Actual source code: lgmres.c
petsc-3.7.1 2016-05-15
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      2: #include <../src/ksp/ksp/impls/gmres/lgmres/lgmresimpl.h>   /*I petscksp.h I*/

      4: #define LGMRES_DELTA_DIRECTIONS 10
      5: #define LGMRES_DEFAULT_MAXK     30
      6: #define LGMRES_DEFAULT_AUGDIM   2 /*default number of augmentation vectors */
      7: static PetscErrorCode    KSPLGMRESGetNewVectors(KSP,PetscInt);
      8: static PetscErrorCode    KSPLGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
      9: static PetscErrorCode    KSPLGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

     13: PetscErrorCode  KSPLGMRESSetAugDim(KSP ksp, PetscInt dim)
     14: {

     18:   PetscTryMethod((ksp),"KSPLGMRESSetAugDim_C",(KSP,PetscInt),(ksp,dim));
     19:   return(0);
     20: }

     24: PetscErrorCode  KSPLGMRESSetConstant(KSP ksp)
     25: {

     29:   PetscTryMethod((ksp),"KSPLGMRESSetConstant_C",(KSP),(ksp));
     30:   return(0);
     31: }

     33: /*
     34:     KSPSetUp_LGMRES - Sets up the workspace needed by lgmres.

     36:     This is called once, usually automatically by KSPSolve() or KSPSetUp(),
     37:     but can be called directly by KSPSetUp().

     39: */
     42: PetscErrorCode    KSPSetUp_LGMRES(KSP ksp)
     43: {
     45:   PetscInt       max_k,k, aug_dim;
     46:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;

     49:   max_k   = lgmres->max_k;
     50:   aug_dim = lgmres->aug_dim;
     51:   KSPSetUp_GMRES(ksp);

     53:   /* need array of pointers to augvecs*/
     54:   PetscMalloc1(2*aug_dim + AUG_OFFSET,&lgmres->augvecs);

     56:   lgmres->aug_vecs_allocated = 2 *aug_dim + AUG_OFFSET;

     58:   PetscMalloc1(2*aug_dim + AUG_OFFSET,&lgmres->augvecs_user_work);
     59:   PetscMalloc1(aug_dim,&lgmres->aug_order);
     60:   PetscLogObjectMemory((PetscObject)ksp,(aug_dim)*(4*sizeof(void*) + sizeof(PetscInt)) + AUG_OFFSET*2*sizeof(void*));

     62:   /*  for now we will preallocate the augvecs - because aug_dim << restart
     63:      ... also keep in mind that we need to keep augvecs from cycle to cycle*/
     64:   lgmres->aug_vv_allocated = 2* aug_dim + AUG_OFFSET;
     65:   lgmres->augwork_alloc    =  2* aug_dim + AUG_OFFSET;

     67:   KSPCreateVecs(ksp,lgmres->aug_vv_allocated,&lgmres->augvecs_user_work[0],0,NULL);
     68:   PetscMalloc1(max_k+1,&lgmres->hwork);
     69:   PetscLogObjectParents(ksp,lgmres->aug_vv_allocated,lgmres->augvecs_user_work[0]);
     70:   for (k=0; k<lgmres->aug_vv_allocated; k++) {
     71:     lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
     72:   }
     73:   return(0);
     74: }

     77: /*

     79:     KSPLGMRESCycle - Run lgmres, possibly with restart.  Return residual
     80:                   history if requested.

     82:     input parameters:
     83: .        lgmres  - structure containing parameters and work areas

     85:     output parameters:
     86: .        nres    - residuals (from preconditioned system) at each step.
     87:                   If restarting, consider passing nres+it.  If null,
     88:                   ignored
     89: .        itcount - number of iterations used.   nres[0] to nres[itcount]
     90:                   are defined.  If null, ignored.  If null, ignored.
     91: .        converged - 0 if not converged

     94:     Notes:
     95:     On entry, the value in vector VEC_VV(0) should be
     96:     the initial residual.

     99:  */
    102: PetscErrorCode KSPLGMRESCycle(PetscInt *itcount,KSP ksp)
    103: {
    104:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)(ksp->data);
    105:   PetscReal      res_norm, res;
    106:   PetscReal      hapbnd, tt;
    107:   PetscScalar    tmp;
    108:   PetscBool      hapend = PETSC_FALSE;  /* indicates happy breakdown ending */
    110:   PetscInt       loc_it;                /* local count of # of dir. in Krylov space */
    111:   PetscInt       max_k  = lgmres->max_k; /* max approx space size */
    112:   PetscInt       max_it = ksp->max_it;  /* max # of overall iterations for the method */

    114:   /* LGMRES_MOD - new variables*/
    115:   PetscInt    aug_dim = lgmres->aug_dim;
    116:   PetscInt    spot    = 0;
    117:   PetscInt    order   = 0;
    118:   PetscInt    it_arnoldi;                /* number of arnoldi steps to take */
    119:   PetscInt    it_total;                  /* total number of its to take (=approx space size)*/
    120:   PetscInt    ii, jj;
    121:   PetscReal   tmp_norm;
    122:   PetscScalar inv_tmp_norm;
    123:   PetscScalar *avec;

    126:   /* Number of pseudo iterations since last restart is the number
    127:      of prestart directions */
    128:   loc_it = 0;

    130:   /* LGMRES_MOD: determine number of arnoldi steps to take */
    131:   /* if approx_constant then we keep the space the same size even if
    132:      we don't have the full number of aug vectors yet*/
    133:   if (lgmres->approx_constant) it_arnoldi = max_k - lgmres->aug_ct;
    134:   else it_arnoldi = max_k - aug_dim;

    136:   it_total =  it_arnoldi + lgmres->aug_ct;

    138:   /* initial residual is in VEC_VV(0)  - compute its norm*/
    139:   VecNorm(VEC_VV(0),NORM_2,&res_norm);
    140:   KSPCheckNorm(ksp,res_norm);
    141:   res  = res_norm;

    143:   /* first entry in right-hand-side of hessenberg system is just
    144:      the initial residual norm */
    145:   *GRS(0) = res_norm;

    147:   /* check for the convergence */
    148:   if (!res) {
    149:     if (itcount) *itcount = 0;
    150:     ksp->reason = KSP_CONVERGED_ATOL;
    151:     PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
    152:     return(0);
    153:   }

    155:   /* scale VEC_VV (the initial residual) */
    156:   tmp = 1.0/res_norm; VecScale(VEC_VV(0),tmp);

    158:   ksp->rnorm = res;

    161:   /* note: (lgmres->it) is always set one less than (loc_it) It is used in
    162:      KSPBUILDSolution_LGMRES, where it is passed to KSPLGMRESBuildSoln.
    163:      Note that when KSPLGMRESBuildSoln is called from this function,
    164:      (loc_it -1) is passed, so the two are equivalent */
    165:   lgmres->it = (loc_it - 1);

    168:   /* MAIN ITERATION LOOP BEGINNING*/

    171:   /* keep iterating until we have converged OR generated the max number
    172:      of directions OR reached the max number of iterations for the method */
    173:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);

    175:   while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
    176:     KSPLogResidualHistory(ksp,res);
    177:     lgmres->it = (loc_it - 1);
    178:     KSPMonitor(ksp,ksp->its,res);

    180:     /* see if more space is needed for work vectors */
    181:     if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
    182:       KSPLGMRESGetNewVectors(ksp,loc_it+1);
    183:       /* (loc_it+1) is passed in as number of the first vector that should
    184:           be allocated */
    185:     }

    187:     /*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
    188:     if (loc_it < it_arnoldi) { /* Arnoldi */
    189:       KSP_PCApplyBAorAB(ksp,VEC_VV(loc_it),VEC_VV(1+loc_it),VEC_TEMP_MATOP);
    190:     } else { /*aug step */
    191:       order = loc_it - it_arnoldi + 1; /* which aug step */
    192:       for (ii=0; ii<aug_dim; ii++) {
    193:         if (lgmres->aug_order[ii] == order) {
    194:           spot = ii;
    195:           break; /* must have this because there will be duplicates before aug_ct = aug_dim */
    196:         }
    197:       }

    199:       VecCopy(A_AUGVEC(spot), VEC_VV(1+loc_it));
    200:       /*note: an alternate implementation choice would be to only save the AUGVECS and
    201:         not A_AUGVEC and then apply the PC here to the augvec */
    202:     }

    204:     /* update hessenberg matrix and do Gram-Schmidt - new direction is in
    205:        VEC_VV(1+loc_it)*/
    206:     (*lgmres->orthog)(ksp,loc_it);

    208:     /* new entry in hessenburg is the 2-norm of our new direction */
    209:     VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);

    211:     *HH(loc_it+1,loc_it)  = tt;
    212:     *HES(loc_it+1,loc_it) = tt;

    215:     /* check for the happy breakdown */
    216:     hapbnd = PetscAbsScalar(tt / *GRS(loc_it)); /* GRS(loc_it) contains the res_norm from the last iteration  */
    217:     if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
    218:     if (tt > hapbnd) {
    219:       tmp  = 1.0/tt;
    220:       VecScale(VEC_VV(loc_it+1),tmp); /* scale new direction by its norm */
    221:     } else {
    222:       PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %g tt = %g\n",(double)hapbnd,(double)tt);
    223:       hapend = PETSC_TRUE;
    224:     }

    226:     /* Now apply rotations to new col of hessenberg (and right side of system),
    227:        calculate new rotation, and get new residual norm at the same time*/
    228:     KSPLGMRESUpdateHessenberg(ksp,loc_it,hapend,&res);
    229:     if (ksp->reason) break;

    231:     loc_it++;
    232:     lgmres->it = (loc_it-1);   /* Add this here in case it has converged */

    234:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
    235:     ksp->its++;
    236:     ksp->rnorm = res;
    237:     PetscObjectSAWsGrantAccess((PetscObject)ksp);

    239:     (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);

    241:     /* Catch error in happy breakdown and signal convergence and break from loop */
    242:     if (hapend) {
    243:       if (!ksp->reason) {
    244:         if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %g",(double)res);
    245:         else {
    246:           ksp->reason = KSP_DIVERGED_BREAKDOWN;
    247:           break;
    248:         }
    249:       }
    250:     }
    251:   }
    252:   /* END OF ITERATION LOOP */
    253:   KSPLogResidualHistory(ksp,res);

    255:   /* Monitor if we know that we will not return for a restart */
    256:   if (ksp->reason || ksp->its >= max_it) {
    257:     KSPMonitor(ksp, ksp->its, res);
    258:   }

    260:   if (itcount) *itcount = loc_it;

    262:   /*
    263:     Down here we have to solve for the "best" coefficients of the Krylov
    264:     columns, add the solution values together, and possibly unwind the
    265:     preconditioning from the solution
    266:    */

    268:   /* Form the solution (or the solution so far) */
    269:   /* Note: must pass in (loc_it-1) for iteration count so that KSPLGMRESBuildSoln
    270:      properly navigates */

    272:   KSPLGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);

    275:   /* LGMRES_MOD collect aug vector and A*augvector for future restarts -
    276:      only if we will be restarting (i.e. this cycle performed it_total
    277:      iterations)  */
    278:   if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {

    280:     /*AUG_TEMP contains the new augmentation vector (assigned in  KSPLGMRESBuildSoln) */
    281:     if (!lgmres->aug_ct) {
    282:       spot = 0;
    283:       lgmres->aug_ct++;
    284:     } else if (lgmres->aug_ct < aug_dim) {
    285:       spot = lgmres->aug_ct;
    286:       lgmres->aug_ct++;
    287:     } else { /* truncate */
    288:       for (ii=0; ii<aug_dim; ii++) {
    289:         if (lgmres->aug_order[ii] == aug_dim) spot = ii;
    290:       }
    291:     }

    295:     VecCopy(AUG_TEMP, AUGVEC(spot));
    296:     /*need to normalize */
    297:     VecNorm(AUGVEC(spot), NORM_2, &tmp_norm);

    299:     inv_tmp_norm = 1.0/tmp_norm;

    301:     VecScale(AUGVEC(spot),inv_tmp_norm);

    303:     /*set new aug vector to order 1  - move all others back one */
    304:     for (ii=0; ii < aug_dim; ii++) AUG_ORDER(ii)++;
    305:     AUG_ORDER(spot) = 1;

    307:     /*now add the A*aug vector to A_AUGVEC(spot)  - this is independ. of preconditioning type*/
    308:     /* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */

    311:     /* first do H+*y */
    312:     avec = lgmres->hwork;
    313:     PetscMemzero(avec,(it_total+1)*sizeof(*avec));
    314:     for (ii=0; ii < it_total + 1; ii++) {
    315:       for (jj=0; jj <= ii+1 && jj < it_total+1; jj++) {
    316:         avec[jj] += *HES(jj ,ii) * *GRS(ii);
    317:       }
    318:     }

    320:     /*now multiply result by V+ */
    321:     VecSet(VEC_TEMP,0.0);
    322:     VecMAXPY(VEC_TEMP, it_total+1, avec, &VEC_VV(0)); /*answer is in VEC_TEMP*/

    324:     /*copy answer to aug location  and scale*/
    325:     VecCopy(VEC_TEMP,  A_AUGVEC(spot));
    326:     VecScale(A_AUGVEC(spot),inv_tmp_norm);
    327:   }
    328:   return(0);
    329: }

    331: /*
    332:     KSPSolve_LGMRES - This routine applies the LGMRES method.

    335:    Input Parameter:
    336: .     ksp - the Krylov space object that was set to use lgmres

    338:    Output Parameter:
    339: .     outits - number of iterations used

    341: */

    345: PetscErrorCode KSPSolve_LGMRES(KSP ksp)
    346: {
    348:   PetscInt       cycle_its; /* iterations done in a call to KSPLGMRESCycle */
    349:   PetscInt       itcount;   /* running total of iterations, incl. those in restarts */
    350:   KSP_LGMRES     *lgmres    = (KSP_LGMRES*)ksp->data;
    351:   PetscBool      guess_zero = ksp->guess_zero;
    352:   PetscInt       ii;        /*LGMRES_MOD variable */

    355:   if (ksp->calc_sings && !lgmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");

    357:   PetscObjectSAWsTakeAccess((PetscObject)ksp);

    359:   ksp->its        = 0;
    360:   lgmres->aug_ct  = 0;
    361:   lgmres->matvecs = 0;

    363:   PetscObjectSAWsGrantAccess((PetscObject)ksp);

    365:   /* initialize */
    366:   itcount     = 0;
    367:   ksp->reason = KSP_CONVERGED_ITERATING;
    368:   /*LGMRES_MOD*/
    369:   for (ii=0; ii<lgmres->aug_dim; ii++) lgmres->aug_order[ii] = 0;

    371:   while (!ksp->reason) {
    372:     /* calc residual - puts in VEC_VV(0) */
    373:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
    374:     KSPLGMRESCycle(&cycle_its,ksp);
    375:     itcount += cycle_its;
    376:     if (itcount >= ksp->max_it) {
    377:       if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    378:       break;
    379:     }
    380:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
    381:   }
    382:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
    383:   return(0);
    384: }

    386: /*

    388:    KSPDestroy_LGMRES - Frees all memory space used by the Krylov method.

    390: */
    393: PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
    394: {
    395:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;

    399:   PetscFree(lgmres->augvecs);
    400:   if (lgmres->augwork_alloc) {
    401:     VecDestroyVecs(lgmres->augwork_alloc,&lgmres->augvecs_user_work[0]);
    402:   }
    403:   PetscFree(lgmres->augvecs_user_work);
    404:   PetscFree(lgmres->aug_order);
    405:   PetscFree(lgmres->hwork);
    406:   KSPDestroy_GMRES(ksp);
    407:   return(0);
    408: }

    410: /*
    411:     KSPLGMRESBuildSoln - create the solution from the starting vector and the
    412:                       current iterates.

    414:     Input parameters:
    415:         nrs - work area of size it + 1.
    416:         vguess  - index of initial guess
    417:         vdest - index of result.  Note that vguess may == vdest (replace
    418:                 guess with the solution).
    419:         it - HH upper triangular part is a block of size (it+1) x (it+1)

    421:      This is an internal routine that knows about the LGMRES internals.
    422:  */
    425: static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
    426: {
    427:   PetscScalar    tt;
    429:   PetscInt       ii,k,j;
    430:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)(ksp->data);
    431:   /*LGMRES_MOD */
    432:   PetscInt it_arnoldi, it_aug;
    433:   PetscInt jj, spot = 0;

    436:   /* Solve for solution vector that minimizes the residual */

    438:   /* If it is < 0, no lgmres steps have been performed */
    439:   if (it < 0) {
    440:     VecCopy(vguess,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
    441:     return(0);
    442:   }

    444:   /* so (it+1) lgmres steps HAVE been performed */

    446:   /* LGMRES_MOD - determine if we need to use augvecs for the soln  - do not assume that
    447:      this is called after the total its allowed for an approx space */
    448:   if (lgmres->approx_constant) {
    449:     it_arnoldi = lgmres->max_k - lgmres->aug_ct;
    450:   } else {
    451:     it_arnoldi = lgmres->max_k - lgmres->aug_dim;
    452:   }
    453:   if (it_arnoldi >= it +1) {
    454:     it_aug     = 0;
    455:     it_arnoldi = it+1;
    456:   } else {
    457:     it_aug = (it + 1) - it_arnoldi;
    458:   }

    460:   /* now it_arnoldi indicates the number of matvecs that took place */
    461:   lgmres->matvecs += it_arnoldi;

    464:   /* solve the upper triangular system - GRS is the right side and HH is
    465:      the upper triangular matrix  - put soln in nrs */
    466:   if (*HH(it,it) == 0.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"HH(it,it) is identically zero; it = %D GRS(it) = %g",it,(double)PetscAbsScalar(*GRS(it)));
    467:   if (*HH(it,it) != 0.0) {
    468:     nrs[it] = *GRS(it) / *HH(it,it);
    469:   } else {
    470:     nrs[it] = 0.0;
    471:   }

    473:   for (ii=1; ii<=it; ii++) {
    474:     k  = it - ii;
    475:     tt = *GRS(k);
    476:     for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
    477:     nrs[k] = tt / *HH(k,k);
    478:   }

    480:   /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
    481:   VecSet(VEC_TEMP,0.0); /* set VEC_TEMP components to 0 */

    483:   /*LGMRES_MOD - if augmenting has happened we need to form the solution
    484:     using the augvecs */
    485:   if (!it_aug) { /* all its are from arnoldi */
    486:     VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
    487:   } else { /*use aug vecs */
    488:     /*first do regular krylov directions */
    489:     VecMAXPY(VEC_TEMP,it_arnoldi,nrs,&VEC_VV(0));
    490:     /*now add augmented portions - add contribution of aug vectors one at a time*/

    493:     for (ii=0; ii<it_aug; ii++) {
    494:       for (jj=0; jj<lgmres->aug_dim; jj++) {
    495:         if (lgmres->aug_order[jj] == (ii+1)) {
    496:           spot = jj;
    497:           break; /* must have this because there will be duplicates before aug_ct = aug_dim */
    498:         }
    499:       }
    500:       VecAXPY(VEC_TEMP,nrs[it_arnoldi+ii],AUGVEC(spot));
    501:     }
    502:   }
    503:   /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
    504:      preconditioner is "unwound" from right-precondtioning*/
    505:   VecCopy(VEC_TEMP, AUG_TEMP);

    507:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);

    509:   /* add solution to previous solution */
    510:   /* put updated solution into vdest.*/
    511:   VecCopy(vguess,vdest);
    512:   VecAXPY(vdest,1.0,VEC_TEMP);
    513:   return(0);
    514: }

    516: /*

    518:     KSPLGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
    519:                             Return new residual.

    521:     input parameters:

    523: .        ksp -    Krylov space object
    524: .        it  -    plane rotations are applied to the (it+1)th column of the
    525:                   modified hessenberg (i.e. HH(:,it))
    526: .        hapend - PETSC_FALSE not happy breakdown ending.

    528:     output parameters:
    529: .        res - the new residual

    531:  */
    534: static PetscErrorCode KSPLGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
    535: {
    536:   PetscScalar *hh,*cc,*ss,tt;
    537:   PetscInt    j;
    538:   KSP_LGMRES  *lgmres = (KSP_LGMRES*)(ksp->data);

    541:   hh = HH(0,it);   /* pointer to beginning of column to update - so
    542:                       incrementing hh "steps down" the (it+1)th col of HH*/
    543:   cc = CC(0);      /* beginning of cosine rotations */
    544:   ss = SS(0);      /* beginning of sine rotations */

    546:   /* Apply all the previously computed plane rotations to the new column
    547:      of the Hessenberg matrix */
    548:   /* Note: this uses the rotation [conj(c)  s ; -s   c], c= cos(theta), s= sin(theta) */

    550:   for (j=1; j<=it; j++) {
    551:     tt  = *hh;
    552:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
    553:     hh++;
    554:     *hh = *cc++ * *hh - (*ss++ * tt);
    555:     /* hh, cc, and ss have all been incremented one by end of loop */
    556:   }

    558:   /*
    559:     compute the new plane rotation, and apply it to:
    560:      1) the right-hand-side of the Hessenberg system (GRS)
    561:         note: it affects GRS(it) and GRS(it+1)
    562:      2) the new column of the Hessenberg matrix
    563:         note: it affects HH(it,it) which is currently pointed to
    564:         by hh and HH(it+1, it) (*(hh+1))
    565:     thus obtaining the updated value of the residual...
    566:   */

    568:   /* compute new plane rotation */

    570:   if (!hapend) {
    571:     tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
    572:     if (tt == 0.0) {
    573:       ksp->reason = KSP_DIVERGED_NULL;
    574:       return(0);
    575:     }
    576:     *cc = *hh / tt;         /* new cosine value */
    577:     *ss = *(hh+1) / tt;        /* new sine value */

    579:     /* apply to 1) and 2) */
    580:     *GRS(it+1) = -(*ss * *GRS(it));
    581:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
    582:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);

    584:     /* residual is the last element (it+1) of right-hand side! */
    585:     *res = PetscAbsScalar(*GRS(it+1));

    587:   } else { /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
    588:             another rotation matrix (so RH doesn't change).  The new residual is
    589:             always the new sine term times the residual from last time (GRS(it)),
    590:             but now the new sine rotation would be zero...so the residual should
    591:             be zero...so we will multiply "zero" by the last residual.  This might
    592:             not be exactly what we want to do here -could just return "zero". */

    594:     *res = 0.0;
    595:   }
    596:   return(0);
    597: }

    599: /*

    601:    KSPLGMRESGetNewVectors - This routine allocates more work vectors, starting from
    602:                          VEC_VV(it)

    604: */
    607: static PetscErrorCode KSPLGMRESGetNewVectors(KSP ksp,PetscInt it)
    608: {
    609:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;
    610:   PetscInt       nwork   = lgmres->nwork_alloc; /* number of work vector chunks allocated */
    611:   PetscInt       nalloc;                      /* number to allocate */
    613:   PetscInt       k;

    616:   nalloc = lgmres->delta_allocate; /* number of vectors to allocate
    617:                                       in a single chunk */

    619:   /* Adjust the number to allocate to make sure that we don't exceed the
    620:      number of available slots (lgmres->vecs_allocated)*/
    621:   if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated) {
    622:     nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
    623:   }
    624:   if (!nalloc) return(0);

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

    628:   /* work vectors */
    629:   KSPCreateVecs(ksp,nalloc,&lgmres->user_work[nwork],0,NULL);
    630:   PetscLogObjectParents(ksp,nalloc,lgmres->user_work[nwork]);
    631:   /* specify size of chunk allocated */
    632:   lgmres->mwork_alloc[nwork] = nalloc;

    634:   for (k=0; k < nalloc; k++) {
    635:     lgmres->vecs[it+VEC_OFFSET+k] = lgmres->user_work[nwork][k];
    636:   }

    639:   /* LGMRES_MOD - for now we are preallocating the augmentation vectors */

    642:   /* increment the number of work vector chunks */
    643:   lgmres->nwork_alloc++;
    644:   return(0);
    645: }

    647: /*

    649:    KSPBuildSolution_LGMRES

    651:      Input Parameter:
    652: .     ksp - the Krylov space object
    653: .     ptr-

    655:    Output Parameter:
    656: .     result - the solution

    658:    Note: this calls KSPLGMRESBuildSoln - the same function that KSPLGMRESCycle
    659:    calls directly.

    661: */
    664: PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp,Vec ptr,Vec *result)
    665: {
    666:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;

    670:   if (!ptr) {
    671:     if (!lgmres->sol_temp) {
    672:       VecDuplicate(ksp->vec_sol,&lgmres->sol_temp);
    673:       PetscLogObjectParent((PetscObject)ksp,(PetscObject)lgmres->sol_temp);
    674:     }
    675:     ptr = lgmres->sol_temp;
    676:   }
    677:   if (!lgmres->nrs) {
    678:     /* allocate the work area */
    679:     PetscMalloc1(lgmres->max_k,&lgmres->nrs);
    680:     PetscLogObjectMemory((PetscObject)ksp,lgmres->max_k*sizeof(PetscScalar));
    681:   }

    683:   KSPLGMRESBuildSoln(lgmres->nrs,ksp->vec_sol,ptr,ksp,lgmres->it);
    684:   if (result) *result = ptr;
    685:   return(0);
    686: }

    690: PetscErrorCode KSPView_LGMRES(KSP ksp,PetscViewer viewer)
    691: {
    692:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;
    694:   PetscBool      iascii;

    697:   KSPView_GMRES(ksp,viewer);
    698:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    699:   if (iascii) {
    700:     /*LGMRES_MOD */
    701:     PetscViewerASCIIPrintf(viewer,"  LGMRES: aug. dimension=%D\n",lgmres->aug_dim);
    702:     if (lgmres->approx_constant) {
    703:       PetscViewerASCIIPrintf(viewer,"  LGMRES: approx. space size was kept constant.\n");
    704:     }
    705:     PetscViewerASCIIPrintf(viewer,"  LGMRES: number of matvecs=%D\n",lgmres->matvecs);
    706:   }
    707:   return(0);
    708: }

    712: PetscErrorCode KSPSetFromOptions_LGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
    713: {
    715:   PetscInt       aug;
    716:   KSP_LGMRES     *lgmres = (KSP_LGMRES*) ksp->data;
    717:   PetscBool      flg     = PETSC_FALSE;

    720:   KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
    721:   PetscOptionsHead(PetscOptionsObject,"KSP LGMRES Options");
    722:   PetscOptionsBool("-ksp_lgmres_constant","Use constant approx. space size","KSPGMRESSetConstant",lgmres->approx_constant,&lgmres->approx_constant,NULL);
    723:   PetscOptionsInt("-ksp_lgmres_augment","Number of error approximations to augment the Krylov space with","KSPLGMRESSetAugDim",lgmres->aug_dim,&aug,&flg);
    724:   if (flg) { KSPLGMRESSetAugDim(ksp,aug); }
    725:   PetscOptionsTail();
    726:   return(0);
    727: }

    729: /*functions for extra lgmres options here*/
    732: static PetscErrorCode  KSPLGMRESSetConstant_LGMRES(KSP ksp)
    733: {
    734:   KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;

    737:   lgmres->approx_constant = PETSC_TRUE;
    738:   return(0);
    739: }

    743: static PetscErrorCode  KSPLGMRESSetAugDim_LGMRES(KSP ksp,PetscInt aug_dim)
    744: {
    745:   KSP_LGMRES *lgmres = (KSP_LGMRES*)ksp->data;

    748:   if (aug_dim < 0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Augmentation dimension must be positive");
    749:   if (aug_dim > (lgmres->max_k -1)) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Augmentation dimension must be <= (restart size-1)");
    750:   lgmres->aug_dim = aug_dim;
    751:   return(0);
    752: }

    754: /* end new lgmres functions */

    756: /*MC
    757:     KSPLGMRES - Augments the standard GMRES approximation space with approximations to
    758:                 the error from previous restart cycles.

    760:   Options Database Keys:
    761: +   -ksp_gmres_restart <restart> - total approximation space size (Krylov directions + error approximations)
    762: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    763: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    764:                             vectors are allocated as needed)
    765: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    766: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    767: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
    768:                                   stability of the classical Gram-Schmidt  orthogonalization.
    769: .   -ksp_gmres_krylov_monitor - plot the Krylov space generated
    770: .   -ksp_lgmres_augment <k> - number of error approximations to augment the Krylov space with
    771: -   -ksp_lgmres_constant - use a constant approx. space size (only affects restart cycles < num. error approx.(k), i.e. the first k restarts)

    773:     To run LGMRES(m, k) as described in the above paper, use:
    774:        -ksp_gmres_restart <m+k>
    775:        -ksp_lgmres_augment <k>

    777:   Level: beginner

    779:    Notes: Supports both left and right preconditioning, but not symmetric.

    781:    References:
    782: .    1. - A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for accelerating the convergence of restarted GMRES. SIAM Journal on Matrix Analysis and Applications, 26 (2005).

    784:   Developer Notes:  This object is subclassed off of KSPGMRES

    786:   Contributed by: Allison Baker

    788: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPGMRES,
    789:           KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
    790:           KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    791:           KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPLGMRESSetAugDim(),
    792:           KSPGMRESSetConstant()

    794: M*/

    798: PETSC_EXTERN PetscErrorCode KSPCreate_LGMRES(KSP ksp)
    799: {
    800:   KSP_LGMRES     *lgmres;

    804:   PetscNewLog(ksp,&lgmres);

    806:   ksp->data               = (void*)lgmres;
    807:   ksp->ops->buildsolution = KSPBuildSolution_LGMRES;

    809:   ksp->ops->setup                        = KSPSetUp_LGMRES;
    810:   ksp->ops->solve                        = KSPSolve_LGMRES;
    811:   ksp->ops->destroy                      = KSPDestroy_LGMRES;
    812:   ksp->ops->view                         = KSPView_LGMRES;
    813:   ksp->ops->setfromoptions               = KSPSetFromOptions_LGMRES;
    814:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    815:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

    817:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    818:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);

    820:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
    821:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
    822:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
    823:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
    824:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
    825:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
    826:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
    827:   PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);

    829:   /*LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
    830:   PetscObjectComposeFunction((PetscObject)ksp,"KSPLGMRESSetConstant_C",KSPLGMRESSetConstant_LGMRES);
    831:   PetscObjectComposeFunction((PetscObject)ksp,"KSPLGMRESSetAugDim_C",KSPLGMRESSetAugDim_LGMRES);

    834:   /*defaults */
    835:   lgmres->haptol         = 1.0e-30;
    836:   lgmres->q_preallocate  = 0;
    837:   lgmres->delta_allocate = LGMRES_DELTA_DIRECTIONS;
    838:   lgmres->orthog         = KSPGMRESClassicalGramSchmidtOrthogonalization;
    839:   lgmres->nrs            = 0;
    840:   lgmres->sol_temp       = 0;
    841:   lgmres->max_k          = LGMRES_DEFAULT_MAXK;
    842:   lgmres->Rsvd           = 0;
    843:   lgmres->cgstype        = KSP_GMRES_CGS_REFINE_NEVER;
    844:   lgmres->orthogwork     = 0;

    846:   /*LGMRES_MOD - new defaults */
    847:   lgmres->aug_dim         = LGMRES_DEFAULT_AUGDIM;
    848:   lgmres->aug_ct          = 0;     /* start with no aug vectors */
    849:   lgmres->approx_constant = PETSC_FALSE;
    850:   lgmres->matvecs         = 0;
    851:   return(0);
    852: }