Actual source code: pipefgmres.c

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

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

 17: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP, PetscInt);
 18: static PetscErrorCode KSPPIPEFGMRESUpdateHessenberg(KSP, PetscInt, PetscBool *, PetscReal *);
 19: static PetscErrorCode KSPPIPEFGMRESBuildSoln(PetscScalar *, Vec, Vec, KSP, PetscInt);
 20: extern PetscErrorCode KSPReset_PIPEFGMRES(KSP);

 22: static PetscErrorCode KSPSetUp_PIPEFGMRES(KSP ksp)
 23: {
 24:   PetscInt        k;
 25:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
 26:   const PetscInt  max_k      = pipefgmres->max_k;

 28:   PetscFunctionBegin;
 29:   PetscCall(KSPSetUp_GMRES(ksp));

 31:   PetscCall(PetscMalloc1(VEC_OFFSET + max_k, &pipefgmres->prevecs));
 32:   PetscCall(PetscMalloc1(VEC_OFFSET + max_k, &pipefgmres->prevecs_user_work));

 34:   PetscCall(KSPCreateVecs(ksp, pipefgmres->vv_allocated, &pipefgmres->prevecs_user_work[0], 0, NULL));
 35:   for (k = 0; k < pipefgmres->vv_allocated; k++) pipefgmres->prevecs[k] = pipefgmres->prevecs_user_work[0][k];

 37:   PetscCall(PetscMalloc1(VEC_OFFSET + max_k, &pipefgmres->zvecs));
 38:   PetscCall(PetscMalloc1(VEC_OFFSET + max_k, &pipefgmres->zvecs_user_work));

 40:   PetscCall(PetscMalloc1(VEC_OFFSET + max_k, &pipefgmres->redux));

 42:   PetscCall(KSPCreateVecs(ksp, pipefgmres->vv_allocated, &pipefgmres->zvecs_user_work[0], 0, NULL));
 43:   for (k = 0; k < pipefgmres->vv_allocated; k++) pipefgmres->zvecs[k] = pipefgmres->zvecs_user_work[0][k];
 44:   PetscFunctionReturn(PETSC_SUCCESS);
 45: }

 47: static PetscErrorCode KSPPIPEFGMRESCycle(PetscInt *itcount, KSP ksp)
 48: {
 49:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
 50:   PetscReal       res_norm;
 51:   PetscReal       hapbnd, tt;
 52:   PetscScalar    *hh, *hes, *lhh, shift = pipefgmres->shift;
 53:   PetscBool       hapend = PETSC_FALSE;      /* indicates happy breakdown ending */
 54:   PetscInt        loc_it;                    /* local count of # of dir. in Krylov space */
 55:   PetscInt        max_k = pipefgmres->max_k; /* max # of directions Krylov space */
 56:   PetscInt        i, j, k;
 57:   Mat             Amat, Pmat;
 58:   Vec             Q, W;                      /* Pipelining vectors */
 59:   Vec            *redux = pipefgmres->redux; /* workspace for single reduction */

 61:   PetscFunctionBegin;
 62:   if (itcount) *itcount = 0;

 64:   /* Assign simpler names to these vectors, allocated as pipelining workspace */
 65:   Q = VEC_Q;
 66:   W = VEC_W;

 68:   /* Allocate memory for orthogonalization work */
 69:   /* Note that we add an extra value here to allow for a single reduction */
 70:   if (ksp->lorthogwork < pipefgmres->max_k + 2) {
 71:     PetscCall(PetscFree(ksp->orthogwork));
 72:     ksp->lorthogwork = pipefgmres->max_k + 2;
 73:     PetscCall(PetscMalloc1(ksp->lorthogwork, &ksp->orthogwork));
 74:   }
 75:   lhh = ksp->orthogwork;
 76:   /* Number of pseudo iterations since last restart is the number
 77:      of prestart directions */
 78:   loc_it = 0;

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

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

 89:   /* first entry in the right-hand side of the Hessenberg system is just
 90:      the initial residual norm */
 91:   *RS(0) = res_norm;

 93:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
 94:   if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res_norm;
 95:   else ksp->rnorm = 0;
 96:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
 97:   PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
 98:   PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));

100:   /* check for the convergence - maybe the current guess is good enough */
101:   PetscCall((*ksp->converged)(ksp, ksp->its, ksp->rnorm, &ksp->reason, ksp->cnvP));
102:   if (ksp->reason) {
103:     if (itcount) *itcount = 0;
104:     PetscFunctionReturn(PETSC_SUCCESS);
105:   }

107:   /* scale VEC_VV (the initial residual) */
108:   PetscCall(VecScale(VEC_VV(0), 1.0 / res_norm));

110:   /* Fill the pipeline */
111:   PetscCall(KSP_PCApply(ksp, VEC_VV(loc_it), PREVEC(loc_it)));
112:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
113:   PetscCall(KSP_MatMult(ksp, Amat, PREVEC(loc_it), ZVEC(loc_it)));
114:   PetscCall(VecAXPY(ZVEC(loc_it), -shift, VEC_VV(loc_it))); /* Note shift */

116:   /* MAIN ITERATION LOOP BEGINNING*/
117:   /* keep iterating until we have converged OR generated the max number
118:      of directions OR reached the max number of iterations for the method */
119:   while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
120:     if (loc_it) {
121:       PetscCall(KSPLogResidualHistory(ksp, res_norm));
122:       PetscCall(KSPMonitor(ksp, ksp->its, res_norm));
123:     }
124:     pipefgmres->it = (loc_it - 1);

126:     /* see if more space is needed for work vectors */
127:     if (pipefgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
128:       PetscCall(KSPPIPEFGMRESGetNewVectors(ksp, loc_it + 1));
129:       /* (loc_it+1) is passed in as number of the first vector that should be allocated */
130:     }

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

138:     /* Do some local twiddling to allow for a single reduction */
139:     for (i = 0; i < loc_it + 1; i++) redux[i] = VEC_VV(i);
140:     redux[loc_it + 1] = ZVEC(loc_it);

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

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

148:     /* The work to be overlapped with the inner products follows.
149:        This is application of the preconditioner and the operator
150:        to compute intermediate quantities which will be combined (locally)
151:        with the results of the inner products.
152:        */
153:     PetscCall(KSP_PCApply(ksp, ZVEC(loc_it), Q));
154:     PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
155:     PetscCall(KSP_MatMult(ksp, Amat, Q, W));

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

166:     /* Finish the dot product, retrieving the extra entry */
167:     PetscCall(VecMDotEnd(ZVEC(loc_it), loc_it + 2, redux, lhh));
168:     tt = PetscRealPart(lhh[loc_it + 1]);

170:     /* Hessenberg entries, and entries for (naive) classical Gram-Schmidt
171:       Note that the Hessenberg entries require a shift, as these are for the
172:       relation AU = VH, which is wrt unshifted basis vectors */
173:     hh  = HH(0, loc_it);
174:     hes = HES(0, loc_it);
175:     for (j = 0; j < loc_it; j++) {
176:       hh[j]  = lhh[j];
177:       hes[j] = lhh[j];
178:     }
179:     hh[loc_it]  = lhh[loc_it] + shift;
180:     hes[loc_it] = lhh[loc_it] + shift;

182:     /* we delay applying the shift here */
183:     for (j = 0; j <= loc_it; j++) lhh[j] = -lhh[j]; /* flip sign */

185:     /* Compute the norm of the un-normalized new direction using the rearranged formula
186:        Note that these are shifted ("barred") quantities */
187:     for (k = 0; k <= loc_it; k++) tt -= PetscAbsScalar(lhh[k]) * PetscAbsScalar(lhh[k]);
188:     /* On AVX512 this is accumulating roundoff errors for eg: tt=-2.22045e-16 */
189:     if ((tt < 0.0) && tt > -PETSC_SMALL) tt = 0.0;
190:     if (tt < 0.0) {
191:       /* If we detect square root breakdown in the norm, we must restart the algorithm.
192:          Here this means we simply break the current loop and reconstruct the solution
193:          using the basis we have computed thus far. Note that by breaking immediately,
194:          we do not update the iteration count, so computation done in this iteration
195:          should be disregarded.
196:          */
197:       PetscCall(PetscInfo(ksp, "Restart due to square root breakdown at it = %" PetscInt_FMT ", tt=%g\n", ksp->its, (double)tt));
198:       break;
199:     } else {
200:       tt = PetscSqrtReal(tt);
201:     }

203:     /* new entry in Hessenberg is the 2-norm of our new direction */
204:     hh[loc_it + 1]  = tt;
205:     hes[loc_it + 1] = tt;

207:     /* The recurred computation for the new direction
208:        The division by tt is delayed to the happy breakdown check later
209:        Note placement BEFORE the unshift
210:        */
211:     PetscCall(VecCopy(ZVEC(loc_it), VEC_VV(loc_it + 1)));
212:     PetscCall(VecMAXPY(VEC_VV(loc_it + 1), loc_it + 1, lhh, &VEC_VV(0)));
213:     /* (VEC_VV(loc_it+1) is not normalized yet) */

215:     /* The recurred computation for the preconditioned vector (u) */
216:     PetscCall(VecCopy(Q, PREVEC(loc_it + 1)));
217:     PetscCall(VecMAXPY(PREVEC(loc_it + 1), loc_it + 1, lhh, &PREVEC(0)));
218:     if (tt) PetscCall(VecScale(PREVEC(loc_it + 1), 1.0 / tt));

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

223:     /* The recurred computation for z (Au)
224:        Note placement AFTER the "unshift" */
225:     PetscCall(VecCopy(W, ZVEC(loc_it + 1)));
226:     PetscCall(VecMAXPY(ZVEC(loc_it + 1), loc_it + 1, lhh, &ZVEC(0)));
227:     if (tt) PetscCall(VecScale(ZVEC(loc_it + 1), 1.0 / tt));

229:     /* Happy Breakdown Check */
230:     hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
231:     /* RS(loc_it) contains the res_norm from the last iteration  */
232:     hapbnd = PetscMin(pipefgmres->haptol, hapbnd);
233:     if (tt > hapbnd) {
234:       /* scale new direction by its norm  */
235:       PetscCall(VecScale(VEC_VV(loc_it + 1), 1.0 / tt));
236:     } else {
237:       /* This happens when the solution is exactly reached. */
238:       /* So there is no new direction... */
239:       PetscCall(VecSet(VEC_TEMP, 0.0)); /* set VEC_TEMP to 0 */
240:       hapend = PETSC_TRUE;
241:     }
242:     /* note that for pipefgmres we could get HES(loc_it+1, loc_it)  = 0 and the
243:        current solution would not be exact if HES was singular.  Note that
244:        HH non-singular implies that HES is not singular, and HES is guaranteed
245:        to be nonsingular when PREVECS are linearly independent and A is
246:        nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity
247:        of HES). So we should really add a check to verify that HES is nonsingular.*/

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

253:     /* Now apply rotations to new col of Hessenberg (and right side of system),
254:        calculate new rotation, and get new residual norm at the same time*/
255:     PetscCall(KSPPIPEFGMRESUpdateHessenberg(ksp, loc_it, &hapend, &res_norm));
256:     if (ksp->reason) break;

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

261:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
262:     ksp->its++;
263:     if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res_norm;
264:     else ksp->rnorm = 0;
265:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));

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

269:     /* Catch error in happy breakdown and signal convergence and break from loop */
270:     if (hapend) {
271:       if (!ksp->reason) {
272:         PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "Reached happy break down, but convergence was not indicated. Residual norm = %g", (double)res_norm);
273:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
274:         break;
275:       }
276:     }
277:   }
278:   /* END OF ITERATION LOOP */

280:   if (itcount) *itcount = loc_it;

282:   /*
283:     Solve for the "best" coefficients of the Krylov
284:     columns, add the solution values together, and possibly unwind the
285:     preconditioning from the solution
286:    */

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

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

293:   /*
294:      Monitor if we know that we will not return for a restart
295:   */
296:   if (ksp->reason == KSP_CONVERGED_ITERATING && ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
297:   if (loc_it && ksp->reason) {
298:     PetscCall(KSPMonitor(ksp, ksp->its, ksp->rnorm));
299:     PetscCall(KSPLogResidualHistory(ksp, ksp->rnorm));
300:   }
301:   PetscFunctionReturn(PETSC_SUCCESS);
302: }

304: static PetscErrorCode KSPSolve_PIPEFGMRES(KSP ksp)
305: {
306:   PetscInt        its, itcount;
307:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
308:   PetscBool       guess_zero = ksp->guess_zero;

310:   PetscFunctionBegin;
311:   /* We have not checked these routines for use with complex numbers. The inner products are likely not defined correctly for that case */
312:   PetscCheck(!PetscDefined(USE_COMPLEX) || PetscDefined(SKIP_COMPLEX), PETSC_COMM_WORLD, PETSC_ERR_SUP, "PIPEFGMRES has not been implemented for use with complex scalars");

314:   PetscCall(PetscCitationsRegister(citation, &cited));

316:   PetscCheck(!ksp->calc_sings || pipefgmres->Rsvd, PetscObjectComm((PetscObject)ksp), PETSC_ERR_ORDER, "Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
317:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
318:   ksp->its = 0;
319:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));

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

337: static PetscErrorCode KSPDestroy_PIPEFGMRES(KSP ksp)
338: {
339:   PetscFunctionBegin;
340:   PetscCall(KSPReset_PIPEFGMRES(ksp));
341:   PetscCall(KSPDestroy_GMRES(ksp));
342:   PetscFunctionReturn(PETSC_SUCCESS);
343: }

345: static PetscErrorCode KSPPIPEFGMRESBuildSoln(PetscScalar *nrs, Vec vguess, Vec vdest, KSP ksp, PetscInt it)
346: {
347:   PetscScalar     tt;
348:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;

350:   PetscFunctionBegin;
351:   if (it < 0) {                        /* no pipefgmres steps have been performed */
352:     PetscCall(VecCopy(vguess, vdest)); /* VecCopy() is smart, exits immediately if vguess == vdest */
353:     PetscFunctionReturn(PETSC_SUCCESS);
354:   }

356:   /* Solve for solution vector that minimizes the residual */
357:   /* solve the upper triangular system - RS is the right side and HH is
358:      the upper triangular matrix  - put soln in nrs */
359:   if (*HH(it, it) != 0.0) nrs[it] = *RS(it) / *HH(it, it);
360:   else nrs[it] = 0.0;

362:   for (PetscInt k = it - 1; k >= 0; k--) {
363:     tt = *RS(k);
364:     for (PetscInt j = k + 1; j <= it; j++) tt -= *HH(k, j) * nrs[j];
365:     nrs[k] = tt / *HH(k, k);
366:   }

368:   /* Accumulate the correction to the solution of the preconditioned problem in VEC_TEMP */
369:   PetscCall(VecMAXPBY(VEC_TEMP, it + 1, nrs, 0, &PREVEC(0)));

371:   /* add solution to previous solution */
372:   if (vdest == vguess) PetscCall(VecAXPY(vdest, 1.0, VEC_TEMP));
373:   else PetscCall(VecWAXPY(vdest, 1.0, VEC_TEMP, vguess));
374:   PetscFunctionReturn(PETSC_SUCCESS);
375: }

377: static PetscErrorCode KSPPIPEFGMRESUpdateHessenberg(KSP ksp, PetscInt it, PetscBool *hapend, PetscReal *res)
378: {
379:   PetscScalar    *hh, *cc, *ss, *rs;
380:   PetscReal       hapbnd;
381:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;

383:   PetscFunctionBegin;
384:   hh = HH(0, it); /* pointer to beginning of column to update */
385:   cc = CC(0);     /* beginning of cosine rotations */
386:   ss = SS(0);     /* beginning of sine rotations */
387:   rs = RS(0);     /* right-hand side of least squares system */

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

392:   /* check for the happy breakdown */
393:   hapbnd = PetscMin(PetscAbsScalar(hh[it + 1] / rs[it]), pipefgmres->haptol);
394:   if (PetscAbsScalar(hh[it + 1]) < hapbnd) {
395:     PetscCall(PetscInfo(ksp, "Detected happy breakdown, current hapbnd = %14.12e H(%" PetscInt_FMT ",%" PetscInt_FMT ") = %14.12e\n", (double)hapbnd, it + 1, it, (double)PetscAbsScalar(*HH(it + 1, it))));
396:     *hapend = PETSC_TRUE;
397:   }

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

403:   for (PetscInt j = 0; j < it; j++) {
404:     PetscScalar hhj = hh[j];
405:     hh[j]           = PetscConj(cc[j]) * hhj + ss[j] * hh[j + 1];
406:     hh[j + 1]       = -ss[j] * hhj + cc[j] * hh[j + 1];
407:   }

409:   /*
410:     compute the new plane rotation, and apply it to:
411:      1) the right-hand side of the Hessenberg system (RS)
412:         note: it affects RS(it) and RS(it+1)
413:      2) the new column of the Hessenberg matrix
414:         note: it affects HH(it,it) which is currently pointed to
415:         by hh and HH(it+1, it) (*(hh+1))
416:     thus obtaining the updated value of the residual...
417:   */

419:   /* compute new plane rotation */

421:   if (!*hapend) {
422:     PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it + 1])));
423:     if (delta == 0.0) {
424:       ksp->reason = KSP_DIVERGED_NULL;
425:       PetscFunctionReturn(PETSC_SUCCESS);
426:     }

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

431:     hh[it]     = PetscConj(cc[it]) * hh[it] + ss[it] * hh[it + 1];
432:     rs[it + 1] = -ss[it] * rs[it];
433:     rs[it]     = PetscConj(cc[it]) * rs[it];
434:     *res       = PetscAbsScalar(rs[it + 1]);
435:   } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
436:             another rotation matrix (so RH doesn't change).  The new residual is
437:             always the new sine term times the residual from last time (RS(it)),
438:             but now the new sine rotation would be zero...so the residual should
439:             be zero...so we will multiply "zero" by the last residual.  This might
440:             not be exactly what we want to do here -could just return "zero". */
441:     *res = 0.0;
442:   }
443:   PetscFunctionReturn(PETSC_SUCCESS);
444: }

446: static PetscErrorCode KSPBuildSolution_PIPEFGMRES(KSP ksp, Vec ptr, Vec *result)
447: {
448:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;

450:   PetscFunctionBegin;
451:   if (!ptr) {
452:     if (!pipefgmres->sol_temp) PetscCall(VecDuplicate(ksp->vec_sol, &pipefgmres->sol_temp));
453:     ptr = pipefgmres->sol_temp;
454:   }
455:   if (!pipefgmres->nrs) {
456:     /* allocate the work area */
457:     PetscCall(PetscMalloc1(pipefgmres->max_k, &pipefgmres->nrs));
458:   }

460:   PetscCall(KSPPIPEFGMRESBuildSoln(pipefgmres->nrs, ksp->vec_sol, ptr, ksp, pipefgmres->it));
461:   if (result) *result = ptr;
462:   PetscFunctionReturn(PETSC_SUCCESS);
463: }

465: static PetscErrorCode KSPSetFromOptions_PIPEFGMRES(KSP ksp, PetscOptionItems PetscOptionsObject)
466: {
467:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
468:   PetscBool       flg;
469:   PetscScalar     shift;

471:   PetscFunctionBegin;
472:   PetscCall(KSPSetFromOptions_GMRES(ksp, PetscOptionsObject));
473:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP pipelined FGMRES Options");
474:   PetscCall(PetscOptionsScalar("-ksp_pipefgmres_shift", "shift parameter", "KSPPIPEFGMRESSetShift", pipefgmres->shift, &shift, &flg));
475:   if (flg) PetscCall(KSPPIPEFGMRESSetShift(ksp, shift));
476:   PetscOptionsHeadEnd();
477:   PetscFunctionReturn(PETSC_SUCCESS);
478: }

480: static PetscErrorCode KSPView_PIPEFGMRES(KSP ksp, PetscViewer viewer)
481: {
482:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
483:   PetscBool       isascii, isstring;

485:   PetscFunctionBegin;
486:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
487:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));

489:   if (isascii) {
490:     PetscCall(PetscViewerASCIIPrintf(viewer, "  restart=%" PetscInt_FMT "\n", pipefgmres->max_k));
491:     PetscCall(PetscViewerASCIIPrintf(viewer, "  happy breakdown tolerance=%g\n", (double)pipefgmres->haptol));
492:     if (PetscDefined(USE_COMPLEX)) PetscCall(PetscViewerASCIIPrintf(viewer, "  shift=%g+%gi\n", (double)PetscRealPart(pipefgmres->shift), (double)PetscImaginaryPart(pipefgmres->shift)));
493:     else PetscCall(PetscViewerASCIIPrintf(viewer, "  shift=%g\n", (double)PetscRealPart(pipefgmres->shift)));
494:   } else if (isstring) {
495:     PetscCall(PetscViewerStringSPrintf(viewer, "restart %" PetscInt_FMT, pipefgmres->max_k));
496:     if (PetscDefined(USE_COMPLEX)) PetscCall(PetscViewerStringSPrintf(viewer, "   shift=%g+%gi\n", (double)PetscRealPart(pipefgmres->shift), (double)PetscImaginaryPart(pipefgmres->shift)));
497:     else PetscCall(PetscViewerStringSPrintf(viewer, "   shift=%g\n", (double)PetscRealPart(pipefgmres->shift)));
498:   }
499:   PetscFunctionReturn(PETSC_SUCCESS);
500: }

502: PetscErrorCode KSPReset_PIPEFGMRES(KSP ksp)
503: {
504:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;

506:   PetscFunctionBegin;
507:   PetscCall(PetscFree(pipefgmres->prevecs));
508:   PetscCall(PetscFree(pipefgmres->zvecs));
509:   for (PetscInt i = 0; i < pipefgmres->nwork_alloc; i++) {
510:     PetscCall(VecDestroyVecs(pipefgmres->mwork_alloc[i], &pipefgmres->prevecs_user_work[i]));
511:     PetscCall(VecDestroyVecs(pipefgmres->mwork_alloc[i], &pipefgmres->zvecs_user_work[i]));
512:   }
513:   PetscCall(PetscFree(pipefgmres->prevecs_user_work));
514:   PetscCall(PetscFree(pipefgmres->zvecs_user_work));
515:   PetscCall(PetscFree(pipefgmres->redux));
516:   PetscCall(KSPReset_GMRES(ksp));
517:   PetscFunctionReturn(PETSC_SUCCESS);
518: }

520: /*MC
521:    KSPPIPEFGMRES - Implements the Pipelined (1-stage) Flexible Generalized Minimal Residual method {cite}`sananschneppmay2016`. [](sec_pipelineksp). [](sec_flexibleksp)

523:    Options Database Keys:
524: +   -ksp_gmres_restart restart - the number of Krylov directions to orthogonalize against
525: .   -ksp_gmres_haptol tol      - sets the tolerance for "happy breakdown" (exact convergence)
526: .   -ksp_gmres_preallocate     - preallocate all the Krylov search directions initially (otherwise groups of vectors are allocated as needed)
527: .   -ksp_pipefgmres_shift      - the shift to use (defaults to 1. See `KSPPIPEFGMRESSetShift()`
528: -   -ksp_gmres_krylov_monitor  - plot the Krylov space generated

530:    Level: intermediate

532:    Notes:
533:    Compare to `KSPPGMRES` and `KSPFGMRES`

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

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

539:    Only right preconditioning is supported (but this preconditioner may be nonlinear/variable/inexact, as with `KSPFGMRES`).

541:    MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
542:    See [](doc_faq_pipelined)

544:    Developer Note:
545:    This class is subclassed off of `KSPGMRES`, see the source code in src/ksp/ksp/impls/gmres for comments on the structure of the code

547:    Contributed by:
548:    P. Sanan and S.M. Schnepp

550: .seealso: [](ch_ksp), [](doc_faq_pipelined), [](sec_pipelineksp), [](sec_flexibleksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`, `KSPLGMRES`, `KSPPIPECG`, `KSPPIPECR`, `KSPPGMRES`, `KSPFGMRES`,
551:           `KSPGMRESSetRestart()`, `KSPGMRESSetHapTol()`, `KSPGMRESSetPreAllocateVectors()`, `KSPGMRESMonitorKrylov()`, `KSPPIPEFGMRESSetShift()`
552: M*/

554: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEFGMRES(KSP ksp)
555: {
556:   KSP_PIPEFGMRES *pipefgmres;

558:   PetscFunctionBegin;
559:   PetscCall(PetscNew(&pipefgmres));

561:   ksp->data                              = (void *)pipefgmres;
562:   ksp->ops->buildsolution                = KSPBuildSolution_PIPEFGMRES;
563:   ksp->ops->setup                        = KSPSetUp_PIPEFGMRES;
564:   ksp->ops->solve                        = KSPSolve_PIPEFGMRES;
565:   ksp->ops->reset                        = KSPReset_PIPEFGMRES;
566:   ksp->ops->destroy                      = KSPDestroy_PIPEFGMRES;
567:   ksp->ops->view                         = KSPView_PIPEFGMRES;
568:   ksp->ops->setfromoptions               = KSPSetFromOptions_PIPEFGMRES;
569:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
570:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

572:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 3));
573:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));

575:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetPreAllocateVectors_C", KSPGMRESSetPreAllocateVectors_GMRES));
576:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetRestart_C", KSPGMRESSetRestart_GMRES));
577:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESGetRestart_C", KSPGMRESGetRestart_GMRES));
578:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPGMRESSetHapTol_C", KSPGMRESSetHapTol_GMRES));

580:   pipefgmres->nextra_vecs    = 1;
581:   pipefgmres->haptol         = 1.0e-30;
582:   pipefgmres->q_preallocate  = PETSC_FALSE;
583:   pipefgmres->delta_allocate = PIPEFGMRES_DELTA_DIRECTIONS;
584:   pipefgmres->nrs            = NULL;
585:   pipefgmres->sol_temp       = NULL;
586:   pipefgmres->max_k          = PIPEFGMRES_DEFAULT_MAXK;
587:   pipefgmres->Rsvd           = NULL;
588:   pipefgmres->shift          = 1.0;
589:   PetscFunctionReturn(PETSC_SUCCESS);
590: }

592: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP ksp, PetscInt it)
593: {
594:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;
595:   PetscInt        nwork      = pipefgmres->nwork_alloc; /* number of work vector chunks allocated */
596:   PetscInt        nalloc;                               /* number to allocate */

598:   PetscFunctionBegin;
599:   nalloc = pipefgmres->delta_allocate; /* number of vectors to allocate
600:                                       in a single chunk */

602:   /* Adjust the number to allocate to make sure that we don't exceed the
603:      number of available slots (pipefgmres->vecs_allocated)*/
604:   if (it + VEC_OFFSET + nalloc >= pipefgmres->vecs_allocated) nalloc = pipefgmres->vecs_allocated - it - VEC_OFFSET;
605:   if (!nalloc) PetscFunctionReturn(PETSC_SUCCESS);

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

609:   /* work vectors */
610:   PetscCall(KSPCreateVecs(ksp, nalloc, &pipefgmres->user_work[nwork], 0, NULL));
611:   for (PetscInt k = 0; k < nalloc; k++) pipefgmres->vecs[it + VEC_OFFSET + k] = pipefgmres->user_work[nwork][k];
612:   /* specify size of chunk allocated */
613:   pipefgmres->mwork_alloc[nwork] = nalloc;

615:   /* preconditioned vectors (note we don't use VEC_OFFSET) */
616:   PetscCall(KSPCreateVecs(ksp, nalloc, &pipefgmres->prevecs_user_work[nwork], 0, NULL));
617:   for (PetscInt k = 0; k < nalloc; k++) pipefgmres->prevecs[it + k] = pipefgmres->prevecs_user_work[nwork][k];

619:   PetscCall(KSPCreateVecs(ksp, nalloc, &pipefgmres->zvecs_user_work[nwork], 0, NULL));
620:   for (PetscInt k = 0; k < nalloc; k++) pipefgmres->zvecs[it + k] = pipefgmres->zvecs_user_work[nwork][k];

622:   /* increment the number of work vector chunks */
623:   pipefgmres->nwork_alloc++;
624:   PetscFunctionReturn(PETSC_SUCCESS);
625: }

627: /*@
628:   KSPPIPEFGMRESSetShift - Set the shift parameter for the flexible, pipelined `KSPPIPEFGMRES` solver.

630:   Logically Collective

632:   Input Parameters:
633: + ksp   - the Krylov space context
634: - shift - the shift

636:   Options Database Key:
637: . -ksp_pipefgmres_shift shift - set the shift parameter

639:   Level: intermediate

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

646: .seealso: [](ch_ksp), `KSPPIPEFGMRES`, `KSPComputeEigenvalues()`
647: @*/
648: PetscErrorCode KSPPIPEFGMRESSetShift(KSP ksp, PetscScalar shift)
649: {
650:   KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES *)ksp->data;

652:   PetscFunctionBegin;
655:   pipefgmres->shift = shift;
656:   PetscFunctionReturn(PETSC_SUCCESS);
657: }