Actual source code: pipefgmres.c

  1: /*
  2:   Contributed by Patrick Sanan and Sascha M. Schnepp
  3: */

  5: #include <../src/ksp/ksp/impls/gmres/pipefgmres/pipefgmresimpl.h>

  7: static PetscBool  cited = PETSC_FALSE;
  8: static const char citation[] =
  9:   "@article{SSM2016,\n"
 10:   "  author = {P. Sanan and S.M. Schnepp and D.A. May},\n"
 11:   "  title = {Pipelined, Flexible Krylov Subspace Methods},\n"
 12:   "  journal = {SIAM Journal on Scientific Computing},\n"
 13:   "  volume = {38},\n"
 14:   "  number = {5},\n"
 15:   "  pages = {C441-C470},\n"
 16:   "  year = {2016},\n"
 17:   "  doi = {10.1137/15M1049130},\n"
 18:   "  URL = {http://dx.doi.org/10.1137/15M1049130},\n"
 19:   "  eprint = {http://dx.doi.org/10.1137/15M1049130}\n"
 20:   "}\n";

 22: #define PIPEFGMRES_DELTA_DIRECTIONS 10
 23: #define PIPEFGMRES_DEFAULT_MAXK     30

 25: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP,PetscInt);
 26: static PetscErrorCode KSPPIPEFGMRESUpdateHessenberg(KSP,PetscInt,PetscBool*,PetscReal*);
 27: static PetscErrorCode KSPPIPEFGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);
 28: extern PetscErrorCode KSPReset_PIPEFGMRES(KSP);

 30: /*

 32:     KSPSetUp_PIPEFGMRES - Sets up the workspace needed by pipefgmres.

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

 37: */
 38: static PetscErrorCode KSPSetUp_PIPEFGMRES(KSP ksp)
 39: {
 40:   PetscInt       k;
 41:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
 42:   const PetscInt max_k = pipefgmres->max_k;

 44:   KSPSetUp_GMRES(ksp);

 46:   PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->prevecs);
 47:   PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->prevecs_user_work);
 48:   PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+max_k)*(2*sizeof(void*)));

 50:   KSPCreateVecs(ksp,pipefgmres->vv_allocated,&pipefgmres->prevecs_user_work[0],0,NULL);
 51:   PetscLogObjectParents(ksp,pipefgmres->vv_allocated,pipefgmres->prevecs_user_work[0]);
 52:   for (k=0; k < pipefgmres->vv_allocated; k++) {
 53:     pipefgmres->prevecs[k] = pipefgmres->prevecs_user_work[0][k];
 54:   }

 56:   PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->zvecs);
 57:   PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->zvecs_user_work);
 58:   PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+max_k)*(2*sizeof(void*)));

 60:   PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->redux);
 61:   PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+max_k)*(sizeof(void*)));

 63:   KSPCreateVecs(ksp,pipefgmres->vv_allocated,&pipefgmres->zvecs_user_work[0],0,NULL);
 64:   PetscLogObjectParents(ksp,pipefgmres->vv_allocated,pipefgmres->zvecs_user_work[0]);
 65:   for (k=0; k < pipefgmres->vv_allocated; k++) {
 66:     pipefgmres->zvecs[k] = pipefgmres->zvecs_user_work[0][k];
 67:   }

 69:   return 0;
 70: }

 72: /*

 74:     KSPPIPEFGMRESCycle - Run pipefgmres, possibly with restart.  Return residual
 75:                   history if requested.

 77:     input parameters:
 78: .        pipefgmres  - structure containing parameters and work areas

 80:     output parameters:
 81: .        itcount - number of iterations used.  If null, ignored.
 82: .        converged - 0 if not converged

 84:     Notes:
 85:     On entry, the value in vector VEC_VV(0) should be
 86:     the initial residual.

 88: */
 89: static PetscErrorCode KSPPIPEFGMRESCycle(PetscInt *itcount,KSP ksp)
 90: {
 91:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)(ksp->data);
 92:   PetscReal      res_norm;
 93:   PetscReal      hapbnd,tt;
 94:   PetscScalar    *hh,*hes,*lhh,shift = pipefgmres->shift;
 95:   PetscBool      hapend = PETSC_FALSE;  /* indicates happy breakdown ending */
 96:   PetscInt       loc_it;                /* local count of # of dir. in Krylov space */
 97:   PetscInt       max_k = pipefgmres->max_k; /* max # of directions Krylov space */
 98:   PetscInt       i,j,k;
 99:   Mat            Amat,Pmat;
100:   Vec            Q,W; /* Pipelining vectors */
101:   Vec            *redux = pipefgmres->redux; /* workspace for single reduction */

103:   if (itcount) *itcount = 0;

105:   /* Assign simpler names to these vectors, allocated as pipelining workspace */
106:   Q = VEC_Q;
107:   W = VEC_W;

109:   /* Allocate memory for orthogonalization work (freed in the GMRES Destroy routine)*/
110:   /* Note that we add an extra value here to allow for a single reduction */
111:   if (!pipefgmres->orthogwork) { PetscMalloc1(pipefgmres->max_k + 2 ,&pipefgmres->orthogwork);
112:   }
113:   lhh = pipefgmres->orthogwork;

115:   /* Number of pseudo iterations since last restart is the number
116:      of prestart directions */
117:   loc_it = 0;

119:   /* note: (pipefgmres->it) is always set one less than (loc_it) It is used in
120:      KSPBUILDSolution_PIPEFGMRES, where it is passed to KSPPIPEFGMRESBuildSoln.
121:      Note that when KSPPIPEFGMRESBuildSoln is called from this function,
122:      (loc_it -1) is passed, so the two are equivalent */
123:   pipefgmres->it = (loc_it - 1);

125:   /* initial residual is in VEC_VV(0)  - compute its norm*/
126:   VecNorm(VEC_VV(0),NORM_2,&res_norm);

128:   /* first entry in right-hand-side of hessenberg system is just
129:      the initial residual norm */
130:   *RS(0) = res_norm;

132:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
133:   if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res_norm;
134:   else ksp->rnorm = 0;
135:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
136:   KSPLogResidualHistory(ksp,ksp->rnorm);
137:   KSPMonitor(ksp,ksp->its,ksp->rnorm);

139:   /* check for the convergence - maybe the current guess is good enough */
140:   (*ksp->converged)(ksp,ksp->its,ksp->rnorm,&ksp->reason,ksp->cnvP);
141:   if (ksp->reason) {
142:     if (itcount) *itcount = 0;
143:     return 0;
144:   }

146:   /* scale VEC_VV (the initial residual) */
147:   VecScale(VEC_VV(0),1.0/res_norm);

149:   /* Fill the pipeline */
150:   KSP_PCApply(ksp,VEC_VV(loc_it),PREVEC(loc_it));
151:   PCGetOperators(ksp->pc,&Amat,&Pmat);
152:   KSP_MatMult(ksp,Amat,PREVEC(loc_it),ZVEC(loc_it));
153:   VecAXPY(ZVEC(loc_it),-shift,VEC_VV(loc_it)); /* Note shift */

155:   /* MAIN ITERATION LOOP BEGINNING*/
156:   /* keep iterating until we have converged OR generated the max number
157:      of directions OR reached the max number of iterations for the method */
158:   while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
159:     if (loc_it) {
160:       KSPLogResidualHistory(ksp,res_norm);
161:       KSPMonitor(ksp,ksp->its,res_norm);
162:     }
163:     pipefgmres->it = (loc_it - 1);

165:     /* see if more space is needed for work vectors */
166:     if (pipefgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
167:       KSPPIPEFGMRESGetNewVectors(ksp,loc_it+1);
168:       /* (loc_it+1) is passed in as number of the first vector that should
169:          be allocated */
170:     }

172:     /* Note that these inner products are with "Z" now, so
173:        in particular, lhh[loc_it] is the 'barred' or 'shifted' value,
174:        not the value from the equivalent FGMRES run (even in exact arithmetic)
175:        That is, the H we need for the Arnoldi relation is different from the
176:        coefficients we use in the orthogonalization process,because of the shift */

178:     /* Do some local twiddling to allow for a single reduction */
179:     for (i=0;i<loc_it+1;i++) {
180:       redux[i] = VEC_VV(i);
181:     }
182:     redux[loc_it+1] = ZVEC(loc_it);

184:     /* note the extra dot product which ends up in lh[loc_it+1], which computes ||z||^2 */
185:     VecMDotBegin(ZVEC(loc_it),loc_it+2,redux,lhh);

187:     /* Start the split reduction (This actually calls the MPI_Iallreduce, otherwise, the reduction is simply delayed until the "end" call)*/
188:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)ZVEC(loc_it)));

190:     /* The work to be overlapped with the inner products follows.
191:        This is application of the preconditioner and the operator
192:        to compute intermediate quantites which will be combined (locally)
193:        with the results of the inner products.
194:        */
195:     KSP_PCApply(ksp,ZVEC(loc_it),Q);
196:     PCGetOperators(ksp->pc,&Amat,&Pmat);
197:     KSP_MatMult(ksp,Amat,Q,W);

199:     /* Compute inner products of the new direction with previous directions,
200:        and the norm of the to-be-orthogonalized direction "Z".
201:        This information is enough to build the required entries
202:        of H. The inner product with VEC_VV(it_loc) is
203:        *different* than in the standard FGMRES and need to be dealt with specially.
204:        That is, for standard FGMRES the orthogonalization coefficients are the same
205:        as the coefficients used in the Arnoldi relation to reconstruct, but here this
206:        is not true (albeit only for the one entry of H which we "unshift" below. */

208:     /* Finish the dot product, retrieving the extra entry */
209:     VecMDotEnd(ZVEC(loc_it),loc_it+2,redux,lhh);
210:     tt = PetscRealPart(lhh[loc_it+1]);

212:     /* Hessenberg entries, and entries for (naive) classical Graham-Schmidt
213:       Note that the Hessenberg entries require a shift, as these are for the
214:       relation AU = VH, which is wrt unshifted basis vectors */
215:     hh = HH(0,loc_it); hes=HES(0,loc_it);
216:     for (j=0; j<loc_it; j++) {
217:       hh[j]  = lhh[j];
218:       hes[j] = lhh[j];
219:     }
220:     hh[loc_it]  = lhh[loc_it] + shift;
221:     hes[loc_it] = lhh[loc_it] + shift;

223:     /* we delay applying the shift here */
224:     for (j=0; j<=loc_it; j++) {
225:       lhh[j]        = -lhh[j]; /* flip sign */
226:     }

228:     /* Compute the norm of the un-normalized new direction using the rearranged formula
229:        Note that these are shifted ("barred") quantities */
230:     for (k=0;k<=loc_it;k++) tt -= ((PetscReal)(PetscAbsScalar(lhh[k]) * PetscAbsScalar(lhh[k])));
231:     /* On AVX512 this is accumulating roundoff errors for eg: tt=-2.22045e-16 */
232:     if ((tt < 0.0) && tt > -PETSC_SMALL) tt = 0.0 ;
233:     if (tt < 0.0) {
234:       /* If we detect square root breakdown in the norm, we must restart the algorithm.
235:          Here this means we simply break the current loop and reconstruct the solution
236:          using the basis we have computed thus far. Note that by breaking immediately,
237:          we do not update the iteration count, so computation done in this iteration
238:          should be disregarded.
239:          */
240:       PetscInfo(ksp,"Restart due to square root breakdown at it = %D, tt=%g\n",ksp->its,(double)tt);
241:       break;
242:     } else {
243:       tt = PetscSqrtReal(tt);
244:     }

246:     /* new entry in hessenburg is the 2-norm of our new direction */
247:     hh[loc_it+1]  = tt;
248:     hes[loc_it+1] = tt;

250:     /* The recurred computation for the new direction
251:        The division by tt is delayed to the happy breakdown check later
252:        Note placement BEFORE the unshift
253:        */
254:     VecCopy(ZVEC(loc_it),VEC_VV(loc_it+1));
255:     VecMAXPY(VEC_VV(loc_it+1),loc_it+1,lhh,&VEC_VV(0));
256:     /* (VEC_VV(loc_it+1) is not normalized yet) */

258:     /* The recurred computation for the preconditioned vector (u) */
259:     VecCopy(Q,PREVEC(loc_it+1));
260:     VecMAXPY(PREVEC(loc_it+1),loc_it+1,lhh,&PREVEC(0));
261:     VecScale(PREVEC(loc_it+1),1.0/tt);

263:     /* Unshift an entry in the GS coefficients ("removing the bar") */
264:     lhh[loc_it]         -= shift;

266:     /* The recurred computation for z (Au)
267:        Note placement AFTER the "unshift" */
268:     VecCopy(W,ZVEC(loc_it+1));
269:     VecMAXPY(ZVEC(loc_it+1),loc_it+1,lhh,&ZVEC(0));
270:     VecScale(ZVEC(loc_it+1),1.0/tt);

272:     /* Happy Breakdown Check */
273:     hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
274:     /* RS(loc_it) contains the res_norm from the last iteration  */
275:     hapbnd = PetscMin(pipefgmres->haptol,hapbnd);
276:     if (tt > hapbnd) {
277:       /* scale new direction by its norm  */
278:       VecScale(VEC_VV(loc_it+1),1.0/tt);
279:     } else {
280:       /* This happens when the solution is exactly reached. */
281:       /* So there is no new direction... */
282:       VecSet(VEC_TEMP,0.0);     /* set VEC_TEMP to 0 */
283:       hapend = PETSC_TRUE;
284:     }
285:     /* note that for pipefgmres we could get HES(loc_it+1, loc_it)  = 0 and the
286:        current solution would not be exact if HES was singular.  Note that
287:        HH non-singular implies that HES is not singular, and HES is guaranteed
288:        to be nonsingular when PREVECS are linearly independent and A is
289:        nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity
290:        of HES). So we should really add a check to verify that HES is nonsingular.*/

292:     /* Note that to be thorough, in debug mode, one could call a LAPACK routine
293:        here to check that the hessenberg matrix is indeed non-singular (since
294:        FGMRES does not guarantee this) */

296:     /* Now apply rotations to new col of hessenberg (and right side of system),
297:        calculate new rotation, and get new residual norm at the same time*/
298:     KSPPIPEFGMRESUpdateHessenberg(ksp,loc_it,&hapend,&res_norm);
299:     if (ksp->reason) break;

301:     loc_it++;
302:     pipefgmres->it = (loc_it-1);   /* Add this here in case it has converged */

304:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
305:     ksp->its++;
306:     if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res_norm;
307:     else ksp->rnorm = 0;
308:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

310:     (*ksp->converged)(ksp,ksp->its,ksp->rnorm,&ksp->reason,ksp->cnvP);

312:     /* Catch error in happy breakdown and signal convergence and break from loop */
313:     if (hapend) {
314:       if (!ksp->reason) {
316:         else {
317:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
318:           break;
319:         }
320:       }
321:     }
322:   }
323:   /* END OF ITERATION LOOP */
324:   KSPLogResidualHistory(ksp,ksp->rnorm);

326:   /*
327:      Monitor if we know that we will not return for a restart */
328:   if (loc_it && (ksp->reason || ksp->its >= ksp->max_it)) {
329:     KSPMonitor(ksp,ksp->its,ksp->rnorm);
330:   }

332:   if (itcount) *itcount = loc_it;

334:   /*
335:     Down here we have to solve for the "best" coefficients of the Krylov
336:     columns, add the solution values together, and possibly unwind the
337:     preconditioning from the solution
338:    */

340:   /* Form the solution (or the solution so far) */
341:   /* Note: must pass in (loc_it-1) for iteration count so that KSPPIPEGMRESIIBuildSoln
342:      properly navigates */

344:   KSPPIPEFGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);

346:   return 0;
347: }

349: /*
350:     KSPSolve_PIPEFGMRES - This routine applies the PIPEFGMRES method.

352:    Input Parameter:
353: .     ksp - the Krylov space object that was set to use pipefgmres

355:    Output Parameter:
356: .     outits - number of iterations used

358: */
359: static PetscErrorCode KSPSolve_PIPEFGMRES(KSP ksp)
360: {
361:   PetscInt       its,itcount;
362:   KSP_PIPEFGMRES *pipefgmres    = (KSP_PIPEFGMRES*)ksp->data;
363:   PetscBool      guess_zero = ksp->guess_zero;

365:   /* We have not checked these routines for use with complex numbers. The inner products
366:      are likely not defined correctly for that case */

369:   PetscCitationsRegister(citation,&cited);

372:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
373:   ksp->its = 0;
374:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

376:   itcount     = 0;
377:   ksp->reason = KSP_CONVERGED_ITERATING;
378:   while (!ksp->reason) {
379:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
380:     KSPPIPEFGMRESCycle(&its,ksp);
381:     itcount += its;
382:     if (itcount >= ksp->max_it) {
383:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
384:       break;
385:     }
386:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
387:   }
388:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
389:   return 0;
390: }

392: static PetscErrorCode KSPDestroy_PIPEFGMRES(KSP ksp)
393: {
394:   KSPReset_PIPEFGMRES(ksp);
395:   KSPDestroy_GMRES(ksp);
396:   return 0;
397: }

399: /*
400:     KSPPIPEFGMRESBuildSoln - create the solution from the starting vector and the
401:                       current iterates.

403:     Input parameters:
404:         nrs - work area of size it + 1.
405:         vguess  - index of initial guess
406:         vdest - index of result.  Note that vguess may == vdest (replace
407:                 guess with the solution).
408:         it - HH upper triangular part is a block of size (it+1) x (it+1)

410:      This is an internal routine that knows about the PIPEFGMRES internals.
411:  */
412: static PetscErrorCode KSPPIPEFGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
413: {
414:   PetscScalar    tt;
415:   PetscInt       k,j;
416:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)(ksp->data);

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

420:   if (it < 0) {                                 /* no pipefgmres steps have been performed */
421:     VecCopy(vguess,vdest); /* VecCopy() is smart, exits immediately if vguess == vdest */
422:     return 0;
423:   }

425:   /* solve the upper triangular system - RS is the right side and HH is
426:      the upper triangular matrix  - put soln in nrs */
427:   if (*HH(it,it) != 0.0) nrs[it] = *RS(it) / *HH(it,it);
428:   else nrs[it] = 0.0;

430:   for (k=it-1; k>=0; k--) {
431:     tt = *RS(k);
432:     for (j=k+1; j<=it; j++) tt -= *HH(k,j) * nrs[j];
433:     nrs[k] = tt / *HH(k,k);
434:   }

436:   /* Accumulate the correction to the solution of the preconditioned problem in VEC_TEMP */
437:   VecZeroEntries(VEC_TEMP);
438:   VecMAXPY(VEC_TEMP,it+1,nrs,&PREVEC(0));

440:   /* add solution to previous solution */
441:   if (vdest == vguess) {
442:     VecAXPY(vdest,1.0,VEC_TEMP);
443:   } else {
444:     VecWAXPY(vdest,1.0,VEC_TEMP,vguess);
445:   }
446:   return 0;
447: }

449: /*

451:     KSPPIPEFGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
452:                             Return new residual.

454:     input parameters:

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

461:     output parameters:
462: .        res - the new residual

464:  */
465: /*
466: .  it - column of the Hessenberg that is complete, PIPEFGMRES is actually computing two columns ahead of this
467:  */
468: static PetscErrorCode KSPPIPEFGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool *hapend,PetscReal *res)
469: {
470:   PetscScalar    *hh,*cc,*ss,*rs;
471:   PetscInt       j;
472:   PetscReal      hapbnd;
473:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)(ksp->data);

475:   hh = HH(0,it);   /* pointer to beginning of column to update */
476:   cc = CC(0);      /* beginning of cosine rotations */
477:   ss = SS(0);      /* beginning of sine rotations */
478:   rs = RS(0);      /* right hand side of least squares system */

480:   /* The Hessenberg matrix is now correct through column it, save that form for possible spectral analysis */
481:   for (j=0; j<=it+1; j++) *HES(j,it) = hh[j];

483:   /* check for the happy breakdown */
484:   hapbnd = PetscMin(PetscAbsScalar(hh[it+1] / rs[it]),pipefgmres->haptol);
485:   if (PetscAbsScalar(hh[it+1]) < hapbnd) {
486:     PetscInfo(ksp,"Detected happy breakdown, current hapbnd = %14.12e H(%D,%D) = %14.12e\n",(double)hapbnd,it+1,it,(double)PetscAbsScalar(*HH(it+1,it)));
487:     *hapend = PETSC_TRUE;
488:   }

490:   /* Apply all the previously computed plane rotations to the new column
491:      of the Hessenberg matrix */
492:   /* Note: this uses the rotation [conj(c)  s ; -s   c], c= cos(theta), s= sin(theta),
493:      and some refs have [c   s ; -conj(s)  c] (don't be confused!) */

495:   for (j=0; j<it; j++) {
496:     PetscScalar hhj = hh[j];
497:     hh[j]   = PetscConj(cc[j])*hhj + ss[j]*hh[j+1];
498:     hh[j+1] =          -ss[j] *hhj + cc[j]*hh[j+1];
499:   }

501:   /*
502:     compute the new plane rotation, and apply it to:
503:      1) the right-hand-side of the Hessenberg system (RS)
504:         note: it affects RS(it) and RS(it+1)
505:      2) the new column of the Hessenberg matrix
506:         note: it affects HH(it,it) which is currently pointed to
507:         by hh and HH(it+1, it) (*(hh+1))
508:     thus obtaining the updated value of the residual...
509:   */

511:   /* compute new plane rotation */

513:   if (!*hapend) {
514:     PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it+1])));
515:     if (delta == 0.0) {
516:       ksp->reason = KSP_DIVERGED_NULL;
517:       return 0;
518:     }

520:     cc[it] = hh[it] / delta;    /* new cosine value */
521:     ss[it] = hh[it+1] / delta;  /* new sine value */

523:     hh[it]   = PetscConj(cc[it])*hh[it] + ss[it]*hh[it+1];
524:     rs[it+1] = -ss[it]*rs[it];
525:     rs[it]   = PetscConj(cc[it])*rs[it];
526:     *res     = PetscAbsScalar(rs[it+1]);
527:   } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
528:             another rotation matrix (so RH doesn't change).  The new residual is
529:             always the new sine term times the residual from last time (RS(it)),
530:             but now the new sine rotation would be zero...so the residual should
531:             be zero...so we will multiply "zero" by the last residual.  This might
532:             not be exactly what we want to do here -could just return "zero". */

534:     *res = 0.0;
535:   }
536:   return 0;
537: }

539: /*
540:    KSPBuildSolution_PIPEFGMRES

542:      Input Parameter:
543: .     ksp - the Krylov space object
544: .     ptr-

546:    Output Parameter:
547: .     result - the solution

549:    Note: this calls KSPPIPEFGMRESBuildSoln - the same function that KSPPIPEFGMRESCycle
550:    calls directly.

552: */
553: PetscErrorCode KSPBuildSolution_PIPEFGMRES(KSP ksp,Vec ptr,Vec *result)
554: {
555:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;

557:   if (!ptr) {
558:     if (!pipefgmres->sol_temp) {
559:       VecDuplicate(ksp->vec_sol,&pipefgmres->sol_temp);
560:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)pipefgmres->sol_temp);
561:     }
562:     ptr = pipefgmres->sol_temp;
563:   }
564:   if (!pipefgmres->nrs) {
565:     /* allocate the work area */
566:     PetscMalloc1(pipefgmres->max_k,&pipefgmres->nrs);
567:     PetscLogObjectMemory((PetscObject)ksp,pipefgmres->max_k*sizeof(PetscScalar));
568:   }

570:   KSPPIPEFGMRESBuildSoln(pipefgmres->nrs,ksp->vec_sol,ptr,ksp,pipefgmres->it);
571:   if (result) *result = ptr;
572:   return 0;
573: }

575: PetscErrorCode KSPSetFromOptions_PIPEFGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
576: {
577:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
578:   PetscBool      flg;
579:   PetscScalar    shift;

581:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
582:   PetscOptionsHead(PetscOptionsObject,"KSP pipelined FGMRES Options");
583:   PetscOptionsScalar("-ksp_pipefgmres_shift","shift parameter","KSPPIPEFGMRESSetShift",pipefgmres->shift,&shift,&flg);
584:   if (flg) KSPPIPEFGMRESSetShift(ksp,shift);
585:   PetscOptionsTail();
586:   return 0;
587: }

589: PetscErrorCode KSPView_PIPEFGMRES(KSP ksp,PetscViewer viewer)
590: {
591:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
592:   PetscBool      iascii,isstring;

594:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
595:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);

597:   if (iascii) {
598:     PetscViewerASCIIPrintf(viewer,"  restart=%D\n",pipefgmres->max_k);
599:     PetscViewerASCIIPrintf(viewer,"  happy breakdown tolerance %g\n",(double)pipefgmres->haptol);
600: #if defined(PETSC_USE_COMPLEX)
601:     PetscViewerASCIIPrintf(viewer,"  shift=%g+%gi\n",PetscRealPart(pipefgmres->shift),PetscImaginaryPart(pipefgmres->shift));
602: #else
603:     PetscViewerASCIIPrintf(viewer,"  shift=%g\n",pipefgmres->shift);
604: #endif
605:   } else if (isstring) {
606:     PetscViewerStringSPrintf(viewer,"restart %D",pipefgmres->max_k);
607: #if defined(PETSC_USE_COMPLEX)
608:     PetscViewerStringSPrintf(viewer,"   shift=%g+%gi\n",PetscRealPart(pipefgmres->shift),PetscImaginaryPart(pipefgmres->shift));
609: #else
610:     PetscViewerStringSPrintf(viewer,"   shift=%g\n",pipefgmres->shift);
611: #endif
612:   }
613:   return 0;
614: }

616: PetscErrorCode KSPReset_PIPEFGMRES(KSP ksp)
617: {
618:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
619:   PetscInt         i;

621:   PetscFree(pipefgmres->prevecs);
622:   PetscFree(pipefgmres->zvecs);
623:   for (i=0; i<pipefgmres->nwork_alloc; i++) {
624:     VecDestroyVecs(pipefgmres->mwork_alloc[i],&pipefgmres->prevecs_user_work[i]);
625:     VecDestroyVecs(pipefgmres->mwork_alloc[i],&pipefgmres->zvecs_user_work[i]);
626:   }
627:   PetscFree(pipefgmres->prevecs_user_work);
628:   PetscFree(pipefgmres->zvecs_user_work);
629:   PetscFree(pipefgmres->redux);
630:   KSPReset_GMRES(ksp);
631:   return 0;
632: }

634: /*MC
635:    KSPPIPEFGMRES - Implements the Pipelined Generalized Minimal Residual method.

637:    A flexible, 1-stage pipelined variant of GMRES.

639:    Options Database Keys:
640: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
641: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
642: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
643: .   -ksp_pipefgmres_shift - the shift to use (defaults to 1. See KSPPIPEFGMRESSetShift()
644:                              vectors are allocated as needed)
645: -   -ksp_gmres_krylov_monitor - plot the Krylov space generated

647:    Level: intermediate

649:    Notes:

651:    This variant is not "explicitly normalized" like KSPPGMRES, and requires a shift parameter.

653:    A heuristic for choosing the shift parameter is the largest eigenvalue of the preconditioned operator.

655:    Only right preconditioning is supported (but this preconditioner may be nonlinear/variable/inexact, as with KSPFGMRES).
656:    MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
657:    See the FAQ on the PETSc website for details.

659:    Developer Notes:
660:     This class is subclassed off of KSPGMRES.

662:    Reference:
663:     P. Sanan, S.M. Schnepp, and D.A. May,
664:     "Pipelined, Flexible Krylov Subspace Methods,"
665:     SIAM Journal on Scientific Computing 2016 38:5, C441-C470,
666:     DOI: 10.1137/15M1049130

668: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPLGMRES, KSPPIPECG, KSPPIPECR, KSPPGMRES, KSPFGMRES
669:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESMonitorKrylov(), KSPPIPEFGMRESSetShift()
670: M*/

672: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEFGMRES(KSP ksp)
673: {
674:   KSP_PIPEFGMRES *pipefgmres;

676:   PetscNewLog(ksp,&pipefgmres);

678:   ksp->data                              = (void*)pipefgmres;
679:   ksp->ops->buildsolution                = KSPBuildSolution_PIPEFGMRES;
680:   ksp->ops->setup                        = KSPSetUp_PIPEFGMRES;
681:   ksp->ops->solve                        = KSPSolve_PIPEFGMRES;
682:   ksp->ops->reset                        = KSPReset_PIPEFGMRES;
683:   ksp->ops->destroy                      = KSPDestroy_PIPEFGMRES;
684:   ksp->ops->view                         = KSPView_PIPEFGMRES;
685:   ksp->ops->setfromoptions               = KSPSetFromOptions_PIPEFGMRES;
686:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
687:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

689:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
690:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);

692:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
693:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
694:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);

696:   pipefgmres->nextra_vecs    = 1;
697:   pipefgmres->haptol         = 1.0e-30;
698:   pipefgmres->q_preallocate  = 0;
699:   pipefgmres->delta_allocate = PIPEFGMRES_DELTA_DIRECTIONS;
700:   pipefgmres->orthog         = NULL;
701:   pipefgmres->nrs            = NULL;
702:   pipefgmres->sol_temp       = NULL;
703:   pipefgmres->max_k          = PIPEFGMRES_DEFAULT_MAXK;
704:   pipefgmres->Rsvd           = NULL;
705:   pipefgmres->orthogwork     = NULL;
706:   pipefgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
707:   pipefgmres->shift          = 1.0;
708:   return 0;
709: }

711: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP ksp,PetscInt it)
712: {
713:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
714:   PetscInt       nwork   = pipefgmres->nwork_alloc; /* number of work vector chunks allocated */
715:   PetscInt       nalloc;                            /* number to allocate */
716:   PetscInt       k;

718:   nalloc = pipefgmres->delta_allocate; /* number of vectors to allocate
719:                                       in a single chunk */

721:   /* Adjust the number to allocate to make sure that we don't exceed the
722:      number of available slots (pipefgmres->vecs_allocated)*/
723:   if (it + VEC_OFFSET + nalloc >= pipefgmres->vecs_allocated) {
724:     nalloc = pipefgmres->vecs_allocated - it - VEC_OFFSET;
725:   }
726:   if (!nalloc) return 0;

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

730:   /* work vectors */
731:   KSPCreateVecs(ksp,nalloc,&pipefgmres->user_work[nwork],0,NULL);
732:   PetscLogObjectParents(ksp,nalloc,pipefgmres->user_work[nwork]);
733:   for (k=0; k < nalloc; k++) {
734:     pipefgmres->vecs[it+VEC_OFFSET+k] = pipefgmres->user_work[nwork][k];
735:   }
736:   /* specify size of chunk allocated */
737:   pipefgmres->mwork_alloc[nwork] = nalloc;

739:   /* preconditioned vectors (note we don't use VEC_OFFSET) */
740:   KSPCreateVecs(ksp,nalloc,&pipefgmres->prevecs_user_work[nwork],0,NULL);
741:   PetscLogObjectParents(ksp,nalloc,pipefgmres->prevecs_user_work[nwork]);
742:   for (k=0; k < nalloc; k++) {
743:     pipefgmres->prevecs[it+k] = pipefgmres->prevecs_user_work[nwork][k];
744:   }

746:   KSPCreateVecs(ksp,nalloc,&pipefgmres->zvecs_user_work[nwork],0,NULL);
747:   PetscLogObjectParents(ksp,nalloc,pipefgmres->zvecs_user_work[nwork]);
748:   for (k=0; k < nalloc; k++) {
749:     pipefgmres->zvecs[it+k] = pipefgmres->zvecs_user_work[nwork][k];
750:   }

752:   /* increment the number of work vector chunks */
753:   pipefgmres->nwork_alloc++;
754:   return 0;
755: }

757: /*@
758:   KSPPIPEFGMRESSetShift - Set the shift parameter for the flexible, pipelined GMRES solver.

760:   A heuristic is to set this to be comparable to the largest eigenvalue of the preconditioned operator. This can be acheived with PETSc itself by using a few iterations of a Krylov method. See KSPComputeEigenvalues (and note the caveats there).

762: Logically Collective on ksp

764: Input Parameters:
765: +  ksp - the Krylov space context
766: -  shift - the shift

768: Level: intermediate

770: Options Database:
771: . -ksp_pipefgmres_shift <shift> - set the shift parameter

773: .seealso: KSPComputeEigenvalues()
774: @*/
775: PetscErrorCode KSPPIPEFGMRESSetShift(KSP ksp,PetscScalar shift)
776: {
777:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;

781:   pipefgmres->shift = shift;
782:   return 0;
783: }