impls/mg/mg.c

/*
    Defines the multigrid preconditioner interface.
*/
#include <petsc-private/pcmgimpl.h>                    /*I "petscksp.h" I*/
#include <petscdm.h>

#undef __FUNCT__
#define __FUNCT__ "PCMGMCycle_Private"
PetscErrorCode PCMGMCycle_Private(PC pc,PC_MG_Levels **mglevelsin,PCRichardsonConvergedReason *reason)
{
  PC_MG          *mg = (PC_MG*)pc->data;
  PC_MG_Levels   *mgc,*mglevels = *mglevelsin;
  PetscErrorCode ierr;
  PetscInt       cycles = (mglevels->level == 1) ? 1 : (PetscInt) mglevels->cycles;

  PetscFunctionBegin;
  if (mglevels->eventsmoothsolve) {ierr = PetscLogEventBegin(mglevels->eventsmoothsolve,0,0,0,0);CHKERRQ(ierr);}
  ierr = KSPSolve(mglevels->smoothd,mglevels->b,mglevels->x);CHKERRQ(ierr);  /* pre-smooth */
  if (mglevels->eventsmoothsolve) {ierr = PetscLogEventEnd(mglevels->eventsmoothsolve,0,0,0,0);CHKERRQ(ierr);}
  if (mglevels->level) {  /* not the coarsest grid */
    if (mglevels->eventresidual) {ierr = PetscLogEventBegin(mglevels->eventresidual,0,0,0,0);CHKERRQ(ierr);}
    ierr = (*mglevels->residual)(mglevels->A,mglevels->b,mglevels->x,mglevels->r);CHKERRQ(ierr);
    if (mglevels->eventresidual) {ierr = PetscLogEventEnd(mglevels->eventresidual,0,0,0,0);CHKERRQ(ierr);}

    /* if on finest level and have convergence criteria set */
    if (mglevels->level == mglevels->levels-1 && mg->ttol && reason) {
      PetscReal rnorm;
      ierr = VecNorm(mglevels->r,NORM_2,&rnorm);CHKERRQ(ierr);
      if (rnorm <= mg->ttol) {
        if (rnorm < mg->abstol) {
          *reason = PCRICHARDSON_CONVERGED_ATOL;
          ierr    = PetscInfo2(pc,"Linear solver has converged. Residual norm %g is less than absolute tolerance %g\n",(double)rnorm,(double)mg->abstol);CHKERRQ(ierr);
        } else {
          *reason = PCRICHARDSON_CONVERGED_RTOL;
          ierr    = PetscInfo2(pc,"Linear solver has converged. Residual norm %g is less than relative tolerance times initial residual norm %g\n",(double)rnorm,(double)mg->ttol);CHKERRQ(ierr);
        }
        PetscFunctionReturn(0);
      }
    }

    mgc = *(mglevelsin - 1);
    if (mglevels->eventinterprestrict) {ierr = PetscLogEventBegin(mglevels->eventinterprestrict,0,0,0,0);CHKERRQ(ierr);}
    ierr = MatRestrict(mglevels->restrct,mglevels->r,mgc->b);CHKERRQ(ierr);
    if (mglevels->eventinterprestrict) {ierr = PetscLogEventEnd(mglevels->eventinterprestrict,0,0,0,0);CHKERRQ(ierr);}
    ierr = VecSet(mgc->x,0.0);CHKERRQ(ierr);
    while (cycles--) {
      ierr = PCMGMCycle_Private(pc,mglevelsin-1,reason);CHKERRQ(ierr);
    }
    if (mglevels->eventinterprestrict) {ierr = PetscLogEventBegin(mglevels->eventinterprestrict,0,0,0,0);CHKERRQ(ierr);}
    ierr = MatInterpolateAdd(mglevels->interpolate,mgc->x,mglevels->x,mglevels->x);CHKERRQ(ierr);
    if (mglevels->eventinterprestrict) {ierr = PetscLogEventEnd(mglevels->eventinterprestrict,0,0,0,0);CHKERRQ(ierr);}
    if (mglevels->eventsmoothsolve) {ierr = PetscLogEventBegin(mglevels->eventsmoothsolve,0,0,0,0);CHKERRQ(ierr);}
    ierr = KSPSolve(mglevels->smoothu,mglevels->b,mglevels->x);CHKERRQ(ierr);    /* post smooth */
    if (mglevels->eventsmoothsolve) {ierr = PetscLogEventEnd(mglevels->eventsmoothsolve,0,0,0,0);CHKERRQ(ierr);}
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCApplyRichardson_MG"
static PetscErrorCode PCApplyRichardson_MG(PC pc,Vec b,Vec x,Vec w,PetscReal rtol,PetscReal abstol, PetscReal dtol,PetscInt its,PetscBool zeroguess,PetscInt *outits,PCRichardsonConvergedReason *reason)
{
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscErrorCode ierr;
  PetscInt       levels = mglevels[0]->levels,i;

  PetscFunctionBegin;
  /* When the DM is supplying the matrix then it will not exist until here */
  for (i=0; i<levels; i++) {
    if (!mglevels[i]->A) {
      ierr = KSPGetOperators(mglevels[i]->smoothu,&mglevels[i]->A,NULL);CHKERRQ(ierr);
      ierr = PetscObjectReference((PetscObject)mglevels[i]->A);CHKERRQ(ierr);
    }
  }
  mglevels[levels-1]->b = b;
  mglevels[levels-1]->x = x;

  mg->rtol   = rtol;
  mg->abstol = abstol;
  mg->dtol   = dtol;
  if (rtol) {
    /* compute initial residual norm for relative convergence test */
    PetscReal rnorm;
    if (zeroguess) {
      ierr = VecNorm(b,NORM_2,&rnorm);CHKERRQ(ierr);
    } else {
      ierr = (*mglevels[levels-1]->residual)(mglevels[levels-1]->A,b,x,w);CHKERRQ(ierr);
      ierr = VecNorm(w,NORM_2,&rnorm);CHKERRQ(ierr);
    }
    mg->ttol = PetscMax(rtol*rnorm,abstol);
  } else if (abstol) mg->ttol = abstol;
  else mg->ttol = 0.0;

  /* since smoother is applied to full system, not just residual we need to make sure that smoothers don't
     stop prematurely due to small residual */
  for (i=1; i<levels; i++) {
    ierr = KSPSetTolerances(mglevels[i]->smoothu,0,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
    if (mglevels[i]->smoothu != mglevels[i]->smoothd) {
      ierr = KSPSetTolerances(mglevels[i]->smoothd,0,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
    }
  }

  *reason = (PCRichardsonConvergedReason)0;
  for (i=0; i<its; i++) {
    ierr = PCMGMCycle_Private(pc,mglevels+levels-1,reason);CHKERRQ(ierr);
    if (*reason) break;
  }
  if (!*reason) *reason = PCRICHARDSON_CONVERGED_ITS;
  *outits = i;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCReset_MG"
PetscErrorCode PCReset_MG(PC pc)
{
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscErrorCode ierr;
  PetscInt       i,n;

  PetscFunctionBegin;
  if (mglevels) {
    n = mglevels[0]->levels;
    for (i=0; i<n-1; i++) {
      ierr = VecDestroy(&mglevels[i+1]->r);CHKERRQ(ierr);
      ierr = VecDestroy(&mglevels[i]->b);CHKERRQ(ierr);
      ierr = VecDestroy(&mglevels[i]->x);CHKERRQ(ierr);
      ierr = MatDestroy(&mglevels[i+1]->restrct);CHKERRQ(ierr);
      ierr = MatDestroy(&mglevels[i+1]->interpolate);CHKERRQ(ierr);
      ierr = VecDestroy(&mglevels[i+1]->rscale);CHKERRQ(ierr);
    }

    for (i=0; i<n; i++) {
      ierr = MatDestroy(&mglevels[i]->A);CHKERRQ(ierr);
      if (mglevels[i]->smoothd != mglevels[i]->smoothu) {
        ierr = KSPReset(mglevels[i]->smoothd);CHKERRQ(ierr);
      }
      ierr = KSPReset(mglevels[i]->smoothu);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCMGSetLevels"
/*@C
   PCMGSetLevels - Sets the number of levels to use with MG.
   Must be called before any other MG routine.

   Logically Collective on PC

   Input Parameters:
+  pc - the preconditioner context
.  levels - the number of levels
-  comms - optional communicators for each level; this is to allow solving the coarser problems
           on smaller sets of processors. Use NULL_OBJECT for default in Fortran

   Level: intermediate

   Notes:
     If the number of levels is one then the multigrid uses the -mg_levels prefix
  for setting the level options rather than the -mg_coarse prefix.

.keywords: MG, set, levels, multigrid

.seealso: PCMGSetType(), PCMGGetLevels()
@*/
PetscErrorCode  PCMGSetLevels(PC pc,PetscInt levels,MPI_Comm *comms)
{
  PetscErrorCode ierr;
  PC_MG          *mg        = (PC_MG*)pc->data;
  MPI_Comm       comm;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscInt       i;
  PetscMPIInt    size;
  const char     *prefix;
  PC             ipc;
  PetscInt       n;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscValidLogicalCollectiveInt(pc,levels,2);
  ierr = PetscObjectGetComm((PetscObject)pc,&comm);CHKERRQ(ierr);
  if (mg->nlevels == levels) PetscFunctionReturn(0);
  if (mglevels) {
    /* changing the number of levels so free up the previous stuff */
    ierr = PCReset_MG(pc);CHKERRQ(ierr);
    n    = mglevels[0]->levels;
    for (i=0; i<n; i++) {
      if (mglevels[i]->smoothd != mglevels[i]->smoothu) {
        ierr = KSPDestroy(&mglevels[i]->smoothd);CHKERRQ(ierr);
      }
      ierr = KSPDestroy(&mglevels[i]->smoothu);CHKERRQ(ierr);
      ierr = PetscFree(mglevels[i]);CHKERRQ(ierr);
    }
    ierr = PetscFree(mg->levels);CHKERRQ(ierr);
  }

  mg->nlevels = levels;

  ierr = PetscMalloc1(levels,&mglevels);CHKERRQ(ierr);
  ierr = PetscLogObjectMemory((PetscObject)pc,levels*(sizeof(PC_MG*)));CHKERRQ(ierr);

  ierr = PCGetOptionsPrefix(pc,&prefix);CHKERRQ(ierr);

  mg->stageApply = 0;
  for (i=0; i<levels; i++) {
    ierr = PetscNewLog(pc,&mglevels[i]);CHKERRQ(ierr);

    mglevels[i]->level               = i;
    mglevels[i]->levels              = levels;
    mglevels[i]->cycles              = PC_MG_CYCLE_V;
    mg->default_smoothu              = 2;
    mg->default_smoothd              = 2;
    mglevels[i]->eventsmoothsetup    = 0;
    mglevels[i]->eventsmoothsolve    = 0;
    mglevels[i]->eventresidual       = 0;
    mglevels[i]->eventinterprestrict = 0;

    if (comms) comm = comms[i];
    ierr = KSPCreate(comm,&mglevels[i]->smoothd);CHKERRQ(ierr);
    ierr = KSPSetType(mglevels[i]->smoothd,KSPCHEBYSHEV);CHKERRQ(ierr);
    ierr = KSPSetConvergenceTest(mglevels[i]->smoothd,KSPConvergedSkip,NULL,NULL);CHKERRQ(ierr);
    ierr = KSPSetNormType(mglevels[i]->smoothd,KSP_NORM_NONE);CHKERRQ(ierr);
    ierr = KSPGetPC(mglevels[i]->smoothd,&ipc);CHKERRQ(ierr);
    ierr = PCSetType(ipc,PCSOR);CHKERRQ(ierr);
    ierr = PetscObjectIncrementTabLevel((PetscObject)mglevels[i]->smoothd,(PetscObject)pc,levels-i);CHKERRQ(ierr);
    ierr = KSPSetTolerances(mglevels[i]->smoothd,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT, i ? mg->default_smoothd : 1);CHKERRQ(ierr);
    ierr = KSPSetOptionsPrefix(mglevels[i]->smoothd,prefix);CHKERRQ(ierr);

    /* do special stuff for coarse grid */
    if (!i && levels > 1) {
      ierr = KSPAppendOptionsPrefix(mglevels[0]->smoothd,"mg_coarse_");CHKERRQ(ierr);

      /* coarse solve is (redundant) LU by default; set shifttype NONZERO to avoid annoying zero-pivot in LU preconditioner */
      ierr = KSPSetType(mglevels[0]->smoothd,KSPPREONLY);CHKERRQ(ierr);
      ierr = KSPGetPC(mglevels[0]->smoothd,&ipc);CHKERRQ(ierr);
      ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
      if (size > 1) {
        KSP innerksp;
        PC  innerpc;
        ierr = PCSetType(ipc,PCREDUNDANT);CHKERRQ(ierr);
        ierr = PCRedundantGetKSP(ipc,&innerksp);CHKERRQ(ierr);
        ierr = KSPGetPC(innerksp,&innerpc);CHKERRQ(ierr);
        ierr = PCFactorSetShiftType(innerpc,MAT_SHIFT_INBLOCKS);CHKERRQ(ierr);
      } else {
        ierr = PCSetType(ipc,PCLU);CHKERRQ(ierr);
        ierr = PCFactorSetShiftType(ipc,MAT_SHIFT_INBLOCKS);CHKERRQ(ierr);
      }
    } else {
      char tprefix[128];
      sprintf(tprefix,"mg_levels_%d_",(int)i);
      ierr = KSPAppendOptionsPrefix(mglevels[i]->smoothd,tprefix);CHKERRQ(ierr);
    }
    ierr = PetscLogObjectParent((PetscObject)pc,(PetscObject)mglevels[i]->smoothd);CHKERRQ(ierr);

    mglevels[i]->smoothu = mglevels[i]->smoothd;
    mg->rtol             = 0.0;
    mg->abstol           = 0.0;
    mg->dtol             = 0.0;
    mg->ttol             = 0.0;
    mg->cyclesperpcapply = 1;
  }
  mg->am                   = PC_MG_MULTIPLICATIVE;
  mg->levels               = mglevels;
  pc->ops->applyrichardson = PCApplyRichardson_MG;
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "PCDestroy_MG"
PetscErrorCode PCDestroy_MG(PC pc)
{
  PetscErrorCode ierr;
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscInt       i,n;

  PetscFunctionBegin;
  ierr = PCReset_MG(pc);CHKERRQ(ierr);
  if (mglevels) {
    n = mglevels[0]->levels;
    for (i=0; i<n; i++) {
      if (mglevels[i]->smoothd != mglevels[i]->smoothu) {
        ierr = KSPDestroy(&mglevels[i]->smoothd);CHKERRQ(ierr);
      }
      ierr = KSPDestroy(&mglevels[i]->smoothu);CHKERRQ(ierr);
      ierr = PetscFree(mglevels[i]);CHKERRQ(ierr);
    }
    ierr = PetscFree(mg->levels);CHKERRQ(ierr);
  }
  ierr = PetscFree(pc->data);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


extern PetscErrorCode PCMGACycle_Private(PC,PC_MG_Levels**);
extern PetscErrorCode PCMGFCycle_Private(PC,PC_MG_Levels**);
extern PetscErrorCode PCMGKCycle_Private(PC,PC_MG_Levels**);

/*
   PCApply_MG - Runs either an additive, multiplicative, Kaskadic
             or full cycle of multigrid.

  Note:
  A simple wrapper which calls PCMGMCycle(),PCMGACycle(), or PCMGFCycle().
*/
#undef __FUNCT__
#define __FUNCT__ "PCApply_MG"
static PetscErrorCode PCApply_MG(PC pc,Vec b,Vec x)
{
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscErrorCode ierr;
  PetscInt       levels = mglevels[0]->levels,i;

  PetscFunctionBegin;
  if (mg->stageApply) {ierr = PetscLogStagePush(mg->stageApply);CHKERRQ(ierr);}
  /* When the DM is supplying the matrix then it will not exist until here */
  for (i=0; i<levels; i++) {
    if (!mglevels[i]->A) {
      ierr = KSPGetOperators(mglevels[i]->smoothu,&mglevels[i]->A,NULL);CHKERRQ(ierr);
      ierr = PetscObjectReference((PetscObject)mglevels[i]->A);CHKERRQ(ierr);
    }
  }

  mglevels[levels-1]->b = b;
  mglevels[levels-1]->x = x;
  if (mg->am == PC_MG_MULTIPLICATIVE) {
    ierr = VecSet(x,0.0);CHKERRQ(ierr);
    for (i=0; i<mg->cyclesperpcapply; i++) {
      ierr = PCMGMCycle_Private(pc,mglevels+levels-1,NULL);CHKERRQ(ierr);
    }
  } else if (mg->am == PC_MG_ADDITIVE) {
    ierr = PCMGACycle_Private(pc,mglevels);CHKERRQ(ierr);
  } else if (mg->am == PC_MG_KASKADE) {
    ierr = PCMGKCycle_Private(pc,mglevels);CHKERRQ(ierr);
  } else {
    ierr = PCMGFCycle_Private(pc,mglevels);CHKERRQ(ierr);
  }
  if (mg->stageApply) {ierr = PetscLogStagePop();CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "PCSetFromOptions_MG"
PetscErrorCode PCSetFromOptions_MG(PetscOptions *PetscOptionsObject,PC pc)
{
  PetscErrorCode ierr;
  PetscInt       m,levels = 1,cycles;
  PetscBool      flg,set;
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PCMGType       mgtype;
  PCMGCycleType  mgctype;

  PetscFunctionBegin;
  ierr = PetscOptionsHead(PetscOptionsObject,"Multigrid options");CHKERRQ(ierr);
  if (!mg->levels) {
    ierr = PetscOptionsInt("-pc_mg_levels","Number of Levels","PCMGSetLevels",levels,&levels,&flg);CHKERRQ(ierr);
    if (!flg && pc->dm) {
      ierr = DMGetRefineLevel(pc->dm,&levels);CHKERRQ(ierr);
      levels++;
      mg->usedmfornumberoflevels = PETSC_TRUE;
    }
    ierr = PCMGSetLevels(pc,levels,NULL);CHKERRQ(ierr);
  }
  mglevels = mg->levels;

  mgctype = (PCMGCycleType) mglevels[0]->cycles;
  ierr    = PetscOptionsEnum("-pc_mg_cycle_type","V cycle or for W-cycle","PCMGSetCycleType",PCMGCycleTypes,(PetscEnum)mgctype,(PetscEnum*)&mgctype,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PCMGSetCycleType(pc,mgctype);CHKERRQ(ierr);
  }
  flg  = PETSC_FALSE;
  ierr = PetscOptionsBool("-pc_mg_galerkin","Use Galerkin process to compute coarser operators","PCMGSetGalerkin",flg,&flg,&set);CHKERRQ(ierr);
  if (set) {
    ierr = PCMGSetGalerkin(pc,flg);CHKERRQ(ierr);
  }
  ierr = PetscOptionsInt("-pc_mg_smoothup","Number of post-smoothing steps","PCMGSetNumberSmoothUp",mg->default_smoothu,&m,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PCMGSetNumberSmoothUp(pc,m);CHKERRQ(ierr);
  }
  ierr = PetscOptionsInt("-pc_mg_smoothdown","Number of pre-smoothing steps","PCMGSetNumberSmoothDown",mg->default_smoothd,&m,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PCMGSetNumberSmoothDown(pc,m);CHKERRQ(ierr);
  }
  mgtype = mg->am;
  ierr   = PetscOptionsEnum("-pc_mg_type","Multigrid type","PCMGSetType",PCMGTypes,(PetscEnum)mgtype,(PetscEnum*)&mgtype,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PCMGSetType(pc,mgtype);CHKERRQ(ierr);
  }
  if (mg->am == PC_MG_MULTIPLICATIVE) {
    ierr = PetscOptionsInt("-pc_mg_multiplicative_cycles","Number of cycles for each preconditioner step","PCMGSetLevels",mg->cyclesperpcapply,&cycles,&flg);CHKERRQ(ierr);
    if (flg) {
      ierr = PCMGMultiplicativeSetCycles(pc,cycles);CHKERRQ(ierr);
    }
  }
  flg  = PETSC_FALSE;
  ierr = PetscOptionsBool("-pc_mg_log","Log times for each multigrid level","None",flg,&flg,NULL);CHKERRQ(ierr);
  if (flg) {
    PetscInt i;
    char     eventname[128];
    if (!mglevels) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must set MG levels before calling");
    levels = mglevels[0]->levels;
    for (i=0; i<levels; i++) {
      sprintf(eventname,"MGSetup Level %d",(int)i);
      ierr = PetscLogEventRegister(eventname,((PetscObject)pc)->classid,&mglevels[i]->eventsmoothsetup);CHKERRQ(ierr);
      sprintf(eventname,"MGSmooth Level %d",(int)i);
      ierr = PetscLogEventRegister(eventname,((PetscObject)pc)->classid,&mglevels[i]->eventsmoothsolve);CHKERRQ(ierr);
      if (i) {
        sprintf(eventname,"MGResid Level %d",(int)i);
        ierr = PetscLogEventRegister(eventname,((PetscObject)pc)->classid,&mglevels[i]->eventresidual);CHKERRQ(ierr);
        sprintf(eventname,"MGInterp Level %d",(int)i);
        ierr = PetscLogEventRegister(eventname,((PetscObject)pc)->classid,&mglevels[i]->eventinterprestrict);CHKERRQ(ierr);
      }
    }

#if defined(PETSC_USE_LOG)
    {
      const char    *sname = "MG Apply";
      PetscStageLog stageLog;
      PetscInt      st;

      PetscFunctionBegin;
      ierr = PetscLogGetStageLog(&stageLog);CHKERRQ(ierr);
      for (st = 0; st < stageLog->numStages; ++st) {
        PetscBool same;

        ierr = PetscStrcmp(stageLog->stageInfo[st].name, sname, &same);CHKERRQ(ierr);
        if (same) mg->stageApply = st;
      }
      if (!mg->stageApply) {
        ierr = PetscLogStageRegister(sname, &mg->stageApply);CHKERRQ(ierr);
      }
    }
#endif
  }
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

const char *const PCMGTypes[] = {"MULTIPLICATIVE","ADDITIVE","FULL","KASKADE","PCMGType","PC_MG",0};
const char *const PCMGCycleTypes[] = {"invalid","v","w","PCMGCycleType","PC_MG_CYCLE",0};

#include <petscdraw.h>
#undef __FUNCT__
#define __FUNCT__ "PCView_MG"
PetscErrorCode PCView_MG(PC pc,PetscViewer viewer)
{
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscErrorCode ierr;
  PetscInt       levels = mglevels ? mglevels[0]->levels : 0,i;
  PetscBool      iascii,isbinary,isdraw;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
  if (iascii) {
    const char *cyclename = levels ? (mglevels[0]->cycles == PC_MG_CYCLE_V ? "v" : "w") : "unknown";
    ierr = PetscViewerASCIIPrintf(viewer,"  MG: type is %s, levels=%D cycles=%s\n", PCMGTypes[mg->am],levels,cyclename);CHKERRQ(ierr);
    if (mg->am == PC_MG_MULTIPLICATIVE) {
      ierr = PetscViewerASCIIPrintf(viewer,"    Cycles per PCApply=%d\n",mg->cyclesperpcapply);CHKERRQ(ierr);
    }
    if (mg->galerkin) {
      ierr = PetscViewerASCIIPrintf(viewer,"    Using Galerkin computed coarse grid matrices\n");CHKERRQ(ierr);
    } else {
      ierr = PetscViewerASCIIPrintf(viewer,"    Not using Galerkin computed coarse grid matrices\n");CHKERRQ(ierr);
    }
    for (i=0; i<levels; i++) {
      if (!i) {
        ierr = PetscViewerASCIIPrintf(viewer,"Coarse grid solver -- level -------------------------------\n",i);CHKERRQ(ierr);
      } else {
        ierr = PetscViewerASCIIPrintf(viewer,"Down solver (pre-smoother) on level %D -------------------------------\n",i);CHKERRQ(ierr);
      }
      ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
      ierr = KSPView(mglevels[i]->smoothd,viewer);CHKERRQ(ierr);
      ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
      if (i && mglevels[i]->smoothd == mglevels[i]->smoothu) {
        ierr = PetscViewerASCIIPrintf(viewer,"Up solver (post-smoother) same as down solver (pre-smoother)\n");CHKERRQ(ierr);
      } else if (i) {
        ierr = PetscViewerASCIIPrintf(viewer,"Up solver (post-smoother) on level %D -------------------------------\n",i);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
        ierr = KSPView(mglevels[i]->smoothu,viewer);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
      }
    }
  } else if (isbinary) {
    for (i=levels-1; i>=0; i--) {
      ierr = KSPView(mglevels[i]->smoothd,viewer);CHKERRQ(ierr);
      if (i && mglevels[i]->smoothd != mglevels[i]->smoothu) {
        ierr = KSPView(mglevels[i]->smoothu,viewer);CHKERRQ(ierr);
      }
    }
  } else if (isdraw) {
    PetscDraw draw;
    PetscReal x,w,y,bottom,th;
    ierr   = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
    ierr   = PetscDrawGetCurrentPoint(draw,&x,&y);CHKERRQ(ierr);
    ierr   = PetscDrawStringGetSize(draw,NULL,&th);CHKERRQ(ierr);
    bottom = y - th;
    for (i=levels-1; i>=0; i--) {
      if (!mglevels[i]->smoothu || (mglevels[i]->smoothu == mglevels[i]->smoothd)) {
        ierr = PetscDrawPushCurrentPoint(draw,x,bottom);CHKERRQ(ierr);
        ierr = KSPView(mglevels[i]->smoothd,viewer);CHKERRQ(ierr);
        ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
      } else {
        w    = 0.5*PetscMin(1.0-x,x);
        ierr = PetscDrawPushCurrentPoint(draw,x+w,bottom);CHKERRQ(ierr);
        ierr = KSPView(mglevels[i]->smoothd,viewer);CHKERRQ(ierr);
        ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
        ierr = PetscDrawPushCurrentPoint(draw,x-w,bottom);CHKERRQ(ierr);
        ierr = KSPView(mglevels[i]->smoothu,viewer);CHKERRQ(ierr);
        ierr = PetscDrawPopCurrentPoint(draw);CHKERRQ(ierr);
      }
      ierr    = PetscDrawGetBoundingBox(draw,NULL,&bottom,NULL,NULL);CHKERRQ(ierr);
      bottom -= th;
    }
  }
  PetscFunctionReturn(0);
}

#include <petsc-private/dmimpl.h>
#include <petsc-private/kspimpl.h>

/*
    Calls setup for the KSP on each level
*/
#undef __FUNCT__
#define __FUNCT__ "PCSetUp_MG"
PetscErrorCode PCSetUp_MG(PC pc)
{
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscErrorCode ierr;
  PetscInt       i,n = mglevels[0]->levels;
  PC             cpc;
  PetscBool      preonly,lu,redundant,cholesky,svd,dump = PETSC_FALSE,opsset,use_amat;
  Mat            dA,dB;
  Vec            tvec;
  DM             *dms;
  PetscViewer    viewer = 0;

  PetscFunctionBegin;
  /* FIX: Move this to PCSetFromOptions_MG? */
  if (mg->usedmfornumberoflevels) {
    PetscInt levels;
    ierr = DMGetRefineLevel(pc->dm,&levels);CHKERRQ(ierr);
    levels++;
    if (levels > n) { /* the problem is now being solved on a finer grid */
      ierr     = PCMGSetLevels(pc,levels,NULL);CHKERRQ(ierr);
      n        = levels;
      ierr     = PCSetFromOptions(pc);CHKERRQ(ierr); /* it is bad to call this here, but otherwise will never be called for the new hierarchy */
      mglevels =  mg->levels;
    }
  }
  ierr = KSPGetPC(mglevels[0]->smoothd,&cpc);CHKERRQ(ierr);


  /* If user did not provide fine grid operators OR operator was not updated since last global KSPSetOperators() */
  /* so use those from global PC */
  /* Is this what we always want? What if user wants to keep old one? */
  ierr = KSPGetOperatorsSet(mglevels[n-1]->smoothd,NULL,&opsset);CHKERRQ(ierr);
  if (opsset) {
    Mat mmat;
    ierr = KSPGetOperators(mglevels[n-1]->smoothd,NULL,&mmat);CHKERRQ(ierr);
    if (mmat == pc->pmat) opsset = PETSC_FALSE;
  }

  if (!opsset) {
    ierr = PCGetUseAmat(pc,&use_amat);CHKERRQ(ierr);
    if(use_amat){
      ierr = PetscInfo(pc,"Using outer operators to define finest grid operator \n  because PCMGGetSmoother(pc,nlevels-1,&ksp);KSPSetOperators(ksp,...); was not called.\n");CHKERRQ(ierr);
      ierr = KSPSetOperators(mglevels[n-1]->smoothd,pc->mat,pc->pmat);CHKERRQ(ierr);
    }
    else {
      ierr = PetscInfo(pc,"Using matrix (pmat) operators to define finest grid operator \n  because PCMGGetSmoother(pc,nlevels-1,&ksp);KSPSetOperators(ksp,...); was not called.\n");CHKERRQ(ierr);
      ierr = KSPSetOperators(mglevels[n-1]->smoothd,pc->pmat,pc->pmat);CHKERRQ(ierr);
    }
  }

  /* Skipping this for galerkin==2 (externally managed hierarchy such as ML and GAMG). Cleaner logic here would be great. Wrap ML/GAMG as DMs? */
  if (pc->dm && mg->galerkin != 2 && !pc->setupcalled) {
    /* construct the interpolation from the DMs */
    Mat p;
    Vec rscale;
    ierr     = PetscMalloc1(n,&dms);CHKERRQ(ierr);
    dms[n-1] = pc->dm;
    /* Separately create them so we do not get DMKSP interference between levels */
    for (i=n-2; i>-1; i--) {ierr = DMCoarsen(dms[i+1],MPI_COMM_NULL,&dms[i]);CHKERRQ(ierr);}
    for (i=n-2; i>-1; i--) {
      DMKSP kdm;
      ierr = KSPSetDM(mglevels[i]->smoothd,dms[i]);CHKERRQ(ierr);
      if (mg->galerkin) {ierr = KSPSetDMActive(mglevels[i]->smoothd,PETSC_FALSE);CHKERRQ(ierr);}
      ierr = DMGetDMKSPWrite(dms[i],&kdm);CHKERRQ(ierr);
      /* Ugly hack so that the next KSPSetUp() will use the RHS that we set. A better fix is to change dmActive to take
       * a bitwise OR of computing the matrix, RHS, and initial iterate. */
      kdm->ops->computerhs = NULL;
      kdm->rhsctx          = NULL;
      if (!mglevels[i+1]->interpolate) {
        ierr = DMCreateInterpolation(dms[i],dms[i+1],&p,&rscale);CHKERRQ(ierr);
        ierr = PCMGSetInterpolation(pc,i+1,p);CHKERRQ(ierr);
        if (rscale) {ierr = PCMGSetRScale(pc,i+1,rscale);CHKERRQ(ierr);}
        ierr = VecDestroy(&rscale);CHKERRQ(ierr);
        ierr = MatDestroy(&p);CHKERRQ(ierr);
      }
    }

    for (i=n-2; i>-1; i--) {ierr = DMDestroy(&dms[i]);CHKERRQ(ierr);}
    ierr = PetscFree(dms);CHKERRQ(ierr);
  }

  if (pc->dm && !pc->setupcalled) {
    /* finest smoother also gets DM but it is not active, independent of whether galerkin==2 */
    ierr = KSPSetDM(mglevels[n-1]->smoothd,pc->dm);CHKERRQ(ierr);
    ierr = KSPSetDMActive(mglevels[n-1]->smoothd,PETSC_FALSE);CHKERRQ(ierr);
  }

  if (mg->galerkin == 1) {
    Mat B;
    /* currently only handle case where mat and pmat are the same on coarser levels */
    ierr = KSPGetOperators(mglevels[n-1]->smoothd,&dA,&dB);CHKERRQ(ierr);
    if (!pc->setupcalled) {
      for (i=n-2; i>-1; i--) {
        if (!mglevels[i+1]->restrct && !mglevels[i+1]->interpolate) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must provide interpolation or restriction for each MG level except level 0");
        if (!mglevels[i+1]->interpolate) {
          ierr = PCMGSetInterpolation(pc,i+1,mglevels[i+1]->restrct);CHKERRQ(ierr);
        }
        if (!mglevels[i+1]->restrct) {
          ierr = PCMGSetRestriction(pc,i+1,mglevels[i+1]->interpolate);CHKERRQ(ierr);
        }
        if (mglevels[i+1]->interpolate == mglevels[i+1]->restrct) {
          ierr = MatPtAP(dB,mglevels[i+1]->interpolate,MAT_INITIAL_MATRIX,1.0,&B);CHKERRQ(ierr);
        } else {
          ierr = MatMatMatMult(mglevels[i+1]->restrct,dB,mglevels[i+1]->interpolate,MAT_INITIAL_MATRIX,1.0,&B);CHKERRQ(ierr);
        }
        ierr = KSPSetOperators(mglevels[i]->smoothd,B,B);CHKERRQ(ierr);
        if (i != n-2) {ierr = PetscObjectDereference((PetscObject)dB);CHKERRQ(ierr);}
        dB = B;
      }
      if (n > 1) {ierr = PetscObjectDereference((PetscObject)dB);CHKERRQ(ierr);}
    } else {
      for (i=n-2; i>-1; i--) {
        if (!mglevels[i+1]->restrct && !mglevels[i+1]->interpolate) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must provide interpolation or restriction for each MG level except level 0");
        if (!mglevels[i+1]->interpolate) {
          ierr = PCMGSetInterpolation(pc,i+1,mglevels[i+1]->restrct);CHKERRQ(ierr);
        }
        if (!mglevels[i+1]->restrct) {
          ierr = PCMGSetRestriction(pc,i+1,mglevels[i+1]->interpolate);CHKERRQ(ierr);
        }
        ierr = KSPGetOperators(mglevels[i]->smoothd,NULL,&B);CHKERRQ(ierr);
        if (mglevels[i+1]->interpolate == mglevels[i+1]->restrct) {
          ierr = MatPtAP(dB,mglevels[i+1]->interpolate,MAT_REUSE_MATRIX,1.0,&B);CHKERRQ(ierr);
        } else {
          ierr = MatMatMatMult(mglevels[i+1]->restrct,dB,mglevels[i+1]->interpolate,MAT_REUSE_MATRIX,1.0,&B);CHKERRQ(ierr);
        }
        ierr = KSPSetOperators(mglevels[i]->smoothd,B,B);CHKERRQ(ierr);
        dB   = B;
      }
    }
  } else if (!mg->galerkin && pc->dm && pc->dm->x) {
    /* need to restrict Jacobian location to coarser meshes for evaluation */
    for (i=n-2; i>-1; i--) {
      Mat R;
      Vec rscale;
      if (!mglevels[i]->smoothd->dm->x) {
        Vec *vecs;
        ierr = KSPCreateVecs(mglevels[i]->smoothd,1,&vecs,0,NULL);CHKERRQ(ierr);

        mglevels[i]->smoothd->dm->x = vecs[0];

        ierr = PetscFree(vecs);CHKERRQ(ierr);
      }
      ierr = PCMGGetRestriction(pc,i+1,&R);CHKERRQ(ierr);
      ierr = PCMGGetRScale(pc,i+1,&rscale);CHKERRQ(ierr);
      ierr = MatRestrict(R,mglevels[i+1]->smoothd->dm->x,mglevels[i]->smoothd->dm->x);CHKERRQ(ierr);
      ierr = VecPointwiseMult(mglevels[i]->smoothd->dm->x,mglevels[i]->smoothd->dm->x,rscale);CHKERRQ(ierr);
    }
  }
  if (!mg->galerkin && pc->dm) {
    for (i=n-2; i>=0; i--) {
      DM  dmfine,dmcoarse;
      Mat Restrict,Inject;
      Vec rscale;
      ierr   = KSPGetDM(mglevels[i+1]->smoothd,&dmfine);CHKERRQ(ierr);
      ierr   = KSPGetDM(mglevels[i]->smoothd,&dmcoarse);CHKERRQ(ierr);
      ierr   = PCMGGetRestriction(pc,i+1,&Restrict);CHKERRQ(ierr);
      ierr   = PCMGGetRScale(pc,i+1,&rscale);CHKERRQ(ierr);
      Inject = NULL;      /* Callback should create it if it needs Injection */
      ierr   = DMRestrict(dmfine,Restrict,rscale,Inject,dmcoarse);CHKERRQ(ierr);
    }
  }

  if (!pc->setupcalled) {
    for (i=0; i<n; i++) {
      ierr = KSPSetFromOptions(mglevels[i]->smoothd);CHKERRQ(ierr);
    }
    for (i=1; i<n; i++) {
      if (mglevels[i]->smoothu && (mglevels[i]->smoothu != mglevels[i]->smoothd)) {
        ierr = KSPSetFromOptions(mglevels[i]->smoothu);CHKERRQ(ierr);
      }
    }
    for (i=1; i<n; i++) {
      ierr = PCMGGetInterpolation(pc,i,&mglevels[i]->interpolate);CHKERRQ(ierr);
      ierr = PCMGGetRestriction(pc,i,&mglevels[i]->restrct);CHKERRQ(ierr);
    }
    for (i=0; i<n-1; i++) {
      if (!mglevels[i]->b) {
        Vec *vec;
        ierr = KSPCreateVecs(mglevels[i]->smoothd,1,&vec,0,NULL);CHKERRQ(ierr);
        ierr = PCMGSetRhs(pc,i,*vec);CHKERRQ(ierr);
        ierr = VecDestroy(vec);CHKERRQ(ierr);
        ierr = PetscFree(vec);CHKERRQ(ierr);
      }
      if (!mglevels[i]->r && i) {
        ierr = VecDuplicate(mglevels[i]->b,&tvec);CHKERRQ(ierr);
        ierr = PCMGSetR(pc,i,tvec);CHKERRQ(ierr);
        ierr = VecDestroy(&tvec);CHKERRQ(ierr);
      }
      if (!mglevels[i]->x) {
        ierr = VecDuplicate(mglevels[i]->b,&tvec);CHKERRQ(ierr);
        ierr = PCMGSetX(pc,i,tvec);CHKERRQ(ierr);
        ierr = VecDestroy(&tvec);CHKERRQ(ierr);
      }
    }
    if (n != 1 && !mglevels[n-1]->r) {
      /* PCMGSetR() on the finest level if user did not supply it */
      Vec *vec;
      ierr = KSPCreateVecs(mglevels[n-1]->smoothd,1,&vec,0,NULL);CHKERRQ(ierr);
      ierr = PCMGSetR(pc,n-1,*vec);CHKERRQ(ierr);
      ierr = VecDestroy(vec);CHKERRQ(ierr);
      ierr = PetscFree(vec);CHKERRQ(ierr);
    }
  }

  if (pc->dm) {
    /* need to tell all the coarser levels to rebuild the matrix using the DM for that level */
    for (i=0; i<n-1; i++) {
      if (mglevels[i]->smoothd->setupstage != KSP_SETUP_NEW) mglevels[i]->smoothd->setupstage = KSP_SETUP_NEWMATRIX;
    }
  }

  for (i=1; i<n; i++) {
    if (mglevels[i]->smoothu == mglevels[i]->smoothd || mg->am == PC_MG_FULL || mg->am == PC_MG_KASKADE || mg->cyclesperpcapply > 1){
      /* if doing only down then initial guess is zero */
      ierr = KSPSetInitialGuessNonzero(mglevels[i]->smoothd,PETSC_TRUE);CHKERRQ(ierr);
    }
    if (mglevels[i]->eventsmoothsetup) {ierr = PetscLogEventBegin(mglevels[i]->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
    ierr = KSPSetUp(mglevels[i]->smoothd);CHKERRQ(ierr);
    if (mglevels[i]->eventsmoothsetup) {ierr = PetscLogEventEnd(mglevels[i]->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
    if (!mglevels[i]->residual) {
      Mat mat;
      ierr = KSPGetOperators(mglevels[i]->smoothd,NULL,&mat);CHKERRQ(ierr);
      ierr = PCMGSetResidual(pc,i,PCMGResidualDefault,mat);CHKERRQ(ierr);
    }
  }
  for (i=1; i<n; i++) {
    if (mglevels[i]->smoothu && mglevels[i]->smoothu != mglevels[i]->smoothd) {
      Mat          downmat,downpmat;

      /* check if operators have been set for up, if not use down operators to set them */
      ierr = KSPGetOperatorsSet(mglevels[i]->smoothu,&opsset,NULL);CHKERRQ(ierr);
      if (!opsset) {
        ierr = KSPGetOperators(mglevels[i]->smoothd,&downmat,&downpmat);CHKERRQ(ierr);
        ierr = KSPSetOperators(mglevels[i]->smoothu,downmat,downpmat);CHKERRQ(ierr);
      }

      ierr = KSPSetInitialGuessNonzero(mglevels[i]->smoothu,PETSC_TRUE);CHKERRQ(ierr);
      if (mglevels[i]->eventsmoothsetup) {ierr = PetscLogEventBegin(mglevels[i]->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
      ierr = KSPSetUp(mglevels[i]->smoothu);CHKERRQ(ierr);
      if (mglevels[i]->eventsmoothsetup) {ierr = PetscLogEventEnd(mglevels[i]->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
    }
  }

  /*
      If coarse solver is not direct method then DO NOT USE preonly
  */
  ierr = PetscObjectTypeCompare((PetscObject)mglevels[0]->smoothd,KSPPREONLY,&preonly);CHKERRQ(ierr);
  if (preonly) {
    ierr = PetscObjectTypeCompare((PetscObject)cpc,PCLU,&lu);CHKERRQ(ierr);
    ierr = PetscObjectTypeCompare((PetscObject)cpc,PCREDUNDANT,&redundant);CHKERRQ(ierr);
    ierr = PetscObjectTypeCompare((PetscObject)cpc,PCCHOLESKY,&cholesky);CHKERRQ(ierr);
    ierr = PetscObjectTypeCompare((PetscObject)cpc,PCSVD,&svd);CHKERRQ(ierr);
    if (!lu && !redundant && !cholesky && !svd) {
      ierr = KSPSetType(mglevels[0]->smoothd,KSPGMRES);CHKERRQ(ierr);
    }
  }

  if (!pc->setupcalled) {
    ierr = KSPSetFromOptions(mglevels[0]->smoothd);CHKERRQ(ierr);
  }

  if (mglevels[0]->eventsmoothsetup) {ierr = PetscLogEventBegin(mglevels[0]->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}
  ierr = KSPSetUp(mglevels[0]->smoothd);CHKERRQ(ierr);
  if (mglevels[0]->eventsmoothsetup) {ierr = PetscLogEventEnd(mglevels[0]->eventsmoothsetup,0,0,0,0);CHKERRQ(ierr);}

  /*
     Dump the interpolation/restriction matrices plus the
   Jacobian/stiffness on each level. This allows MATLAB users to
   easily check if the Galerkin condition A_c = R A_f R^T is satisfied.

   Only support one or the other at the same time.
  */
#if defined(PETSC_USE_SOCKET_VIEWER)
  ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_mg_dump_matlab",&dump,NULL);CHKERRQ(ierr);
  if (dump) viewer = PETSC_VIEWER_SOCKET_(PetscObjectComm((PetscObject)pc));
  dump = PETSC_FALSE;
#endif
  ierr = PetscOptionsGetBool(((PetscObject)pc)->prefix,"-pc_mg_dump_binary",&dump,NULL);CHKERRQ(ierr);
  if (dump) viewer = PETSC_VIEWER_BINARY_(PetscObjectComm((PetscObject)pc));

  if (viewer) {
    for (i=1; i<n; i++) {
      ierr = MatView(mglevels[i]->restrct,viewer);CHKERRQ(ierr);
    }
    for (i=0; i<n; i++) {
      ierr = KSPGetPC(mglevels[i]->smoothd,&pc);CHKERRQ(ierr);
      ierr = MatView(pc->mat,viewer);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------------------*/

#undef __FUNCT__
#define __FUNCT__ "PCMGGetLevels"
/*@
   PCMGGetLevels - Gets the number of levels to use with MG.

   Not Collective

   Input Parameter:
.  pc - the preconditioner context

   Output parameter:
.  levels - the number of levels

   Level: advanced

.keywords: MG, get, levels, multigrid

.seealso: PCMGSetLevels()
@*/
PetscErrorCode  PCMGGetLevels(PC pc,PetscInt *levels)
{
  PC_MG *mg = (PC_MG*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscValidIntPointer(levels,2);
  *levels = mg->nlevels;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCMGSetType"
/*@
   PCMGSetType - Determines the form of multigrid to use:
   multiplicative, additive, full, or the Kaskade algorithm.

   Logically Collective on PC

   Input Parameters:
+  pc - the preconditioner context
-  form - multigrid form, one of PC_MG_MULTIPLICATIVE, PC_MG_ADDITIVE,
   PC_MG_FULL, PC_MG_KASKADE

   Options Database Key:
.  -pc_mg_type <form> - Sets <form>, one of multiplicative,
   additive, full, kaskade

   Level: advanced

.keywords: MG, set, method, multiplicative, additive, full, Kaskade, multigrid

.seealso: PCMGSetLevels()
@*/
PetscErrorCode  PCMGSetType(PC pc,PCMGType form)
{
  PC_MG *mg = (PC_MG*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscValidLogicalCollectiveEnum(pc,form,2);
  mg->am = form;
  if (form == PC_MG_MULTIPLICATIVE) pc->ops->applyrichardson = PCApplyRichardson_MG;
  else pc->ops->applyrichardson = NULL;
  PetscFunctionReturn(0);
}

/*@
   PCMGGetType - Determines the form of multigrid to use:
   multiplicative, additive, full, or the Kaskade algorithm.

   Logically Collective on PC

   Input Parameter:
.  pc - the preconditioner context

   Output Parameter:
.  type - one of PC_MG_MULTIPLICATIVE, PC_MG_ADDITIVE,PC_MG_FULL, PC_MG_KASKADE


   Level: advanced

.keywords: MG, set, method, multiplicative, additive, full, Kaskade, multigrid

.seealso: PCMGSetLevels()
@*/
PetscErrorCode  PCMGGetType(PC pc,PCMGType *type)
{
  PC_MG *mg = (PC_MG*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  *type = mg->am;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCMGSetCycleType"
/*@
   PCMGSetCycleType - Sets the type cycles to use.  Use PCMGSetCycleTypeOnLevel() for more
   complicated cycling.

   Logically Collective on PC

   Input Parameters:
+  pc - the multigrid context
-  PC_MG_CYCLE_V or PC_MG_CYCLE_W

   Options Database Key:
.  -pc_mg_cycle_type <v,w>

   Level: advanced

.keywords: MG, set, cycles, V-cycle, W-cycle, multigrid

.seealso: PCMGSetCycleTypeOnLevel()
@*/
PetscErrorCode  PCMGSetCycleType(PC pc,PCMGCycleType n)
{
  PC_MG        *mg        = (PC_MG*)pc->data;
  PC_MG_Levels **mglevels = mg->levels;
  PetscInt     i,levels;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  if (!mglevels) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must set MG levels before calling");
  PetscValidLogicalCollectiveInt(pc,n,2);
  levels = mglevels[0]->levels;

  for (i=0; i<levels; i++) mglevels[i]->cycles = n;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCMGMultiplicativeSetCycles"
/*@
   PCMGMultiplicativeSetCycles - Sets the number of cycles to use for each preconditioner step
         of multigrid when PCMGType of PC_MG_MULTIPLICATIVE is used

   Logically Collective on PC

   Input Parameters:
+  pc - the multigrid context
-  n - number of cycles (default is 1)

   Options Database Key:
.  -pc_mg_multiplicative_cycles n

   Level: advanced

   Notes: This is not associated with setting a v or w cycle, that is set with PCMGSetCycleType()

.keywords: MG, set, cycles, V-cycle, W-cycle, multigrid

.seealso: PCMGSetCycleTypeOnLevel(), PCMGSetCycleType()
@*/
PetscErrorCode  PCMGMultiplicativeSetCycles(PC pc,PetscInt n)
{
  PC_MG        *mg        = (PC_MG*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  PetscValidLogicalCollectiveInt(pc,n,2);
  mg->cyclesperpcapply = n;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCMGSetGalerkin"
/*@
   PCMGSetGalerkin - Causes the coarser grid matrices to be computed from the
      finest grid via the Galerkin process: A_i-1 = r_i * A_i * p_i

   Logically Collective on PC

   Input Parameters:
+  pc - the multigrid context
-  use - PETSC_TRUE to use the Galerkin process to compute coarse-level operators

   Options Database Key:
.  -pc_mg_galerkin

   Level: intermediate

.keywords: MG, set, Galerkin

.seealso: PCMGGetGalerkin()

@*/
PetscErrorCode PCMGSetGalerkin(PC pc,PetscBool use)
{
  PC_MG *mg = (PC_MG*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  mg->galerkin = use ? 1 : 0;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCMGGetGalerkin"
/*@
   PCMGGetGalerkin - Checks if Galerkin multigrid is being used, i.e.
      A_i-1 = r_i * A_i * p_i

   Not Collective

   Input Parameter:
.  pc - the multigrid context

   Output Parameter:
.  galerkin - PETSC_TRUE or PETSC_FALSE

   Options Database Key:
.  -pc_mg_galerkin

   Level: intermediate

.keywords: MG, set, Galerkin

.seealso: PCMGSetGalerkin()

@*/
PetscErrorCode  PCMGGetGalerkin(PC pc,PetscBool  *galerkin)
{
  PC_MG *mg = (PC_MG*)pc->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  *galerkin = (PetscBool)mg->galerkin;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCMGSetNumberSmoothDown"
/*@
   PCMGSetNumberSmoothDown - Sets the number of pre-smoothing steps to
   use on all levels. Use PCMGGetSmootherDown() to set different
   pre-smoothing steps on different levels.

   Logically Collective on PC

   Input Parameters:
+  mg - the multigrid context
-  n - the number of smoothing steps

   Options Database Key:
.  -pc_mg_smoothdown <n> - Sets number of pre-smoothing steps

   Level: advanced

.keywords: MG, smooth, down, pre-smoothing, steps, multigrid

.seealso: PCMGSetNumberSmoothUp()
@*/
PetscErrorCode  PCMGSetNumberSmoothDown(PC pc,PetscInt n)
{
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscErrorCode ierr;
  PetscInt       i,levels;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  if (!mglevels) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must set MG levels before calling");
  PetscValidLogicalCollectiveInt(pc,n,2);
  levels = mglevels[0]->levels;

  for (i=1; i<levels; i++) {
    /* make sure smoother up and down are different */
    ierr = PCMGGetSmootherUp(pc,i,NULL);CHKERRQ(ierr);
    ierr = KSPSetTolerances(mglevels[i]->smoothd,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,n);CHKERRQ(ierr);

    mg->default_smoothd = n;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCMGSetNumberSmoothUp"
/*@
   PCMGSetNumberSmoothUp - Sets the number of post-smoothing steps to use
   on all levels. Use PCMGGetSmootherUp() to set different numbers of
   post-smoothing steps on different levels.

   Logically Collective on PC

   Input Parameters:
+  mg - the multigrid context
-  n - the number of smoothing steps

   Options Database Key:
.  -pc_mg_smoothup <n> - Sets number of post-smoothing steps

   Level: advanced

   Note: this does not set a value on the coarsest grid, since we assume that
    there is no separate smooth up on the coarsest grid.

.keywords: MG, smooth, up, post-smoothing, steps, multigrid

.seealso: PCMGSetNumberSmoothDown()
@*/
PetscErrorCode  PCMGSetNumberSmoothUp(PC pc,PetscInt n)
{
  PC_MG          *mg        = (PC_MG*)pc->data;
  PC_MG_Levels   **mglevels = mg->levels;
  PetscErrorCode ierr;
  PetscInt       i,levels;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  if (!mglevels) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Must set MG levels before calling");
  PetscValidLogicalCollectiveInt(pc,n,2);
  levels = mglevels[0]->levels;

  for (i=1; i<levels; i++) {
    /* make sure smoother up and down are different */
    ierr = PCMGGetSmootherUp(pc,i,NULL);CHKERRQ(ierr);
    ierr = KSPSetTolerances(mglevels[i]->smoothu,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,n);CHKERRQ(ierr);

    mg->default_smoothu = n;
  }
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------------------------------*/

/*MC
   PCMG - Use multigrid preconditioning. This preconditioner requires you provide additional
    information about the coarser grid matrices and restriction/interpolation operators.

   Options Database Keys:
+  -pc_mg_levels <nlevels> - number of levels including finest
.  -pc_mg_cycles <v,w> -
.  -pc_mg_smoothup <n> - number of smoothing steps after interpolation
.  -pc_mg_smoothdown <n> - number of smoothing steps before applying restriction operator
.  -pc_mg_type <additive,multiplicative,full,kaskade> - multiplicative is the default
.  -pc_mg_log - log information about time spent on each level of the solver
.  -pc_mg_monitor - print information on the multigrid convergence
.  -pc_mg_galerkin - use Galerkin process to compute coarser operators, i.e. Acoarse = R A R'
.  -pc_mg_multiplicative_cycles - number of cycles to use as the preconditioner (defaults to 1)
.  -pc_mg_dump_matlab - dumps the matrices for each level and the restriction/interpolation matrices
                        to the Socket viewer for reading from MATLAB.
-  -pc_mg_dump_binary - dumps the matrices for each level and the restriction/interpolation matrices
                        to the binary output file called binaryoutput

   Notes: By default this uses GMRES on the fine grid smoother so this should be used with KSPFGMRES or the smoother changed to not use GMRES

       When run with a single level the smoother options are used on that level NOT the coarse grid solver options

   Level: intermediate

   Concepts: multigrid/multilevel

.seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC, PCMGType, PCEXOTIC, PCGAMG, PCML, PCHYPRE
           PCMGSetLevels(), PCMGGetLevels(), PCMGSetType(), PCMGSetCycleType(), PCMGSetNumberSmoothDown(),
           PCMGSetNumberSmoothUp(), PCMGGetCoarseSolve(), PCMGSetResidual(), PCMGSetInterpolation(),
           PCMGSetRestriction(), PCMGGetSmoother(), PCMGGetSmootherUp(), PCMGGetSmootherDown(),
           PCMGSetCycleTypeOnLevel(), PCMGSetRhs(), PCMGSetX(), PCMGSetR()
M*/

#undef __FUNCT__
#define __FUNCT__ "PCCreate_MG"
PETSC_EXTERN PetscErrorCode PCCreate_MG(PC pc)
{
  PC_MG          *mg;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr        = PetscNewLog(pc,&mg);CHKERRQ(ierr);
  pc->data    = (void*)mg;
  mg->nlevels = -1;

  pc->useAmat = PETSC_TRUE;

  pc->ops->apply          = PCApply_MG;
  pc->ops->setup          = PCSetUp_MG;
  pc->ops->reset          = PCReset_MG;
  pc->ops->destroy        = PCDestroy_MG;
  pc->ops->setfromoptions = PCSetFromOptions_MG;
  pc->ops->view           = PCView_MG;
  PetscFunctionReturn(0);
}