Actual source code: lgmres.c

  1: #include <../src/ksp/ksp/impls/gmres/lgmres/lgmresimpl.h>

  3: static PetscErrorCode KSPLGMRESGetNewVectors(KSP, PetscInt);
  4: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP, PetscInt, PetscBool, PetscReal *);
  5: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);

  7: /*@
  8:   KSPLGMRESSetAugDim - Set the number of error approximations to include in the approximation space (default is 2) for `KSPLGMRES`

 10:   Collective

 12:   Input Parameters:
 13: + ksp - the `KSP` context
 14: - dim - the number of vectors to use

 16:   Options Database Key:
 17: . -ksp_lgmres_augment dim - the number of error approximations to include

 19:   Level: intermediate

 21:   Note:
 22:   If this is set to zero, then this method is equivalent to `KSPGMRES`

 24: .seealso: [](ch_ksp), `KSPLGMRES`, `KSPLGMRESSetConstant()`
 25: @*/
 26: PetscErrorCode KSPLGMRESSetAugDim(KSP ksp, PetscInt dim)
 27: {
 28:   PetscFunctionBegin;
 29:   PetscTryMethod(ksp, "KSPLGMRESSetAugDim_C", (KSP, PetscInt), (ksp, dim));
 30:   PetscFunctionReturn(PETSC_SUCCESS);
 31: }

 33: /*@
 34:   KSPLGMRESSetConstant - keep the error approximation space a constant size for every restart cycle

 36:   Collective

 38:   Input Parameters:
 39: . ksp - the `KSP` context

 41:   Options Database Key:
 42: . -ksp_lgmres_constant - set the size to be constant

 44:   Level: intermediate

 46:   Note:
 47:   This only affects the first couple of restart cycles when the total number of desired error approximations may not
 48:   be available.

 50: .seealso: [](ch_ksp), `KSPLGMRES`, `KSPLGMRESSetAugDim()`
 51: @*/
 52: PetscErrorCode KSPLGMRESSetConstant(KSP ksp)
 53: {
 54:   PetscFunctionBegin;
 55:   PetscTryMethod(ksp, "KSPLGMRESSetConstant_C", (KSP), (ksp));
 56:   PetscFunctionReturn(PETSC_SUCCESS);
 57: }

 59: static PetscErrorCode KSPSetUp_LGMRES(KSP ksp)
 60: {
 61:   PetscInt    max_k, k, aug_dim;
 62:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

 64:   PetscFunctionBegin;
 65:   max_k   = lgmres->max_k;
 66:   aug_dim = lgmres->aug_dim;
 67:   PetscCall(KSPSetUp_GMRES(ksp));

 69:   /* need array of pointers to augvecs*/
 70:   PetscCall(PetscMalloc1(2 * aug_dim + AUG_OFFSET, &lgmres->augvecs));

 72:   lgmres->aug_vecs_allocated = 2 * aug_dim + AUG_OFFSET;

 74:   PetscCall(PetscMalloc1(2 * aug_dim + AUG_OFFSET, &lgmres->augvecs_user_work));
 75:   PetscCall(PetscMalloc1(aug_dim, &lgmres->aug_order));

 77:   /*  for now we will preallocate the augvecs - because aug_dim << restart
 78:      ... also keep in mind that we need to keep augvecs from cycle to cycle*/
 79:   lgmres->aug_vv_allocated = 2 * aug_dim + AUG_OFFSET;
 80:   lgmres->augwork_alloc    = 2 * aug_dim + AUG_OFFSET;

 82:   PetscCall(KSPCreateVecs(ksp, lgmres->aug_vv_allocated, &lgmres->augvecs_user_work[0], 0, NULL));
 83:   PetscCall(PetscMalloc1(max_k + 1, &lgmres->hwork));
 84:   for (k = 0; k < lgmres->aug_vv_allocated; k++) lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
 85:   PetscFunctionReturn(PETSC_SUCCESS);
 86: }

 88: static PetscErrorCode KSPLGMRESCycle(PetscInt *itcount, KSP ksp)
 89: {
 90:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
 91:   PetscReal   res_norm, res;
 92:   PetscReal   hapbnd, tt;
 93:   PetscScalar tmp;
 94:   PetscBool   hapend = PETSC_FALSE;   /* indicates happy breakdown ending */
 95:   PetscInt    loc_it;                 /* local count of # of dir. in Krylov space */
 96:   PetscInt    max_k  = lgmres->max_k; /* max approx space size */
 97:   PetscInt    max_it = ksp->max_it;   /* max # of overall iterations for the method */

 99:   /* LGMRES_MOD - new variables*/
100:   PetscInt     aug_dim = lgmres->aug_dim;
101:   PetscInt     spot    = 0;
102:   PetscInt     order   = 0;
103:   PetscInt     it_arnoldi; /* number of arnoldi steps to take */
104:   PetscInt     it_total;   /* total number of its to take (=approx space size)*/
105:   PetscInt     ii, jj;
106:   PetscReal    tmp_norm;
107:   PetscScalar  inv_tmp_norm;
108:   PetscScalar *avec;

110:   PetscFunctionBegin;
111:   /* Number of pseudo iterations since last restart is the number of prestart directions */
112:   loc_it = 0;

114:   /* LGMRES_MOD: determine number of arnoldi steps to take */
115:   /* if approx_constant then we keep the space the same size even if
116:      we don't have the full number of aug vectors yet*/
117:   if (lgmres->approx_constant) it_arnoldi = max_k - lgmres->aug_ct;
118:   else it_arnoldi = max_k - aug_dim;

120:   it_total = it_arnoldi + lgmres->aug_ct;

122:   /* initial residual is in VEC_VV(0)  - compute its norm*/
123:   PetscCall(VecNorm(VEC_VV(0), NORM_2, &res_norm));
124:   KSPCheckNorm(ksp, res_norm);
125:   res = res_norm;

127:   /* first entry in the right-hand side of the Hessenberg system is just the initial residual norm */
128:   *GRS(0) = res_norm;

130:   /* check for the convergence */
131:   if (!res) {
132:     if (itcount) *itcount = 0;
133:     ksp->reason = KSP_CONVERGED_ATOL;
134:     PetscCall(PetscInfo(ksp, "Converged due to zero residual norm on entry\n"));
135:     PetscFunctionReturn(PETSC_SUCCESS);
136:   }

138:   /* scale VEC_VV (the initial residual) */
139:   tmp = 1.0 / res_norm;
140:   PetscCall(VecScale(VEC_VV(0), tmp));

142:   if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
143:   else ksp->rnorm = 0.0;

145:   /* note: (lgmres->it) is always set one less than (loc_it) It is used in
146:      KSPBUILDSolution_LGMRES, where it is passed to KSPLGMRESBuildSoln.
147:      Note that when KSPLGMRESBuildSoln is called from this function,
148:      (loc_it -1) is passed, so the two are equivalent */
149:   lgmres->it = (loc_it - 1);

151:   /* MAIN ITERATION LOOP BEGINNING*/

153:   /* keep iterating until we have converged OR generated the max number
154:      of directions OR reached the max number of iterations for the method */
155:   PetscCall((*ksp->converged)(ksp, ksp->its, res, &ksp->reason, ksp->cnvP));

157:   while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
158:     PetscCall(KSPLogResidualHistory(ksp, res));
159:     lgmres->it = (loc_it - 1);
160:     PetscCall(KSPMonitor(ksp, ksp->its, res));

162:     /* see if more space is needed for work vectors */
163:     if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
164:       PetscCall(KSPLGMRESGetNewVectors(ksp, loc_it + 1));
165:       /* (loc_it+1) is passed in as number of the first vector that should be allocated */
166:     }

168:     /* LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
169:     if (loc_it < it_arnoldi) { /* Arnoldi */
170:       PetscCall(KSP_PCApplyBAorAB(ksp, VEC_VV(loc_it), VEC_VV(1 + loc_it), VEC_TEMP_MATOP));
171:     } else {                           /* aug step */
172:       order = loc_it - it_arnoldi + 1; /* which aug step */
173:       for (ii = 0; ii < aug_dim; ii++) {
174:         if (lgmres->aug_order[ii] == order) {
175:           spot = ii;
176:           break; /* must have this because there will be duplicates before aug_ct = aug_dim */
177:         }
178:       }

180:       PetscCall(VecCopy(A_AUGVEC(spot), VEC_VV(1 + loc_it)));
181:       /* note: an alternate implementation choice would be to only save the AUGVECS and
182:          not A_AUGVEC and then apply the PC here to the augvec */
183:     }

185:     /* update Hessenberg matrix and do Gram-Schmidt - new direction is in VEC_VV(1+loc_it)*/
186:     PetscCall((*ksp->orthog)(ksp, &VEC_VV(0), loc_it + 1, NULL, HH(0, loc_it)));
187:     PetscCall(PetscArraycpy(HES(0, loc_it), HH(0, loc_it), loc_it + 1));

189:     /* new entry in Hessenberg is the 2-norm of our new direction */
190:     PetscCall(VecNorm(VEC_VV(loc_it + 1), NORM_2, &tt));

192:     *HH(loc_it + 1, loc_it)  = tt;
193:     *HES(loc_it + 1, loc_it) = tt;

195:     /* check for the happy breakdown */
196:     hapbnd = PetscAbsScalar(tt / *GRS(loc_it)); /* GRS(loc_it) contains the res_norm from the last iteration  */
197:     if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
198:     if (tt > hapbnd) {
199:       tmp = 1.0 / tt;
200:       PetscCall(VecScale(VEC_VV(loc_it + 1), tmp)); /* scale new direction by its norm */
201:     } else {
202:       PetscCall(PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %g tt = %g\n", (double)hapbnd, (double)tt));
203:       hapend = PETSC_TRUE;
204:     }

206:     /* apply rotations to the new column of the Hessenberg (and the right-hand side of the system),
207:        calculate new rotation, and get new residual norm at the same time*/
208:     PetscCall(KSPLGMRESUpdateHessenberg(ksp, loc_it, hapend, &res));
209:     if (ksp->reason) break;

211:     loc_it++;
212:     lgmres->it = (loc_it - 1); /* Add this here in case it has converged */

214:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
215:     ksp->its++;
216:     if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
217:     else ksp->rnorm = 0.0;
218:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));

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

222:     /* Catch error in happy breakdown and signal convergence and break from loop */
223:     if (hapend) {
224:       if (!ksp->reason) {
225:         PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res);
226:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
227:         break;
228:       }
229:     }
230:   }
231:   /* END OF ITERATION LOOP */
232:   PetscCall(KSPLogResidualHistory(ksp, res));

234:   if (itcount) *itcount = loc_it;

236:   /*
237:     Solve for the "best" coefficients of the Krylov
238:     columns, add the solution values together, and possibly unwind the
239:     preconditioning from the solution
240:    */

242:   /* Form the solution (or the solution so far) */
243:   /* Note: must pass in (loc_it-1) for iteration count so that KSPLGMRESBuildSoln properly navigates */

245:   PetscCall(KSPLGMRESBuildSoln(GRS(0), ksp->vec_sol, ksp->vec_sol, ksp, loc_it - 1));

247:   /* Monitor if we know that we will not return for a restart */
248:   if (ksp->reason == KSP_CONVERGED_ITERATING && ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
249:   if (ksp->reason) PetscCall(KSPMonitor(ksp, ksp->its, res));

251:   /* LGMRES_MOD collect aug vector and A*augvector for future restarts -
252:      only if we will be restarting (i.e. this cycle performed it_total iterations)  */
253:   if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {
254:     /* AUG_TEMP contains the new augmentation vector (assigned in  KSPLGMRESBuildSoln) */
255:     if (!lgmres->aug_ct) {
256:       spot = 0;
257:       lgmres->aug_ct++;
258:     } else if (lgmres->aug_ct < aug_dim) {
259:       spot = lgmres->aug_ct;
260:       lgmres->aug_ct++;
261:     } else { /* truncate */
262:       for (ii = 0; ii < aug_dim; ii++) {
263:         if (lgmres->aug_order[ii] == aug_dim) spot = ii;
264:       }
265:     }

267:     PetscCall(VecCopy(AUG_TEMP, AUGVEC(spot)));
268:     /* need to normalize */
269:     PetscCall(VecNorm(AUGVEC(spot), NORM_2, &tmp_norm));

271:     inv_tmp_norm = 1.0 / tmp_norm;

273:     PetscCall(VecScale(AUGVEC(spot), inv_tmp_norm));

275:     /* set new aug vector to order 1  - move all others back one */
276:     for (ii = 0; ii < aug_dim; ii++) AUG_ORDER(ii)++;
277:     AUG_ORDER(spot) = 1;

279:     /* now add the A*aug vector to A_AUGVEC(spot) - this is independent of preconditioning type */
280:     /* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */

282:     /* do H+*y */
283:     avec = lgmres->hwork;
284:     PetscCall(PetscArrayzero(avec, it_total + 1));
285:     for (ii = 0; ii < it_total + 1; ii++) {
286:       for (jj = 0; jj <= ii + 1 && jj < it_total + 1; jj++) avec[jj] += *HES(jj, ii) * *GRS(ii);
287:     }

289:     /* multiply result by V+ */
290:     PetscCall(VecMAXPBY(VEC_TEMP, it_total + 1, avec, 0, &VEC_VV(0))); /* answer is in VEC_TEMP */

292:     /* copy answer to aug location  and scale */
293:     PetscCall(VecCopy(VEC_TEMP, A_AUGVEC(spot)));
294:     PetscCall(VecScale(A_AUGVEC(spot), inv_tmp_norm));
295:   }
296:   PetscFunctionReturn(PETSC_SUCCESS);
297: }

299: static PetscErrorCode KSPSolve_LGMRES(KSP ksp)
300: {
301:   PetscInt    itcount; /* running total of iterations, incl. those in restarts */
302:   KSP_LGMRES *lgmres     = (KSP_LGMRES *)ksp->data;
303:   PetscBool   guess_zero = ksp->guess_zero;
304:   PetscInt    ii; /* LGMRES_MOD variable */

306:   PetscFunctionBegin;
307:   PetscCheck(!ksp->calc_sings || lgmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");

309:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));

311:   ksp->its        = 0;
312:   lgmres->aug_ct  = 0;
313:   lgmres->matvecs = 0;

315:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));

317:   /* initialize */
318:   itcount = 0;
319:   /* LGMRES_MOD */
320:   for (ii = 0; ii < lgmres->aug_dim; ii++) lgmres->aug_order[ii] = 0;

322:   while (!ksp->reason) {
323:     PetscInt cycle_its = 0; /* iterations done in a call to KSPLGMRESCycle */
324:     /* calc residual - puts in VEC_VV(0) */
325:     PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
326:     PetscCall(KSPLGMRESCycle(&cycle_its, ksp));
327:     itcount += cycle_its;
328:     if (itcount >= ksp->max_it) {
329:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
330:       break;
331:     }
332:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
333:   }
334:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
335:   PetscFunctionReturn(PETSC_SUCCESS);
336: }

338: static PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
339: {
340:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

342:   PetscFunctionBegin;
343:   PetscCall(PetscFree(lgmres->augvecs));
344:   if (lgmres->augwork_alloc) PetscCall(VecDestroyVecs(lgmres->augwork_alloc, &lgmres->augvecs_user_work[0]));
345:   PetscCall(PetscFree(lgmres->augvecs_user_work));
346:   PetscCall(PetscFree(lgmres->aug_order));
347:   PetscCall(PetscFree(lgmres->hwork));
348:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", NULL));
349:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", NULL));
350:   PetscCall(KSPDestroy_GMRES(ksp));
351:   PetscFunctionReturn(PETSC_SUCCESS);
352: }

354: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
355: {
356:   PetscScalar tt;
357:   PetscInt    ii, k, j;
358:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
359:   /* LGMRES_MOD */
360:   PetscInt it_arnoldi, it_aug;
361:   PetscInt jj, spot = 0;

363:   PetscFunctionBegin;
364:   /* Solve for solution vector that minimizes the residual */

366:   /* If it is < 0, no lgmres steps have been performed */
367:   if (it < 0) {
368:     PetscCall(VecCopy(vguess, vdest)); /* VecCopy() is smart, exists immediately if vguess == vdest */
369:     PetscFunctionReturn(PETSC_SUCCESS);
370:   }

372:   /* so (it+1) lgmres steps HAVE been performed */

374:   /* LGMRES_MOD - determine if we need to use augvecs for the soln  - do not assume that
375:      this is called after the total its allowed for an approx space */
376:   if (lgmres->approx_constant) {
377:     it_arnoldi = lgmres->max_k - lgmres->aug_ct;
378:   } else {
379:     it_arnoldi = lgmres->max_k - lgmres->aug_dim;
380:   }
381:   if (it_arnoldi >= it + 1) {
382:     it_aug     = 0;
383:     it_arnoldi = it + 1;
384:   } else {
385:     it_aug = (it + 1) - it_arnoldi;
386:   }

388:   /* now it_arnoldi indicates the number of matvecs that took place */
389:   lgmres->matvecs += it_arnoldi;

391:   /* solve the upper triangular system - GRS is the right side and HH is
392:      the upper triangular matrix  - put soln in nrs */
393:   PetscCheck(*HH(it, it) != 0.0, PETSC_COMM_SELF, PETSC_ERR_CONV_FAILED, "HH(it,it) is identically zero; it = %" PetscInt_FMT " GRS(it) = %g", it, (double)PetscAbsScalar(*GRS(it)));
394:   if (*HH(it, it) != 0.0) {
395:     nrs[it] = *GRS(it) / *HH(it, it);
396:   } else {
397:     nrs[it] = 0.0;
398:   }

400:   for (ii = 1; ii <= it; ii++) {
401:     k  = it - ii;
402:     tt = *GRS(k);
403:     for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
404:     nrs[k] = tt / *HH(k, k);
405:   }

407:   /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */

409:   /* LGMRES_MOD - if augmenting has happened we need to form the solution using the augvecs */
410:   if (!it_aug) { /* all its are from arnoldi */
411:     PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &VEC_VV(0)));
412:   } else { /* use aug vecs */
413:     /* first do regular Krylov directions */
414:     PetscCall(VecMAXPBY(VEC_TEMP, it_arnoldi, nrs, 0, &VEC_VV(0)));
415:     /* now add augmented portions - add contribution of aug vectors one at a time*/

417:     for (ii = 0; ii < it_aug; ii++) {
418:       for (jj = 0; jj < lgmres->aug_dim; jj++) {
419:         if (lgmres->aug_order[jj] == (ii + 1)) {
420:           spot = jj;
421:           break; /* must have this because there will be duplicates before aug_ct = aug_dim */
422:         }
423:       }
424:       PetscCall(VecAXPY(VEC_TEMP, nrs[it_arnoldi + ii], AUGVEC(spot)));
425:     }
426:   }
427:   /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
428:      preconditioner is "unwound" from right-precondtioning*/
429:   PetscCall(VecCopy(VEC_TEMP, AUG_TEMP));

431:   PetscCall(KSPUnwindPreconditioner(ksp, VEC_TEMP, VEC_TEMP_MATOP));

433:   /* add solution to previous solution */
434:   /* put updated solution into vdest.*/
435:   PetscCall(VecCopy(vguess, vdest));
436:   PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
437:   PetscFunctionReturn(PETSC_SUCCESS);
438: }

440: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
441: {
442:   PetscScalar *hh, *cc, *ss, tt;
443:   KSP_LGMRES  *lgmres = (KSP_LGMRES *)ksp->data;

445:   PetscFunctionBegin;
446:   hh = HH(0, it); /* pointer to beginning of column to update - so incrementing hh "steps down" the (it+1)th col of HH*/
447:   cc = CC(0);     /* beginning of cosine rotations */
448:   ss = SS(0);     /* beginning of sine rotations */

450:   /* Apply all the previously computed plane rotations to the new column
451:      of the Hessenberg matrix */
452:   /* Note: this uses the rotation [conj(c)  s ; -s   c], c= cos(theta), s= sin(theta) */

454:   for (PetscInt j = 1; j <= it; j++) {
455:     tt  = *hh;
456:     *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
457:     hh++;
458:     *hh = *cc++ * *hh - (*ss++ * tt);
459:     /* hh, cc, and ss have all been incremented one by end of loop */
460:   }

462:   /*
463:     compute the new plane rotation, and apply it to:
464:      1) the right-hand side of the Hessenberg system (GRS)
465:         note: it affects GRS(it) and GRS(it+1)
466:      2) the new column of the Hessenberg matrix
467:         note: it affects HH(it,it) which is currently pointed to
468:         by hh and HH(it+1, it) (*(hh+1))
469:     thus obtaining the updated value of the residual...
470:   */

472:   /* compute new plane rotation */

474:   if (!hapend) {
475:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
476:     if (tt == 0.0) {
477:       ksp->reason = KSP_DIVERGED_NULL;
478:       PetscFunctionReturn(PETSC_SUCCESS);
479:     }
480:     *cc = *hh / tt;       /* new cosine value */
481:     *ss = *(hh + 1) / tt; /* new sine value */

483:     /* apply to 1) and 2) */
484:     *GRS(it + 1) = -(*ss * *GRS(it));
485:     *GRS(it)     = PetscConj(*cc) * *GRS(it);
486:     *hh          = PetscConj(*cc) * *hh + *ss * *(hh + 1);

488:     /* residual is the last element (it+1) of right-hand side! */
489:     *res = PetscAbsScalar(*GRS(it + 1));

491:   } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
492:             another rotation matrix (so RH doesn't change).  The new residual is
493:             always the new sine term times the residual from last time (GRS(it)),
494:             but now the new sine rotation would be zero...so the residual should
495:             be zero...so we will multiply "zero" by the last residual.  This might
496:             not be exactly what we want to do here -could just return "zero". */

498:     *res = 0.0;
499:   }
500:   PetscFunctionReturn(PETSC_SUCCESS);
501: }

503: /*
504:    KSPLGMRESGetNewVectors - Allocates more work vectors, starting from VEC_VV(it)

506: */
507: static PetscErrorCode KSPLGMRESGetNewVectors(KSP ksp, PetscInt it)
508: {
509:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
510:   PetscInt    nwork  = lgmres->nwork_alloc; /* number of work vector chunks allocated */
511:   PetscInt    nalloc;                       /* number to allocate */

513:   PetscFunctionBegin;
514:   nalloc = lgmres->delta_allocate; /* number of vectors to allocate in a single chunk */

516:   /* Adjust the number to allocate to make sure that we don't exceed the
517:      number of available slots (lgmres->vecs_allocated)*/
518:   if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated) nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
519:   if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);

521:   lgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */

523:   /* work vectors */
524:   PetscCall(KSPCreateVecs(ksp, nalloc, &lgmres->user_work[nwork], 0, NULL));
525:   /* specify size of chunk allocated */
526:   lgmres->mwork_alloc[nwork] = nalloc;

528:   for (PetscInt k = 0; k < nalloc; k++) lgmres->vecs[it + VEC_OFFSET + k] = lgmres->user_work[nwork][k];

530:   /* LGMRES_MOD - for now we are preallocating the augmentation vectors */

532:   /* increment the number of work vector chunks */
533:   lgmres->nwork_alloc++;
534:   PetscFunctionReturn(PETSC_SUCCESS);
535: }

537: static PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp, Vec ptr, Vec *result)
538: {
539:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

541:   PetscFunctionBegin;
542:   if (!ptr) {
543:     if (!lgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &lgmres->sol_temp));
544:     ptr = lgmres->sol_temp;
545:   }
546:   if (!lgmres->nrs) {
547:     /* allocate the work area */
548:     PetscCall(PetscMalloc1(lgmres->max_k, &lgmres->nrs));
549:   }

551:   PetscCall(KSPLGMRESBuildSoln(lgmres->nrs, ksp->vec_sol, ptr, ksp, lgmres->it));
552:   if (result) *result = ptr;
553:   PetscFunctionReturn(PETSC_SUCCESS);
554: }

556: static PetscErrorCode KSPView_LGMRES(KSP ksp, PetscViewer viewer)
557: {
558:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
559:   PetscBool   isascii;

561:   PetscFunctionBegin;
562:   PetscCall(KSPView_GMRES(ksp, viewer));
563:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
564:   if (isascii) {
565:     /* LGMRES_MOD */
566:     PetscCall(PetscViewerASCIIPrintf(viewer, "  aug. dimension=%" PetscInt_FMT "\n", lgmres->aug_dim));
567:     if (lgmres->approx_constant) PetscCall(PetscViewerASCIIPrintf(viewer, "  approx. space size was kept constant.\n"));
568:     PetscCall(PetscViewerASCIIPrintf(viewer, "  number of matvecs=%" PetscInt_FMT "\n", lgmres->matvecs));
569:   }
570:   PetscFunctionReturn(PETSC_SUCCESS);
571: }

573: static PetscErrorCode KSPSetFromOptions_LGMRES(KSP ksp, PetscOptionItems PetscOptionsObject)
574: {
575:   PetscInt    aug;
576:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
577:   PetscBool   flg    = PETSC_FALSE;

579:   PetscFunctionBegin;
580:   PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
581:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP LGMRES Options");
582:   PetscCall(PetscOptionsBool("-ksp_lgmres_constant", "Use constant approx. space size", "KSPGMRESSetConstant", lgmres->approx_constant, &lgmres->approx_constant, NULL));
583:   PetscCall(PetscOptionsInt("-ksp_lgmres_augment", "Number of error approximations to augment the Krylov space with", "KSPLGMRESSetAugDim", lgmres->aug_dim, &aug, &flg));
584:   if (flg) PetscCall(KSPLGMRESSetAugDim(ksp, aug));
585:   PetscOptionsHeadEnd();
586:   PetscFunctionReturn(PETSC_SUCCESS);
587: }

589: static PetscErrorCode KSPLGMRESSetConstant_LGMRES(KSP ksp)
590: {
591:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

593:   PetscFunctionBegin;
594:   lgmres->approx_constant = PETSC_TRUE;
595:   PetscFunctionReturn(PETSC_SUCCESS);
596: }

598: static PetscErrorCode KSPLGMRESSetAugDim_LGMRES(KSP ksp, PetscInt aug_dim)
599: {
600:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

602:   PetscFunctionBegin;
603:   PetscCheck(aug_dim >= 0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Augmentation dimension must be nonegative");
604:   PetscCheck(aug_dim <= (lgmres->max_k - 1), PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Augmentation dimension must be <= (restart size-1)");
605:   lgmres->aug_dim = aug_dim;
606:   PetscFunctionReturn(PETSC_SUCCESS);
607: }

609: /*MC
610:   KSPLGMRES - Augments the standard GMRES approximation space with approximations to the error from previous restart cycles as in {cite}`bjm2005`.

612:   Options Database Keys:
613: +   -ksp_gmres_restart restart                                                  - total approximation space size (Krylov directions + error approximations)
614: .   -ksp_gmres_haptol tol                                                       - sets the tolerance for "happy breakdown" (exact convergence)
615: .   -ksp_gmres_preallocate                                                      - preallocate all the Krylov search directions initially
616:                                                                                   (otherwise groups of vectors are allocated as needed)
617: .   -ksp_gmres_krylov_monitor                                                   - plot the Krylov space generated
618: .   -ksp_lgmres_augment k                                                       - number of error approximations to augment the Krylov space with
619: -   -ksp_lgmres_constant                                                        - use a constant approximate space size
620:                                                                                   (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)

622:   Level: beginner

624:   Notes:
625:   Supports both left and right preconditioning, but not symmetric.

627:   Augmenting with 1,2, or 3 approximations is generally optimal.

629:   This method is an accelerator for `KSPGMRES` - it is not useful for problems that stall. When gmres(m) stalls then lgmres with a size m
630:   approximation space will also generally stall.

632:   If gmres(m) converges in a small number of restart cycles, then lgmres also tends not to be very helpful.

634:   Developer Notes:
635:   To run LGMRES(m, k) as described in {cite}`bjm2005`, use\:
636: .vb
637:   -ksp_gmres_restart <m+k>
638:   -ksp_lgmres_augment <k>
639: .ve

641:   This object is subclassed off of `KSPGMRES`, see the source code in src/ksp/ksp/impls/gmres for comments on the structure of the code

643:   Contributed by:
644:   Allison Baker

646: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPGMRES`,
647:           `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPOrthogonalizationSet()`, `KSPOrthogonalizationGet()`,
648:           `KSPOrthogonalizationClassicalGramSchmidt()`, `KSPOrthogonalizationModifiedGramSchmidt()`,
649:           `KSPOrthogonalizationCGSRefinementType`, `KSPOrthogonalizationSetCGSRefinementType()`, `KSPOrthogonalizationGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPLGMRESSetAugDim()`,
650:           `KSPGMRESSetConstant()`, `KSPLGMRESSetConstant()`
651: M*/

653: PETSC_EXTERN PetscErrorCode KSPCreate_LGMRES(KSP ksp)
654: {
655:   KSP_LGMRES *lgmres;

657:   PetscFunctionBegin;
658:   PetscCall(PetscNew(&lgmres));

660:   ksp->data               = (void *)lgmres;
661:   ksp->ops->buildsolution = KSPBuildSolution_LGMRES;

663:   ksp->ops->setup                        = KSPSetUp_LGMRES;
664:   ksp->ops->solve                        = KSPSolve_LGMRES;
665:   ksp->ops->destroy                      = KSPDestroy_LGMRES;
666:   ksp->ops->view                         = KSPView_LGMRES;
667:   ksp->ops->setfromoptions               = KSPSetFromOptions_LGMRES;
668:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
669:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

671:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
672:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
673:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));

675:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
676:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
677:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES));
678:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES));

680:   /* LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
681:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", KSPLGMRESSetConstant_LGMRES));
682:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", KSPLGMRESSetAugDim_LGMRES));

684:   /* defaults */
685:   lgmres->haptol         = 1.0e-30;
686:   lgmres->q_preallocate  = PETSC_FALSE;
687:   lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
688:   lgmres->nrs            = NULL;
689:   lgmres->sol_temp       = NULL;
690:   lgmres->max_k          = LGMRES_DEFAULT_MAXK;
691:   lgmres->Rsvd           = NULL;

693:   /* LGMRES_MOD - new defaults */
694:   lgmres->aug_dim         = LGMRES_DEFAULT_AUGDIM;
695:   lgmres->aug_ct          = 0; /* start with no aug vectors */
696:   lgmres->approx_constant = PETSC_FALSE;
697:   lgmres->matvecs         = 0;
698:   PetscFunctionReturn(PETSC_SUCCESS);
699: }