impls/mg/mg.c

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

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;
  PC             subpc;
  PCFailedReason pcreason;

  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 */
  ierr = KSPGetPC(mglevels->smoothd,&subpc);CHKERRQ(ierr);
  ierr = PCGetSetUpFailedReason(subpc,&pcreason);CHKERRQ(ierr);
  if (pcreason) {
    pc->failedreason = PC_SUBPC_ERROR;
  }
  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);
}

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) {
      /* For Richardson the initial guess is nonzero since it is solving in each cycle the original system not just applying as a preconditioner */
      ierr = KSPSetInitialGuessNonzero(mglevels[i]->smoothd,PETSC_TRUE);CHKERRQ(ierr);
      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);
}

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);
}

/*@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.

   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;
  PCMGType       mgtype     = mg->am;
  PetscInt       mgctype    = (PetscInt) PC_MG_CYCLE_V;
  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) {
    mgctype = mglevels[0]->cycles;
    /* 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              = mgctype;
    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 = KSPSetErrorIfNotConverged(mglevels[i]->smoothd,pc->erroriffailure);CHKERRQ(ierr);
    ierr = PetscObjectIncrementTabLevel((PetscObject)mglevels[i]->smoothd,(PetscObject)pc,levels-i);CHKERRQ(ierr);
    ierr = KSPSetOptionsPrefix(mglevels[i]->smoothd,prefix);CHKERRQ(ierr);
    ierr = PetscObjectComposedDataSetInt((PetscObject) mglevels[i]->smoothd, PetscMGLevelId, mglevels[i]->level);CHKERRQ(ierr);
    if (i || levels == 1) {
      char tprefix[128];

      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 = KSPSetTolerances(mglevels[i]->smoothd,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT, mg->default_smoothd);CHKERRQ(ierr);

      sprintf(tprefix,"mg_levels_%d_",(int)i);
      ierr = KSPAppendOptionsPrefix(mglevels[i]->smoothd,tprefix);CHKERRQ(ierr);
    } else {
      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) {
        ierr = PCSetType(ipc,PCREDUNDANT);CHKERRQ(ierr);
      } else {
        ierr = PCSetType(ipc,PCLU);CHKERRQ(ierr);
      }
      ierr = PCFactorSetShiftType(ipc,MAT_SHIFT_INBLOCKS);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->levels = mglevels;
  ierr = PCMGSetType(pc,mgtype);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


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().
*/
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);
}


PetscErrorCode PCSetFromOptions_MG(PetscOptionItems *PetscOptionsObject,PC pc)
{
  PetscErrorCode   ierr;
  PetscInt         m,levels = 1,cycles;
  PetscBool        flg;
  PC_MG            *mg        = (PC_MG*)pc->data;
  PC_MG_Levels     **mglevels;
  PCMGType         mgtype;
  PCMGCycleType    mgctype;
  PCMGGalerkinType gtype;

  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);
  }
  gtype = mg->galerkin;
  ierr = PetscOptionsEnum("-pc_mg_galerkin","Use Galerkin process to compute coarser operators","PCMGSetGalerkin",PCMGGalerkinTypes,(PetscEnum)gtype,(PetscEnum*)&gtype,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PCMGSetGalerkin(pc,gtype);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","PCMGMultiplicativeSetCycles",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};
const char *const PCMGGalerkinTypes[] = {"both","pmat","mat","none","external","PCMGGalerkinType","PC_MG_GALERKIN",0};

#include <petscdraw.h>
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,"  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 == PC_MG_GALERKIN_BOTH) {
      ierr = PetscViewerASCIIPrintf(viewer,"    Using Galerkin computed coarse grid matrices\n");CHKERRQ(ierr);
    } else if (mg->galerkin == PC_MG_GALERKIN_PMAT) {
      ierr = PetscViewerASCIIPrintf(viewer,"    Using Galerkin computed coarse grid matrices for pmat\n");CHKERRQ(ierr);
    } else if (mg->galerkin == PC_MG_GALERKIN_MAT) {
      ierr = PetscViewerASCIIPrintf(viewer,"    Using Galerkin computed coarse grid matrices for mat\n");CHKERRQ(ierr);
    } else if (mg->galerkin == PC_MG_GALERKIN_EXTERNAL) {
      ierr = PetscViewerASCIIPrintf(viewer,"    Using externally compute Galerkin coarse grid matrices\n");CHKERRQ(ierr);
    } else {
      ierr = PetscViewerASCIIPrintf(viewer,"    Not using Galerkin computed coarse grid matrices\n");CHKERRQ(ierr);
    }
    if (mg->view){
      ierr = (*mg->view)(pc,viewer);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
*/
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      dump = PETSC_FALSE,opsset,use_amat,missinginterpolate = PETSC_FALSE;
  Mat            dA,dB;
  Vec            tvec;
  DM             *dms;
  PetscViewer    viewer = 0;
  PetscBool      dAeqdB = PETSC_FALSE, needRestricts = PETSC_FALSE;

  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);
    }
  }

  for (i=n-1; i>0; i--) {
    if (!(mglevels[i]->interpolate || mglevels[i]->restrct)) {
      missinginterpolate = PETSC_TRUE;
      continue;
    }
  }

  ierr = KSPGetOperators(mglevels[n-1]->smoothd,&dA,&dB);CHKERRQ(ierr);
  if (dA == dB) dAeqdB = PETSC_TRUE;
  if ((mg->galerkin == PC_MG_GALERKIN_NONE) || (((mg->galerkin == PC_MG_GALERKIN_PMAT) || (mg->galerkin == PC_MG_GALERKIN_MAT)) && !dAeqdB)) {
    needRestricts = PETSC_TRUE;  /* user must compute either mat, pmat, or both so must restrict x to coarser levels */
  }


  /*
   Skipping if user has provided all interpolation/restriction needed (since DM might not be able to produce them (when coming from SNES/TS)
   Skipping for galerkin==2 (externally managed hierarchy such as ML and GAMG). Cleaner logic here would be great. Wrap ML/GAMG as DMs?
  */
  if (missinginterpolate && pc->dm && mg->galerkin != PC_MG_GALERKIN_EXTERNAL && !pc->setupcalled) {
	/* set the mat type of coarse level operators to be AIJ.
	   It can be overwritten by -mat_type because KSPSetUp() reads command line options.
	   So we suggest to use -dm_mat_type for the fine level operator */
	ierr = DMSetMatType(pc->dm,MATAIJ);CHKERRQ(ierr);
	/* 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;
      PetscBool dmhasrestrict;
      ierr = KSPSetDM(mglevels[i]->smoothd,dms[i]);CHKERRQ(ierr);
      if (!needRestricts) {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);
      }
      ierr = DMHasCreateRestriction(dms[i],&dmhasrestrict);CHKERRQ(ierr);
      if (dmhasrestrict && !mglevels[i+1]->restrct){
        ierr = DMCreateRestriction(dms[i],dms[i+1],&p);CHKERRQ(ierr);
        ierr = PCMGSetRestriction(pc,i+1,p);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==PC_MG_GALERKIN_EXTERNAL */
    ierr = KSPSetDM(mglevels[n-1]->smoothd,pc->dm);CHKERRQ(ierr);
    ierr = KSPSetDMActive(mglevels[n-1]->smoothd,PETSC_FALSE);CHKERRQ(ierr);
  }

  if (mg->galerkin < PC_MG_GALERKIN_NONE) {
    Mat       A,B;
    PetscBool doA = PETSC_FALSE,doB = PETSC_FALSE;
    MatReuse  reuse = MAT_INITIAL_MATRIX;

    if ((mg->galerkin == PC_MG_GALERKIN_PMAT) || (mg->galerkin == PC_MG_GALERKIN_BOTH)) doB = PETSC_TRUE;
    if ((mg->galerkin == PC_MG_GALERKIN_MAT) || ((mg->galerkin == PC_MG_GALERKIN_BOTH) && (dA != dB))) doA = PETSC_TRUE;
    if (pc->setupcalled) reuse = MAT_REUSE_MATRIX;
    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 (reuse == MAT_REUSE_MATRIX) {
        ierr = KSPGetOperators(mglevels[i]->smoothd,&A,&B);CHKERRQ(ierr);
      }
      if (doA) {
        ierr = MatGalerkin(mglevels[i+1]->restrct,dA,mglevels[i+1]->interpolate,reuse,1.0,&A);CHKERRQ(ierr);
      }
      if (doB) {
        ierr = MatGalerkin(mglevels[i+1]->restrct,dB,mglevels[i+1]->interpolate,reuse,1.0,&B);CHKERRQ(ierr);
      }
      /* the management of the PetscObjectReference() and PetscObjecDereference() below is rather delicate */
      if (!doA && dAeqdB) {
        if (reuse == MAT_INITIAL_MATRIX) {ierr = PetscObjectReference((PetscObject)B);CHKERRQ(ierr);}
        A = B;
      } else if (!doA && reuse == MAT_INITIAL_MATRIX ) {
        ierr = KSPGetOperators(mglevels[i]->smoothd,&A,NULL);CHKERRQ(ierr);
        ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);
      }
      if (!doB && dAeqdB) {
        if (reuse == MAT_INITIAL_MATRIX) {ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);}
        B = A;
      } else if (!doB && reuse == MAT_INITIAL_MATRIX) {
        ierr = KSPGetOperators(mglevels[i]->smoothd,NULL,&B);CHKERRQ(ierr);
        ierr = PetscObjectReference((PetscObject)B);CHKERRQ(ierr);
      }
      if (reuse == MAT_INITIAL_MATRIX) {
        ierr = KSPSetOperators(mglevels[i]->smoothd,A,B);CHKERRQ(ierr);
        ierr = PetscObjectDereference((PetscObject)A);CHKERRQ(ierr);
        ierr = PetscObjectDereference((PetscObject)B);CHKERRQ(ierr);
      }
      dA = A;
      dB = B;
    }
  }
  if (needRestricts && 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 (needRestricts && 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);
      }
    }
    /* insure that if either interpolation or restriction is set the other other one is set */
    for (i=1; i<n; i++) {
      ierr = PCMGGetInterpolation(pc,i,NULL);CHKERRQ(ierr);
      ierr = PCMGGetRestriction(pc,i,NULL);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]->smoothd->reason == KSP_DIVERGED_PCSETUP_FAILED) {
      pc->failedreason = PC_SUBPC_ERROR;
    }
    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,&mat,NULL);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]->smoothu->reason == KSP_DIVERGED_PCSETUP_FAILED) {
        pc->failedreason = PC_SUBPC_ERROR;
      }
      if (mglevels[i]->eventsmoothsetup) {ierr = PetscLogEventEnd(mglevels[i]->eventsmoothsetup,0,0,0,0);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]->smoothd->reason == KSP_DIVERGED_PCSETUP_FAILED) {
    pc->failedreason = PC_SUBPC_ERROR;
  }
  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)->options,((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)->options,((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);
}

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

/*@
   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);
}

/*@
   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);
}

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

   Logically Collective on PC

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

   Options Database Key:
.  -pc_mg_cycle_type <v,w> - provide the cycle desired

   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");
  PetscValidLogicalCollectiveEnum(pc,n,2);
  levels = mglevels[0]->levels;

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

/*@
   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);
}

PetscErrorCode PCMGSetGalerkin_MG(PC pc,PCMGGalerkinType use)
{
  PC_MG *mg = (PC_MG*)pc->data;

  PetscFunctionBegin;
  mg->galerkin = use;
  PetscFunctionReturn(0);
}

/*@
   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 - one of PC_MG_GALERKIN_BOTH,PC_MG_GALERKIN_PMAT,PC_MG_GALERKIN_MAT, or PC_MG_GALERKIN_NONE

   Options Database Key:
.  -pc_mg_galerkin <both,pmat,mat,none>

   Level: intermediate

   Notes: Some codes that use PCMG such as PCGAMG use Galerkin internally while constructing the hierarchy and thus do not
     use the PCMG construction of the coarser grids.

.keywords: MG, set, Galerkin

.seealso: PCMGGetGalerkin(), PCMGGalerkinType

@*/
PetscErrorCode PCMGSetGalerkin(PC pc,PCMGGalerkinType use)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(pc,PC_CLASSID,1);
  ierr = PetscTryMethod(pc,"PCMGSetGalerkin_C",(PC,PCMGGalerkinType),(pc,use));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
   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 - one of PC_MG_GALERKIN_BOTH,PC_MG_GALERKIN_PMAT,PC_MG_GALERKIN_MAT, PC_MG_GALERKIN_NONE, or PC_MG_GALERKIN_EXTERNAL

   Level: intermediate

.keywords: MG, set, Galerkin

.seealso: PCMGSetGalerkin(), PCMGGalerkinType

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

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

/*@
   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
    If the number of smoothing steps is changed in this call then the PCMGGetSmoothUp() will be called and now the
   up smoother will no longer share the same KSP object as the down smoother. Use PCMGSetNumberSmooth() to set the same
   number of smoothing steps for pre and post smoothing.

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

.seealso: PCMGSetNumberSmoothUp(), PCMGSetNumberSmooth()
@*/
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++) {
    PetscInt nc;
    ierr = KSPGetTolerances(mglevels[i]->smoothd,NULL,NULL,NULL,&nc);CHKERRQ(ierr);
    if (nc == n) continue;

    /* 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);
}

/*@
   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

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

    If the number of smoothing steps is changed in this call then the PCMGGetSmoothUp() will be called and now the
   up smoother will no longer share the same KSP object as the down smoother. Use PCMGSetNumberSmooth() to set the same
   number of smoothing steps for pre and post smoothing.


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

.seealso: PCMGSetNumberSmoothDown(), PCMGSetNumberSmooth()
@*/
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++) {
    if (mglevels[i]->smoothu == mglevels[i]->smoothd) {
      PetscInt nc;
      ierr = KSPGetTolerances(mglevels[i]->smoothd,NULL,NULL,NULL,&nc);CHKERRQ(ierr);
      if (nc == n) continue;
    }

    /* 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);
}

/*@
   PCMGSetNumberSmooth - Sets the number of pre and post-smoothing steps to use
   on all levels. Use PCMGSetSmoothUp() and PCMGSetSmoothDown() set different numbers of
   pre ad post-smoothing steps

   Logically Collective on PC

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

   Options Database Key:
+  -mg_levels_ksp_max_it <n> - Sets number of pre and post-smoothing steps
.  -pc_mg_smooth_down <n> - Sets number of pre-smoothing steps (if setting different pre and post amounts)
-  -pc_mg_smooth_up <n> - Sets number of post-smoothing steps (if setting different pre and post amounts)

   Level: advanced

   Notes: 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(), PCMGSetNumberSmoothUp()
@*/
PetscErrorCode  PCMGSetNumberSmooth(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++) {
    ierr = KSPSetTolerances(mglevels[i]->smoothu,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,n);CHKERRQ(ierr);
    ierr = KSPSetTolerances(mglevels[i]->smoothd,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,n);CHKERRQ(ierr);
    mg->default_smoothu = n;
    mg->default_smoothd = 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_cycle_type <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_galerkin <both,pmat,mat,none> - 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: If one uses a Krylov method such GMRES or CG as the smoother than one must use KSPFGMRES, KSPGCG, or KSPRICHARDSON as the outer Krylov method

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

       When run with KSPRICHARDSON the convergence test changes slightly if monitor is turned on. The iteration count may change slightly. This
       is because without monitoring the residual norm is computed WITHIN each multigrid cycle on the finest level after the pre-smoothing
       (because the residual has just been computed for the multigrid algorithm and is hence available for free) while with monitoring the
       residual is computed at the end of each cycle.

   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*/

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;
  mg->am       = PC_MG_MULTIPLICATIVE;
  mg->galerkin = PC_MG_GALERKIN_NONE;

  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;

  ierr = PetscObjectComposeFunction((PetscObject)pc,"PCMGSetGalerkin_C",PCMGSetGalerkin_MG);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}