Actual source code: pipegcr.c

petsc-main 2021-04-20
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  1: /*
  2:     Contributed by Sascha M. Schnepp and Patrick Sanan
  3: */

  5: #include "petscsys.h"
  6: #include <../src/ksp/ksp/impls/gcr/pipegcr/pipegcrimpl.h>

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

 23: #define KSPPIPEGCR_DEFAULT_MMAX 15
 24: #define KSPPIPEGCR_DEFAULT_NPREALLOC 5
 25: #define KSPPIPEGCR_DEFAULT_VECB 5
 26: #define KSPPIPEGCR_DEFAULT_TRUNCSTRAT KSP_FCD_TRUNC_TYPE_NOTAY
 27: #define KSPPIPEGCR_DEFAULT_UNROLL_W PETSC_TRUE

 29: #include <petscksp.h>

 31: static PetscErrorCode KSPAllocateVectors_PIPEGCR(KSP ksp, PetscInt nvecsneeded, PetscInt chunksize)
 32: {
 33:   PetscErrorCode  ierr;
 34:   PetscInt        i;
 35:   KSP_PIPEGCR     *pipegcr;
 36:   PetscInt        nnewvecs, nvecsprev;

 39:   pipegcr = (KSP_PIPEGCR*)ksp->data;

 41:   /* Allocate enough new vectors to add chunksize new vectors, reach nvecsneedtotal, or to reach mmax+1, whichever is smallest */
 42:   if (pipegcr->nvecs < PetscMin(pipegcr->mmax+1,nvecsneeded)){
 43:     nvecsprev = pipegcr->nvecs;
 44:     nnewvecs = PetscMin(PetscMax(nvecsneeded-pipegcr->nvecs,chunksize),pipegcr->mmax+1-pipegcr->nvecs);
 45:     KSPCreateVecs(ksp,nnewvecs,&pipegcr->ppvecs[pipegcr->nchunks],0,NULL);
 46:     PetscLogObjectParents((PetscObject)ksp,nnewvecs,pipegcr->ppvecs[pipegcr->nchunks]);
 47:     KSPCreateVecs(ksp,nnewvecs,&pipegcr->psvecs[pipegcr->nchunks],0,NULL);
 48:     PetscLogObjectParents((PetscObject)ksp,nnewvecs,pipegcr->psvecs[pipegcr->nchunks]);
 49:     KSPCreateVecs(ksp,nnewvecs,&pipegcr->pqvecs[pipegcr->nchunks],0,NULL);
 50:     PetscLogObjectParents((PetscObject)ksp,nnewvecs,pipegcr->pqvecs[pipegcr->nchunks]);
 51:     if (pipegcr->unroll_w) {
 52:       KSPCreateVecs(ksp,nnewvecs,&pipegcr->ptvecs[pipegcr->nchunks],0,NULL);
 53:       PetscLogObjectParents((PetscObject)ksp,nnewvecs,pipegcr->ptvecs[pipegcr->nchunks]);
 54:     }
 55:     pipegcr->nvecs += nnewvecs;
 56:     for (i=0;i<nnewvecs;i++){
 57:       pipegcr->qvecs[nvecsprev+i] = pipegcr->pqvecs[pipegcr->nchunks][i];
 58:       pipegcr->pvecs[nvecsprev+i] = pipegcr->ppvecs[pipegcr->nchunks][i];
 59:       pipegcr->svecs[nvecsprev+i] = pipegcr->psvecs[pipegcr->nchunks][i];
 60:       if (pipegcr->unroll_w) {
 61:         pipegcr->tvecs[nvecsprev+i] = pipegcr->ptvecs[pipegcr->nchunks][i];
 62:       }
 63:     }
 64:     pipegcr->chunksizes[pipegcr->nchunks] = nnewvecs;
 65:     pipegcr->nchunks++;
 66:   }
 67:   return(0);
 68: }

 70: static PetscErrorCode KSPSolve_PIPEGCR_cycle(KSP ksp)
 71: {
 72:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;
 74:   Mat            A, B;
 75:   Vec            x,r,b,z,w,m,n,p,s,q,t,*redux;
 76:   PetscInt       i,j,k,idx,kdx,mi;
 77:   PetscScalar    alpha=0.0,gamma,*betas,*dots;
 78:   PetscReal      rnorm=0.0, delta,*eta,*etas;

 81:   /* !!PS We have not checked these routines for use with complex numbers. The inner products
 82:      are likely not defined correctly for that case */
 83:   if (PetscDefined(USE_COMPLEX) && !PetscDefined(SKIP_COMPLEX)) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"PIPEFGMRES has not been implemented for use with complex scalars");

 85:   KSPGetOperators(ksp, &A, &B);
 86:   x = ksp->vec_sol;
 87:   b = ksp->vec_rhs;
 88:   r = ksp->work[0];
 89:   z = ksp->work[1];
 90:   w = ksp->work[2]; /* w = Az = AB(r)                 (pipelining intermediate) */
 91:   m = ksp->work[3]; /* m = B(w) = B(Az) = B(AB(r))    (pipelining intermediate) */
 92:   n = ksp->work[4]; /* n = AB(w) = AB(Az) = AB(AB(r)) (pipelining intermediate) */
 93:   p = pipegcr->pvecs[0];
 94:   s = pipegcr->svecs[0];
 95:   q = pipegcr->qvecs[0];
 96:   t = pipegcr->unroll_w ? pipegcr->tvecs[0] : NULL;

 98:   redux = pipegcr->redux;
 99:   dots  = pipegcr->dots;
100:   etas  = pipegcr->etas;
101:   betas = dots;        /* dots takes the result of all dot products of which the betas are a subset */

103:   /* cycle initial residual */
104:   KSP_MatMult(ksp,A,x,r);
105:   VecAYPX(r,-1.0,b);                   /* r <- b - Ax */
106:   KSP_PCApply(ksp,r,z);                /* z <- B(r)   */
107:   KSP_MatMult(ksp,A,z,w);              /* w <- Az     */

109:   /* initialization of other variables and pipelining intermediates */
110:   VecCopy(z,p);
111:   KSP_MatMult(ksp,A,p,s);

113:   /* overlap initial computation of delta, gamma */
114:   redux[0] = w;
115:   redux[1] = r;
116:   VecMDotBegin(w,2,redux,dots);    /* Start split reductions for gamma = (w,r), delta = (w,w) */
117:   PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)s)); /* perform asynchronous reduction */
118:   KSP_PCApply(ksp,s,q);            /* q = B(s) */
119:   if (pipegcr->unroll_w) {
120:     KSP_MatMult(ksp,A,q,t);        /* t = Aq   */
121:   }
122:   VecMDotEnd(w,2,redux,dots);      /* Finish split reduction */
123:   delta    = PetscRealPart(dots[0]);
124:   etas[0]  = delta;
125:   gamma    = dots[1];
126:   alpha    = gamma/delta;

128:   i = 0;
129:   do {
130:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
131:     ksp->its++;
132:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

134:     /* update solution, residuals, .. */
135:     VecAXPY(x,+alpha,p);
136:     VecAXPY(r,-alpha,s);
137:     VecAXPY(z,-alpha,q);
138:     if (pipegcr->unroll_w){
139:       VecAXPY(w,-alpha,t);
140:     } else {
141:       KSP_MatMult(ksp,A,z,w);
142:     }

144:     /* Computations of current iteration done */
145:     i++;

147:     if (pipegcr->modifypc) {
148:       (*pipegcr->modifypc)(ksp,ksp->its,ksp->rnorm,pipegcr->modifypc_ctx);
149:     }

151:     /* If needbe, allocate a new chunk of vectors */
152:     KSPAllocateVectors_PIPEGCR(ksp,i+1,pipegcr->vecb);

154:     /* Note that we wrap around and start clobbering old vectors */
155:     idx = i % (pipegcr->mmax+1);
156:     p   = pipegcr->pvecs[idx];
157:     s   = pipegcr->svecs[idx];
158:     q   = pipegcr->qvecs[idx];
159:     if (pipegcr->unroll_w) {
160:       t   = pipegcr->tvecs[idx];
161:     }
162:     eta = pipegcr->etas+idx;

164:     /* number of old directions to orthogonalize against */
165:     switch(pipegcr->truncstrat){
166:       case KSP_FCD_TRUNC_TYPE_STANDARD:
167:         mi = pipegcr->mmax;
168:         break;
169:       case KSP_FCD_TRUNC_TYPE_NOTAY:
170:         mi = ((i-1) % pipegcr->mmax)+1;
171:         break;
172:       default:
173:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unrecognized Truncation Strategy");
174:     }

176:     /* Pick old p,s,q,zeta in a way suitable for VecMDot */
177:     for (k=PetscMax(0,i-mi),j=0;k<i;j++,k++){
178:       kdx = k % (pipegcr->mmax+1);
179:       pipegcr->pold[j] = pipegcr->pvecs[kdx];
180:       pipegcr->sold[j] = pipegcr->svecs[kdx];
181:       pipegcr->qold[j] = pipegcr->qvecs[kdx];
182:       if (pipegcr->unroll_w) {
183:         pipegcr->told[j] = pipegcr->tvecs[kdx];
184:       }
185:       redux[j]         = pipegcr->svecs[kdx];
186:     }
187:     /* If the above loop is not run redux contains only r and w => all beta_k = 0, only gamma, delta != 0 */
188:     redux[j]   = r;
189:     redux[j+1] = w;

191:     /* Dot products */
192:     /* Start split reductions for beta_k = (w,s_k), gamma = (w,r), delta = (w,w) */
193:     VecMDotBegin(w,j+2,redux,dots);
194:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)w));

196:     /* B(w-r) + u stabilization */
197:     VecWAXPY(n,-1.0,r,w);              /* m = u + B(w-r): (a) ntmp = w-r              */
198:     KSP_PCApply(ksp,n,m);              /* m = u + B(w-r): (b) mtmp = B(ntmp) = B(w-r) */
199:     VecAXPY(m,1.0,z);                  /* m = u + B(w-r): (c) m = z + mtmp            */
200:     if (pipegcr->unroll_w){
201:       KSP_MatMult(ksp,A,m,n);          /* n = Am                                      */
202:     }

204:     /* Finish split reductions for beta_k = (w,s_k), gamma = (w,r), delta = (w,w) */
205:     VecMDotEnd(w,j+2,redux,dots);
206:     gamma = dots[j];
207:     delta = PetscRealPart(dots[j+1]);

209:     /* compute new residual norm.
210:        this cannot be done before this point so that the natural norm
211:        is available for free and the communication involved is overlapped */
212:     switch (ksp->normtype) {
213:     case KSP_NORM_PRECONDITIONED:
214:       VecNorm(z,NORM_2,&rnorm);        /* ||r|| <- sqrt(z'*z) */
215:       break;
216:     case KSP_NORM_UNPRECONDITIONED:
217:       VecNorm(r,NORM_2,&rnorm);        /* ||r|| <- sqrt(r'*r) */
218:       break;
219:     case KSP_NORM_NATURAL:
220:       rnorm = PetscSqrtReal(PetscAbsScalar(gamma));         /* ||r|| <- sqrt(r,w)  */
221:       break;
222:     case KSP_NORM_NONE:
223:       rnorm = 0.0;
224:       break;
225:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
226:     }

228:     /* Check for convergence */
229:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
230:     ksp->rnorm = rnorm;
231:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
232:     KSPLogResidualHistory(ksp,rnorm);
233:     KSPMonitor(ksp,ksp->its,rnorm);
234:     (*ksp->converged)(ksp,ksp->its,rnorm,&ksp->reason,ksp->cnvP);
235:     if (ksp->reason) return(0);

237:     /* compute new eta and scale beta */
238:     *eta = 0.;
239:     for (k=PetscMax(0,i-mi),j=0;k<i;j++,k++){
240:       kdx = k % (pipegcr->mmax+1);
241:       betas[j] /= -etas[kdx];                               /* betak  /= etak */
242:       *eta -= ((PetscReal)(PetscAbsScalar(betas[j])*PetscAbsScalar(betas[j]))) * etas[kdx];
243:                                                             /* etaitmp = -betaik^2 * etak */
244:     }
245:     *eta += delta;                                          /* etai    = delta -betaik^2 * etak */

247:     /* check breakdown of eta = (s,s) */
248:     if (*eta < 0.) {
249:       pipegcr->norm_breakdown = PETSC_TRUE;
250:       PetscInfo1(ksp,"Restart due to square root breakdown at it = \n",ksp->its);
251:       break;
252:     } else {
253:       alpha= gamma/(*eta);                                  /* alpha = gamma/etai */
254:     }

256:     /* project out stored search directions using classical G-S */
257:     VecCopy(z,p);
258:     VecCopy(w,s);
259:     VecCopy(m,q);
260:     if (pipegcr->unroll_w) {
261:       VecCopy(n,t);
262:       VecMAXPY(t,j,betas,pipegcr->told); /* ti <- n  - sum_k beta_k t_k */
263:     }
264:     VecMAXPY(p,j,betas,pipegcr->pold); /* pi <- ui - sum_k beta_k p_k */
265:     VecMAXPY(s,j,betas,pipegcr->sold); /* si <- wi - sum_k beta_k s_k */
266:     VecMAXPY(q,j,betas,pipegcr->qold); /* qi <- m  - sum_k beta_k q_k */

268:   } while (ksp->its < ksp->max_it);
269:   if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
270:   return(0);
271: }

273: static PetscErrorCode KSPSolve_PIPEGCR(KSP ksp)
274: {
275:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;
277:   Mat            A, B;
278:   Vec            x,b,r,z,w;
279:   PetscScalar    gamma;
280:   PetscReal      rnorm=0.0;
281:   PetscBool      issym;

284:   PetscCitationsRegister(citation,&cited);

286:   KSPGetOperators(ksp, &A, &B);
287:   x = ksp->vec_sol;
288:   b = ksp->vec_rhs;
289:   r = ksp->work[0];
290:   z = ksp->work[1];
291:   w = ksp->work[2]; /* w = Az = AB(r)                 (pipelining intermediate) */

293:   /* compute initial residual */
294:   if (!ksp->guess_zero) {
295:     KSP_MatMult(ksp,A,x,r);
296:     VecAYPX(r,-1.0,b);                 /* r <- b - Ax       */
297:   } else {
298:     VecCopy(b,r);                      /* r <- b            */
299:   }

301:   /* initial residual norm */
302:   KSP_PCApply(ksp,r,z);                /* z <- B(r)         */
303:   KSP_MatMult(ksp,A,z,w);              /* w <- Az           */
304:   VecDot(r,w,&gamma);                  /* gamma = (r,w)     */

306:   switch (ksp->normtype) {
307:     case KSP_NORM_PRECONDITIONED:
308:       VecNorm(z,NORM_2,&rnorm);        /* ||r|| <- sqrt(z'*z) */
309:       break;
310:     case KSP_NORM_UNPRECONDITIONED:
311:       VecNorm(r,NORM_2,&rnorm);        /* ||r|| <- sqrt(r'*r) */
312:       break;
313:     case KSP_NORM_NATURAL:
314:       rnorm = PetscSqrtReal(PetscAbsScalar(gamma));         /* ||r|| <- sqrt(r,w)  */
315:       break;
316:     case KSP_NORM_NONE:
317:       rnorm = 0.0;
318:       break;
319:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
320:   }

322:   /* Is A symmetric? */
323:   PetscObjectTypeCompareAny((PetscObject)A,&issym,MATSBAIJ,MATSEQSBAIJ,MATMPISBAIJ,"");
324:   if (!issym) {
325:     PetscInfo(A,"Matrix type is not any of MATSBAIJ,MATSEQSBAIJ,MATMPISBAIJ. Is matrix A symmetric (as required by CR methods)?");
326:   }

328:   /* logging */
329:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
330:   ksp->its    = 0;
331:   ksp->rnorm0 = rnorm;
332:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
333:   KSPLogResidualHistory(ksp,ksp->rnorm0);
334:   KSPMonitor(ksp,ksp->its,ksp->rnorm0);
335:   (*ksp->converged)(ksp,ksp->its,ksp->rnorm0,&ksp->reason,ksp->cnvP);
336:   if (ksp->reason) return(0);

338:   do {
339:     KSPSolve_PIPEGCR_cycle(ksp);
340:     if (ksp->reason) return(0);
341:     if (pipegcr->norm_breakdown) {
342:       pipegcr->n_restarts++;
343:       pipegcr->norm_breakdown = PETSC_FALSE;
344:     }
345:   } while (ksp->its < ksp->max_it);

347:   if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
348:   return(0);
349: }

351: static PetscErrorCode KSPView_PIPEGCR(KSP ksp, PetscViewer viewer)
352: {
353:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;
355:   PetscBool      isascii,isstring;
356:   const char     *truncstr;

359:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII, &isascii);
360:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);

362:   if (pipegcr->truncstrat == KSP_FCD_TRUNC_TYPE_STANDARD){
363:     truncstr = "Using standard truncation strategy";
364:   } else if (pipegcr->truncstrat == KSP_FCD_TRUNC_TYPE_NOTAY){
365:     truncstr = "Using Notay's truncation strategy";
366:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Undefined FCD truncation strategy");


369:   if (isascii) {
370:     PetscViewerASCIIPrintf(viewer,"  max previous directions = %D\n",pipegcr->mmax);
371:     PetscViewerASCIIPrintf(viewer,"  preallocated %D directions\n",PetscMin(pipegcr->nprealloc,pipegcr->mmax+1));
372:     PetscViewerASCIIPrintf(viewer,"  %s\n",truncstr);
373:     PetscViewerASCIIPrintf(viewer,"  w unrolling = %D \n", pipegcr->unroll_w);
374:     PetscViewerASCIIPrintf(viewer,"  restarts performed = %D \n", pipegcr->n_restarts);
375:   } else if (isstring) {
376:     PetscViewerStringSPrintf(viewer, "max previous directions = %D, preallocated %D directions, %s truncation strategy", pipegcr->mmax,pipegcr->nprealloc,truncstr);
377:   }
378:   return(0);
379: }


382: static PetscErrorCode KSPSetUp_PIPEGCR(KSP ksp)
383: {
384:   KSP_PIPEGCR   *pipegcr = (KSP_PIPEGCR*)ksp->data;
386:   Mat            A;
387:   PetscBool      diagonalscale;
388:   const PetscInt nworkstd = 5;

391:   PCGetDiagonalScale(ksp->pc,&diagonalscale);
392:   if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);

394:   KSPGetOperators(ksp, &A, NULL);

396:   /* Allocate "standard" work vectors */
397:   KSPSetWorkVecs(ksp,nworkstd);

399:   /* Allocated space for pointers to additional work vectors
400:     note that mmax is the number of previous directions, so we add 1 for the current direction */
401:   PetscMalloc6(pipegcr->mmax+1,&(pipegcr->pvecs),pipegcr->mmax+1,&(pipegcr->ppvecs),pipegcr->mmax+1,&(pipegcr->svecs), pipegcr->mmax+1,&(pipegcr->psvecs),pipegcr->mmax+1,&(pipegcr->qvecs),pipegcr->mmax+1,&(pipegcr->pqvecs));
402:   if (pipegcr->unroll_w) {
403:     PetscMalloc3(pipegcr->mmax+1,&(pipegcr->tvecs),pipegcr->mmax+1,&(pipegcr->ptvecs),pipegcr->mmax+2,&(pipegcr->told));
404:   }
405:   PetscMalloc4(pipegcr->mmax+2,&(pipegcr->pold),pipegcr->mmax+2,&(pipegcr->sold),pipegcr->mmax+2,&(pipegcr->qold),pipegcr->mmax+2,&(pipegcr->chunksizes));
406:   PetscMalloc3(pipegcr->mmax+2,&(pipegcr->dots),pipegcr->mmax+1,&(pipegcr->etas),pipegcr->mmax+2,&(pipegcr->redux));
407:   /* If the requested number of preallocated vectors is greater than mmax reduce nprealloc */
408:   if (pipegcr->nprealloc > pipegcr->mmax+1){
409:     PetscInfo2(NULL,"Requested nprealloc=%d is greater than m_max+1=%d. Resetting nprealloc = m_max+1.\n",pipegcr->nprealloc, pipegcr->mmax+1);
410:   }

412:   /* Preallocate additional work vectors */
413:   KSPAllocateVectors_PIPEGCR(ksp,pipegcr->nprealloc,pipegcr->nprealloc);

415:   PetscLogObjectMemory(
416:     (PetscObject)ksp,
417:     (pipegcr->mmax + 1) * 4 * sizeof(Vec*) +        /* old dirs  */
418:     (pipegcr->mmax + 1) * 4 * sizeof(Vec**) +       /* old pdirs */
419:     (pipegcr->mmax + 1) * 4 * sizeof(Vec*) +        /* p/s/qold/told */
420:     (pipegcr->mmax + 1) *     sizeof(PetscInt) +    /* chunksizes */
421:     (pipegcr->mmax + 2) *     sizeof(Vec*) +        /* redux */
422:     (pipegcr->mmax + 2) *     sizeof(PetscScalar) + /* dots */
423:     (pipegcr->mmax + 1) *     sizeof(PetscReal)     /* etas */
424: );
425:   return(0);
426: }

428: static PetscErrorCode KSPReset_PIPEGCR(KSP ksp)
429: {
431:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;

434:   if (pipegcr->modifypc_destroy) {
435:     (*pipegcr->modifypc_destroy)(pipegcr->modifypc_ctx);
436:   }
437:   return(0);
438: }

440: static PetscErrorCode KSPDestroy_PIPEGCR(KSP ksp)
441: {
443:   PetscInt       i;
444:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;

447:   VecDestroyVecs(ksp->nwork,&ksp->work); /* Destroy "standard" work vecs */

449:   /* Destroy vectors for old directions and the arrays that manage pointers to them */
450:   if (pipegcr->nvecs){
451:     for (i=0;i<pipegcr->nchunks;i++){
452:       VecDestroyVecs(pipegcr->chunksizes[i],&pipegcr->ppvecs[i]);
453:       VecDestroyVecs(pipegcr->chunksizes[i],&pipegcr->psvecs[i]);
454:       VecDestroyVecs(pipegcr->chunksizes[i],&pipegcr->pqvecs[i]);
455:       if (pipegcr->unroll_w) {
456:         VecDestroyVecs(pipegcr->chunksizes[i],&pipegcr->ptvecs[i]);
457:       }
458:     }
459:   }

461:   PetscFree6(pipegcr->pvecs,pipegcr->ppvecs,pipegcr->svecs,pipegcr->psvecs,pipegcr->qvecs,pipegcr->pqvecs);
462:   PetscFree4(pipegcr->pold,pipegcr->sold,pipegcr->qold,pipegcr->chunksizes);
463:   PetscFree3(pipegcr->dots,pipegcr->etas,pipegcr->redux);
464:   if (pipegcr->unroll_w) {
465:     PetscFree3(pipegcr->tvecs,pipegcr->ptvecs,pipegcr->told);
466:   }

468:   KSPReset_PIPEGCR(ksp);
469:   KSPDestroyDefault(ksp);
470:   return(0);
471: }

473: /*@
474:   KSPPIPEGCRSetUnrollW - Set to PETSC_TRUE to use PIPEGCR with unrolling of the w vector

476:   Logically Collective on ksp

478:   Input Parameters:
479: +  ksp - the Krylov space context
480: -  unroll_w - use unrolling

482:   Level: intermediate

484:   Options Database:
485: . -ksp_pipegcr_unroll_w

487: .seealso: KSPPIPEGCR, KSPPIPEGCRSetTruncationType(), KSPPIPEGCRSetNprealloc(),KSPPIPEGCRGetUnrollW()
488: @*/
489: PetscErrorCode KSPPIPEGCRSetUnrollW(KSP ksp,PetscBool unroll_w)
490: {
491:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

496:   pipegcr->unroll_w=unroll_w;
497:   return(0);
498: }

500: /*@
501:   KSPPIPEGCRGetUnrollW - Get information on PIPEGCR unrolling the w vector

503:   Logically Collective on ksp

505:    Input Parameter:
506: .  ksp - the Krylov space context

508:    Output Parameter:
509: .  unroll_w - PIPEGCR uses unrolling (bool)

511:   Level: intermediate

513:   Options Database:
514: . -ksp_pipegcr_unroll_w

516: .seealso: KSPPIPEGCR, KSPPIPEGCRGetTruncationType(), KSPPIPEGCRGetNprealloc(),KSPPIPEGCRSetUnrollW()
517: @*/
518: PetscErrorCode KSPPIPEGCRGetUnrollW(KSP ksp,PetscBool *unroll_w)
519: {
520:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

524:   *unroll_w=pipegcr->unroll_w;
525:   return(0);
526: }

528: /*@
529:   KSPPIPEGCRSetMmax - set the maximum number of previous directions PIPEGCR will store for orthogonalization

531:   Note: mmax + 1 directions are stored (mmax previous ones along with a current one)
532:   and whether all are used in each iteration also depends on the truncation strategy
533:   (see KSPPIPEGCRSetTruncationType)

535:   Logically Collective on ksp

537:   Input Parameters:
538: +  ksp - the Krylov space context
539: -  mmax - the maximum number of previous directions to orthogonalize againt

541:   Level: intermediate

543:   Options Database:
544: . -ksp_pipegcr_mmax <N>

546: .seealso: KSPPIPEGCR, KSPPIPEGCRSetTruncationType(), KSPPIPEGCRSetNprealloc()
547: @*/
548: PetscErrorCode KSPPIPEGCRSetMmax(KSP ksp,PetscInt mmax)
549: {
550:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

555:   pipegcr->mmax=mmax;
556:   return(0);
557: }

559: /*@
560:   KSPPIPEGCRGetMmax - get the maximum number of previous directions PIPEGCR will store

562:   Note: PIPEGCR stores mmax+1 directions at most (mmax previous ones, and one current one)

564:    Not Collective

566:    Input Parameter:
567: .  ksp - the Krylov space context

569:    Output Parameter:
570: .  mmax - the maximum number of previous directons allowed for orthogonalization

572:   Options Database:
573: . -ksp_pipegcr_mmax <N>

575:    Level: intermediate

577: .seealso: KSPPIPEGCR, KSPPIPEGCRGetTruncationType(), KSPPIPEGCRGetNprealloc(), KSPPIPEGCRSetMmax()
578: @*/

580: PetscErrorCode KSPPIPEGCRGetMmax(KSP ksp,PetscInt *mmax)
581: {
582:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

586:   *mmax=pipegcr->mmax;
587:   return(0);
588: }

590: /*@
591:   KSPPIPEGCRSetNprealloc - set the number of directions to preallocate with PIPEGCR

593:   Logically Collective on ksp

595:   Input Parameters:
596: +  ksp - the Krylov space context
597: -  nprealloc - the number of vectors to preallocate

599:   Level: advanced

601:   Options Database:
602: . -ksp_pipegcr_nprealloc <N>

604: .seealso: KSPPIPEGCR, KSPPIPEGCRGetTruncationType(), KSPPIPEGCRGetNprealloc()
605: @*/
606: PetscErrorCode KSPPIPEGCRSetNprealloc(KSP ksp,PetscInt nprealloc)
607: {
608:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

613:   pipegcr->nprealloc = nprealloc;
614:   return(0);
615: }

617: /*@
618:   KSPPIPEGCRGetNprealloc - get the number of directions preallocate by PIPEGCR

620:    Not Collective

622:    Input Parameter:
623: .  ksp - the Krylov space context

625:    Output Parameter:
626: .  nprealloc - the number of directions preallocated

628:   Options Database:
629: . -ksp_pipegcr_nprealloc <N>

631:    Level: advanced

633: .seealso: KSPPIPEGCR, KSPPIPEGCRGetTruncationType(), KSPPIPEGCRSetNprealloc()
634: @*/
635: PetscErrorCode KSPPIPEGCRGetNprealloc(KSP ksp,PetscInt *nprealloc)
636: {
637:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

641:   *nprealloc = pipegcr->nprealloc;
642:   return(0);
643: }

645: /*@
646:   KSPPIPEGCRSetTruncationType - specify how many of its stored previous directions PIPEGCR uses during orthoganalization

648:   Logically Collective on ksp

650:   KSP_FCD_TRUNC_TYPE_STANDARD uses all (up to mmax) stored directions
651:   KSP_FCD_TRUNC_TYPE_NOTAY uses the last max(1,mod(i,mmax)) directions at iteration i=0,1,..

653:   Input Parameters:
654: +  ksp - the Krylov space context
655: -  truncstrat - the choice of strategy

657:   Level: intermediate

659:   Options Database:
660: . -ksp_pipegcr_truncation_type <standard,notay> - which stored basis vectors to orthogonalize against

662: .seealso: KSPPIPEGCR, KSPPIPEGCRSetTruncationType, KSPPIPEGCRTruncationType, KSPFCDTruncationType
663: @*/
664: PetscErrorCode KSPPIPEGCRSetTruncationType(KSP ksp,KSPFCDTruncationType truncstrat)
665: {
666:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

671:   pipegcr->truncstrat=truncstrat;
672:   return(0);
673: }

675: /*@
676:   KSPPIPEGCRGetTruncationType - get the truncation strategy employed by PIPEGCR

678:   Not Collective

680:   KSP_FCD_TRUNC_TYPE_STANDARD uses all (up to mmax) stored directions
681:   KSP_FCD_TRUNC_TYPE_NOTAY uses the last max(1,mod(i,mmax)) directions at iteration i=0,1,..

683:    Input Parameter:
684: .  ksp - the Krylov space context

686:    Output Parameter:
687: .  truncstrat - the strategy type

689:   Options Database:
690: . -ksp_pipegcr_truncation_type <standard,notay> - which stored basis vectors to orthogonalize against

692:    Level: intermediate

694: .seealso: KSPPIPEGCR, KSPPIPEGCRSetTruncationType, KSPPIPEGCRTruncationType, KSPFCDTruncationType
695: @*/
696: PetscErrorCode KSPPIPEGCRGetTruncationType(KSP ksp,KSPFCDTruncationType *truncstrat)
697: {
698:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

702:   *truncstrat=pipegcr->truncstrat;
703:   return(0);
704: }

706: static PetscErrorCode KSPSetFromOptions_PIPEGCR(PetscOptionItems *PetscOptionsObject,KSP ksp)
707: {
709:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;
710:   PetscInt       mmax,nprealloc;
711:   PetscBool      flg;

714:   PetscOptionsHead(PetscOptionsObject,"KSP PIPEGCR options");
715:   PetscOptionsInt("-ksp_pipegcr_mmax","Number of search directions to storue","KSPPIPEGCRSetMmax",pipegcr->mmax,&mmax,&flg);
716:   if (flg) KSPPIPEGCRSetMmax(ksp,mmax);
717:   PetscOptionsInt("-ksp_pipegcr_nprealloc","Number of directions to preallocate","KSPPIPEGCRSetNprealloc",pipegcr->nprealloc,&nprealloc,&flg);
718:   if (flg) { KSPPIPEGCRSetNprealloc(ksp,nprealloc); }
719:   PetscOptionsEnum("-ksp_pipegcr_truncation_type","Truncation approach for directions","KSPFCGSetTruncationType",KSPFCDTruncationTypes,(PetscEnum)pipegcr->truncstrat,(PetscEnum*)&pipegcr->truncstrat,NULL);
720:   PetscOptionsBool("-ksp_pipegcr_unroll_w","Use unrolling of w","KSPPIPEGCRSetUnrollW",pipegcr->unroll_w,&pipegcr->unroll_w,NULL);
721:   PetscOptionsTail();
722:   return(0);
723: }

726: typedef PetscErrorCode (*KSPPIPEGCRModifyPCFunction)(KSP,PetscInt,PetscReal,void*);
727: typedef PetscErrorCode (*KSPPIPEGCRDestroyFunction)(void*);

729: static PetscErrorCode  KSPPIPEGCRSetModifyPC_PIPEGCR(KSP ksp,KSPPIPEGCRModifyPCFunction function,void *data,KSPPIPEGCRDestroyFunction destroy)
730: {
731:   KSP_PIPEGCR *pipegcr = (KSP_PIPEGCR*)ksp->data;

735:   pipegcr->modifypc         = function;
736:   pipegcr->modifypc_destroy = destroy;
737:   pipegcr->modifypc_ctx     = data;
738:   return(0);
739: }

741: /*@C
742:  KSPPIPEGCRSetModifyPC - Sets the routine used by PIPEGCR to modify the preconditioner.

744:  Logically Collective on ksp

746:  Input Parameters:
747:  +  ksp      - iterative context obtained from KSPCreate()
748:  .  function - user defined function to modify the preconditioner
749:  .  ctx      - user provided contex for the modify preconditioner function
750:  -  destroy  - the function to use to destroy the user provided application context.

752:  Calling Sequence of function:
753:   PetscErrorCode function (KSP ksp, PetscInt n, PetscReal rnorm, void *ctx)

755:  ksp   - iterative context
756:  n     - the total number of PIPEGCR iterations that have occurred
757:  rnorm - 2-norm residual value
758:  ctx   - the user provided application context

760:  Level: intermediate

762:  Notes:
763:  The default modifypc routine is KSPPIPEGCRModifyPCNoChange()

765:  .seealso: KSPPIPEGCRModifyPCNoChange()

767:  @*/
768: PetscErrorCode  KSPPIPEGCRSetModifyPC(KSP ksp,PetscErrorCode (*function)(KSP,PetscInt,PetscReal,void*),void *data,PetscErrorCode (*destroy)(void*))
769: {

773:   PetscUseMethod(ksp,"KSPPIPEGCRSetModifyPC_C",(KSP,PetscErrorCode (*)(KSP,PetscInt,PetscReal,void*),void *data,PetscErrorCode (*)(void*)),(ksp,function,data,destroy));
774:   return(0);
775: }

777: /*MC
778:      KSPPIPEGCR - Implements a Pipelined Generalized Conjugate Residual method.

780:   Options Database Keys:
781: +   -ksp_pipegcr_mmax <N>  - the max number of Krylov directions to orthogonalize against
782: .   -ksp_pipegcr_unroll_w - unroll w at the storage cost of a maximum of (mmax+1) extra vectors with the benefit of better pipelining (default: PETSC_TRUE)
783: .   -ksp_pipegcr_nprealloc <N> - the number of vectors to preallocated for storing Krylov directions. Once exhausted new directions are allocated blockwise (default: 5)
784: -   -ksp_pipegcr_truncation_type <standard,notay> - which previous search directions to orthogonalize against


787:   Notes:
788:     The PIPEGCR Krylov method supports non-symmetric matrices and permits the use of a preconditioner
789:     which may vary from one iteration to the next. Users can can define a method to vary the
790:     preconditioner between iterates via KSPPIPEGCRSetModifyPC().
791:     Restarts are solves with x0 not equal to zero. When a restart occurs, the initial starting
792:     solution is given by the current estimate for x which was obtained by the last restart
793:     iterations of the PIPEGCR algorithm.
794:     The method implemented requires at most the storage of 4 x mmax + 5 vectors, roughly twice as much as GCR.

796:     Only supports left preconditioning.

798:     The natural "norm" for this method is (u,Au), where u is the preconditioned residual. This norm is available at no additional computational cost, as with standard CG. Choosing preconditioned or unpreconditioned norm types involves a blocking reduction which prevents any benefit from pipelining.

800:   Reference:
801:     P. Sanan, S.M. Schnepp, and D.A. May,
802:     "Pipelined, Flexible Krylov Subspace Methods,"
803:     SIAM Journal on Scientific Computing 2016 38:5, C441-C470,
804:     DOI: 10.1137/15M1049130

806:    Level: intermediate

808: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
809:            KSPPIPEFGMRES, KSPPIPECG, KSPPIPECR, KSPPIPEFCG,KSPPIPEGCRSetTruncationType(),KSPPIPEGCRSetNprealloc(),KSPPIPEGCRSetUnrollW(),KSPPIPEGCRSetMmax()


812: M*/
813: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEGCR(KSP ksp)
814: {
816:   KSP_PIPEGCR    *pipegcr;

819:   PetscNewLog(ksp,&pipegcr);
820:   pipegcr->mmax       = KSPPIPEGCR_DEFAULT_MMAX;
821:   pipegcr->nprealloc  = KSPPIPEGCR_DEFAULT_NPREALLOC;
822:   pipegcr->nvecs      = 0;
823:   pipegcr->vecb       = KSPPIPEGCR_DEFAULT_VECB;
824:   pipegcr->nchunks    = 0;
825:   pipegcr->truncstrat = KSPPIPEGCR_DEFAULT_TRUNCSTRAT;
826:   pipegcr->n_restarts = 0;
827:   pipegcr->unroll_w   = KSPPIPEGCR_DEFAULT_UNROLL_W;

829:   ksp->data       = (void*)pipegcr;

831:   /* natural norm is for free, precond+unprecond norm require non-overlapped reduction */
832:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
833:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,1);
834:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,1);
835:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

837:   ksp->ops->setup          = KSPSetUp_PIPEGCR;
838:   ksp->ops->solve          = KSPSolve_PIPEGCR;
839:   ksp->ops->reset          = KSPReset_PIPEGCR;
840:   ksp->ops->destroy        = KSPDestroy_PIPEGCR;
841:   ksp->ops->view           = KSPView_PIPEGCR;
842:   ksp->ops->setfromoptions = KSPSetFromOptions_PIPEGCR;
843:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
844:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

846:   PetscObjectComposeFunction((PetscObject)ksp,"KSPPIPEGCRSetModifyPC_C",KSPPIPEGCRSetModifyPC_PIPEGCR);
847:   return(0);
848: }