Date: 2016-07-24T17:07:07+00:00

Actual source code: fcg.c
petsc-3.7.3 2016-07-24
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      1: /*
      2:     This file implements the FCG (Flexible Conjugate Gradient) method

      4: */

      6: #include <../src/ksp/ksp/impls/fcg/fcgimpl.h>       /*I  "petscksp.h"  I*/
      7: extern PetscErrorCode KSPComputeExtremeSingularValues_CG(KSP,PetscReal*,PetscReal*);
      8: extern PetscErrorCode KSPComputeEigenvalues_CG(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);

     10: #define KSPFCG_DEFAULT_MMAX 30          /* maximum number of search directions to keep */
     11: #define KSPFCG_DEFAULT_NPREALLOC 10     /* number of search directions to preallocate */
     12: #define KSPFCG_DEFAULT_VECB 5           /* number of search directions to allocate each time new direction vectors are needed */
     13: #define KSPFCG_DEFAULT_TRUNCSTRAT KSP_FCD_TRUNC_TYPE_NOTAY

     17: static PetscErrorCode KSPAllocateVectors_FCG(KSP ksp, PetscInt nvecsneeded, PetscInt chunksize)
     18: {
     19:   PetscErrorCode  ierr;
     20:   PetscInt        i;
     21:   KSP_FCG         *fcg = (KSP_FCG*)ksp->data;
     22:   PetscInt        nnewvecs, nvecsprev;

     25:   /* Allocate enough new vectors to add chunksize new vectors, reach nvecsneedtotal, or to reach mmax+1, whichever is smallest */
     26:   if (fcg->nvecs < PetscMin(fcg->mmax+1,nvecsneeded)){
     27:     nvecsprev = fcg->nvecs;
     28:     nnewvecs = PetscMin(PetscMax(nvecsneeded-fcg->nvecs,chunksize),fcg->mmax+1-fcg->nvecs);
     29:     KSPCreateVecs(ksp,nnewvecs,&fcg->pCvecs[fcg->nchunks],0,NULL);
     30:     PetscLogObjectParents((PetscObject)ksp,nnewvecs,fcg->pCvecs[fcg->nchunks]);
     31:     KSPCreateVecs(ksp,nnewvecs,&fcg->pPvecs[fcg->nchunks],0,NULL);
     32:     PetscLogObjectParents((PetscObject)ksp,nnewvecs,fcg->pPvecs[fcg->nchunks]);
     33:     fcg->nvecs += nnewvecs;
     34:     for (i=0;i<nnewvecs;++i){
     35:       fcg->Cvecs[nvecsprev + i] = fcg->pCvecs[fcg->nchunks][i];
     36:       fcg->Pvecs[nvecsprev + i] = fcg->pPvecs[fcg->nchunks][i];
     37:     }
     38:     fcg->chunksizes[fcg->nchunks] = nnewvecs;
     39:     ++fcg->nchunks;
     40:   }
     41:   return(0);
     42: }

     46: PetscErrorCode    KSPSetUp_FCG(KSP ksp)
     47: {
     49:   KSP_FCG        *fcg = (KSP_FCG*)ksp->data;
     50:   PetscInt       maxit = ksp->max_it;
     51:   const PetscInt nworkstd = 2;

     55:   /* Allocate "standard" work vectors (not including the basis and transformed basis vectors) */
     56:   KSPSetWorkVecs(ksp,nworkstd);

     58:   /* Allocated space for pointers to additional work vectors
     59:    note that mmax is the number of previous directions, so we add 1 for the current direction,
     60:    and an extra 1 for the prealloc (which might be empty) */
     61:   PetscMalloc5(fcg->mmax+1,&fcg->Pvecs,fcg->mmax+1,&fcg->Cvecs,fcg->mmax+1,&fcg->pPvecs,fcg->mmax+1,&fcg->pCvecs,fcg->mmax+2,&fcg->chunksizes);
     62:   PetscLogObjectMemory((PetscObject)ksp,2*(fcg->mmax+1)*sizeof(Vec*) + 2*(fcg->mmax + 1)*sizeof(Vec**) + (fcg->mmax + 2)*sizeof(PetscInt));

     64:   /* If the requested number of preallocated vectors is greater than mmax reduce nprealloc */
     65:   if(fcg->nprealloc > fcg->mmax+1){
     66:     PetscInfo2(NULL,"Requested nprealloc=%d is greater than m_max+1=%d. Resetting nprealloc = m_max+1.\n",fcg->nprealloc, fcg->mmax+1);
     67:   }

     69:   /* Preallocate additional work vectors */
     70:   KSPAllocateVectors_FCG(ksp,fcg->nprealloc,fcg->nprealloc);
     71:   /*
     72:   If user requested computations of eigenvalues then allocate work
     73:   work space needed
     74:   */
     75:   if (ksp->calc_sings) {
     76:     /* get space to store tridiagonal matrix for Lanczos */
     77:     PetscMalloc4(maxit,&fcg->e,maxit,&fcg->d,maxit,&fcg->ee,maxit,&fcg->dd);
     78:     PetscLogObjectMemory((PetscObject)ksp,2*(maxit+1)*(sizeof(PetscScalar)+sizeof(PetscReal)));

     80:     ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_CG;
     81:     ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_CG;
     82:   }
     83:   return(0);
     84: }

     88: PetscErrorCode KSPSolve_FCG(KSP ksp)
     89: {
     91:   PetscInt       i,k,idx,mi;
     92:   KSP_FCG        *fcg = (KSP_FCG*)ksp->data;
     93:   PetscScalar    alpha=0.0,beta = 0.0,dpi,s;
     94:   PetscReal      dp=0.0;
     95:   Vec            B,R,Z,X,Pcurr,Ccurr;
     96:   Mat            Amat,Pmat;
     97:   PetscInt       eigs = ksp->calc_sings; /* Variables for eigen estimation - START*/
     98:   PetscInt       stored_max_it = ksp->max_it;
     99:   PetscScalar    alphaold = 0,betaold = 1.0,*e = 0,*d = 0;/* Variables for eigen estimation  - FINISH */

    103: #define VecXDot(x,y,a) (((fcg->type) == (KSP_CG_HERMITIAN)) ? VecDot(x,y,a) : VecTDot(x,y,a))
    104: #define VecXMDot(a,b,c,d) (((fcg->type) == (KSP_CG_HERMITIAN)) ? VecMDot(a,b,c,d) : VecMTDot(a,b,c,d))

    106:   X             = ksp->vec_sol;
    107:   B             = ksp->vec_rhs;
    108:   R             = ksp->work[0];
    109:   Z             = ksp->work[1];

    111:   PCGetOperators(ksp->pc,&Amat,&Pmat);
    112:   if (eigs) {e = fcg->e; d = fcg->d; e[0] = 0.0; }
    113:   /* Compute initial residual needed for convergence check*/
    114:   ksp->its = 0;
    115:   if (!ksp->guess_zero) {
    116:     KSP_MatMult(ksp,Amat,X,R);
    117:     VecAYPX(R,-1.0,B);                    /*   r <- b - Ax     */
    118:   } else {
    119:     VecCopy(B,R);                         /*   r <- b (x is 0) */
    120:   }
    121:   switch (ksp->normtype) {
    122:     case KSP_NORM_PRECONDITIONED:
    123:       KSP_PCApply(ksp,R,Z);               /*   z <- Br         */
    124:       VecNorm(Z,NORM_2,&dp);              /*   dp <- dqrt(z'*z) = sqrt(e'*A'*B'*B*A*e)     */
    125:       break;
    126:     case KSP_NORM_UNPRECONDITIONED:
    127:       VecNorm(R,NORM_2,&dp);              /*   dp <- sqrt(r'*r) = sqrt(e'*A'*A*e)     */
    128:       break;
    129:     case KSP_NORM_NATURAL:
    130:       KSP_PCApply(ksp,R,Z);               /*   z <- Br         */
    131:       VecXDot(R,Z,&s);
    132:       dp = PetscSqrtReal(PetscAbsScalar(s));                   /*   dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e)  */
    133:       break;
    134:     case KSP_NORM_NONE:
    135:       dp = 0.0;
    136:       break;
    137:     default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
    138:   }

    140:   /* Initial Convergence Check */
    141:   KSPLogResidualHistory(ksp,dp);
    142:   KSPMonitor(ksp,0,dp);
    143:   ksp->rnorm = dp;
    144:   if (ksp->normtype == KSP_NORM_NONE) {
    145:     KSPConvergedSkip(ksp,0,dp,&ksp->reason,ksp->cnvP);
    146:   } else {
    147:     (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
    148:   }
    149:   if (ksp->reason) return(0);

    151:   /* Apply PC if not already done for convergence check */
    152:   if(ksp->normtype == KSP_NORM_UNPRECONDITIONED || ksp->normtype == KSP_NORM_NONE){
    153:     KSP_PCApply(ksp,R,Z);               /*   z <- Br         */
    154:   }

    156:   i = 0;
    157:   do {
    158:     ksp->its = i+1;

    160:     /*  If needbe, allocate a new chunk of vectors in P and C */
    161:     KSPAllocateVectors_FCG(ksp,i+1,fcg->vecb);

    163:     /* Note that we wrap around and start clobbering old vectors */
    164:     idx = i % (fcg->mmax+1);
    165:     Pcurr = fcg->Pvecs[idx];
    166:     Ccurr = fcg->Cvecs[idx];

    168:     /* number of old directions to orthogonalize against */
    169:     switch(fcg->truncstrat){
    170:       case KSP_FCD_TRUNC_TYPE_STANDARD:
    171:         mi = fcg->mmax;
    172:         break;
    173:       case KSP_FCD_TRUNC_TYPE_NOTAY:
    174:         mi = ((i-1) % fcg->mmax)+1;
    175:         break;
    176:       default:
    177:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Unrecognized Truncation Strategy");
    178:     }

    180:     /* Compute a new column of P (Currently does not support modified G-S or iterative refinement)*/
    181:     VecCopy(Z,Pcurr);

    183:     {
    184:       PetscInt l,ndots;

    186:       l = PetscMax(0,i-mi);
    187:       ndots = i-l;
    188:       if (ndots){
    189:         PetscInt    j;
    190:         Vec         *Pold,  *Cold;
    191:         PetscScalar *dots;

    193:         PetscMalloc3(ndots,&dots,ndots,&Cold,ndots,&Pold);
    194:         for(k=l,j=0;j<ndots;++k,++j){
    195:           idx = k % (fcg->mmax+1);
    196:           Cold[j] = fcg->Cvecs[idx];
    197:           Pold[j] = fcg->Pvecs[idx];
    198:         }
    199:         VecXMDot(Z,ndots,Cold,dots);
    200:         for(k=0;k<ndots;++k){
    201:           dots[k] = -dots[k];
    202:         }
    203:         VecMAXPY(Pcurr,ndots,dots,Pold);
    204:         PetscFree3(dots,Cold,Pold);
    205:       }
    206:     }

    208:     /* Update X and R */
    209:     betaold = beta;
    210:     VecXDot(Pcurr,R,&beta);                 /*  beta <- pi'*r       */
    211:     KSP_MatMult(ksp,Amat,Pcurr,Ccurr);      /*  w <- A*pi (stored in ci)   */
    212:     VecXDot(Pcurr,Ccurr,&dpi);              /*  dpi <- pi'*w        */
    213:     alphaold = alpha;
    214:     alpha = beta / dpi;                                          /*  alpha <- beta/dpi    */
    215:     VecAXPY(X,alpha,Pcurr);                 /*  x <- x + alpha * pi  */
    216:     VecAXPY(R,-alpha,Ccurr);                /*  r <- r - alpha * wi  */

    218:     /* Compute norm for convergence check */
    219:     switch (ksp->normtype) {
    220:       case KSP_NORM_PRECONDITIONED:
    221:         KSP_PCApply(ksp,R,Z);               /*   z <- Br             */
    222:         VecNorm(Z,NORM_2,&dp);              /*   dp <- sqrt(z'*z) = sqrt(e'*A'*B'*B*A*e)  */
    223:         break;
    224:       case KSP_NORM_UNPRECONDITIONED:
    225:         VecNorm(R,NORM_2,&dp);              /*   dp <- sqrt(r'*r) = sqrt(e'*A'*A*e)   */
    226:         break;
    227:       case KSP_NORM_NATURAL:
    228:         KSP_PCApply(ksp,R,Z);               /*   z <- Br             */
    229:         VecXDot(R,Z,&s);
    230:         dp = PetscSqrtReal(PetscAbsScalar(s));                   /*   dp <- sqrt(r'*z) = sqrt(e'*A'*B*A*e)  */
    231:         break;
    232:       case KSP_NORM_NONE:
    233:         dp = 0.0;
    234:         break;
    235:       default: SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"%s",KSPNormTypes[ksp->normtype]);
    236:     }

    238:     /* Check for convergence */
    239:     ksp->rnorm = dp;
    240:     KSPLogResidualHistory(ksp,dp);
    241:     KSPMonitor(ksp,i+1,dp);
    242:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    243:     if (ksp->reason) break;

    245:     /* Apply PC if not already done for convergence check */
    246:     if(ksp->normtype == KSP_NORM_UNPRECONDITIONED || ksp->normtype == KSP_NORM_NONE){
    247:       KSP_PCApply(ksp,R,Z);               /*   z <- Br         */
    248:     }

    250:     /* Compute current C (which is W/dpi) */
    251:     VecScale(Ccurr,1.0/dpi);              /*   w <- ci/dpi   */

    253:     if (eigs) {
    254:       if (i > 0) {
    255:         if (ksp->max_it != stored_max_it) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Can not change maxit AND calculate eigenvalues");
    256:         e[i] = PetscSqrtReal(PetscAbsScalar(beta/betaold))/alphaold;
    257:         d[i] = PetscSqrtReal(PetscAbsScalar(beta/betaold))*e[i] + 1.0/alpha;
    258:       } else {
    259:         d[i] = PetscSqrtReal(PetscAbsScalar(beta))*e[i] + 1.0/alpha;
    260:       }
    261:       fcg->ned = ksp->its-1;
    262:     }
    263:     ++i;
    264:   } while (i<ksp->max_it);
    265:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    266:   return(0);
    267: }

    271: PetscErrorCode KSPDestroy_FCG(KSP ksp)
    272: {
    274:   PetscInt       i;
    275:   KSP_FCG        *fcg = (KSP_FCG*)ksp->data;

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

    282:   /* Destroy P and C vectors and the arrays that manage pointers to them */
    283:   if (fcg->nvecs){
    284:     for (i=0;i<fcg->nchunks;++i){
    285:       VecDestroyVecs(fcg->chunksizes[i],&fcg->pPvecs[i]);
    286:       VecDestroyVecs(fcg->chunksizes[i],&fcg->pCvecs[i]);
    287:     }
    288:   }
    289:   PetscFree5(fcg->Pvecs,fcg->Cvecs,fcg->pPvecs,fcg->pCvecs,fcg->chunksizes);
    290:   /* free space used for singular value calculations */
    291:   if (ksp->calc_sings) {
    292:     PetscFree4(fcg->e,fcg->d,fcg->ee,fcg->dd);
    293:   }
    294:   KSPDestroyDefault(ksp);
    295:   return(0);
    296: }

    300: PetscErrorCode KSPView_FCG(KSP ksp,PetscViewer viewer)
    301: {
    302:   KSP_FCG        *fcg = (KSP_FCG*)ksp->data;
    304:   PetscBool      iascii,isstring;
    305:   const char     *truncstr;

    308:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    309:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);

    311:   if (fcg->truncstrat == KSP_FCD_TRUNC_TYPE_STANDARD) truncstr = "Using standard truncation strategy";
    312:   else if (fcg->truncstrat == KSP_FCD_TRUNC_TYPE_NOTAY) truncstr = "Using Notay's truncation strategy";
    313:   else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Undefined FCG truncation strategy");

    315:   if (iascii) {
    316:     PetscViewerASCIIPrintf(viewer,"  FCG: m_max=%D\n",fcg->mmax);
    317:     PetscViewerASCIIPrintf(viewer,"  FCG: preallocated %D directions\n",PetscMin(fcg->nprealloc,fcg->mmax+1));
    318:     PetscViewerASCIIPrintf(viewer,"  FCG: %s\n",truncstr);
    319:   } else if (isstring) {
    320:     PetscViewerStringSPrintf(viewer,"m_max %D nprealloc %D %s",fcg->mmax,fcg->nprealloc,truncstr);
    321:   }
    322:   return(0);
    323: }

    327: /*@
    328:   KSPFCGSetMmax - set the maximum number of previous directions FCG will store for orthogonalization

    330:   Note: mmax + 1 directions are stored (mmax previous ones along with a current one)
    331:   and whether all are used in each iteration also depends on the truncation strategy
    332:   (see KSPFCGSetTruncationType())

    334:   Logically Collective on KSP

    336:   Input Parameters:
    337: +  ksp - the Krylov space context
    338: -  mmax - the maximum number of previous directions to orthogonalize againt

    340:   Level: intermediate

    342:   Options Database:
    343: . -ksp_fcg_mmax <N>

    345: .seealso: KSPFCG, KSPFCGGetTruncationType(), KSPFCGGetNprealloc()
    346: @*/
    347: PetscErrorCode KSPFCGSetMmax(KSP ksp,PetscInt mmax)
    348: {
    349:   KSP_FCG *fcg = (KSP_FCG*)ksp->data;

    354:   fcg->mmax = mmax;
    355:   return(0);
    356: }

    360: /*@
    361:   KSPFCGGetMmax - get the maximum number of previous directions FCG will store

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

    365:    Not Collective

    367:    Input Parameter:
    368: .  ksp - the Krylov space context

    370:    Output Parameter:
    371: .  mmax - the maximum number of previous directons allowed for orthogonalization

    373:   Options Database:
    374: . -ksp_fcg_mmax <N>

    376:    Level: intermediate

    378: .keywords: KSP, FCG, truncation

    380: .seealso: KSPFCG, KSPFCGGetTruncationType(), KSPFCGGetNprealloc(), KSPFCGSetMmax()
    381: @*/

    383: PetscErrorCode KSPFCGGetMmax(KSP ksp,PetscInt *mmax)
    384: {
    385:   KSP_FCG *fcg=(KSP_FCG*)ksp->data;

    389:   *mmax = fcg->mmax;
    390:   return(0);
    391: }

    395: /*@
    396:   KSPFCGSetNprealloc - set the number of directions to preallocate with FCG

    398:   Logically Collective on KSP

    400:   Input Parameters:
    401: +  ksp - the Krylov space context
    402: -  nprealloc - the number of vectors to preallocate

    404:   Level: advanced

    406:   Options Database:
    407: . -ksp_fcg_nprealloc <N> - number of directions to preallocate

    409: .seealso: KSPFCG, KSPFCGGetTruncationType(), KSPFCGGetNprealloc()
    410: @*/
    411: PetscErrorCode KSPFCGSetNprealloc(KSP ksp,PetscInt nprealloc)
    412: {
    413:   KSP_FCG *fcg=(KSP_FCG*)ksp->data;

    418:   if(nprealloc > fcg->mmax+1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Cannot preallocate more than m_max+1 vectors");
    419:   fcg->nprealloc = nprealloc;
    420:   return(0);
    421: }

    425: /*@
    426:   KSPFCGGetNprealloc - get the number of directions preallocate by FCG

    428:    Not Collective

    430:    Input Parameter:
    431: .  ksp - the Krylov space context

    433:    Output Parameter:
    434: .  nprealloc - the number of directions preallocated

    436:    Level: advanced

    438: .keywords: KSP, FCG, truncation

    440: .seealso: KSPFCG, KSPFCGGetTruncationType(), KSPFCGSetNprealloc()
    441: @*/
    442: PetscErrorCode KSPFCGGetNprealloc(KSP ksp,PetscInt *nprealloc)
    443: {
    444:   KSP_FCG *fcg=(KSP_FCG*)ksp->data;

    448:   *nprealloc = fcg->nprealloc;
    449:   return(0);
    450: }

    454: /*@
    455:   KSPFCGSetTruncationType - specify how many of its stored previous directions FCG uses during orthoganalization

    457:   Logically Collective on KSP

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

    462:   Input Parameters:
    463: +  ksp - the Krylov space context
    464: -  truncstrat - the choice of strategy

    466:   Level: intermediate

    468:   Options Database:
    469: . -ksp_fcg_truncation_type <standard, notay> - specify how many of its stored previous directions FCG uses during orthoganalization

    471:   .seealso: KSPFCDTruncationType, KSPFCGGetTruncationType
    472: @*/
    473: PetscErrorCode KSPFCGSetTruncationType(KSP ksp,KSPFCDTruncationType truncstrat)
    474: {
    475:   KSP_FCG *fcg=(KSP_FCG*)ksp->data;

    480:   fcg->truncstrat=truncstrat;
    481:   return(0);
    482: }

    486: /*@
    487:   KSPFCGGetTruncationType - get the truncation strategy employed by FCG

    489:    Not Collective

    491:    Input Parameter:
    492: .  ksp - the Krylov space context

    494:    Output Parameter:
    495: .  truncstrat - the strategy type

    497:    Level: intermediate

    499: .keywords: KSP, FCG, truncation

    501: .seealso: KSPFCG, KSPFCGSetTruncationType, KSPFCDTruncationType
    502: @*/
    503: PetscErrorCode KSPFCGGetTruncationType(KSP ksp,KSPFCDTruncationType *truncstrat)
    504: {
    505:   KSP_FCG *fcg=(KSP_FCG*)ksp->data;

    509:   *truncstrat=fcg->truncstrat;
    510:   return(0);
    511: }

    515: PetscErrorCode KSPSetFromOptions_FCG(PetscOptionItems *PetscOptionsObject,KSP ksp)
    516: {
    518:   KSP_FCG        *fcg=(KSP_FCG*)ksp->data;
    519:   PetscInt       mmax,nprealloc;
    520:   PetscBool      flg;

    523:   PetscOptionsHead(PetscOptionsObject,"KSP FCG Options");
    524:   PetscOptionsInt("-ksp_fcg_mmax","Maximum number of search directions to store","KSPFCGSetMmax",fcg->mmax,&mmax,&flg);
    525:   if (flg) {
    526:     KSPFCGSetMmax(ksp,mmax);
    527:   }
    528:   PetscOptionsInt("-ksp_fcg_nprealloc","Number of directions to preallocate","KSPFCGSetNprealloc",fcg->nprealloc,&nprealloc,&flg);
    529:   if (flg) {
    530:     KSPFCGSetNprealloc(ksp,nprealloc);
    531:   }
    532:   PetscOptionsEnum("-ksp_fcg_truncation_type","Truncation approach for directions","KSPFCGSetTruncationType",KSPFCDTruncationTypes,(PetscEnum)fcg->truncstrat,(PetscEnum*)&fcg->truncstrat,NULL);
    533:   PetscOptionsTail();
    534:   return(0);
    535: }

    537: /*MC
    538:       KSPFCG - Implements the Flexible Conjugate Gradient method (FCG)

    540:   Options Database Keys:
    541: +   -ksp_fcg_mmax <N>  - maximum number of search directions
    542: .   -ksp_fcg_nprealloc <N> - number of directions to preallocate
    543: -   -ksp_fcg_truncation_type <standard,notay> - truncation approach for directions

    545:     Contributed by Patrick Sanan

    547:    Notes:
    548:    Supports left preconditioning only.

    550:    Level: beginner

    552:   References:
    553: +    1. - Notay, Y."Flexible Conjugate Gradients", SIAM J. Sci. Comput. 22:4, 2000
    554: -    2. - Axelsson, O. and Vassilevski, P. S. "A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable step Preconditioning",
    555:     SIAM J. Matrix Anal. Appl. 12:4, 1991

    557:  .seealso : KSPGCR, KSPFGMRES, KSPCG, KSPFCGSetMmax(), KSPFCGGetMmax(), KSPFCGSetNprealloc(), KSPFCGGetNprealloc(), KSPFCGSetTruncationType(), KSPFCGGetTruncationType()

    559: M*/
    562: PETSC_EXTERN PetscErrorCode KSPCreate_FCG(KSP ksp)
    563: {
    565:   KSP_FCG        *fcg;

    568:   PetscNewLog(ksp,&fcg);
    569: #if !defined(PETSC_USE_COMPLEX)
    570:   fcg->type       = KSP_CG_SYMMETRIC;
    571: #else
    572:   fcg->type       = KSP_CG_HERMITIAN;
    573: #endif
    574:   fcg->mmax       = KSPFCG_DEFAULT_MMAX;
    575:   fcg->nprealloc  = KSPFCG_DEFAULT_NPREALLOC;
    576:   fcg->nvecs      = 0;
    577:   fcg->vecb       = KSPFCG_DEFAULT_VECB;
    578:   fcg->nchunks    = 0;
    579:   fcg->truncstrat = KSPFCG_DEFAULT_TRUNCSTRAT;

    581:   ksp->data = (void*)fcg;

    583:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,2);
    584:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_LEFT,1);
    585:   KSPSetSupportedNorm(ksp,KSP_NORM_NATURAL,PC_LEFT,1);

    587:   ksp->ops->setup          = KSPSetUp_FCG;
    588:   ksp->ops->solve          = KSPSolve_FCG;
    589:   ksp->ops->destroy        = KSPDestroy_FCG;
    590:   ksp->ops->view           = KSPView_FCG;
    591:   ksp->ops->setfromoptions = KSPSetFromOptions_FCG;
    592:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    593:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    594:   return(0);
    595: }