Actual source code: pipegcr.c

  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:   PetscInt        i;
 34:   KSP_PIPEGCR     *pipegcr;
 35:   PetscInt        nnewvecs, nvecsprev;

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

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

 68: static PetscErrorCode KSPSolve_PIPEGCR_cycle(KSP ksp)
 69: {
 70:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;
 71:   Mat            A, B;
 72:   Vec            x,r,b,z,w,m,n,p,s,q,t,*redux;
 73:   PetscInt       i,j,k,idx,kdx,mi;
 74:   PetscScalar    alpha=0.0,gamma,*betas,*dots;
 75:   PetscReal      rnorm=0.0, delta,*eta,*etas;

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

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

 94:   redux = pipegcr->redux;
 95:   dots  = pipegcr->dots;
 96:   etas  = pipegcr->etas;
 97:   betas = dots;        /* dots takes the result of all dot products of which the betas are a subset */

 99:   /* cycle initial residual */
100:   KSP_MatMult(ksp,A,x,r);
101:   VecAYPX(r,-1.0,b);                   /* r <- b - Ax */
102:   KSP_PCApply(ksp,r,z);                /* z <- B(r)   */
103:   KSP_MatMult(ksp,A,z,w);              /* w <- Az     */

105:   /* initialization of other variables and pipelining intermediates */
106:   VecCopy(z,p);
107:   KSP_MatMult(ksp,A,p,s);

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

124:   i = 0;
125:   do {
126:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
127:     ksp->its++;
128:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

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

140:     /* Computations of current iteration done */
141:     i++;

143:     if (pipegcr->modifypc) {
144:       (*pipegcr->modifypc)(ksp,ksp->its,ksp->rnorm,pipegcr->modifypc_ctx);
145:     }

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

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

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

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

187:     /* Dot products */
188:     /* Start split reductions for beta_k = (w,s_k), gamma = (w,r), delta = (w,w) */
189:     VecMDotBegin(w,j+2,redux,dots);
190:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)w));

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

200:     /* Finish split reductions for beta_k = (w,s_k), gamma = (w,r), delta = (w,w) */
201:     VecMDotEnd(w,j+2,redux,dots);
202:     gamma = dots[j];
203:     delta = PetscRealPart(dots[j+1]);

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

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

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

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

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

264:   } while (ksp->its < ksp->max_it);
265:   if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
266:   return 0;
267: }

269: static PetscErrorCode KSPSolve_PIPEGCR(KSP ksp)
270: {
271:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;
272:   Mat            A, B;
273:   Vec            x,b,r,z,w;
274:   PetscScalar    gamma;
275:   PetscReal      rnorm=0.0;
276:   PetscBool      issym;

278:   PetscCitationsRegister(citation,&cited);

280:   KSPGetOperators(ksp, &A, &B);
281:   x = ksp->vec_sol;
282:   b = ksp->vec_rhs;
283:   r = ksp->work[0];
284:   z = ksp->work[1];
285:   w = ksp->work[2]; /* w = Az = AB(r)                 (pipelining intermediate) */

287:   /* compute initial residual */
288:   if (!ksp->guess_zero) {
289:     KSP_MatMult(ksp,A,x,r);
290:     VecAYPX(r,-1.0,b);                 /* r <- b - Ax       */
291:   } else {
292:     VecCopy(b,r);                      /* r <- b            */
293:   }

295:   /* initial residual norm */
296:   KSP_PCApply(ksp,r,z);                /* z <- B(r)         */
297:   KSP_MatMult(ksp,A,z,w);              /* w <- Az           */
298:   VecDot(r,w,&gamma);                  /* gamma = (r,w)     */

300:   switch (ksp->normtype) {
301:     case KSP_NORM_PRECONDITIONED:
302:       VecNorm(z,NORM_2,&rnorm);        /* ||r|| <- sqrt(z'*z) */
303:       break;
304:     case KSP_NORM_UNPRECONDITIONED:
305:       VecNorm(r,NORM_2,&rnorm);        /* ||r|| <- sqrt(r'*r) */
306:       break;
307:     case KSP_NORM_NATURAL:
308:       rnorm = PetscSqrtReal(PetscAbsScalar(gamma));         /* ||r|| <- sqrt(r,w)  */
309:       break;
310:     case KSP_NORM_NONE:
311:       rnorm = 0.0;
312:       break;
313:     default: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
314:   }

316:   /* Is A symmetric? */
317:   PetscObjectTypeCompareAny((PetscObject)A,&issym,MATSBAIJ,MATSEQSBAIJ,MATMPISBAIJ,"");
318:   if (!issym) {
319:     PetscInfo(A,"Matrix type is not any of MATSBAIJ,MATSEQSBAIJ,MATMPISBAIJ. Is matrix A symmetric (as required by CR methods)?");
320:   }

322:   /* logging */
323:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
324:   ksp->its    = 0;
325:   ksp->rnorm0 = rnorm;
326:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
327:   KSPLogResidualHistory(ksp,ksp->rnorm0);
328:   KSPMonitor(ksp,ksp->its,ksp->rnorm0);
329:   (*ksp->converged)(ksp,ksp->its,ksp->rnorm0,&ksp->reason,ksp->cnvP);
330:   if (ksp->reason) return 0;

332:   do {
333:     KSPSolve_PIPEGCR_cycle(ksp);
334:     if (ksp->reason) return 0;
335:     if (pipegcr->norm_breakdown) {
336:       pipegcr->n_restarts++;
337:       pipegcr->norm_breakdown = PETSC_FALSE;
338:     }
339:   } while (ksp->its < ksp->max_it);

341:   if (ksp->its >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
342:   return 0;
343: }

345: static PetscErrorCode KSPView_PIPEGCR(KSP ksp, PetscViewer viewer)
346: {
347:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;
348:   PetscBool      isascii,isstring;
349:   const char     *truncstr;

351:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII, &isascii);
352:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);

354:   if (pipegcr->truncstrat == KSP_FCD_TRUNC_TYPE_STANDARD) {
355:     truncstr = "Using standard truncation strategy";
356:   } else if (pipegcr->truncstrat == KSP_FCD_TRUNC_TYPE_NOTAY) {
357:     truncstr = "Using Notay's truncation strategy";
358:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Undefined FCD truncation strategy");

360:   if (isascii) {
361:     PetscViewerASCIIPrintf(viewer,"  max previous directions = %D\n",pipegcr->mmax);
362:     PetscViewerASCIIPrintf(viewer,"  preallocated %D directions\n",PetscMin(pipegcr->nprealloc,pipegcr->mmax+1));
363:     PetscViewerASCIIPrintf(viewer,"  %s\n",truncstr);
364:     PetscViewerASCIIPrintf(viewer,"  w unrolling = %D \n", pipegcr->unroll_w);
365:     PetscViewerASCIIPrintf(viewer,"  restarts performed = %D \n", pipegcr->n_restarts);
366:   } else if (isstring) {
367:     PetscViewerStringSPrintf(viewer, "max previous directions = %D, preallocated %D directions, %s truncation strategy", pipegcr->mmax,pipegcr->nprealloc,truncstr);
368:   }
369:   return 0;
370: }

372: static PetscErrorCode KSPSetUp_PIPEGCR(KSP ksp)
373: {
374:   KSP_PIPEGCR   *pipegcr = (KSP_PIPEGCR*)ksp->data;
375:   Mat            A;
376:   PetscBool      diagonalscale;
377:   const PetscInt nworkstd = 5;

379:   PCGetDiagonalScale(ksp->pc,&diagonalscale);

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

384:   /* Allocate "standard" work vectors */
385:   KSPSetWorkVecs(ksp,nworkstd);

387:   /* Allocated space for pointers to additional work vectors
388:     note that mmax is the number of previous directions, so we add 1 for the current direction */
389:   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));
390:   if (pipegcr->unroll_w) {
391:     PetscMalloc3(pipegcr->mmax+1,&(pipegcr->tvecs),pipegcr->mmax+1,&(pipegcr->ptvecs),pipegcr->mmax+2,&(pipegcr->told));
392:   }
393:   PetscMalloc4(pipegcr->mmax+2,&(pipegcr->pold),pipegcr->mmax+2,&(pipegcr->sold),pipegcr->mmax+2,&(pipegcr->qold),pipegcr->mmax+2,&(pipegcr->chunksizes));
394:   PetscMalloc3(pipegcr->mmax+2,&(pipegcr->dots),pipegcr->mmax+1,&(pipegcr->etas),pipegcr->mmax+2,&(pipegcr->redux));
395:   /* If the requested number of preallocated vectors is greater than mmax reduce nprealloc */
396:   if (pipegcr->nprealloc > pipegcr->mmax+1) {
397:     PetscInfo(NULL,"Requested nprealloc=%d is greater than m_max+1=%d. Resetting nprealloc = m_max+1.\n",pipegcr->nprealloc, pipegcr->mmax+1);
398:   }

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

403:   PetscCall(PetscLogObjectMemory(
404:             (PetscObject)ksp,
405:             (pipegcr->mmax + 1) * 4 * sizeof(Vec*) +        /* old dirs  */
406:             (pipegcr->mmax + 1) * 4 * sizeof(Vec**) +       /* old pdirs */
407:             (pipegcr->mmax + 1) * 4 * sizeof(Vec*) +        /* p/s/qold/told */
408:             (pipegcr->mmax + 1) *     sizeof(PetscInt) +    /* chunksizes */
409:             (pipegcr->mmax + 2) *     sizeof(Vec*) +        /* redux */
410:             (pipegcr->mmax + 2) *     sizeof(PetscScalar) + /* dots */
411:             (pipegcr->mmax + 1) *     sizeof(PetscReal)     /* etas */));
412:   return 0;
413: }

415: static PetscErrorCode KSPReset_PIPEGCR(KSP ksp)
416: {
417:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;

419:   if (pipegcr->modifypc_destroy) {
420:     (*pipegcr->modifypc_destroy)(pipegcr->modifypc_ctx);
421:   }
422:   return 0;
423: }

425: static PetscErrorCode KSPDestroy_PIPEGCR(KSP ksp)
426: {
427:   PetscInt       i;
428:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;

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

432:   /* Destroy vectors for old directions and the arrays that manage pointers to them */
433:   if (pipegcr->nvecs) {
434:     for (i=0;i<pipegcr->nchunks;i++) {
435:       VecDestroyVecs(pipegcr->chunksizes[i],&pipegcr->ppvecs[i]);
436:       VecDestroyVecs(pipegcr->chunksizes[i],&pipegcr->psvecs[i]);
437:       VecDestroyVecs(pipegcr->chunksizes[i],&pipegcr->pqvecs[i]);
438:       if (pipegcr->unroll_w) {
439:         VecDestroyVecs(pipegcr->chunksizes[i],&pipegcr->ptvecs[i]);
440:       }
441:     }
442:   }

444:   PetscFree6(pipegcr->pvecs,pipegcr->ppvecs,pipegcr->svecs,pipegcr->psvecs,pipegcr->qvecs,pipegcr->pqvecs);
445:   PetscFree4(pipegcr->pold,pipegcr->sold,pipegcr->qold,pipegcr->chunksizes);
446:   PetscFree3(pipegcr->dots,pipegcr->etas,pipegcr->redux);
447:   if (pipegcr->unroll_w) {
448:     PetscFree3(pipegcr->tvecs,pipegcr->ptvecs,pipegcr->told);
449:   }

451:   KSPReset_PIPEGCR(ksp);
452:   KSPDestroyDefault(ksp);
453:   return 0;
454: }

456: /*@
457:   KSPPIPEGCRSetUnrollW - Set to PETSC_TRUE to use PIPEGCR with unrolling of the w vector

459:   Logically Collective on ksp

461:   Input Parameters:
462: +  ksp - the Krylov space context
463: -  unroll_w - use unrolling

465:   Level: intermediate

467:   Options Database:
468: . -ksp_pipegcr_unroll_w <bool> -  use unrolling

470: .seealso: KSPPIPEGCR, KSPPIPEGCRSetTruncationType(), KSPPIPEGCRSetNprealloc(),KSPPIPEGCRGetUnrollW()
471: @*/
472: PetscErrorCode KSPPIPEGCRSetUnrollW(KSP ksp,PetscBool unroll_w)
473: {
474:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

478:   pipegcr->unroll_w=unroll_w;
479:   return 0;
480: }

482: /*@
483:   KSPPIPEGCRGetUnrollW - Get information on PIPEGCR unrolling the w vector

485:   Logically Collective on ksp

487:    Input Parameter:
488: .  ksp - the Krylov space context

490:    Output Parameter:
491: .  unroll_w - PIPEGCR uses unrolling (bool)

493:   Level: intermediate

495: .seealso: KSPPIPEGCR, KSPPIPEGCRGetTruncationType(), KSPPIPEGCRGetNprealloc(),KSPPIPEGCRSetUnrollW()
496: @*/
497: PetscErrorCode KSPPIPEGCRGetUnrollW(KSP ksp,PetscBool *unroll_w)
498: {
499:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

502:   *unroll_w=pipegcr->unroll_w;
503:   return 0;
504: }

506: /*@
507:   KSPPIPEGCRSetMmax - set the maximum number of previous directions PIPEGCR will store for orthogonalization

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

513:   Logically Collective on ksp

515:   Input Parameters:
516: +  ksp - the Krylov space context
517: -  mmax - the maximum number of previous directions to orthogonalize againt

519:   Level: intermediate

521:   Options Database:
522: . -ksp_pipegcr_mmax <N> - maximum number of previous directions

524: .seealso: KSPPIPEGCR, KSPPIPEGCRSetTruncationType(), KSPPIPEGCRSetNprealloc()
525: @*/
526: PetscErrorCode KSPPIPEGCRSetMmax(KSP ksp,PetscInt mmax)
527: {
528:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

532:   pipegcr->mmax=mmax;
533:   return 0;
534: }

536: /*@
537:   KSPPIPEGCRGetMmax - get the maximum number of previous directions PIPEGCR will store

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

541:    Not Collective

543:    Input Parameter:
544: .  ksp - the Krylov space context

546:    Output Parameter:
547: .  mmax - the maximum number of previous directions allowed for orthogonalization

549:    Level: intermediate

551: .seealso: KSPPIPEGCR, KSPPIPEGCRGetTruncationType(), KSPPIPEGCRGetNprealloc(), KSPPIPEGCRSetMmax()
552: @*/

554: PetscErrorCode KSPPIPEGCRGetMmax(KSP ksp,PetscInt *mmax)
555: {
556:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

559:   *mmax=pipegcr->mmax;
560:   return 0;
561: }

563: /*@
564:   KSPPIPEGCRSetNprealloc - set the number of directions to preallocate with PIPEGCR

566:   Logically Collective on ksp

568:   Input Parameters:
569: +  ksp - the Krylov space context
570: -  nprealloc - the number of vectors to preallocate

572:   Level: advanced

574:   Options Database:
575: . -ksp_pipegcr_nprealloc <N> - number of vectors to preallocate

577: .seealso: KSPPIPEGCR, KSPPIPEGCRGetTruncationType(), KSPPIPEGCRGetNprealloc()
578: @*/
579: PetscErrorCode KSPPIPEGCRSetNprealloc(KSP ksp,PetscInt nprealloc)
580: {
581:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

585:   pipegcr->nprealloc = nprealloc;
586:   return 0;
587: }

589: /*@
590:   KSPPIPEGCRGetNprealloc - get the number of directions preallocate by PIPEGCR

592:    Not Collective

594:    Input Parameter:
595: .  ksp - the Krylov space context

597:    Output Parameter:
598: .  nprealloc - the number of directions preallocated

600:    Level: advanced

602: .seealso: KSPPIPEGCR, KSPPIPEGCRGetTruncationType(), KSPPIPEGCRSetNprealloc()
603: @*/
604: PetscErrorCode KSPPIPEGCRGetNprealloc(KSP ksp,PetscInt *nprealloc)
605: {
606:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

609:   *nprealloc = pipegcr->nprealloc;
610:   return 0;
611: }

613: /*@
614:   KSPPIPEGCRSetTruncationType - specify how many of its stored previous directions PIPEGCR uses during orthoganalization

616:   Logically Collective on ksp

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

621:   Input Parameters:
622: +  ksp - the Krylov space context
623: -  truncstrat - the choice of strategy

625:   Level: intermediate

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

630: .seealso: KSPPIPEGCR, KSPPIPEGCRSetTruncationType, KSPPIPEGCRTruncationType, KSPFCDTruncationType
631: @*/
632: PetscErrorCode KSPPIPEGCRSetTruncationType(KSP ksp,KSPFCDTruncationType truncstrat)
633: {
634:   KSP_PIPEGCR *pipegcr=(KSP_PIPEGCR*)ksp->data;

638:   pipegcr->truncstrat=truncstrat;
639:   return 0;
640: }

642: /*@
643:   KSPPIPEGCRGetTruncationType - get the truncation strategy employed by PIPEGCR

645:   Not Collective

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

650:    Input Parameter:
651: .  ksp - the Krylov space context

653:    Output Parameter:
654: .  truncstrat - the strategy type

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

659:    Level: intermediate

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

668:   *truncstrat=pipegcr->truncstrat;
669:   return 0;
670: }

672: static PetscErrorCode KSPSetFromOptions_PIPEGCR(PetscOptionItems *PetscOptionsObject,KSP ksp)
673: {
674:   KSP_PIPEGCR    *pipegcr = (KSP_PIPEGCR*)ksp->data;
675:   PetscInt       mmax,nprealloc;
676:   PetscBool      flg;

678:   PetscOptionsHead(PetscOptionsObject,"KSP PIPEGCR options");
679:   PetscOptionsInt("-ksp_pipegcr_mmax","Number of search directions to storue","KSPPIPEGCRSetMmax",pipegcr->mmax,&mmax,&flg);
680:   if (flg) KSPPIPEGCRSetMmax(ksp,mmax);
681:   PetscOptionsInt("-ksp_pipegcr_nprealloc","Number of directions to preallocate","KSPPIPEGCRSetNprealloc",pipegcr->nprealloc,&nprealloc,&flg);
682:   if (flg) KSPPIPEGCRSetNprealloc(ksp,nprealloc);
683:   PetscOptionsEnum("-ksp_pipegcr_truncation_type","Truncation approach for directions","KSPFCGSetTruncationType",KSPFCDTruncationTypes,(PetscEnum)pipegcr->truncstrat,(PetscEnum*)&pipegcr->truncstrat,NULL);
684:   PetscOptionsBool("-ksp_pipegcr_unroll_w","Use unrolling of w","KSPPIPEGCRSetUnrollW",pipegcr->unroll_w,&pipegcr->unroll_w,NULL);
685:   PetscOptionsTail();
686:   return 0;
687: }

690: typedef PetscErrorCode (*KSPPIPEGCRModifyPCFunction)(KSP,PetscInt,PetscReal,void*);
691: typedef PetscErrorCode (*KSPPIPEGCRDestroyFunction)(void*);

693: static PetscErrorCode  KSPPIPEGCRSetModifyPC_PIPEGCR(KSP ksp,KSPPIPEGCRModifyPCFunction function,void *data,KSPPIPEGCRDestroyFunction destroy)
694: {
695:   KSP_PIPEGCR *pipegcr = (KSP_PIPEGCR*)ksp->data;

698:   pipegcr->modifypc         = function;
699:   pipegcr->modifypc_destroy = destroy;
700:   pipegcr->modifypc_ctx     = data;
701:   return 0;
702: }

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

707:  Logically Collective on ksp

709:  Input Parameters:
710:  +  ksp      - iterative context obtained from KSPCreate()
711:  .  function - user defined function to modify the preconditioner
712:  .  ctx      - user provided context for the modify preconditioner function
713:  -  destroy  - the function to use to destroy the user provided application context.

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

718:  ksp   - iterative context
719:  n     - the total number of PIPEGCR iterations that have occurred
720:  rnorm - 2-norm residual value
721:  ctx   - the user provided application context

723:  Level: intermediate

725:  Notes:
726:  The default modifypc routine is KSPPIPEGCRModifyPCNoChange()

728:  .seealso: KSPPIPEGCRModifyPCNoChange()

730:  @*/
731: PetscErrorCode  KSPPIPEGCRSetModifyPC(KSP ksp,PetscErrorCode (*function)(KSP,PetscInt,PetscReal,void*),void *data,PetscErrorCode (*destroy)(void*))
732: {
733:   PetscUseMethod(ksp,"KSPPIPEGCRSetModifyPC_C",(KSP,PetscErrorCode (*)(KSP,PetscInt,PetscReal,void*),void *data,PetscErrorCode (*)(void*)),(ksp,function,data,destroy));
734:   return 0;
735: }

737: /*MC
738:      KSPPIPEGCR - Implements a Pipelined Generalized Conjugate Residual method.

740:   Options Database Keys:
741: +   -ksp_pipegcr_mmax <N>  - the max number of Krylov directions to orthogonalize against
742: .   -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)
743: .   -ksp_pipegcr_nprealloc <N> - the number of vectors to preallocated for storing Krylov directions. Once exhausted new directions are allocated blockwise (default: 5)
744: -   -ksp_pipegcr_truncation_type <standard,notay> - which previous search directions to orthogonalize against

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

755:     Only supports left preconditioning.

757:     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.

759:   Reference:
760:     P. Sanan, S.M. Schnepp, and D.A. May,
761:     "Pipelined, Flexible Krylov Subspace Methods,"
762:     SIAM Journal on Scientific Computing 2016 38:5, C441-C470,
763:     DOI: 10.1137/15M1049130

765:    Level: intermediate

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

770: M*/
771: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEGCR(KSP ksp)
772: {
773:   KSP_PIPEGCR    *pipegcr;

775:   PetscNewLog(ksp,&pipegcr);
776:   pipegcr->mmax       = KSPPIPEGCR_DEFAULT_MMAX;
777:   pipegcr->nprealloc  = KSPPIPEGCR_DEFAULT_NPREALLOC;
778:   pipegcr->nvecs      = 0;
779:   pipegcr->vecb       = KSPPIPEGCR_DEFAULT_VECB;
780:   pipegcr->nchunks    = 0;
781:   pipegcr->truncstrat = KSPPIPEGCR_DEFAULT_TRUNCSTRAT;
782:   pipegcr->n_restarts = 0;
783:   pipegcr->unroll_w   = KSPPIPEGCR_DEFAULT_UNROLL_W;

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

787:   /* natural norm is for free, precond+unprecond norm require non-overlapped reduction */
788:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,2);
789:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,1);
790:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,1);
791:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);

793:   ksp->ops->setup          = KSPSetUp_PIPEGCR;
794:   ksp->ops->solve          = KSPSolve_PIPEGCR;
795:   ksp->ops->reset          = KSPReset_PIPEGCR;
796:   ksp->ops->destroy        = KSPDestroy_PIPEGCR;
797:   ksp->ops->view           = KSPView_PIPEGCR;
798:   ksp->ops->setfromoptions = KSPSetFromOptions_PIPEGCR;
799:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
800:   ksp->ops->buildresidual  = KSPBuildResidualDefault;

802:   PetscObjectComposeFunction((PetscObject)ksp,"KSPPIPEGCRSetModifyPC_C",KSPPIPEGCRSetModifyPC_PIPEGCR);
803:   return 0;
804: }