xref: /petsc/src/mat/impls/aij/seq/superlu/superlu.c (revision 98921bda46e76d7aaed9e0138c5ff9d0ce93f355)

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

     This file implements a subclass of the SeqAIJ matrix class that uses
     the SuperLU sparse solver.
*/

/*
     Defines the data structure for the base matrix type (SeqAIJ)
*/
#include <../src/mat/impls/aij/seq/aij.h>    /*I "petscmat.h" I*/

/*
     SuperLU include files
*/
EXTERN_C_BEGIN
#if defined(PETSC_USE_COMPLEX)
#if defined(PETSC_USE_REAL_SINGLE)
#include <slu_cdefs.h>
#else
#include <slu_zdefs.h>
#endif
#else
#if defined(PETSC_USE_REAL_SINGLE)
#include <slu_sdefs.h>
#else
#include <slu_ddefs.h>
#endif
#endif
#include <slu_util.h>
EXTERN_C_END

/*
     This is the data that defines the SuperLU factored matrix type
*/
typedef struct {
  SuperMatrix       A,L,U,B,X;
  superlu_options_t options;
  PetscInt          *perm_c; /* column permutation vector */
  PetscInt          *perm_r; /* row permutations from partial pivoting */
  PetscInt          *etree;
  PetscReal         *R, *C;
  char              equed[1];
  PetscInt          lwork;
  void              *work;
  PetscReal         rpg, rcond;
  mem_usage_t       mem_usage;
  MatStructure      flg;
  SuperLUStat_t     stat;
  Mat               A_dup;
  PetscScalar       *rhs_dup;
  GlobalLU_t        Glu;
  PetscBool         needconversion;

  /* Flag to clean up (non-global) SuperLU objects during Destroy */
  PetscBool CleanUpSuperLU;
} Mat_SuperLU;

/*
    Utility function
*/
static PetscErrorCode MatView_Info_SuperLU(Mat A,PetscViewer viewer)
{
  Mat_SuperLU       *lu= (Mat_SuperLU*)A->data;
  PetscErrorCode    ierr;
  superlu_options_t options;

  PetscFunctionBegin;
  options = lu->options;

  ierr = PetscViewerASCIIPrintf(viewer,"SuperLU run parameters:\n");CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  Equil: %s\n",(options.Equil != NO) ? "YES" : "NO");CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ColPerm: %" PetscInt_FMT "\n",options.ColPerm);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  IterRefine: %" PetscInt_FMT "\n",options.IterRefine);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  SymmetricMode: %s\n",(options.SymmetricMode != NO) ? "YES" : "NO");CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  DiagPivotThresh: %g\n",options.DiagPivotThresh);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  PivotGrowth: %s\n",(options.PivotGrowth != NO) ? "YES" : "NO");CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ConditionNumber: %s\n",(options.ConditionNumber != NO) ? "YES" : "NO");CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  RowPerm: %" PetscInt_FMT "\n",options.RowPerm);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ReplaceTinyPivot: %s\n",(options.ReplaceTinyPivot != NO) ? "YES" : "NO");CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  PrintStat: %s\n",(options.PrintStat != NO) ? "YES" : "NO");CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  lwork: %" PetscInt_FMT "\n",lu->lwork);CHKERRQ(ierr);
  if (A->factortype == MAT_FACTOR_ILU) {
    ierr = PetscViewerASCIIPrintf(viewer,"  ILU_DropTol: %g\n",options.ILU_DropTol);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  ILU_FillTol: %g\n",options.ILU_FillTol);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  ILU_FillFactor: %g\n",options.ILU_FillFactor);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  ILU_DropRule: %" PetscInt_FMT "\n",options.ILU_DropRule);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  ILU_Norm: %" PetscInt_FMT "\n",options.ILU_Norm);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  ILU_MILU: %" PetscInt_FMT "\n",options.ILU_MILU);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatSolve_SuperLU_Private(Mat A,Vec b,Vec x)
{
  Mat_SuperLU       *lu = (Mat_SuperLU*)A->data;
  const PetscScalar *barray;
  PetscScalar       *xarray;
  PetscErrorCode    ierr;
  PetscInt          info,i,n;
  PetscReal         ferr,berr;
  static PetscBool  cite = PETSC_FALSE;

  PetscFunctionBegin;
  if (lu->lwork == -1) PetscFunctionReturn(0);
  ierr = PetscCitationsRegister("@article{superlu99,\n  author  = {James W. Demmel and Stanley C. Eisenstat and\n             John R. Gilbert and Xiaoye S. Li and Joseph W. H. Liu},\n  title = {A supernodal approach to sparse partial pivoting},\n  journal = {SIAM J. Matrix Analysis and Applications},\n  year = {1999},\n  volume  = {20},\n  number = {3},\n  pages = {720-755}\n}\n",&cite);CHKERRQ(ierr);

  ierr = VecGetLocalSize(x,&n);CHKERRQ(ierr);
  lu->B.ncol = 1;   /* Set the number of right-hand side */
  if (lu->options.Equil && !lu->rhs_dup) {
    /* superlu overwrites b when Equil is used, thus create rhs_dup to keep user's b unchanged */
    ierr = PetscMalloc1(n,&lu->rhs_dup);CHKERRQ(ierr);
  }
  if (lu->options.Equil) {
    /* Copy b into rsh_dup */
    ierr   = VecGetArrayRead(b,&barray);CHKERRQ(ierr);
    ierr   = PetscArraycpy(lu->rhs_dup,barray,n);CHKERRQ(ierr);
    ierr   = VecRestoreArrayRead(b,&barray);CHKERRQ(ierr);
    barray = lu->rhs_dup;
  } else {
    ierr = VecGetArrayRead(b,&barray);CHKERRQ(ierr);
  }
  ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);

#if defined(PETSC_USE_COMPLEX)
#if defined(PETSC_USE_REAL_SINGLE)
  ((DNformat*)lu->B.Store)->nzval = (singlecomplex*)barray;
  ((DNformat*)lu->X.Store)->nzval = (singlecomplex*)xarray;
#else
  ((DNformat*)lu->B.Store)->nzval = (doublecomplex*)barray;
  ((DNformat*)lu->X.Store)->nzval = (doublecomplex*)xarray;
#endif
#else
  ((DNformat*)lu->B.Store)->nzval = (void*)barray;
  ((DNformat*)lu->X.Store)->nzval = xarray;
#endif

  lu->options.Fact = FACTORED; /* Indicate the factored form of A is supplied. */
  if (A->factortype == MAT_FACTOR_LU) {
#if defined(PETSC_USE_COMPLEX)
#if defined(PETSC_USE_REAL_SINGLE)
    PetscStackCall("SuperLU:cgssvx",cgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &info));
#else
    PetscStackCall("SuperLU:zgssvx",zgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &info));
#endif
#else
#if defined(PETSC_USE_REAL_SINGLE)
    PetscStackCall("SuperLU:sgssvx",sgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &info));
#else
    PetscStackCall("SuperLU:dgssvx",dgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
                                     &lu->Glu,&lu->mem_usage, &lu->stat, &info));
#endif
#endif
  } else if (A->factortype == MAT_FACTOR_ILU) {
#if defined(PETSC_USE_COMPLEX)
#if defined(PETSC_USE_REAL_SINGLE)
    PetscStackCall("SuperLU:cgsisx",cgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &info));
#else
    PetscStackCall("SuperLU:zgsisx",zgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &info));
#endif
#else
#if defined(PETSC_USE_REAL_SINGLE)
    PetscStackCall("SuperLU:sgsisx",sgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &info));
#else
    PetscStackCall("SuperLU:dgsisx",dgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &info));
#endif
#endif
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
  if (!lu->options.Equil) {
    ierr = VecRestoreArrayRead(b,&barray);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);

  if (!info || info == lu->A.ncol+1) {
    if (lu->options.IterRefine) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"Iterative Refinement:\n");
      ierr = PetscPrintf(PETSC_COMM_SELF,"  %8s%8s%16s%16s\n", "rhs", "Steps", "FERR", "BERR");
      for (i = 0; i < 1; ++i) {
        ierr = PetscPrintf(PETSC_COMM_SELF,"  %8d%8d%16e%16e\n", i+1, lu->stat.RefineSteps, ferr, berr);
      }
    }
  } else if (info > 0) {
    if (lu->lwork == -1) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"  ** Estimated memory: %" PetscInt_FMT " bytes\n", info - lu->A.ncol);
    } else {
      ierr = PetscPrintf(PETSC_COMM_SELF,"  Warning: gssvx() returns info %" PetscInt_FMT "\n",info);
    }
  } else if (info < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB, "info = %" PetscInt_FMT ", the %" PetscInt_FMT "-th argument in gssvx() had an illegal value", info,-info);

  if (lu->options.PrintStat) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolve__SuperLU():\n");
    PetscStackCall("SuperLU:StatPrint",StatPrint(&lu->stat));
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatSolve_SuperLU(Mat A,Vec b,Vec x)
{
  Mat_SuperLU    *lu = (Mat_SuperLU*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (A->factorerrortype) {
    ierr = PetscInfo(A,"MatSolve is called with singular matrix factor, skip\n");CHKERRQ(ierr);
    ierr = VecSetInf(x);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  lu->options.Trans = TRANS;
  ierr = MatSolve_SuperLU_Private(A,b,x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatSolveTranspose_SuperLU(Mat A,Vec b,Vec x)
{
  Mat_SuperLU    *lu = (Mat_SuperLU*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (A->factorerrortype) {
    ierr = PetscInfo(A,"MatSolve is called with singular matrix factor, skip\n");CHKERRQ(ierr);
    ierr = VecSetInf(x);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  lu->options.Trans = NOTRANS;
  ierr = MatSolve_SuperLU_Private(A,b,x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatLUFactorNumeric_SuperLU(Mat F,Mat A,const MatFactorInfo *info)
{
  Mat_SuperLU    *lu = (Mat_SuperLU*)F->data;
  Mat_SeqAIJ     *aa;
  PetscErrorCode ierr;
  PetscInt       sinfo;
  PetscReal      ferr, berr;
  NCformat       *Ustore;
  SCformat       *Lstore;

  PetscFunctionBegin;
  if (lu->flg == SAME_NONZERO_PATTERN) { /* successing numerical factorization */
    lu->options.Fact = SamePattern;
    /* Ref: ~SuperLU_3.0/EXAMPLE/dlinsolx2.c */
    Destroy_SuperMatrix_Store(&lu->A);
    if (lu->A_dup) {
      ierr = MatCopy_SeqAIJ(A,lu->A_dup,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
    }

    if (lu->lwork >= 0) {
      PetscStackCall("SuperLU:Destroy_SuperNode_Matrix",Destroy_SuperNode_Matrix(&lu->L));
      PetscStackCall("SuperLU:Destroy_CompCol_Matrix",Destroy_CompCol_Matrix(&lu->U));
      lu->options.Fact = SamePattern;
    }
  }

  /* Create the SuperMatrix for lu->A=A^T:
       Since SuperLU likes column-oriented matrices,we pass it the transpose,
       and then solve A^T X = B in MatSolve(). */
  if (lu->A_dup) {
    aa = (Mat_SeqAIJ*)(lu->A_dup)->data;
  } else {
    aa = (Mat_SeqAIJ*)(A)->data;
  }
#if defined(PETSC_USE_COMPLEX)
#if defined(PETSC_USE_REAL_SINGLE)
  PetscStackCall("SuperLU:cCreate_CompCol_Matrix",cCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,(singlecomplex*)aa->a,aa->j,aa->i,SLU_NC,SLU_C,SLU_GE));
#else
  PetscStackCall("SuperLU:zCreate_CompCol_Matrix",zCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,(doublecomplex*)aa->a,aa->j,aa->i,SLU_NC,SLU_Z,SLU_GE));
#endif
#else
#if defined(PETSC_USE_REAL_SINGLE)
  PetscStackCall("SuperLU:sCreate_CompCol_Matrix",sCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,aa->a,aa->j,aa->i,SLU_NC,SLU_S,SLU_GE));
#else
  PetscStackCall("SuperLU:dCreate_CompCol_Matrix",dCreate_CompCol_Matrix(&lu->A,A->cmap->n,A->rmap->n,aa->nz,aa->a,aa->j,aa->i,SLU_NC,SLU_D,SLU_GE));
#endif
#endif

  /* Numerical factorization */
  lu->B.ncol = 0;  /* Indicate not to solve the system */
  if (F->factortype == MAT_FACTOR_LU) {
#if defined(PETSC_USE_COMPLEX)
#if defined(PETSC_USE_REAL_SINGLE)
    PetscStackCall("SuperLU:cgssvx",cgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
#else
    PetscStackCall("SuperLU:zgssvx",zgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
#endif
#else
#if defined(PETSC_USE_REAL_SINGLE)
    PetscStackCall("SuperLU:sgssvx",sgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
#else
    PetscStackCall("SuperLU:dgssvx",dgssvx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond, &ferr, &berr,
                                     &lu->Glu,&lu->mem_usage, &lu->stat, &sinfo));
#endif
#endif
  } else if (F->factortype == MAT_FACTOR_ILU) {
    /* Compute the incomplete factorization, condition number and pivot growth */
#if defined(PETSC_USE_COMPLEX)
#if defined(PETSC_USE_REAL_SINGLE)
    PetscStackCall("SuperLU:cgsisx",cgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r,lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
#else
    PetscStackCall("SuperLU:zgsisx",zgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r,lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
#endif
#else
#if defined(PETSC_USE_REAL_SINGLE)
    PetscStackCall("SuperLU:sgsisx",sgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
#else
    PetscStackCall("SuperLU:dgsisx",dgsisx(&lu->options, &lu->A, lu->perm_c, lu->perm_r, lu->etree, lu->equed, lu->R, lu->C,
                                     &lu->L, &lu->U, lu->work, lu->lwork, &lu->B, &lu->X, &lu->rpg, &lu->rcond,
                                     &lu->Glu, &lu->mem_usage, &lu->stat, &sinfo));
#endif
#endif
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
  if (!sinfo || sinfo == lu->A.ncol+1) {
    if (lu->options.PivotGrowth) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"  Recip. pivot growth = %e\n", lu->rpg);CHKERRQ(ierr);
    }
    if (lu->options.ConditionNumber) {
      ierr = PetscPrintf(PETSC_COMM_SELF,"  Recip. condition number = %e\n", lu->rcond);CHKERRQ(ierr);
    }
  } else if (sinfo > 0) {
    if (A->erroriffailure) {
      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot in row %" PetscInt_FMT,sinfo);
    } else {
      if (sinfo <= lu->A.ncol) {
        if (lu->options.ILU_FillTol == 0.0) {
          F->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
        }
        ierr = PetscInfo2(F,"Number of zero pivots %" PetscInt_FMT ", ILU_FillTol %g\n",sinfo,lu->options.ILU_FillTol);CHKERRQ(ierr);
      } else if (sinfo == lu->A.ncol + 1) {
        /*
         U is nonsingular, but RCOND is less than machine
                      precision, meaning that the matrix is singular to
                      working precision. Nevertheless, the solution and
                      error bounds are computed because there are a number
                      of situations where the computed solution can be more
                      accurate than the value of RCOND would suggest.
         */
        ierr = PetscInfo1(F,"Matrix factor U is nonsingular, but is singular to working precision. The solution is computed. info %" PetscInt_FMT,sinfo);CHKERRQ(ierr);
      } else { /* sinfo > lu->A.ncol + 1 */
        F->factorerrortype = MAT_FACTOR_OUTMEMORY;
        ierr = PetscInfo1(F,"Number of bytes allocated when memory allocation fails %" PetscInt_FMT "\n",sinfo);CHKERRQ(ierr);
      }
    }
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB, "info = %" PetscInt_FMT ", the %" PetscInt_FMT "-th argument in gssvx() had an illegal value", sinfo,-sinfo);

  if (lu->options.PrintStat) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"MatLUFactorNumeric_SuperLU():\n");CHKERRQ(ierr);
    PetscStackCall("SuperLU:StatPrint",StatPrint(&lu->stat));
    Lstore = (SCformat*) lu->L.Store;
    Ustore = (NCformat*) lu->U.Store;
    ierr   = PetscPrintf(PETSC_COMM_SELF,"  No of nonzeros in factor L = %" PetscInt_FMT "\n", Lstore->nnz);
    ierr   = PetscPrintf(PETSC_COMM_SELF,"  No of nonzeros in factor U = %" PetscInt_FMT "\n", Ustore->nnz);
    ierr   = PetscPrintf(PETSC_COMM_SELF,"  No of nonzeros in L+U = %" PetscInt_FMT "\n", Lstore->nnz + Ustore->nnz - lu->A.ncol);
    ierr   = PetscPrintf(PETSC_COMM_SELF,"  L\\U MB %.3f\ttotal MB needed %.3f\n",
                         lu->mem_usage.for_lu/1e6, lu->mem_usage.total_needed/1e6);
  }

  lu->flg                = SAME_NONZERO_PATTERN;
  F->ops->solve          = MatSolve_SuperLU;
  F->ops->solvetranspose = MatSolveTranspose_SuperLU;
  F->ops->matsolve       = NULL;
  PetscFunctionReturn(0);
}

static PetscErrorCode MatDestroy_SuperLU(Mat A)
{
  PetscErrorCode ierr;
  Mat_SuperLU    *lu=(Mat_SuperLU*)A->data;

  PetscFunctionBegin;
  if (lu->CleanUpSuperLU) { /* Free the SuperLU datastructures */
    PetscStackCall("SuperLU:Destroy_SuperMatrix_Store",Destroy_SuperMatrix_Store(&lu->A));
    PetscStackCall("SuperLU:Destroy_SuperMatrix_Store",Destroy_SuperMatrix_Store(&lu->B));
    PetscStackCall("SuperLU:Destroy_SuperMatrix_Store",Destroy_SuperMatrix_Store(&lu->X));
    PetscStackCall("SuperLU:StatFree",StatFree(&lu->stat));
    if (lu->lwork >= 0) {
      PetscStackCall("SuperLU:Destroy_SuperNode_Matrix",Destroy_SuperNode_Matrix(&lu->L));
      PetscStackCall("SuperLU:Destroy_CompCol_Matrix",Destroy_CompCol_Matrix(&lu->U));
    }
  }
  ierr = PetscFree(lu->etree);CHKERRQ(ierr);
  ierr = PetscFree(lu->perm_r);CHKERRQ(ierr);
  ierr = PetscFree(lu->perm_c);CHKERRQ(ierr);
  ierr = PetscFree(lu->R);CHKERRQ(ierr);
  ierr = PetscFree(lu->C);CHKERRQ(ierr);
  ierr = PetscFree(lu->rhs_dup);CHKERRQ(ierr);
  ierr = MatDestroy(&lu->A_dup);CHKERRQ(ierr);
  ierr = PetscFree(A->data);CHKERRQ(ierr);

  /* clear composed functions */
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatFactorGetSolverType_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatSuperluSetILUDropTol_C",NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode MatView_SuperLU(Mat A,PetscViewer viewer)
{
  PetscErrorCode    ierr;
  PetscBool         iascii;
  PetscViewerFormat format;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  if (iascii) {
    ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
    if (format == PETSC_VIEWER_ASCII_INFO) {
      ierr = MatView_Info_SuperLU(A,viewer);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatMatSolve_SuperLU(Mat A,Mat B,Mat X)
{
  Mat_SuperLU    *lu = (Mat_SuperLU*)A->data;
  PetscBool      flg;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompareAny((PetscObject)B,&flg,MATSEQDENSE,MATMPIDENSE,NULL);CHKERRQ(ierr);
  if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Matrix B must be MATDENSE matrix");
  ierr = PetscObjectTypeCompareAny((PetscObject)X,&flg,MATSEQDENSE,MATMPIDENSE,NULL);CHKERRQ(ierr);
  if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONG,"Matrix X must be MATDENSE matrix");
  lu->options.Trans = TRANS;
  SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatSolve_SuperLU() is not implemented yet");
  PetscFunctionReturn(0);
}

static PetscErrorCode MatLUFactorSymbolic_SuperLU(Mat F,Mat A,IS r,IS c,const MatFactorInfo *info)
{
  Mat_SuperLU    *lu = (Mat_SuperLU*)(F->data);
  PetscErrorCode ierr;

  PetscFunctionBegin;
  lu->flg                 = DIFFERENT_NONZERO_PATTERN;
  lu->CleanUpSuperLU      = PETSC_TRUE;
  F->ops->lufactornumeric = MatLUFactorNumeric_SuperLU;

  /* if we are here, the nonzero pattern has changed unless the user explicitly called MatLUFactorSymbolic */
  ierr = MatDestroy(&lu->A_dup);CHKERRQ(ierr);
  if (lu->needconversion) {
    ierr = MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&lu->A_dup);CHKERRQ(ierr);
  }
  if (lu->options.Equil == YES && !lu->A_dup) { /* superlu overwrites input matrix and rhs when Equil is used, thus create A_dup to keep user's A unchanged */
    ierr = MatDuplicate_SeqAIJ(A,MAT_COPY_VALUES,&lu->A_dup);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode MatSuperluSetILUDropTol_SuperLU(Mat F,PetscReal dtol)
{
  Mat_SuperLU *lu= (Mat_SuperLU*)F->data;

  PetscFunctionBegin;
  lu->options.ILU_DropTol = dtol;
  PetscFunctionReturn(0);
}

/*@
  MatSuperluSetILUDropTol - Set SuperLU ILU drop tolerance
   Logically Collective on Mat

   Input Parameters:
+  F - the factored matrix obtained by calling MatGetFactor() from PETSc-SuperLU interface
-  dtol - drop tolerance

  Options Database:
.   -mat_superlu_ilu_droptol <dtol>

   Level: beginner

   References:
.      SuperLU Users' Guide

.seealso: MatGetFactor()
@*/
PetscErrorCode MatSuperluSetILUDropTol(Mat F,PetscReal dtol)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(F,MAT_CLASSID,1);
  PetscValidLogicalCollectiveReal(F,dtol,2);
  ierr = PetscTryMethod(F,"MatSuperluSetILUDropTol_C",(Mat,PetscReal),(F,dtol));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatFactorGetSolverType_seqaij_superlu(Mat A,MatSolverType *type)
{
  PetscFunctionBegin;
  *type = MATSOLVERSUPERLU;
  PetscFunctionReturn(0);
}

/*MC
  MATSOLVERSUPERLU = "superlu" - A solver package providing solvers LU and ILU for sequential matrices
  via the external package SuperLU.

  Use ./configure --download-superlu to have PETSc installed with SuperLU

  Use -pc_type lu -pc_factor_mat_solver_type superlu to use this direct solver

  Options Database Keys:
+ -mat_superlu_equil <FALSE>            - Equil (None)
. -mat_superlu_colperm <COLAMD>         - (choose one of) NATURAL MMD_ATA MMD_AT_PLUS_A COLAMD
. -mat_superlu_iterrefine <NOREFINE>    - (choose one of) NOREFINE SINGLE DOUBLE EXTRA
. -mat_superlu_symmetricmode: <FALSE>   - SymmetricMode (None)
. -mat_superlu_diagpivotthresh <1>      - DiagPivotThresh (None)
. -mat_superlu_pivotgrowth <FALSE>      - PivotGrowth (None)
. -mat_superlu_conditionnumber <FALSE>  - ConditionNumber (None)
. -mat_superlu_rowperm <NOROWPERM>      - (choose one of) NOROWPERM LargeDiag
. -mat_superlu_replacetinypivot <FALSE> - ReplaceTinyPivot (None)
. -mat_superlu_printstat <FALSE>        - PrintStat (None)
. -mat_superlu_lwork <0>                - size of work array in bytes used by factorization (None)
. -mat_superlu_ilu_droptol <0>          - ILU_DropTol (None)
. -mat_superlu_ilu_filltol <0>          - ILU_FillTol (None)
. -mat_superlu_ilu_fillfactor <0>       - ILU_FillFactor (None)
. -mat_superlu_ilu_droprull <0>         - ILU_DropRule (None)
. -mat_superlu_ilu_norm <0>             - ILU_Norm (None)
- -mat_superlu_ilu_milu <0>             - ILU_MILU (None)

   Notes:
    Do not confuse this with MATSOLVERSUPERLU_DIST which is for parallel sparse solves

    Cannot currently use ordering provided by PETSc.

   Level: beginner

.seealso: PCLU, PCILU, MATSOLVERSUPERLU_DIST, MATSOLVERMUMPS, PCFactorSetMatSolverType(), MatSolverType
M*/

static PetscErrorCode MatGetFactor_seqaij_superlu(Mat A,MatFactorType ftype,Mat *F)
{
  Mat            B;
  Mat_SuperLU    *lu;
  PetscErrorCode ierr;
  PetscInt       indx,m=A->rmap->n,n=A->cmap->n;
  PetscBool      flg,set;
  PetscReal      real_input;
  const char     *colperm[]   ={"NATURAL","MMD_ATA","MMD_AT_PLUS_A","COLAMD"}; /* MY_PERMC - not supported by the petsc interface yet */
  const char     *iterrefine[]={"NOREFINE", "SINGLE", "DOUBLE", "EXTRA"};
  const char     *rowperm[]   ={"NOROWPERM", "LargeDiag"}; /* MY_PERMC - not supported by the petsc interface yet */

  PetscFunctionBegin;
  ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
  ierr = MatSetSizes(B,A->rmap->n,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = PetscStrallocpy("superlu",&((PetscObject)B)->type_name);CHKERRQ(ierr);
  ierr = MatSetUp(B);CHKERRQ(ierr);
  B->trivialsymbolic = PETSC_TRUE;
  if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU) {
    B->ops->lufactorsymbolic  = MatLUFactorSymbolic_SuperLU;
    B->ops->ilufactorsymbolic = MatLUFactorSymbolic_SuperLU;
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");

  ierr = PetscFree(B->solvertype);CHKERRQ(ierr);
  ierr = PetscStrallocpy(MATSOLVERSUPERLU,&B->solvertype);CHKERRQ(ierr);

  B->ops->getinfo     = MatGetInfo_External;
  B->ops->destroy     = MatDestroy_SuperLU;
  B->ops->view        = MatView_SuperLU;
  B->factortype       = ftype;
  B->assembled        = PETSC_TRUE;           /* required by -ksp_view */
  B->preallocated     = PETSC_TRUE;

  ierr = PetscNewLog(B,&lu);CHKERRQ(ierr);

  if (ftype == MAT_FACTOR_LU) {
    set_default_options(&lu->options);
    /* Comments from SuperLU_4.0/SRC/dgssvx.c:
      "Whether or not the system will be equilibrated depends on the
       scaling of the matrix A, but if equilibration is used, A is
       overwritten by diag(R)*A*diag(C) and B by diag(R)*B
       (if options->Trans=NOTRANS) or diag(C)*B (if options->Trans = TRANS or CONJ)."
     We set 'options.Equil = NO' as default because additional space is needed for it.
    */
    lu->options.Equil = NO;
  } else if (ftype == MAT_FACTOR_ILU) {
    /* Set the default input options of ilu: */
    PetscStackCall("SuperLU:ilu_set_default_options",ilu_set_default_options(&lu->options));
  }
  lu->options.PrintStat = NO;

  /* Initialize the statistics variables. */
  PetscStackCall("SuperLU:StatInit",StatInit(&lu->stat));
  lu->lwork = 0;   /* allocate space internally by system malloc */

  ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"SuperLU Options","Mat");CHKERRQ(ierr);
  ierr = PetscOptionsBool("-mat_superlu_equil","Equil","None",(PetscBool)lu->options.Equil,(PetscBool*)&lu->options.Equil,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsEList("-mat_superlu_colperm","ColPerm","None",colperm,4,colperm[3],&indx,&flg);CHKERRQ(ierr);
  if (flg) lu->options.ColPerm = (colperm_t)indx;
  ierr = PetscOptionsEList("-mat_superlu_iterrefine","IterRefine","None",iterrefine,4,iterrefine[0],&indx,&flg);CHKERRQ(ierr);
  if (flg) lu->options.IterRefine = (IterRefine_t)indx;
  ierr = PetscOptionsBool("-mat_superlu_symmetricmode","SymmetricMode","None",(PetscBool)lu->options.SymmetricMode,&flg,&set);CHKERRQ(ierr);
  if (set && flg) lu->options.SymmetricMode = YES;
  ierr = PetscOptionsReal("-mat_superlu_diagpivotthresh","DiagPivotThresh","None",lu->options.DiagPivotThresh,&real_input,&flg);CHKERRQ(ierr);
  if (flg) lu->options.DiagPivotThresh = (double) real_input;
  ierr = PetscOptionsBool("-mat_superlu_pivotgrowth","PivotGrowth","None",(PetscBool)lu->options.PivotGrowth,&flg,&set);CHKERRQ(ierr);
  if (set && flg) lu->options.PivotGrowth = YES;
  ierr = PetscOptionsBool("-mat_superlu_conditionnumber","ConditionNumber","None",(PetscBool)lu->options.ConditionNumber,&flg,&set);CHKERRQ(ierr);
  if (set && flg) lu->options.ConditionNumber = YES;
  ierr = PetscOptionsEList("-mat_superlu_rowperm","rowperm","None",rowperm,2,rowperm[lu->options.RowPerm],&indx,&flg);CHKERRQ(ierr);
  if (flg) lu->options.RowPerm = (rowperm_t)indx;
  ierr = PetscOptionsBool("-mat_superlu_replacetinypivot","ReplaceTinyPivot","None",(PetscBool)lu->options.ReplaceTinyPivot,&flg,&set);CHKERRQ(ierr);
  if (set && flg) lu->options.ReplaceTinyPivot = YES;
  ierr = PetscOptionsBool("-mat_superlu_printstat","PrintStat","None",(PetscBool)lu->options.PrintStat,&flg,&set);CHKERRQ(ierr);
  if (set && flg) lu->options.PrintStat = YES;
  ierr = PetscOptionsInt("-mat_superlu_lwork","size of work array in bytes used by factorization","None",lu->lwork,&lu->lwork,NULL);CHKERRQ(ierr);
  if (lu->lwork > 0) {
    /* lwork is in bytes, hence PetscMalloc() is used here, not PetscMalloc1()*/
    ierr = PetscMalloc(lu->lwork,&lu->work);CHKERRQ(ierr);
  } else if (lu->lwork != 0 && lu->lwork != -1) {
    ierr      = PetscPrintf(PETSC_COMM_SELF,"   Warning: lwork %" PetscInt_FMT " is not supported by SUPERLU. The default lwork=0 is used.\n",lu->lwork);
    lu->lwork = 0;
  }
  /* ilu options */
  ierr = PetscOptionsReal("-mat_superlu_ilu_droptol","ILU_DropTol","None",lu->options.ILU_DropTol,&real_input,&flg);CHKERRQ(ierr);
  if (flg) lu->options.ILU_DropTol = (double) real_input;
  ierr = PetscOptionsReal("-mat_superlu_ilu_filltol","ILU_FillTol","None",lu->options.ILU_FillTol,&real_input,&flg);CHKERRQ(ierr);
  if (flg) lu->options.ILU_FillTol = (double) real_input;
  ierr = PetscOptionsReal("-mat_superlu_ilu_fillfactor","ILU_FillFactor","None",lu->options.ILU_FillFactor,&real_input,&flg);CHKERRQ(ierr);
  if (flg) lu->options.ILU_FillFactor = (double) real_input;
  ierr = PetscOptionsInt("-mat_superlu_ilu_droprull","ILU_DropRule","None",lu->options.ILU_DropRule,&lu->options.ILU_DropRule,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsInt("-mat_superlu_ilu_norm","ILU_Norm","None",lu->options.ILU_Norm,&indx,&flg);CHKERRQ(ierr);
  if (flg) lu->options.ILU_Norm = (norm_t)indx;
  ierr = PetscOptionsInt("-mat_superlu_ilu_milu","ILU_MILU","None",lu->options.ILU_MILU,&indx,&flg);CHKERRQ(ierr);
  if (flg) lu->options.ILU_MILU = (milu_t)indx;
  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  /* Allocate spaces (notice sizes are for the transpose) */
  ierr = PetscMalloc1(m,&lu->etree);CHKERRQ(ierr);
  ierr = PetscMalloc1(n,&lu->perm_r);CHKERRQ(ierr);
  ierr = PetscMalloc1(m,&lu->perm_c);CHKERRQ(ierr);
  ierr = PetscMalloc1(n,&lu->R);CHKERRQ(ierr);
  ierr = PetscMalloc1(m,&lu->C);CHKERRQ(ierr);

  /* create rhs and solution x without allocate space for .Store */
#if defined(PETSC_USE_COMPLEX)
#if defined(PETSC_USE_REAL_SINGLE)
  PetscStackCall("SuperLU:cCreate_Dense_Matrix(",cCreate_Dense_Matrix(&lu->B, m, 1, NULL, m, SLU_DN, SLU_C, SLU_GE));
  PetscStackCall("SuperLU:cCreate_Dense_Matrix(",cCreate_Dense_Matrix(&lu->X, m, 1, NULL, m, SLU_DN, SLU_C, SLU_GE));
#else
  PetscStackCall("SuperLU:zCreate_Dense_Matrix",zCreate_Dense_Matrix(&lu->B, m, 1, NULL, m, SLU_DN, SLU_Z, SLU_GE));
  PetscStackCall("SuperLU:zCreate_Dense_Matrix",zCreate_Dense_Matrix(&lu->X, m, 1, NULL, m, SLU_DN, SLU_Z, SLU_GE));
#endif
#else
#if defined(PETSC_USE_REAL_SINGLE)
  PetscStackCall("SuperLU:sCreate_Dense_Matrix",sCreate_Dense_Matrix(&lu->B, m, 1, NULL, m, SLU_DN, SLU_S, SLU_GE));
  PetscStackCall("SuperLU:sCreate_Dense_Matrix",sCreate_Dense_Matrix(&lu->X, m, 1, NULL, m, SLU_DN, SLU_S, SLU_GE));
#else
  PetscStackCall("SuperLU:dCreate_Dense_Matrix",dCreate_Dense_Matrix(&lu->B, m, 1, NULL, m, SLU_DN, SLU_D, SLU_GE));
  PetscStackCall("SuperLU:dCreate_Dense_Matrix",dCreate_Dense_Matrix(&lu->X, m, 1, NULL, m, SLU_DN, SLU_D, SLU_GE));
#endif
#endif

  ierr     = PetscObjectComposeFunction((PetscObject)B,"MatFactorGetSolverType_C",MatFactorGetSolverType_seqaij_superlu);CHKERRQ(ierr);
  ierr     = PetscObjectComposeFunction((PetscObject)B,"MatSuperluSetILUDropTol_C",MatSuperluSetILUDropTol_SuperLU);CHKERRQ(ierr);
  B->data  = lu;

  *F       = B;
  PetscFunctionReturn(0);
}

static PetscErrorCode MatGetFactor_seqsell_superlu(Mat A,MatFactorType ftype,Mat *F)
{
  Mat_SuperLU    *lu;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatGetFactor_seqaij_superlu(A,ftype,F);CHKERRQ(ierr);
  lu   = (Mat_SuperLU*)((*F)->data);
  lu->needconversion = PETSC_TRUE;
  PetscFunctionReturn(0);
}

PETSC_EXTERN PetscErrorCode MatSolverTypeRegister_SuperLU(void)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatSolverTypeRegister(MATSOLVERSUPERLU,MATSEQAIJ,MAT_FACTOR_LU,MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
  ierr = MatSolverTypeRegister(MATSOLVERSUPERLU,MATSEQAIJ,MAT_FACTOR_ILU,MatGetFactor_seqaij_superlu);CHKERRQ(ierr);
  ierr = MatSolverTypeRegister(MATSOLVERSUPERLU,MATSEQSELL,MAT_FACTOR_LU,MatGetFactor_seqsell_superlu);CHKERRQ(ierr);
  ierr = MatSolverTypeRegister(MATSOLVERSUPERLU,MATSEQSELL,MAT_FACTOR_ILU,MatGetFactor_seqsell_superlu);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}