Actual source code: lgmres.c

      1: #define PETSCKSP_DLL

     3:  #include src/ksp/ksp/impls/gmres/lgmres/lgmresp.h

      5: #define LGMRES_DELTA_DIRECTIONS 10
      6: #define LGMRES_DEFAULT_MAXK     30
      7: #define LGMRES_DEFAULT_AUGDIM   2 /*default number of augmentation vectors */
      8: static PetscErrorCode    LGMRESGetNewVectors(KSP,PetscInt);
      9: static PetscErrorCode    LGMRESUpdateHessenberg(KSP,PetscInt,PetscTruth,PetscReal *);
     10: static PetscErrorCode    BuildLgmresSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);

     14: PetscErrorCode PETSCKSP_DLLEXPORT KSPLGMRESSetAugDim(KSP ksp, PetscInt dim)
     15: {

     19:   PetscTryMethod((ksp),KSPLGMRESSetAugDim_C,(KSP,PetscInt),(ksp,dim));
     20:   return(0);
     21: }

     25: PetscErrorCode PETSCKSP_DLLEXPORT KSPLGMRESSetConstant(KSP ksp)
     26: {

     30:   PetscTryMethod((ksp),KSPLGMRESSetConstant_C,(KSP),(ksp));
     31:   return(0);
     32: }

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

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

     40: */
     43: PetscErrorCode    KSPSetUp_LGMRES(KSP ksp)
     44: {
     45:   PetscInt       size,hh,hes,rs,cc;
     47:   PetscInt       max_k,k, aug_dim;
     48:   KSP_LGMRES     *lgmres = (KSP_LGMRES *)ksp->data;

     51:   if (ksp->pc_side == PC_SYMMETRIC) {
     52:     SETERRQ(PETSC_ERR_SUP,"no symmetric preconditioning for KSPLGMRES");
     53:   }
     54:   max_k         = lgmres->max_k;
     55:   aug_dim       = lgmres->aug_dim;
     56:   hh            = (max_k + 2) * (max_k + 1);
     57:   hes           = (max_k + 1) * (max_k + 1);
     58:   rs            = (max_k + 2);
     59:   cc            = (max_k + 1);  /* SS and CC are the same size */
     60:   size          = (hh + hes + rs + 2*cc) * sizeof(PetscScalar);

     62:   /* Allocate space and set pointers to beginning */
     63:   PetscMalloc(size,&lgmres->hh_origin);
     64:   PetscMemzero(lgmres->hh_origin,size);
     65:   PetscLogObjectMemory(ksp,size);  /* HH - modified (by plane rotations) hessenburg */
     66:   lgmres->hes_origin = lgmres->hh_origin + hh;     /* HES - unmodified hessenburg */
     67:   lgmres->rs_origin  = lgmres->hes_origin + hes;   /* RS - the right-hand-side of the
     68:                                                       Hessenberg system */
     69:   lgmres->cc_origin  = lgmres->rs_origin + rs;     /* CC - cosines for rotations */
     70:   lgmres->ss_origin  = lgmres->cc_origin + cc;     /* SS - sines for rotations */

     72:   if (ksp->calc_sings) {
     73:     /* Allocate workspace to hold Hessenberg matrix needed by Eispack */
     74:     size = (max_k + 3)*(max_k + 9)*sizeof(PetscScalar);
     75:     PetscMalloc(size,&lgmres->Rsvd);
     76:     PetscMalloc(5*(max_k+2)*sizeof(PetscReal),&lgmres->Dsvd);
     77:     PetscLogObjectMemory(ksp,size+5*(max_k+2)*sizeof(PetscReal));
     78:   }

     80:   /* Allocate array to hold pointers to user vectors.  Note that we need
     81:   we need it+1 vectors, and it <= max_k)  - vec_offset indicates some initial work vectors*/
     82:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void*),&lgmres->vecs);
     83:   lgmres->vecs_allocated = VEC_OFFSET + 2 + max_k;
     84:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(void*),&lgmres->user_work);
     85:   PetscMalloc((VEC_OFFSET+2+max_k)*sizeof(PetscInt),&lgmres->mwork_alloc);
     86:   PetscLogObjectMemory(ksp,(VEC_OFFSET+2+max_k)*(2*sizeof(void*)+sizeof(PetscInt)));

     88:   /* LGMRES_MOD: need array of pointers to augvecs*/
     89:   PetscMalloc((2 * aug_dim + AUG_OFFSET)*sizeof(void*),&lgmres->augvecs);
     90:   lgmres->aug_vecs_allocated = 2 *aug_dim + AUG_OFFSET;
     91:   PetscMalloc((2* aug_dim + AUG_OFFSET)*sizeof(void*),&lgmres->augvecs_user_work);
     92:   PetscMalloc(aug_dim*sizeof(PetscInt),&lgmres->aug_order);
     93:   PetscLogObjectMemory(ksp,(aug_dim)*(4*sizeof(void*) + sizeof(PetscInt)) + AUG_OFFSET*2*sizeof(void*));

     95:
     96:  /* if q_preallocate = 0 then only allocate one "chunk" of space (for
     97:      5 vectors) - additional will then be allocated from LGMREScycle()
     98:      as needed.  Otherwise, allocate all of the space that could be needed */
     99:   if (lgmres->q_preallocate) {
    100:     lgmres->vv_allocated   = VEC_OFFSET + 2 + max_k;
    101:     KSPGetVecs(ksp,lgmres->vv_allocated,&lgmres->user_work[0]);
    102:     PetscLogObjectParents(ksp,lgmres->vv_allocated,lgmres->user_work[0]);
    103:     lgmres->mwork_alloc[0] = lgmres->vv_allocated;
    104:     lgmres->nwork_alloc    = 1;
    105:     for (k=0; k<lgmres->vv_allocated; k++) {
    106:       lgmres->vecs[k] = lgmres->user_work[0][k];
    107:     }
    108:   } else {
    109:     lgmres->vv_allocated    = 5;
    110:     KSPGetVecs(ksp,5,&lgmres->user_work[0]);
    111:     PetscLogObjectParents(ksp,5,lgmres->user_work[0]);
    112:     lgmres->mwork_alloc[0]  = 5;
    113:     lgmres->nwork_alloc     = 1;
    114:     for (k=0; k<lgmres->vv_allocated; k++) {
    115:       lgmres->vecs[k] = lgmres->user_work[0][k];
    116:     }
    117:   }
    118:   /* LGMRES_MOD - for now we will preallocate the augvecs - because aug_dim << restart
    119:      ... also keep in mind that we need to keep augvecs from cycle to cycle*/
    120:   lgmres->aug_vv_allocated = 2* aug_dim + AUG_OFFSET;
    121:   lgmres->augwork_alloc =  2* aug_dim + AUG_OFFSET;
    122:   KSPGetVecs(ksp,lgmres->aug_vv_allocated,&lgmres->augvecs_user_work[0]);
    123:   PetscLogObjectParents(ksp,lgmres->aug_vv_allocated,lgmres->augvecs_user_work[0]);
    124:   for (k=0; k<lgmres->aug_vv_allocated; k++) {
    125:       lgmres->augvecs[k] = lgmres->augvecs_user_work[0][k];
    126:     }

    128:   return(0);
    129: }

    132: /*

    134:     LGMRESCycle - Run lgmres, possibly with restart.  Return residual
    135:                   history if requested.

    137:     input parameters:
    138: .         lgmres  - structure containing parameters and work areas

    140:     output parameters:
    141: .        nres    - residuals (from preconditioned system) at each step.
    142:                   If restarting, consider passing nres+it.  If null,
    143:                   ignored
    144: .        itcount - number of iterations used.   nres[0] to nres[itcount]
    145:                   are defined.  If null, ignored.  If null, ignored.
    146: .        converged - 0 if not converged

    148:
    149:     Notes:
    150:     On entry, the value in vector VEC_VV(0) should be
    151:     the initial residual.

    154:  */
    157: PetscErrorCode LGMREScycle(PetscInt *itcount,KSP ksp)
    158: {

    160:   KSP_LGMRES     *lgmres = (KSP_LGMRES *)(ksp->data);
    161:   PetscReal      res_norm, res;
    162:   PetscReal      hapbnd, tt;
    163:   PetscScalar    zero = 0.0;
    164:   PetscScalar    tmp;
    165:   PetscTruth     hapend = PETSC_FALSE;  /* indicates happy breakdown ending */
    167:   PetscInt       loc_it;                /* local count of # of dir. in Krylov space */
    168:   PetscInt       max_k = lgmres->max_k; /* max approx space size */
    169:   PetscInt       max_it = ksp->max_it;  /* max # of overall iterations for the method */
    170:   /* LGMRES_MOD - new variables*/
    171:   PetscInt       aug_dim = lgmres->aug_dim;
    172:   PetscInt       spot = 0;
    173:   PetscInt       order = 0;
    174:   PetscInt       it_arnoldi;             /* number of arnoldi steps to take */
    175:   PetscInt       it_total;               /* total number of its to take (=approx space size)*/
    176:   PetscInt       ii, jj;
    177:   PetscReal      tmp_norm;
    178:   PetscScalar    inv_tmp_norm;
    179:   PetscScalar    *avec;

    182:   /* Number of pseudo iterations since last restart is the number
    183:      of prestart directions */
    184:   loc_it = 0;

    186:   /* LGMRES_MOD: determine number of arnoldi steps to take */
    187:   /* if approx_constant then we keep the space the same size even if
    188:      we don't have the full number of aug vectors yet*/
    189:   if (lgmres->approx_constant) {
    190:      it_arnoldi = max_k - lgmres->aug_ct;
    191:   } else {
    192:       it_arnoldi = max_k - aug_dim;
    193:   }

    195:   it_total =  it_arnoldi + lgmres->aug_ct;

    197:   /* initial residual is in VEC_VV(0)  - compute its norm*/
    198:   VecNorm(VEC_VV(0),NORM_2,&res_norm);
    199:   res    = res_norm;
    200:
    201:   /* first entry in right-hand-side of hessenberg system is just
    202:      the initial residual norm */
    203:   *GRS(0) = res_norm;

    205:  /* check for the convergence */
    206:   if (!res) {
    207:      if (itcount) *itcount = 0;
    208:      ksp->reason = KSP_CONVERGED_ATOL;
    209:      PetscLogInfo((ksp,"LGMRESCycle: Converged due to zero residual norm on entry\n"));
    210:      return(0);
    211:   }

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

    216:   /* FYI: AMS calls are for memory snooper */
    217:   PetscObjectTakeAccess(ksp);
    218:   ksp->rnorm = res;
    219:   PetscObjectGrantAccess(ksp);

    222:   /* note: (lgmres->it) is always set one less than (loc_it) It is used in
    223:      KSPBUILDSolution_LGMRES, where it is passed to BuildLgmresSoln.
    224:      Note that when BuildLgmresSoln is called from this function,
    225:      (loc_it -1) is passed, so the two are equivalent */
    226:   lgmres->it = (loc_it - 1);

    228:
    229:   /* MAIN ITERATION LOOP BEGINNING*/

    232:   /* keep iterating until we have converged OR generated the max number
    233:      of directions OR reached the max number of iterations for the method */
    234:   (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
    235:
    236:   while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
    237:      KSPLogResidualHistory(ksp,res);
    238:      lgmres->it = (loc_it - 1);
    239:      KSPMonitor(ksp,ksp->its,res);

    241:     /* see if more space is needed for work vectors */
    242:     if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
    243:        LGMRESGetNewVectors(ksp,loc_it+1);
    244:       /* (loc_it+1) is passed in as number of the first vector that should
    245:          be allocated */
    246:     }

    248:     /*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
    249:     if (loc_it < it_arnoldi) { /* Arnoldi */
    250:        KSP_PCApplyBAorAB(ksp,VEC_VV(loc_it),VEC_VV(1+loc_it),VEC_TEMP_MATOP);
    251:     } else { /*aug step */
    252:        order = loc_it - it_arnoldi + 1; /* which aug step */
    253:        for (ii=0; ii<aug_dim; ii++) {
    254:            if (lgmres->aug_order[ii] == order) {
    255:               spot = ii;
    256:               break; /* must have this because there will be duplicates before aug_ct = aug_dim */
    257:             }
    258:         }

    260:        VecCopy(A_AUGVEC(spot), VEC_VV(1+loc_it));
    261:        /*note: an alternate implementation choice would be to only save the AUGVECS and
    262:          not A_AUGVEC and then apply the PC here to the augvec */
    263:     }

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

    269:     /* new entry in hessenburg is the 2-norm of our new direction */
    270:     VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);
    271:     *HH(loc_it+1,loc_it)   = tt;
    272:     *HES(loc_it+1,loc_it)  = tt;

    275:     /* check for the happy breakdown */
    276:     hapbnd  = PetscAbsScalar(tt / *GRS(loc_it));/* GRS(loc_it) contains the res_norm from the last iteration  */
    277:     if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
    278:     if (tt > hapbnd) {
    279:        tmp = 1.0/tt;
    280:        VecScale(VEC_VV(loc_it+1),tmp); /* scale new direction by its norm */
    281:     } else {
    282:        PetscLogInfo((ksp,"GMREScycle:Detected happy breakdown, current hapbnd = %g tt = %g\n",hapbnd,tt));
    283:        hapend = PETSC_TRUE;
    284:     }

    286:     /* Now apply rotations to new col of hessenberg (and right side of system),
    287:        calculate new rotation, and get new residual norm at the same time*/
    288:     LGMRESUpdateHessenberg(ksp,loc_it,hapend,&res);
    289:     if (ksp->reason) break;

    291:     loc_it++;
    292:     lgmres->it  = (loc_it-1);  /* Add this here in case it has converged */
    293:
    294:     PetscObjectTakeAccess(ksp);
    295:     ksp->its++;
    296:     ksp->rnorm = res;
    297:     PetscObjectGrantAccess(ksp);

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

    301:     /* Catch error in happy breakdown and signal convergence and break from loop */
    302:     if (hapend) {
    303:       if (!ksp->reason) {
    304:         SETERRQ1(0,"You reached the happy break down,but convergence was not indicated. Residual norm = %g",res);
    305:       }
    306:       break;
    307:     }
    308:   }
    309:   /* END OF ITERATION LOOP */

    311:   KSPLogResidualHistory(ksp,res);

    313:   /* Monitor if we know that we will not return for a restart */
    314:   if (ksp->reason || ksp->its >= max_it) {
    315:     KSPMonitor(ksp, ksp->its, res);
    316:   }

    318:   if (itcount) *itcount    = loc_it;

    320:   /*
    321:     Down here we have to solve for the "best" coefficients of the Krylov
    322:     columns, add the solution values together, and possibly unwind the
    323:     preconditioning from the solution
    324:    */
    325:
    326:   /* Form the solution (or the solution so far) */
    327:   /* Note: must pass in (loc_it-1) for iteration count so that BuildLgmresSoln
    328:      properly navigates */

    330:   BuildLgmresSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);

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

    338:      /*AUG_TEMP contains the new augmentation vector (assigned in  BuildLgmresSoln) */
    339:     if (!lgmres->aug_ct) {
    340:         spot = 0;
    341:         lgmres->aug_ct++;
    342:      } else if (lgmres->aug_ct < aug_dim) {
    343:         spot = lgmres->aug_ct;
    344:         lgmres->aug_ct++;
    345:      } else { /* truncate */
    346:         for (ii=0; ii<aug_dim; ii++) {
    347:            if (lgmres->aug_order[ii] == aug_dim) {
    348:               spot = ii;
    349:             }
    350:         }
    351:      }

    353:

    355:      VecCopy(AUG_TEMP, AUGVEC(spot));
    356:      /*need to normalize */
    357:      VecNorm(AUGVEC(spot), NORM_2, &tmp_norm);
    358:      inv_tmp_norm = 1.0/tmp_norm;
    359:      VecScale(AUGVEC(spot),inv_tmp_norm);

    361:      /*set new aug vector to order 1  - move all others back one */
    362:      for (ii=0; ii < aug_dim; ii++) {
    363:         AUG_ORDER(ii)++;
    364:      }
    365:      AUG_ORDER(spot) = 1;

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

    370:
    371:      /* first do H+*y */
    372:      VecSet(AUG_TEMP,zero);
    373:      VecGetArray(AUG_TEMP, &avec);
    374:      for (ii=0; ii < it_total + 1; ii++) {
    375:         for (jj=0; jj <= ii+1; jj++) {
    376:            avec[jj] += *HES(jj ,ii) * *GRS(ii);
    377:         }
    378:      }

    380:      /*now multiply result by V+ */
    381:      VecSet(VEC_TEMP,zero);
    382:      VecMAXPY(VEC_TEMP, it_total+1, avec, &VEC_VV(0)); /*answer is in VEC_TEMP*/
    383:      VecRestoreArray(AUG_TEMP, &avec);
    384:
    385:      /*copy answer to aug location  and scale*/
    386:      VecCopy(VEC_TEMP,  A_AUGVEC(spot));
    387:      VecScale(A_AUGVEC(spot),inv_tmp_norm);

    390:   }
    391:   return(0);
    392: }

    394: /*
    395:     KSPSolve_LGMRES - This routine applies the LGMRES method.

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

    401:    Output Parameter:
    402: .     outits - number of iterations used

    404: */

    408: PetscErrorCode KSPSolve_LGMRES(KSP ksp)
    409: {
    411:   PetscInt       cycle_its; /* iterations done in a call to LGMREScycle */
    412:   PetscInt       itcount;   /* running total of iterations, incl. those in restarts */
    413:   KSP_LGMRES     *lgmres = (KSP_LGMRES *)ksp->data;
    414:   PetscTruth     guess_zero = ksp->guess_zero;
    415:   PetscInt       ii;        /*LGMRES_MOD variable */

    418:   if (ksp->calc_sings && !lgmres->Rsvd) {
    419:      SETERRQ(PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
    420:   }
    421:   PetscObjectTakeAccess(ksp);
    422:   ksp->its        = 0;
    423:   lgmres->aug_ct  = 0;
    424:   lgmres->matvecs = 0;
    425:   PetscObjectGrantAccess(ksp);

    427:   /* initialize */
    428:   itcount  = 0;
    429:   ksp->reason = KSP_CONVERGED_ITERATING;
    430:   /*LGMRES_MOD*/
    431:   for (ii=0; ii<lgmres->aug_dim; ii++) {
    432:      lgmres->aug_order[ii] = 0;
    433:   }

    435:   while (!ksp->reason) {
    436:      /* calc residual - puts in VEC_VV(0) */
    437:     KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
    438:     LGMREScycle(&cycle_its,ksp);
    439:     itcount += cycle_its;
    440:     if (itcount >= ksp->max_it) {
    441:       ksp->reason = KSP_DIVERGED_ITS;
    442:       break;
    443:     }
    444:     ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
    445:   }
    446:   ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
    447:   return(0);
    448: }

    450: /*

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

    454: */
    457: PetscErrorCode KSPDestroy_LGMRES(KSP ksp)
    458: {
    459:   KSP_LGMRES     *lgmres = (KSP_LGMRES*)ksp->data;
    461:   PetscInt       i;

    464:   /* Free the Hessenberg matrices */
    465:   if (lgmres->hh_origin) {PetscFree(lgmres->hh_origin);}

    467:   /* Free pointers to user variables */
    468:   if (lgmres->vecs) {PetscFree(lgmres->vecs);}

    470:   /*LGMRES_MOD - free pointers for extra vectors */
    471:   if (lgmres->augvecs) {PetscFree(lgmres->augvecs);}

    473:   /* free work vectors */
    474:   for (i=0; i < lgmres->nwork_alloc; i++) {
    475:     VecDestroyVecs(lgmres->user_work[i],lgmres->mwork_alloc[i]);
    476:   }
    477:   if (lgmres->user_work)  {PetscFree(lgmres->user_work);}

    479:   /*LGMRES_MOD - free aug work vectors also */
    480:   /*this was all allocated as one "chunk" */
    481:   VecDestroyVecs(lgmres->augvecs_user_work[0],lgmres->augwork_alloc);
    482:   if (lgmres->augvecs_user_work)  {PetscFree(lgmres->augvecs_user_work);}
    483:   if (lgmres->aug_order) {PetscFree(lgmres->aug_order);}

    485:   if (lgmres->mwork_alloc) {PetscFree(lgmres->mwork_alloc);}
    486:   if (lgmres->nrs) {PetscFree(lgmres->nrs);}
    487:   if (lgmres->sol_temp) {VecDestroy(lgmres->sol_temp);}
    488:   if (lgmres->Rsvd) {PetscFree(lgmres->Rsvd);}
    489:   if (lgmres->Dsvd) {PetscFree(lgmres->Dsvd);}
    490:   PetscFree(lgmres);
    491:   return(0);
    492: }

    494: /*
    495:     BuildLgmresSoln - create the solution from the starting vector and the
    496:                       current iterates.

    498:     Input parameters:
    499:         nrs - work area of size it + 1.
    500:         vguess  - index of initial guess
    501:         vdest - index of result.  Note that vguess may == vdest (replace
    502:                 guess with the solution).
    503:         it - HH upper triangular part is a block of size (it+1) x (it+1)

    505:      This is an internal routine that knows about the LGMRES internals.
    506:  */
    509: static PetscErrorCode BuildLgmresSoln(PetscScalar* nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
    510: {
    511:   PetscScalar    tt,zero = 0.0,one = 1.0;
    513:   PetscInt       ii,k,j;
    514:   KSP_LGMRES     *lgmres = (KSP_LGMRES *)(ksp->data);
    515:   /*LGMRES_MOD */
    516:   PetscInt       it_arnoldi, it_aug;
    517:   PetscInt       jj, spot = 0;

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

    522:   /* If it is < 0, no lgmres steps have been performed */
    523:   if (it < 0) {
    524:     if (vdest != vguess) {
    525:       VecCopy(vguess,vdest);
    526:     }
    527:     return(0);
    528:   }

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

    532:   /* LGMRES_MOD - determine if we need to use augvecs for the soln  - do not assume that
    533:      this is called after the total its allowed for an approx space */
    534:    if (lgmres->approx_constant) {
    535:      it_arnoldi = lgmres->max_k - lgmres->aug_ct;
    536:    } else {
    537:      it_arnoldi = lgmres->max_k - lgmres->aug_dim;
    538:    }
    539:    if (it_arnoldi >= it +1) {
    540:       it_aug = 0;
    541:       it_arnoldi = it+1;
    542:    } else {
    543:       it_aug = (it + 1) - it_arnoldi;
    544:    }

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

    549:
    550:   /* solve the upper triangular system - GRS is the right side and HH is
    551:      the upper triangular matrix  - put soln in nrs */
    552:   if (*HH(it,it) == 0.0) SETERRQ2(PETSC_ERR_CONV_FAILED,"HH(it,it) is identically zero; it = %D GRS(it) = %g",it,PetscAbsScalar(*GRS(it)));
    553:   if (*HH(it,it) != 0.0) {
    554:      nrs[it] = *GRS(it) / *HH(it,it);
    555:   } else {
    556:      nrs[it] = 0.0;
    557:   }

    559:   for (ii=1; ii<=it; ii++) {
    560:     k   = it - ii;
    561:     tt  = *GRS(k);
    562:     for (j=k+1; j<=it; j++) tt  = tt - *HH(k,j) * nrs[j];
    563:     nrs[k]   = tt / *HH(k,k);
    564:   }

    566:   /* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
    567:   VecSet(VEC_TEMP,zero); /* set VEC_TEMP components to 0 */

    569:   /*LGMRES_MOD - if augmenting has happened we need to form the solution
    570:     using the augvecs */
    571:   if (!it_aug) { /* all its are from arnoldi */
    572:      VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
    573:   } else { /*use aug vecs */
    574:      /*first do regular krylov directions */
    575:      VecMAXPY(VEC_TEMP,it_arnoldi,nrs,&VEC_VV(0));
    576:      /*now add augmented portions - add contribution of aug vectors one at a time*/

    579:      for (ii=0; ii<it_aug; ii++) {
    580:         for (jj=0; jj<lgmres->aug_dim; jj++) {
    581:            if (lgmres->aug_order[jj] == (ii+1)) {
    582:               spot = jj;
    583:               break; /* must have this because there will be duplicates before aug_ct = aug_dim */
    584:             }
    585:         }
    586:         VecAXPY(VEC_TEMP,nrs[it_arnoldi+ii],AUGVEC(spot));
    587:       }
    588:   }
    589:   /* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
    590:      preconditioner is "unwound" from right-precondtioning*/
    591:   VecCopy(VEC_TEMP, AUG_TEMP);

    593:   KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);

    595:   /* add solution to previous solution */
    596:   /* put updated solution into vdest.*/
    597:   if (vdest != vguess) {
    598:     VecCopy(VEC_TEMP,vdest);
    599:   }
    600:   VecAXPY(vdest,one,VEC_TEMP);

    602:   return(0);
    603: }

    605: /*

    607:     LGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
    608:                             Return new residual.

    610:     input parameters:

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

    617:     output parameters:
    618: .        res - the new residual
    619:
    620:  */
    623: static PetscErrorCode LGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscTruth hapend,PetscReal *res)
    624: {
    625:   PetscScalar   *hh,*cc,*ss,tt;
    626:   PetscInt      j;
    627:   KSP_LGMRES    *lgmres = (KSP_LGMRES *)(ksp->data);

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

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

    639:   for (j=1; j<=it; j++) {
    640:     tt  = *hh;
    641: #if defined(PETSC_USE_COMPLEX)
    642:     *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
    643: #else
    644:     *hh = *cc * tt + *ss * *(hh+1);
    645: #endif
    646:     hh++;
    647:     *hh = *cc++ * *hh - (*ss++ * tt);
    648:     /* hh, cc, and ss have all been incremented one by end of loop */
    649:   }

    651:   /*
    652:     compute the new plane rotation, and apply it to:
    653:      1) the right-hand-side of the Hessenberg system (GRS)
    654:         note: it affects GRS(it) and GRS(it+1)
    655:      2) the new column of the Hessenberg matrix
    656:         note: it affects HH(it,it) which is currently pointed to
    657:         by hh and HH(it+1, it) (*(hh+1))
    658:     thus obtaining the updated value of the residual...
    659:   */

    661:   /* compute new plane rotation */

    663:   if (!hapend) {
    664: #if defined(PETSC_USE_COMPLEX)
    665:     tt        = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
    666: #else
    667:     tt        = PetscSqrtScalar(*hh * *hh + *(hh+1) * *(hh+1));
    668: #endif
    669:     if (tt == 0.0) {
    670:       ksp->reason = KSP_DIVERGED_NULL;
    671:       return(0);
    672:     }
    673:     *cc       = *hh / tt;   /* new cosine value */
    674:     *ss       = *(hh+1) / tt;  /* new sine value */

    676:     /* apply to 1) and 2) */
    677:     *GRS(it+1) = - (*ss * *GRS(it));
    678: #if defined(PETSC_USE_COMPLEX)
    679:     *GRS(it)   = PetscConj(*cc) * *GRS(it);
    680:     *hh        = PetscConj(*cc) * *hh + *ss * *(hh+1);
    681: #else
    682:     *GRS(it)   = *cc * *GRS(it);
    683:     *hh        = *cc * *hh + *ss * *(hh+1);
    684: #endif

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

    689:   } else { /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
    690:             another rotation matrix (so RH doesn't change).  The new residual is
    691:             always the new sine term times the residual from last time (GRS(it)),
    692:             but now the new sine rotation would be zero...so the residual should
    693:             be zero...so we will multiply "zero" by the last residual.  This might
    694:             not be exactly what we want to do here -could just return "zero". */
    695:
    696:     *res = 0.0;
    697:   }
    698:   return(0);
    699: }

    701: /*

    703:    LGMRESGetNewVectors - This routine allocates more work vectors, starting from
    704:                          VEC_VV(it)
    705:
    706: */
    709: static PetscErrorCode LGMRESGetNewVectors(KSP ksp,PetscInt it)
    710: {
    711:   KSP_LGMRES     *lgmres = (KSP_LGMRES *)ksp->data;
    712:   PetscInt       nwork = lgmres->nwork_alloc; /* number of work vector chunks allocated */
    713:   PetscInt       nalloc;                      /* number to allocate */
    715:   PetscInt       k;
    716:
    718:   nalloc = lgmres->delta_allocate; /* number of vectors to allocate
    719:                                       in a single chunk */

    721:   /* Adjust the number to allocate to make sure that we don't exceed the
    722:      number of available slots (lgmres->vecs_allocated)*/
    723:   if (it + VEC_OFFSET + nalloc >= lgmres->vecs_allocated){
    724:     nalloc = lgmres->vecs_allocated - it - VEC_OFFSET;
    725:   }
    726:   if (!nalloc) return(0);

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

    730:   /* work vectors */
    731:   KSPGetVecs(ksp,nalloc,&lgmres->user_work[nwork]);
    732:   PetscLogObjectParents(ksp,nalloc,lgmres->user_work[nwork]);
    733:   /* specify size of chunk allocated */
    734:   lgmres->mwork_alloc[nwork] = nalloc;

    736:   for (k=0; k < nalloc; k++) {
    737:     lgmres->vecs[it+VEC_OFFSET+k] = lgmres->user_work[nwork][k];
    738:   }
    739:

    741:   /* LGMRES_MOD - for now we are preallocating the augmentation vectors */
    742:

    744:   /* increment the number of work vector chunks */
    745:   lgmres->nwork_alloc++;
    746:   return(0);
    747: }

    749: /*

    751:    KSPBuildSolution_LGMRES

    753:      Input Parameter:
    754: .     ksp - the Krylov space object
    755: .     ptr-

    757:    Output Parameter:
    758: .     result - the solution

    760:    Note: this calls BuildLgmresSoln - the same function that LGMREScycle
    761:    calls directly.

    763: */
    766: PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp,Vec ptr,Vec *result)
    767: {
    768:   KSP_LGMRES     *lgmres = (KSP_LGMRES *)ksp->data;

    772:   if (!ptr) {
    773:     if (!lgmres->sol_temp) {
    774:       VecDuplicate(ksp->vec_sol,&lgmres->sol_temp);
    775:       PetscLogObjectParent(ksp,lgmres->sol_temp);
    776:     }
    777:     ptr = lgmres->sol_temp;
    778:   }
    779:   if (!lgmres->nrs) {
    780:     /* allocate the work area */
    781:     PetscMalloc(lgmres->max_k*sizeof(PetscScalar),&lgmres->nrs);
    782:     PetscLogObjectMemory(ksp,lgmres->max_k*sizeof(PetscScalar));
    783:   }
    784:
    785:   BuildLgmresSoln(lgmres->nrs,ksp->vec_sol,ptr,ksp,lgmres->it);
    786:   *result = ptr;
    787:
    788:   return(0);
    789: }

    795: PetscErrorCode KSPView_LGMRES(KSP ksp,PetscViewer viewer)
    796: {
    797:   KSP_LGMRES     *lgmres = (KSP_LGMRES *)ksp->data;
    799:   PetscTruth     iascii;

    802:   KSPView_GMRES(ksp,viewer);
    803:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
    804:   if (iascii) {
    805:     /*LGMRES_MOD */
    806:     PetscViewerASCIIPrintf(viewer,"  LGMRES: aug. dimension=%D\n",lgmres->aug_dim);
    807:     if (lgmres->approx_constant) {
    808:        PetscViewerASCIIPrintf(viewer,"  LGMRES: approx. space size was kept constant.\n");
    809:     }
    810:     PetscViewerASCIIPrintf(viewer,"  LGMRES: number of matvecs=%D\n",lgmres->matvecs);
    811:   } else {
    812:     SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for KSP LGMRES",((PetscObject)viewer)->type_name);
    813:   }
    814:   return(0);
    815: }

    821: PetscErrorCode KSPSetFromOptions_LGMRES(KSP ksp)
    822: {
    824:   PetscInt       aug;
    825:   KSP_LGMRES     *lgmres = (KSP_LGMRES*) ksp->data;
    826:   PetscTruth     flg;

    829:   KSPSetFromOptions_GMRES(ksp);
    830:   PetscOptionsHead("KSP LGMRES Options");
    831:      PetscOptionsName("-ksp_lgmres_constant","Use constant approx. space size","KSPGMRESSetConstant",&flg);
    832:     if (flg) { lgmres->approx_constant = 1; }
    833:     PetscOptionsInt("-ksp_lgmres_augment","Number of error approximations to augment the Krylov space with","KSPLGMRESSetAugDim",lgmres->aug_dim,&aug,&flg);
    834:     if (flg) { KSPLGMRESSetAugDim(ksp,aug); }
    835:   PetscOptionsTail();
    836:   return(0);
    837: }

    840: EXTERN PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal *,PetscReal *);
    841: EXTERN PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal *,PetscReal *,PetscInt *);

    843: /*functions for extra lgmres options here*/
    847: PetscErrorCode PETSCKSP_DLLEXPORT KSPLGMRESSetConstant_LGMRES(KSP ksp)
    848: {
    849:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
    851:   lgmres->approx_constant = 1;
    852:   return(0);
    853: }

    859: PetscErrorCode PETSCKSP_DLLEXPORT KSPLGMRESSetAugDim_LGMRES(KSP ksp,PetscInt aug_dim)
    860: {
    861:   KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;

    864:   if (aug_dim < 0) SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Augmentation dimension must be positive");
    865:   if (aug_dim > (lgmres->max_k -1))  SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Augmentation dimension must be <= (restart size-1)");
    866:   lgmres->aug_dim = aug_dim;
    867:   return(0);
    868: }

    872: /* end new lgmres functions */

    875: /* use these options from gmres */
    877: EXTERN PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetHapTol_GMRES(KSP,double);
    878: EXTERN PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetPreAllocateVectors_GMRES(KSP);
    879: EXTERN PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetRestart_GMRES(KSP,PetscInt);
    880: EXTERN PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetOrthogonalization_GMRES(KSP,PetscErrorCode (*)(KSP,PetscInt));
    881: EXTERN PetscErrorCode PETSCKSP_DLLEXPORT KSPGMRESSetCGSRefinementType_GMRES(KSP,KSPGMRESCGSRefinementType);

    884: /*MC
    885:      KSPLGMRES - Augments the standard GMRES approximation space with approximation to
    886:                  the error from previous restart cycles.

    888:    Options Database Keys:
    889: +   -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
    890: .   -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
    891: .   -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
    892:                              vectors are allocated as needed)
    893: .   -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
    894: .   -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
    895: .   -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
    896:                                    stability of the classical Gram-Schmidt  orthogonalization.
    897: .   -ksp_gmres_krylov_monitor - plot the Krylov space generated
    898: .   -ksp_lgmres_constant - Use constant approx. space size
    899: -   -ksp_lgmres_augment <n> - Number of error approximations to augment the Krylov space with

    901:     Described in:
    902:      A. H. Baker, E.R. Jessup, and T.A. Manteuffel. A technique for
    903:      accelerating the convergence of restarted GMRES. Submitted to SIAM
    904:      Journal on Matrix Analysis and Applications. Also available as
    905:      Technical Report #CU-CS-945-03, University of Colorado, Department of
    906:      Computer Science, January, 2003.

    908:    Level: beginner

    910:    Notes:  This object is subclassed off of KSPGMRES

    912:    Contributed by: Allison Baker

    914: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPGMRES,
    915:            KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization()
    916:            KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
    917:            KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESKrylovMonitor(), KSPLGMRESSetAugDim(),
    918:            KSPGMRESSetConstant()

    920: M*/

    925: PetscErrorCode PETSCKSP_DLLEXPORT KSPCreate_LGMRES(KSP ksp)
    926: {
    927:   KSP_LGMRES     *lgmres;

    931:   PetscNew(KSP_LGMRES,&lgmres);
    932:   PetscLogObjectMemory(ksp,sizeof(KSP_LGMRES));
    933:   ksp->data                              = (void*)lgmres;
    934:   ksp->ops->buildsolution                = KSPBuildSolution_LGMRES;

    936:   ksp->ops->setup                        = KSPSetUp_LGMRES;
    937:   ksp->ops->solve                        = KSPSolve_LGMRES;
    938:   ksp->ops->destroy                      = KSPDestroy_LGMRES;
    939:   ksp->ops->view                         = KSPView_LGMRES;
    940:   ksp->ops->setfromoptions               = KSPSetFromOptions_LGMRES;
    941:   ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
    942:   ksp->ops->computeeigenvalues           = KSPComputeEigenvalues_GMRES;

    944:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",
    945:                                     "KSPGMRESSetPreAllocateVectors_GMRES",
    946:                                      KSPGMRESSetPreAllocateVectors_GMRES);
    947:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",
    948:                                     "KSPGMRESSetOrthogonalization_GMRES",
    949:                                      KSPGMRESSetOrthogonalization_GMRES);
    950:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetRestart_C",
    951:                                     "KSPGMRESSetRestart_GMRES",
    952:                                      KSPGMRESSetRestart_GMRES);
    953:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetHapTol_C",
    954:                                     "KSPGMRESSetHapTol_GMRES",
    955:                                      KSPGMRESSetHapTol_GMRES);
    956:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",
    957:                                     "KSPGMRESSetCGSRefinementType_GMRES",
    958:                                      KSPGMRESSetCGSRefinementType_GMRES);

    960:   /*LGMRES_MOD add extra functions here - like the one to set num of aug vectors */
    961:    PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPLGMRESSetConstant_C",
    962:                                      "KSPLGMRESSetConstant_LGMRES",
    963:                                       KSPLGMRESSetConstant_LGMRES);

    965:   PetscObjectComposeFunctionDynamic((PetscObject)ksp,"KSPLGMRESSetAugDim_C",
    966:                                     "KSPLGMRESSetAugDim_LGMRES",
    967:                                      KSPLGMRESSetAugDim_LGMRES);
    968:

    970:   /*defaults */
    971:   lgmres->haptol              = 1.0e-30;
    972:   lgmres->q_preallocate       = 0;
    973:   lgmres->delta_allocate      = LGMRES_DELTA_DIRECTIONS;
    974:   lgmres->orthog              = KSPGMRESClassicalGramSchmidtOrthogonalization;
    975:   lgmres->nrs                 = 0;
    976:   lgmres->sol_temp            = 0;
    977:   lgmres->max_k               = LGMRES_DEFAULT_MAXK;
    978:   lgmres->Rsvd                = 0;
    979:   lgmres->cgstype             = KSP_GMRES_CGS_REFINE_NEVER;
    980:   /*LGMRES_MOD - new defaults */
    981:   lgmres->aug_dim             = LGMRES_DEFAULT_AUGDIM;
    982:   lgmres->aug_ct              = 0; /* start with no aug vectors */
    983:   lgmres->approx_constant     = 0;
    984:   lgmres->matvecs             = 0;

    986:   return(0);
    987: }