xref: /petsc/src/ksp/pc/impls/ml/ml.c (revision 7c4f633dc6bb6149cca88d301ead35a99e103cbb)

#define PETSCKSP_DLL

/*
   Provides an interface to the ML smoothed Aggregation
   Note: Something non-obvious breaks -pc_mg_type ADDITIVE for parallel runs
                                    Jed Brown, see [PETSC #18321, #18449].
*/
#include "private/pcimpl.h"   /*I "petscpc.h" I*/
#include "../src/ksp/pc/impls/mg/mgimpl.h"                    /*I "petscmg.h" I*/
#include "../src/mat/impls/aij/seq/aij.h"
#include "../src/mat/impls/aij/mpi/mpiaij.h"

#include <math.h>
EXTERN_C_BEGIN
/* HAVE_CONFIG_H flag is required by ML include files */
#if !defined(HAVE_CONFIG_H)
#define HAVE_CONFIG_H
#endif
#include "ml_include.h"
EXTERN_C_END

/* The context (data structure) at each grid level */
typedef struct {
  Vec        x,b,r;           /* global vectors */
  Mat        A,P,R;
  KSP        ksp;
} GridCtx;

/* The context used to input PETSc matrix into ML at fine grid */
typedef struct {
  Mat          A;      /* Petsc matrix in aij format */
  Mat          Aloc;   /* local portion of A to be used by ML */
  Vec          x,y;
  ML_Operator  *mlmat;
  PetscScalar  *pwork; /* tmp array used by PetscML_comm() */
} FineGridCtx;

/* The context associates a ML matrix with a PETSc shell matrix */
typedef struct {
  Mat          A;       /* PETSc shell matrix associated with mlmat */
  ML_Operator  *mlmat;  /* ML matrix assorciated with A */
  Vec          y;
} Mat_MLShell;

/* Private context for the ML preconditioner */
typedef struct {
  ML             *ml_object;
  ML_Aggregate   *agg_object;
  GridCtx        *gridctx;
  FineGridCtx    *PetscMLdata;
  PetscInt       Nlevels,MaxNlevels,MaxCoarseSize,CoarsenScheme;
  PetscReal      Threshold,DampingFactor;
  PetscTruth     SpectralNormScheme_Anorm;
  PetscMPIInt    size; /* size of communicator for pc->pmat */
  PetscErrorCode (*PCSetUp)(PC);
  PetscErrorCode (*PCDestroy)(PC);
} PC_ML;

extern int PetscML_getrow(ML_Operator *ML_data,int N_requested_rows,int requested_rows[],
                          int allocated_space,int columns[],double values[],int row_lengths[]);
extern int PetscML_matvec(ML_Operator *ML_data, int in_length, double p[], int out_length,double ap[]);
extern int PetscML_comm(double x[], void *ML_data);
extern PetscErrorCode MatMult_ML(Mat,Vec,Vec);
extern PetscErrorCode MatMultAdd_ML(Mat,Vec,Vec,Vec);
extern PetscErrorCode MatConvert_MPIAIJ_ML(Mat,MatType,MatReuse,Mat*);
extern PetscErrorCode MatDestroy_ML(Mat);
extern PetscErrorCode MatWrapML_SeqAIJ(ML_Operator*,MatReuse,Mat*);
extern PetscErrorCode MatWrapML_MPIAIJ(ML_Operator*,Mat*);
extern PetscErrorCode MatWrapML_SHELL(ML_Operator*,MatReuse,Mat*);
extern PetscErrorCode PetscContainerDestroy_PC_ML(void *);

/* -------------------------------------------------------------------------- */
/*
   PCSetUp_ML - Prepares for the use of the ML preconditioner
                    by setting data structures and options.

   Input Parameter:
.  pc - the preconditioner context

   Application Interface Routine: PCSetUp()

   Notes:
   The interface routine PCSetUp() is not usually called directly by
   the user, but instead is called by PCApply() if necessary.
*/
extern PetscErrorCode PCSetFromOptions_MG(PC);
#undef __FUNCT__
#define __FUNCT__ "PCSetUp_ML"
PetscErrorCode PCSetUp_ML(PC pc)
{
  PetscErrorCode  ierr;
  PetscMPIInt     size;
  FineGridCtx     *PetscMLdata;
  ML              *ml_object;
  ML_Aggregate    *agg_object;
  ML_Operator     *mlmat;
  PetscInt        nlocal_allcols,Nlevels,mllevel,level,level1,m,fine_level;
  Mat             A,Aloc;
  GridCtx         *gridctx;
  PC_ML           *pc_ml=PETSC_NULL;
  PetscContainer  container;
  MatReuse        reuse = MAT_INITIAL_MATRIX;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)pc,"PC_ML",(PetscObject *)&container);CHKERRQ(ierr);
  if (container) {
    ierr = PetscContainerGetPointer(container,(void **)&pc_ml);CHKERRQ(ierr);
  } else {
    SETERRQ(PETSC_ERR_ARG_NULL,"Container does not exit");
  }

  if (pc->setupcalled){
    if (pc->flag == SAME_NONZERO_PATTERN){
      reuse = MAT_REUSE_MATRIX;
      PetscMLdata = pc_ml->PetscMLdata;
      gridctx     = pc_ml->gridctx;
      /* ML objects cannot be reused */
      ML_Destroy(&pc_ml->ml_object);
      ML_Aggregate_Destroy(&pc_ml->agg_object);
    } else {
      PC_ML           *pc_ml_new = PETSC_NULL;
      PetscContainer  container_new;
      ierr = PetscNewLog(pc,PC_ML,&pc_ml_new);CHKERRQ(ierr);
      ierr = PetscContainerCreate(PETSC_COMM_SELF,&container_new);CHKERRQ(ierr);
      ierr = PetscContainerSetPointer(container_new,pc_ml_new);CHKERRQ(ierr);
      ierr = PetscContainerSetUserDestroy(container_new,PetscContainerDestroy_PC_ML);CHKERRQ(ierr);
      ierr = PetscObjectCompose((PetscObject)pc,"PC_ML",(PetscObject)container_new);CHKERRQ(ierr);

      ierr = PetscMemcpy(pc_ml_new,pc_ml,sizeof(PC_ML));CHKERRQ(ierr);
      ierr = PetscContainerDestroy(container);CHKERRQ(ierr);
      pc_ml = pc_ml_new;
    }
  }

  /* setup special features of PCML */
  /*--------------------------------*/
  /* covert A to Aloc to be used by ML at fine grid */
  A = pc->pmat;
  ierr = MPI_Comm_size(((PetscObject)A)->comm,&size);CHKERRQ(ierr);
  pc_ml->size = size;
  if (size > 1){
    if (reuse) Aloc = PetscMLdata->Aloc;
    ierr = MatConvert_MPIAIJ_ML(A,PETSC_NULL,reuse,&Aloc);CHKERRQ(ierr);
  } else {
    Aloc = A;
  }

  /* create and initialize struct 'PetscMLdata' */
  if (!reuse){
    ierr = PetscNewLog(pc,FineGridCtx,&PetscMLdata);CHKERRQ(ierr);
    pc_ml->PetscMLdata = PetscMLdata;
    ierr = PetscMalloc((Aloc->cmap->n+1)*sizeof(PetscScalar),&PetscMLdata->pwork);CHKERRQ(ierr);

    ierr = VecCreate(PETSC_COMM_SELF,&PetscMLdata->x);CHKERRQ(ierr);
    ierr = VecSetSizes(PetscMLdata->x,Aloc->cmap->n,Aloc->cmap->n);CHKERRQ(ierr);
    ierr = VecSetType(PetscMLdata->x,VECSEQ);CHKERRQ(ierr);

    ierr = VecCreate(PETSC_COMM_SELF,&PetscMLdata->y);CHKERRQ(ierr);
    ierr = VecSetSizes(PetscMLdata->y,A->rmap->n,PETSC_DECIDE);CHKERRQ(ierr);
    ierr = VecSetType(PetscMLdata->y,VECSEQ);CHKERRQ(ierr);
  }
  PetscMLdata->A    = A;
  PetscMLdata->Aloc = Aloc;

  /* create ML discretization matrix at fine grid */
  /* ML requires input of fine-grid matrix. It determines nlevels. */
  ierr = MatGetSize(Aloc,&m,&nlocal_allcols);CHKERRQ(ierr);
  ML_Create(&ml_object,pc_ml->MaxNlevels);
  pc_ml->ml_object = ml_object;
  ML_Init_Amatrix(ml_object,0,m,m,PetscMLdata);
  ML_Set_Amatrix_Getrow(ml_object,0,PetscML_getrow,PetscML_comm,nlocal_allcols);
  ML_Set_Amatrix_Matvec(ml_object,0,PetscML_matvec);

  /* aggregation */
  ML_Aggregate_Create(&agg_object);
  pc_ml->agg_object = agg_object;

  ML_Aggregate_Set_MaxCoarseSize(agg_object,pc_ml->MaxCoarseSize);
  /* set options */
  switch (pc_ml->CoarsenScheme) {
  case 1:
    ML_Aggregate_Set_CoarsenScheme_Coupled(agg_object);break;
  case 2:
    ML_Aggregate_Set_CoarsenScheme_MIS(agg_object);break;
  case 3:
    ML_Aggregate_Set_CoarsenScheme_METIS(agg_object);break;
  }
  ML_Aggregate_Set_Threshold(agg_object,pc_ml->Threshold);
  ML_Aggregate_Set_DampingFactor(agg_object,pc_ml->DampingFactor);
  if (pc_ml->SpectralNormScheme_Anorm){
    ML_Set_SpectralNormScheme_Anorm(ml_object);
  }

  Nlevels = ML_Gen_MGHierarchy_UsingAggregation(ml_object,0,ML_INCREASING,agg_object);
  if (Nlevels<=0) SETERRQ1(PETSC_ERR_ARG_OUTOFRANGE,"Nlevels %d must > 0",Nlevels);
  if (pc->setupcalled && pc_ml->Nlevels != Nlevels) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"previous Nlevels %D and current Nlevels %d must be same", pc_ml->Nlevels,Nlevels);
  pc_ml->Nlevels = Nlevels;
  fine_level = Nlevels - 1;
  if (!pc->setupcalled){
    ierr = PCMGSetLevels(pc,Nlevels,PETSC_NULL);CHKERRQ(ierr);
    /* set default smoothers */
    KSP smoother;
    PC  subpc;
    for (level=1; level<=fine_level; level++){
      if (size == 1){
        ierr = PCMGGetSmoother(pc,level,&smoother);CHKERRQ(ierr);
        ierr = KSPSetType(smoother,KSPRICHARDSON);CHKERRQ(ierr);
        ierr = KSPGetPC(smoother,&subpc);CHKERRQ(ierr);
        ierr = PCSetType(subpc,PCSOR);CHKERRQ(ierr);
      } else {
        ierr = PCMGGetSmoother(pc,level,&smoother);CHKERRQ(ierr);
        ierr = KSPSetType(smoother,KSPRICHARDSON);CHKERRQ(ierr);
        ierr = KSPGetPC(smoother,&subpc);CHKERRQ(ierr);
        ierr = PCSetType(subpc,PCSOR);CHKERRQ(ierr);
      }
    }
    ierr = PCSetFromOptions_MG(pc);CHKERRQ(ierr); /* should be called in PCSetFromOptions_ML(), but cannot be called prior to PCMGSetLevels() */
  }

  if (!reuse){
    ierr = PetscMalloc(Nlevels*sizeof(GridCtx),&gridctx);CHKERRQ(ierr);
    pc_ml->gridctx = gridctx;
  }

  /* wrap ML matrices by PETSc shell matrices at coarsened grids.
     Level 0 is the finest grid for ML, but coarsest for PETSc! */
  gridctx[fine_level].A = A;

  level = fine_level - 1;
  if (size == 1){ /* convert ML P, R and A into seqaij format */
    for (mllevel=1; mllevel<Nlevels; mllevel++){
      mlmat = &(ml_object->Pmat[mllevel]);
      ierr  = MatWrapML_SeqAIJ(mlmat,reuse,&gridctx[level].P);CHKERRQ(ierr);
      mlmat = &(ml_object->Rmat[mllevel-1]);
      ierr  = MatWrapML_SeqAIJ(mlmat,reuse,&gridctx[level].R);CHKERRQ(ierr);

      mlmat = &(ml_object->Amat[mllevel]);
      if (reuse){
        /* ML matrix A changes sparse pattern although PETSc A doesn't, thus gridctx[level].A must be recreated! */
        ierr = MatDestroy(gridctx[level].A);CHKERRQ(ierr);
      }
      ierr  = MatWrapML_SeqAIJ(mlmat,MAT_INITIAL_MATRIX,&gridctx[level].A);CHKERRQ(ierr);
      level--;
    }
  } else { /* convert ML P and R into shell format, ML A into mpiaij format */
    for (mllevel=1; mllevel<Nlevels; mllevel++){
      mlmat  = &(ml_object->Pmat[mllevel]);
      ierr = MatWrapML_SHELL(mlmat,reuse,&gridctx[level].P);CHKERRQ(ierr);
      mlmat  = &(ml_object->Rmat[mllevel-1]);
      ierr = MatWrapML_SHELL(mlmat,reuse,&gridctx[level].R);CHKERRQ(ierr);

      mlmat  = &(ml_object->Amat[mllevel]);
      if (reuse){
        ierr = MatDestroy(gridctx[level].A);CHKERRQ(ierr);
      }
      ierr = MatWrapML_MPIAIJ(mlmat,&gridctx[level].A);CHKERRQ(ierr);
      level--;
    }
  }

  /* create vectors and ksp at all levels */
  if (!reuse){
    for (level=0; level<fine_level; level++){
      level1 = level + 1;
      ierr = VecCreate(((PetscObject)gridctx[level].A)->comm,&gridctx[level].x);CHKERRQ(ierr);
      ierr = VecSetSizes(gridctx[level].x,gridctx[level].A->cmap->n,PETSC_DECIDE);CHKERRQ(ierr);
      ierr = VecSetType(gridctx[level].x,VECMPI);CHKERRQ(ierr);
      ierr = PCMGSetX(pc,level,gridctx[level].x);CHKERRQ(ierr);

      ierr = VecCreate(((PetscObject)gridctx[level].A)->comm,&gridctx[level].b);CHKERRQ(ierr);
      ierr = VecSetSizes(gridctx[level].b,gridctx[level].A->rmap->n,PETSC_DECIDE);CHKERRQ(ierr);
      ierr = VecSetType(gridctx[level].b,VECMPI);CHKERRQ(ierr);
      ierr = PCMGSetRhs(pc,level,gridctx[level].b);CHKERRQ(ierr);

      ierr = VecCreate(((PetscObject)gridctx[level1].A)->comm,&gridctx[level1].r);CHKERRQ(ierr);
      ierr = VecSetSizes(gridctx[level1].r,gridctx[level1].A->rmap->n,PETSC_DECIDE);CHKERRQ(ierr);
      ierr = VecSetType(gridctx[level1].r,VECMPI);CHKERRQ(ierr);
      ierr = PCMGSetR(pc,level1,gridctx[level1].r);CHKERRQ(ierr);

      if (level == 0){
        ierr = PCMGGetCoarseSolve(pc,&gridctx[level].ksp);CHKERRQ(ierr);
      } else {
        ierr = PCMGGetSmoother(pc,level,&gridctx[level].ksp);CHKERRQ(ierr);
      }
    }
    ierr = PCMGGetSmoother(pc,fine_level,&gridctx[fine_level].ksp);CHKERRQ(ierr);
  }

  /* create coarse level and the interpolation between the levels */
  for (level=0; level<fine_level; level++){
    level1 = level + 1;
    ierr = PCMGSetInterpolation(pc,level1,gridctx[level].P);CHKERRQ(ierr);
    ierr = PCMGSetRestriction(pc,level1,gridctx[level].R);CHKERRQ(ierr);
    if (level > 0){
      ierr = PCMGSetResidual(pc,level,PCMGDefaultResidual,gridctx[level].A);CHKERRQ(ierr);
    }
    ierr = KSPSetOperators(gridctx[level].ksp,gridctx[level].A,gridctx[level].A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
  }
  ierr = PCMGSetResidual(pc,fine_level,PCMGDefaultResidual,gridctx[fine_level].A);CHKERRQ(ierr);
  ierr = KSPSetOperators(gridctx[fine_level].ksp,gridctx[level].A,gridctx[fine_level].A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);

  /* now call PCSetUp_MG()         */
  /*-------------------------------*/
  ierr = (*pc_ml->PCSetUp)(pc);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscContainerDestroy_PC_ML"
PetscErrorCode PetscContainerDestroy_PC_ML(void *ptr)
{
  PetscErrorCode  ierr;
  PC_ML           *pc_ml = (PC_ML*)ptr;
  PetscInt        level,fine_level=pc_ml->Nlevels-1;

  PetscFunctionBegin;
  ML_Aggregate_Destroy(&pc_ml->agg_object);
  ML_Destroy(&pc_ml->ml_object);

  if (pc_ml->PetscMLdata) {
    ierr = PetscFree(pc_ml->PetscMLdata->pwork);CHKERRQ(ierr);
    if (pc_ml->size > 1)      {ierr = MatDestroy(pc_ml->PetscMLdata->Aloc);CHKERRQ(ierr);}
    if (pc_ml->PetscMLdata->x){ierr = VecDestroy(pc_ml->PetscMLdata->x);CHKERRQ(ierr);}
    if (pc_ml->PetscMLdata->y){ierr = VecDestroy(pc_ml->PetscMLdata->y);CHKERRQ(ierr);}
  }
  ierr = PetscFree(pc_ml->PetscMLdata);CHKERRQ(ierr);

  for (level=0; level<fine_level; level++){
    if (pc_ml->gridctx[level].A){ierr = MatDestroy(pc_ml->gridctx[level].A);CHKERRQ(ierr);}
    if (pc_ml->gridctx[level].P){ierr = MatDestroy(pc_ml->gridctx[level].P);CHKERRQ(ierr);}
    if (pc_ml->gridctx[level].R){ierr = MatDestroy(pc_ml->gridctx[level].R);CHKERRQ(ierr);}
    if (pc_ml->gridctx[level].x){ierr = VecDestroy(pc_ml->gridctx[level].x);CHKERRQ(ierr);}
    if (pc_ml->gridctx[level].b){ierr = VecDestroy(pc_ml->gridctx[level].b);CHKERRQ(ierr);}
    if (pc_ml->gridctx[level+1].r){ierr = VecDestroy(pc_ml->gridctx[level+1].r);CHKERRQ(ierr);}
  }
  ierr = PetscFree(pc_ml->gridctx);CHKERRQ(ierr);
  ierr = PetscFree(pc_ml);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/* -------------------------------------------------------------------------- */
/*
   PCDestroy_ML - Destroys the private context for the ML preconditioner
   that was created with PCCreate_ML().

   Input Parameter:
.  pc - the preconditioner context

   Application Interface Routine: PCDestroy()
*/
#undef __FUNCT__
#define __FUNCT__ "PCDestroy_ML"
PetscErrorCode PCDestroy_ML(PC pc)
{
  PetscErrorCode  ierr;
  PC_ML           *pc_ml=PETSC_NULL;
  PetscContainer  container;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)pc,"PC_ML",(PetscObject *)&container);CHKERRQ(ierr);
  if (container) {
    ierr = PetscContainerGetPointer(container,(void **)&pc_ml);CHKERRQ(ierr);
    pc->ops->destroy = pc_ml->PCDestroy;
  } else {
    SETERRQ(PETSC_ERR_ARG_NULL,"Container does not exit");
  }
  /* detach pc and PC_ML and dereference container */
  ierr = PetscContainerDestroy(container);CHKERRQ(ierr);
  ierr = PetscObjectCompose((PetscObject)pc,"PC_ML",0);CHKERRQ(ierr);
  if (pc->ops->destroy) {
    ierr = (*pc->ops->destroy)(pc);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PCSetFromOptions_ML"
PetscErrorCode PCSetFromOptions_ML(PC pc)
{
  PetscErrorCode  ierr;
  PetscInt        indx,m,PrintLevel;
  PetscTruth      flg;
  const char      *scheme[] = {"Uncoupled","Coupled","MIS","METIS"};
  PC_ML           *pc_ml=PETSC_NULL;
  PetscContainer  container;
  PCMGType        mgtype;

  PetscFunctionBegin;
  ierr = PetscObjectQuery((PetscObject)pc,"PC_ML",(PetscObject *)&container);CHKERRQ(ierr);
  if (container) {
    ierr = PetscContainerGetPointer(container,(void **)&pc_ml);CHKERRQ(ierr);
  } else {
    SETERRQ(PETSC_ERR_ARG_NULL,"Container does not exit");
  }

  /* inherited MG options */
  ierr = PetscOptionsHead("Multigrid options(inherited)");CHKERRQ(ierr);
    ierr = PetscOptionsInt("-pc_mg_cycles","1 for V cycle, 2 for W-cycle","MGSetCycles",1,&m,&flg);CHKERRQ(ierr);
    ierr = PetscOptionsInt("-pc_mg_smoothup","Number of post-smoothing steps","MGSetNumberSmoothUp",1,&m,&flg);CHKERRQ(ierr);
    ierr = PetscOptionsInt("-pc_mg_smoothdown","Number of pre-smoothing steps","MGSetNumberSmoothDown",1,&m,&flg);CHKERRQ(ierr);
    ierr = PetscOptionsEnum("-pc_mg_type","Multigrid type","PCMGSetType",PCMGTypes,(PetscEnum)PC_MG_MULTIPLICATIVE,(PetscEnum*)&mgtype,&flg);CHKERRQ(ierr);
  ierr = PetscOptionsTail();CHKERRQ(ierr);

  /* ML options */
  ierr = PetscOptionsHead("ML options");CHKERRQ(ierr);
  /* set defaults */
  PrintLevel    = 0;
  indx          = 0;
  ierr = PetscOptionsInt("-pc_ml_PrintLevel","Print level","ML_Set_PrintLevel",PrintLevel,&PrintLevel,PETSC_NULL);CHKERRQ(ierr);
  ML_Set_PrintLevel(PrintLevel);
  ierr = PetscOptionsInt("-pc_ml_maxNlevels","Maximum number of levels","None",pc_ml->MaxNlevels,&pc_ml->MaxNlevels,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsInt("-pc_ml_maxCoarseSize","Maximum coarsest mesh size","ML_Aggregate_Set_MaxCoarseSize",pc_ml->MaxCoarseSize,&pc_ml->MaxCoarseSize,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsEList("-pc_ml_CoarsenScheme","Aggregate Coarsen Scheme","ML_Aggregate_Set_CoarsenScheme_*",scheme,4,scheme[0],&indx,PETSC_NULL);CHKERRQ(ierr); /* ??? */
  pc_ml->CoarsenScheme = indx;

  ierr = PetscOptionsReal("-pc_ml_DampingFactor","P damping factor","ML_Aggregate_Set_DampingFactor",pc_ml->DampingFactor,&pc_ml->DampingFactor,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscOptionsReal("-pc_ml_Threshold","Smoother drop tol","ML_Aggregate_Set_Threshold",pc_ml->Threshold,&pc_ml->Threshold,PETSC_NULL);CHKERRQ(ierr);

  ierr = PetscOptionsTruth("-pc_ml_SpectralNormScheme_Anorm","Method used for estimating spectral radius","ML_Set_SpectralNormScheme_Anorm",pc_ml->SpectralNormScheme_Anorm,&pc_ml->SpectralNormScheme_Anorm,PETSC_NULL);

  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */
/*
   PCCreate_ML - Creates a ML preconditioner context, PC_ML,
   and sets this as the private data within the generic preconditioning
   context, PC, that was created within PCCreate().

   Input Parameter:
.  pc - the preconditioner context

   Application Interface Routine: PCCreate()
*/

/*MC
     PCML - Use algebraic multigrid preconditioning. This preconditioner requires you provide
       fine grid discretization matrix. The coarser grid matrices and restriction/interpolation
       operators are computed by ML, with the matrices coverted to PETSc matrices in aij format
       and the restriction/interpolation operators wrapped as PETSc shell matrices.

   Options Database Key:
   Multigrid options(inherited)
+  -pc_mg_cycles <1>: 1 for V cycle, 2 for W-cycle (MGSetCycles)
.  -pc_mg_smoothup <1>: Number of post-smoothing steps (MGSetNumberSmoothUp)
.  -pc_mg_smoothdown <1>: Number of pre-smoothing steps (MGSetNumberSmoothDown)
-  -pc_mg_type <multiplicative>: (one of) additive multiplicative full cascade kascade

   ML options:
+  -pc_ml_PrintLevel <0>: Print level (ML_Set_PrintLevel)
.  -pc_ml_maxNlevels <10>: Maximum number of levels (None)
.  -pc_ml_maxCoarseSize <1>: Maximum coarsest mesh size (ML_Aggregate_Set_MaxCoarseSize)
.  -pc_ml_CoarsenScheme <Uncoupled>: (one of) Uncoupled Coupled MIS METIS
.  -pc_ml_DampingFactor <1.33333>: P damping factor (ML_Aggregate_Set_DampingFactor)
.  -pc_ml_Threshold <0>: Smoother drop tol (ML_Aggregate_Set_Threshold)
-  -pc_ml_SpectralNormScheme_Anorm <false>: Method used for estimating spectral radius (ML_Set_SpectralNormScheme_Anorm)

   Level: intermediate

  Concepts: multigrid

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

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "PCCreate_ML"
PetscErrorCode PETSCKSP_DLLEXPORT PCCreate_ML(PC pc)
{
  PetscErrorCode  ierr;
  PC_ML           *pc_ml;
  PetscContainer  container;

  PetscFunctionBegin;
  /* PCML is an inherited class of PCMG. Initialize pc as PCMG */
  ierr = PCSetType(pc,PCMG);CHKERRQ(ierr); /* calls PCCreate_MG() and MGCreate_Private() */

  /* create a supporting struct and attach it to pc */
  ierr = PetscNewLog(pc,PC_ML,&pc_ml);CHKERRQ(ierr);
  ierr = PetscContainerCreate(PETSC_COMM_SELF,&container);CHKERRQ(ierr);
  ierr = PetscContainerSetPointer(container,pc_ml);CHKERRQ(ierr);
  ierr = PetscContainerSetUserDestroy(container,PetscContainerDestroy_PC_ML);CHKERRQ(ierr);
  ierr = PetscObjectCompose((PetscObject)pc,"PC_ML",(PetscObject)container);CHKERRQ(ierr);

  pc_ml->ml_object     = 0;
  pc_ml->agg_object    = 0;
  pc_ml->gridctx       = 0;
  pc_ml->PetscMLdata   = 0;
  pc_ml->Nlevels       = -1;
  pc_ml->MaxNlevels    = 10;
  pc_ml->MaxCoarseSize = 1;
  pc_ml->CoarsenScheme = 1; /* ??? */
  pc_ml->Threshold     = 0.0;
  pc_ml->DampingFactor = 4.0/3.0;
  pc_ml->SpectralNormScheme_Anorm = PETSC_FALSE;
  pc_ml->size          = 0;

  pc_ml->PCSetUp   = pc->ops->setup;
  pc_ml->PCDestroy = pc->ops->destroy;

  /* overwrite the pointers of PCMG by the functions of PCML */
  pc->ops->setfromoptions = PCSetFromOptions_ML;
  pc->ops->setup          = PCSetUp_ML;
  pc->ops->destroy        = PCDestroy_ML;
  PetscFunctionReturn(0);
}
EXTERN_C_END

int PetscML_getrow(ML_Operator *ML_data, int N_requested_rows, int requested_rows[],
   int allocated_space, int columns[], double values[], int row_lengths[])
{
  PetscErrorCode ierr;
  Mat            Aloc;
  Mat_SeqAIJ     *a;
  PetscInt       m,i,j,k=0,row,*aj;
  PetscScalar    *aa;
  FineGridCtx    *ml=(FineGridCtx*)ML_Get_MyGetrowData(ML_data);

  Aloc = ml->Aloc;
  a    = (Mat_SeqAIJ*)Aloc->data;
  ierr = MatGetSize(Aloc,&m,PETSC_NULL);CHKERRQ(ierr);

  for (i = 0; i<N_requested_rows; i++) {
    row   = requested_rows[i];
    row_lengths[i] = a->ilen[row];
    if (allocated_space < k+row_lengths[i]) return(0);
    if ( (row >= 0) || (row <= (m-1)) ) {
      aj = a->j + a->i[row];
      aa = a->a + a->i[row];
      for (j=0; j<row_lengths[i]; j++){
        columns[k]  = aj[j];
        values[k++] = aa[j];
      }
    }
  }
  return(1);
}

int PetscML_matvec(ML_Operator *ML_data,int in_length,double p[],int out_length,double ap[])
{
  PetscErrorCode ierr;
  FineGridCtx    *ml=(FineGridCtx*)ML_Get_MyMatvecData(ML_data);
  Mat            A=ml->A, Aloc=ml->Aloc;
  PetscMPIInt    size;
  PetscScalar    *pwork=ml->pwork;
  PetscInt       i;

  ierr = MPI_Comm_size(((PetscObject)A)->comm,&size);CHKERRQ(ierr);
  if (size == 1){
    ierr = VecPlaceArray(ml->x,p);CHKERRQ(ierr);
  } else {
    for (i=0; i<in_length; i++) pwork[i] = p[i];
    PetscML_comm(pwork,ml);
    ierr = VecPlaceArray(ml->x,pwork);CHKERRQ(ierr);
  }
  ierr = VecPlaceArray(ml->y,ap);CHKERRQ(ierr);
  ierr = MatMult(Aloc,ml->x,ml->y);CHKERRQ(ierr);
  ierr = VecResetArray(ml->x);CHKERRQ(ierr);
  ierr = VecResetArray(ml->y);CHKERRQ(ierr);
  return 0;
}

int PetscML_comm(double p[],void *ML_data)
{
  PetscErrorCode ierr;
  FineGridCtx    *ml=(FineGridCtx*)ML_data;
  Mat            A=ml->A;
  Mat_MPIAIJ     *a = (Mat_MPIAIJ*)A->data;
  PetscMPIInt    size;
  PetscInt       i,in_length=A->rmap->n,out_length=ml->Aloc->cmap->n;
  PetscScalar    *array;

  ierr = MPI_Comm_size(((PetscObject)A)->comm,&size);CHKERRQ(ierr);
  if (size == 1) return 0;

  ierr = VecPlaceArray(ml->y,p);CHKERRQ(ierr);
  ierr = VecScatterBegin(a->Mvctx,ml->y,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecScatterEnd(a->Mvctx,ml->y,a->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = VecResetArray(ml->y);CHKERRQ(ierr);
  ierr = VecGetArray(a->lvec,&array);CHKERRQ(ierr);
  for (i=in_length; i<out_length; i++){
    p[i] = array[i-in_length];
  }
  ierr = VecRestoreArray(a->lvec,&array);CHKERRQ(ierr);
  return 0;
}
#undef __FUNCT__
#define __FUNCT__ "MatMult_ML"
PetscErrorCode MatMult_ML(Mat A,Vec x,Vec y)
{
  PetscErrorCode   ierr;
  Mat_MLShell      *shell;
  PetscScalar      *xarray,*yarray;
  PetscInt         x_length,y_length;

  PetscFunctionBegin;
  ierr = MatShellGetContext(A,(void **)&shell);CHKERRQ(ierr);
  ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
  ierr = VecGetArray(y,&yarray);CHKERRQ(ierr);
  x_length = shell->mlmat->invec_leng;
  y_length = shell->mlmat->outvec_leng;

  ML_Operator_Apply(shell->mlmat,x_length,xarray,y_length,yarray);

  ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
  ierr = VecRestoreArray(y,&yarray);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/* MatMultAdd_ML -  Compute y = w + A*x */
#undef __FUNCT__
#define __FUNCT__ "MatMultAdd_ML"
PetscErrorCode MatMultAdd_ML(Mat A,Vec x,Vec w,Vec y)
{
  PetscErrorCode    ierr;
  Mat_MLShell       *shell;
  PetscScalar       *xarray,*yarray;
  PetscInt          x_length,y_length;

  PetscFunctionBegin;
  ierr = MatShellGetContext(A,(void **)&shell);CHKERRQ(ierr);
  ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
  ierr = VecGetArray(y,&yarray);CHKERRQ(ierr);

  x_length = shell->mlmat->invec_leng;
  y_length = shell->mlmat->outvec_leng;

  ML_Operator_Apply(shell->mlmat,x_length,xarray,y_length,yarray);

  ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);
  ierr = VecRestoreArray(y,&yarray);CHKERRQ(ierr);
  ierr = VecAXPY(y,1.0,w);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

/* newtype is ignored because "ml" is not listed under Petsc MatType yet */
#undef __FUNCT__
#define __FUNCT__ "MatConvert_MPIAIJ_ML"
PetscErrorCode MatConvert_MPIAIJ_ML(Mat A,MatType newtype,MatReuse scall,Mat *Aloc)
{
  PetscErrorCode  ierr;
  Mat_MPIAIJ      *mpimat=(Mat_MPIAIJ*)A->data;
  Mat_SeqAIJ      *mat,*a=(Mat_SeqAIJ*)(mpimat->A)->data,*b=(Mat_SeqAIJ*)(mpimat->B)->data;
  PetscInt        *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
  PetscScalar     *aa=a->a,*ba=b->a,*ca;
  PetscInt        am=A->rmap->n,an=A->cmap->n,i,j,k;
  PetscInt        *ci,*cj,ncols;

  PetscFunctionBegin;
  if (am != an) SETERRQ2(PETSC_ERR_ARG_WRONG,"A must have a square diagonal portion, am: %d != an: %d",am,an);

  if (scall == MAT_INITIAL_MATRIX){
    ierr = PetscMalloc((1+am)*sizeof(PetscInt),&ci);CHKERRQ(ierr);
    ci[0] = 0;
    for (i=0; i<am; i++){
      ci[i+1] = ci[i] + (ai[i+1] - ai[i]) + (bi[i+1] - bi[i]);
    }
    ierr = PetscMalloc((1+ci[am])*sizeof(PetscInt),&cj);CHKERRQ(ierr);
    ierr = PetscMalloc((1+ci[am])*sizeof(PetscScalar),&ca);CHKERRQ(ierr);

    k = 0;
    for (i=0; i<am; i++){
      /* diagonal portion of A */
      ncols = ai[i+1] - ai[i];
      for (j=0; j<ncols; j++) {
        cj[k]   = *aj++;
        ca[k++] = *aa++;
      }
      /* off-diagonal portion of A */
      ncols = bi[i+1] - bi[i];
      for (j=0; j<ncols; j++) {
        cj[k]   = an + (*bj); bj++;
        ca[k++] = *ba++;
      }
    }
    if (k != ci[am]) SETERRQ2(PETSC_ERR_ARG_WRONG,"k: %d != ci[am]: %d",k,ci[am]);

    /* put together the new matrix */
    an = mpimat->A->cmap->n+mpimat->B->cmap->n;
    ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,am,an,ci,cj,ca,Aloc);CHKERRQ(ierr);

    /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    /* Since these are PETSc arrays, change flags to free them as necessary. */
    mat = (Mat_SeqAIJ*)(*Aloc)->data;
    mat->free_a       = PETSC_TRUE;
    mat->free_ij      = PETSC_TRUE;

    mat->nonew    = 0;
  } else if (scall == MAT_REUSE_MATRIX){
    mat=(Mat_SeqAIJ*)(*Aloc)->data;
    ci = mat->i; cj = mat->j; ca = mat->a;
    for (i=0; i<am; i++) {
      /* diagonal portion of A */
      ncols = ai[i+1] - ai[i];
      for (j=0; j<ncols; j++) *ca++ = *aa++;
      /* off-diagonal portion of A */
      ncols = bi[i+1] - bi[i];
      for (j=0; j<ncols; j++) *ca++ = *ba++;
    }
  } else {
    SETERRQ1(PETSC_ERR_ARG_WRONG,"Invalid MatReuse %d",(int)scall);
  }
  PetscFunctionReturn(0);
}
extern PetscErrorCode MatDestroy_Shell(Mat);
#undef __FUNCT__
#define __FUNCT__ "MatDestroy_ML"
PetscErrorCode MatDestroy_ML(Mat A)
{
  PetscErrorCode ierr;
  Mat_MLShell    *shell;

  PetscFunctionBegin;
  ierr = MatShellGetContext(A,(void **)&shell);CHKERRQ(ierr);
  ierr = VecDestroy(shell->y);CHKERRQ(ierr);
  ierr = PetscFree(shell);CHKERRQ(ierr);
  ierr = MatDestroy_Shell(A);CHKERRQ(ierr);
  ierr = PetscObjectChangeTypeName((PetscObject)A,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatWrapML_SeqAIJ"
PetscErrorCode MatWrapML_SeqAIJ(ML_Operator *mlmat,MatReuse reuse,Mat *newmat)
{
  struct ML_CSR_MSRdata *matdata = (struct ML_CSR_MSRdata *)mlmat->data;
  PetscErrorCode        ierr;
  PetscInt              m=mlmat->outvec_leng,n=mlmat->invec_leng,*nnz,nz_max;
  PetscInt              *ml_cols=matdata->columns,*ml_rowptr=matdata->rowptr,*aj,i,j,k;
  PetscScalar           *ml_vals=matdata->values,*aa;

  PetscFunctionBegin;
  if ( mlmat->getrow == NULL) SETERRQ(PETSC_ERR_ARG_NULL,"mlmat->getrow = NULL");
  if (m != n){ /* ML Pmat and Rmat are in CSR format. Pass array pointers into SeqAIJ matrix */
    if (reuse){
      Mat_SeqAIJ  *aij= (Mat_SeqAIJ*)(*newmat)->data;
      aij->i = ml_rowptr;
      aij->j = ml_cols;
      aij->a = ml_vals;
    } else {
      /* sort ml_cols and ml_vals */
      ierr = PetscMalloc((m+1)*sizeof(PetscInt),&nnz);
      for (i=0; i<m; i++) {
        nnz[i] = ml_rowptr[i+1] - ml_rowptr[i];
      }
      aj = ml_cols; aa = ml_vals;
      for (i=0; i<m; i++){
        ierr = PetscSortIntWithScalarArray(nnz[i],aj,aa);CHKERRQ(ierr);
        aj += nnz[i]; aa += nnz[i];
      }
      ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,m,n,ml_rowptr,ml_cols,ml_vals,newmat);CHKERRQ(ierr);
      ierr = PetscFree(nnz);CHKERRQ(ierr);
    }
    PetscFunctionReturn(0);
  }

  /* ML Amat is in MSR format. Copy its data into SeqAIJ matrix */
  ierr = MatCreate(PETSC_COMM_SELF,newmat);CHKERRQ(ierr);
  ierr = MatSetSizes(*newmat,m,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
  ierr = MatSetType(*newmat,MATSEQAIJ);CHKERRQ(ierr);

  ierr = PetscMalloc((m+1)*sizeof(PetscInt),&nnz);
  nz_max = 1;
  for (i=0; i<m; i++) {
    nnz[i] = ml_cols[i+1] - ml_cols[i] + 1;
    if (nnz[i] > nz_max) nz_max += nnz[i];
  }

  ierr = MatSeqAIJSetPreallocation(*newmat,0,nnz);CHKERRQ(ierr);
  ierr = PetscMalloc(nz_max*(sizeof(PetscInt)+sizeof(PetscScalar)),&aj);CHKERRQ(ierr);
  aa = (PetscScalar*)(aj + nz_max);

  for (i=0; i<m; i++){
    k = 0;
    /* diagonal entry */
    aj[k] = i; aa[k++] = ml_vals[i];
    /* off diagonal entries */
    for (j=ml_cols[i]; j<ml_cols[i+1]; j++){
      aj[k] = ml_cols[j]; aa[k++] = ml_vals[j];
    }
    /* sort aj and aa */
    ierr = PetscSortIntWithScalarArray(nnz[i],aj,aa);CHKERRQ(ierr);
    ierr = MatSetValues(*newmat,1,&i,nnz[i],aj,aa,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = PetscFree(aj);CHKERRQ(ierr);
  ierr = PetscFree(nnz);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatWrapML_SHELL"
PetscErrorCode MatWrapML_SHELL(ML_Operator *mlmat,MatReuse reuse,Mat *newmat)
{
  PetscErrorCode ierr;
  PetscInt       m,n;
  ML_Comm        *MLcomm;
  Mat_MLShell    *shellctx;

  PetscFunctionBegin;
  m = mlmat->outvec_leng;
  n = mlmat->invec_leng;
  if (!m || !n){
    newmat = PETSC_NULL;
    PetscFunctionReturn(0);
  }

  if (reuse){
    ierr = MatShellGetContext(*newmat,(void **)&shellctx);CHKERRQ(ierr);
    shellctx->mlmat = mlmat;
    PetscFunctionReturn(0);
  }

  MLcomm = mlmat->comm;
  ierr = PetscNew(Mat_MLShell,&shellctx);CHKERRQ(ierr);
  ierr = MatCreateShell(MLcomm->USR_comm,m,n,PETSC_DETERMINE,PETSC_DETERMINE,shellctx,newmat);CHKERRQ(ierr);
  ierr = MatShellSetOperation(*newmat,MATOP_MULT,(void(*)(void))MatMult_ML);CHKERRQ(ierr);
  ierr = MatShellSetOperation(*newmat,MATOP_MULT_ADD,(void(*)(void))MatMultAdd_ML);CHKERRQ(ierr);
  shellctx->A         = *newmat;
  shellctx->mlmat     = mlmat;
  ierr = VecCreate(PETSC_COMM_WORLD,&shellctx->y);CHKERRQ(ierr);
  ierr = VecSetSizes(shellctx->y,m,PETSC_DECIDE);CHKERRQ(ierr);
  ierr = VecSetFromOptions(shellctx->y);CHKERRQ(ierr);
  (*newmat)->ops->destroy = MatDestroy_ML;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatWrapML_MPIAIJ"
PetscErrorCode MatWrapML_MPIAIJ(ML_Operator *mlmat,Mat *newmat)
{
  struct ML_CSR_MSRdata *matdata = (struct ML_CSR_MSRdata *)mlmat->data;
  PetscInt              *ml_cols=matdata->columns,*aj;
  PetscScalar           *ml_vals=matdata->values,*aa;
  PetscErrorCode        ierr;
  PetscInt              i,j,k,*gordering;
  PetscInt              m=mlmat->outvec_leng,n,*nnzA,*nnzB,*nnz,nz_max,row;
  Mat                   A;

  PetscFunctionBegin;
  if (mlmat->getrow == NULL) SETERRQ(PETSC_ERR_ARG_NULL,"mlmat->getrow = NULL");
  n = mlmat->invec_leng;
  if (m != n) SETERRQ2(PETSC_ERR_ARG_OUTOFRANGE,"m %d must equal to n %d",m,n);

  ierr = MatCreate(mlmat->comm->USR_comm,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,m,n,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
  ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
  ierr = PetscMalloc3(m,PetscInt,&nnzA,m,PetscInt,&nnzB,m,PetscInt,&nnz);CHKERRQ(ierr);

  nz_max = 0;
  for (i=0; i<m; i++){
    nnz[i] = ml_cols[i+1] - ml_cols[i] + 1;
    if (nz_max < nnz[i]) nz_max = nnz[i];
    nnzA[i] = 1; /* diag */
    for (j=ml_cols[i]; j<ml_cols[i+1]; j++){
      if (ml_cols[j] < m) nnzA[i]++;
    }
    nnzB[i] = nnz[i] - nnzA[i];
  }
  ierr = MatMPIAIJSetPreallocation(A,0,nnzA,0,nnzB);CHKERRQ(ierr);

  /* insert mat values -- remap row and column indices */
  nz_max++;
  ierr = PetscMalloc(nz_max*(sizeof(PetscInt)+sizeof(PetscScalar)),&aj);CHKERRQ(ierr);
  aa = (PetscScalar*)(aj + nz_max);
  /* create global row numbering for a ML_Operator */
  ML_build_global_numbering(mlmat,&gordering,"rows");
  for (i=0; i<m; i++){
    row = gordering[i];
    k = 0;
    /* diagonal entry */
    aj[k] = row; aa[k++] = ml_vals[i];
    /* off diagonal entries */
    for (j=ml_cols[i]; j<ml_cols[i+1]; j++){
      aj[k] = gordering[ml_cols[j]]; aa[k++] = ml_vals[j];
    }
    ierr = MatSetValues(A,1,&row,nnz[i],aj,aa,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  *newmat = A;

  ierr = PetscFree3(nnzA,nnzB,nnz);
  ierr = PetscFree(aj);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}