Actual source code: lgmres.c


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

  4: #define LGMRES_DELTA_DIRECTIONS 10
  5: #define LGMRES_DEFAULT_MAXK     30
  6: #define LGMRES_DEFAULT_AUGDIM   2 /*default number of augmentation vectors */
  7: static PetscErrorCode KSPLGMRESGetNewVectors(KSP, PetscInt);
  8: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP, PetscInt, PetscBool, PetscReal *);
  9: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);

 11: PetscErrorCode KSPLGMRESSetAugDim(KSP ksp, PetscInt dim)
 12: {
 13:   PetscFunctionBegin;
 14:   PetscTryMethod((ksp), "KSPLGMRESSetAugDim_C", (KSP, PetscInt), (ksp, dim));
 15:   PetscFunctionReturn(PETSC_SUCCESS);
 16: }

 18: PetscErrorCode KSPLGMRESSetConstant(KSP ksp)
 19: {
 20:   PetscFunctionBegin;
 21:   PetscTryMethod((ksp), "KSPLGMRESSetConstant_C", (KSP), (ksp));
 22:   PetscFunctionReturn(PETSC_SUCCESS);
 23: }

 25: /*
 26:     KSPSetUp_LGMRES - Sets up the workspace needed by lgmres.

 28:     This is called once, usually automatically by KSPSolve() or KSPSetUp(),
 29:     but can be called directly by KSPSetUp().

 31: */
 32: PetscErrorCode KSPSetUp_LGMRES(KSP ksp)
 33: {
 34:   PetscInt    max_k, k, aug_dim;
 35:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

 37:   PetscFunctionBegin;
 38:   max_k   = lgmres->max_k;
 39:   aug_dim = lgmres->aug_dim;
 40:   PetscCall(KSPSetUp_GMRES(ksp));

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

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

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

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

 55:   PetscCall(KSPCreateVecs(ksp, lgmres->aug_vv_allocated, &lgmres->augvecs_user_work[0], 0, NULL));
 56:   PetscCall(PetscMalloc1(max_k + 1, &lgmres->hwork));
 57:   for (k = 0; k < lgmres->aug_vv_allocated; k++) lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
 58:   PetscFunctionReturn(PETSC_SUCCESS);
 59: }

 61: /*
 62:     KSPLGMRESCycle - Run lgmres, possibly with restart.  Return residual
 63:                   history if requested.

 65:     input parameters:
 66: .        lgmres  - structure containing parameters and work areas

 68:     output parameters:
 69: .        nres    - residuals (from preconditioned system) at each step.
 70:                   If restarting, consider passing nres+it.  If null,
 71:                   ignored
 72: .        itcount - number of iterations used.   nres[0] to nres[itcount]
 73:                   are defined.  If null, ignored.  If null, ignored.
 74: .        converged - 0 if not converged

 76:     Notes:
 77:     On entry, the value in vector VEC_VV(0) should be
 78:     the initial residual.
 79:  */
 80: PetscErrorCode KSPLGMRESCycle(PetscInt *itcount, KSP ksp)
 81: {
 82:   KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
 83:   PetscReal   res_norm, res;
 84:   PetscReal   hapbnd, tt;
 85:   PetscScalar tmp;
 86:   PetscBool   hapend = PETSC_FALSE;   /* indicates happy breakdown ending */
 87:   PetscInt    loc_it;                 /* local count of # of dir. in Krylov space */
 88:   PetscInt    max_k  = lgmres->max_k; /* max approx space size */
 89:   PetscInt    max_it = ksp->max_it;   /* max # of overall iterations for the method */

 91:   /* LGMRES_MOD - new variables*/
 92:   PetscInt     aug_dim = lgmres->aug_dim;
 93:   PetscInt     spot    = 0;
 94:   PetscInt     order   = 0;
 95:   PetscInt     it_arnoldi; /* number of arnoldi steps to take */
 96:   PetscInt     it_total;   /* total number of its to take (=approx space size)*/
 97:   PetscInt     ii, jj;
 98:   PetscReal    tmp_norm;
 99:   PetscScalar  inv_tmp_norm;
100:   PetscScalar *avec;

102:   PetscFunctionBegin;
103:   /* Number of pseudo iterations since last restart is the number
104:      of prestart directions */
105:   loc_it = 0;

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

113:   it_total = it_arnoldi + lgmres->aug_ct;

115:   /* initial residual is in VEC_VV(0)  - compute its norm*/
116:   PetscCall(VecNorm(VEC_VV(0), NORM_2, &res_norm));
117:   KSPCheckNorm(ksp, res_norm);
118:   res = res_norm;

120:   /* first entry in right-hand-side of hessenberg system is just
121:      the initial residual norm */
122:   *GRS(0) = res_norm;

124:   /* check for the convergence */
125:   if (!res) {
126:     if (itcount) *itcount = 0;
127:     ksp->reason = KSP_CONVERGED_ATOL;
128:     PetscCall(PetscInfo(ksp, "Converged due to zero residual norm on entry\n"));
129:     PetscFunctionReturn(PETSC_SUCCESS);
130:   }

132:   /* scale VEC_VV (the initial residual) */
133:   tmp = 1.0 / res_norm;
134:   PetscCall(VecScale(VEC_VV(0), tmp));

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

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

145:   /* MAIN ITERATION LOOP BEGINNING*/

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

151:   while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
152:     PetscCall(KSPLogResidualHistory(ksp, res));
153:     lgmres->it = (loc_it - 1);
154:     PetscCall(KSPMonitor(ksp, ksp->its, res));

156:     /* see if more space is needed for work vectors */
157:     if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
158:       PetscCall(KSPLGMRESGetNewVectors(ksp, loc_it + 1));
159:       /* (loc_it+1) is passed in as number of the first vector that should
160:           be allocated */
161:     }

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

175:       PetscCall(VecCopy(A_AUGVEC(spot), VEC_VV(1 + loc_it)));
176:       /*note: an alternate implementation choice would be to only save the AUGVECS and
177:         not A_AUGVEC and then apply the PC here to the augvec */
178:     }

180:     /* update hessenberg matrix and do Gram-Schmidt - new direction is in
181:        VEC_VV(1+loc_it)*/
182:     PetscCall((*lgmres->orthog)(ksp, loc_it));

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

187:     *HH(loc_it + 1, loc_it)  = tt;
188:     *HES(loc_it + 1, loc_it) = tt;

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

201:     /* Now apply rotations to new col of hessenberg (and right side of system),
202:        calculate new rotation, and get new residual norm at the same time*/
203:     PetscCall(KSPLGMRESUpdateHessenberg(ksp, loc_it, hapend, &res));
204:     if (ksp->reason) break;

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

209:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
210:     ksp->its++;
211:     if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res;
212:     else ksp->rnorm = 0.0;
213:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));

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

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

229:   /* Monitor if we know that we will not return for a restart */
230:   if (ksp->reason || ksp->its >= max_it) PetscCall(KSPMonitor(ksp, ksp->its, res));

232:   if (itcount) *itcount = loc_it;

234:   /*
235:     Down here we have to solve for the "best" coefficients of the Krylov
236:     columns, add the solution values together, and possibly unwind the
237:     preconditioning from the solution
238:    */

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

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

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

263:     PetscCall(VecCopy(AUG_TEMP, AUGVEC(spot)));
264:     /*need to normalize */
265:     PetscCall(VecNorm(AUGVEC(spot), NORM_2, &tmp_norm));

267:     inv_tmp_norm = 1.0 / tmp_norm;

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

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

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

278:     /* first do H+*y */
279:     avec = lgmres->hwork;
280:     PetscCall(PetscArrayzero(avec, it_total + 1));
281:     for (ii = 0; ii < it_total + 1; ii++) {
282:       for (jj = 0; jj <= ii + 1 && jj < it_total + 1; jj++) avec[jj] += *HES(jj, ii) * *GRS(ii);
283:     }

285:     /*now multiply result by V+ */
286:     PetscCall(VecSet(VEC_TEMP, 0.0));
287:     PetscCall(VecMAXPY(VEC_TEMP, it_total + 1, avec, &VEC_VV(0))); /*answer is in VEC_TEMP*/

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

296: /*
297:     KSPSolve_LGMRES - This routine applies the LGMRES method.

299:    Input Parameter:
300: .     ksp - the Krylov space object that was set to use lgmres

302:    Output Parameter:
303: .     outits - number of iterations used

305: */
306: PetscErrorCode KSPSolve_LGMRES(KSP ksp)
307: {
308:   PetscInt    cycle_its; /* iterations done in a call to KSPLGMRESCycle */
309:   PetscInt    itcount;   /* running total of iterations, incl. those in restarts */
310:   KSP_LGMRES *lgmres     = (KSP_LGMRES *)ksp->data;
311:   PetscBool   guess_zero = ksp->guess_zero;
312:   PetscInt    ii; /*LGMRES_MOD variable */

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

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

319:   ksp->its        = 0;
320:   lgmres->aug_ct  = 0;
321:   lgmres->matvecs = 0;

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

325:   /* initialize */
326:   itcount = 0;
327:   /*LGMRES_MOD*/
328:   for (ii = 0; ii < lgmres->aug_dim; ii++) lgmres->aug_order[ii] = 0;

330:   while (!ksp->reason) {
331:     /* calc residual - puts in VEC_VV(0) */
332:     PetscCall(KSPInitialResidual(ksp, ksp->vec_sol, VEC_TEMP, VEC_TEMP_MATOP, VEC_VV(0), ksp->vec_rhs));
333:     PetscCall(KSPLGMRESCycle(&cycle_its, ksp));
334:     itcount += cycle_its;
335:     if (itcount >= ksp->max_it) {
336:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
337:       break;
338:     }
339:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
340:   }
341:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
342:   PetscFunctionReturn(PETSC_SUCCESS);
343: }

345: /*
346:    KSPDestroy_LGMRES - Frees all memory space used by the Krylov method.
347: */
348: PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
349: {
350:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

352:   PetscFunctionBegin;
353:   PetscCall(PetscFree(lgmres->augvecs));
354:   if (lgmres->augwork_alloc) PetscCall(VecDestroyVecs(lgmres->augwork_alloc, &lgmres->augvecs_user_work[0]));
355:   PetscCall(PetscFree(lgmres->augvecs_user_work));
356:   PetscCall(PetscFree(lgmres->aug_order));
357:   PetscCall(PetscFree(lgmres->hwork));
358:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetConstant_C", NULL));
359:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPLGMRESSetAugDim_C", NULL));
360:   PetscCall(KSPDestroy_GMRES(ksp));
361:   PetscFunctionReturn(PETSC_SUCCESS);
362: }

364: /*
365:     KSPLGMRESBuildSoln - create the solution from the starting vector and the
366:                       current iterates.

368:     Input parameters:
369:         nrs - work area of size it + 1.
370:         vguess  - index of initial guess
371:         vdest - index of result.  Note that vguess may == vdest (replace
372:                 guess with the solution).
373:         it - HH upper triangular part is a block of size (it+1) x (it+1)

375:      This is an internal routine that knows about the LGMRES internals.
376:  */
377: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
378: {
379:   PetscScalar tt;
380:   PetscInt    ii, k, j;
381:   KSP_LGMRES *lgmres = (KSP_LGMRES *)(ksp->data);
382:   /*LGMRES_MOD */
383:   PetscInt it_arnoldi, it_aug;
384:   PetscInt jj, spot = 0;

386:   PetscFunctionBegin;
387:   /* Solve for solution vector that minimizes the residual */

389:   /* If it is < 0, no lgmres steps have been performed */
390:   if (it < 0) {
391:     PetscCall(VecCopy(vguess, vdest)); /* VecCopy() is smart, exists immediately if vguess == vdest */
392:     PetscFunctionReturn(PETSC_SUCCESS);
393:   }

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

397:   /* LGMRES_MOD - determine if we need to use augvecs for the soln  - do not assume that
398:      this is called after the total its allowed for an approx space */
399:   if (lgmres->approx_constant) {
400:     it_arnoldi = lgmres->max_k - lgmres->aug_ct;
401:   } else {
402:     it_arnoldi = lgmres->max_k - lgmres->aug_dim;
403:   }
404:   if (it_arnoldi >= it + 1) {
405:     it_aug     = 0;
406:     it_arnoldi = it + 1;
407:   } else {
408:     it_aug = (it + 1) - it_arnoldi;
409:   }

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

414:   /* solve the upper triangular system - GRS is the right side and HH is
415:      the upper triangular matrix  - put soln in nrs */
416:   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)));
417:   if (*HH(it, it) != 0.0) {
418:     nrs[it] = *GRS(it) / *HH(it, it);
419:   } else {
420:     nrs[it] = 0.0;
421:   }

423:   for (ii = 1; ii <= it; ii++) {
424:     k  = it - ii;
425:     tt = *GRS(k);
426:     for (j = k + 1; j <= it; j++) tt = tt - *HH(k, j) * nrs[j];
427:     nrs[k] = tt / *HH(k, k);
428:   }

430:   /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
431:   PetscCall(VecSet(VEC_TEMP, 0.0)); /* set VEC_TEMP components to 0 */

433:   /*LGMRES_MOD - if augmenting has happened we need to form the solution
434:     using the augvecs */
435:   if (!it_aug) { /* all its are from arnoldi */
436:     PetscCall(VecMAXPY(VEC_TEMP, it + 1, nrs, &VEC_VV(0)));
437:   } else { /*use aug vecs */
438:     /*first do regular krylov directions */
439:     PetscCall(VecMAXPY(VEC_TEMP, it_arnoldi, nrs, &VEC_VV(0)));
440:     /*now add augmented portions - add contribution of aug vectors one at a time*/

442:     for (ii = 0; ii < it_aug; ii++) {
443:       for (jj = 0; jj < lgmres->aug_dim; jj++) {
444:         if (lgmres->aug_order[jj] == (ii + 1)) {
445:           spot = jj;
446:           break; /* must have this because there will be duplicates before aug_ct = aug_dim */
447:         }
448:       }
449:       PetscCall(VecAXPY(VEC_TEMP, nrs[it_arnoldi + ii], AUGVEC(spot)));
450:     }
451:   }
452:   /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
453:      preconditioner is "unwound" from right-precondtioning*/
454:   PetscCall(VecCopy(VEC_TEMP, AUG_TEMP));

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

458:   /* add solution to previous solution */
459:   /* put updated solution into vdest.*/
460:   PetscCall(VecCopy(vguess, vdest));
461:   PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
462:   PetscFunctionReturn(PETSC_SUCCESS);
463: }

465: /*
466:     KSPLGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
467:                             Return new residual.

469:     input parameters:

471: .        ksp -    Krylov space object
472: .        it  -    plane rotations are applied to the (it+1)th column of the
473:                   modified hessenberg (i.e. HH(:,it))
474: .        hapend - PETSC_FALSE not happy breakdown ending.

476:     output parameters:
477: .        res - the new residual

479:  */
480: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool hapend, PetscReal *res)
481: {
482:   PetscScalar *hh, *cc, *ss, tt;
483:   PetscInt     j;
484:   KSP_LGMRES  *lgmres = (KSP_LGMRES *)(ksp->data);

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

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

496:   for (j = 1; j <= it; j++) {
497:     tt  = *hh;
498:     *hh = PetscConj(*cc) * tt + *ss * *(hh + 1);
499:     hh++;
500:     *hh = *cc++ * *hh - (*ss++ * tt);
501:     /* hh, cc, and ss have all been incremented one by end of loop */
502:   }

504:   /*
505:     compute the new plane rotation, and apply it to:
506:      1) the right-hand-side of the Hessenberg system (GRS)
507:         note: it affects GRS(it) and GRS(it+1)
508:      2) the new column of the Hessenberg matrix
509:         note: it affects HH(it,it) which is currently pointed to
510:         by hh and HH(it+1, it) (*(hh+1))
511:     thus obtaining the updated value of the residual...
512:   */

514:   /* compute new plane rotation */

516:   if (!hapend) {
517:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh + 1)) * *(hh + 1));
518:     if (tt == 0.0) {
519:       ksp->reason = KSP_DIVERGED_NULL;
520:       PetscFunctionReturn(PETSC_SUCCESS);
521:     }
522:     *cc = *hh / tt;       /* new cosine value */
523:     *ss = *(hh + 1) / tt; /* new sine value */

525:     /* apply to 1) and 2) */
526:     *GRS(it + 1) = -(*ss * *GRS(it));
527:     *GRS(it)     = PetscConj(*cc) * *GRS(it);
528:     *hh          = PetscConj(*cc) * *hh + *ss * *(hh + 1);

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

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

540:     *res = 0.0;
541:   }
542:   PetscFunctionReturn(PETSC_SUCCESS);
543: }

545: /*

547:    KSPLGMRESGetNewVectors - This routine allocates more work vectors, starting from
548:                          VEC_VV(it)

550: */
551: static PetscErrorCode KSPLGMRESGetNewVectors(KSP ksp, PetscInt it)
552: {
553:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
554:   PetscInt    nwork  = lgmres->nwork_alloc; /* number of work vector chunks allocated */
555:   PetscInt    nalloc;                       /* number to allocate */
556:   PetscInt    k;

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

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

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

569:   /* work vectors */
570:   PetscCall(KSPCreateVecs(ksp, nalloc, &lgmres->user_work[nwork], 0, NULL));
571:   /* specify size of chunk allocated */
572:   lgmres->mwork_alloc[nwork] = nalloc;

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

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

578:   /* increment the number of work vector chunks */
579:   lgmres->nwork_alloc++;
580:   PetscFunctionReturn(PETSC_SUCCESS);
581: }

583: /*
584:    KSPBuildSolution_LGMRES

586:      Input Parameter:
587: .     ksp - the Krylov space object
588: .     ptr-

590:    Output Parameter:
591: .     result - the solution

593:    Note: this calls KSPLGMRESBuildSoln - the same function that KSPLGMRESCycle
594:    calls directly.

596: */
597: PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp, Vec ptr, Vec *result)
598: {
599:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

601:   PetscFunctionBegin;
602:   if (!ptr) {
603:     if (!lgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &lgmres->sol_temp));
604:     ptr = lgmres->sol_temp;
605:   }
606:   if (!lgmres->nrs) {
607:     /* allocate the work area */
608:     PetscCall(PetscMalloc1(lgmres->max_k, &lgmres->nrs));
609:   }

611:   PetscCall(KSPLGMRESBuildSoln(lgmres->nrs, ksp->vec_sol, ptr, ksp, lgmres->it));
612:   if (result) *result = ptr;
613:   PetscFunctionReturn(PETSC_SUCCESS);
614: }

616: PetscErrorCode KSPView_LGMRES(KSP ksp, PetscViewer viewer)
617: {
618:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
619:   PetscBool   iascii;

621:   PetscFunctionBegin;
622:   PetscCall(KSPView_GMRES(ksp, viewer));
623:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
624:   if (iascii) {
625:     /*LGMRES_MOD */
626:     PetscCall(PetscViewerASCIIPrintf(viewer, "  aug. dimension=%" PetscInt_FMT "\n", lgmres->aug_dim));
627:     if (lgmres->approx_constant) PetscCall(PetscViewerASCIIPrintf(viewer, "  approx. space size was kept constant.\n"));
628:     PetscCall(PetscViewerASCIIPrintf(viewer, "  number of matvecs=%" PetscInt_FMT "\n", lgmres->matvecs));
629:   }
630:   PetscFunctionReturn(PETSC_SUCCESS);
631: }

633: PetscErrorCode KSPSetFromOptions_LGMRES(KSP ksp, PetscOptionItems *PetscOptionsObject)
634: {
635:   PetscInt    aug;
636:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
637:   PetscBool   flg    = PETSC_FALSE;

639:   PetscFunctionBegin;
640:   PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
641:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP LGMRES Options");
642:   PetscCall(PetscOptionsBool("-ksp_lgmres_constant", "Use constant approx. space size", "KSPGMRESSetConstant", lgmres->approx_constant, &lgmres->approx_constant, NULL));
643:   PetscCall(PetscOptionsInt("-ksp_lgmres_augment", "Number of error approximations to augment the Krylov space with", "KSPLGMRESSetAugDim", lgmres->aug_dim, &aug, &flg));
644:   if (flg) PetscCall(KSPLGMRESSetAugDim(ksp, aug));
645:   PetscOptionsHeadEnd();
646:   PetscFunctionReturn(PETSC_SUCCESS);
647: }

649: /*functions for extra lgmres options here*/
650: static PetscErrorCode KSPLGMRESSetConstant_LGMRES(KSP ksp)
651: {
652:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

654:   PetscFunctionBegin;
655:   lgmres->approx_constant = PETSC_TRUE;
656:   PetscFunctionReturn(PETSC_SUCCESS);
657: }

659: static PetscErrorCode KSPLGMRESSetAugDim_LGMRES(KSP ksp, PetscInt aug_dim)
660: {
661:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

663:   PetscFunctionBegin;
664:   PetscCheck(aug_dim >= 0, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Augmentation dimension must be positive");
665:   PetscCheck(aug_dim <= (lgmres->max_k - 1), PetscObjectComm((PetscObject)ksp), PETSC_ERR_ARG_OUTOFRANGE, "Augmentation dimension must be <= (restart size-1)");
666:   lgmres->aug_dim = aug_dim;
667:   PetscFunctionReturn(PETSC_SUCCESS);
668: }

670: /*MC
671:     KSPLGMRES - Augments the standard GMRES approximation space with approximations to
672:                 the error from previous restart cycles.

674:   Options Database Keys:
675: +   -ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
676: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
677: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
678:                             vectors are allocated as needed)
679: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
680: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
681: .   -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
682:                                   stability of the classical Gram-Schmidt  orthogonalization.
683: .   -ksp_gmres_krylov_monitor - plot the Krylov space generated
684: .   -ksp_lgmres_augment <k> - number of error approximations to augment the Krylov space with
685: -   -ksp_lgmres_constant - use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)

687:     To run LGMRES(m, k) as described in [1], use:
688:        -ksp_gmres_restart <m+k>
689:        -ksp_lgmres_augment <k>

691:   Level: beginner

693:    Note:
694:     Supports both left and right preconditioning, but not symmetric.

696:   Developer Note:
697:     This object is subclassed off of `KSPGMRES`

699:   Contributed by:
700:   Allison Baker

702:    References:
703: .  [1] - A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for accelerating the convergence of restarted GMRES. SIAM Journal on Matrix Analysis and Applications, 26 (2005).

705: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPFGMRES`, `KSPGMRES`,
706:           `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESSetOrthogonalization()`, `KSPGMRESGetOrthogonalization()`,
707:           `KSPGMRESClassicalGramSchmidtOrthogonalization()`, `KSPGMRESModifiedGramSchmidtOrthogonalization()`,
708:           `KSPGMRESCGSRefinementType`, `KSPGMRESSetCGSRefinementType()`, `KSPGMRESGetCGSRefinementType()`, `KSPGMRESMonitorKrylov()`, `KSPLGMRESSetAugDim()`,
709:           `KSPGMRESSetConstant()`
710: M*/

712: PETSC_EXTERN PetscErrorCode KSPCreate_LGMRES(KSP ksp)
713: {
714:   KSP_LGMRES *lgmres;

716:   PetscFunctionBegin;
717:   PetscCall(PetscNew(&lgmres));

719:   ksp->data               = (void *)lgmres;
720:   ksp->ops->buildsolution = KSPBuildSolution_LGMRES;

722:   ksp->ops->setup                        = KSPSetUp_LGMRES;
723:   ksp->ops->solve                        = KSPSolve_LGMRES;
724:   ksp->ops->destroy                      = KSPDestroy_LGMRES;
725:   ksp->ops->view                         = KSPView_LGMRES;
726:   ksp->ops->setfromoptions               = KSPSetFromOptions_LGMRES;
727:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
728:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

730:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
731:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
732:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));

734:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
735:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetOrthogonalization_C", KSPGMRESSetOrthogonalization_GMRES));
736:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetOrthogonalization_C", KSPGMRESGetOrthogonalization_GMRES));
737:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
738:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES));
739:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES));
740:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetCGSRefinementType_C", KSPGMRESSetCGSRefinementType_GMRES));
741:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetCGSRefinementType_C", KSPGMRESGetCGSRefinementType_GMRES));

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

747:   /*defaults */
748:   lgmres->haptol         = 1.0e-30;
749:   lgmres->q_preallocate  = 0;
750:   lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
751:   lgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
752:   lgmres->nrs            = NULL;
753:   lgmres->sol_temp       = NULL;
754:   lgmres->max_k          = LGMRES_DEFAULT_MAXK;
755:   lgmres->Rsvd           = NULL;
756:   lgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
757:   lgmres->orthogwork     = NULL;

759:   /*LGMRES_MOD - new defaults */
760:   lgmres->aug_dim         = LGMRES_DEFAULT_AUGDIM;
761:   lgmres->aug_ct          = 0; /* start with no aug vectors */
762:   lgmres->approx_constant = PETSC_FALSE;
763:   lgmres->matvecs         = 0;
764:   PetscFunctionReturn(PETSC_SUCCESS);
765: }