| 206 |
|
|
errCode = 1 |
| 207 |
|
|
ENDIF |
| 208 |
|
|
yTu(1,j,bi,bj) = ( yTu(1,j,bi,bj) |
| 209 |
|
|
& - aTu(1,j,bi,bj)*yTu(2,j,bm,bj) |
| 210 |
|
|
& )*tmpVar |
| 211 |
|
|
cTu(1,j,bi,bj) = cTu(1,j,bi,bj)*tmpVar |
| 212 |
|
|
aTu(1,j,bi,bj) = - aTu(1,j,bi,bj)*aTu(2,j,bm,bj)*tmpVar |
| 213 |
|
|
|
| 214 |
|
|
C- update row [2,bi] <- [2,bi] - a(2,bi)*[2,bi-1] + a(2,bi)*c(2,bi-1)*[1,bi] |
| 215 |
|
|
tmpVar = aTu(2,j,bi,bj)*cTu(2,j,bm,bj) |
| 216 |
|
|
yTu(2,j,bi,bj) = yTu(2,j,bi,bj) |
| 217 |
|
|
& - aTu(2,j,bi,bj)*yTu(2,j,bm,bj) |
| 218 |
|
|
& + tmpVar*yTu(1,j,bi,bj) |
| 219 |
|
|
cTu(2,j,bi,bj) = cTu(2,j,bi,bj) |
| 220 |
|
|
& + tmpVar*cTu(1,j,bi,bj) |
| 221 |
|
|
aTu(2,j,bi,bj) = -aTu(2,j,bi,bj)*aTu(2,j,bm,bj) |
| 222 |
|
|
& + tmpVar*aTu(1,j,bi,bj) |
| 223 |
|
|
ENDDO |
| 224 |
|
|
|
| 225 |
|
|
DO bi=nSx-1,1,-1 |
| 226 |
|
|
bp = bi+1 |
| 227 |
|
|
DO i=1,2 |
| 228 |
|
|
C- update row [1,bi] <- [1,bi] - c(1,bi)*[1,bi+1] |
| 229 |
|
|
C- update row [2,bi] <- [2,bi] - c(2,bi)*[1,bi+1] |
| 230 |
|
|
aTu(i,j,bi,bj) = aTu(i,j,bi,bj) |
| 231 |
|
|
& - cTu(i,j,bi,bj)*aTu(1,j,bp,bj) |
| 232 |
|
|
yTu(i,j,bi,bj) = yTu(i,j,bi,bj) |
| 233 |
|
|
& - cTu(i,j,bi,bj)*yTu(1,j,bp,bj) |
| 234 |
|
|
cTu(i,j,bi,bj) = -cTu(i,j,bi,bj)*cTu(1,j,bp,bj) |
| 235 |
|
|
ENDDO |
| 236 |
|
|
ENDDO |
| 237 |
|
|
|
| 238 |
|
|
C-- periodic in X: X_0 <=> X_Nx and X_(N+1) <=> X_1 ; |
| 239 |
|
|
C find the value at the 2 opposite location (i=1 and i=Nx) |
| 240 |
|
|
bm = 1 |
| 241 |
|
|
bp = nSx |
| 242 |
|
|
cTu(1,j,bm,bj) = oneRL + cTu(1,j,bm,bj) |
| 243 |
|
|
aTu(2,j,bp,bj) = oneRL + aTu(2,j,bp,bj) |
| 244 |
|
|
tmpVar = cTu(1,j,bm,bj) * aTu(2,j,bp,bj) |
| 245 |
|
|
& - aTu(1,j,bm,bj) * cTu(2,j,bp,bj) |
| 246 |
|
|
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 247 |
|
|
tmpVar = 1. _d 0 / tmpVar |
| 248 |
|
|
ELSE |
| 249 |
|
|
tmpVar = 0. _d 0 |
| 250 |
|
|
errCode = 1 |
| 251 |
|
|
ENDIF |
| 252 |
|
|
uTmp1 = ( aTu(2,j,bp,bj) * yTu(1,j,bm,bj) |
| 253 |
|
|
& - aTu(1,j,bm,bj) * yTu(2,j,bp,bj) |
| 254 |
|
|
& )*tmpVar |
| 255 |
|
|
uTmp2 = ( cTu(1,j,bm,bj) * yTu(2,j,bp,bj) |
| 256 |
|
|
& - cTu(2,j,bp,bj) * yTu(1,j,bm,bj) |
| 257 |
|
|
& )*tmpVar |
| 258 |
|
|
|
| 259 |
|
|
C- finalise tile-edges solution (put into RHS "yTu"): |
| 260 |
|
|
DO bi=1,nSx |
| 261 |
|
|
DO i=1,2 |
| 262 |
|
|
IF ( bi+i .EQ.2 ) THEN |
| 263 |
|
|
yTu(i,j,bi,bj) = uTmp1 |
| 264 |
|
|
ELSEIF ( bi+i .EQ. nSx+2 ) THEN |
| 265 |
|
|
yTu(i,j,bi,bj) = uTmp2 |
| 266 |
|
|
ELSE |
| 267 |
|
|
yTu(i,j,bi,bj) = yTu(i,j,bi,bj) |
| 268 |
|
|
& - aTu(i,j,bi,bj) * uTmp2 |
| 269 |
|
|
& - cTu(i,j,bi,bj) * uTmp1 |
| 270 |
|
|
ENDIF |
| 271 |
|
|
ENDDO |
| 272 |
|
|
ENDDO |
| 273 |
|
|
|
| 274 |
|
|
ENDDO |
| 275 |
|
|
ENDDO |
| 276 |
|
|
_END_MASTER(myThid) |
| 277 |
|
|
_BARRIER |
| 278 |
|
|
|
| 279 |
|
|
DO bj=myByLo(myThid),myByHi(myThid) |
| 280 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 281 |
|
|
bm = 1 + MOD(bi-2+nSx,nSx) |
| 282 |
|
|
bp = 1 + MOD(bi-0+nSx,nSx) |
| 283 |
|
|
DO j= 1,sNy |
| 284 |
|
|
DO i= 1,sNx |
| 285 |
|
|
uFld(i,j,k,bi,bj) = yy_U(i,j,bi,bj) |
| 286 |
|
|
& - alpU(i,j,bi,bj) * yTu(2,j,bm,bj) |
| 287 |
|
|
& - gamU(i,j,bi,bj) * yTu(1,j,bp,bj) |
| 288 |
|
|
ENDDO |
| 289 |
|
|
ENDDO |
| 290 |
|
|
ENDDO |
| 291 |
|
|
ENDDO |
| 292 |
|
|
|
| 293 |
|
|
C end solve for uFld |
| 294 |
|
|
ENDIF |
| 295 |
|
|
|
| 296 |
|
|
IF ( solve4v ) THEN |
| 297 |
|
|
DO bj=myByLo(myThid),myByHi(myThid) |
| 298 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 299 |
|
|
|
| 300 |
|
|
C-- work on local copy: |
| 301 |
|
|
DO j= 1,sNy |
| 302 |
|
|
DO i= 1,sNx |
| 303 |
|
|
alpV(i,j,bi,bj) = aV(i,j,k,bi,bj) |
| 304 |
|
|
gamV(i,j,bi,bj) = cV(i,j,k,bi,bj) |
| 305 |
|
|
yy_V(i,j,bi,bj) = rhsV(i,j,k,bi,bj) |
| 306 |
|
|
ENDDO |
| 307 |
|
|
ENDDO |
| 308 |
|
|
|
| 309 |
|
|
C-- Beginning of forward sweep (j=1) |
| 310 |
|
|
j = 1 |
| 311 |
|
|
DO i= 1,sNx |
| 312 |
|
|
C- normalise row [1] ( 1 on main diagonal) |
| 313 |
|
|
tmpVar = bV(i,j,k,bi,bj) |
| 314 |
|
|
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 315 |
|
|
tmpVar = 1. _d 0 / tmpVar |
| 316 |
|
|
ELSE |
| 317 |
|
|
tmpVar = 0. _d 0 |
| 318 |
|
|
errCode = 1 |
| 319 |
|
|
ENDIF |
| 320 |
|
|
gamV(i,j,bi,bj) = gamV(i,j,bi,bj)*tmpVar |
| 321 |
|
|
alpV(i,j,bi,bj) = alpV(i,j,bi,bj)*tmpVar |
| 322 |
|
|
yy_V(i,j,bi,bj) = yy_V(i,j,bi,bj)*tmpVar |
| 323 |
|
|
ENDDO |
| 324 |
|
|
|
| 325 |
|
|
C-- Middle of forward sweep (j=2:sNy) |
| 326 |
|
|
DO i= 1,sNx |
| 327 |
|
|
DO j= 2,sNy |
| 328 |
|
|
jm = j-1 |
| 329 |
|
|
C- update row [j] <-- [j] - alp_j * [j-1] and normalise (main diagonal = 1) |
| 330 |
|
|
tmpVar = bV(i,j,k,bi,bj) - alpV(i,j,bi,bj)*gamV(i,jm,bi,bj) |
| 331 |
|
|
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 332 |
|
|
tmpVar = 1. _d 0 / tmpVar |
| 333 |
|
|
ELSE |
| 334 |
|
|
tmpVar = 0. _d 0 |
| 335 |
|
|
errCode = 1 |
| 336 |
|
|
ENDIF |
| 337 |
|
|
yy_V(i,j,bi,bj) = ( yy_V(i,j,bi,bj) |
| 338 |
|
|
& - alpV(i,j,bi,bj)*yy_V(i,jm,bi,bj) |
| 339 |
|
|
& )*tmpVar |
| 340 |
|
|
gamV(i,j,bi,bj) = gamV(i,j,bi,bj)*tmpVar |
| 341 |
|
|
alpV(i,j,bi,bj) = - alpV(i,j,bi,bj)*alpV(i,jm,bi,bj)*tmpVar |
| 342 |
|
|
ENDDO |
| 343 |
|
|
ENDDO |
| 344 |
|
|
|
| 345 |
|
|
C-- Backward sweep (j=sNy-1:-1:1) |
| 346 |
|
|
DO i= 1,sNx |
| 347 |
|
|
DO jj= 1,sNy-1 |
| 348 |
|
|
j = sNy - jj |
| 349 |
|
|
jp = j+1 |
| 350 |
|
|
C- update row [j] <-- [j] - gam_j * [j+1] |
| 351 |
|
|
yy_V(i,j,bi,bj) = yy_V(i,j,bi,bj) |
| 352 |
|
|
& - gamV(i,j,bi,bj)*yy_V(i,jp,bi,bj) |
| 353 |
|
|
alpV(i,j,bi,bj) = alpV(i,j,bi,bj) |
| 354 |
|
|
& - gamV(i,j,bi,bj)*alpV(i,jp,bi,bj) |
| 355 |
|
|
gamV(i,j,bi,bj) = -gamV(i,j,bi,bj)*gamV(i,jp,bi,bj) |
| 356 |
|
|
ENDDO |
| 357 |
|
|
ENDDO |
| 358 |
|
|
|
| 359 |
|
|
C-- At this stage, the 3-diagonal system is reduced to Identity with two |
| 360 |
|
|
C more columns (alp & gam) corresponding to unknow X(j=0) and X(j=sNy+1) |
| 361 |
|
|
|
| 362 |
|
|
C-- Store tile edges coeff: (1) <--> j=1 ; (2) <--> j=sNy |
| 363 |
|
|
DO i= 1,sNx |
| 364 |
|
|
aTv(1,i,bi,bj) = alpV(i, 1, bi,bj) |
| 365 |
|
|
cTv(1,i,bi,bj) = gamV(i, 1, bi,bj) |
| 366 |
|
|
yTv(1,i,bi,bj) = yy_V(i, 1, bi,bj) |
| 367 |
|
|
aTv(2,i,bi,bj) = alpV(i,sNy,bi,bj) |
| 368 |
|
|
cTv(2,i,bi,bj) = gamV(i,sNy,bi,bj) |
| 369 |
|
|
yTv(2,i,bi,bj) = yy_V(i,sNy,bi,bj) |
| 370 |
|
|
ENDDO |
| 371 |
|
|
|
| 372 |
|
|
C end bi,bj-loops |
| 373 |
|
|
ENDDO |
| 374 |
|
|
ENDDO |
| 375 |
|
|
|
| 376 |
|
|
C-- Solve for tile edges values |
| 377 |
|
|
IF ( nPx*nPy.GT.1 .OR. useCubedSphereExchange ) THEN |
| 378 |
|
|
STOP 'ABNORMAL END: S/R SOLVE_UV_TRIDIAGO: missing code' |
| 379 |
|
|
ENDIF |
| 380 |
|
|
_BARRIER |
| 381 |
|
|
_BEGIN_MASTER(myThid) |
| 382 |
|
|
DO bi=1,nSx |
| 383 |
|
|
DO i=1,sNx |
| 384 |
|
|
|
| 385 |
|
|
DO bj=2,nSy |
| 386 |
|
|
bm = bj-1 |
| 387 |
|
|
C- update row [1,bj] <- [1,bj] - a(1,bj)*[2,bj-1] (& normalise diag) |
| 388 |
|
|
tmpVar = oneRL - aTv(1,i,bi,bj)*cTv(2,i,bi,bm) |
| 389 |
|
|
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 390 |
|
|
tmpVar = 1. _d 0 / tmpVar |
| 391 |
|
|
ELSE |
| 392 |
|
|
tmpVar = 0. _d 0 |
| 393 |
|
|
errCode = 1 |
| 394 |
|
|
ENDIF |
| 395 |
|
|
yTv(1,i,bi,bj) = ( yTv(1,i,bi,bj) |
| 396 |
|
|
& - aTv(1,i,bi,bj)*yTv(2,i,bi,bm) |
| 397 |
|
|
& )*tmpVar |
| 398 |
|
|
cTv(1,i,bi,bj) = cTv(1,i,bi,bj)*tmpVar |
| 399 |
|
|
aTv(1,i,bi,bj) = - aTv(1,i,bi,bj)*aTv(2,i,bi,bm)*tmpVar |
| 400 |
|
|
|
| 401 |
|
|
C- update row [2,bj] <- [2,bj] - a(2,bj)*[2,bj-1] + a(2,bj)*c(2,bj-1)*[1,bj] |
| 402 |
|
|
tmpVar = aTv(2,i,bi,bj)*cTv(2,i,bi,bm) |
| 403 |
|
|
yTv(2,i,bi,bj) = yTv(2,i,bi,bj) |
| 404 |
|
|
& - aTv(2,i,bi,bj)*yTv(2,i,bi,bm) |
| 405 |
|
|
& + tmpVar*yTv(1,i,bi,bj) |
| 406 |
|
|
cTv(2,i,bi,bj) = cTv(2,i,bi,bj) |
| 407 |
|
|
& + tmpVar*cTv(1,i,bi,bj) |
| 408 |
|
|
aTv(2,i,bi,bj) = -aTv(2,i,bi,bj)*aTv(2,i,bi,bm) |
| 409 |
|
|
& + tmpVar*aTv(1,i,bi,bj) |
| 410 |
|
|
ENDDO |
| 411 |
|
|
|
| 412 |
|
|
DO bj=nSy-1,1,-1 |
| 413 |
|
|
bp = bj+1 |
| 414 |
|
|
DO j=1,2 |
| 415 |
|
|
C- update row [1,bj] <- [1,bj] - c(1,bj)*[1,bj+1] |
| 416 |
|
|
C- update row [2,bj] <- [2,bj] - c(2,bj)*[1,bj+1] |
| 417 |
|
|
aTv(j,i,bi,bj) = aTv(j,i,bi,bj) |
| 418 |
|
|
& - cTv(j,i,bi,bj)*aTv(1,i,bi,bp) |
| 419 |
|
|
yTv(j,i,bi,bj) = yTv(j,i,bi,bj) |
| 420 |
|
|
& - cTv(j,i,bi,bj)*yTv(1,i,bi,bp) |
| 421 |
|
|
cTv(j,i,bi,bj) = -cTv(j,i,bi,bj)*cTv(1,i,bi,bp) |
| 422 |
|
|
ENDDO |
| 423 |
|
|
ENDDO |
| 424 |
|
|
|
| 425 |
|
|
C-- periodic in Y: X_0 <=> X_Ny and X_(N+1) <=> X_1 ; |
| 426 |
|
|
C find the value at the 2 opposite location (j=1 and j=Ny) |
| 427 |
|
|
bm = 1 |
| 428 |
|
|
bp = nSy |
| 429 |
|
|
cTv(1,i,bi,bm) = oneRL + cTv(1,i,bi,bm) |
| 430 |
|
|
aTv(2,i,bi,bp) = oneRL + aTv(2,i,bi,bp) |
| 431 |
|
|
tmpVar = cTv(1,i,bi,bm) * aTv(2,i,bi,bp) |
| 432 |
|
|
& - aTv(1,i,bi,bm) * cTv(2,i,bi,bp) |
| 433 |
|
|
IF ( tmpVar.NE.0. _d 0 ) THEN |
| 434 |
|
|
tmpVar = 1. _d 0 / tmpVar |
| 435 |
|
|
ELSE |
| 436 |
|
|
tmpVar = 0. _d 0 |
| 437 |
|
|
errCode = 1 |
| 438 |
|
|
ENDIF |
| 439 |
|
|
vTmp1 = ( aTv(2,i,bi,bp) * yTv(1,i,bi,bm) |
| 440 |
|
|
& - aTv(1,i,bi,bm) * yTv(2,i,bi,bp) |
| 441 |
|
|
& )*tmpVar |
| 442 |
|
|
vTmp2 = ( cTv(1,i,bi,bm) * yTv(2,i,bi,bp) |
| 443 |
|
|
& - cTv(2,i,bi,bp) * yTv(1,i,bi,bm) |
| 444 |
|
|
& )*tmpVar |
| 445 |
|
|
|
| 446 |
|
|
C- finalise tile-edges solution (put into RHS "yTv"): |
| 447 |
|
|
DO bj=1,nSy |
| 448 |
|
|
DO j=1,2 |
| 449 |
|
|
IF ( bj+j .EQ.2 ) THEN |
| 450 |
|
|
yTv(j,i,bi,bj) = vTmp1 |
| 451 |
|
|
ELSEIF ( bj+j .EQ. nSy+2 ) THEN |
| 452 |
|
|
yTv(j,i,bi,bj) = vTmp2 |
| 453 |
|
|
ELSE |
| 454 |
|
|
yTv(j,i,bi,bj) = yTv(j,i,bi,bj) |
| 455 |
|
|
& - aTv(j,i,bi,bj) * vTmp2 |
| 456 |
|
|
& - cTv(j,i,bi,bj) * vTmp1 |
| 457 |
|
|
ENDIF |
| 458 |
|
|
ENDDO |
| 459 |
|
|
ENDDO |
| 460 |
|
|
|
| 461 |
|
|
ENDDO |
| 462 |
|
|
ENDDO |
| 463 |
|
|
_END_MASTER(myThid) |
| 464 |
|
|
_BARRIER |
| 465 |
|
|
|
| 466 |
|
|
DO bj=myByLo(myThid),myByHi(myThid) |
| 467 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
| 468 |
|
|
bm = 1 + MOD(bj-2+nSy,nSy) |
| 469 |
|
|
bp = 1 + MOD(bj-0+nSy,nSy) |
| 470 |
|
|
DO j= 1,sNy |
| 471 |
|
|
DO i= 1,sNx |
| 472 |
|
|
vFld(i,j,k,bi,bj) = yy_V(i,j,bi,bj) |
| 473 |
|
|
& - alpV(i,j,bi,bj) * yTv(2,i,bi,bm) |
| 474 |
|
|
& - gamV(i,j,bi,bj) * yTv(1,i,bi,bp) |
| 475 |
|
|
ENDDO |
| 476 |
|
|
ENDDO |
| 477 |
|
|
ENDDO |
| 478 |
|
|
ENDDO |
| 479 |
|
|
|
| 480 |
|
|
C end solve for vFld |
| 481 |
|
|
ENDIF |
| 482 |
|
|
|
| 483 |
|
|
C end k-loop |
| 484 |
|
|
ENDDO |
| 485 |
|
|
|
| 486 |
|
|
RETURN |
| 487 |
|
|
END |
Parent Directory
| 
Revision Log
| 
Revision Graph