mpi/mumps/mumps.c

/*$Id: mumps.c,v 1.10 2001/08/15 15:56:50 bsmith Exp $*/
/*
    Provides an interface to the MUMPS_4.2_beta sparse solver
*/

#include "src/mat/impls/aij/seq/aij.h"
#include "src/mat/impls/aij/mpi/mpiaij.h"
#include "src/mat/impls/sbaij/seq/sbaij.h"
#include "src/mat/impls/sbaij/mpi/mpisbaij.h"

EXTERN_C_BEGIN
#if defined(PETSC_USE_COMPLEX)
#include "zmumps_c.h"
#else
#include "dmumps_c.h"
#endif
EXTERN_C_END
#define JOB_INIT -1
#define JOB_END -2
/* macros s.t. indices match MUMPS documentation */
#define ICNTL(I) icntl[(I)-1]
#define CNTL(I) cntl[(I)-1]
#define INFOG(I) infog[(I)-1]
#define RINFOG(I) rinfog[(I)-1]

typedef struct {
#if defined(PETSC_USE_COMPLEX)
  ZMUMPS_STRUC_C id;
#else
  DMUMPS_STRUC_C id;
#endif
  MatStructure   matstruc;
  int            myid,size,*irn,*jcn,sym;
  PetscScalar    *val;
  MPI_Comm       comm_mumps;

  MatType        basetype;
  PetscTruth     isAIJ,CleanUpMUMPS;
  int (*MatDuplicate)(Mat,MatDuplicateOption,Mat*);
  int (*MatView)(Mat,PetscViewer);
  int (*MatAssemblyEnd)(Mat,MatAssemblyType);
  int (*MatLUFactorSymbolic)(Mat,IS,IS,MatFactorInfo*,Mat*);
  int (*MatCholeskyFactorSymbolic)(Mat,IS,MatFactorInfo*,Mat*);
  int (*MatDestroy)(Mat);
} Mat_MUMPS;

EXTERN int MatDuplicate_AIJMUMPS(Mat,MatDuplicateOption,Mat*);
EXTERN int MatDuplicate_SBAIJMUMPS(Mat,MatDuplicateOption,Mat*);

/* convert Petsc mpiaij matrix to triples: row[nz], col[nz], val[nz] */
/*
  input:
    A       - matrix in mpiaij format
    shift   - 0: C style output triple; 1: Fortran style output triple.
    valOnly - FALSE: spaces are allocated and values are set for the triple
              TRUE:  only the values in v array are updated
  output:
    nnz     - dim of r, c, and v (number of local nonzero entries of A)
    r, c, v - row and col index, matrix values (matrix triples)
 */
int MatConvertToTriples(Mat A,int shift,PetscTruth valOnly,int *nnz,int **r, int **c, PetscScalar **v) {
  int         *ai, *aj, *bi, *bj, rstart,nz, *garray;
  int         ierr,i,j,jj,jB,irow,m=A->m,*ajj,*bjj,countA,countB,colA_start,jcol;
  int         *row,*col;
  PetscScalar *av, *bv,*val;
  Mat_MUMPS   *mumps=(Mat_MUMPS*)A->spptr;

  PetscFunctionBegin;

  if (mumps->isAIJ){
    Mat_MPIAIJ    *mat =  (Mat_MPIAIJ*)A->data;
    Mat_SeqAIJ    *aa=(Mat_SeqAIJ*)(mat->A)->data;
    Mat_SeqAIJ    *bb=(Mat_SeqAIJ*)(mat->B)->data;
    nz = aa->nz + bb->nz;
    ai=aa->i; aj=aa->j; bi=bb->i; bj=bb->j; rstart= mat->rstart;
    garray = mat->garray;
    av=aa->a; bv=bb->a;

  } else {
    Mat_MPISBAIJ  *mat =  (Mat_MPISBAIJ*)A->data;
    Mat_SeqSBAIJ  *aa=(Mat_SeqSBAIJ*)(mat->A)->data;
    Mat_SeqBAIJ    *bb=(Mat_SeqBAIJ*)(mat->B)->data;
    if (mat->bs > 1) SETERRQ1(PETSC_ERR_SUP," bs=%d is not supported yet\n", mat->bs);
    nz = aa->s_nz + bb->nz;
    ai=aa->i; aj=aa->j; bi=bb->i; bj=bb->j; rstart= mat->rstart;
    garray = mat->garray;
    av=aa->a; bv=bb->a;
  }

  if (!valOnly){
    ierr = PetscMalloc(nz*sizeof(int),&row);CHKERRQ(ierr);
    ierr = PetscMalloc(nz*sizeof(int),&col);CHKERRQ(ierr);
    ierr = PetscMalloc(nz*sizeof(PetscScalar),&val);CHKERRQ(ierr);
    *r = row; *c = col; *v = val;
  } else {
    row = *r; col = *c; val = *v;
  }
  *nnz = nz;

  jj = 0; jB = 0; irow = rstart;
  for ( i=0; i<m; i++ ) {
    ajj = aj + ai[i];                 /* ptr to the beginning of this row */
    countA = ai[i+1] - ai[i];
    countB = bi[i+1] - bi[i];
    bjj = bj + bi[i];

    /* get jB, the starting local col index for the 2nd B-part */
    colA_start = rstart + ajj[0]; /* the smallest col index for A */
    for (j=0; j<countB; j++){
      jcol = garray[bjj[j]];
      if (jcol > colA_start) { jB = j; break; }
      if (j==countB-1) jB = countB;
    }

    /* B-part, smaller col index */
    colA_start = rstart + ajj[0]; /* the smallest col index for A */
    for (j=0; j<jB; j++){
      jcol = garray[bjj[j]];
      if (!valOnly){
        row[jj] = irow + shift; col[jj] = jcol + shift;
      }
      val[jj++] = *bv++;
    }
    /* A-part */
    for (j=0; j<countA; j++){
      if (!valOnly){
        row[jj] = irow + shift; col[jj] = rstart + ajj[j] + shift;
      }
      val[jj++] = *av++;
    }
    /* B-part, larger col index */
    for (j=jB; j<countB; j++){
      if (!valOnly){
        row[jj] = irow + shift; col[jj] = garray[bjj[j]] + shift;
      }
      val[jj++] = *bv++;
    }
    irow++;
  }

  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatConvert_MUMPS_Base"
int MatConvert_MUMPS_Base(Mat A,MatType type,Mat *newmat) {
  int       ierr;
  Mat       B=*newmat;
  Mat_MUMPS *mumps=(Mat_MUMPS*)A->spptr;

  PetscFunctionBegin;
  if (B != A) {
    ierr = MatDuplicate(A,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
  }
  B->ops->duplicate              = mumps->MatDuplicate;
  B->ops->view                   = mumps->MatView;
  B->ops->assemblyend            = mumps->MatAssemblyEnd;
  B->ops->lufactorsymbolic       = mumps->MatLUFactorSymbolic;
  B->ops->choleskyfactorsymbolic = mumps->MatCholeskyFactorSymbolic;
  B->ops->destroy                = mumps->MatDestroy;
  ierr = PetscObjectChangeTypeName((PetscObject)B,type);CHKERRQ(ierr);
  ierr = PetscStrfree(mumps->basetype);CHKERRQ(ierr);
  ierr = PetscFree(mumps);CHKERRQ(ierr);
  *newmat = B;
  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatDestroy_MUMPS"
int MatDestroy_MUMPS(Mat A) {
  Mat_MUMPS *lu=(Mat_MUMPS*)A->spptr;
  int       ierr,size=lu->size;

  PetscFunctionBegin;
  if (lu->CleanUpMUMPS) {
    /* Terminate instance, deallocate memories */
    lu->id.job=JOB_END;
#if defined(PETSC_USE_COMPLEX)
    zmumps_c(&lu->id);
#else
    dmumps_c(&lu->id);
#endif
    if (lu->irn) {
      ierr = PetscFree(lu->irn);CHKERRQ(ierr);
    }
    if (lu->jcn) {
      ierr = PetscFree(lu->jcn);CHKERRQ(ierr);
    }
    if (size>1 && lu->val) {
      ierr = PetscFree(lu->val);CHKERRQ(ierr);
    }
    ierr = MPI_Comm_free(&(lu->comm_mumps));CHKERRQ(ierr);
  }
  ierr = MatConvert_MUMPS_Base(A,lu->basetype,&A);CHKERRQ(ierr);
  ierr = (*A->ops->destroy)(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFactorInfo_MUMPS"
int MatFactorInfo_MUMPS(Mat A,PetscViewer viewer) {
  Mat_MUMPS *lu=(Mat_MUMPS*)A->spptr;
  int       ierr;

  PetscFunctionBegin;
  ierr = PetscViewerASCIIPrintf(viewer,"MUMPS run parameters:\n");CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  SYM (matrix type):                  %d \n",lu->id.sym);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  PAR (host participation):           %d \n",lu->id.par);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(4) (level of printing):       %d \n",lu->id.ICNTL(4));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(5) (input mat struct):        %d \n",lu->id.ICNTL(5));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(6) (matrix prescaling):       %d \n",lu->id.ICNTL(6));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(7) (matrix ordering):         %d \n",lu->id.ICNTL(7));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(9) (A/A^T x=b is solved):     %d \n",lu->id.ICNTL(9));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(10) (max num of refinements): %d \n",lu->id.ICNTL(10));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(11) (error analysis):         %d \n",lu->id.ICNTL(11));CHKERRQ(ierr);
  if (lu->myid == 0 && lu->id.ICNTL(11)>0) {
    ierr = PetscPrintf(PETSC_COMM_SELF,"        RINFOG(4) (inf norm of input mat):        %g\n",lu->id.RINFOG(4));CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_SELF,"        RINFOG(5) (inf norm of solution):         %g\n",lu->id.RINFOG(5));CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_SELF,"        RINFOG(6) (inf norm of residual):         %g\n",lu->id.RINFOG(6));CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_SELF,"        RINFOG(7),RINFOG(8) (backward error est): %g, %g\n",lu->id.RINFOG(7),lu->id.RINFOG(8));CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_SELF,"        RINFOG(9) (error estimate):               %g \n",lu->id.RINFOG(9));CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_SELF,"        RINFOG(10),RINFOG(11)(condition numbers): %g, %g\n",lu->id.RINFOG(10),lu->id.RINFOG(11));CHKERRQ(ierr);

  }
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(12) (efficiency control):     %d \n",lu->id.ICNTL(12));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(13) (efficiency control):     %d \n",lu->id.ICNTL(13));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(14) (efficiency control):     %d \n",lu->id.ICNTL(14));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(15) (efficiency control):     %d \n",lu->id.ICNTL(15));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  ICNTL(18) (input mat struct):       %d \n",lu->id.ICNTL(18));CHKERRQ(ierr);

  ierr = PetscViewerASCIIPrintf(viewer,"  CNTL(1) (relative pivoting threshold):      %g \n",lu->id.CNTL(1));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  CNTL(2) (stopping criterion of refinement): %g \n",lu->id.CNTL(2));CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer,"  CNTL(3) (absolute pivoting threshold):      %g \n",lu->id.CNTL(3));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatView_AIJMUMPS"
int MatView_AIJMUMPS(Mat A,PetscViewer viewer) {
  int               ierr;
  PetscTruth        isascii;
  PetscViewerFormat format;
  Mat_MUMPS         *mumps=(Mat_MUMPS*)(A->spptr);

  PetscFunctionBegin;
  ierr = (*mumps->MatView)(A,viewer);CHKERRQ(ierr);

  ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&isascii);CHKERRQ(ierr);
  if (isascii) {
    ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
    if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
      ierr = MatFactorInfo_MUMPS(A,viewer);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolve_AIJMUMPS"
int MatSolve_AIJMUMPS(Mat A,Vec b,Vec x) {
  Mat_MUMPS   *lu=(Mat_MUMPS*)A->spptr;
  PetscScalar *array;
  Vec         x_seq;
  IS          iden;
  VecScatter  scat;
  int         ierr;

  PetscFunctionBegin;
  if (lu->size > 1){
    if (!lu->myid){
      ierr = VecCreateSeq(PETSC_COMM_SELF,A->N,&x_seq);CHKERRQ(ierr);
      ierr = ISCreateStride(PETSC_COMM_SELF,A->N,0,1,&iden);CHKERRQ(ierr);
    } else {
      ierr = VecCreateSeq(PETSC_COMM_SELF,0,&x_seq);CHKERRQ(ierr);
      ierr = ISCreateStride(PETSC_COMM_SELF,0,0,1,&iden);CHKERRQ(ierr);
    }
    ierr = VecScatterCreate(b,iden,x_seq,iden,&scat);CHKERRQ(ierr);
    ierr = ISDestroy(iden);CHKERRQ(ierr);

    ierr = VecScatterBegin(b,x_seq,INSERT_VALUES,SCATTER_FORWARD,scat);CHKERRQ(ierr);
    ierr = VecScatterEnd(b,x_seq,INSERT_VALUES,SCATTER_FORWARD,scat);CHKERRQ(ierr);
    if (!lu->myid) {ierr = VecGetArray(x_seq,&array);CHKERRQ(ierr);}
  } else {  /* size == 1 */
    ierr = VecCopy(b,x);CHKERRQ(ierr);
    ierr = VecGetArray(x,&array);CHKERRQ(ierr);
  }
  if (!lu->myid) { /* define rhs on the host */
#if defined(PETSC_USE_COMPLEX)
    lu->id.rhs = (mumps_double_complex*)array;
#else
    lu->id.rhs = array;
#endif
  }

  /* solve phase */
  lu->id.job=3;
#if defined(PETSC_USE_COMPLEX)
  zmumps_c(&lu->id);
#else
  dmumps_c(&lu->id);
#endif
  if (lu->id.INFOG(1) < 0) {
    SETERRQ1(1,"Error reported by MUMPS in solve phase: INFOG(1)=%d\n",lu->id.INFOG(1));
  }

  /* convert mumps solution x_seq to petsc mpi x */
  if (lu->size > 1) {
    if (!lu->myid){
      ierr = VecRestoreArray(x_seq,&array);CHKERRQ(ierr);
    }
    ierr = VecScatterBegin(x_seq,x,INSERT_VALUES,SCATTER_REVERSE,scat);CHKERRQ(ierr);
    ierr = VecScatterEnd(x_seq,x,INSERT_VALUES,SCATTER_REVERSE,scat);CHKERRQ(ierr);
    ierr = VecScatterDestroy(scat);CHKERRQ(ierr);
    ierr = VecDestroy(x_seq);CHKERRQ(ierr);
  } else {
    ierr = VecRestoreArray(x,&array);CHKERRQ(ierr);
  }

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFactorNumeric_MPIAIJMUMPS"
int MatFactorNumeric_AIJMUMPS(Mat A,Mat *F) {
  Mat_MUMPS  *lu =(Mat_MUMPS*)(*F)->spptr;
  Mat_MUMPS  *lua=(Mat_MUMPS*)(A)->spptr;
  int        rnz,nnz,ierr,nz,i,M=A->M,*ai,*aj,icntl;
  PetscTruth valOnly,flg;

  PetscFunctionBegin;
  if (lu->matstruc == DIFFERENT_NONZERO_PATTERN){
    (*F)->ops->solve    = MatSolve_AIJMUMPS;

    /* Initialize a MUMPS instance */
    ierr = MPI_Comm_rank(A->comm, &lu->myid);
    ierr = MPI_Comm_size(A->comm,&lu->size);CHKERRQ(ierr);
    lu->id.job = JOB_INIT;
    ierr = MPI_Comm_dup(A->comm,&(lu->comm_mumps));CHKERRQ(ierr);
    lu->id.comm_fortran = lu->comm_mumps;

    /* Set mumps options */
    ierr = PetscOptionsBegin(A->comm,A->prefix,"MUMPS Options","Mat");CHKERRQ(ierr);
    lu->id.par=1;  /* host participates factorizaton and solve */
    lu->id.sym=lu->sym;
    if (lu->sym == 2){
      ierr = PetscOptionsInt("-mat_mumps_sym","SYM: (1,2)","None",lu->id.sym,&icntl,&flg);CHKERRQ(ierr);
      if (flg && icntl == 1) lu->id.sym=icntl;  /* matrix is spd */
    }
#if defined(PETSC_USE_COMPLEX)
  zmumps_c(&lu->id);
#else
  dmumps_c(&lu->id);
#endif

    if (lu->size == 1){
      lu->id.ICNTL(18) = 0;   /* centralized assembled matrix input */
    } else {
      lu->id.ICNTL(18) = 3;   /* distributed assembled matrix input */
    }

    icntl=-1;
    ierr = PetscOptionsInt("-mat_mumps_icntl_4","ICNTL(4): level of printing (0 to 4)","None",lu->id.ICNTL(4),&icntl,&flg);CHKERRQ(ierr);
    if (flg && icntl > 0) {
      lu->id.ICNTL(4)=icntl; /* and use mumps default icntl(i), i=1,2,3 */
    } else { /* no output */
      lu->id.ICNTL(1) = 0;  /* error message, default= 6 */
      lu->id.ICNTL(2) = -1; /* output stream for diagnostic printing, statistics, and warning. default=0 */
      lu->id.ICNTL(3) = -1; /* output stream for global information, default=6 */
      lu->id.ICNTL(4) = 0;  /* level of printing, 0,1,2,3,4, default=2 */
    }
    ierr = PetscOptionsInt("-mat_mumps_icntl_6","ICNTL(6): matrix prescaling (0 to 7)","None",lu->id.ICNTL(6),&lu->id.ICNTL(6),PETSC_NULL);CHKERRQ(ierr);
    icntl=-1;
    ierr = PetscOptionsInt("-mat_mumps_icntl_7","ICNTL(7): matrix ordering (0 to 7)","None",lu->id.ICNTL(7),&icntl,&flg);CHKERRQ(ierr);
    if (flg) {
      if (icntl== 1){
        SETERRQ(PETSC_ERR_SUP,"pivot order be set by the user in PERM_IN -- not supported by the PETSc/MUMPS interface\n");
      } else {
        lu->id.ICNTL(7) = icntl;
      }
    }
    ierr = PetscOptionsInt("-mat_mumps_icntl_9","ICNTL(9): A or A^T x=b to be solved. 1: A; otherwise: A^T","None",lu->id.ICNTL(9),&lu->id.ICNTL(9),PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscOptionsInt("-mat_mumps_icntl_10","ICNTL(10): max num of refinements","None",lu->id.ICNTL(10),&lu->id.ICNTL(10),PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscOptionsInt("-mat_mumps_icntl_11","ICNTL(11): error analysis, a positive value returns statistics (by -sles_view)","None",lu->id.ICNTL(11),&lu->id.ICNTL(11),PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscOptionsInt("-mat_mumps_icntl_12","ICNTL(12): efficiency control","None",lu->id.ICNTL(12),&lu->id.ICNTL(12),PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscOptionsInt("-mat_mumps_icntl_13","ICNTL(13): efficiency control","None",lu->id.ICNTL(13),&lu->id.ICNTL(13),PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscOptionsInt("-mat_mumps_icntl_14","ICNTL(14): efficiency control","None",lu->id.ICNTL(14),&lu->id.ICNTL(14),PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscOptionsInt("-mat_mumps_icntl_15","ICNTL(15): efficiency control","None",lu->id.ICNTL(15),&lu->id.ICNTL(15),PETSC_NULL);CHKERRQ(ierr);

    /*
    ierr = PetscOptionsInt("-mat_mumps_icntl_16","ICNTL(16): 1: rank detection; 2: rank detection and nullspace","None",lu->id.ICNTL(16),&icntl,&flg);CHKERRQ(ierr);
    if (flg){
      if (icntl >-1 && icntl <3 ){
        if (lu->myid==0) lu->id.ICNTL(16) = icntl;
      } else {
        SETERRQ1(PETSC_ERR_SUP,"ICNTL(16)=%d -- not supported\n",icntl);
      }
    }
    */

    ierr = PetscOptionsReal("-mat_mumps_cntl_1","CNTL(1): relative pivoting threshold","None",lu->id.CNTL(1),&lu->id.CNTL(1),PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-mat_mumps_cntl_2","CNTL(2): stopping criterion of refinement","None",lu->id.CNTL(2),&lu->id.CNTL(2),PETSC_NULL);CHKERRQ(ierr);
    ierr = PetscOptionsReal("-mat_mumps_cntl_3","CNTL(3): absolute pivoting threshold","None",lu->id.CNTL(3),&lu->id.CNTL(3),PETSC_NULL);CHKERRQ(ierr);
    PetscOptionsEnd();
  }

  /* define matrix A */
  switch (lu->id.ICNTL(18)){
  case 0:  /* centralized assembled matrix input (size=1) */
    if (!lu->myid) {
      if (lua->isAIJ){
        Mat_SeqAIJ   *aa = (Mat_SeqAIJ*)A->data;
        nz               = aa->nz;
        ai = aa->i; aj = aa->j; lu->val = aa->a;
      } else {
        Mat_SeqSBAIJ *aa = (Mat_SeqSBAIJ*)A->data;
        nz                  =  aa->s_nz;
        ai = aa->i; aj = aa->j; lu->val = aa->a;
      }
      if (lu->matstruc == DIFFERENT_NONZERO_PATTERN){ /* first numeric factorization, get irn and jcn */
        ierr = PetscMalloc(nz*sizeof(int),&lu->irn);CHKERRQ(ierr);
        ierr = PetscMalloc(nz*sizeof(int),&lu->jcn);CHKERRQ(ierr);
        nz = 0;
        for (i=0; i<M; i++){
          rnz = ai[i+1] - ai[i];
          while (rnz--) {  /* Fortran row/col index! */
            lu->irn[nz] = i+1; lu->jcn[nz] = (*aj)+1; aj++; nz++;
          }
        }
      }
    }
    break;
  case 3:  /* distributed assembled matrix input (size>1) */
    if (lu->matstruc == DIFFERENT_NONZERO_PATTERN){
      valOnly = PETSC_FALSE;
    } else {
      valOnly = PETSC_TRUE; /* only update mat values, not row and col index */
    }
    ierr = MatConvertToTriples(A,1,valOnly, &nnz, &lu->irn, &lu->jcn, &lu->val);CHKERRQ(ierr);
    break;
  default: SETERRQ(PETSC_ERR_SUP,"Matrix input format is not supported by MUMPS.");
  }

  /* analysis phase */
  if (lu->matstruc == DIFFERENT_NONZERO_PATTERN){
     lu->id.n = M;
    switch (lu->id.ICNTL(18)){
    case 0:  /* centralized assembled matrix input */
      if (!lu->myid) {
        lu->id.nz =nz; lu->id.irn=lu->irn; lu->id.jcn=lu->jcn;
        if (lu->id.ICNTL(6)>1){
#if defined(PETSC_USE_COMPLEX)
          lu->id.a = (mumps_double_complex*)lu->val;
#else
          lu->id.a = lu->val;
#endif
        }
      }
      break;
    case 3:  /* distributed assembled matrix input (size>1) */
      lu->id.nz_loc = nnz;
      lu->id.irn_loc=lu->irn; lu->id.jcn_loc=lu->jcn;
      if (lu->id.ICNTL(6)>1) {
#if defined(PETSC_USE_COMPLEX)
        lu->id.a_loc = (mumps_double_complex*)lu->val;
#else
        lu->id.a_loc = lu->val;
#endif
      }
      break;
    }
    lu->id.job=1;
#if defined(PETSC_USE_COMPLEX)
  zmumps_c(&lu->id);
#else
  dmumps_c(&lu->id);
#endif
    if (lu->id.INFOG(1) < 0) {
      SETERRQ1(1,"Error reported by MUMPS in analysis phase: INFOG(1)=%d\n",lu->id.INFOG(1));
    }
  }

  /* numerical factorization phase */
  if(lu->id.ICNTL(18) == 0) {
    if (lu->myid == 0) {
#if defined(PETSC_USE_COMPLEX)
      lu->id.a = (mumps_double_complex*)lu->val;
#else
      lu->id.a = lu->val;
#endif
    }
  } else {
#if defined(PETSC_USE_COMPLEX)
    lu->id.a_loc = (mumps_double_complex*)lu->val;
#else
    lu->id.a_loc = lu->val;
#endif
  }
  lu->id.job=2;
#if defined(PETSC_USE_COMPLEX)
  zmumps_c(&lu->id);
#else
  dmumps_c(&lu->id);
#endif
  if (lu->id.INFOG(1) < 0) {
    SETERRQ1(1,"1, Error reported by MUMPS in numerical factorization phase: INFOG(1)=%d\n",lu->id.INFOG(1));
  }

  if (lu->myid==0 && lu->id.ICNTL(16) > 0){
    SETERRQ1(1,"  lu->id.ICNTL(16):=%d\n",lu->id.INFOG(16));
  }

  (*F)->assembled  = PETSC_TRUE;
  lu->matstruc     = SAME_NONZERO_PATTERN;
  lu->CleanUpMUMPS = PETSC_TRUE;
  PetscFunctionReturn(0);
}

/* Note the Petsc r and c permutations are ignored */
#undef __FUNCT__
#define __FUNCT__ "MatLUFactorSymbolic_AIJMUMPS"
int MatLUFactorSymbolic_AIJMUMPS(Mat A,IS r,IS c,MatFactorInfo *info,Mat *F) {
  Mat       B;
  Mat_MUMPS *lu;
  int       ierr;

  PetscFunctionBegin;

  /* Create the factorization matrix */
  ierr = MatCreate(A->comm,A->m,A->n,A->M,A->N,&B);CHKERRQ(ierr);
  ierr = MatSetType(B,MATAIJMUMPS);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(B,0,PETSC_NULL);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(B,0,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);

  B->ops->lufactornumeric = MatFactorNumeric_AIJMUMPS;
  B->factor               = FACTOR_LU;
  lu                      = (Mat_MUMPS*)B->spptr;
  lu->sym                 = 0;
  lu->matstruc            = DIFFERENT_NONZERO_PATTERN;

  *F = B;
  PetscFunctionReturn(0);
}

/* Note the Petsc r permutation is ignored */
#undef __FUNCT__
#define __FUNCT__ "MatCholeskyFactorSymbolic_SBAIJMUMPS"
int MatCholeskyFactorSymbolic_SBAIJMUMPS(Mat A,IS r,MatFactorInfo *info,Mat *F) {
  Mat       B;
  Mat_MUMPS *lu;
  int       ierr;

  PetscFunctionBegin;

  /* Create the factorization matrix */
  ierr = MatCreate(A->comm,A->m,A->n,A->M,A->N,&B);CHKERRQ(ierr);
  ierr = MatSetType(B,MATAIJMUMPS);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(B,0,PETSC_NULL);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(B,0,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);

  B->ops->choleskyfactornumeric = MatFactorNumeric_AIJMUMPS;
  B->factor                     = FACTOR_CHOLESKY;
  lu                            = (Mat_MUMPS*)B->spptr;
  lu->sym                       = 2;
  lu->matstruc                  = DIFFERENT_NONZERO_PATTERN;

  *F = B;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatAssemblyEnd_AIJMUMPS"
int MatAssemblyEnd_AIJMUMPS(Mat A,MatAssemblyType mode) {
  int       ierr;
  Mat_MUMPS *mumps=(Mat_MUMPS*)A->spptr;

  PetscFunctionBegin;
  ierr = (*mumps->MatAssemblyEnd)(A,mode);CHKERRQ(ierr);

  mumps->MatLUFactorSymbolic       = A->ops->lufactorsymbolic;
  mumps->MatCholeskyFactorSymbolic = A->ops->choleskyfactorsymbolic;
  A->ops->lufactorsymbolic         = MatLUFactorSymbolic_AIJMUMPS;
  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatConvert_AIJ_AIJMUMPS"
int MatConvert_AIJ_AIJMUMPS(Mat A,MatType newtype,Mat *newmat) {
  int       ierr,size;
  MPI_Comm  comm;
  Mat       B=*newmat;
  Mat_MUMPS *mumps;

  PetscFunctionBegin;
  if (B != A) {
    ierr = MatDuplicate(A,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
  }

  ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
  ierr = PetscNew(Mat_MUMPS,&mumps);CHKERRQ(ierr);

  mumps->MatDuplicate              = A->ops->duplicate;
  mumps->MatView                   = A->ops->view;
  mumps->MatAssemblyEnd            = A->ops->assemblyend;
  mumps->MatLUFactorSymbolic       = A->ops->lufactorsymbolic;
  mumps->MatCholeskyFactorSymbolic = A->ops->choleskyfactorsymbolic;
  mumps->MatDestroy                = A->ops->destroy;
  mumps->CleanUpMUMPS              = PETSC_FALSE;
  mumps->isAIJ                     = PETSC_TRUE;

  B->spptr                         = (void *)mumps;
  B->ops->duplicate                = MatDuplicate_AIJMUMPS;
  B->ops->view                     = MatView_AIJMUMPS;
  B->ops->assemblyend              = MatAssemblyEnd_AIJMUMPS;
  B->ops->lufactorsymbolic         = MatLUFactorSymbolic_AIJMUMPS;
  B->ops->destroy                  = MatDestroy_MUMPS;

  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);CHKERRQ(ierr);
  if (size == 1) {
    ierr = PetscStrallocpy(MATSEQAIJ,&(mumps->basetype));CHKERRQ(ierr);
    ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_seqaij_aijmumps_C",
                                             "MatConvert_AIJ_AIJMUMPS",MatConvert_AIJ_AIJMUMPS);CHKERRQ(ierr);
    ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_aijmumps_seqaij_C",
                                             "MatConvert_MUMPS_Base",MatConvert_MUMPS_Base);CHKERRQ(ierr);
  } else {
    ierr = PetscStrallocpy(MATMPIAIJ,&(mumps->basetype));CHKERRQ(ierr);
    ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_mpiaij_aijmumps_C",
                                             "MatConvert_AIJ_AIJMUMPS",MatConvert_AIJ_AIJMUMPS);CHKERRQ(ierr);
    ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_aijmumps_mpiaij_C",
                                             "MatConvert_MUMPS_Base",MatConvert_MUMPS_Base);CHKERRQ(ierr);
  }

  PetscLogInfo(0,"Using MUMPS for LU factorization and solves.");
  ierr = PetscObjectChangeTypeName((PetscObject)B,newtype);CHKERRQ(ierr);
  *newmat = B;
  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatDuplicate_AIJMUMPS"
int MatDuplicate_AIJMUMPS(Mat A, MatDuplicateOption op, Mat *M) {
  int ierr;
  PetscFunctionBegin;
  ierr = (*A->ops->duplicate)(A,op,M);CHKERRQ(ierr);
  ierr = MatConvert_AIJ_AIJMUMPS(*M,MATAIJMUMPS,M);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*MC
  MATAIJMUMPS = "aijmumps" - A matrix type providing direct solvers (LU) for distributed
  and sequential matrices via the external package MUMPS.

  If MUMPS is installed (see the manual for instructions
  on how to declare the existence of external packages),
  a matrix type can be constructed which invokes MUMPS solvers.
  After calling MatCreate(...,A), simply call MatSetType(A,MATAIJMUMPS).
  This matrix type is only supported for double precision real.

  If created with a single process communicator, this matrix type inherits from MATSEQAIJ.
  Otherwise, this matrix type inherits from MATMPIAIJ.  Hence for single process communicators,
  MatSeqAIJSetPreallocation is supported, and similarly MatMPIAIJSetPreallocation is supported
  for communicators controlling multiple processes.  It is recommended that you call both of
  the above preallocation routines for simplicity.  One can also call MatConvert for an inplace
  conversion to or from the MATSEQAIJ or MATMPIAIJ type (depending on the communicator size)
  without data copy.

  Options Database Keys:
+ -mat_type aijmumps - sets the matrix type to "aijmumps" during a call to MatSetFromOptions()
. -mat_mumps_sym <0,1,2> - 0 the matrix is unsymmetric, 1 symmetric positive definite, 2 symmetric
. -mat_mumps_icntl_4 <0,1,2,3,4> - print level
. -mat_mumps_icntl_6 <0,...,7> - matrix prescaling options (see MUMPS User's Guide)
. -mat_mumps_icntl_7 <0,...,7> - matrix orderings (see MUMPS User's Guide)
. -mat_mumps_icntl_9 <1,2> - A or A^T x=b to be solved: 1 denotes A, 2 denotes A^T
. -mat_mumps_icntl_10 <n> - maximum number of iterative refinements
. -mat_mumps_icntl_11 <n> - error analysis, a positive value returns statistics during -sles_view
. -mat_mumps_icntl_12 <n> - efficiency control (see MUMPS User's Guide)
. -mat_mumps_icntl_13 <n> - efficiency control (see MUMPS User's Guide)
. -mat_mumps_icntl_14 <n> - efficiency control (see MUMPS User's Guide)
. -mat_mumps_icntl_15 <n> - efficiency control (see MUMPS User's Guide)
. -mat_mumps_cntl_1 <delta> - relative pivoting threshold
. -mat_mumps_cntl_2 <tol> - stopping criterion for refinement
- -mat_mumps_cntl_3 <adelta> - absolute pivoting threshold

  Level: beginner

.seealso: MATSBAIJMUMPS
M*/

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatCreate_AIJMUMPS"
int MatCreate_AIJMUMPS(Mat A) {
  int           ierr,size;
  MPI_Comm      comm;

  PetscFunctionBegin;
  /* Change type name before calling MatSetType to force proper construction of SeqAIJ or MPIAIJ */
  /*   and AIJMUMPS types */
  ierr = PetscObjectChangeTypeName((PetscObject)A,MATAIJMUMPS);CHKERRQ(ierr);
  ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);CHKERRQ(ierr);
  if (size == 1) {
    ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
  } else {
    ierr = MatSetType(A,MATMPIAIJ);CHKERRQ(ierr);
  }
  ierr = MatConvert_AIJ_AIJMUMPS(A,MATAIJMUMPS,&A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatAssemblyEnd_SBAIJMUMPS"
int MatAssemblyEnd_SBAIJMUMPS(Mat A,MatAssemblyType mode) {
  int       ierr;
  Mat_MUMPS *mumps=(Mat_MUMPS*)A->spptr;

  PetscFunctionBegin;
  ierr = (*mumps->MatAssemblyEnd)(A,mode);CHKERRQ(ierr);
  mumps->MatLUFactorSymbolic       = A->ops->lufactorsymbolic;
  mumps->MatCholeskyFactorSymbolic = A->ops->choleskyfactorsymbolic;
  A->ops->choleskyfactorsymbolic   = MatCholeskyFactorSymbolic_SBAIJMUMPS;
  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatConvert_SBAIJ_SBAIJMUMPS"
int MatConvert_SBAIJ_SBAIJMUMPS(Mat A,MatType newtype,Mat *newmat) {
  int       ierr,size;
  MPI_Comm  comm;
  Mat       B=*newmat;
  Mat_MUMPS *mumps;

  PetscFunctionBegin;
  if (B != A) {
    ierr = MatDuplicate(A,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
  }

  ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
  ierr = PetscNew(Mat_MUMPS,&mumps);CHKERRQ(ierr);

  mumps->MatDuplicate              = A->ops->duplicate;
  mumps->MatView                   = A->ops->view;
  mumps->MatAssemblyEnd            = A->ops->assemblyend;
  mumps->MatLUFactorSymbolic       = A->ops->lufactorsymbolic;
  mumps->MatCholeskyFactorSymbolic = A->ops->choleskyfactorsymbolic;
  mumps->MatDestroy                = A->ops->destroy;
  mumps->CleanUpMUMPS              = PETSC_FALSE;
  mumps->isAIJ                     = PETSC_FALSE;

  B->spptr                         = (void *)mumps;
  B->ops->duplicate                = MatDuplicate_SBAIJMUMPS;
  B->ops->view                     = MatView_AIJMUMPS;
  B->ops->assemblyend              = MatAssemblyEnd_SBAIJMUMPS;
  B->ops->choleskyfactorsymbolic   = MatCholeskyFactorSymbolic_SBAIJMUMPS;
  B->ops->destroy                  = MatDestroy_MUMPS;

  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);CHKERRQ(ierr);
  if (size == 1) {
    ierr = PetscStrallocpy(MATSEQSBAIJ,&(mumps->basetype));CHKERRQ(ierr);
    ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_seqsbaij_sbaijmumps_C",
                                             "MatConvert_SBAIJ_SBAIJMUMPS",MatConvert_SBAIJ_SBAIJMUMPS);CHKERRQ(ierr);
    ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_sbaijmumps_seqsbaij_C",
                                             "MatConvert_MUMPS_Base",MatConvert_MUMPS_Base);CHKERRQ(ierr);
  } else {
    ierr = PetscStrallocpy(MATMPISBAIJ,&(mumps->basetype));CHKERRQ(ierr);
    ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_mpisbaij_sbaijmumps_C",
                                             "MatConvert_SBAIJ_SBAIJMUMPS",MatConvert_SBAIJ_SBAIJMUMPS);CHKERRQ(ierr);
    ierr = PetscObjectComposeFunctionDynamic((PetscObject)B,"MatConvert_sbaijmumps_mpisbaij_C",
                                             "MatConvert_MUMPS_Base",MatConvert_MUMPS_Base);CHKERRQ(ierr);
  }

  PetscLogInfo(0,"Using MUMPS for Cholesky factorization and solves.");
  ierr = PetscObjectChangeTypeName((PetscObject)B,newtype);CHKERRQ(ierr);
  *newmat = B;
  PetscFunctionReturn(0);
}
EXTERN_C_END

#undef __FUNCT__
#define __FUNCT__ "MatDuplicate_SBAIJMUMPS"
int MatDuplicate_SBAIJMUMPS(Mat A, MatDuplicateOption op, Mat *M) {
  int ierr;
  PetscFunctionBegin;
  ierr = (*A->ops->duplicate)(A,op,M);CHKERRQ(ierr);
  ierr = MatConvert_SBAIJ_SBAIJMUMPS(*M,MATSBAIJMUMPS,M);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*MC
  MATSBAIJMUMPS = "sbaijmumps" - A symmetric matrix type providing direct solvers (Cholesky) for
  distributed and sequential matrices via the external package MUMPS.

  If MUMPS is installed (see the manual for instructions
  on how to declare the existence of external packages),
  a matrix type can be constructed which invokes MUMPS solvers.
  After calling MatCreate(...,A), simply call MatSetType(A,MATSBAIJMUMPS).
  This matrix type is only supported for double precision real.

  If created with a single process communicator, this matrix type inherits from MATSEQSBAIJ.
  Otherwise, this matrix type inherits from MATMPISBAIJ.  Hence for single process communicators,
  MatSeqSBAIJSetPreallocation is supported, and similarly MatMPISBAIJSetPreallocation is supported
  for communicators controlling multiple processes.  It is recommended that you call both of
  the above preallocation routines for simplicity.  One can also call MatConvert for an inplace
  conversion to or from the MATSEQSBAIJ or MATMPISBAIJ type (depending on the communicator size)
  without data copy.

  Options Database Keys:
+ -mat_type sbaijmumps - sets the matrix type to "sbaijmumps" during a call to MatSetFromOptions()
. -mat_mumps_sym <0,1,2> - 0 the matrix is unsymmetric, 1 symmetric positive definite, 2 symmetric
. -mat_mumps_icntl_4 <0,...,4> - print level
. -mat_mumps_icntl_6 <0,...,7> - matrix prescaling options (see MUMPS User's Guide)
. -mat_mumps_icntl_7 <0,...,7> - matrix orderings (see MUMPS User's Guide)
. -mat_mumps_icntl_9 <1,2> - A or A^T x=b to be solved: 1 denotes A, 2 denotes A^T
. -mat_mumps_icntl_10 <n> - maximum number of iterative refinements
. -mat_mumps_icntl_11 <n> - error analysis, a positive value returns statistics during -sles_view
. -mat_mumps_icntl_12 <n> - efficiency control (see MUMPS User's Guide)
. -mat_mumps_icntl_13 <n> - efficiency control (see MUMPS User's Guide)
. -mat_mumps_icntl_14 <n> - efficiency control (see MUMPS User's Guide)
. -mat_mumps_icntl_15 <n> - efficiency control (see MUMPS User's Guide)
. -mat_mumps_cntl_1 <delta> - relative pivoting threshold
. -mat_mumps_cntl_2 <tol> - stopping criterion for refinement
- -mat_mumps_cntl_3 <adelta> - absolute pivoting threshold

  Level: beginner

.seealso: MATAIJMUMPS
M*/

EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "MatCreate_SBAIJMUMPS"
int MatCreate_SBAIJMUMPS(Mat A) {
  int ierr,size;

  PetscFunctionBegin;
  /* Change type name before calling MatSetType to force proper construction of SeqSBAIJ or MPISBAIJ */
  /*   and SBAIJMUMPS types */
  ierr = PetscObjectChangeTypeName((PetscObject)A,MATSBAIJMUMPS);CHKERRQ(ierr);
  ierr = MPI_Comm_size(A->comm,&size);CHKERRQ(ierr);CHKERRQ(ierr);
  if (size == 1) {
    ierr = MatSetType(A,MATSEQSBAIJ);CHKERRQ(ierr);
  } else {
    ierr = MatSetType(A,MATMPISBAIJ);CHKERRQ(ierr);
  }
  ierr = MatConvert_SBAIJ_SBAIJMUMPS(A,MATSBAIJMUMPS,&A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
EXTERN_C_END