Date: 2022-08-02T03:14:42+00:00

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: }