1 |
torge |
1.3 |
C $Header: /u/gcmpack/MITgcm/pkg/seaice/seaice_fgmres.F,v 1.8 2012/11/09 22:19:29 heimbach Exp $ |
2 |
torge |
1.1 |
C $Name: $ |
3 |
|
|
|
4 |
|
|
#include "SEAICE_OPTIONS.h" |
5 |
|
|
|
6 |
|
|
C-- File seaice_fgmres.F: seaice fgmres dynamical (linear) solver S/R: |
7 |
|
|
C-- Contents |
8 |
|
|
C-- o SEAICE_FGMRES_DRIVER |
9 |
|
|
C-- o SEAICE_MAP2VEC |
10 |
|
|
C-- o SEAICE_FGMRES |
11 |
|
|
C-- o SCALPROD |
12 |
|
|
|
13 |
|
|
CBOP |
14 |
|
|
C !ROUTINE: SEAICE_FGMRES_DRIVER |
15 |
|
|
C !INTERFACE: |
16 |
|
|
|
17 |
|
|
SUBROUTINE SEAICE_FGMRES_DRIVER( |
18 |
torge |
1.2 |
I uIceRes, vIceRes, |
19 |
|
|
U duIce, dvIce, |
20 |
|
|
U iCode, |
21 |
torge |
1.3 |
I FGMRESeps, iOutFGMRES, |
22 |
torge |
1.1 |
I newtonIter, krylovIter, myTime, myIter, myThid ) |
23 |
|
|
|
24 |
|
|
C !DESCRIPTION: \bv |
25 |
|
|
C *==========================================================* |
26 |
|
|
C | SUBROUTINE SEAICE_FGMRES_DRIVER |
27 |
|
|
C | o driver routine for fgmres |
28 |
|
|
C | o does the conversion between 2D fields and 1D vector |
29 |
|
|
C | back and forth |
30 |
|
|
C *==========================================================* |
31 |
|
|
C | written by Martin Losch, Oct 2012 |
32 |
|
|
C *==========================================================* |
33 |
|
|
C \ev |
34 |
|
|
|
35 |
|
|
C !USES: |
36 |
|
|
IMPLICIT NONE |
37 |
|
|
|
38 |
|
|
C === Global variables === |
39 |
|
|
#include "SIZE.h" |
40 |
|
|
#include "EEPARAMS.h" |
41 |
|
|
#include "SEAICE_SIZE.h" |
42 |
|
|
#include "SEAICE_PARAMS.h" |
43 |
|
|
|
44 |
|
|
C !INPUT/OUTPUT PARAMETERS: |
45 |
|
|
C === Routine arguments === |
46 |
|
|
C myTime :: Simulation time |
47 |
|
|
C myIter :: Simulation timestep number |
48 |
|
|
C myThid :: my Thread Id. number |
49 |
|
|
C newtonIter :: current iterate of Newton iteration |
50 |
|
|
C krylovIter :: current iterate of Newton iteration |
51 |
torge |
1.3 |
C iCode :: FGMRES parameter to determine next step |
52 |
|
|
C iOutFGMRES :: control output of fgmres |
53 |
torge |
1.1 |
_RL myTime |
54 |
|
|
INTEGER myIter |
55 |
|
|
INTEGER myThid |
56 |
|
|
INTEGER newtonIter |
57 |
|
|
INTEGER krylovIter |
58 |
torge |
1.3 |
INTEGER iOutFGMRES |
59 |
torge |
1.1 |
INTEGER iCode |
60 |
|
|
C FGMRESeps :: tolerance for FGMRES |
61 |
|
|
_RL FGMRESeps |
62 |
|
|
C du/vIce :: solution vector |
63 |
|
|
_RL duIce(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
64 |
|
|
_RL dvIce(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
65 |
|
|
C u/vIceRes :: residual F(u) |
66 |
|
|
_RL uIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
67 |
|
|
_RL vIceRes(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
68 |
|
|
|
69 |
|
|
#if ( defined (SEAICE_CGRID) && \ |
70 |
|
|
defined (SEAICE_ALLOW_JFNK) && \ |
71 |
|
|
defined (SEAICE_ALLOW_DYNAMICS) ) |
72 |
|
|
C Local variables: |
73 |
|
|
C k :: loop indices |
74 |
|
|
INTEGER k |
75 |
|
|
C FGMRES parameters |
76 |
|
|
C n :: size of the input vector(s) |
77 |
|
|
C im :: size of Krylov space |
78 |
|
|
C ifgmres :: interation counter |
79 |
|
|
INTEGER n |
80 |
|
|
PARAMETER ( n = 2*sNx*sNy*nSx*nSy ) |
81 |
|
|
INTEGER im |
82 |
|
|
PARAMETER ( im = 50 ) |
83 |
torge |
1.3 |
INTEGER ifgmres |
84 |
torge |
1.1 |
C work arrays |
85 |
|
|
_RL rhs(n), sol(n) |
86 |
|
|
_RL vv(n,im+1), w(n,im) |
87 |
|
|
_RL wk1(n), wk2(n) |
88 |
|
|
C need to store some of the fgmres parameters and fields so that |
89 |
|
|
C they are not forgotten between Krylov iterations |
90 |
|
|
COMMON /FGMRES_I/ ifgmres |
91 |
|
|
COMMON /FGMRES_RL/ sol, rhs, vv, w |
92 |
|
|
CEOP |
93 |
|
|
|
94 |
|
|
C For now, let only the master thread do all the work |
95 |
|
|
C - copy from 2D arrays to 1D-vector |
96 |
|
|
C - perform fgmres step (including global sums) |
97 |
|
|
C - copy from 1D-vector to 2D arrays |
98 |
|
|
C not sure if this works properly |
99 |
|
|
|
100 |
|
|
_BEGIN_MASTER ( myThid ) |
101 |
|
|
IF ( iCode .EQ. 0 ) THEN |
102 |
torge |
1.3 |
C The first guess is zero because it is a correction, but this |
103 |
|
|
C is implemented by setting du/vIce=0 outside of this routine; |
104 |
|
|
C this make it possible to restart FGMRES with a nonzero sol |
105 |
|
|
CALL SEAICE_MAP2VEC(n,duIce,dvIce,sol,.TRUE.,myThid) |
106 |
torge |
1.2 |
C wk2 needs to be reset for iCode = 0, because it may contain |
107 |
torge |
1.1 |
C remains of the previous Krylov iteration |
108 |
|
|
DO k=1,n |
109 |
|
|
wk2(k) = 0. _d 0 |
110 |
|
|
ENDDO |
111 |
|
|
ELSEIF ( iCode .EQ. 3 ) THEN |
112 |
|
|
CALL SEAICE_MAP2VEC(n,uIceRes,vIceRes,rhs,.TRUE.,myThid) |
113 |
torge |
1.2 |
C change sign of rhs because we are solving J*u = -F |
114 |
|
|
C wk2 needs to be initialised for iCode = 3, because it may contain |
115 |
|
|
C garbage |
116 |
torge |
1.1 |
DO k=1,n |
117 |
|
|
rhs(k) = -rhs(k) |
118 |
torge |
1.2 |
wk2(k) = 0. _d 0 |
119 |
torge |
1.1 |
ENDDO |
120 |
|
|
ELSE |
121 |
torge |
1.2 |
C map preconditioner results or Jacobian times vector, |
122 |
torge |
1.1 |
C stored in du/vIce to wk2 |
123 |
|
|
CALL SEAICE_MAP2VEC(n,duIce,dvIce,wk2,.TRUE.,myThid) |
124 |
|
|
ENDIF |
125 |
torge |
1.2 |
C |
126 |
|
|
CALL SEAICE_FGMRES (n,im,rhs,sol,ifgmres,vv,w,wk1,wk2, |
127 |
torge |
1.1 |
& FGMRESeps,SEAICEkrylovIterMax, |
128 |
torge |
1.3 |
& iOutFGMRES,iCode,krylovIter,myThid) |
129 |
torge |
1.2 |
C |
130 |
torge |
1.1 |
IF ( iCode .EQ. 0 ) THEN |
131 |
|
|
C map sol(ution) vector to du/vIce |
132 |
|
|
CALL SEAICE_MAP2VEC(n,duIce,dvIce,sol,.FALSE.,myThid) |
133 |
|
|
ELSE |
134 |
|
|
C map work vector to du/vIce to either compute a preconditioner |
135 |
|
|
C solution (wk1=rhs) or a Jacobian times wk1 |
136 |
|
|
CALL SEAICE_MAP2VEC(n,duIce,dvIce,wk1,.FALSE.,myThid) |
137 |
|
|
ENDIF |
138 |
|
|
_END_MASTER ( myThid ) |
139 |
torge |
1.2 |
|
140 |
torge |
1.1 |
C Fill overlaps in updated fields |
141 |
|
|
CALL EXCH_UV_XY_RL( duIce, dvIce,.TRUE.,myThid) |
142 |
|
|
|
143 |
|
|
RETURN |
144 |
|
|
END |
145 |
|
|
|
146 |
|
|
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
147 |
|
|
CBOP |
148 |
|
|
C !ROUTINE: SEAICE_MAP2VEC |
149 |
|
|
C !INTERFACE: |
150 |
|
|
|
151 |
|
|
SUBROUTINE SEAICE_MAP2VEC( |
152 |
torge |
1.2 |
I n, |
153 |
|
|
O xfld2d, yfld2d, |
154 |
|
|
U vector, |
155 |
torge |
1.1 |
I map2vec, myThid ) |
156 |
|
|
|
157 |
|
|
C !DESCRIPTION: \bv |
158 |
|
|
C *==========================================================* |
159 |
|
|
C | SUBROUTINE SEAICE_MAP2VEC |
160 |
|
|
C | o maps 2 2D-fields to vector and back |
161 |
|
|
C *==========================================================* |
162 |
|
|
C | written by Martin Losch, Oct 2012 |
163 |
|
|
C *==========================================================* |
164 |
|
|
C \ev |
165 |
|
|
|
166 |
|
|
C !USES: |
167 |
|
|
IMPLICIT NONE |
168 |
|
|
|
169 |
|
|
C === Global variables === |
170 |
|
|
#include "SIZE.h" |
171 |
|
|
#include "EEPARAMS.h" |
172 |
|
|
C === Routine arguments === |
173 |
|
|
INTEGER n |
174 |
|
|
LOGICAL map2vec |
175 |
|
|
INTEGER myThid |
176 |
|
|
_RL xfld2d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
177 |
|
|
_RL yfld2d (1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
178 |
|
|
_RL vector (n) |
179 |
|
|
C === local variables === |
180 |
|
|
INTEGER I, J, bi, bj |
181 |
|
|
INTEGER ii, jj, ib, jb, m |
182 |
|
|
CEOP |
183 |
torge |
1.2 |
|
184 |
torge |
1.1 |
m = n/2 |
185 |
|
|
IF ( map2vec ) THEN |
186 |
|
|
DO bj=myByLo(myThid),myByHi(myThid) |
187 |
|
|
jb = nSx*sNy*sNx*(bj-1) |
188 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
189 |
|
|
ib = jb + sNy*sNx*(bi-1) |
190 |
|
|
DO J=1,sNy |
191 |
|
|
jj = ib + sNx*(J-1) |
192 |
|
|
DO I=1,sNx |
193 |
|
|
ii = jj + I |
194 |
|
|
vector(ii) = xfld2d(I,J,bi,bj) |
195 |
|
|
vector(ii+m) = yfld2d(I,J,bi,bj) |
196 |
|
|
ENDDO |
197 |
|
|
ENDDO |
198 |
|
|
ENDDO |
199 |
torge |
1.2 |
ENDDO |
200 |
torge |
1.1 |
ELSE |
201 |
|
|
DO bj=myByLo(myThid),myByHi(myThid) |
202 |
|
|
jb = nSx*sNy*sNx*(bj-1) |
203 |
|
|
DO bi=myBxLo(myThid),myBxHi(myThid) |
204 |
|
|
ib = jb + sNy*sNx*(bi-1) |
205 |
|
|
DO J=1,sNy |
206 |
|
|
jj = ib + sNx*(J-1) |
207 |
|
|
DO I=1,sNx |
208 |
|
|
ii = jj + I |
209 |
|
|
xfld2d(I,J,bi,bj) = vector(ii) |
210 |
|
|
yfld2d(I,J,bi,bj) = vector(ii+m) |
211 |
|
|
ENDDO |
212 |
|
|
ENDDO |
213 |
|
|
ENDDO |
214 |
torge |
1.2 |
ENDDO |
215 |
torge |
1.1 |
ENDIF |
216 |
|
|
|
217 |
|
|
RETURN |
218 |
|
|
END |
219 |
|
|
|
220 |
|
|
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
221 |
|
|
CBOP |
222 |
|
|
C !ROUTINE: SEAICE_FGMRES |
223 |
|
|
C !INTERFACE: |
224 |
|
|
|
225 |
torge |
1.2 |
SUBROUTINE SEAICE_FGMRES (n,im,rhs,sol,i,vv,w,wk1, wk2, |
226 |
|
|
& eps,maxits,iout,icode,its,myThid) |
227 |
torge |
1.1 |
|
228 |
|
|
C----------------------------------------------------------------------- |
229 |
|
|
C mlosch Oct 2012: modified the routine further to be compliant with |
230 |
|
|
C MITgcm standards: |
231 |
|
|
C f90 -> F |
232 |
|
|
C !-comment -> C-comment |
233 |
|
|
C double precision -> _RL |
234 |
|
|
C implicit none |
235 |
torge |
1.2 |
C |
236 |
torge |
1.1 |
C jfl Dec 1st 2006. We modified the routine so that it is double precison. |
237 |
|
|
C Here are the modifications: |
238 |
torge |
1.2 |
C 1) implicit real (a-h,o-z) becomes implicit real*8 (a-h,o-z) |
239 |
torge |
1.1 |
C 2) real bocomes real*8 |
240 |
|
|
C 3) subroutine scopy.f has been changed for dcopy.f |
241 |
|
|
C 4) subroutine saxpy.f has been changed for daxpy.f |
242 |
|
|
C 5) function sdot.f has been changed for ddot.f |
243 |
|
|
C 6) 1e-08 becomes 1d-08 |
244 |
|
|
C |
245 |
torge |
1.2 |
C Be careful with the dcopy, daxpy and ddot code...there is a slight |
246 |
torge |
1.1 |
C difference with the single precision versions (scopy, saxpy and sdot). |
247 |
|
|
C In the single precision versions, the array are declared sightly differently. |
248 |
|
|
C It is written for single precision: |
249 |
|
|
C |
250 |
|
|
C modified 12/3/93, array(1) declarations changed to array(*) |
251 |
|
|
C----------------------------------------------------------------------- |
252 |
|
|
|
253 |
|
|
implicit none |
254 |
|
|
CML implicit double precision (a-h,o-z) !jfl modification |
255 |
|
|
integer myThid |
256 |
|
|
integer n, im, maxits, iout, icode |
257 |
|
|
_RL rhs(*), sol(*), vv(n,im+1), w(n,im) |
258 |
|
|
_RL wk1(n), wk2(n), eps |
259 |
|
|
C----------------------------------------------------------------------- |
260 |
torge |
1.2 |
C flexible GMRES routine. This is a version of GMRES which allows a |
261 |
|
|
C a variable preconditioner. Implemented with a reverse communication |
262 |
torge |
1.1 |
C protocole for flexibility - |
263 |
torge |
1.2 |
C DISTRIBUTED VERSION (USES DISTDOT FOR DDOT) |
264 |
|
|
C explicit (exact) residual norms for restarts |
265 |
torge |
1.1 |
C written by Y. Saad, modified by A. Malevsky, version February 1, 1995 |
266 |
|
|
C----------------------------------------------------------------------- |
267 |
torge |
1.2 |
C This Is A Reverse Communication Implementation. |
268 |
|
|
C------------------------------------------------- |
269 |
torge |
1.1 |
C USAGE: (see also comments for icode below). FGMRES |
270 |
|
|
C should be put in a loop and the loop should be active for as |
271 |
|
|
C long as icode is not equal to 0. On return fgmres will |
272 |
|
|
C 1) either be requesting the new preconditioned vector applied |
273 |
torge |
1.2 |
C to wk1 in case icode.eq.1 (result should be put in wk2) |
274 |
torge |
1.1 |
C 2) or be requesting the product of A applied to the vector wk1 |
275 |
torge |
1.2 |
C in case icode.eq.2 (result should be put in wk2) |
276 |
|
|
C 3) or be terminated in case icode .eq. 0. |
277 |
torge |
1.1 |
C on entry always set icode = 0. So icode should be set back to zero |
278 |
|
|
C upon convergence. |
279 |
|
|
C----------------------------------------------------------------------- |
280 |
torge |
1.2 |
C Here is a typical way of running fgmres: |
281 |
torge |
1.1 |
C |
282 |
|
|
C icode = 0 |
283 |
|
|
C 1 continue |
284 |
|
|
C call fgmres (n,im,rhs,sol,i,vv,w,wk1, wk2,eps,maxits,iout,icode) |
285 |
|
|
C |
286 |
|
|
C if (icode .eq. 1) then |
287 |
|
|
C call precon(n, wk1, wk2) <--- user variable preconditioning |
288 |
|
|
C goto 1 |
289 |
|
|
C else if (icode .ge. 2) then |
290 |
torge |
1.2 |
C call matvec (n,wk1, wk2) <--- user matrix vector product. |
291 |
torge |
1.1 |
C goto 1 |
292 |
torge |
1.2 |
C else |
293 |
|
|
C ----- done ---- |
294 |
torge |
1.1 |
C ......... |
295 |
|
|
C----------------------------------------------------------------------- |
296 |
torge |
1.2 |
C list of parameters |
297 |
|
|
C------------------- |
298 |
torge |
1.1 |
C |
299 |
|
|
C n == integer. the dimension of the problem |
300 |
|
|
C im == size of Krylov subspace: should not exceed 50 in this |
301 |
|
|
C version (can be reset in code. looking at comment below) |
302 |
|
|
C rhs == vector of length n containing the right hand side |
303 |
|
|
C sol == initial guess on input, approximate solution on output |
304 |
|
|
C vv == work space of size n x (im+1) |
305 |
torge |
1.2 |
C w == work space of length n x im |
306 |
torge |
1.1 |
C wk1, |
307 |
|
|
C wk2, == two work vectors of length n each used for the reverse |
308 |
|
|
C communication protocole. When on return (icode .ne. 1) |
309 |
|
|
C the user should call fgmres again with wk2 = precon * wk1 |
310 |
|
|
C and icode untouched. When icode.eq.1 then it means that |
311 |
|
|
C convergence has taken place. |
312 |
torge |
1.2 |
C |
313 |
torge |
1.1 |
C eps == tolerance for stopping criterion. process is stopped |
314 |
|
|
C as soon as ( ||.|| is the euclidean norm): |
315 |
|
|
C || current residual||/||initial residual|| <= eps |
316 |
|
|
C |
317 |
|
|
C maxits== maximum number of iterations allowed |
318 |
|
|
C |
319 |
|
|
C iout == output unit number number for printing intermediate results |
320 |
|
|
C if (iout .le. 0) no statistics are printed. |
321 |
torge |
1.2 |
C |
322 |
torge |
1.1 |
C icode = integer. indicator for the reverse communication protocole. |
323 |
|
|
C ON ENTRY : icode should be set to icode = 0. |
324 |
torge |
1.2 |
C ON RETURN: |
325 |
torge |
1.1 |
C * icode .eq. 1 value means that fgmres has not finished |
326 |
|
|
C and that it is requesting a preconditioned vector before |
327 |
|
|
C continuing. The user must compute M**(-1) wk1, where M is |
328 |
|
|
C the preconditioing matrix (may vary at each call) and wk1 is |
329 |
torge |
1.2 |
C the vector as provided by fgmres upun return, and put the |
330 |
torge |
1.1 |
C result in wk2. Then fgmres must be called again without |
331 |
torge |
1.2 |
C changing any other argument. |
332 |
torge |
1.1 |
C * icode .eq. 2 value means that fgmres has not finished |
333 |
|
|
C and that it is requesting a matrix vector product before |
334 |
|
|
C continuing. The user must compute A * wk1, where A is the |
335 |
torge |
1.2 |
C coefficient matrix and wk1 is the vector provided by |
336 |
torge |
1.1 |
C upon return. The result of the operation is to be put in |
337 |
|
|
C the vector wk2. Then fgmres must be called again without |
338 |
torge |
1.2 |
C changing any other argument. |
339 |
|
|
C * icode .eq. 0 means that fgmres has finished and sol contains |
340 |
torge |
1.1 |
C the approximate solution. |
341 |
|
|
C comment: typically fgmres must be implemented in a loop |
342 |
torge |
1.2 |
C with fgmres being called as long icode is returned with |
343 |
|
|
C a value .ne. 0. |
344 |
torge |
1.1 |
C----------------------------------------------------------------------- |
345 |
|
|
C local variables -- !jfl modif |
346 |
torge |
1.2 |
integer imax |
347 |
torge |
1.1 |
parameter ( imax = 50 ) |
348 |
|
|
_RL hh(4*imax+1,4*imax),c(4*imax),s(4*imax) |
349 |
|
|
_RL rs(4*imax+1),t,ro |
350 |
|
|
C------------------------------------------------------------- |
351 |
|
|
C arnoldi size should not exceed 50 in this version.. |
352 |
|
|
C------------------------------------------------------------- |
353 |
|
|
integer i, its, i1, ii, j, jj, k, k1!, n1 |
354 |
|
|
_RL r0, gam, epsmac, eps1 |
355 |
|
|
|
356 |
|
|
CEOP |
357 |
|
|
save |
358 |
|
|
data epsmac/1.d-16/ |
359 |
torge |
1.2 |
C |
360 |
|
|
C computed goto |
361 |
|
|
C |
362 |
torge |
1.1 |
if ( im .gt. imax ) stop 'size of krylov space > 50' |
363 |
|
|
goto (100,200,300,11) icode +1 |
364 |
|
|
100 continue |
365 |
|
|
CML n1 = n + 1 |
366 |
|
|
its = 0 |
367 |
|
|
C------------------------------------------------------------- |
368 |
|
|
C ** outer loop starts here.. |
369 |
|
|
C--------------compute initial residual vector -------------- |
370 |
|
|
C 10 continue |
371 |
|
|
CML call dcopy (n, sol, 1, wk1, 1) !jfl modification |
372 |
|
|
do k=1,n |
373 |
|
|
wk1(k)=sol(k) |
374 |
|
|
enddo |
375 |
|
|
icode = 3 |
376 |
torge |
1.2 |
RETURN |
377 |
torge |
1.1 |
11 continue |
378 |
|
|
do j=1,n |
379 |
torge |
1.2 |
vv(j,1) = rhs(j) - wk2(j) |
380 |
torge |
1.1 |
enddo |
381 |
|
|
CML 20 ro = ddot(n, vv, 1, vv,1) !jfl modification |
382 |
|
|
20 call scalprod(n, vv, vv, ro, myThid) |
383 |
|
|
ro = sqrt(ro) |
384 |
torge |
1.2 |
if (ro .eq. 0.0d0) goto 999 |
385 |
|
|
t = 1.0d0/ ro |
386 |
torge |
1.1 |
do j=1, n |
387 |
torge |
1.2 |
vv(j,1) = vv(j,1)*t |
388 |
torge |
1.1 |
enddo |
389 |
|
|
if (its .eq. 0) eps1=eps |
390 |
|
|
if (its .eq. 0) r0 = ro |
391 |
|
|
if (iout .gt. 0) write(*, 199) its, ro!& |
392 |
|
|
C print *,'chau',its, ro !write(iout, 199) its, ro |
393 |
torge |
1.2 |
C |
394 |
torge |
1.1 |
C initialize 1-st term of rhs of hessenberg system.. |
395 |
torge |
1.2 |
C |
396 |
torge |
1.1 |
rs(1) = ro |
397 |
|
|
i = 0 |
398 |
|
|
4 i=i+1 |
399 |
|
|
its = its + 1 |
400 |
|
|
i1 = i + 1 |
401 |
|
|
do k=1, n |
402 |
torge |
1.2 |
wk1(k) = vv(k,i) |
403 |
torge |
1.1 |
enddo |
404 |
torge |
1.2 |
C |
405 |
torge |
1.1 |
C return |
406 |
torge |
1.2 |
C |
407 |
torge |
1.1 |
icode = 1 |
408 |
|
|
|
409 |
torge |
1.2 |
RETURN |
410 |
torge |
1.1 |
200 continue |
411 |
|
|
do k=1, n |
412 |
torge |
1.2 |
w(k,i) = wk2(k) |
413 |
torge |
1.1 |
enddo |
414 |
torge |
1.2 |
C |
415 |
torge |
1.1 |
C call matvec operation |
416 |
torge |
1.2 |
C |
417 |
torge |
1.1 |
icode = 2 |
418 |
|
|
CML call dcopy(n, wk2, 1, wk1, 1) !jfl modification |
419 |
|
|
do k=1,n |
420 |
|
|
wk1(k)=wk2(k) |
421 |
|
|
enddo |
422 |
|
|
C |
423 |
|
|
C return |
424 |
torge |
1.2 |
C |
425 |
|
|
RETURN |
426 |
torge |
1.1 |
300 continue |
427 |
torge |
1.2 |
C |
428 |
torge |
1.1 |
C first call to ope corresponds to intialization goto back to 11. |
429 |
torge |
1.2 |
C |
430 |
torge |
1.1 |
C if (icode .eq. 3) goto 11 |
431 |
|
|
CML call dcopy (n, wk2, 1, vv(1,i1), 1) !jfl modification |
432 |
|
|
do k=1,n |
433 |
|
|
vv(k,i1)=wk2(k) |
434 |
|
|
enddo |
435 |
torge |
1.2 |
C |
436 |
torge |
1.1 |
C modified gram - schmidt... |
437 |
torge |
1.2 |
C |
438 |
torge |
1.1 |
do j=1, i |
439 |
|
|
CML t = ddot(n, vv(1,j), 1, vv(1,i1), 1) !jfl modification |
440 |
|
|
call scalprod(n, vv(1,j), vv(1,i1), t, myThid) |
441 |
|
|
hh(j,i) = t |
442 |
|
|
CML call daxpy(n, -t, vv(1,j), 1, vv(1,i1), 1) !jfl modification |
443 |
|
|
CML enddo |
444 |
|
|
CML do j=1, i |
445 |
|
|
CML t = hh(j,i) |
446 |
|
|
do k=1,n |
447 |
|
|
vv(k,i1) = vv(k,i1) - t*vv(k,j) |
448 |
|
|
enddo |
449 |
|
|
enddo |
450 |
|
|
CML t = sqrt(ddot(n, vv(1,i1), 1, vv(1,i1), 1)) !jfl modification |
451 |
|
|
call scalprod(n, vv(1,i1), vv(1,i1), t, myThid) |
452 |
|
|
t = sqrt(t) |
453 |
|
|
hh(i1,i) = t |
454 |
|
|
if (t .eq. 0.0d0) goto 58 |
455 |
|
|
t = 1.0d0 / t |
456 |
|
|
do k=1,n |
457 |
|
|
vv(k,i1) = vv(k,i1)*t |
458 |
|
|
enddo |
459 |
torge |
1.2 |
C |
460 |
|
|
C done with modified gram schimd and arnoldi step. |
461 |
torge |
1.1 |
C now update factorization of hh |
462 |
torge |
1.2 |
C |
463 |
torge |
1.1 |
58 if (i .eq. 1) goto 121 |
464 |
torge |
1.2 |
C |
465 |
torge |
1.1 |
C perfrom previous transformations on i-th column of h |
466 |
torge |
1.2 |
C |
467 |
torge |
1.1 |
do k=2,i |
468 |
|
|
k1 = k-1 |
469 |
|
|
t = hh(k1,i) |
470 |
|
|
hh(k1,i) = c(k1)*t + s(k1)*hh(k,i) |
471 |
|
|
hh(k,i) = -s(k1)*t + c(k1)*hh(k,i) |
472 |
|
|
enddo |
473 |
|
|
121 gam = sqrt(hh(i,i)**2 + hh(i1,i)**2) |
474 |
|
|
if (gam .eq. 0.0d0) gam = epsmac |
475 |
|
|
C-----------#determine next plane rotation #------------------- |
476 |
|
|
c(i) = hh(i,i)/gam |
477 |
|
|
s(i) = hh(i1,i)/gam |
478 |
|
|
rs(i1) = -s(i)*rs(i) |
479 |
|
|
rs(i) = c(i)*rs(i) |
480 |
torge |
1.2 |
C |
481 |
torge |
1.1 |
C determine res. norm. and test for convergence- |
482 |
torge |
1.2 |
C |
483 |
torge |
1.1 |
hh(i,i) = c(i)*hh(i,i) + s(i)*hh(i1,i) |
484 |
|
|
ro = abs(rs(i1)) |
485 |
|
|
if (iout .gt. 0) write(*, 199) its, ro |
486 |
|
|
if (i .lt. im .and. (ro .gt. eps1)) goto 4 |
487 |
torge |
1.2 |
C |
488 |
torge |
1.1 |
C now compute solution. first solve upper triangular system. |
489 |
torge |
1.2 |
C |
490 |
torge |
1.1 |
rs(i) = rs(i)/hh(i,i) |
491 |
|
|
do ii=2,i |
492 |
|
|
k=i-ii+1 |
493 |
|
|
k1 = k+1 |
494 |
|
|
t=rs(k) |
495 |
|
|
do j=k1,i |
496 |
|
|
t = t-hh(k,j)*rs(j) |
497 |
|
|
enddo |
498 |
|
|
rs(k) = t/hh(k,k) |
499 |
|
|
enddo |
500 |
torge |
1.2 |
C |
501 |
torge |
1.1 |
C done with back substitution.. |
502 |
|
|
C now form linear combination to get solution |
503 |
torge |
1.2 |
C |
504 |
torge |
1.1 |
do j=1, i |
505 |
|
|
t = rs(j) |
506 |
|
|
C call daxpy(n, t, w(1,j), 1, sol,1) !jfl modification |
507 |
|
|
do k=1,n |
508 |
|
|
sol(k) = sol(k) + t*w(k,j) |
509 |
|
|
enddo |
510 |
|
|
enddo |
511 |
torge |
1.2 |
C |
512 |
|
|
C test for return |
513 |
|
|
C |
514 |
torge |
1.1 |
if (ro .le. eps1 .or. its .ge. maxits) goto 999 |
515 |
torge |
1.2 |
C |
516 |
torge |
1.1 |
C else compute residual vector and continue.. |
517 |
torge |
1.2 |
C |
518 |
torge |
1.1 |
C goto 10 |
519 |
|
|
|
520 |
|
|
do j=1,i |
521 |
|
|
jj = i1-j+1 |
522 |
|
|
rs(jj-1) = -s(jj-1)*rs(jj) |
523 |
|
|
rs(jj) = c(jj-1)*rs(jj) |
524 |
|
|
enddo |
525 |
|
|
do j=1,i1 |
526 |
|
|
t = rs(j) |
527 |
|
|
if (j .eq. 1) t = t-1.0d0 |
528 |
|
|
CML call daxpy (n, t, vv(1,j), 1, vv, 1) |
529 |
|
|
do k=1,n |
530 |
|
|
vv(k,1) = vv(k,1) + t*vv(k,j) |
531 |
|
|
enddo |
532 |
|
|
enddo |
533 |
torge |
1.2 |
C |
534 |
torge |
1.1 |
C restart outer loop. |
535 |
torge |
1.2 |
C |
536 |
torge |
1.1 |
goto 20 |
537 |
|
|
999 icode = 0 |
538 |
|
|
|
539 |
|
|
199 format(' -- fgmres its =', i4, ' res. norm =', d26.16) |
540 |
torge |
1.2 |
C |
541 |
|
|
RETURN |
542 |
|
|
C-----end-of-fgmres----------------------------------------------------- |
543 |
torge |
1.1 |
C----------------------------------------------------------------------- |
544 |
torge |
1.2 |
END |
545 |
torge |
1.1 |
|
546 |
|
|
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
547 |
|
|
CBOP |
548 |
|
|
C !ROUTINE: SCALPROD |
549 |
|
|
C !INTERFACE: |
550 |
|
|
|
551 |
|
|
subroutine scalprod(n,dx,dy,t,myThid) |
552 |
|
|
|
553 |
|
|
C forms the dot product of two vectors. |
554 |
|
|
C uses unrolled loops for increments equal to one. |
555 |
|
|
C jack dongarra, linpack, 3/11/78. |
556 |
|
|
C ML: code stolen from BLAS and adapted for parallel applications |
557 |
torge |
1.2 |
|
558 |
torge |
1.1 |
implicit none |
559 |
|
|
#include "SIZE.h" |
560 |
|
|
#include "EEPARAMS.h" |
561 |
|
|
#include "EESUPPORT.h" |
562 |
torge |
1.2 |
integer n |
563 |
|
|
_RL dx(n),dy(n) |
564 |
|
|
real*8 t |
565 |
torge |
1.1 |
integer myThid |
566 |
torge |
1.2 |
|
567 |
torge |
1.1 |
real*8 dtemp |
568 |
torge |
1.2 |
integer i,m,mp1 |
569 |
torge |
1.1 |
#ifdef ALLOW_USE_MPI |
570 |
|
|
INTEGER mpiRC |
571 |
|
|
#endif /* ALLOW_USE_MPI */ |
572 |
|
|
CEOP |
573 |
|
|
C |
574 |
|
|
m = mod(n,5) |
575 |
|
|
dtemp = 0. _d 0 |
576 |
|
|
t = 0. _d 0 |
577 |
|
|
if( m .eq. 0 ) go to 40 |
578 |
|
|
do i = 1,m |
579 |
|
|
dtemp = dtemp + dx(i)*dy(i) |
580 |
|
|
enddo |
581 |
|
|
if( n .lt. 5 ) go to 60 |
582 |
|
|
40 mp1 = m + 1 |
583 |
|
|
do i = mp1,n,5 |
584 |
torge |
1.2 |
dtemp = dtemp + dx(i)*dy(i) + dx(i + 1)*dy(i + 1) + |
585 |
|
|
& dx(i + 2)*dy(i + 2) + dx(i + 3)*dy(i + 3) + |
586 |
torge |
1.1 |
& dx(i + 4)*dy(i + 4) |
587 |
|
|
enddo |
588 |
|
|
60 continue |
589 |
|
|
C sum over all processors |
590 |
|
|
#ifdef ALLOW_USE_MPI |
591 |
|
|
t = dtemp |
592 |
|
|
IF ( usingMPI ) THEN |
593 |
|
|
CALL MPI_Allreduce(t,dtemp,1,MPI_DOUBLE_PRECISION,MPI_SUM, |
594 |
|
|
& MPI_COMM_MODEL,mpiRC) |
595 |
|
|
ENDIF |
596 |
|
|
#endif /* ALLOW_USE_MPI */ |
597 |
|
|
t = dtemp |
598 |
torge |
1.2 |
|
599 |
torge |
1.1 |
CML return |
600 |
|
|
CML end |
601 |
|
|
CML |
602 |
|
|
CML subroutine daxpy(n,da,dx,incx,dy,incy) |
603 |
torge |
1.2 |
CMLC |
604 |
|
|
CMLC constant times a vector plus a vector. |
605 |
|
|
CMLC uses unrolled loops for increments equal to one. |
606 |
|
|
CMLC jack dongarra, linpack, 3/11/78. |
607 |
|
|
CMLC |
608 |
torge |
1.1 |
CML _RL dx(n),dy(n),da |
609 |
|
|
CML integer i,incx,incy,ix,iy,m,mp1,n |
610 |
torge |
1.2 |
CMLC |
611 |
torge |
1.1 |
CML if(n.le.0)return |
612 |
|
|
CML if (da .eq. 0.0d0) return |
613 |
|
|
CML if(incx.eq.1.and.incy.eq.1)go to 20 |
614 |
torge |
1.2 |
CMLC |
615 |
|
|
CMLC code for unequal increments or equal increments |
616 |
|
|
CMLC not equal to 1 |
617 |
|
|
CMLC |
618 |
torge |
1.1 |
CML ix = 1 |
619 |
|
|
CML iy = 1 |
620 |
|
|
CML if(incx.lt.0)ix = (-n+1)*incx + 1 |
621 |
|
|
CML if(incy.lt.0)iy = (-n+1)*incy + 1 |
622 |
|
|
CML do 10 i = 1,n |
623 |
|
|
CML dy(iy) = dy(iy) + da*dx(ix) |
624 |
|
|
CML ix = ix + incx |
625 |
|
|
CML iy = iy + incy |
626 |
|
|
CML 10 continue |
627 |
|
|
CML return |
628 |
torge |
1.2 |
CMLC |
629 |
|
|
CMLC code for both increments equal to 1 |
630 |
|
|
CMLC |
631 |
|
|
CMLC |
632 |
|
|
CMLC clean-up loop |
633 |
|
|
CMLC |
634 |
torge |
1.1 |
CML 20 m = mod(n,4) |
635 |
|
|
CML if( m .eq. 0 ) go to 40 |
636 |
|
|
CML do 30 i = 1,m |
637 |
|
|
CML dy(i) = dy(i) + da*dx(i) |
638 |
|
|
CML 30 continue |
639 |
|
|
CML if( n .lt. 4 ) return |
640 |
|
|
CML 40 mp1 = m + 1 |
641 |
|
|
CML do 50 i = mp1,n,4 |
642 |
|
|
CML dy(i) = dy(i) + da*dx(i) |
643 |
|
|
CML dy(i + 1) = dy(i + 1) + da*dx(i + 1) |
644 |
|
|
CML dy(i + 2) = dy(i + 2) + da*dx(i + 2) |
645 |
|
|
CML dy(i + 3) = dy(i + 3) + da*dx(i + 3) |
646 |
|
|
CML 50 continue |
647 |
|
|
CML return |
648 |
|
|
CML end |
649 |
|
|
CML |
650 |
|
|
CML subroutine dcopy(n,dx,incx,dy,incy) |
651 |
torge |
1.2 |
CMLC |
652 |
|
|
CMLC copies a vector, x, to a vector, y. |
653 |
|
|
CMLC uses unrolled loops for increments equal to one. |
654 |
|
|
CMLC jack dongarra, linpack, 3/11/78. |
655 |
|
|
CMLC |
656 |
torge |
1.1 |
CML _RL dx(n),dy(n) |
657 |
|
|
CML integer i,incx,incy,ix,iy,m,mp1,n |
658 |
torge |
1.2 |
CMLC |
659 |
torge |
1.1 |
CML if(n.le.0)return |
660 |
|
|
CML if(incx.eq.1.and.incy.eq.1)go to 20 |
661 |
torge |
1.2 |
CMLC |
662 |
|
|
CMLC code for unequal increments or equal increments |
663 |
|
|
CMLC not equal to 1 |
664 |
|
|
CMLC |
665 |
torge |
1.1 |
CML ix = 1 |
666 |
|
|
CML iy = 1 |
667 |
|
|
CML if(incx.lt.0)ix = (-n+1)*incx + 1 |
668 |
|
|
CML if(incy.lt.0)iy = (-n+1)*incy + 1 |
669 |
|
|
CML do 10 i = 1,n |
670 |
|
|
CML dy(iy) = dx(ix) |
671 |
|
|
CML ix = ix + incx |
672 |
|
|
CML iy = iy + incy |
673 |
|
|
CML 10 continue |
674 |
|
|
CML return |
675 |
torge |
1.2 |
CMLC |
676 |
|
|
CMLC code for both increments equal to 1 |
677 |
|
|
CMLC |
678 |
|
|
CMLC |
679 |
|
|
CMLC clean-up loop |
680 |
|
|
CMLC |
681 |
torge |
1.1 |
CML 20 m = mod(n,7) |
682 |
|
|
CML if( m .eq. 0 ) go to 40 |
683 |
|
|
CML do 30 i = 1,m |
684 |
|
|
CML dy(i) = dx(i) |
685 |
|
|
CML 30 continue |
686 |
|
|
CML if( n .lt. 7 ) return |
687 |
|
|
CML 40 mp1 = m + 1 |
688 |
|
|
CML do 50 i = mp1,n,7 |
689 |
|
|
CML dy(i) = dx(i) |
690 |
|
|
CML dy(i + 1) = dx(i + 1) |
691 |
|
|
CML dy(i + 2) = dx(i + 2) |
692 |
|
|
CML dy(i + 3) = dx(i + 3) |
693 |
|
|
CML dy(i + 4) = dx(i + 4) |
694 |
|
|
CML dy(i + 5) = dx(i + 5) |
695 |
|
|
CML dy(i + 6) = dx(i + 6) |
696 |
|
|
CML 50 continue |
697 |
|
|
|
698 |
|
|
#endif /* SEAICE_ALLOW_DYNAMICS and SEAICE_CGRID and SEAICE_ALLOW_JFNK */ |
699 |
|
|
|
700 |
|
|
RETURN |
701 |
|
|
END |