Actual source code: gmres.c

petsc-master 2019-08-22
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2: /*
3:     This file implements GMRES (a Generalized Minimal Residual) method.
4:     Reference:  Saad and Schultz, 1986.

7:     Some comments on left vs. right preconditioning, and restarts.
8:     Left and right preconditioning.
9:     If right preconditioning is chosen, then the problem being solved
10:     by gmres is actually
11:        My =  AB^-1 y = f
12:     so the initial residual is
13:           r = f - Mx
14:     Note that B^-1 y = x or y = B x, and if x is non-zero, the initial
15:     residual is
16:           r = f - A x
17:     The final solution is then
18:           x = B^-1 y

20:     If left preconditioning is chosen, then the problem being solved is
21:        My = B^-1 A x = B^-1 f,
22:     and the initial residual is
23:        r  = B^-1(f - Ax)

25:     Restarts:  Restarts are basically solves with x0 not equal to zero.
26:     Note that we can eliminate an extra application of B^-1 between
27:     restarts as long as we don't require that the solution at the end
28:     of an unsuccessful gmres iteration always be the solution x.
29:  */

31:  #include <../src/ksp/ksp/impls/gmres/gmresimpl.h>
32: #define GMRES_DELTA_DIRECTIONS 10
33: #define GMRES_DEFAULT_MAXK     30
34: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
35: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

37: PetscErrorCode    KSPSetUp_GMRES(KSP ksp)
38: {
39:   PetscInt       hh,hes,rs,cc;
41:   PetscInt       max_k,k;
42:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

45:   max_k = gmres->max_k;          /* restart size */
46:   hh    = (max_k + 2) * (max_k + 1);
47:   hes   = (max_k + 1) * (max_k + 1);
48:   rs    = (max_k + 2);
49:   cc    = (max_k + 1);

51:   PetscCalloc5(hh,&gmres->hh_origin,hes,&gmres->hes_origin,rs,&gmres->rs_origin,cc,&gmres->cc_origin,cc,&gmres->ss_origin);
52:   PetscLogObjectMemory((PetscObject)ksp,(hh + hes + rs + 2*cc)*sizeof(PetscScalar));

54:   if (ksp->calc_sings) {
55:     /* Allocate workspace to hold Hessenberg matrix needed by lapack */
56:     PetscMalloc1((max_k + 3)*(max_k + 9),&gmres->Rsvd);
57:     PetscLogObjectMemory((PetscObject)ksp,(max_k + 3)*(max_k + 9)*sizeof(PetscScalar));
58:     PetscMalloc1(6*(max_k+2),&gmres->Dsvd);
59:     PetscLogObjectMemory((PetscObject)ksp,6*(max_k+2)*sizeof(PetscReal));
60:   }

62:   /* Allocate array to hold pointers to user vectors.  Note that we need
63:    4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
64:   gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;

66:   PetscMalloc1(gmres->vecs_allocated,&gmres->vecs);
67:   PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->user_work);
68:   PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->mwork_alloc);
69:   PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+2+max_k)*(sizeof(Vec*)+sizeof(PetscInt)) + gmres->vecs_allocated*sizeof(Vec));

71:   if (gmres->q_preallocate) {
72:     gmres->vv_allocated = VEC_OFFSET + 2 + max_k;

74:     KSPCreateVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,NULL);
75:     PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);

77:     gmres->mwork_alloc[0] = gmres->vv_allocated;
78:     gmres->nwork_alloc    = 1;
79:     for (k=0; k<gmres->vv_allocated; k++) {
80:       gmres->vecs[k] = gmres->user_work[0][k];
81:     }
82:   } else {
83:     gmres->vv_allocated = 5;

85:     KSPCreateVecs(ksp,5,&gmres->user_work[0],0,NULL);
86:     PetscLogObjectParents(ksp,5,gmres->user_work[0]);

88:     gmres->mwork_alloc[0] = 5;
89:     gmres->nwork_alloc    = 1;
90:     for (k=0; k<gmres->vv_allocated; k++) {
91:       gmres->vecs[k] = gmres->user_work[0][k];
92:     }
93:   }
94:   return(0);
95: }

97: /*
98:     Run gmres, possibly with restart.  Return residual history if requested.
99:     input parameters:

101: .        gmres  - structure containing parameters and work areas

103:     output parameters:
104: .        nres    - residuals (from preconditioned system) at each step.
105:                   If restarting, consider passing nres+it.  If null,
106:                   ignored
107: .        itcount - number of iterations used.  nres[0] to nres[itcount]
108:                   are defined.  If null, ignored.

110:     Notes:
111:     On entry, the value in vector VEC_VV(0) should be the initial residual
112:     (this allows shortcuts where the initial preconditioned residual is 0).
113:  */
114: PetscErrorCode KSPGMRESCycle(PetscInt *itcount,KSP ksp)
115: {
116:   KSP_GMRES      *gmres = (KSP_GMRES*)(ksp->data);
117:   PetscReal      res_norm,res,hapbnd,tt;
119:   PetscInt       it     = 0, max_k = gmres->max_k;
120:   PetscBool      hapend = PETSC_FALSE;

123:   if (itcount) *itcount = 0;
124:   VecNormalize(VEC_VV(0),&res_norm);
125:   KSPCheckNorm(ksp,res_norm);
126:   res     = res_norm;
127:   *GRS(0) = res_norm;

129:   /* check for the convergence */
130:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
131:   ksp->rnorm = res;
132:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
133:   gmres->it  = (it - 1);
134:   KSPLogResidualHistory(ksp,res);
135:   KSPMonitor(ksp,ksp->its,res);
136:   if (!res) {
137:     ksp->reason = KSP_CONVERGED_ATOL;
138:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
139:     return(0);
140:   }

142:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
143:   while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
144:     if (it) {
145:       KSPLogResidualHistory(ksp,res);
146:       KSPMonitor(ksp,ksp->its,res);
147:     }
148:     gmres->it = (it - 1);
149:     if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
150:       KSPGMRESGetNewVectors(ksp,it+1);
151:     }
152:     KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);

154:     /* update hessenberg matrix and do Gram-Schmidt */
155:     (*gmres->orthog)(ksp,it);
156:     if (ksp->reason) break;

158:     /* vv(i+1) . vv(i+1) */
159:     VecNormalize(VEC_VV(it+1),&tt);
160:     KSPCheckNorm(ksp,tt);

162:     /* save the magnitude */
163:     *HH(it+1,it)  = tt;
164:     *HES(it+1,it) = tt;

166:     /* check for the happy breakdown */
167:     hapbnd = PetscAbsScalar(tt / *GRS(it));
168:     if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
169:     if (tt < hapbnd) {
170:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
171:       hapend = PETSC_TRUE;
172:     }
173:     KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);

175:     it++;
176:     gmres->it = (it-1);   /* For converged */
177:     ksp->its++;
178:     ksp->rnorm = res;
179:     if (ksp->reason) break;

181:     (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);

183:     /* Catch error in happy breakdown and signal convergence and break from loop */
184:     if (hapend) {
185:       if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
186:         ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
187:       } else if (!ksp->reason) {
188:         if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %g",(double)res);
189:         else {
190:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
191:           break;
192:         }
193:       }
194:     }
195:   }

197:   /* Monitor if we know that we will not return for a restart */
198:   if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
199:     KSPLogResidualHistory(ksp,res);
200:     KSPMonitor(ksp,ksp->its,res);
201:   }

203:   if (itcount) *itcount = it;

206:   /*
207:     Down here we have to solve for the "best" coefficients of the Krylov
208:     columns, add the solution values together, and possibly unwind the
209:     preconditioning from the solution
210:    */
211:   /* Form the solution (or the solution so far) */
212:   KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
213:   return(0);
214: }

216: PetscErrorCode KSPSolve_GMRES(KSP ksp)
217: {
219:   PetscInt       its,itcount,i;
220:   KSP_GMRES      *gmres     = (KSP_GMRES*)ksp->data;
221:   PetscBool      guess_zero = ksp->guess_zero;
222:   PetscInt       N = gmres->max_k + 1;
223:   PetscBLASInt   bN;

226:   if (ksp->calc_sings && !gmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");

228:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
229:   ksp->its = 0;
230:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

232:   itcount     = 0;
233:   gmres->fullcycle = 0;
234:   ksp->reason = KSP_CONVERGED_ITERATING;
235:   while (!ksp->reason) {
236:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
237:     KSPGMRESCycle(&its,ksp);
238:     /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
239:     if the cycle is complete for the computation of the Ritz pairs */
240:     if (its == gmres->max_k) {
241:       gmres->fullcycle++;
242:       if (ksp->calc_ritz) {
243:         if (!gmres->hes_ritz) {
244:           PetscMalloc1(N*N,&gmres->hes_ritz);
245:           PetscLogObjectMemory((PetscObject)ksp,N*N*sizeof(PetscScalar));
246:           VecDuplicateVecs(VEC_VV(0),N,&gmres->vecb);
247:         }
248:         PetscBLASIntCast(N,&bN);
249:         PetscArraycpy(gmres->hes_ritz,gmres->hes_origin,bN*bN);
250:         for (i=0; i<gmres->max_k+1; i++) {
251:           VecCopy(VEC_VV(i),gmres->vecb[i]);
252:         }
253:       }
254:     }
255:     itcount += its;
256:     if (itcount >= ksp->max_it) {
257:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
258:       break;
259:     }
260:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
261:   }
262:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
263:   return(0);
264: }

266: PetscErrorCode KSPReset_GMRES(KSP ksp)
267: {
268:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
270:   PetscInt       i;

273:   /* Free the Hessenberg matrices */
274:   PetscFree6(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin,gmres->hes_ritz);

276:   /* free work vectors */
277:   PetscFree(gmres->vecs);
278:   for (i=0; i<gmres->nwork_alloc; i++) {
279:     VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
280:   }
281:   gmres->nwork_alloc = 0;
282:   if (gmres->vecb)  {
283:     VecDestroyVecs(gmres->max_k+1,&gmres->vecb);
284:   }

286:   PetscFree(gmres->user_work);
287:   PetscFree(gmres->mwork_alloc);
288:   PetscFree(gmres->nrs);
289:   VecDestroy(&gmres->sol_temp);
290:   PetscFree(gmres->Rsvd);
291:   PetscFree(gmres->Dsvd);
292:   PetscFree(gmres->orthogwork);

294:   gmres->sol_temp       = 0;
295:   gmres->vv_allocated   = 0;
296:   gmres->vecs_allocated = 0;
297:   gmres->sol_temp       = 0;
298:   return(0);
299: }

301: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
302: {

306:   KSPReset_GMRES(ksp);
307:   PetscFree(ksp->data);
308:   /* clear composed functions */
309:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);
310:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);
311:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);
312:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);
313:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);
314:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);
315:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);
316:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);
317:   return(0);
318: }
319: /*
320:     KSPGMRESBuildSoln - create the solution from the starting vector and the
321:     current iterates.

323:     Input parameters:
324:         nrs - work area of size it + 1.
325:         vs  - index of initial guess
326:         vdest - index of result.  Note that vs may == vdest (replace
327:                 guess with the solution).

329:      This is an internal routine that knows about the GMRES internals.
330:  */
331: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
332: {
333:   PetscScalar    tt;
335:   PetscInt       ii,k,j;
336:   KSP_GMRES      *gmres = (KSP_GMRES*)(ksp->data);

339:   /* Solve for solution vector that minimizes the residual */

341:   /* If it is < 0, no gmres steps have been performed */
342:   if (it < 0) {
343:     VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
344:     return(0);
345:   }
346:   if (*HH(it,it) != 0.0) {
347:     nrs[it] = *GRS(it) / *HH(it,it);
348:   } else {
349:     if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the break down in GMRES; HH(it,it) = 0");
350:     else ksp->reason = KSP_DIVERGED_BREAKDOWN;

352:     PetscInfo2(ksp,"Likely your matrix or preconditioner is singular. HH(it,it) is identically zero; it = %D GRS(it) = %g\n",it,(double)PetscAbsScalar(*GRS(it)));
353:     return(0);
354:   }
355:   for (ii=1; ii<=it; ii++) {
356:     k  = it - ii;
357:     tt = *GRS(k);
358:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
359:     if (*HH(k,k) == 0.0) {
360:       if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
361:       else {
362:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
363:         PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
364:         return(0);
365:       }
366:     }
367:     nrs[k] = tt / *HH(k,k);
368:   }

370:   /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
371:   VecSet(VEC_TEMP,0.0);
372:   VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));

374:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
375:   /* add solution to previous solution */
376:   if (vdest != vs) {
377:     VecCopy(vs,vdest);
378:   }
379:   VecAXPY(vdest,1.0,VEC_TEMP);
380:   return(0);
381: }
382: /*
383:    Do the scalar work for the orthogonalization.  Return new residual norm.
384:  */
385: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
386: {
387:   PetscScalar *hh,*cc,*ss,tt;
388:   PetscInt    j;
389:   KSP_GMRES   *gmres = (KSP_GMRES*)(ksp->data);

392:   hh = HH(0,it);
393:   cc = CC(0);
394:   ss = SS(0);

396:   /* Apply all the previously computed plane rotations to the new column
397:      of the Hessenberg matrix */
398:   for (j=1; j<=it; j++) {
399:     tt  = *hh;
400:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
401:     hh++;
402:     *hh = *cc++ * *hh - (*ss++ * tt);
403:   }

405:   /*
406:     compute the new plane rotation, and apply it to:
407:      1) the right-hand-side of the Hessenberg system
408:      2) the new column of the Hessenberg matrix
409:     thus obtaining the updated value of the residual
410:   */
411:   if (!hapend) {
412:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
413:     if (tt == 0.0) {
414:       if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"tt == 0.0");
415:       else {
416:         ksp->reason = KSP_DIVERGED_NULL;
417:         return(0);
418:       }
419:     }
420:     *cc        = *hh / tt;
421:     *ss        = *(hh+1) / tt;
422:     *GRS(it+1) = -(*ss * *GRS(it));
423:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
424:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);
425:     *res       = PetscAbsScalar(*GRS(it+1));
426:   } else {
427:     /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
428:             another rotation matrix (so RH doesn't change).  The new residual is
429:             always the new sine term times the residual from last time (GRS(it)),
430:             but now the new sine rotation would be zero...so the residual should
431:             be zero...so we will multiply "zero" by the last residual.  This might
432:             not be exactly what we want to do here -could just return "zero". */

434:     *res = 0.0;
435:   }
436:   return(0);
437: }
438: /*
439:    This routine allocates more work vectors, starting from VEC_VV(it).
440:  */
441: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
442: {
443:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
445:   PetscInt       nwork = gmres->nwork_alloc,k,nalloc;

448:   nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
449:   /* Adjust the number to allocate to make sure that we don't exceed the
450:     number of available slots */
451:   if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
452:     nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
453:   }
454:   if (!nalloc) return(0);

456:   gmres->vv_allocated += nalloc;

458:   KSPCreateVecs(ksp,nalloc,&gmres->user_work[nwork],0,NULL);
459:   PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);

461:   gmres->mwork_alloc[nwork] = nalloc;
462:   for (k=0; k<nalloc; k++) {
463:     gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
464:   }
465:   gmres->nwork_alloc++;
466:   return(0);
467: }

469: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
470: {
471:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

475:   if (!ptr) {
476:     if (!gmres->sol_temp) {
477:       VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
478:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);
479:     }
480:     ptr = gmres->sol_temp;
481:   }
482:   if (!gmres->nrs) {
483:     /* allocate the work area */
484:     PetscMalloc1(gmres->max_k,&gmres->nrs);
485:     PetscLogObjectMemory((PetscObject)ksp,gmres->max_k);
486:   }

488:   KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
489:   if (result) *result = ptr;
490:   return(0);
491: }

493: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
494: {
495:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
496:   const char     *cstr;
498:   PetscBool      iascii,isstring;

501:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
502:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
503:   if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
504:     switch (gmres->cgstype) {
505:     case (KSP_GMRES_CGS_REFINE_NEVER):
506:       cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
507:       break;
508:     case (KSP_GMRES_CGS_REFINE_ALWAYS):
509:       cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
510:       break;
511:     case (KSP_GMRES_CGS_REFINE_IFNEEDED):
512:       cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
513:       break;
514:     default:
515:       SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
516:     }
517:   } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
518:     cstr = "Modified Gram-Schmidt Orthogonalization";
519:   } else {
520:     cstr = "unknown orthogonalization";
521:   }
522:   if (iascii) {
523:     PetscViewerASCIIPrintf(viewer,"  restart=%D, using %s\n",gmres->max_k,cstr);
524:     PetscViewerASCIIPrintf(viewer,"  happy breakdown tolerance %g\n",(double)gmres->haptol);
525:   } else if (isstring) {
526:     PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
527:   }
528:   return(0);
529: }

531: /*@C
532:    KSPGMRESMonitorKrylov - Calls VecView() for each new direction in the GMRES accumulated Krylov space.

534:    Collective on ksp

536:    Input Parameters:
537: +  ksp - the KSP context
538: .  its - iteration number
539: .  fgnorm - 2-norm of residual (or gradient)
540: -  dummy - an collection of viewers created with KSPViewerCreate()

542:    Options Database Keys:
543: .   -ksp_gmres_kyrlov_monitor

545:    Notes:
546:     A new PETSCVIEWERDRAW is created for each Krylov vector so they can all be simultaneously viewed
547:    Level: intermediate

549: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
550: @*/
551: PetscErrorCode  KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
552: {
553:   PetscViewers   viewers = (PetscViewers)dummy;
554:   KSP_GMRES      *gmres  = (KSP_GMRES*)ksp->data;
556:   Vec            x;
557:   PetscViewer    viewer;
558:   PetscBool      flg;

561:   PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
562:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
563:   if (!flg) {
564:     PetscViewerSetType(viewer,PETSCVIEWERDRAW);
565:     PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
566:   }
567:   x    = VEC_VV(gmres->it+1);
568:   VecView(x,viewer);
569:   return(0);
570: }

572: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
573: {
575:   PetscInt       restart;
576:   PetscReal      haptol;
577:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;
578:   PetscBool      flg;

582:   PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
583:   if (flg) { KSPGMRESSetRestart(ksp,restart); }
584:   PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
585:   if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
586:   flg  = PETSC_FALSE;
587:   PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
588:   if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
589:   PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
590:   if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
591:   PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
592:   if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
593:   PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
594:                           KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
595:   flg  = PETSC_FALSE;
596:   PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
597:   if (flg) {
598:     PetscViewers viewers;
599:     PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
600:     KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
601:   }
602:   PetscOptionsTail();
603:   return(0);
604: }

606: PetscErrorCode  KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
607: {
608:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

611:   if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
612:   gmres->haptol = tol;
613:   return(0);
614: }

616: PetscErrorCode  KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
617: {
618:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

621:   *max_k = gmres->max_k;
622:   return(0);
623: }

625: PetscErrorCode  KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
626: {
627:   KSP_GMRES      *gmres = (KSP_GMRES*)ksp->data;

631:   if (max_k < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
632:   if (!ksp->setupstage) {
633:     gmres->max_k = max_k;
634:   } else if (gmres->max_k != max_k) {
635:     gmres->max_k    = max_k;
636:     ksp->setupstage = KSP_SETUP_NEW;
637:     /* free the data structures, then create them again */
638:     KSPReset_GMRES(ksp);
639:   }
640:   return(0);
641: }

643: PetscErrorCode  KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
644: {
646:   ((KSP_GMRES*)ksp->data)->orthog = fcn;
647:   return(0);
648: }

650: PetscErrorCode  KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
651: {
653:   *fcn = ((KSP_GMRES*)ksp->data)->orthog;
654:   return(0);
655: }

657: PetscErrorCode  KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
658: {
659:   KSP_GMRES *gmres;

662:   gmres = (KSP_GMRES*)ksp->data;
663:   gmres->q_preallocate = 1;
664:   return(0);
665: }

667: PetscErrorCode  KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
668: {
669:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

672:   gmres->cgstype = type;
673:   return(0);
674: }

676: PetscErrorCode  KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
677: {
678:   KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;

681:   *type = gmres->cgstype;
682:   return(0);
683: }

685: /*@
686:    KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
687:          in the classical Gram Schmidt orthogonalization.

689:    Logically Collective on ksp

691:    Input Parameters:
692: +  ksp - the Krylov space context
693: -  type - the type of refinement

695:   Options Database:
696: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

698:    Level: intermediate

700: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
701:           KSPGMRESGetOrthogonalization()
702: @*/
703: PetscErrorCode  KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
704: {

710:   PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
711:   return(0);
712: }

714: /*@
715:    KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
716:          in the classical Gram Schmidt orthogonalization.

718:    Not Collective

720:    Input Parameter:
721: .  ksp - the Krylov space context

723:    Output Parameter:
724: .  type - the type of refinement

726:   Options Database:
727: .  -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>

729:    Level: intermediate

731: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
732:           KSPGMRESGetOrthogonalization()
733: @*/
734: PetscErrorCode  KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
735: {

740:   PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
741:   return(0);
742: }

745: /*@
746:    KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.

748:    Logically Collective on ksp

750:    Input Parameters:
751: +  ksp - the Krylov space context
752: -  restart - integer restart value

754:   Options Database:
755: .  -ksp_gmres_restart <positive integer>

757:     Note: The default value is 30.

759:    Level: intermediate

761: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
762: @*/
763: PetscErrorCode  KSPGMRESSetRestart(KSP ksp, PetscInt restart)
764: {

770:   PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
771:   return(0);
772: }

774: /*@
775:    KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.

777:    Not Collective

779:    Input Parameter:
780: .  ksp - the Krylov space context

782:    Output Parameter:
783: .   restart - integer restart value

785:     Note: The default value is 30.

787:    Level: intermediate

789: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
790: @*/
791: PetscErrorCode  KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
792: {

796:   PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
797:   return(0);
798: }

800: /*@
801:    KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.

803:    Logically Collective on ksp

805:    Input Parameters:
806: +  ksp - the Krylov space context
807: -  tol - the tolerance

809:   Options Database:
810: .  -ksp_gmres_haptol <positive real value>

812:    Note: Happy breakdown is the rare case in GMRES where an 'exact' solution is obtained after
813:          a certain number of iterations. If you attempt more iterations after this point unstable
814:          things can happen hence very occasionally you may need to set this value to detect this condition

816:    Level: intermediate

818: .seealso: KSPSetTolerances()
819: @*/
820: PetscErrorCode  KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
821: {

826:   PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
827:   return(0);
828: }

830: /*MC
831:      KSPGMRES - Implements the Generalized Minimal Residual method.
832:                 (Saad and Schultz, 1986) with restart

835:    Options Database Keys:
836: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
837: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
838: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
839:                              vectors are allocated as needed)
840: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
841: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
842: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
843:                                    stability of the classical Gram-Schmidt  orthogonalization.
844: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

846:    Level: beginner

848:    Notes:
849:     Left and right preconditioning are supported, but not symmetric preconditioning.

851:    References:
852: .     1. - YOUCEF SAAD AND MARTIN H. SCHULTZ, GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS.
853:           SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986.

855: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
856:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
857:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
858:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()

860: M*/

862: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
863: {
864:   KSP_GMRES      *gmres;

868:   PetscNewLog(ksp,&gmres);
869:   ksp->data = (void*)gmres;

871:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
872:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
873:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);
874:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
875:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

877:   ksp->ops->buildsolution                = KSPBuildSolution_GMRES;
878:   ksp->ops->setup                        = KSPSetUp_GMRES;
879:   ksp->ops->solve                        = KSPSolve_GMRES;
880:   ksp->ops->reset                        = KSPReset_GMRES;
881:   ksp->ops->destroy                      = KSPDestroy_GMRES;
882:   ksp->ops->view                         = KSPView_GMRES;
883:   ksp->ops->setfromoptions               = KSPSetFromOptions_GMRES;
884:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
885:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;
886: #if !defined(PETSC_USE_COMPLEX) && !defined(PETSC_HAVE_ESSL)
887:   ksp->ops->computeritz                  = KSPComputeRitz_GMRES;
888: #endif
889:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
890:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
891:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
892:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
893:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
894:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
895:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
896:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

898:   gmres->haptol         = 1.0e-30;
899:   gmres->q_preallocate  = 0;
900:   gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
901:   gmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
902:   gmres->nrs            = 0;
903:   gmres->sol_temp       = 0;
904:   gmres->max_k          = GMRES_DEFAULT_MAXK;
905:   gmres->Rsvd           = 0;
906:   gmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
907:   gmres->orthogwork     = 0;
908:   return(0);
909: }

```