xref: /petsc/src/mat/interface/matrix.c (revision 28b2187440207f11a58212034c4be33c129502bf)

/*
   This is where the abstract matrix operations are defined
*/

#include <petsc/private/matimpl.h>        /*I "petscmat.h" I*/
#include <petsc/private/vecimpl.h>
#include <petsc/private/isimpl.h>

/* Logging support */
PetscClassId MAT_CLASSID;
PetscClassId MAT_COLORING_CLASSID;
PetscClassId MAT_FDCOLORING_CLASSID;
PetscClassId MAT_TRANSPOSECOLORING_CLASSID;

PetscLogEvent MAT_Mult, MAT_Mults, MAT_MultConstrained, MAT_MultAdd, MAT_MultTranspose;
PetscLogEvent MAT_MultTransposeConstrained, MAT_MultTransposeAdd, MAT_Solve, MAT_Solves, MAT_SolveAdd, MAT_SolveTranspose, MAT_MatSolve;
PetscLogEvent MAT_SolveTransposeAdd, MAT_SOR, MAT_ForwardSolve, MAT_BackwardSolve, MAT_LUFactor, MAT_LUFactorSymbolic;
PetscLogEvent MAT_LUFactorNumeric, MAT_CholeskyFactor, MAT_CholeskyFactorSymbolic, MAT_CholeskyFactorNumeric, MAT_ILUFactor;
PetscLogEvent MAT_ILUFactorSymbolic, MAT_ICCFactorSymbolic, MAT_Copy, MAT_Convert, MAT_Scale, MAT_AssemblyBegin;
PetscLogEvent MAT_AssemblyEnd, MAT_SetValues, MAT_GetValues, MAT_GetRow, MAT_GetRowIJ, MAT_GetSubMatrices, MAT_GetOrdering, MAT_RedundantMat, MAT_GetSeqNonzeroStructure;
PetscLogEvent MAT_IncreaseOverlap, MAT_Partitioning, MAT_Coarsen, MAT_ZeroEntries, MAT_Load, MAT_View, MAT_AXPY, MAT_FDColoringCreate;
PetscLogEvent MAT_FDColoringSetUp, MAT_FDColoringApply,MAT_Transpose,MAT_FDColoringFunction, MAT_GetSubMatrix;
PetscLogEvent MAT_TransposeColoringCreate;
PetscLogEvent MAT_MatMult, MAT_MatMultSymbolic, MAT_MatMultNumeric;
PetscLogEvent MAT_PtAP, MAT_PtAPSymbolic, MAT_PtAPNumeric,MAT_RARt, MAT_RARtSymbolic, MAT_RARtNumeric;
PetscLogEvent MAT_MatTransposeMult, MAT_MatTransposeMultSymbolic, MAT_MatTransposeMultNumeric;
PetscLogEvent MAT_TransposeMatMult, MAT_TransposeMatMultSymbolic, MAT_TransposeMatMultNumeric;
PetscLogEvent MAT_MatMatMult, MAT_MatMatMultSymbolic, MAT_MatMatMultNumeric;
PetscLogEvent MAT_MultHermitianTranspose,MAT_MultHermitianTransposeAdd;
PetscLogEvent MAT_Getsymtranspose, MAT_Getsymtransreduced, MAT_Transpose_SeqAIJ, MAT_GetBrowsOfAcols;
PetscLogEvent MAT_GetBrowsOfAocols, MAT_Getlocalmat, MAT_Getlocalmatcondensed, MAT_Seqstompi, MAT_Seqstompinum, MAT_Seqstompisym;
PetscLogEvent MAT_Applypapt, MAT_Applypapt_numeric, MAT_Applypapt_symbolic, MAT_GetSequentialNonzeroStructure;
PetscLogEvent MAT_GetMultiProcBlock;
PetscLogEvent MAT_CUSPCopyToGPU, MAT_CUSPARSECopyToGPU, MAT_SetValuesBatch, MAT_SetValuesBatchI, MAT_SetValuesBatchII, MAT_SetValuesBatchIII, MAT_SetValuesBatchIV;
PetscLogEvent MAT_ViennaCLCopyToGPU;
PetscLogEvent MAT_Merge,MAT_Residual;
PetscLogEvent Mat_Coloring_Apply,Mat_Coloring_Comm,Mat_Coloring_Local,Mat_Coloring_ISCreate,Mat_Coloring_SetUp,Mat_Coloring_Weights;

const char *const MatFactorTypes[] = {"NONE","LU","CHOLESKY","ILU","ICC","ILUDT","MatFactorType","MAT_FACTOR_",0};

#undef __FUNCT__
#define __FUNCT__ "MatSetRandom"
/*@
   MatSetRandom - Sets all components of a matrix to random numbers. For sparse matrices that have been preallocated it randomly selects appropriate locations

   Logically Collective on Vec

   Input Parameters:
+  x  - the vector
-  rctx - the random number context, formed by PetscRandomCreate(), or NULL and
          it will create one internally.

   Output Parameter:
.  x  - the vector

   Example of Usage:
.vb
     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
     VecSetRandom(x,rctx);
     PetscRandomDestroy(rctx);
.ve

   Level: intermediate

   Concepts: vector^setting to random
   Concepts: random^vector

.seealso: MatZeroEntries(), MatSetValues(), PetscRandomCreate(), PetscRandomDestroy()
@*/
PetscErrorCode  MatSetRandom(Mat x,PetscRandom rctx)
{
  PetscErrorCode ierr;
  PetscRandom    randObj = NULL;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x,MAT_CLASSID,1);
  if (rctx) PetscValidHeaderSpecific(rctx,PETSC_RANDOM_CLASSID,2);
  PetscValidType(x,1);

  if (!rctx) {
    MPI_Comm comm;
    ierr = PetscObjectGetComm((PetscObject)x,&comm);CHKERRQ(ierr);
    ierr = PetscRandomCreate(comm,&randObj);CHKERRQ(ierr);
    ierr = PetscRandomSetFromOptions(randObj);CHKERRQ(ierr);
    rctx = randObj;
  }

  ierr = PetscLogEventBegin(VEC_SetRandom,x,rctx,0,0);CHKERRQ(ierr);
  ierr = (*x->ops->setrandom)(x,rctx);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(VEC_SetRandom,x,rctx,0,0);CHKERRQ(ierr);

  x->assembled = PETSC_TRUE;
  ierr         = PetscRandomDestroy(&randObj);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatFindNonzeroRows"
/*@
      MatFindNonzeroRows - Locate all rows that are not completely zero in the matrix

  Input Parameter:
.    A  - the matrix

  Output Parameter:
.    keptrows - the rows that are not completely zero

  Level: intermediate

 @*/
PetscErrorCode MatFindNonzeroRows(Mat mat,IS *keptrows)
{
  PetscErrorCode ierr;

  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->findnonzerorows) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not coded for this matrix type");
  ierr = (*mat->ops->findnonzerorows)(mat,keptrows);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetDiagonalBlock"
/*@
   MatGetDiagonalBlock - Returns the part of the matrix associated with the on-process coupling

   Not Collective

   Input Parameters:
.   A - the matrix

   Output Parameters:
.   a - the diagonal part (which is a SEQUENTIAL matrix)

   Notes: see the manual page for MatCreateAIJ() for more information on the "diagonal part" of the matrix.
          Use caution, as the reference count on the returned matrix is not incremented and it is used as
	  part of the containing MPI Mat's normal operation.

   Level: advanced

@*/
PetscErrorCode  MatGetDiagonalBlock(Mat A,Mat *a)
{
  PetscErrorCode ierr,(*f)(Mat,Mat*);
  PetscMPIInt    size;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  PetscValidPointer(a,3);
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRQ(ierr);
  ierr = PetscObjectQueryFunction((PetscObject)A,"MatGetDiagonalBlock_C",&f);CHKERRQ(ierr);
  if (f) {
    ierr = (*f)(A,a);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  } else if (size == 1) {
    *a = A;
  } else {
    MatType mattype;
    ierr = MatGetType(A,&mattype);CHKERRQ(ierr);
    SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Matrix type %s does not support getting diagonal block",mattype);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetTrace"
/*@
   MatGetTrace - Gets the trace of a matrix. The sum of the diagonal entries.

   Collective on Mat

   Input Parameters:
.  mat - the matrix

   Output Parameter:
.   trace - the sum of the diagonal entries

   Level: advanced

@*/
PetscErrorCode  MatGetTrace(Mat mat,PetscScalar *trace)
{
  PetscErrorCode ierr;
  Vec            diag;

  PetscFunctionBegin;
  ierr = MatCreateVecs(mat,&diag,NULL);CHKERRQ(ierr);
  ierr = MatGetDiagonal(mat,diag);CHKERRQ(ierr);
  ierr = VecSum(diag,trace);CHKERRQ(ierr);
  ierr = VecDestroy(&diag);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRealPart"
/*@
   MatRealPart - Zeros out the imaginary part of the matrix

   Logically Collective on Mat

   Input Parameters:
.  mat - the matrix

   Level: advanced


.seealso: MatImaginaryPart()
@*/
PetscErrorCode  MatRealPart(Mat mat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->realpart) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  ierr = (*mat->ops->realpart)(mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetGhosts"
/*@C
   MatGetGhosts - Get the global index of all ghost nodes defined by the sparse matrix

   Collective on Mat

   Input Parameter:
.  mat - the matrix

   Output Parameters:
+   nghosts - number of ghosts (note for BAIJ matrices there is one ghost for each block)
-   ghosts - the global indices of the ghost points

   Notes: the nghosts and ghosts are suitable to pass into VecCreateGhost()

   Level: advanced

@*/
PetscErrorCode  MatGetGhosts(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->getghosts) {
    if (nghosts) *nghosts = 0;
    if (ghosts) *ghosts = 0;
  } else {
    ierr = (*mat->ops->getghosts)(mat,nghosts,ghosts);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatImaginaryPart"
/*@
   MatImaginaryPart - Moves the imaginary part of the matrix to the real part and zeros the imaginary part

   Logically Collective on Mat

   Input Parameters:
.  mat - the matrix

   Level: advanced


.seealso: MatRealPart()
@*/
PetscErrorCode  MatImaginaryPart(Mat mat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->imaginarypart) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  ierr = (*mat->ops->imaginarypart)(mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMissingDiagonal"
/*@
   MatMissingDiagonal - Determine if sparse matrix is missing a diagonal entry (or block entry for BAIJ matrices)

   Collective on Mat

   Input Parameter:
.  mat - the matrix

   Output Parameters:
+  missing - is any diagonal missing
-  dd - first diagonal entry that is missing (optional)

   Level: advanced


.seealso: MatRealPart()
@*/
PetscErrorCode  MatMissingDiagonal(Mat mat,PetscBool *missing,PetscInt *dd)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->missingdiagonal) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  ierr = (*mat->ops->missingdiagonal)(mat,missing,dd);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRow"
/*@C
   MatGetRow - Gets a row of a matrix.  You MUST call MatRestoreRow()
   for each row that you get to ensure that your application does
   not bleed memory.

   Not Collective

   Input Parameters:
+  mat - the matrix
-  row - the row to get

   Output Parameters:
+  ncols -  if not NULL, the number of nonzeros in the row
.  cols - if not NULL, the column numbers
-  vals - if not NULL, the values

   Notes:
   This routine is provided for people who need to have direct access
   to the structure of a matrix.  We hope that we provide enough
   high-level matrix routines that few users will need it.

   MatGetRow() always returns 0-based column indices, regardless of
   whether the internal representation is 0-based (default) or 1-based.

   For better efficiency, set cols and/or vals to NULL if you do
   not wish to extract these quantities.

   The user can only examine the values extracted with MatGetRow();
   the values cannot be altered.  To change the matrix entries, one
   must use MatSetValues().

   You can only have one call to MatGetRow() outstanding for a particular
   matrix at a time, per processor. MatGetRow() can only obtain rows
   associated with the given processor, it cannot get rows from the
   other processors; for that we suggest using MatGetSubMatrices(), then
   MatGetRow() on the submatrix. The row indix passed to MatGetRows()
   is in the global number of rows.

   Fortran Notes:
   The calling sequence from Fortran is
.vb
   MatGetRow(matrix,row,ncols,cols,values,ierr)
         Mat     matrix (input)
         integer row    (input)
         integer ncols  (output)
         integer cols(maxcols) (output)
         double precision (or double complex) values(maxcols) output
.ve
   where maxcols >= maximum nonzeros in any row of the matrix.


   Caution:
   Do not try to change the contents of the output arrays (cols and vals).
   In some cases, this may corrupt the matrix.

   Level: advanced

   Concepts: matrices^row access

.seealso: MatRestoreRow(), MatSetValues(), MatGetValues(), MatGetSubMatrices(), MatGetDiagonal()
@*/
PetscErrorCode MatGetRow(Mat mat,PetscInt row,PetscInt *ncols,const PetscInt *cols[],const PetscScalar *vals[])
{
  PetscErrorCode ierr;
  PetscInt       incols;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->getrow) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  ierr = PetscLogEventBegin(MAT_GetRow,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->getrow)(mat,row,&incols,(PetscInt**)cols,(PetscScalar**)vals);CHKERRQ(ierr);
  if (ncols) *ncols = incols;
  ierr = PetscLogEventEnd(MAT_GetRow,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatConjugate"
/*@
   MatConjugate - replaces the matrix values with their complex conjugates

   Logically Collective on Mat

   Input Parameters:
.  mat - the matrix

   Level: advanced

.seealso:  VecConjugate()
@*/
PetscErrorCode  MatConjugate(Mat mat)
{
#if defined(PETSC_USE_COMPLEX)
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!mat->ops->conjugate) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not provided for this matrix format, send email to petsc-maint@mcs.anl.gov");
  ierr = (*mat->ops->conjugate)(mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
#else
  return 0;
#endif
}

#undef __FUNCT__
#define __FUNCT__ "MatRestoreRow"
/*@C
   MatRestoreRow - Frees any temporary space allocated by MatGetRow().

   Not Collective

   Input Parameters:
+  mat - the matrix
.  row - the row to get
.  ncols, cols - the number of nonzeros and their columns
-  vals - if nonzero the column values

   Notes:
   This routine should be called after you have finished examining the entries.

   This routine zeros out ncols, cols, and vals. This is to prevent accidental
   us of the array after it has been restored. If you pass NULL, it will
   not zero the pointers.  Use of cols or vals after MatRestoreRow is invalid.

   Fortran Notes:
   The calling sequence from Fortran is
.vb
   MatRestoreRow(matrix,row,ncols,cols,values,ierr)
      Mat     matrix (input)
      integer row    (input)
      integer ncols  (output)
      integer cols(maxcols) (output)
      double precision (or double complex) values(maxcols) output
.ve
   Where maxcols >= maximum nonzeros in any row of the matrix.

   In Fortran MatRestoreRow() MUST be called after MatGetRow()
   before another call to MatGetRow() can be made.

   Level: advanced

.seealso:  MatGetRow()
@*/
PetscErrorCode MatRestoreRow(Mat mat,PetscInt row,PetscInt *ncols,const PetscInt *cols[],const PetscScalar *vals[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (ncols) PetscValidIntPointer(ncols,3);
  if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!mat->ops->restorerow) PetscFunctionReturn(0);
  ierr = (*mat->ops->restorerow)(mat,row,ncols,(PetscInt **)cols,(PetscScalar **)vals);CHKERRQ(ierr);
  if (ncols) *ncols = 0;
  if (cols)  *cols = NULL;
  if (vals)  *vals = NULL;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRowUpperTriangular"
/*@
   MatGetRowUpperTriangular - Sets a flag to enable calls to MatGetRow() for matrix in MATSBAIJ format.
   You should call MatRestoreRowUpperTriangular() after calling MatGetRow/MatRestoreRow() to disable the flag.

   Not Collective

   Input Parameters:
+  mat - the matrix

   Notes:
   The flag is to ensure that users are aware of MatGetRow() only provides the upper trianglular part of the row for the matrices in MATSBAIJ format.

   Level: advanced

   Concepts: matrices^row access

.seealso: MatRestoreRowRowUpperTriangular()
@*/
PetscErrorCode  MatGetRowUpperTriangular(Mat mat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->getrowuppertriangular) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  ierr = (*mat->ops->getrowuppertriangular)(mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRestoreRowUpperTriangular"
/*@
   MatRestoreRowUpperTriangular - Disable calls to MatGetRow() for matrix in MATSBAIJ format.

   Not Collective

   Input Parameters:
+  mat - the matrix

   Notes:
   This routine should be called after you have finished MatGetRow/MatRestoreRow().


   Level: advanced

.seealso:  MatGetRowUpperTriangular()
@*/
PetscErrorCode  MatRestoreRowUpperTriangular(Mat mat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!mat->ops->restorerowuppertriangular) PetscFunctionReturn(0);
  ierr = (*mat->ops->restorerowuppertriangular)(mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetOptionsPrefix"
/*@C
   MatSetOptionsPrefix - Sets the prefix used for searching for all
   Mat options in the database.

   Logically Collective on Mat

   Input Parameter:
+  A - the Mat context
-  prefix - the prefix to prepend to all option names

   Notes:
   A hyphen (-) must NOT be given at the beginning of the prefix name.
   The first character of all runtime options is AUTOMATICALLY the hyphen.

   Level: advanced

.keywords: Mat, set, options, prefix, database

.seealso: MatSetFromOptions()
@*/
PetscErrorCode  MatSetOptionsPrefix(Mat A,const char prefix[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  ierr = PetscObjectSetOptionsPrefix((PetscObject)A,prefix);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatAppendOptionsPrefix"
/*@C
   MatAppendOptionsPrefix - Appends to the prefix used for searching for all
   Mat options in the database.

   Logically Collective on Mat

   Input Parameters:
+  A - the Mat context
-  prefix - the prefix to prepend to all option names

   Notes:
   A hyphen (-) must NOT be given at the beginning of the prefix name.
   The first character of all runtime options is AUTOMATICALLY the hyphen.

   Level: advanced

.keywords: Mat, append, options, prefix, database

.seealso: MatGetOptionsPrefix()
@*/
PetscErrorCode  MatAppendOptionsPrefix(Mat A,const char prefix[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  ierr = PetscObjectAppendOptionsPrefix((PetscObject)A,prefix);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetOptionsPrefix"
/*@C
   MatGetOptionsPrefix - Sets the prefix used for searching for all
   Mat options in the database.

   Not Collective

   Input Parameter:
.  A - the Mat context

   Output Parameter:
.  prefix - pointer to the prefix string used

   Notes: On the fortran side, the user should pass in a string 'prefix' of
   sufficient length to hold the prefix.

   Level: advanced

.keywords: Mat, get, options, prefix, database

.seealso: MatAppendOptionsPrefix()
@*/
PetscErrorCode  MatGetOptionsPrefix(Mat A,const char *prefix[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  ierr = PetscObjectGetOptionsPrefix((PetscObject)A,prefix);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetUp"
/*@
   MatSetUp - Sets up the internal matrix data structures for the later use.

   Collective on Mat

   Input Parameters:
.  A - the Mat context

   Notes:
   If the user has not set preallocation for this matrix then a default preallocation that is likely to be inefficient is used.

   If a suitable preallocation routine is used, this function does not need to be called.

   See the Performance chapter of the PETSc users manual for how to preallocate matrices

   Level: beginner

.keywords: Mat, setup

.seealso: MatCreate(), MatDestroy()
@*/
PetscErrorCode  MatSetUp(Mat A)
{
  PetscMPIInt    size;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  if (!((PetscObject)A)->type_name) {
    ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A), &size);CHKERRQ(ierr);
    if (size == 1) {
      ierr = MatSetType(A, MATSEQAIJ);CHKERRQ(ierr);
    } else {
      ierr = MatSetType(A, MATMPIAIJ);CHKERRQ(ierr);
    }
  }
  if (!A->preallocated && A->ops->setup) {
    ierr = PetscInfo(A,"Warning not preallocating matrix storage\n");CHKERRQ(ierr);
    ierr = (*A->ops->setup)(A);CHKERRQ(ierr);
  }
  A->preallocated = PETSC_TRUE;
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_SAWS)
#include <petscviewersaws.h>
#endif
#undef __FUNCT__
#define __FUNCT__ "MatView"
/*@C
   MatView - Visualizes a matrix object.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
-  viewer - visualization context

  Notes:
  The available visualization contexts include
+    PETSC_VIEWER_STDOUT_SELF - standard output (default)
.    PETSC_VIEWER_STDOUT_WORLD - synchronized standard
        output where only the first processor opens
        the file.  All other processors send their
        data to the first processor to print.
-     PETSC_VIEWER_DRAW_WORLD - graphical display of nonzero structure

   The user can open alternative visualization contexts with
+    PetscViewerASCIIOpen() - Outputs matrix to a specified file
.    PetscViewerBinaryOpen() - Outputs matrix in binary to a
         specified file; corresponding input uses MatLoad()
.    PetscViewerDrawOpen() - Outputs nonzero matrix structure to
         an X window display
-    PetscViewerSocketOpen() - Outputs matrix to Socket viewer.
         Currently only the sequential dense and AIJ
         matrix types support the Socket viewer.

   The user can call PetscViewerSetFormat() to specify the output
   format of ASCII printed objects (when using PETSC_VIEWER_STDOUT_SELF,
   PETSC_VIEWER_STDOUT_WORLD and PetscViewerASCIIOpen).  Available formats include
+    PETSC_VIEWER_DEFAULT - default, prints matrix contents
.    PETSC_VIEWER_ASCII_MATLAB - prints matrix contents in Matlab format
.    PETSC_VIEWER_ASCII_DENSE - prints entire matrix including zeros
.    PETSC_VIEWER_ASCII_COMMON - prints matrix contents, using a sparse
         format common among all matrix types
.    PETSC_VIEWER_ASCII_IMPL - prints matrix contents, using an implementation-specific
         format (which is in many cases the same as the default)
.    PETSC_VIEWER_ASCII_INFO - prints basic information about the matrix
         size and structure (not the matrix entries)
.    PETSC_VIEWER_ASCII_INFO_DETAIL - prints more detailed information about
         the matrix structure

   Options Database Keys:
+  -mat_view ::ascii_info - Prints info on matrix at conclusion of MatEndAssembly()
.  -mat_view ::ascii_info_detail - Prints more detailed info
.  -mat_view - Prints matrix in ASCII format
.  -mat_view ::ascii_matlab - Prints matrix in Matlab format
.  -mat_view draw - PetscDraws nonzero structure of matrix, using MatView() and PetscDrawOpenX().
.  -display <name> - Sets display name (default is host)
.  -draw_pause <sec> - Sets number of seconds to pause after display
.  -mat_view socket - Sends matrix to socket, can be accessed from Matlab (see Users-Manual: ch_matlab for details)
.  -viewer_socket_machine <machine> -
.  -viewer_socket_port <port> -
.  -mat_view binary - save matrix to file in binary format
-  -viewer_binary_filename <name> -
   Level: beginner

   Notes: see the manual page for MatLoad() for the exact format of the binary file when the binary
      viewer is used.

      See share/petsc/matlab/PetscBinaryRead.m for a Matlab code that can read in the binary file when the binary
      viewer is used.

      One can use '-mat_view draw -draw_pause -1' to pause the graphical display of matrix nonzero structure.
      And then use the following mouse functions:
          left mouse: zoom in
          middle mouse: zoom out
          right mouse: continue with the simulation

   Concepts: matrices^viewing
   Concepts: matrices^plotting
   Concepts: matrices^printing

.seealso: PetscViewerSetFormat(), PetscViewerASCIIOpen(), PetscViewerDrawOpen(),
          PetscViewerSocketOpen(), PetscViewerBinaryOpen(), MatLoad()
@*/
PetscErrorCode  MatView(Mat mat,PetscViewer viewer)
{
  PetscErrorCode    ierr;
  PetscInt          rows,cols,rbs,cbs;
  PetscBool         iascii;
  PetscViewerFormat format;
#if defined(PETSC_HAVE_SAWS)
  PetscBool         issaws;
#endif

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!viewer) {
    ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)mat),&viewer);CHKERRQ(ierr);
  }
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
  PetscCheckSameComm(mat,1,viewer,2);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_View,mat,viewer,0,0);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
  if ((!iascii || (format != PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL)) && mat->factortype) {
    SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"No viewers for factored matrix except ASCII info or info_detailed");
  }

#if defined(PETSC_HAVE_SAWS)
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSAWS,&issaws);CHKERRQ(ierr);
#endif
  if (iascii) {
    if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ORDER,"Must call MatAssemblyBegin/End() before viewing matrix");
    ierr = PetscObjectPrintClassNamePrefixType((PetscObject)mat,viewer);CHKERRQ(ierr);
    if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
      ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
      ierr = MatGetSize(mat,&rows,&cols);CHKERRQ(ierr);
      ierr = MatGetBlockSizes(mat,&rbs,&cbs);CHKERRQ(ierr);
      if (rbs != 1 || cbs != 1) {
        if (rbs != cbs) {ierr = PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D, rbs=%D, cbs = %D\n",rows,cols,rbs,cbs);CHKERRQ(ierr);}
        else            {ierr = PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D, bs=%D\n",rows,cols,rbs);CHKERRQ(ierr);}
      } else {
        ierr = PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D\n",rows,cols);CHKERRQ(ierr);
      }
      if (mat->factortype) {
        const MatSolverPackage solver;
        ierr = MatFactorGetSolverPackage(mat,&solver);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(viewer,"package used to perform factorization: %s\n",solver);CHKERRQ(ierr);
      }
      if (mat->ops->getinfo) {
        MatInfo info;
        ierr = MatGetInfo(mat,MAT_GLOBAL_SUM,&info);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(viewer,"total: nonzeros=%g, allocated nonzeros=%g\n",info.nz_used,info.nz_allocated);CHKERRQ(ierr);
        ierr = PetscViewerASCIIPrintf(viewer,"total number of mallocs used during MatSetValues calls =%D\n",(PetscInt)info.mallocs);CHKERRQ(ierr);
      }
      if (mat->nullsp) {ierr = PetscViewerASCIIPrintf(viewer,"  has attached null space\n");CHKERRQ(ierr);}
      if (mat->nearnullsp) {ierr = PetscViewerASCIIPrintf(viewer,"  has attached near null space\n");CHKERRQ(ierr);}
    }
#if defined(PETSC_HAVE_SAWS)
  } else if (issaws) {
    PetscMPIInt rank;

    ierr = PetscObjectName((PetscObject)mat);CHKERRQ(ierr);
    ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
    if (!((PetscObject)mat)->amsmem && !rank) {
      ierr = PetscObjectViewSAWs((PetscObject)mat,viewer);CHKERRQ(ierr);
    }
#endif
  }
  if (mat->ops->view) {
    ierr = PetscViewerASCIIPushTab(viewer);CHKERRQ(ierr);
    ierr = (*mat->ops->view)(mat,viewer);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
  }
  if (iascii) {
    if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ORDER,"Must call MatAssemblyBegin/End() before viewing matrix");
    ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
    if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
      ierr = PetscViewerASCIIPopTab(viewer);CHKERRQ(ierr);
    }
  }
  ierr = PetscLogEventEnd(MAT_View,mat,viewer,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#if defined(PETSC_USE_DEBUG)
#include <../src/sys/totalview/tv_data_display.h>
PETSC_UNUSED static int TV_display_type(const struct _p_Mat *mat)
{
  TV_add_row("Local rows", "int", &mat->rmap->n);
  TV_add_row("Local columns", "int", &mat->cmap->n);
  TV_add_row("Global rows", "int", &mat->rmap->N);
  TV_add_row("Global columns", "int", &mat->cmap->N);
  TV_add_row("Typename", TV_ascii_string_type, ((PetscObject)mat)->type_name);
  return TV_format_OK;
}
#endif

#undef __FUNCT__
#define __FUNCT__ "MatLoad"
/*@C
   MatLoad - Loads a matrix that has been stored in binary format
   with MatView().  The matrix format is determined from the options database.
   Generates a parallel MPI matrix if the communicator has more than one
   processor.  The default matrix type is AIJ.

   Collective on PetscViewer

   Input Parameters:
+  newmat - the newly loaded matrix, this needs to have been created with MatCreate()
            or some related function before a call to MatLoad()
-  viewer - binary file viewer, created with PetscViewerBinaryOpen()

   Options Database Keys:
   Used with block matrix formats (MATSEQBAIJ,  ...) to specify
   block size
.    -matload_block_size <bs>

   Level: beginner

   Notes:
   If the Mat type has not yet been given then MATAIJ is used, call MatSetFromOptions() on the
   Mat before calling this routine if you wish to set it from the options database.

   MatLoad() automatically loads into the options database any options
   given in the file filename.info where filename is the name of the file
   that was passed to the PetscViewerBinaryOpen(). The options in the info
   file will be ignored if you use the -viewer_binary_skip_info option.

   If the type or size of newmat is not set before a call to MatLoad, PETSc
   sets the default matrix type AIJ and sets the local and global sizes.
   If type and/or size is already set, then the same are used.

   In parallel, each processor can load a subset of rows (or the
   entire matrix).  This routine is especially useful when a large
   matrix is stored on disk and only part of it is desired on each
   processor.  For example, a parallel solver may access only some of
   the rows from each processor.  The algorithm used here reads
   relatively small blocks of data rather than reading the entire
   matrix and then subsetting it.

   Notes for advanced users:
   Most users should not need to know the details of the binary storage
   format, since MatLoad() and MatView() completely hide these details.
   But for anyone who's interested, the standard binary matrix storage
   format is

$    int    MAT_FILE_CLASSID
$    int    number of rows
$    int    number of columns
$    int    total number of nonzeros
$    int    *number nonzeros in each row
$    int    *column indices of all nonzeros (starting index is zero)
$    PetscScalar *values of all nonzeros

   PETSc automatically does the byte swapping for
machines that store the bytes reversed, e.g.  DEC alpha, freebsd,
linux, Windows and the paragon; thus if you write your own binary
read/write routines you have to swap the bytes; see PetscBinaryRead()
and PetscBinaryWrite() to see how this may be done.

.keywords: matrix, load, binary, input

.seealso: PetscViewerBinaryOpen(), MatView(), VecLoad()

 @*/
PetscErrorCode  MatLoad(Mat newmat,PetscViewer viewer)
{
  PetscErrorCode ierr;
  PetscBool      isbinary,flg;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(newmat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,2);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
  if (!isbinary) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Invalid viewer; open viewer with PetscViewerBinaryOpen()");

  if (!((PetscObject)newmat)->type_name) {
    ierr = MatSetType(newmat,MATAIJ);CHKERRQ(ierr);
  }

  if (!newmat->ops->load) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatLoad is not supported for type");
  ierr = PetscLogEventBegin(MAT_Load,viewer,0,0,0);CHKERRQ(ierr);
  ierr = (*newmat->ops->load)(newmat,viewer);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_Load,viewer,0,0,0);CHKERRQ(ierr);

  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(((PetscObject)newmat)->prefix,"-matload_symmetric",&flg,NULL);CHKERRQ(ierr);
  if (flg) {
    ierr = MatSetOption(newmat,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
    ierr = MatSetOption(newmat,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);CHKERRQ(ierr);
  }
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(((PetscObject)newmat)->prefix,"-matload_spd",&flg,NULL);CHKERRQ(ierr);
  if (flg) {
    ierr = MatSetOption(newmat,MAT_SPD,PETSC_TRUE);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroy_Redundant"
PetscErrorCode MatDestroy_Redundant(Mat_Redundant **redundant)
{
  PetscErrorCode ierr;
  Mat_Redundant  *redund = *redundant;
  PetscInt       i;

  PetscFunctionBegin;
  if (redund){
    if (redund->matseq) { /* via MatGetSubMatrices()  */
      ierr = ISDestroy(&redund->isrow);CHKERRQ(ierr);
      ierr = ISDestroy(&redund->iscol);CHKERRQ(ierr);
      ierr = MatDestroy(&redund->matseq[0]);CHKERRQ(ierr);
      ierr = PetscFree(redund->matseq);CHKERRQ(ierr);
    } else {
      ierr = PetscFree2(redund->send_rank,redund->recv_rank);CHKERRQ(ierr);
      ierr = PetscFree(redund->sbuf_j);CHKERRQ(ierr);
      ierr = PetscFree(redund->sbuf_a);CHKERRQ(ierr);
      for (i=0; i<redund->nrecvs; i++) {
        ierr = PetscFree(redund->rbuf_j[i]);CHKERRQ(ierr);
        ierr = PetscFree(redund->rbuf_a[i]);CHKERRQ(ierr);
      }
      ierr = PetscFree4(redund->sbuf_nz,redund->rbuf_nz,redund->rbuf_j,redund->rbuf_a);CHKERRQ(ierr);
    }

    if (redund->subcomm) {
      ierr = PetscCommDestroy(&redund->subcomm);CHKERRQ(ierr);
    }
    ierr = PetscFree(redund);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroy"
/*@
   MatDestroy - Frees space taken by a matrix.

   Collective on Mat

   Input Parameter:
.  A - the matrix

   Level: beginner

@*/
PetscErrorCode  MatDestroy(Mat *A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!*A) PetscFunctionReturn(0);
  PetscValidHeaderSpecific(*A,MAT_CLASSID,1);
  if (--((PetscObject)(*A))->refct > 0) {*A = NULL; PetscFunctionReturn(0);}

  /* if memory was published with SAWs then destroy it */
  ierr = PetscObjectSAWsViewOff((PetscObject)*A);CHKERRQ(ierr);
  if ((*A)->ops->destroy) {
    ierr = (*(*A)->ops->destroy)(*A);CHKERRQ(ierr);
  }
  ierr = MatDestroy_Redundant(&(*A)->redundant);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&(*A)->nullsp);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&(*A)->transnullsp);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&(*A)->nearnullsp);CHKERRQ(ierr);
  ierr = PetscLayoutDestroy(&(*A)->rmap);CHKERRQ(ierr);
  ierr = PetscLayoutDestroy(&(*A)->cmap);CHKERRQ(ierr);
  ierr = PetscHeaderDestroy(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValues"
/*@
   MatSetValues - Inserts or adds a block of values into a matrix.
   These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
   MUST be called after all calls to MatSetValues() have been completed.

   Not Collective

   Input Parameters:
+  mat - the matrix
.  v - a logically two-dimensional array of values
.  m, idxm - the number of rows and their global indices
.  n, idxn - the number of columns and their global indices
-  addv - either ADD_VALUES or INSERT_VALUES, where
   ADD_VALUES adds values to any existing entries, and
   INSERT_VALUES replaces existing entries with new values

   Notes:
   If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
      MatSetUp() before using this routine

   By default the values, v, are row-oriented. See MatSetOption() for other options.

   Calls to MatSetValues() with the INSERT_VALUES and ADD_VALUES
   options cannot be mixed without intervening calls to the assembly
   routines.

   MatSetValues() uses 0-based row and column numbers in Fortran
   as well as in C.

   Negative indices may be passed in idxm and idxn, these rows and columns are
   simply ignored. This allows easily inserting element stiffness matrices
   with homogeneous Dirchlet boundary conditions that you don't want represented
   in the matrix.

   Efficiency Alert:
   The routine MatSetValuesBlocked() may offer much better efficiency
   for users of block sparse formats (MATSEQBAIJ and MATMPIBAIJ).

   Level: beginner

   Concepts: matrices^putting entries in

.seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
          InsertMode, INSERT_VALUES, ADD_VALUES
@*/
PetscErrorCode  MatSetValues(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
{
  PetscErrorCode ierr;
#if defined(PETSC_USE_DEBUG)
  PetscInt       i,j;
#endif

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!m || !n) PetscFunctionReturn(0); /* no values to insert */
  PetscValidIntPointer(idxm,3);
  PetscValidIntPointer(idxn,5);
  PetscValidScalarPointer(v,6);
  MatCheckPreallocated(mat,1);
  if (mat->insertmode == NOT_SET_VALUES) {
    mat->insertmode = addv;
  }
#if defined(PETSC_USE_DEBUG)
  else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);

  for (i=0; i<m; i++) {
    for (j=0; j<n; j++) {
      if (mat->erroriffpe && PetscIsInfOrNanScalar(v[i*n+j]))
#if defined(PETSC_USE_COMPLEX)
        SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_FP,"Inserting %g+ig at matrix entry (%D,%D)",(double)PetscRealPart(v[i*n+j]),(double)PetscImaginaryPart(v[i*n+j]),idxm[i],idxn[j]);
#else
      SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_FP,"Inserting %g at matrix entry (%D,%D)",(double)v[i*n+j],idxm[i],idxn[j]);
#endif
    }
  }
#endif

  if (mat->assembled) {
    mat->was_assembled = PETSC_TRUE;
    mat->assembled     = PETSC_FALSE;
  }
  ierr = PetscLogEventBegin(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->setvalues)(mat,m,idxm,n,idxn,v,addv);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatSetValuesRowLocal"
/*@
   MatSetValuesRowLocal - Inserts a row (block row for BAIJ matrices) of nonzero
        values into a matrix

   Not Collective

   Input Parameters:
+  mat - the matrix
.  row - the (block) row to set
-  v - a logically two-dimensional array of values

   Notes:
   By the values, v, are column-oriented (for the block version) and sorted

   All the nonzeros in the row must be provided

   The matrix must have previously had its column indices set

   The row must belong to this process

   Level: intermediate

   Concepts: matrices^putting entries in

.seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
          InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues(), MatSetValuesRow(), MatSetLocalToGlobalMapping()
@*/
PetscErrorCode  MatSetValuesRowLocal(Mat mat,PetscInt row,const PetscScalar v[])
{
  PetscErrorCode ierr;
  PetscInt       globalrow;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidScalarPointer(v,2);
  ierr = ISLocalToGlobalMappingApply(mat->rmap->mapping,1,&row,&globalrow);CHKERRQ(ierr);
  ierr = MatSetValuesRow(mat,globalrow,v);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesRow"
/*@
   MatSetValuesRow - Inserts a row (block row for BAIJ matrices) of nonzero
        values into a matrix

   Not Collective

   Input Parameters:
+  mat - the matrix
.  row - the (block) row to set
-  v - a logically two-dimensional array of values

   Notes:
   The values, v, are column-oriented for the block version.

   All the nonzeros in the row must be provided

   THE MATRIX MUSAT HAVE PREVIOUSLY HAD ITS COLUMN INDICES SET. IT IS RARE THAT THIS ROUTINE IS USED, usually MatSetValues() is used.

   The row must belong to this process

   Level: advanced

   Concepts: matrices^putting entries in

.seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
          InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues()
@*/
PetscErrorCode  MatSetValuesRow(Mat mat,PetscInt row,const PetscScalar v[])
{
  PetscErrorCode ierr;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  PetscValidScalarPointer(v,2);
#if defined(PETSC_USE_DEBUG)
  if (mat->insertmode == ADD_VALUES) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add and insert values");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
#endif
  mat->insertmode = INSERT_VALUES;

  if (mat->assembled) {
    mat->was_assembled = PETSC_TRUE;
    mat->assembled     = PETSC_FALSE;
  }
  ierr = PetscLogEventBegin(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
  if (!mat->ops->setvaluesrow) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  ierr = (*mat->ops->setvaluesrow)(mat,row,v);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesStencil"
/*@
   MatSetValuesStencil - Inserts or adds a block of values into a matrix.
     Using structured grid indexing

   Not Collective

   Input Parameters:
+  mat - the matrix
.  m - number of rows being entered
.  idxm - grid coordinates (and component number when dof > 1) for matrix rows being entered
.  n - number of columns being entered
.  idxn - grid coordinates (and component number when dof > 1) for matrix columns being entered
.  v - a logically two-dimensional array of values
-  addv - either ADD_VALUES or INSERT_VALUES, where
   ADD_VALUES adds values to any existing entries, and
   INSERT_VALUES replaces existing entries with new values

   Notes:
   By default the values, v, are row-oriented.  See MatSetOption() for other options.

   Calls to MatSetValuesStencil() with the INSERT_VALUES and ADD_VALUES
   options cannot be mixed without intervening calls to the assembly
   routines.

   The grid coordinates are across the entire grid, not just the local portion

   MatSetValuesStencil() uses 0-based row and column numbers in Fortran
   as well as in C.

   For setting/accessing vector values via array coordinates you can use the DMDAVecGetArray() routine

   In order to use this routine you must either obtain the matrix with DMCreateMatrix()
   or call MatSetLocalToGlobalMapping() and MatSetStencil() first.

   The columns and rows in the stencil passed in MUST be contained within the
   ghost region of the given process as set with DMDACreateXXX() or MatSetStencil(). For example,
   if you create a DMDA with an overlap of one grid level and on a particular process its first
   local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
   first i index you can use in your column and row indices in MatSetStencil() is 5.

   In Fortran idxm and idxn should be declared as
$     MatStencil idxm(4,m),idxn(4,n)
   and the values inserted using
$    idxm(MatStencil_i,1) = i
$    idxm(MatStencil_j,1) = j
$    idxm(MatStencil_k,1) = k
$    idxm(MatStencil_c,1) = c
   etc

   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
   DM_BOUNDARY_PERIODIC boundary type.

   For indices that don't mean anything for your case (like the k index when working in 2d) or the c index when you have
   a single value per point) you can skip filling those indices.

   Inspired by the structured grid interface to the HYPRE package
   (http://www.llnl.gov/CASC/hypre)

   Efficiency Alert:
   The routine MatSetValuesBlockedStencil() may offer much better efficiency
   for users of block sparse formats (MATSEQBAIJ and MATMPIBAIJ).

   Level: beginner

   Concepts: matrices^putting entries in

.seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
          MatSetValues(), MatSetValuesBlockedStencil(), MatSetStencil(), DMCreateMatrix(), DMDAVecGetArray(), MatStencil
@*/
PetscErrorCode  MatSetValuesStencil(Mat mat,PetscInt m,const MatStencil idxm[],PetscInt n,const MatStencil idxn[],const PetscScalar v[],InsertMode addv)
{
  PetscErrorCode ierr;
  PetscInt       buf[8192],*bufm=0,*bufn=0,*jdxm,*jdxn;
  PetscInt       j,i,dim = mat->stencil.dim,*dims = mat->stencil.dims+1,tmp;
  PetscInt       *starts = mat->stencil.starts,*dxm = (PetscInt*)idxm,*dxn = (PetscInt*)idxn,sdim = dim - (1 - (PetscInt)mat->stencil.noc);

  PetscFunctionBegin;
  if (!m || !n) PetscFunctionReturn(0); /* no values to insert */
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidIntPointer(idxm,3);
  PetscValidIntPointer(idxn,5);
  PetscValidScalarPointer(v,6);

  if ((m+n) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    jdxm = buf; jdxn = buf+m;
  } else {
    ierr = PetscMalloc2(m,&bufm,n,&bufn);CHKERRQ(ierr);
    jdxm = bufm; jdxn = bufn;
  }
  for (i=0; i<m; i++) {
    for (j=0; j<3-sdim; j++) dxm++;
    tmp = *dxm++ - starts[0];
    for (j=0; j<dim-1; j++) {
      if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
      else                                       tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    }
    if (mat->stencil.noc) dxm++;
    jdxm[i] = tmp;
  }
  for (i=0; i<n; i++) {
    for (j=0; j<3-sdim; j++) dxn++;
    tmp = *dxn++ - starts[0];
    for (j=0; j<dim-1; j++) {
      if ((*dxn++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
      else                                       tmp = tmp*dims[j] + *(dxn-1) - starts[j+1];
    }
    if (mat->stencil.noc) dxn++;
    jdxn[i] = tmp;
  }
  ierr = MatSetValuesLocal(mat,m,jdxm,n,jdxn,v,addv);CHKERRQ(ierr);
  ierr = PetscFree2(bufm,bufn);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesBlockedStencil"
/*@
   MatSetValuesBlockedStencil - Inserts or adds a block of values into a matrix.
     Using structured grid indexing

   Not Collective

   Input Parameters:
+  mat - the matrix
.  m - number of rows being entered
.  idxm - grid coordinates for matrix rows being entered
.  n - number of columns being entered
.  idxn - grid coordinates for matrix columns being entered
.  v - a logically two-dimensional array of values
-  addv - either ADD_VALUES or INSERT_VALUES, where
   ADD_VALUES adds values to any existing entries, and
   INSERT_VALUES replaces existing entries with new values

   Notes:
   By default the values, v, are row-oriented and unsorted.
   See MatSetOption() for other options.

   Calls to MatSetValuesBlockedStencil() with the INSERT_VALUES and ADD_VALUES
   options cannot be mixed without intervening calls to the assembly
   routines.

   The grid coordinates are across the entire grid, not just the local portion

   MatSetValuesBlockedStencil() uses 0-based row and column numbers in Fortran
   as well as in C.

   For setting/accessing vector values via array coordinates you can use the DMDAVecGetArray() routine

   In order to use this routine you must either obtain the matrix with DMCreateMatrix()
   or call MatSetBlockSize(), MatSetLocalToGlobalMapping() and MatSetStencil() first.

   The columns and rows in the stencil passed in MUST be contained within the
   ghost region of the given process as set with DMDACreateXXX() or MatSetStencil(). For example,
   if you create a DMDA with an overlap of one grid level and on a particular process its first
   local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
   first i index you can use in your column and row indices in MatSetStencil() is 5.

   In Fortran idxm and idxn should be declared as
$     MatStencil idxm(4,m),idxn(4,n)
   and the values inserted using
$    idxm(MatStencil_i,1) = i
$    idxm(MatStencil_j,1) = j
$    idxm(MatStencil_k,1) = k
   etc

   Negative indices may be passed in idxm and idxn, these rows and columns are
   simply ignored. This allows easily inserting element stiffness matrices
   with homogeneous Dirchlet boundary conditions that you don't want represented
   in the matrix.

   Inspired by the structured grid interface to the HYPRE package
   (http://www.llnl.gov/CASC/hypre)

   Level: beginner

   Concepts: matrices^putting entries in

.seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
          MatSetValues(), MatSetValuesStencil(), MatSetStencil(), DMCreateMatrix(), DMDAVecGetArray(), MatStencil,
          MatSetBlockSize(), MatSetLocalToGlobalMapping()
@*/
PetscErrorCode  MatSetValuesBlockedStencil(Mat mat,PetscInt m,const MatStencil idxm[],PetscInt n,const MatStencil idxn[],const PetscScalar v[],InsertMode addv)
{
  PetscErrorCode ierr;
  PetscInt       buf[8192],*bufm=0,*bufn=0,*jdxm,*jdxn;
  PetscInt       j,i,dim = mat->stencil.dim,*dims = mat->stencil.dims+1,tmp;
  PetscInt       *starts = mat->stencil.starts,*dxm = (PetscInt*)idxm,*dxn = (PetscInt*)idxn,sdim = dim - (1 - (PetscInt)mat->stencil.noc);

  PetscFunctionBegin;
  if (!m || !n) PetscFunctionReturn(0); /* no values to insert */
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidIntPointer(idxm,3);
  PetscValidIntPointer(idxn,5);
  PetscValidScalarPointer(v,6);

  if ((m+n) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    jdxm = buf; jdxn = buf+m;
  } else {
    ierr = PetscMalloc2(m,&bufm,n,&bufn);CHKERRQ(ierr);
    jdxm = bufm; jdxn = bufn;
  }
  for (i=0; i<m; i++) {
    for (j=0; j<3-sdim; j++) dxm++;
    tmp = *dxm++ - starts[0];
    for (j=0; j<sdim-1; j++) {
      if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
      else                                       tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    }
    dxm++;
    jdxm[i] = tmp;
  }
  for (i=0; i<n; i++) {
    for (j=0; j<3-sdim; j++) dxn++;
    tmp = *dxn++ - starts[0];
    for (j=0; j<sdim-1; j++) {
      if ((*dxn++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
      else                                       tmp = tmp*dims[j] + *(dxn-1) - starts[j+1];
    }
    dxn++;
    jdxn[i] = tmp;
  }
  ierr = MatSetValuesBlockedLocal(mat,m,jdxm,n,jdxn,v,addv);CHKERRQ(ierr);
  ierr = PetscFree2(bufm,bufn);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetStencil"
/*@
   MatSetStencil - Sets the grid information for setting values into a matrix via
        MatSetValuesStencil()

   Not Collective

   Input Parameters:
+  mat - the matrix
.  dim - dimension of the grid 1, 2, or 3
.  dims - number of grid points in x, y, and z direction, including ghost points on your processor
.  starts - starting point of ghost nodes on your processor in x, y, and z direction
-  dof - number of degrees of freedom per node


   Inspired by the structured grid interface to the HYPRE package
   (www.llnl.gov/CASC/hyper)

   For matrices generated with DMCreateMatrix() this routine is automatically called and so not needed by the
   user.

   Level: beginner

   Concepts: matrices^putting entries in

.seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
          MatSetValues(), MatSetValuesBlockedStencil(), MatSetValuesStencil()
@*/
PetscErrorCode  MatSetStencil(Mat mat,PetscInt dim,const PetscInt dims[],const PetscInt starts[],PetscInt dof)
{
  PetscInt i;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidIntPointer(dims,3);
  PetscValidIntPointer(starts,4);

  mat->stencil.dim = dim + (dof > 1);
  for (i=0; i<dim; i++) {
    mat->stencil.dims[i]   = dims[dim-i-1];      /* copy the values in backwards */
    mat->stencil.starts[i] = starts[dim-i-1];
  }
  mat->stencil.dims[dim]   = dof;
  mat->stencil.starts[dim] = 0;
  mat->stencil.noc         = (PetscBool)(dof == 1);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesBlocked"
/*@
   MatSetValuesBlocked - Inserts or adds a block of values into a matrix.

   Not Collective

   Input Parameters:
+  mat - the matrix
.  v - a logically two-dimensional array of values
.  m, idxm - the number of block rows and their global block indices
.  n, idxn - the number of block columns and their global block indices
-  addv - either ADD_VALUES or INSERT_VALUES, where
   ADD_VALUES adds values to any existing entries, and
   INSERT_VALUES replaces existing entries with new values

   Notes:
   If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call
   MatXXXXSetPreallocation() or MatSetUp() before using this routine.

   The m and n count the NUMBER of blocks in the row direction and column direction,
   NOT the total number of rows/columns; for example, if the block size is 2 and
   you are passing in values for rows 2,3,4,5  then m would be 2 (not 4).
   The values in idxm would be 1 2; that is the first index for each block divided by
   the block size.

   Note that you must call MatSetBlockSize() when constructing this matrix (before
   preallocating it).

   By default the values, v, are row-oriented, so the layout of
   v is the same as for MatSetValues(). See MatSetOption() for other options.

   Calls to MatSetValuesBlocked() with the INSERT_VALUES and ADD_VALUES
   options cannot be mixed without intervening calls to the assembly
   routines.

   MatSetValuesBlocked() uses 0-based row and column numbers in Fortran
   as well as in C.

   Negative indices may be passed in idxm and idxn, these rows and columns are
   simply ignored. This allows easily inserting element stiffness matrices
   with homogeneous Dirchlet boundary conditions that you don't want represented
   in the matrix.

   Each time an entry is set within a sparse matrix via MatSetValues(),
   internal searching must be done to determine where to place the the
   data in the matrix storage space.  By instead inserting blocks of
   entries via MatSetValuesBlocked(), the overhead of matrix assembly is
   reduced.

   Example:
$   Suppose m=n=2 and block size(bs) = 2 The array is
$
$   1  2  | 3  4
$   5  6  | 7  8
$   - - - | - - -
$   9  10 | 11 12
$   13 14 | 15 16
$
$   v[] should be passed in like
$   v[] = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
$
$  If you are not using row oriented storage of v (that is you called MatSetOption(mat,MAT_ROW_ORIENTED,PETSC_FALSE)) then
$   v[] = [1,5,9,13,2,6,10,14,3,7,11,15,4,8,12,16]

   Level: intermediate

   Concepts: matrices^putting entries in blocked

.seealso: MatSetBlockSize(), MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetValuesBlockedLocal()
@*/
PetscErrorCode  MatSetValuesBlocked(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
{
  PetscErrorCode ierr;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!m || !n) PetscFunctionReturn(0); /* no values to insert */
  PetscValidIntPointer(idxm,3);
  PetscValidIntPointer(idxn,5);
  PetscValidScalarPointer(v,6);
  MatCheckPreallocated(mat,1);
  if (mat->insertmode == NOT_SET_VALUES) {
    mat->insertmode = addv;
  }
#if defined(PETSC_USE_DEBUG)
  else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->setvaluesblocked && !mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
#endif

  if (mat->assembled) {
    mat->was_assembled = PETSC_TRUE;
    mat->assembled     = PETSC_FALSE;
  }
  ierr = PetscLogEventBegin(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
  if (mat->ops->setvaluesblocked) {
    ierr = (*mat->ops->setvaluesblocked)(mat,m,idxm,n,idxn,v,addv);CHKERRQ(ierr);
  } else {
    PetscInt buf[8192],*bufr=0,*bufc=0,*iidxm,*iidxn;
    PetscInt i,j,bs,cbs;
    ierr = MatGetBlockSizes(mat,&bs,&cbs);CHKERRQ(ierr);
    if (m*bs+n*cbs <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
      iidxm = buf; iidxn = buf + m*bs;
    } else {
      ierr  = PetscMalloc2(m*bs,&bufr,n*cbs,&bufc);CHKERRQ(ierr);
      iidxm = bufr; iidxn = bufc;
    }
    for (i=0; i<m; i++) {
      for (j=0; j<bs; j++) {
        iidxm[i*bs+j] = bs*idxm[i] + j;
      }
    }
    for (i=0; i<n; i++) {
      for (j=0; j<cbs; j++) {
        iidxn[i*cbs+j] = cbs*idxn[i] + j;
      }
    }
    ierr = MatSetValues(mat,m*bs,iidxm,n*cbs,iidxn,v,addv);CHKERRQ(ierr);
    ierr = PetscFree2(bufr,bufc);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetValues"
/*@
   MatGetValues - Gets a block of values from a matrix.

   Not Collective; currently only returns a local block

   Input Parameters:
+  mat - the matrix
.  v - a logically two-dimensional array for storing the values
.  m, idxm - the number of rows and their global indices
-  n, idxn - the number of columns and their global indices

   Notes:
   The user must allocate space (m*n PetscScalars) for the values, v.
   The values, v, are then returned in a row-oriented format,
   analogous to that used by default in MatSetValues().

   MatGetValues() uses 0-based row and column numbers in
   Fortran as well as in C.

   MatGetValues() requires that the matrix has been assembled
   with MatAssemblyBegin()/MatAssemblyEnd().  Thus, calls to
   MatSetValues() and MatGetValues() CANNOT be made in succession
   without intermediate matrix assembly.

   Negative row or column indices will be ignored and those locations in v[] will be
   left unchanged.

   Level: advanced

   Concepts: matrices^accessing values

.seealso: MatGetRow(), MatGetSubMatrices(), MatSetValues()
@*/
PetscErrorCode  MatGetValues(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!m || !n) PetscFunctionReturn(0);
  PetscValidIntPointer(idxm,3);
  PetscValidIntPointer(idxn,5);
  PetscValidScalarPointer(v,6);
  if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->getvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_GetValues,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->getvalues)(mat,m,idxm,n,idxn,v);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_GetValues,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesBatch"
/*@
  MatSetValuesBatch - Adds (ADD_VALUES) many blocks of values into a matrix at once. The blocks must all be square and
  the same size. Currently, this can only be called once and creates the given matrix.

  Not Collective

  Input Parameters:
+ mat - the matrix
. nb - the number of blocks
. bs - the number of rows (and columns) in each block
. rows - a concatenation of the rows for each block
- v - a concatenation of logically two-dimensional arrays of values

  Notes:
  In the future, we will extend this routine to handle rectangular blocks, and to allow multiple calls for a given matrix.

  Level: advanced

  Concepts: matrices^putting entries in

.seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
          InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues()
@*/
PetscErrorCode MatSetValuesBatch(Mat mat, PetscInt nb, PetscInt bs, PetscInt rows[], const PetscScalar v[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidScalarPointer(rows,4);
  PetscValidScalarPointer(v,5);
#if defined(PETSC_USE_DEBUG)
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
#endif

  ierr = PetscLogEventBegin(MAT_SetValuesBatch,mat,0,0,0);CHKERRQ(ierr);
  if (mat->ops->setvaluesbatch) {
    ierr = (*mat->ops->setvaluesbatch)(mat,nb,bs,rows,v);CHKERRQ(ierr);
  } else {
    PetscInt b;
    for (b = 0; b < nb; ++b) {
      ierr = MatSetValues(mat, bs, &rows[b*bs], bs, &rows[b*bs], &v[b*bs*bs], ADD_VALUES);CHKERRQ(ierr);
    }
  }
  ierr = PetscLogEventEnd(MAT_SetValuesBatch,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetLocalToGlobalMapping"
/*@
   MatSetLocalToGlobalMapping - Sets a local-to-global numbering for use by
   the routine MatSetValuesLocal() to allow users to insert matrix entries
   using a local (per-processor) numbering.

   Not Collective

   Input Parameters:
+  x - the matrix
.  rmapping - row mapping created with ISLocalToGlobalMappingCreate()   or ISLocalToGlobalMappingCreateIS()
- cmapping - column mapping

   Level: intermediate

   Concepts: matrices^local to global mapping
   Concepts: local to global mapping^for matrices

.seealso:  MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetValuesLocal()
@*/
PetscErrorCode  MatSetLocalToGlobalMapping(Mat x,ISLocalToGlobalMapping rmapping,ISLocalToGlobalMapping cmapping)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(x,MAT_CLASSID,1);
  PetscValidType(x,1);
  PetscValidHeaderSpecific(rmapping,IS_LTOGM_CLASSID,2);
  PetscValidHeaderSpecific(cmapping,IS_LTOGM_CLASSID,3);

  if (x->ops->setlocaltoglobalmapping) {
    ierr = (*x->ops->setlocaltoglobalmapping)(x,rmapping,cmapping);CHKERRQ(ierr);
  } else {
    ierr = PetscLayoutSetISLocalToGlobalMapping(x->rmap,rmapping);CHKERRQ(ierr);
    ierr = PetscLayoutSetISLocalToGlobalMapping(x->cmap,cmapping);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatGetLocalToGlobalMapping"
/*@
   MatGetLocalToGlobalMapping - Gets the local-to-global numbering set by MatSetLocalToGlobalMapping()

   Not Collective

   Input Parameters:
.  A - the matrix

   Output Parameters:
+ rmapping - row mapping
- cmapping - column mapping

   Level: advanced

   Concepts: matrices^local to global mapping
   Concepts: local to global mapping^for matrices

.seealso:  MatSetValuesLocal()
@*/
PetscErrorCode  MatGetLocalToGlobalMapping(Mat A,ISLocalToGlobalMapping *rmapping,ISLocalToGlobalMapping *cmapping)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (rmapping) PetscValidPointer(rmapping,2);
  if (cmapping) PetscValidPointer(cmapping,3);
  if (rmapping) *rmapping = A->rmap->mapping;
  if (cmapping) *cmapping = A->cmap->mapping;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetLayouts"
/*@
   MatGetLayouts - Gets the PetscLayout objects for rows and columns

   Not Collective

   Input Parameters:
.  A - the matrix

   Output Parameters:
+ rmap - row layout
- cmap - column layout

   Level: advanced

.seealso:  MatCreateVecs(), MatGetLocalToGlobalMapping()
@*/
PetscErrorCode  MatGetLayouts(Mat A,PetscLayout *rmap,PetscLayout *cmap)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (rmap) PetscValidPointer(rmap,2);
  if (cmap) PetscValidPointer(cmap,3);
  if (rmap) *rmap = A->rmap;
  if (cmap) *cmap = A->cmap;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesLocal"
/*@
   MatSetValuesLocal - Inserts or adds values into certain locations of a matrix,
   using a local ordering of the nodes.

   Not Collective

   Input Parameters:
+  x - the matrix
.  nrow, irow - number of rows and their local indices
.  ncol, icol - number of columns and their local indices
.  y -  a logically two-dimensional array of values
-  addv - either INSERT_VALUES or ADD_VALUES, where
   ADD_VALUES adds values to any existing entries, and
   INSERT_VALUES replaces existing entries with new values

   Notes:
   If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
      MatSetUp() before using this routine

   If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatSetLocalToGlobalMapping() before using this routine

   Calls to MatSetValuesLocal() with the INSERT_VALUES and ADD_VALUES
   options cannot be mixed without intervening calls to the assembly
   routines.

   These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
   MUST be called after all calls to MatSetValuesLocal() have been completed.

   Level: intermediate

   Concepts: matrices^putting entries in with local numbering

.seealso:  MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetLocalToGlobalMapping(),
           MatSetValueLocal()
@*/
PetscErrorCode  MatSetValuesLocal(Mat mat,PetscInt nrow,const PetscInt irow[],PetscInt ncol,const PetscInt icol[],const PetscScalar y[],InsertMode addv)
{
  PetscErrorCode ierr;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  if (!nrow || !ncol) PetscFunctionReturn(0); /* no values to insert */
  PetscValidIntPointer(irow,3);
  PetscValidIntPointer(icol,5);
  PetscValidScalarPointer(y,6);
  if (mat->insertmode == NOT_SET_VALUES) {
    mat->insertmode = addv;
  }
#if defined(PETSC_USE_DEBUG)
  else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->setvalueslocal && !mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
#endif

  if (mat->assembled) {
    mat->was_assembled = PETSC_TRUE;
    mat->assembled     = PETSC_FALSE;
  }
  ierr = PetscLogEventBegin(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
  if (mat->ops->setvalueslocal) {
    ierr = (*mat->ops->setvalueslocal)(mat,nrow,irow,ncol,icol,y,addv);CHKERRQ(ierr);
  } else {
    PetscInt buf[8192],*bufr=0,*bufc=0,*irowm,*icolm;
    if ((nrow+ncol) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
      irowm = buf; icolm = buf+nrow;
    } else {
      ierr  = PetscMalloc2(nrow,&bufr,ncol,&bufc);CHKERRQ(ierr);
      irowm = bufr; icolm = bufc;
    }
    ierr = ISLocalToGlobalMappingApply(mat->rmap->mapping,nrow,irow,irowm);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingApply(mat->cmap->mapping,ncol,icol,icolm);CHKERRQ(ierr);
    ierr = MatSetValues(mat,nrow,irowm,ncol,icolm,y,addv);CHKERRQ(ierr);
    ierr = PetscFree2(bufr,bufc);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesBlockedLocal"
/*@
   MatSetValuesBlockedLocal - Inserts or adds values into certain locations of a matrix,
   using a local ordering of the nodes a block at a time.

   Not Collective

   Input Parameters:
+  x - the matrix
.  nrow, irow - number of rows and their local indices
.  ncol, icol - number of columns and their local indices
.  y -  a logically two-dimensional array of values
-  addv - either INSERT_VALUES or ADD_VALUES, where
   ADD_VALUES adds values to any existing entries, and
   INSERT_VALUES replaces existing entries with new values

   Notes:
   If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
      MatSetUp() before using this routine

   If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatSetBlockSize() and MatSetLocalToGlobalMapping()
      before using this routineBefore calling MatSetValuesLocal(), the user must first set the

   Calls to MatSetValuesBlockedLocal() with the INSERT_VALUES and ADD_VALUES
   options cannot be mixed without intervening calls to the assembly
   routines.

   These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
   MUST be called after all calls to MatSetValuesBlockedLocal() have been completed.

   Level: intermediate

   Concepts: matrices^putting blocked values in with local numbering

.seealso:  MatSetBlockSize(), MatSetLocalToGlobalMapping(), MatAssemblyBegin(), MatAssemblyEnd(),
           MatSetValuesLocal(),  MatSetValuesBlocked()
@*/
PetscErrorCode  MatSetValuesBlockedLocal(Mat mat,PetscInt nrow,const PetscInt irow[],PetscInt ncol,const PetscInt icol[],const PetscScalar y[],InsertMode addv)
{
  PetscErrorCode ierr;

  PetscFunctionBeginHot;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  if (!nrow || !ncol) PetscFunctionReturn(0); /* no values to insert */
  PetscValidIntPointer(irow,3);
  PetscValidIntPointer(icol,5);
  PetscValidScalarPointer(y,6);
  if (mat->insertmode == NOT_SET_VALUES) {
    mat->insertmode = addv;
  }
#if defined(PETSC_USE_DEBUG)
  else if (mat->insertmode != addv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->setvaluesblockedlocal && !mat->ops->setvaluesblocked && !mat->ops->setvalueslocal && !mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
#endif

  if (mat->assembled) {
    mat->was_assembled = PETSC_TRUE;
    mat->assembled     = PETSC_FALSE;
  }
  ierr = PetscLogEventBegin(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
  if (mat->ops->setvaluesblockedlocal) {
    ierr = (*mat->ops->setvaluesblockedlocal)(mat,nrow,irow,ncol,icol,y,addv);CHKERRQ(ierr);
  } else {
    PetscInt buf[8192],*bufr=0,*bufc=0,*irowm,*icolm;
    if ((nrow+ncol) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
      irowm = buf; icolm = buf + nrow;
    } else {
      ierr  = PetscMalloc2(nrow,&bufr,ncol,&bufc);CHKERRQ(ierr);
      irowm = bufr; icolm = bufc;
    }
    ierr = ISLocalToGlobalMappingApplyBlock(mat->rmap->mapping,nrow,irow,irowm);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingApplyBlock(mat->cmap->mapping,ncol,icol,icolm);CHKERRQ(ierr);
    ierr = MatSetValuesBlocked(mat,nrow,irowm,ncol,icolm,y,addv);CHKERRQ(ierr);
    ierr = PetscFree2(bufr,bufc);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultDiagonalBlock"
/*@
   MatMultDiagonalBlock - Computes the matrix-vector product, y = Dx. Where D is defined by the inode or block structure of the diagonal

   Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  x   - the vector to be multiplied

   Output Parameters:
.  y - the result

   Notes:
   The vectors x and y cannot be the same.  I.e., one cannot
   call MatMult(A,y,y).

   Level: developer

   Concepts: matrix-vector product

.seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
@*/
PetscErrorCode  MatMultDiagonalBlock(Mat mat,Vec x,Vec y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
  MatCheckPreallocated(mat,1);

  if (!mat->ops->multdiagonalblock) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"This matrix type does not have a multiply defined");
  ierr = (*mat->ops->multdiagonalblock)(mat,x,y);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* --------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "MatMult"
/*@
   MatMult - Computes the matrix-vector product, y = Ax.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  x   - the vector to be multiplied

   Output Parameters:
.  y - the result

   Notes:
   The vectors x and y cannot be the same.  I.e., one cannot
   call MatMult(A,y,y).

   Level: beginner

   Concepts: matrix-vector product

.seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
@*/
PetscErrorCode  MatMult(Mat mat,Vec x,Vec y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
#if !defined(PETSC_HAVE_CONSTRAINTS)
  if (mat->cmap->N != x->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->cmap->N,x->map->N);
  if (mat->rmap->N != y->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: global dim %D %D",mat->rmap->N,y->map->N);
  if (mat->rmap->n != y->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: local dim %D %D",mat->rmap->n,y->map->n);
#endif
  VecLocked(y,3);
  if (mat->erroriffpe) {ierr = VecValidValues(x,2,PETSC_TRUE);CHKERRQ(ierr);}
  MatCheckPreallocated(mat,1);

  ierr = VecLockPush(x);CHKERRQ(ierr);
  if (!mat->ops->mult) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"This matrix type does not have a multiply defined");
  ierr = PetscLogEventBegin(MAT_Mult,mat,x,y,0);CHKERRQ(ierr);
  ierr = (*mat->ops->mult)(mat,x,y);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_Mult,mat,x,y,0);CHKERRQ(ierr);
  if (mat->erroriffpe) {ierr = VecValidValues(y,3,PETSC_FALSE);CHKERRQ(ierr);}
  ierr = VecLockPop(x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultTranspose"
/*@
   MatMultTranspose - Computes matrix transpose times a vector.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  x   - the vector to be multilplied

   Output Parameters:
.  y - the result

   Notes:
   The vectors x and y cannot be the same.  I.e., one cannot
   call MatMultTranspose(A,y,y).

   For complex numbers this does NOT compute the Hermitian (complex conjugate) transpose multiple,
   use MatMultHermitianTranspose()

   Level: beginner

   Concepts: matrix vector product^transpose

.seealso: MatMult(), MatMultAdd(), MatMultTransposeAdd(), MatMultHermitianTranspose(), MatTranspose()
@*/
PetscErrorCode  MatMultTranspose(Mat mat,Vec x,Vec y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
#if !defined(PETSC_HAVE_CONSTRAINTS)
  if (mat->rmap->N != x->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->rmap->N,x->map->N);
  if (mat->cmap->N != y->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: global dim %D %D",mat->cmap->N,y->map->N);
#endif
  if (mat->erroriffpe) {ierr = VecValidValues(x,2,PETSC_TRUE);CHKERRQ(ierr);}
  MatCheckPreallocated(mat,1);

  if (!mat->ops->multtranspose) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"This matrix type does not have a multiply tranpose defined");
  ierr = PetscLogEventBegin(MAT_MultTranspose,mat,x,y,0);CHKERRQ(ierr);
  ierr = VecLockPush(x);CHKERRQ(ierr);
  ierr = (*mat->ops->multtranspose)(mat,x,y);CHKERRQ(ierr);
  ierr = VecLockPop(x);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MultTranspose,mat,x,y,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)y);CHKERRQ(ierr);
  if (mat->erroriffpe) {ierr = VecValidValues(y,3,PETSC_FALSE);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultHermitianTranspose"
/*@
   MatMultHermitianTranspose - Computes matrix Hermitian transpose times a vector.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  x   - the vector to be multilplied

   Output Parameters:
.  y - the result

   Notes:
   The vectors x and y cannot be the same.  I.e., one cannot
   call MatMultHermitianTranspose(A,y,y).

   Also called the conjugate transpose, complex conjugate transpose, or adjoint.

   For real numbers MatMultTranspose() and MatMultHermitianTranspose() are identical.

   Level: beginner

   Concepts: matrix vector product^transpose

.seealso: MatMult(), MatMultAdd(), MatMultHermitianTransposeAdd(), MatMultTranspose()
@*/
PetscErrorCode  MatMultHermitianTranspose(Mat mat,Vec x,Vec y)
{
  PetscErrorCode ierr;
  Vec            w;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
#if !defined(PETSC_HAVE_CONSTRAINTS)
  if (mat->rmap->N != x->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->rmap->N,x->map->N);
  if (mat->cmap->N != y->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: global dim %D %D",mat->cmap->N,y->map->N);
#endif
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_MultHermitianTranspose,mat,x,y,0);CHKERRQ(ierr);
  if (mat->ops->multhermitiantranspose) {
    ierr = VecLockPush(x);CHKERRQ(ierr);
    ierr = (*mat->ops->multhermitiantranspose)(mat,x,y);CHKERRQ(ierr);
    ierr = VecLockPop(x);CHKERRQ(ierr);
  } else {
    ierr = VecDuplicate(x,&w);CHKERRQ(ierr);
    ierr = VecCopy(x,w);CHKERRQ(ierr);
    ierr = VecConjugate(w);CHKERRQ(ierr);
    ierr = MatMultTranspose(mat,w,y);CHKERRQ(ierr);
    ierr = VecDestroy(&w);CHKERRQ(ierr);
    ierr = VecConjugate(y);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_MultHermitianTranspose,mat,x,y,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultAdd"
/*@
    MatMultAdd -  Computes v3 = v2 + A * v1.

    Neighbor-wise Collective on Mat and Vec

    Input Parameters:
+   mat - the matrix
-   v1, v2 - the vectors

    Output Parameters:
.   v3 - the result

    Notes:
    The vectors v1 and v3 cannot be the same.  I.e., one cannot
    call MatMultAdd(A,v1,v2,v1).

    Level: beginner

    Concepts: matrix vector product^addition

.seealso: MatMultTranspose(), MatMult(), MatMultTransposeAdd()
@*/
PetscErrorCode  MatMultAdd(Mat mat,Vec v1,Vec v2,Vec v3)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v1,VEC_CLASSID,2);
  PetscValidHeaderSpecific(v2,VEC_CLASSID,3);
  PetscValidHeaderSpecific(v3,VEC_CLASSID,4);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (mat->cmap->N != v1->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec v1: global dim %D %D",mat->cmap->N,v1->map->N);
  /* if (mat->rmap->N != v2->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec v2: global dim %D %D",mat->rmap->N,v2->map->N);
     if (mat->rmap->N != v3->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec v3: global dim %D %D",mat->rmap->N,v3->map->N); */
  if (mat->rmap->n != v3->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec v3: local dim %D %D",mat->rmap->n,v3->map->n);
  if (mat->rmap->n != v2->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec v2: local dim %D %D",mat->rmap->n,v2->map->n);
  if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
  MatCheckPreallocated(mat,1);

  if (!mat->ops->multadd) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No MatMultAdd() for matrix type '%s'",((PetscObject)mat)->type_name);
  ierr = PetscLogEventBegin(MAT_MultAdd,mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = VecLockPush(v1);CHKERRQ(ierr);
  ierr = (*mat->ops->multadd)(mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = VecLockPop(v1);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MultAdd,mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)v3);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultTransposeAdd"
/*@
   MatMultTransposeAdd - Computes v3 = v2 + A' * v1.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  v1, v2 - the vectors

   Output Parameters:
.  v3 - the result

   Notes:
   The vectors v1 and v3 cannot be the same.  I.e., one cannot
   call MatMultTransposeAdd(A,v1,v2,v1).

   Level: beginner

   Concepts: matrix vector product^transpose and addition

.seealso: MatMultTranspose(), MatMultAdd(), MatMult()
@*/
PetscErrorCode  MatMultTransposeAdd(Mat mat,Vec v1,Vec v2,Vec v3)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v1,VEC_CLASSID,2);
  PetscValidHeaderSpecific(v2,VEC_CLASSID,3);
  PetscValidHeaderSpecific(v3,VEC_CLASSID,4);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->multtransposeadd) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
  if (mat->rmap->N != v1->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec v1: global dim %D %D",mat->rmap->N,v1->map->N);
  if (mat->cmap->N != v2->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec v2: global dim %D %D",mat->cmap->N,v2->map->N);
  if (mat->cmap->N != v3->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec v3: global dim %D %D",mat->cmap->N,v3->map->N);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_MultTransposeAdd,mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = VecLockPush(v1);CHKERRQ(ierr);
  ierr = (*mat->ops->multtransposeadd)(mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = VecLockPop(v1);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MultTransposeAdd,mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)v3);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultHermitianTransposeAdd"
/*@
   MatMultHermitianTransposeAdd - Computes v3 = v2 + A^H * v1.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  v1, v2 - the vectors

   Output Parameters:
.  v3 - the result

   Notes:
   The vectors v1 and v3 cannot be the same.  I.e., one cannot
   call MatMultHermitianTransposeAdd(A,v1,v2,v1).

   Level: beginner

   Concepts: matrix vector product^transpose and addition

.seealso: MatMultHermitianTranspose(), MatMultTranspose(), MatMultAdd(), MatMult()
@*/
PetscErrorCode  MatMultHermitianTransposeAdd(Mat mat,Vec v1,Vec v2,Vec v3)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v1,VEC_CLASSID,2);
  PetscValidHeaderSpecific(v2,VEC_CLASSID,3);
  PetscValidHeaderSpecific(v3,VEC_CLASSID,4);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->multhermitiantransposeadd) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
  if (mat->rmap->N != v1->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec v1: global dim %D %D",mat->rmap->N,v1->map->N);
  if (mat->cmap->N != v2->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec v2: global dim %D %D",mat->cmap->N,v2->map->N);
  if (mat->cmap->N != v3->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec v3: global dim %D %D",mat->cmap->N,v3->map->N);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_MultHermitianTransposeAdd,mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = VecLockPush(v1);CHKERRQ(ierr);
  ierr = (*mat->ops->multhermitiantransposeadd)(mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = VecLockPop(v1);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MultHermitianTransposeAdd,mat,v1,v2,v3);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)v3);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultConstrained"
/*@
   MatMultConstrained - The inner multiplication routine for a
   constrained matrix P^T A P.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  x   - the vector to be multilplied

   Output Parameters:
.  y - the result

   Notes:
   The vectors x and y cannot be the same.  I.e., one cannot
   call MatMult(A,y,y).

   Level: beginner

.keywords: matrix, multiply, matrix-vector product, constraint
.seealso: MatMult(), MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
@*/
PetscErrorCode  MatMultConstrained(Mat mat,Vec x,Vec y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);
  if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (x == y) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
  if (mat->cmap->N != x->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->cmap->N,x->map->N);
  if (mat->rmap->N != y->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: global dim %D %D",mat->rmap->N,y->map->N);
  if (mat->rmap->n != y->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: local dim %D %D",mat->rmap->n,y->map->n);

  ierr = PetscLogEventBegin(MAT_MultConstrained,mat,x,y,0);CHKERRQ(ierr);
  ierr = VecLockPush(x);CHKERRQ(ierr);
  ierr = (*mat->ops->multconstrained)(mat,x,y);CHKERRQ(ierr);
  ierr = VecLockPop(x);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MultConstrained,mat,x,y,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultTransposeConstrained"
/*@
   MatMultTransposeConstrained - The inner multiplication routine for a
   constrained matrix P^T A^T P.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  x   - the vector to be multilplied

   Output Parameters:
.  y - the result

   Notes:
   The vectors x and y cannot be the same.  I.e., one cannot
   call MatMult(A,y,y).

   Level: beginner

.keywords: matrix, multiply, matrix-vector product, constraint
.seealso: MatMult(), MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
@*/
PetscErrorCode  MatMultTransposeConstrained(Mat mat,Vec x,Vec y)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);
  if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (x == y) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
  if (mat->rmap->N != x->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->cmap->N,x->map->N);
  if (mat->cmap->N != y->map->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: global dim %D %D",mat->rmap->N,y->map->N);

  ierr = PetscLogEventBegin(MAT_MultConstrained,mat,x,y,0);CHKERRQ(ierr);
  ierr = (*mat->ops->multtransposeconstrained)(mat,x,y);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MultConstrained,mat,x,y,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetFactorType"
/*@C
   MatGetFactorType - gets the type of factorization it is

   Note Collective
   as the flag

   Input Parameters:
.  mat - the matrix

   Output Parameters:
.  t - the type, one of MAT_FACTOR_NONE, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ILU, MAT_FACTOR_ICC,MAT_FACTOR_ILUDT

    Level: intermediate

.seealso:    MatFactorType, MatGetFactor()
@*/
PetscErrorCode  MatGetFactorType(Mat mat,MatFactorType *t)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  *t = mat->factortype;
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "MatGetInfo"
/*@C
   MatGetInfo - Returns information about matrix storage (number of
   nonzeros, memory, etc.).

   Collective on Mat if MAT_GLOBAL_MAX or MAT_GLOBAL_SUM is used as the flag

   Input Parameters:
.  mat - the matrix

   Output Parameters:
+  flag - flag indicating the type of parameters to be returned
   (MAT_LOCAL - local matrix, MAT_GLOBAL_MAX - maximum over all processors,
   MAT_GLOBAL_SUM - sum over all processors)
-  info - matrix information context

   Notes:
   The MatInfo context contains a variety of matrix data, including
   number of nonzeros allocated and used, number of mallocs during
   matrix assembly, etc.  Additional information for factored matrices
   is provided (such as the fill ratio, number of mallocs during
   factorization, etc.).  Much of this info is printed to PETSC_STDOUT
   when using the runtime options
$       -info -mat_view ::ascii_info

   Example for C/C++ Users:
   See the file ${PETSC_DIR}/include/petscmat.h for a complete list of
   data within the MatInfo context.  For example,
.vb
      MatInfo info;
      Mat     A;
      double  mal, nz_a, nz_u;

      MatGetInfo(A,MAT_LOCAL,&info);
      mal  = info.mallocs;
      nz_a = info.nz_allocated;
.ve

   Example for Fortran Users:
   Fortran users should declare info as a double precision
   array of dimension MAT_INFO_SIZE, and then extract the parameters
   of interest.  See the file ${PETSC_DIR}/include/petsc/finclude/petscmat.h
   a complete list of parameter names.
.vb
      double  precision info(MAT_INFO_SIZE)
      double  precision mal, nz_a
      Mat     A
      integer ierr

      call MatGetInfo(A,MAT_LOCAL,info,ierr)
      mal = info(MAT_INFO_MALLOCS)
      nz_a = info(MAT_INFO_NZ_ALLOCATED)
.ve

    Level: intermediate

    Concepts: matrices^getting information on

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatInfo]

.seealso: MatStashGetInfo()

@*/
PetscErrorCode  MatGetInfo(Mat mat,MatInfoType flag,MatInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(info,3);
  if (!mat->ops->getinfo) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  ierr = (*mat->ops->getinfo)(mat,flag,info);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

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

#undef __FUNCT__
#define __FUNCT__ "MatLUFactor"
/*@C
   MatLUFactor - Performs in-place LU factorization of matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  row - row permutation
.  col - column permutation
-  info - options for factorization, includes
$          fill - expected fill as ratio of original fill.
$          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
$                   Run with the option -info to determine an optimal value to use

   Notes:
   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   This changes the state of the matrix to a factored matrix; it cannot be used
   for example with MatSetValues() unless one first calls MatSetUnfactored().

   Level: developer

   Concepts: matrices^LU factorization

.seealso: MatLUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor(),
          MatGetOrdering(), MatSetUnfactored(), MatFactorInfo, MatGetFactor()

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatLUFactor(Mat mat,IS row,IS col,const MatFactorInfo *info)
{
  PetscErrorCode ierr;
  MatFactorInfo  tinfo;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (row) PetscValidHeaderSpecific(row,IS_CLASSID,2);
  if (col) PetscValidHeaderSpecific(col,IS_CLASSID,3);
  if (info) PetscValidPointer(info,4);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->lufactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  if (!info) {
    ierr = MatFactorInfoInitialize(&tinfo);CHKERRQ(ierr);
    info = &tinfo;
  }

  ierr = PetscLogEventBegin(MAT_LUFactor,mat,row,col,0);CHKERRQ(ierr);
  ierr = (*mat->ops->lufactor)(mat,row,col,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_LUFactor,mat,row,col,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatILUFactor"
/*@C
   MatILUFactor - Performs in-place ILU factorization of matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  row - row permutation
.  col - column permutation
-  info - structure containing
$      levels - number of levels of fill.
$      expected fill - as ratio of original fill.
$      1 or 0 - indicating force fill on diagonal (improves robustness for matrices
                missing diagonal entries)

   Notes:
   Probably really in-place only when level of fill is zero, otherwise allocates
   new space to store factored matrix and deletes previous memory.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^ILU factorization

.seealso: MatILUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor(), MatFactorInfo

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatILUFactor(Mat mat,IS row,IS col,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (row) PetscValidHeaderSpecific(row,IS_CLASSID,2);
  if (col) PetscValidHeaderSpecific(col,IS_CLASSID,3);
  PetscValidPointer(info,4);
  PetscValidType(mat,1);
  if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"matrix must be square");
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->ilufactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_ILUFactor,mat,row,col,0);CHKERRQ(ierr);
  ierr = (*mat->ops->ilufactor)(mat,row,col,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_ILUFactor,mat,row,col,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatLUFactorSymbolic"
/*@C
   MatLUFactorSymbolic - Performs symbolic LU factorization of matrix.
   Call this routine before calling MatLUFactorNumeric().

   Collective on Mat

   Input Parameters:
+  fact - the factor matrix obtained with MatGetFactor()
.  mat - the matrix
.  row, col - row and column permutations
-  info - options for factorization, includes
$          fill - expected fill as ratio of original fill.
$          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
$                   Run with the option -info to determine an optimal value to use


   Notes: See Users-Manual: ch_mat for additional information about choosing the fill factor for better efficiency.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^LU symbolic factorization

.seealso: MatLUFactor(), MatLUFactorNumeric(), MatCholeskyFactor(), MatFactorInfo, MatFactorInfoInitialize()

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatLUFactorSymbolic(Mat fact,Mat mat,IS row,IS col,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (row) PetscValidHeaderSpecific(row,IS_CLASSID,2);
  if (col) PetscValidHeaderSpecific(col,IS_CLASSID,3);
  if (info) PetscValidPointer(info,4);
  PetscValidType(mat,1);
  PetscValidPointer(fact,5);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!(fact)->ops->lufactorsymbolic) {
    const MatSolverPackage spackage;
    ierr = MatFactorGetSolverPackage(fact,&spackage);CHKERRQ(ierr);
    SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic LU using solver package %s",((PetscObject)mat)->type_name,spackage);
  }
  MatCheckPreallocated(mat,2);

  ierr = PetscLogEventBegin(MAT_LUFactorSymbolic,mat,row,col,0);CHKERRQ(ierr);
  ierr = (fact->ops->lufactorsymbolic)(fact,mat,row,col,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_LUFactorSymbolic,mat,row,col,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)fact);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatLUFactorNumeric"
/*@C
   MatLUFactorNumeric - Performs numeric LU factorization of a matrix.
   Call this routine after first calling MatLUFactorSymbolic().

   Collective on Mat

   Input Parameters:
+  fact - the factor matrix obtained with MatGetFactor()
.  mat - the matrix
-  info - options for factorization

   Notes:
   See MatLUFactor() for in-place factorization.  See
   MatCholeskyFactorNumeric() for the symmetric, positive definite case.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^LU numeric factorization

.seealso: MatLUFactorSymbolic(), MatLUFactor(), MatCholeskyFactor()

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatLUFactorNumeric(Mat fact,Mat mat,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(fact,2);
  PetscValidHeaderSpecific(fact,MAT_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->rmap->N != (fact)->rmap->N || mat->cmap->N != (fact)->cmap->N) SETERRQ4(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Mat fact: global dimensions are different %D should = %D %D should = %D",mat->rmap->N,(fact)->rmap->N,mat->cmap->N,(fact)->cmap->N);

  if (!(fact)->ops->lufactornumeric) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s numeric LU",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,2);
  ierr = PetscLogEventBegin(MAT_LUFactorNumeric,mat,fact,0,0);CHKERRQ(ierr);
  ierr = (fact->ops->lufactornumeric)(fact,mat,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_LUFactorNumeric,mat,fact,0,0);CHKERRQ(ierr);
  ierr = MatViewFromOptions(fact,NULL,"-mat_factor_view");CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)fact);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCholeskyFactor"
/*@C
   MatCholeskyFactor - Performs in-place Cholesky factorization of a
   symmetric matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  perm - row and column permutations
-  f - expected fill as ratio of original fill

   Notes:
   See MatLUFactor() for the nonsymmetric case.  See also
   MatCholeskyFactorSymbolic(), and MatCholeskyFactorNumeric().

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^Cholesky factorization

.seealso: MatLUFactor(), MatCholeskyFactorSymbolic(), MatCholeskyFactorNumeric()
          MatGetOrdering()

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatCholeskyFactor(Mat mat,IS perm,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (perm) PetscValidHeaderSpecific(perm,IS_CLASSID,2);
  if (info) PetscValidPointer(info,3);
  if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Matrix must be square");
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->choleskyfactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_CholeskyFactor,mat,perm,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->choleskyfactor)(mat,perm,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_CholeskyFactor,mat,perm,0,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCholeskyFactorSymbolic"
/*@C
   MatCholeskyFactorSymbolic - Performs symbolic Cholesky factorization
   of a symmetric matrix.

   Collective on Mat

   Input Parameters:
+  fact - the factor matrix obtained with MatGetFactor()
.  mat - the matrix
.  perm - row and column permutations
-  info - options for factorization, includes
$          fill - expected fill as ratio of original fill.
$          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
$                   Run with the option -info to determine an optimal value to use

   Notes:
   See MatLUFactorSymbolic() for the nonsymmetric case.  See also
   MatCholeskyFactor() and MatCholeskyFactorNumeric().

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^Cholesky symbolic factorization

.seealso: MatLUFactorSymbolic(), MatCholeskyFactor(), MatCholeskyFactorNumeric()
          MatGetOrdering()

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatCholeskyFactorSymbolic(Mat fact,Mat mat,IS perm,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (perm) PetscValidHeaderSpecific(perm,IS_CLASSID,2);
  if (info) PetscValidPointer(info,3);
  PetscValidPointer(fact,4);
  if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Matrix must be square");
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!(fact)->ops->choleskyfactorsymbolic) {
    const MatSolverPackage spackage;
    ierr = MatFactorGetSolverPackage(fact,&spackage);CHKERRQ(ierr);
    SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s symbolic factor Cholesky using solver package %s",((PetscObject)mat)->type_name,spackage);
  }
  MatCheckPreallocated(mat,2);

  ierr = PetscLogEventBegin(MAT_CholeskyFactorSymbolic,mat,perm,0,0);CHKERRQ(ierr);
  ierr = (fact->ops->choleskyfactorsymbolic)(fact,mat,perm,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_CholeskyFactorSymbolic,mat,perm,0,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)fact);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCholeskyFactorNumeric"
/*@C
   MatCholeskyFactorNumeric - Performs numeric Cholesky factorization
   of a symmetric matrix. Call this routine after first calling
   MatCholeskyFactorSymbolic().

   Collective on Mat

   Input Parameters:
+  fact - the factor matrix obtained with MatGetFactor()
.  mat - the initial matrix
.  info - options for factorization
-  fact - the symbolic factor of mat


   Notes:
   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^Cholesky numeric factorization

.seealso: MatCholeskyFactorSymbolic(), MatCholeskyFactor(), MatLUFactorNumeric()

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatCholeskyFactorNumeric(Mat fact,Mat mat,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(fact,2);
  PetscValidHeaderSpecific(fact,MAT_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!(fact)->ops->choleskyfactornumeric) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s numeric factor Cholesky",((PetscObject)mat)->type_name);
  if (mat->rmap->N != (fact)->rmap->N || mat->cmap->N != (fact)->cmap->N) SETERRQ4(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Mat fact: global dim %D should = %D %D should = %D",mat->rmap->N,(fact)->rmap->N,mat->cmap->N,(fact)->cmap->N);
  MatCheckPreallocated(mat,2);

  ierr = PetscLogEventBegin(MAT_CholeskyFactorNumeric,mat,fact,0,0);CHKERRQ(ierr);
  ierr = (fact->ops->choleskyfactornumeric)(fact,mat,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_CholeskyFactorNumeric,mat,fact,0,0);CHKERRQ(ierr);
  ierr = MatViewFromOptions(fact,NULL,"-mat_factor_view");CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)fact);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "MatSolve"
/*@
   MatSolve - Solves A x = b, given a factored matrix.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the factored matrix
-  b - the right-hand-side vector

   Output Parameter:
.  x - the result vector

   Notes:
   The vectors b and x cannot be the same.  I.e., one cannot
   call MatSolve(A,x,x).

   Notes:
   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^triangular solves

.seealso: MatSolveAdd(), MatSolveTranspose(), MatSolveTransposeAdd()
@*/
PetscErrorCode  MatSolve(Mat mat,Vec b,Vec x)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(b,VEC_CLASSID,2);
  PetscValidHeaderSpecific(x,VEC_CLASSID,3);
  PetscCheckSameComm(mat,1,b,2);
  PetscCheckSameComm(mat,1,x,3);
  if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (mat->cmap->N != x->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->cmap->N,x->map->N);
  if (mat->rmap->N != b->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: global dim %D %D",mat->rmap->N,b->map->N);
  if (mat->rmap->n != b->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: local dim %D %D",mat->rmap->n,b->map->n);
  if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(0);
  if (!mat->ops->solve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_Solve,mat,b,x,0);CHKERRQ(ierr);
  ierr = (*mat->ops->solve)(mat,b,x);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_Solve,mat,b,x,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatSolve_Basic"
PetscErrorCode  MatMatSolve_Basic(Mat A,Mat B,Mat X)
{
  PetscErrorCode ierr;
  Vec            b,x;
  PetscInt       m,N,i;
  PetscScalar    *bb,*xx;
  PetscBool      flg;

  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");

  ierr = MatDenseGetArray(B,&bb);CHKERRQ(ierr);
  ierr = MatDenseGetArray(X,&xx);CHKERRQ(ierr);
  ierr = MatGetLocalSize(B,&m,NULL);CHKERRQ(ierr);  /* number local rows */
  ierr = MatGetSize(B,NULL,&N);CHKERRQ(ierr);       /* total columns in dense matrix */
  ierr = MatCreateVecs(A,&x,&b);CHKERRQ(ierr);
  for (i=0; i<N; i++) {
    ierr = VecPlaceArray(b,bb + i*m);CHKERRQ(ierr);
    ierr = VecPlaceArray(x,xx + i*m);CHKERRQ(ierr);
    ierr = MatSolve(A,b,x);CHKERRQ(ierr);
    ierr = VecResetArray(x);CHKERRQ(ierr);
    ierr = VecResetArray(b);CHKERRQ(ierr);
  }
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = MatDenseRestoreArray(B,&bb);CHKERRQ(ierr);
  ierr = MatDenseRestoreArray(X,&xx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatSolve"
/*@
   MatMatSolve - Solves A X = B, given a factored matrix.

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the factored matrix
-  B - the right-hand-side matrix  (dense matrix)

   Output Parameter:
.  X - the result matrix (dense matrix)

   Notes:
   The matrices b and x cannot be the same.  I.e., one cannot
   call MatMatSolve(A,x,x).

   Notes:
   Most users should usually employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate(). However KSP can only solve for one vector (column of X)
   at a time.

   When using SuperLU_Dist as a parallel solver PETSc will use the SuperLU_Dist functionality to solve multiple right hand sides simultaneously. For MUMPS
   it calls a separate solve for each right hand side since MUMPS does not yet support distributed right hand sides.

   Since the resulting matrix X must always be dense we do not support sparse representation of the matrix B.

   Level: developer

   Concepts: matrices^triangular solves

.seealso: MatMatSolveAdd(), MatMatSolveTranspose(), MatMatSolveTransposeAdd(), MatLUFactor(), MatCholeskyFactor()
@*/
PetscErrorCode  MatMatSolve(Mat A,Mat B,Mat X)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidHeaderSpecific(X,MAT_CLASSID,3);
  PetscCheckSameComm(A,1,B,2);
  PetscCheckSameComm(A,1,X,3);
  if (X == B) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_IDN,"X and B must be different matrices");
  if (!A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (A->cmap->N != X->rmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Mat A,Mat X: global dim %D %D",A->cmap->N,X->rmap->N);
  if (A->rmap->N != B->rmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Mat A,Mat B: global dim %D %D",A->rmap->N,B->rmap->N);
  if (A->rmap->n != B->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat A,Mat B: local dim %D %D",A->rmap->n,B->rmap->n);
  if (X->cmap->N < B->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Solution matrix must have same number of columns as rhs matrix");
  if (!A->rmap->N && !A->cmap->N) PetscFunctionReturn(0);
  MatCheckPreallocated(A,1);

  ierr = PetscLogEventBegin(MAT_MatSolve,A,B,X,0);CHKERRQ(ierr);
  if (!A->ops->matsolve) {
    ierr = PetscInfo1(A,"Mat type %s using basic MatMatSolve\n",((PetscObject)A)->type_name);CHKERRQ(ierr);
    ierr = MatMatSolve_Basic(A,B,X);CHKERRQ(ierr);
  } else {
    ierr = (*A->ops->matsolve)(A,B,X);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_MatSolve,A,B,X,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)X);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatForwardSolve"
/*@
   MatForwardSolve - Solves L x = b, given a factored matrix, A = LU, or
                            U^T*D^(1/2) x = b, given a factored symmetric matrix, A = U^T*D*U,

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the factored matrix
-  b - the right-hand-side vector

   Output Parameter:
.  x - the result vector

   Notes:
   MatSolve() should be used for most applications, as it performs
   a forward solve followed by a backward solve.

   The vectors b and x cannot be the same,  i.e., one cannot
   call MatForwardSolve(A,x,x).

   For matrix in seqsbaij format with block size larger than 1,
   the diagonal blocks are not implemented as D = D^(1/2) * D^(1/2) yet.
   MatForwardSolve() solves U^T*D y = b, and
   MatBackwardSolve() solves U x = y.
   Thus they do not provide a symmetric preconditioner.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^forward solves

.seealso: MatSolve(), MatBackwardSolve()
@*/
PetscErrorCode  MatForwardSolve(Mat mat,Vec b,Vec x)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(b,VEC_CLASSID,2);
  PetscValidHeaderSpecific(x,VEC_CLASSID,3);
  PetscCheckSameComm(mat,1,b,2);
  PetscCheckSameComm(mat,1,x,3);
  if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (!mat->ops->forwardsolve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (mat->cmap->N != x->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->cmap->N,x->map->N);
  if (mat->rmap->N != b->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: global dim %D %D",mat->rmap->N,b->map->N);
  if (mat->rmap->n != b->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: local dim %D %D",mat->rmap->n,b->map->n);
  MatCheckPreallocated(mat,1);
  ierr = PetscLogEventBegin(MAT_ForwardSolve,mat,b,x,0);CHKERRQ(ierr);
  ierr = (*mat->ops->forwardsolve)(mat,b,x);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_ForwardSolve,mat,b,x,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatBackwardSolve"
/*@
   MatBackwardSolve - Solves U x = b, given a factored matrix, A = LU.
                             D^(1/2) U x = b, given a factored symmetric matrix, A = U^T*D*U,

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the factored matrix
-  b - the right-hand-side vector

   Output Parameter:
.  x - the result vector

   Notes:
   MatSolve() should be used for most applications, as it performs
   a forward solve followed by a backward solve.

   The vectors b and x cannot be the same.  I.e., one cannot
   call MatBackwardSolve(A,x,x).

   For matrix in seqsbaij format with block size larger than 1,
   the diagonal blocks are not implemented as D = D^(1/2) * D^(1/2) yet.
   MatForwardSolve() solves U^T*D y = b, and
   MatBackwardSolve() solves U x = y.
   Thus they do not provide a symmetric preconditioner.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^backward solves

.seealso: MatSolve(), MatForwardSolve()
@*/
PetscErrorCode  MatBackwardSolve(Mat mat,Vec b,Vec x)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(b,VEC_CLASSID,2);
  PetscValidHeaderSpecific(x,VEC_CLASSID,3);
  PetscCheckSameComm(mat,1,b,2);
  PetscCheckSameComm(mat,1,x,3);
  if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (!mat->ops->backwardsolve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (mat->cmap->N != x->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->cmap->N,x->map->N);
  if (mat->rmap->N != b->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: global dim %D %D",mat->rmap->N,b->map->N);
  if (mat->rmap->n != b->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: local dim %D %D",mat->rmap->n,b->map->n);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_BackwardSolve,mat,b,x,0);CHKERRQ(ierr);
  ierr = (*mat->ops->backwardsolve)(mat,b,x);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_BackwardSolve,mat,b,x,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveAdd"
/*@
   MatSolveAdd - Computes x = y + inv(A)*b, given a factored matrix.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the factored matrix
.  b - the right-hand-side vector
-  y - the vector to be added to

   Output Parameter:
.  x - the result vector

   Notes:
   The vectors b and x cannot be the same.  I.e., one cannot
   call MatSolveAdd(A,x,y,x).

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^triangular solves

.seealso: MatSolve(), MatSolveTranspose(), MatSolveTransposeAdd()
@*/
PetscErrorCode  MatSolveAdd(Mat mat,Vec b,Vec y,Vec x)
{
  PetscScalar    one = 1.0;
  Vec            tmp;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(y,VEC_CLASSID,2);
  PetscValidHeaderSpecific(b,VEC_CLASSID,3);
  PetscValidHeaderSpecific(x,VEC_CLASSID,4);
  PetscCheckSameComm(mat,1,b,2);
  PetscCheckSameComm(mat,1,y,2);
  PetscCheckSameComm(mat,1,x,3);
  if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (mat->cmap->N != x->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->cmap->N,x->map->N);
  if (mat->rmap->N != b->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: global dim %D %D",mat->rmap->N,b->map->N);
  if (mat->rmap->N != y->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: global dim %D %D",mat->rmap->N,y->map->N);
  if (mat->rmap->n != b->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: local dim %D %D",mat->rmap->n,b->map->n);
  if (x->map->n != y->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Vec x,Vec y: local dim %D %D",x->map->n,y->map->n);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_SolveAdd,mat,b,x,y);CHKERRQ(ierr);
  if (mat->ops->solveadd) {
    ierr = (*mat->ops->solveadd)(mat,b,y,x);CHKERRQ(ierr);
  } else {
    /* do the solve then the add manually */
    if (x != y) {
      ierr = MatSolve(mat,b,x);CHKERRQ(ierr);
      ierr = VecAXPY(x,one,y);CHKERRQ(ierr);
    } else {
      ierr = VecDuplicate(x,&tmp);CHKERRQ(ierr);
      ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)tmp);CHKERRQ(ierr);
      ierr = VecCopy(x,tmp);CHKERRQ(ierr);
      ierr = MatSolve(mat,b,x);CHKERRQ(ierr);
      ierr = VecAXPY(x,one,tmp);CHKERRQ(ierr);
      ierr = VecDestroy(&tmp);CHKERRQ(ierr);
    }
  }
  ierr = PetscLogEventEnd(MAT_SolveAdd,mat,b,x,y);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTranspose"
/*@
   MatSolveTranspose - Solves A' x = b, given a factored matrix.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the factored matrix
-  b - the right-hand-side vector

   Output Parameter:
.  x - the result vector

   Notes:
   The vectors b and x cannot be the same.  I.e., one cannot
   call MatSolveTranspose(A,x,x).

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^triangular solves

.seealso: MatSolve(), MatSolveAdd(), MatSolveTransposeAdd()
@*/
PetscErrorCode  MatSolveTranspose(Mat mat,Vec b,Vec x)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(b,VEC_CLASSID,2);
  PetscValidHeaderSpecific(x,VEC_CLASSID,3);
  PetscCheckSameComm(mat,1,b,2);
  PetscCheckSameComm(mat,1,x,3);
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
  if (!mat->ops->solvetranspose) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s",((PetscObject)mat)->type_name);
  if (mat->rmap->N != x->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->rmap->N,x->map->N);
  if (mat->cmap->N != b->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: global dim %D %D",mat->cmap->N,b->map->N);
  MatCheckPreallocated(mat,1);
  ierr = PetscLogEventBegin(MAT_SolveTranspose,mat,b,x,0);CHKERRQ(ierr);
  ierr = (*mat->ops->solvetranspose)(mat,b,x);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_SolveTranspose,mat,b,x,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolveTransposeAdd"
/*@
   MatSolveTransposeAdd - Computes x = y + inv(Transpose(A)) b, given a
                      factored matrix.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the factored matrix
.  b - the right-hand-side vector
-  y - the vector to be added to

   Output Parameter:
.  x - the result vector

   Notes:
   The vectors b and x cannot be the same.  I.e., one cannot
   call MatSolveTransposeAdd(A,x,y,x).

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^triangular solves

.seealso: MatSolve(), MatSolveAdd(), MatSolveTranspose()
@*/
PetscErrorCode  MatSolveTransposeAdd(Mat mat,Vec b,Vec y,Vec x)
{
  PetscScalar    one = 1.0;
  PetscErrorCode ierr;
  Vec            tmp;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(y,VEC_CLASSID,2);
  PetscValidHeaderSpecific(b,VEC_CLASSID,3);
  PetscValidHeaderSpecific(x,VEC_CLASSID,4);
  PetscCheckSameComm(mat,1,b,2);
  PetscCheckSameComm(mat,1,y,3);
  PetscCheckSameComm(mat,1,x,4);
  if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (mat->rmap->N != x->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->rmap->N,x->map->N);
  if (mat->cmap->N != b->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: global dim %D %D",mat->cmap->N,b->map->N);
  if (mat->cmap->N != y->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: global dim %D %D",mat->cmap->N,y->map->N);
  if (x->map->n != y->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Vec x,Vec y: local dim %D %D",x->map->n,y->map->n);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_SolveTransposeAdd,mat,b,x,y);CHKERRQ(ierr);
  if (mat->ops->solvetransposeadd) {
    ierr = (*mat->ops->solvetransposeadd)(mat,b,y,x);CHKERRQ(ierr);
  } else {
    /* do the solve then the add manually */
    if (x != y) {
      ierr = MatSolveTranspose(mat,b,x);CHKERRQ(ierr);
      ierr = VecAXPY(x,one,y);CHKERRQ(ierr);
    } else {
      ierr = VecDuplicate(x,&tmp);CHKERRQ(ierr);
      ierr = PetscLogObjectParent((PetscObject)mat,(PetscObject)tmp);CHKERRQ(ierr);
      ierr = VecCopy(x,tmp);CHKERRQ(ierr);
      ierr = MatSolveTranspose(mat,b,x);CHKERRQ(ierr);
      ierr = VecAXPY(x,one,tmp);CHKERRQ(ierr);
      ierr = VecDestroy(&tmp);CHKERRQ(ierr);
    }
  }
  ierr = PetscLogEventEnd(MAT_SolveTransposeAdd,mat,b,x,y);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/* ----------------------------------------------------------------*/

#undef __FUNCT__
#define __FUNCT__ "MatSOR"
/*@
   MatSOR - Computes relaxation (SOR, Gauss-Seidel) sweeps.

   Neighbor-wise Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
.  b - the right hand side
.  omega - the relaxation factor
.  flag - flag indicating the type of SOR (see below)
.  shift -  diagonal shift
.  its - the number of iterations
-  lits - the number of local iterations

   Output Parameters:
.  x - the solution (can contain an initial guess, use option SOR_ZERO_INITIAL_GUESS to indicate no guess)

   SOR Flags:
.     SOR_FORWARD_SWEEP - forward SOR
.     SOR_BACKWARD_SWEEP - backward SOR
.     SOR_SYMMETRIC_SWEEP - SSOR (symmetric SOR)
.     SOR_LOCAL_FORWARD_SWEEP - local forward SOR
.     SOR_LOCAL_BACKWARD_SWEEP - local forward SOR
.     SOR_LOCAL_SYMMETRIC_SWEEP - local SSOR
.     SOR_APPLY_UPPER, SOR_APPLY_LOWER - applies
         upper/lower triangular part of matrix to
         vector (with omega)
.     SOR_ZERO_INITIAL_GUESS - zero initial guess

   Notes:
   SOR_LOCAL_FORWARD_SWEEP, SOR_LOCAL_BACKWARD_SWEEP, and
   SOR_LOCAL_SYMMETRIC_SWEEP perform separate independent smoothings
   on each processor.

   Application programmers will not generally use MatSOR() directly,
   but instead will employ the KSP/PC interface.

   Notes: for BAIJ, SBAIJ, and AIJ matrices with Inodes this does a block SOR smoothing, otherwise it does a pointwise smoothing

   Notes for Advanced Users:
   The flags are implemented as bitwise inclusive or operations.
   For example, use (SOR_ZERO_INITIAL_GUESS | SOR_SYMMETRIC_SWEEP)
   to specify a zero initial guess for SSOR.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Vectors x and b CANNOT be the same

   Developer Note: We should add block SOR support for AIJ matrices with block size set to great than one and no inodes

   Level: developer

   Concepts: matrices^relaxation
   Concepts: matrices^SOR
   Concepts: matrices^Gauss-Seidel

@*/
PetscErrorCode  MatSOR(Mat mat,Vec b,PetscReal omega,MatSORType flag,PetscReal shift,PetscInt its,PetscInt lits,Vec x)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(b,VEC_CLASSID,2);
  PetscValidHeaderSpecific(x,VEC_CLASSID,8);
  PetscCheckSameComm(mat,1,b,2);
  PetscCheckSameComm(mat,1,x,8);
  if (!mat->ops->sor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (mat->cmap->N != x->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: global dim %D %D",mat->cmap->N,x->map->N);
  if (mat->rmap->N != b->map->N) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: global dim %D %D",mat->rmap->N,b->map->N);
  if (mat->rmap->n != b->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec b: local dim %D %D",mat->rmap->n,b->map->n);
  if (its <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D positive",its);
  if (lits <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires local its %D positive",lits);
  if (b == x) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_IDN,"b and x vector cannot be the same");

  MatCheckPreallocated(mat,1);
  ierr = PetscLogEventBegin(MAT_SOR,mat,b,x,0);CHKERRQ(ierr);
  ierr =(*mat->ops->sor)(mat,b,omega,flag,shift,its,lits,x);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_SOR,mat,b,x,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)x);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCopy_Basic"
/*
      Default matrix copy routine.
*/
PetscErrorCode MatCopy_Basic(Mat A,Mat B,MatStructure str)
{
  PetscErrorCode    ierr;
  PetscInt          i,rstart = 0,rend = 0,nz;
  const PetscInt    *cwork;
  const PetscScalar *vwork;

  PetscFunctionBegin;
  if (B->assembled) {
    ierr = MatZeroEntries(B);CHKERRQ(ierr);
  }
  ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
  for (i=rstart; i<rend; i++) {
    ierr = MatGetRow(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
    ierr = MatSetValues(B,1,&i,nz,cwork,vwork,INSERT_VALUES);CHKERRQ(ierr);
    ierr = MatRestoreRow(A,i,&nz,&cwork,&vwork);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCopy"
/*@
   MatCopy - Copys a matrix to another matrix.

   Collective on Mat

   Input Parameters:
+  A - the matrix
-  str - SAME_NONZERO_PATTERN or DIFFERENT_NONZERO_PATTERN

   Output Parameter:
.  B - where the copy is put

   Notes:
   If you use SAME_NONZERO_PATTERN then the two matrices had better have the
   same nonzero pattern or the routine will crash.

   MatCopy() copies the matrix entries of a matrix to another existing
   matrix (after first zeroing the second matrix).  A related routine is
   MatConvert(), which first creates a new matrix and then copies the data.

   Level: intermediate

   Concepts: matrices^copying

.seealso: MatConvert(), MatDuplicate()

@*/
PetscErrorCode  MatCopy(Mat A,Mat B,MatStructure str)
{
  PetscErrorCode ierr;
  PetscInt       i;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidType(A,1);
  PetscValidType(B,2);
  PetscCheckSameComm(A,1,B,2);
  MatCheckPreallocated(B,2);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (A->rmap->N != B->rmap->N || A->cmap->N != B->cmap->N) SETERRQ4(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Mat A,Mat B: global dim (%D,%D) (%D,%D)",A->rmap->N,B->rmap->N,A->cmap->N,B->cmap->N);
  MatCheckPreallocated(A,1);

  ierr = PetscLogEventBegin(MAT_Copy,A,B,0,0);CHKERRQ(ierr);
  if (A->ops->copy) {
    ierr = (*A->ops->copy)(A,B,str);CHKERRQ(ierr);
  } else { /* generic conversion */
    ierr = MatCopy_Basic(A,B,str);CHKERRQ(ierr);
  }

  B->stencil.dim = A->stencil.dim;
  B->stencil.noc = A->stencil.noc;
  for (i=0; i<=A->stencil.dim; i++) {
    B->stencil.dims[i]   = A->stencil.dims[i];
    B->stencil.starts[i] = A->stencil.starts[i];
  }

  ierr = PetscLogEventEnd(MAT_Copy,A,B,0,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatConvert"
/*@C
   MatConvert - Converts a matrix to another matrix, either of the same
   or different type.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  newtype - new matrix type.  Use MATSAME to create a new matrix of the
   same type as the original matrix.
-  reuse - denotes if the destination matrix is to be created or reused.  Currently
   MAT_REUSE_MATRIX is only supported for inplace conversion, otherwise use
   MAT_INITIAL_MATRIX.

   Output Parameter:
.  M - pointer to place new matrix

   Notes:
   MatConvert() first creates a new matrix and then copies the data from
   the first matrix.  A related routine is MatCopy(), which copies the matrix
   entries of one matrix to another already existing matrix context.

   Cannot be used to convert a sequential matrix to parallel or parallel to sequential,
   the MPI communicator of the generated matrix is always the same as the communicator
   of the input matrix.

   Level: intermediate

   Concepts: matrices^converting between storage formats

.seealso: MatCopy(), MatDuplicate()
@*/
PetscErrorCode  MatConvert(Mat mat, MatType newtype,MatReuse reuse,Mat *M)
{
  PetscErrorCode ierr;
  PetscBool      sametype,issame,flg;
  char           convname[256],mtype[256];
  Mat            B;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(M,3);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);
  ierr = MatSetOption(mat,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);

  ierr = PetscOptionsGetString(((PetscObject)mat)->prefix,"-matconvert_type",mtype,256,&flg);CHKERRQ(ierr);
  if (flg) {
    newtype = mtype;
  }
  ierr = PetscObjectTypeCompare((PetscObject)mat,newtype,&sametype);CHKERRQ(ierr);
  ierr = PetscStrcmp(newtype,"same",&issame);CHKERRQ(ierr);
  if ((reuse == MAT_REUSE_MATRIX) && (mat != *M)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"MAT_REUSE_MATRIX only supported for in-place conversion currently");

  if ((reuse == MAT_REUSE_MATRIX) && (issame || sametype)) PetscFunctionReturn(0);

  if ((sametype || issame) && (reuse==MAT_INITIAL_MATRIX) && mat->ops->duplicate) {
    ierr = (*mat->ops->duplicate)(mat,MAT_COPY_VALUES,M);CHKERRQ(ierr);
  } else {
    PetscErrorCode (*conv)(Mat, MatType,MatReuse,Mat*)=NULL;
    const char     *prefix[3] = {"seq","mpi",""};
    PetscInt       i;
    /*
       Order of precedence:
       1) See if a specialized converter is known to the current matrix.
       2) See if a specialized converter is known to the desired matrix class.
       3) See if a good general converter is registered for the desired class
          (as of 6/27/03 only MATMPIADJ falls into this category).
       4) See if a good general converter is known for the current matrix.
       5) Use a really basic converter.
    */

    /* 1) See if a specialized converter is known to the current matrix and the desired class */
    for (i=0; i<3; i++) {
      ierr = PetscStrcpy(convname,"MatConvert_");CHKERRQ(ierr);
      ierr = PetscStrcat(convname,((PetscObject)mat)->type_name);CHKERRQ(ierr);
      ierr = PetscStrcat(convname,"_");CHKERRQ(ierr);
      ierr = PetscStrcat(convname,prefix[i]);CHKERRQ(ierr);
      ierr = PetscStrcat(convname,issame ? ((PetscObject)mat)->type_name : newtype);CHKERRQ(ierr);
      ierr = PetscStrcat(convname,"_C");CHKERRQ(ierr);
      ierr = PetscObjectQueryFunction((PetscObject)mat,convname,&conv);CHKERRQ(ierr);
      if (conv) goto foundconv;
    }

    /* 2)  See if a specialized converter is known to the desired matrix class. */
    ierr = MatCreate(PetscObjectComm((PetscObject)mat),&B);CHKERRQ(ierr);
    ierr = MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->N,mat->cmap->N);CHKERRQ(ierr);
    ierr = MatSetType(B,newtype);CHKERRQ(ierr);
    for (i=0; i<3; i++) {
      ierr = PetscStrcpy(convname,"MatConvert_");CHKERRQ(ierr);
      ierr = PetscStrcat(convname,((PetscObject)mat)->type_name);CHKERRQ(ierr);
      ierr = PetscStrcat(convname,"_");CHKERRQ(ierr);
      ierr = PetscStrcat(convname,prefix[i]);CHKERRQ(ierr);
      ierr = PetscStrcat(convname,newtype);CHKERRQ(ierr);
      ierr = PetscStrcat(convname,"_C");CHKERRQ(ierr);
      ierr = PetscObjectQueryFunction((PetscObject)B,convname,&conv);CHKERRQ(ierr);
      if (conv) {
        ierr = MatDestroy(&B);CHKERRQ(ierr);
        goto foundconv;
      }
    }

    /* 3) See if a good general converter is registered for the desired class */
    conv = B->ops->convertfrom;
    ierr = MatDestroy(&B);CHKERRQ(ierr);
    if (conv) goto foundconv;

    /* 4) See if a good general converter is known for the current matrix */
    if (mat->ops->convert) {
      conv = mat->ops->convert;
    }
    if (conv) goto foundconv;

    /* 5) Use a really basic converter. */
    conv = MatConvert_Basic;

foundconv:
    ierr = PetscLogEventBegin(MAT_Convert,mat,0,0,0);CHKERRQ(ierr);
    ierr = (*conv)(mat,newtype,reuse,M);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_Convert,mat,0,0,0);CHKERRQ(ierr);
  }
  ierr = PetscObjectStateIncrease((PetscObject)*M);CHKERRQ(ierr);

  /* Copy Mat options */
  if (mat->symmetric) {ierr = MatSetOption(*M,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);}
  if (mat->hermitian) {ierr = MatSetOption(*M,MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFactorGetSolverPackage"
/*@C
   MatFactorGetSolverPackage - Returns name of the package providing the factorization routines

   Not Collective

   Input Parameter:
.  mat - the matrix, must be a factored matrix

   Output Parameter:
.   type - the string name of the package (do not free this string)

   Notes:
      In Fortran you pass in a empty string and the package name will be copied into it.
    (Make sure the string is long enough)

   Level: intermediate

.seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatGetFactor()
@*/
PetscErrorCode  MatFactorGetSolverPackage(Mat mat, const MatSolverPackage *type)
{
  PetscErrorCode ierr, (*conv)(Mat,const MatSolverPackage*);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Only for factored matrix");
  ierr = PetscObjectQueryFunction((PetscObject)mat,"MatFactorGetSolverPackage_C",&conv);CHKERRQ(ierr);
  if (!conv) {
    *type = MATSOLVERPETSC;
  } else {
    ierr = (*conv)(mat,type);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

typedef struct _MatSolverPackageForSpecifcType* MatSolverPackageForSpecifcType;
struct _MatSolverPackageForSpecifcType {
  MatType                        mtype;
  PetscErrorCode                 (*getfactor[4])(Mat,MatFactorType,Mat*);
  MatSolverPackageForSpecifcType next;
};

typedef struct _MatSolverPackageHolder* MatSolverPackageHolder;
struct _MatSolverPackageHolder {
  char                           *name;
  MatSolverPackageForSpecifcType handlers;
  MatSolverPackageHolder         next;
};

static MatSolverPackageHolder MatSolverPackageHolders = NULL;

#undef __FUNCT__
#define __FUNCT__ "MatSolverPackageRegister"
/*@C
   MatSolvePackageRegister - Registers a MatSolverPackage that works for a particular matrix type

   Input Parameters:
+    package - name of the package, for example petsc or superlu
.    mtype - the matrix type that works with this package
.    ftype - the type of factorization supported by the package
-    getfactor - routine that will create the factored matrix ready to be used

    Level: intermediate

.seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable()
@*/
PetscErrorCode  MatSolverPackageRegister(const MatSolverPackage package,const MatType mtype,MatFactorType ftype,PetscErrorCode (*getfactor)(Mat,MatFactorType,Mat*))
{
  PetscErrorCode                 ierr;
  MatSolverPackageHolder         next = MatSolverPackageHolders,prev;
  PetscBool                      flg;
  MatSolverPackageForSpecifcType inext,iprev = NULL;

  PetscFunctionBegin;
  if (!MatSolverPackageHolders) {
    ierr = PetscNew(&MatSolverPackageHolders);CHKERRQ(ierr);
    ierr = PetscStrallocpy(package,&MatSolverPackageHolders->name);CHKERRQ(ierr);
    ierr = PetscNew(&MatSolverPackageHolders->handlers);CHKERRQ(ierr);
    ierr = PetscStrallocpy(mtype,(char **)&MatSolverPackageHolders->handlers->mtype);CHKERRQ(ierr);
    MatSolverPackageHolders->handlers->getfactor[(int)ftype-1] = getfactor;
    PetscFunctionReturn(0);
  }
  while (next) {
    ierr = PetscStrcasecmp(package,next->name,&flg);CHKERRQ(ierr);
    if (flg) {
      inext = next->handlers;
      while (inext) {
        ierr = PetscStrcasecmp(mtype,inext->mtype,&flg);CHKERRQ(ierr);
        if (flg) {
          inext->getfactor[(int)ftype-1] = getfactor;
          PetscFunctionReturn(0);
        }
        iprev = inext;
        inext = inext->next;
      }
      ierr = PetscNew(&iprev->next);CHKERRQ(ierr);
      ierr = PetscStrallocpy(mtype,(char **)&iprev->next->mtype);CHKERRQ(ierr);
      iprev->next->getfactor[(int)ftype-1] = getfactor;
      PetscFunctionReturn(0);
    }
    prev = next;
    next = next->next;
  }
  ierr = PetscNew(&prev->next);CHKERRQ(ierr);
  ierr = PetscStrallocpy(package,&prev->next->name);CHKERRQ(ierr);
  ierr = PetscNew(&prev->next->handlers);CHKERRQ(ierr);
  ierr = PetscStrallocpy(mtype,(char **)&prev->next->handlers->mtype);CHKERRQ(ierr);
  prev->next->handlers->getfactor[(int)ftype-1] = getfactor;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolverPackageGet"
/*@C
   MatSolvePackageGet - Get's the function that creates the factor matrix if it exist

   Input Parameters:
+    package - name of the package, for example petsc or superlu
.    ftype - the type of factorization supported by the package
-    mtype - the matrix type that works with this package

   Output Parameters:
+   foundpackage - PETSC_TRUE if the package was registered
.   foundmtype - PETSC_TRUE if the package supports the requested mtype
-   getfactor - routine that will create the factored matrix ready to be used or NULL if not found

    Level: intermediate

.seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable()
@*/
PetscErrorCode  MatSolverPackageGet(const MatSolverPackage package,const MatType mtype,MatFactorType ftype,PetscBool *foundpackage,PetscBool *foundmtype,PetscErrorCode (**getfactor)(Mat,MatFactorType,Mat*))
{
  PetscErrorCode                 ierr;
  MatSolverPackageHolder         next = MatSolverPackageHolders;
  PetscBool                      flg;
  MatSolverPackageForSpecifcType inext;

  PetscFunctionBegin;
  if (foundpackage) *foundpackage = PETSC_FALSE;
  if (foundmtype)   *foundmtype   = PETSC_FALSE;
  if (getfactor)    *getfactor    = NULL;
  while (next) {
    ierr = PetscStrcasecmp(package,next->name,&flg);CHKERRQ(ierr);
    if (flg) {
      if (foundpackage) *foundpackage = PETSC_TRUE;
      inext = next->handlers;
      while (inext) {
        ierr = PetscStrcasecmp(mtype,inext->mtype,&flg);CHKERRQ(ierr);
        if (flg) {
          if (foundmtype) *foundmtype = PETSC_TRUE;
          if (getfactor)  *getfactor  = inext->getfactor[(int)ftype-1];
          PetscFunctionReturn(0);
        }
        inext = inext->next;
      }
    }
    next = next->next;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSolverPackageDestroy"
PetscErrorCode  MatSolverPackageDestroy(void)
{
  PetscErrorCode                 ierr;
  MatSolverPackageHolder         next = MatSolverPackageHolders,prev;
  MatSolverPackageForSpecifcType inext,iprev;

  PetscFunctionBegin;
  while (next) {
    ierr = PetscFree(next->name);CHKERRQ(ierr);
    inext = next->handlers;
    while (inext) {
      ierr = PetscFree(inext->mtype);CHKERRQ(ierr);
      iprev = inext;
      inext = inext->next;
      ierr = PetscFree(iprev);CHKERRQ(ierr);
    }
    prev = next;
    next = next->next;
    ierr = PetscFree(prev);CHKERRQ(ierr);
  }
  MatSolverPackageHolders = NULL;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetFactor"
/*@C
   MatGetFactor - Returns a matrix suitable to calls to MatXXFactorSymbolic()

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  type - name of solver type, for example, superlu, petsc (to use PETSc's default)
-  ftype - factor type, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ICC, MAT_FACTOR_ILU,

   Output Parameters:
.  f - the factor matrix used with MatXXFactorSymbolic() calls

   Notes:
      Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
     such as pastix, superlu, mumps etc.

      PETSc must have been ./configure to use the external solver, using the option --download-package

   Level: intermediate

.seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable()
@*/
PetscErrorCode  MatGetFactor(Mat mat, const MatSolverPackage type,MatFactorType ftype,Mat *f)
{
  PetscErrorCode ierr,(*conv)(Mat,MatFactorType,Mat*);
  PetscBool      foundpackage,foundmtype;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);

  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  ierr = MatSolverPackageGet(type,((PetscObject)mat)->type_name,ftype,&foundpackage,&foundmtype,&conv);CHKERRQ(ierr);
  if (!foundpackage) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_MISSING_FACTOR,"Could not locate solver package %s. Perhaps you must ./configure with --download-%s",type,type);
  if (!foundmtype) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_MISSING_FACTOR,"MatSolverPackage %s does not support matrix type %s",type,((PetscObject)mat)->type_name);
  if (!conv) SETERRQ3(PetscObjectComm((PetscObject)mat),PETSC_ERR_MISSING_FACTOR,"MatSolverPackage %s does not support factorization type %s for  matrix type %s",type,MatFactorTypes[ftype],((PetscObject)mat)->type_name);

  ierr = (*conv)(mat,ftype,f);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetFactorAvailable"
/*@C
   MatGetFactorAvailable - Returns a a flag if matrix supports particular package and factor type

   Not Collective

   Input Parameters:
+  mat - the matrix
.  type - name of solver type, for example, superlu, petsc (to use PETSc's default)
-  ftype - factor type, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ICC, MAT_FACTOR_ILU,

   Output Parameter:
.    flg - PETSC_TRUE if the factorization is available

   Notes:
      Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
     such as pastix, superlu, mumps etc.

      PETSc must have been ./configure to use the external solver, using the option --download-package

   Level: intermediate

.seealso: MatCopy(), MatDuplicate(), MatGetFactor()
@*/
PetscErrorCode  MatGetFactorAvailable(Mat mat, const MatSolverPackage type,MatFactorType ftype,PetscBool  *flg)
{
  PetscErrorCode ierr, (*gconv)(Mat,MatFactorType,Mat*);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);

  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  *flg = PETSC_FALSE;
  ierr = MatSolverPackageGet(type,((PetscObject)mat)->type_name,ftype,NULL,NULL,&gconv);CHKERRQ(ierr);
  if (gconv) {
    *flg = PETSC_TRUE;
  }
  PetscFunctionReturn(0);
}

#include <petscdmtypes.h>

#undef __FUNCT__
#define __FUNCT__ "MatDuplicate"
/*@
   MatDuplicate - Duplicates a matrix including the non-zero structure.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
-  op - either MAT_DO_NOT_COPY_VALUES or MAT_COPY_VALUES, cause it to copy the numerical values in the matrix
        MAT_SHARE_NONZERO_PATTERN to share the nonzero patterns with the previous matrix and not copy them.

   Output Parameter:
.  M - pointer to place new matrix

   Level: intermediate

   Concepts: matrices^duplicating

    Notes: You cannot change the nonzero pattern for the parent or child matrix if you use MAT_SHARE_NONZERO_PATTERN.

.seealso: MatCopy(), MatConvert()
@*/
PetscErrorCode  MatDuplicate(Mat mat,MatDuplicateOption op,Mat *M)
{
  PetscErrorCode ierr;
  Mat            B;
  PetscInt       i;
  DM             dm;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(M,3);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  *M = 0;
  if (!mat->ops->duplicate) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not written for this matrix type");
  ierr = PetscLogEventBegin(MAT_Convert,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->duplicate)(mat,op,M);CHKERRQ(ierr);
  B    = *M;

  B->stencil.dim = mat->stencil.dim;
  B->stencil.noc = mat->stencil.noc;
  for (i=0; i<=mat->stencil.dim; i++) {
    B->stencil.dims[i]   = mat->stencil.dims[i];
    B->stencil.starts[i] = mat->stencil.starts[i];
  }

  B->nooffproczerorows = mat->nooffproczerorows;
  B->nooffprocentries  = mat->nooffprocentries;

  ierr = PetscObjectQuery((PetscObject) mat, "__PETSc_dm", (PetscObject*) &dm);CHKERRQ(ierr);
  if (dm) {
    ierr = PetscObjectCompose((PetscObject) B, "__PETSc_dm", (PetscObject) dm);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_Convert,mat,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetDiagonal"
/*@
   MatGetDiagonal - Gets the diagonal of a matrix.

   Logically Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
-  v - the vector for storing the diagonal

   Output Parameter:
.  v - the diagonal of the matrix

   Level: intermediate

   Note:
   Currently only correct in parallel for square matrices.

   Concepts: matrices^accessing diagonals

.seealso: MatGetRow(), MatGetSubMatrices(), MatGetSubmatrix(), MatGetRowMaxAbs()
@*/
PetscErrorCode  MatGetDiagonal(Mat mat,Vec v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v,VEC_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!mat->ops->getdiagonal) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = (*mat->ops->getdiagonal)(mat,v);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRowMin"
/*@C
   MatGetRowMin - Gets the minimum value (of the real part) of each
        row of the matrix

   Logically Collective on Mat and Vec

   Input Parameters:
.  mat - the matrix

   Output Parameter:
+  v - the vector for storing the maximums
-  idx - the indices of the column found for each row (optional)

   Level: intermediate

   Notes: The result of this call are the same as if one converted the matrix to dense format
      and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    This code is only implemented for a couple of matrix formats.

   Concepts: matrices^getting row maximums

.seealso: MatGetDiagonal(), MatGetSubMatrices(), MatGetSubmatrix(), MatGetRowMaxAbs(),
          MatGetRowMax()
@*/
PetscErrorCode  MatGetRowMin(Mat mat,Vec v,PetscInt idx[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v,VEC_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!mat->ops->getrowmax) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = (*mat->ops->getrowmin)(mat,v,idx);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRowMinAbs"
/*@C
   MatGetRowMinAbs - Gets the minimum value (in absolute value) of each
        row of the matrix

   Logically Collective on Mat and Vec

   Input Parameters:
.  mat - the matrix

   Output Parameter:
+  v - the vector for storing the minimums
-  idx - the indices of the column found for each row (or NULL if not needed)

   Level: intermediate

   Notes: if a row is completely empty or has only 0.0 values then the idx[] value for that
    row is 0 (the first column).

    This code is only implemented for a couple of matrix formats.

   Concepts: matrices^getting row maximums

.seealso: MatGetDiagonal(), MatGetSubMatrices(), MatGetSubmatrix(), MatGetRowMax(), MatGetRowMaxAbs(), MatGetRowMin()
@*/
PetscErrorCode  MatGetRowMinAbs(Mat mat,Vec v,PetscInt idx[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v,VEC_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!mat->ops->getrowminabs) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  if (idx) {ierr = PetscMemzero(idx,mat->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);}

  ierr = (*mat->ops->getrowminabs)(mat,v,idx);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRowMax"
/*@C
   MatGetRowMax - Gets the maximum value (of the real part) of each
        row of the matrix

   Logically Collective on Mat and Vec

   Input Parameters:
.  mat - the matrix

   Output Parameter:
+  v - the vector for storing the maximums
-  idx - the indices of the column found for each row (optional)

   Level: intermediate

   Notes: The result of this call are the same as if one converted the matrix to dense format
      and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    This code is only implemented for a couple of matrix formats.

   Concepts: matrices^getting row maximums

.seealso: MatGetDiagonal(), MatGetSubMatrices(), MatGetSubmatrix(), MatGetRowMaxAbs(), MatGetRowMin()
@*/
PetscErrorCode  MatGetRowMax(Mat mat,Vec v,PetscInt idx[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v,VEC_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!mat->ops->getrowmax) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = (*mat->ops->getrowmax)(mat,v,idx);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRowMaxAbs"
/*@C
   MatGetRowMaxAbs - Gets the maximum value (in absolute value) of each
        row of the matrix

   Logically Collective on Mat and Vec

   Input Parameters:
.  mat - the matrix

   Output Parameter:
+  v - the vector for storing the maximums
-  idx - the indices of the column found for each row (or NULL if not needed)

   Level: intermediate

   Notes: if a row is completely empty or has only 0.0 values then the idx[] value for that
    row is 0 (the first column).

    This code is only implemented for a couple of matrix formats.

   Concepts: matrices^getting row maximums

.seealso: MatGetDiagonal(), MatGetSubMatrices(), MatGetSubmatrix(), MatGetRowMax(), MatGetRowMin()
@*/
PetscErrorCode  MatGetRowMaxAbs(Mat mat,Vec v,PetscInt idx[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v,VEC_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!mat->ops->getrowmaxabs) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  if (idx) {ierr = PetscMemzero(idx,mat->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);}

  ierr = (*mat->ops->getrowmaxabs)(mat,v,idx);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRowSum"
/*@
   MatGetRowSum - Gets the sum of each row of the matrix

   Logically Collective on Mat and Vec

   Input Parameters:
.  mat - the matrix

   Output Parameter:
.  v - the vector for storing the sum of rows

   Level: intermediate

   Notes: This code is slow since it is not currently specialized for different formats

   Concepts: matrices^getting row sums

.seealso: MatGetDiagonal(), MatGetSubMatrices(), MatGetSubmatrix(), MatGetRowMax(), MatGetRowMin()
@*/
PetscErrorCode  MatGetRowSum(Mat mat, Vec v)
{
  PetscInt       start = 0, end = 0, row;
  PetscScalar    *array;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(v,VEC_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  MatCheckPreallocated(mat,1);
  ierr = MatGetOwnershipRange(mat, &start, &end);CHKERRQ(ierr);
  ierr = VecGetArray(v, &array);CHKERRQ(ierr);
  for (row = start; row < end; ++row) {
    PetscInt          ncols, col;
    const PetscInt    *cols;
    const PetscScalar *vals;

    array[row - start] = 0.0;

    ierr = MatGetRow(mat, row, &ncols, &cols, &vals);CHKERRQ(ierr);
    for (col = 0; col < ncols; col++) {
      array[row - start] += vals[col];
    }
    ierr = MatRestoreRow(mat, row, &ncols, &cols, &vals);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(v, &array);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject) v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatTranspose"
/*@
   MatTranspose - Computes an in-place or out-of-place transpose of a matrix.

   Collective on Mat

   Input Parameter:
+  mat - the matrix to transpose
-  reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

   Output Parameters:
.  B - the transpose

   Notes:
     If you  pass in &mat for B the transpose will be done in place, for example MatTranspose(mat,MAT_REUSE_MATRIX,&mat);

     Consider using MatCreateTranspose() instead if you only need a matrix that behaves like the transpose, but don't need the storage to be changed.

   Level: intermediate

   Concepts: matrices^transposing

.seealso: MatMultTranspose(), MatMultTransposeAdd(), MatIsTranspose(), MatReuse
@*/
PetscErrorCode  MatTranspose(Mat mat,MatReuse reuse,Mat *B)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->transpose) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_Transpose,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->transpose)(mat,reuse,B);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_Transpose,mat,0,0,0);CHKERRQ(ierr);
  if (B) {ierr = PetscObjectStateIncrease((PetscObject)*B);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatIsTranspose"
/*@
   MatIsTranspose - Test whether a matrix is another one's transpose,
        or its own, in which case it tests symmetry.

   Collective on Mat

   Input Parameter:
+  A - the matrix to test
-  B - the matrix to test against, this can equal the first parameter

   Output Parameters:
.  flg - the result

   Notes:
   Only available for SeqAIJ/MPIAIJ matrices. The sequential algorithm
   has a running time of the order of the number of nonzeros; the parallel
   test involves parallel copies of the block-offdiagonal parts of the matrix.

   Level: intermediate

   Concepts: matrices^transposing, matrix^symmetry

.seealso: MatTranspose(), MatIsSymmetric(), MatIsHermitian()
@*/
PetscErrorCode  MatIsTranspose(Mat A,Mat B,PetscReal tol,PetscBool  *flg)
{
  PetscErrorCode ierr,(*f)(Mat,Mat,PetscReal,PetscBool*),(*g)(Mat,Mat,PetscReal,PetscBool*);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidPointer(flg,3);
  ierr = PetscObjectQueryFunction((PetscObject)A,"MatIsTranspose_C",&f);CHKERRQ(ierr);
  ierr = PetscObjectQueryFunction((PetscObject)B,"MatIsTranspose_C",&g);CHKERRQ(ierr);
  *flg = PETSC_FALSE;
  if (f && g) {
    if (f == g) {
      ierr = (*f)(A,B,tol,flg);CHKERRQ(ierr);
    } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_NOTSAMETYPE,"Matrices do not have the same comparator for symmetry test");
  } else {
    MatType mattype;
    if (!f) {
      ierr = MatGetType(A,&mattype);CHKERRQ(ierr);
    } else {
      ierr = MatGetType(B,&mattype);CHKERRQ(ierr);
    }
    SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type <%s> does not support checking for transpose",mattype);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatHermitianTranspose"
/*@
   MatHermitianTranspose - Computes an in-place or out-of-place transpose of a matrix in complex conjugate.

   Collective on Mat

   Input Parameter:
+  mat - the matrix to transpose and complex conjugate
-  reuse - store the transpose matrix in the provided B

   Output Parameters:
.  B - the Hermitian

   Notes:
     If you  pass in &mat for B the Hermitian will be done in place

   Level: intermediate

   Concepts: matrices^transposing, complex conjugatex

.seealso: MatTranspose(), MatMultTranspose(), MatMultTransposeAdd(), MatIsTranspose(), MatReuse
@*/
PetscErrorCode  MatHermitianTranspose(Mat mat,MatReuse reuse,Mat *B)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatTranspose(mat,reuse,B);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
  ierr = MatConjugate(*B);CHKERRQ(ierr);
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatIsHermitianTranspose"
/*@
   MatIsHermitianTranspose - Test whether a matrix is another one's Hermitian transpose,

   Collective on Mat

   Input Parameter:
+  A - the matrix to test
-  B - the matrix to test against, this can equal the first parameter

   Output Parameters:
.  flg - the result

   Notes:
   Only available for SeqAIJ/MPIAIJ matrices. The sequential algorithm
   has a running time of the order of the number of nonzeros; the parallel
   test involves parallel copies of the block-offdiagonal parts of the matrix.

   Level: intermediate

   Concepts: matrices^transposing, matrix^symmetry

.seealso: MatTranspose(), MatIsSymmetric(), MatIsHermitian(), MatIsTranspose()
@*/
PetscErrorCode  MatIsHermitianTranspose(Mat A,Mat B,PetscReal tol,PetscBool  *flg)
{
  PetscErrorCode ierr,(*f)(Mat,Mat,PetscReal,PetscBool*),(*g)(Mat,Mat,PetscReal,PetscBool*);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidPointer(flg,3);
  ierr = PetscObjectQueryFunction((PetscObject)A,"MatIsHermitianTranspose_C",&f);CHKERRQ(ierr);
  ierr = PetscObjectQueryFunction((PetscObject)B,"MatIsHermitianTranspose_C",&g);CHKERRQ(ierr);
  if (f && g) {
    if (f==g) {
      ierr = (*f)(A,B,tol,flg);CHKERRQ(ierr);
    } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_NOTSAMETYPE,"Matrices do not have the same comparator for Hermitian test");
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPermute"
/*@
   MatPermute - Creates a new matrix with rows and columns permuted from the
   original.

   Collective on Mat

   Input Parameters:
+  mat - the matrix to permute
.  row - row permutation, each processor supplies only the permutation for its rows
-  col - column permutation, each processor supplies only the permutation for its columns

   Output Parameters:
.  B - the permuted matrix

   Level: advanced

   Note:
   The index sets map from row/col of permuted matrix to row/col of original matrix.
   The index sets should be on the same communicator as Mat and have the same local sizes.

   Concepts: matrices^permuting

.seealso: MatGetOrdering(), ISAllGather()

@*/
PetscErrorCode  MatPermute(Mat mat,IS row,IS col,Mat *B)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(row,IS_CLASSID,2);
  PetscValidHeaderSpecific(col,IS_CLASSID,3);
  PetscValidPointer(B,4);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->permute) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatPermute not available for Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = (*mat->ops->permute)(mat,row,col,B);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)*B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatEqual"
/*@
   MatEqual - Compares two matrices.

   Collective on Mat

   Input Parameters:
+  A - the first matrix
-  B - the second matrix

   Output Parameter:
.  flg - PETSC_TRUE if the matrices are equal; PETSC_FALSE otherwise.

   Level: intermediate

   Concepts: matrices^equality between
@*/
PetscErrorCode  MatEqual(Mat A,Mat B,PetscBool  *flg)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidType(A,1);
  PetscValidType(B,2);
  PetscValidIntPointer(flg,3);
  PetscCheckSameComm(A,1,B,2);
  MatCheckPreallocated(B,2);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (!B->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->rmap->N != B->rmap->N || A->cmap->N != B->cmap->N) SETERRQ4(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Mat A,Mat B: global dim %D %D %D %D",A->rmap->N,B->rmap->N,A->cmap->N,B->cmap->N);
  if (!A->ops->equal) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)A)->type_name);
  if (!B->ops->equal) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)B)->type_name);
  if (A->ops->equal != B->ops->equal) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"A is type: %s\nB is type: %s",((PetscObject)A)->type_name,((PetscObject)B)->type_name);
  MatCheckPreallocated(A,1);

  ierr = (*A->ops->equal)(A,B,flg);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDiagonalScale"
/*@
   MatDiagonalScale - Scales a matrix on the left and right by diagonal
   matrices that are stored as vectors.  Either of the two scaling
   matrices can be NULL.

   Collective on Mat

   Input Parameters:
+  mat - the matrix to be scaled
.  l - the left scaling vector (or NULL)
-  r - the right scaling vector (or NULL)

   Notes:
   MatDiagonalScale() computes A = LAR, where
   L = a diagonal matrix (stored as a vector), R = a diagonal matrix (stored as a vector)
   The L scales the rows of the matrix, the R scales the columns of the matrix.

   Level: intermediate

   Concepts: matrices^diagonal scaling
   Concepts: diagonal scaling of matrices

.seealso: MatScale()
@*/
PetscErrorCode  MatDiagonalScale(Mat mat,Vec l,Vec r)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->ops->diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (l) {PetscValidHeaderSpecific(l,VEC_CLASSID,2);PetscCheckSameComm(mat,1,l,2);}
  if (r) {PetscValidHeaderSpecific(r,VEC_CLASSID,3);PetscCheckSameComm(mat,1,r,3);}
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_Scale,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->diagonalscale)(mat,l,r);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_Scale,mat,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatScale"
/*@
    MatScale - Scales all elements of a matrix by a given number.

    Logically Collective on Mat

    Input Parameters:
+   mat - the matrix to be scaled
-   a  - the scaling value

    Output Parameter:
.   mat - the scaled matrix

    Level: intermediate

    Concepts: matrices^scaling all entries

.seealso: MatDiagonalScale()
@*/
PetscErrorCode  MatScale(Mat mat,PetscScalar a)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (a != (PetscScalar)1.0 && !mat->ops->scale) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidLogicalCollectiveScalar(mat,a,2);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_Scale,mat,0,0,0);CHKERRQ(ierr);
  if (a != (PetscScalar)1.0) {
    ierr = (*mat->ops->scale)(mat,a);CHKERRQ(ierr);
    ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_Scale,mat,0,0,0);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatNorm"
/*@
   MatNorm - Calculates various norms of a matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
-  type - the type of norm, NORM_1, NORM_FROBENIUS, NORM_INFINITY

   Output Parameters:
.  nrm - the resulting norm

   Level: intermediate

   Concepts: matrices^norm
   Concepts: norm^of matrix
@*/
PetscErrorCode  MatNorm(Mat mat,NormType type,PetscReal *nrm)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidScalarPointer(nrm,3);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->norm) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = (*mat->ops->norm)(mat,type,nrm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
     This variable is used to prevent counting of MatAssemblyBegin() that
   are called from within a MatAssemblyEnd().
*/
static PetscInt MatAssemblyEnd_InUse = 0;
#undef __FUNCT__
#define __FUNCT__ "MatAssemblyBegin"
/*@
   MatAssemblyBegin - Begins assembling the matrix.  This routine should
   be called after completing all calls to MatSetValues().

   Collective on Mat

   Input Parameters:
+  mat - the matrix
-  type - type of assembly, either MAT_FLUSH_ASSEMBLY or MAT_FINAL_ASSEMBLY

   Notes:
   MatSetValues() generally caches the values.  The matrix is ready to
   use only after MatAssemblyBegin() and MatAssemblyEnd() have been called.
   Use MAT_FLUSH_ASSEMBLY when switching between ADD_VALUES and INSERT_VALUES
   in MatSetValues(); use MAT_FINAL_ASSEMBLY for the final assembly before
   using the matrix.

   ALL processes that share a matrix MUST call MatAssemblyBegin() and MatAssemblyEnd() the SAME NUMBER of times, and each time with the
   same flag of MAT_FLUSH_ASSEMBLY or MAT_FINAL_ASSEMBLY for all processes. Thus you CANNOT locally change from ADD_VALUES to INSERT_VALUES, that is
   a global collective operation requring all processes that share the matrix.

   Space for preallocated nonzeros that is not filled by a call to MatSetValues() or a related routine are compressed
   out by assembly. If you intend to use that extra space on a subsequent assembly, be sure to insert explicit zeros
   before MAT_FINAL_ASSEMBLY so the space is not compressed out.

   Level: beginner

   Concepts: matrices^assembling

.seealso: MatAssemblyEnd(), MatSetValues(), MatAssembled()
@*/
PetscErrorCode  MatAssemblyBegin(Mat mat,MatAssemblyType type)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix.\nDid you forget to call MatSetUnfactored()?");
  if (mat->assembled) {
    mat->was_assembled = PETSC_TRUE;
    mat->assembled     = PETSC_FALSE;
  }
  if (!MatAssemblyEnd_InUse) {
    ierr = PetscLogEventBegin(MAT_AssemblyBegin,mat,0,0,0);CHKERRQ(ierr);
    if (mat->ops->assemblybegin) {ierr = (*mat->ops->assemblybegin)(mat,type);CHKERRQ(ierr);}
    ierr = PetscLogEventEnd(MAT_AssemblyBegin,mat,0,0,0);CHKERRQ(ierr);
  } else if (mat->ops->assemblybegin) {
    ierr = (*mat->ops->assemblybegin)(mat,type);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatAssembled"
/*@
   MatAssembled - Indicates if a matrix has been assembled and is ready for
     use; for example, in matrix-vector product.

   Not Collective

   Input Parameter:
.  mat - the matrix

   Output Parameter:
.  assembled - PETSC_TRUE or PETSC_FALSE

   Level: advanced

   Concepts: matrices^assembled?

.seealso: MatAssemblyEnd(), MatSetValues(), MatAssemblyBegin()
@*/
PetscErrorCode  MatAssembled(Mat mat,PetscBool  *assembled)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(assembled,2);
  *assembled = mat->assembled;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatAssemblyEnd"
/*@
   MatAssemblyEnd - Completes assembling the matrix.  This routine should
   be called after MatAssemblyBegin().

   Collective on Mat

   Input Parameters:
+  mat - the matrix
-  type - type of assembly, either MAT_FLUSH_ASSEMBLY or MAT_FINAL_ASSEMBLY

   Options Database Keys:
+  -mat_view ::ascii_info - Prints info on matrix at conclusion of MatEndAssembly()
.  -mat_view ::ascii_info_detail - Prints more detailed info
.  -mat_view - Prints matrix in ASCII format
.  -mat_view ::ascii_matlab - Prints matrix in Matlab format
.  -mat_view draw - PetscDraws nonzero structure of matrix, using MatView() and PetscDrawOpenX().
.  -display <name> - Sets display name (default is host)
.  -draw_pause <sec> - Sets number of seconds to pause after display
.  -mat_view socket - Sends matrix to socket, can be accessed from Matlab (See Users-Manual: ch_matlab )
.  -viewer_socket_machine <machine> - Machine to use for socket
.  -viewer_socket_port <port> - Port number to use for socket
-  -mat_view binary:filename[:append] - Save matrix to file in binary format

   Notes:
   MatSetValues() generally caches the values.  The matrix is ready to
   use only after MatAssemblyBegin() and MatAssemblyEnd() have been called.
   Use MAT_FLUSH_ASSEMBLY when switching between ADD_VALUES and INSERT_VALUES
   in MatSetValues(); use MAT_FINAL_ASSEMBLY for the final assembly before
   using the matrix.

   Space for preallocated nonzeros that is not filled by a call to MatSetValues() or a related routine are compressed
   out by assembly. If you intend to use that extra space on a subsequent assembly, be sure to insert explicit zeros
   before MAT_FINAL_ASSEMBLY so the space is not compressed out.

   Level: beginner

.seealso: MatAssemblyBegin(), MatSetValues(), PetscDrawOpenX(), PetscDrawCreate(), MatView(), MatAssembled(), PetscViewerSocketOpen()
@*/
PetscErrorCode  MatAssemblyEnd(Mat mat,MatAssemblyType type)
{
  PetscErrorCode  ierr;
  static PetscInt inassm = 0;
  PetscBool       flg    = PETSC_FALSE;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);

  inassm++;
  MatAssemblyEnd_InUse++;
  if (MatAssemblyEnd_InUse == 1) { /* Do the logging only the first time through */
    ierr = PetscLogEventBegin(MAT_AssemblyEnd,mat,0,0,0);CHKERRQ(ierr);
    if (mat->ops->assemblyend) {
      ierr = (*mat->ops->assemblyend)(mat,type);CHKERRQ(ierr);
    }
    ierr = PetscLogEventEnd(MAT_AssemblyEnd,mat,0,0,0);CHKERRQ(ierr);
  } else if (mat->ops->assemblyend) {
    ierr = (*mat->ops->assemblyend)(mat,type);CHKERRQ(ierr);
  }

  /* Flush assembly is not a true assembly */
  if (type != MAT_FLUSH_ASSEMBLY) {
    mat->assembled = PETSC_TRUE; mat->num_ass++;
  }
  mat->insertmode = NOT_SET_VALUES;
  MatAssemblyEnd_InUse--;
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
  if (!mat->symmetric_eternal) {
    mat->symmetric_set              = PETSC_FALSE;
    mat->hermitian_set              = PETSC_FALSE;
    mat->structurally_symmetric_set = PETSC_FALSE;
  }
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  if (inassm == 1 && type != MAT_FLUSH_ASSEMBLY) {
    ierr = MatViewFromOptions(mat,NULL,"-mat_view");CHKERRQ(ierr);

    if (mat->checksymmetryonassembly) {
      ierr = MatIsSymmetric(mat,mat->checksymmetrytol,&flg);CHKERRQ(ierr);
      if (flg) {
        ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Matrix is symmetric (tolerance %g)\n",(double)mat->checksymmetrytol);CHKERRQ(ierr);
      } else {
        ierr = PetscPrintf(PetscObjectComm((PetscObject)mat),"Matrix is not symmetric (tolerance %g)\n",(double)mat->checksymmetrytol);CHKERRQ(ierr);
      }
    }
    if (mat->nullsp && mat->checknullspaceonassembly) {
      ierr = MatNullSpaceTest(mat->nullsp,mat,NULL);CHKERRQ(ierr);
    }
  }
  inassm--;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetOption"
/*@
   MatSetOption - Sets a parameter option for a matrix. Some options
   may be specific to certain storage formats.  Some options
   determine how values will be inserted (or added). Sorted,
   row-oriented input will generally assemble the fastest. The default
   is row-oriented.

   Logically Collective on Mat for certain operations, such as MAT_SPD, not collective for MAT_ROW_ORIENTED, see MatOption

   Input Parameters:
+  mat - the matrix
.  option - the option, one of those listed below (and possibly others),
-  flg - turn the option on (PETSC_TRUE) or off (PETSC_FALSE)

  Options Describing Matrix Structure:
+    MAT_SPD - symmetric positive definite
.    MAT_SYMMETRIC - symmetric in terms of both structure and value
.    MAT_HERMITIAN - transpose is the complex conjugation
.    MAT_STRUCTURALLY_SYMMETRIC - symmetric nonzero structure
-    MAT_SYMMETRY_ETERNAL - if you would like the symmetry/Hermitian flag
                            you set to be kept with all future use of the matrix
                            including after MatAssemblyBegin/End() which could
                            potentially change the symmetry structure, i.e. you
                            KNOW the matrix will ALWAYS have the property you set.


   Options For Use with MatSetValues():
   Insert a logically dense subblock, which can be
.    MAT_ROW_ORIENTED - row-oriented (default)

   Note these options reflect the data you pass in with MatSetValues(); it has
   nothing to do with how the data is stored internally in the matrix
   data structure.

   When (re)assembling a matrix, we can restrict the input for
   efficiency/debugging purposes.  These options include:
+    MAT_NEW_NONZERO_LOCATIONS - additional insertions will be allowed if they generate a new nonzero (slow)
.    MAT_NEW_DIAGONALS - new diagonals will be allowed (for block diagonal format only)
.    MAT_IGNORE_OFF_PROC_ENTRIES - drops off-processor entries
.    MAT_NEW_NONZERO_LOCATION_ERR - generates an error for new matrix entry
.    MAT_USE_HASH_TABLE - uses a hash table to speed up matrix assembly
+    MAT_NO_OFF_PROC_ENTRIES - you know each process will only set values for its own rows, will generate an error if
        any process sets values for another process. This avoids all reductions in the MatAssembly routines and thus improves
        performance for very large process counts.

   Notes:
   Some options are relevant only for particular matrix types and
   are thus ignored by others.  Other options are not supported by
   certain matrix types and will generate an error message if set.

   If using a Fortran 77 module to compute a matrix, one may need to
   use the column-oriented option (or convert to the row-oriented
   format).

   MAT_NEW_NONZERO_LOCATIONS set to PETSC_FALSE indicates that any add or insertion
   that would generate a new entry in the nonzero structure is instead
   ignored.  Thus, if memory has not alredy been allocated for this particular
   data, then the insertion is ignored. For dense matrices, in which
   the entire array is allocated, no entries are ever ignored.
   Set after the first MatAssemblyEnd()

   MAT_NEW_NONZERO_LOCATION_ERR set to PETSC_TRUE indicates that any add or insertion
   that would generate a new entry in the nonzero structure instead produces
   an error. (Currently supported for AIJ and BAIJ formats only.)

   MAT_NEW_NONZERO_ALLOCATION_ERR set to PETSC_TRUE indicates that any add or insertion
   that would generate a new entry that has not been preallocated will
   instead produce an error. (Currently supported for AIJ and BAIJ formats
   only.) This is a useful flag when debugging matrix memory preallocation.

   MAT_IGNORE_OFF_PROC_ENTRIES set to PETSC_TRUE indicates entries destined for
   other processors should be dropped, rather than stashed.
   This is useful if you know that the "owning" processor is also
   always generating the correct matrix entries, so that PETSc need
   not transfer duplicate entries generated on another processor.

   MAT_USE_HASH_TABLE indicates that a hash table be used to improve the
   searches during matrix assembly. When this flag is set, the hash table
   is created during the first Matrix Assembly. This hash table is
   used the next time through, during MatSetVaules()/MatSetVaulesBlocked()
   to improve the searching of indices. MAT_NEW_NONZERO_LOCATIONS flag
   should be used with MAT_USE_HASH_TABLE flag. This option is currently
   supported by MATMPIBAIJ format only.

   MAT_KEEP_NONZERO_PATTERN indicates when MatZeroRows() is called the zeroed entries
   are kept in the nonzero structure

   MAT_IGNORE_ZERO_ENTRIES - for AIJ/IS matrices this will stop zero values from creating
   a zero location in the matrix

   MAT_USE_INODES - indicates using inode version of the code - works with AIJ and
   ROWBS matrix types

   MAT_NO_OFF_PROC_ZERO_ROWS - you know each process will only zero its own rows. This avoids all reductions in the
        zero row routines and thus improves performance for very large process counts.

   MAT_IGNORE_LOWER_TRIANGULAR - For SBAIJ matrices will ignore any insertions you make in the lower triangular
        part of the matrix (since they should match the upper triangular part).

   Notes: Can only be called after MatSetSizes() and MatSetType() have been set.

   Level: intermediate

   Concepts: matrices^setting options

.seealso:  MatOption, Mat

@*/
PetscErrorCode  MatSetOption(Mat mat,MatOption op,PetscBool flg)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (op > 0) {
    PetscValidLogicalCollectiveEnum(mat,op,2);
    PetscValidLogicalCollectiveBool(mat,flg,3);
  }

  if (((int) op) <= MAT_OPTION_MIN || ((int) op) >= MAT_OPTION_MAX) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Options %d is out of range",(int)op);
  if (!((PetscObject)mat)->type_name) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_TYPENOTSET,"Cannot set options until type and size have been set, see MatSetType() and MatSetSizes()");

  switch (op) {
  case MAT_NO_OFF_PROC_ENTRIES:
    mat->nooffprocentries = flg;
    PetscFunctionReturn(0);
    break;
  case MAT_NO_OFF_PROC_ZERO_ROWS:
    mat->nooffproczerorows = flg;
    PetscFunctionReturn(0);
    break;
  case MAT_SPD:
    mat->spd_set = PETSC_TRUE;
    mat->spd     = flg;
    if (flg) {
      mat->symmetric                  = PETSC_TRUE;
      mat->structurally_symmetric     = PETSC_TRUE;
      mat->symmetric_set              = PETSC_TRUE;
      mat->structurally_symmetric_set = PETSC_TRUE;
    }
    break;
  case MAT_SYMMETRIC:
    mat->symmetric = flg;
    if (flg) mat->structurally_symmetric = PETSC_TRUE;
    mat->symmetric_set              = PETSC_TRUE;
    mat->structurally_symmetric_set = flg;
    break;
  case MAT_HERMITIAN:
    mat->hermitian = flg;
    if (flg) mat->structurally_symmetric = PETSC_TRUE;
    mat->hermitian_set              = PETSC_TRUE;
    mat->structurally_symmetric_set = flg;
    break;
  case MAT_STRUCTURALLY_SYMMETRIC:
    mat->structurally_symmetric     = flg;
    mat->structurally_symmetric_set = PETSC_TRUE;
    break;
  case MAT_SYMMETRY_ETERNAL:
    mat->symmetric_eternal = flg;
    break;
  default:
    break;
  }
  if (mat->ops->setoption) {
    ierr = (*mat->ops->setoption)(mat,op,flg);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetOption"
/*@
   MatGetOption - Gets a parameter option that has been set for a matrix.

   Logically Collective on Mat for certain operations, such as MAT_SPD, not collective for MAT_ROW_ORIENTED, see MatOption

   Input Parameters:
+  mat - the matrix
-  option - the option, this only responds to certain options, check the code for which ones

   Output Parameter:
.  flg - turn the option on (PETSC_TRUE) or off (PETSC_FALSE)

    Notes: Can only be called after MatSetSizes() and MatSetType() have been set.

   Level: intermediate

   Concepts: matrices^setting options

.seealso:  MatOption, MatSetOption()

@*/
PetscErrorCode  MatGetOption(Mat mat,MatOption op,PetscBool *flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);

  if (((int) op) <= MAT_OPTION_MIN || ((int) op) >= MAT_OPTION_MAX) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Options %d is out of range",(int)op);
  if (!((PetscObject)mat)->type_name) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_TYPENOTSET,"Cannot get options until type and size have been set, see MatSetType() and MatSetSizes()");

  switch (op) {
  case MAT_NO_OFF_PROC_ENTRIES:
    *flg = mat->nooffprocentries;
    break;
  case MAT_NO_OFF_PROC_ZERO_ROWS:
    *flg = mat->nooffproczerorows;
    break;
  case MAT_SYMMETRIC:
    *flg = mat->symmetric;
    break;
  case MAT_HERMITIAN:
    *flg = mat->hermitian;
    break;
  case MAT_STRUCTURALLY_SYMMETRIC:
    *flg = mat->structurally_symmetric;
    break;
  case MAT_SYMMETRY_ETERNAL:
    *flg = mat->symmetric_eternal;
    break;
  default:
    break;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroEntries"
/*@
   MatZeroEntries - Zeros all entries of a matrix.  For sparse matrices
   this routine retains the old nonzero structure.

   Logically Collective on Mat

   Input Parameters:
.  mat - the matrix

   Level: intermediate

   Notes: If the matrix was not preallocated then a default, likely poor preallocation will be set in the matrix, so this should be called after the preallocation phase.
   See the Performance chapter of the users manual for information on preallocating matrices.

   Concepts: matrices^zeroing

.seealso: MatZeroRows()
@*/
PetscErrorCode  MatZeroEntries(Mat mat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (mat->insertmode != NOT_SET_VALUES) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for matrices where you have set values but not yet assembled");
  if (!mat->ops->zeroentries) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_ZeroEntries,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->zeroentries)(mat);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_ZeroEntries,mat,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsColumns"
/*@C
   MatZeroRowsColumns - Zeros all entries (except possibly the main diagonal)
   of a set of rows and columns of a matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  numRows - the number of rows to remove
.  rows - the global row indices
.  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   This does not change the nonzero structure of the matrix, it merely zeros those entries in the matrix.

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   For the parallel case, all processes that share the matrix (i.e.,
   those in the communicator used for matrix creation) MUST call this
   routine, regardless of whether any rows being zeroed are owned by
   them.

   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
   list only rows local to itself).

   The option MAT_NO_OFF_PROC_ZERO_ROWS does not apply to this routine.

   Level: intermediate

   Concepts: matrices^zeroing rows

.seealso: MatZeroRowsIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(), MatZeroRowsColumnsIS()
@*/
PetscErrorCode  MatZeroRowsColumns(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (numRows) PetscValidIntPointer(rows,3);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->zerorowscolumns) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = (*mat->ops->zerorowscolumns)(mat,numRows,rows,diag,x,b);CHKERRQ(ierr);
  ierr = MatViewFromOptions(mat,NULL,"-mat_view");CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsColumnsIS"
/*@C
   MatZeroRowsColumnsIS - Zeros all entries (except possibly the main diagonal)
   of a set of rows and columns of a matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  is - the rows to zero
.  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   This does not change the nonzero structure of the matrix, it merely zeros those entries in the matrix.

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   For the parallel case, all processes that share the matrix (i.e.,
   those in the communicator used for matrix creation) MUST call this
   routine, regardless of whether any rows being zeroed are owned by
   them.

   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
   list only rows local to itself).

   The option MAT_NO_OFF_PROC_ZERO_ROWS does not apply to this routine.

   Level: intermediate

   Concepts: matrices^zeroing rows

.seealso: MatZeroRowsIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(), MatZeroRowsColumns()
@*/
PetscErrorCode  MatZeroRowsColumnsIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
{
  PetscErrorCode ierr;
  PetscInt       numRows;
  const PetscInt *rows;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(is,IS_CLASSID,2);
  PetscValidType(mat,1);
  PetscValidType(is,2);
  ierr = ISGetLocalSize(is,&numRows);CHKERRQ(ierr);
  ierr = ISGetIndices(is,&rows);CHKERRQ(ierr);
  ierr = MatZeroRowsColumns(mat,numRows,rows,diag,x,b);CHKERRQ(ierr);
  ierr = ISRestoreIndices(is,&rows);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRows"
/*@C
   MatZeroRows - Zeros all entries (except possibly the main diagonal)
   of a set of rows of a matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  numRows - the number of rows to remove
.  rows - the global row indices
.  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
   but does not release memory.  For the dense and block diagonal
   formats this does not alter the nonzero structure.

   If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
   of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
   merely zeroed.

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   For the parallel case, all processes that share the matrix (i.e.,
   those in the communicator used for matrix creation) MUST call this
   routine, regardless of whether any rows being zeroed are owned by
   them.

   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
   list only rows local to itself).

   You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
   owns that are to be zeroed. This saves a global synchronization in the implementation.

   Level: intermediate

   Concepts: matrices^zeroing rows

.seealso: MatZeroRowsIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption()
@*/
PetscErrorCode  MatZeroRows(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (numRows) PetscValidIntPointer(rows,3);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->zerorows) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);

  ierr = (*mat->ops->zerorows)(mat,numRows,rows,diag,x,b);CHKERRQ(ierr);
  ierr = MatViewFromOptions(mat,NULL,"-mat_view");CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsIS"
/*@C
   MatZeroRowsIS - Zeros all entries (except possibly the main diagonal)
   of a set of rows of a matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  is - index set of rows to remove
.  diag - value put in all diagonals of eliminated rows
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
   but does not release memory.  For the dense and block diagonal
   formats this does not alter the nonzero structure.

   If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
   of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
   merely zeroed.

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   For the parallel case, all processes that share the matrix (i.e.,
   those in the communicator used for matrix creation) MUST call this
   routine, regardless of whether any rows being zeroed are owned by
   them.

   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
   list only rows local to itself).

   You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
   owns that are to be zeroed. This saves a global synchronization in the implementation.

   Level: intermediate

   Concepts: matrices^zeroing rows

.seealso: MatZeroRows(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption()
@*/
PetscErrorCode  MatZeroRowsIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
{
  PetscInt       numRows;
  const PetscInt *rows;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(is,IS_CLASSID,2);
  ierr = ISGetLocalSize(is,&numRows);CHKERRQ(ierr);
  ierr = ISGetIndices(is,&rows);CHKERRQ(ierr);
  ierr = MatZeroRows(mat,numRows,rows,diag,x,b);CHKERRQ(ierr);
  ierr = ISRestoreIndices(is,&rows);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsStencil"
/*@C
   MatZeroRowsStencil - Zeros all entries (except possibly the main diagonal)
   of a set of rows of a matrix. These rows must be local to the process.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  numRows - the number of rows to remove
.  rows - the grid coordinates (and component number when dof > 1) for matrix rows
.  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
   but does not release memory.  For the dense and block diagonal
   formats this does not alter the nonzero structure.

   If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
   of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
   merely zeroed.

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   For the parallel case, all processes that share the matrix (i.e.,
   those in the communicator used for matrix creation) MUST call this
   routine, regardless of whether any rows being zeroed are owned by
   them.

   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
   list only rows local to itself).

   The grid coordinates are across the entire grid, not just the local portion

   In Fortran idxm and idxn should be declared as
$     MatStencil idxm(4,m)
   and the values inserted using
$    idxm(MatStencil_i,1) = i
$    idxm(MatStencil_j,1) = j
$    idxm(MatStencil_k,1) = k
$    idxm(MatStencil_c,1) = c
   etc

   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
   DM_BOUNDARY_PERIODIC boundary type.

   For indices that don't mean anything for your case (like the k index when working in 2d) or the c index when you have
   a single value per point) you can skip filling those indices.

   Level: intermediate

   Concepts: matrices^zeroing rows

.seealso: MatZeroRows(), MatZeroRowsIS(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption()
@*/
PetscErrorCode  MatZeroRowsStencil(Mat mat,PetscInt numRows,const MatStencil rows[],PetscScalar diag,Vec x,Vec b)
{
  PetscInt       dim     = mat->stencil.dim;
  PetscInt       sdim    = dim - (1 - (PetscInt) mat->stencil.noc);
  PetscInt       *dims   = mat->stencil.dims+1;
  PetscInt       *starts = mat->stencil.starts;
  PetscInt       *dxm    = (PetscInt*) rows;
  PetscInt       *jdxm, i, j, tmp, numNewRows = 0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (numRows) PetscValidIntPointer(rows,3);

  ierr = PetscMalloc1(numRows, &jdxm);CHKERRQ(ierr);
  for (i = 0; i < numRows; ++i) {
    /* Skip unused dimensions (they are ordered k, j, i, c) */
    for (j = 0; j < 3-sdim; ++j) dxm++;
    /* Local index in X dir */
    tmp = *dxm++ - starts[0];
    /* Loop over remaining dimensions */
    for (j = 0; j < dim-1; ++j) {
      /* If nonlocal, set index to be negative */
      if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = PETSC_MIN_INT;
      /* Update local index */
      else tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    }
    /* Skip component slot if necessary */
    if (mat->stencil.noc) dxm++;
    /* Local row number */
    if (tmp >= 0) {
      jdxm[numNewRows++] = tmp;
    }
  }
  ierr = MatZeroRowsLocal(mat,numNewRows,jdxm,diag,x,b);CHKERRQ(ierr);
  ierr = PetscFree(jdxm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsColumnsStencil"
/*@C
   MatZeroRowsColumnsStencil - Zeros all row and column entries (except possibly the main diagonal)
   of a set of rows and columns of a matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  numRows - the number of rows/columns to remove
.  rows - the grid coordinates (and component number when dof > 1) for matrix rows
.  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
   but does not release memory.  For the dense and block diagonal
   formats this does not alter the nonzero structure.

   If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
   of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
   merely zeroed.

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   For the parallel case, all processes that share the matrix (i.e.,
   those in the communicator used for matrix creation) MUST call this
   routine, regardless of whether any rows being zeroed are owned by
   them.

   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
   list only rows local to itself, but the row/column numbers are given in local numbering).

   The grid coordinates are across the entire grid, not just the local portion

   In Fortran idxm and idxn should be declared as
$     MatStencil idxm(4,m)
   and the values inserted using
$    idxm(MatStencil_i,1) = i
$    idxm(MatStencil_j,1) = j
$    idxm(MatStencil_k,1) = k
$    idxm(MatStencil_c,1) = c
   etc

   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
   DM_BOUNDARY_PERIODIC boundary type.

   For indices that don't mean anything for your case (like the k index when working in 2d) or the c index when you have
   a single value per point) you can skip filling those indices.

   Level: intermediate

   Concepts: matrices^zeroing rows

.seealso: MatZeroRows(), MatZeroRowsIS(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption()
@*/
PetscErrorCode  MatZeroRowsColumnsStencil(Mat mat,PetscInt numRows,const MatStencil rows[],PetscScalar diag,Vec x,Vec b)
{
  PetscInt       dim     = mat->stencil.dim;
  PetscInt       sdim    = dim - (1 - (PetscInt) mat->stencil.noc);
  PetscInt       *dims   = mat->stencil.dims+1;
  PetscInt       *starts = mat->stencil.starts;
  PetscInt       *dxm    = (PetscInt*) rows;
  PetscInt       *jdxm, i, j, tmp, numNewRows = 0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (numRows) PetscValidIntPointer(rows,3);

  ierr = PetscMalloc1(numRows, &jdxm);CHKERRQ(ierr);
  for (i = 0; i < numRows; ++i) {
    /* Skip unused dimensions (they are ordered k, j, i, c) */
    for (j = 0; j < 3-sdim; ++j) dxm++;
    /* Local index in X dir */
    tmp = *dxm++ - starts[0];
    /* Loop over remaining dimensions */
    for (j = 0; j < dim-1; ++j) {
      /* If nonlocal, set index to be negative */
      if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = PETSC_MIN_INT;
      /* Update local index */
      else tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    }
    /* Skip component slot if necessary */
    if (mat->stencil.noc) dxm++;
    /* Local row number */
    if (tmp >= 0) {
      jdxm[numNewRows++] = tmp;
    }
  }
  ierr = MatZeroRowsColumnsLocal(mat,numNewRows,jdxm,diag,x,b);CHKERRQ(ierr);
  ierr = PetscFree(jdxm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsLocal"
/*@C
   MatZeroRowsLocal - Zeros all entries (except possibly the main diagonal)
   of a set of rows of a matrix; using local numbering of rows.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  numRows - the number of rows to remove
.  rows - the global row indices
.  diag - value put in all diagonals of eliminated rows
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   Before calling MatZeroRowsLocal(), the user must first set the
   local-to-global mapping by calling MatSetLocalToGlobalMapping().

   For the AIJ matrix formats this removes the old nonzero structure,
   but does not release memory.  For the dense and block diagonal
   formats this does not alter the nonzero structure.

   If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
   of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
   merely zeroed.

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
   owns that are to be zeroed. This saves a global synchronization in the implementation.

   Level: intermediate

   Concepts: matrices^zeroing

.seealso: MatZeroRows(), MatZeroRowsLocalIS(), MatZeroEntries(), MatZeroRows(), MatSetLocalToGlobalMapping
@*/
PetscErrorCode  MatZeroRowsLocal(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (numRows) PetscValidIntPointer(rows,3);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  if (mat->ops->zerorowslocal) {
    ierr = (*mat->ops->zerorowslocal)(mat,numRows,rows,diag,x,b);CHKERRQ(ierr);
  } else {
    IS             is, newis;
    const PetscInt *newRows;

    if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Need to provide local to global mapping to matrix first");
    ierr = ISCreateGeneral(PETSC_COMM_SELF,numRows,rows,PETSC_COPY_VALUES,&is);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingApplyIS(mat->rmap->mapping,is,&newis);CHKERRQ(ierr);
    ierr = ISGetIndices(newis,&newRows);CHKERRQ(ierr);
    ierr = (*mat->ops->zerorows)(mat,numRows,newRows,diag,x,b);CHKERRQ(ierr);
    ierr = ISRestoreIndices(newis,&newRows);CHKERRQ(ierr);
    ierr = ISDestroy(&newis);CHKERRQ(ierr);
    ierr = ISDestroy(&is);CHKERRQ(ierr);
  }
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsLocalIS"
/*@C
   MatZeroRowsLocalIS - Zeros all entries (except possibly the main diagonal)
   of a set of rows of a matrix; using local numbering of rows.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  is - index set of rows to remove
.  diag - value put in all diagonals of eliminated rows
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   Before calling MatZeroRowsLocalIS(), the user must first set the
   local-to-global mapping by calling MatSetLocalToGlobalMapping().

   For the AIJ matrix formats this removes the old nonzero structure,
   but does not release memory.  For the dense and block diagonal
   formats this does not alter the nonzero structure.

   If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
   of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
   merely zeroed.

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
   owns that are to be zeroed. This saves a global synchronization in the implementation.

   Level: intermediate

   Concepts: matrices^zeroing

.seealso: MatZeroRows(), MatZeroRowsLocal(), MatZeroEntries(), MatZeroRows(), MatSetLocalToGlobalMapping
@*/
PetscErrorCode  MatZeroRowsLocalIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
{
  PetscErrorCode ierr;
  PetscInt       numRows;
  const PetscInt *rows;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(is,IS_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  ierr = ISGetLocalSize(is,&numRows);CHKERRQ(ierr);
  ierr = ISGetIndices(is,&rows);CHKERRQ(ierr);
  ierr = MatZeroRowsLocal(mat,numRows,rows,diag,x,b);CHKERRQ(ierr);
  ierr = ISRestoreIndices(is,&rows);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsColumnsLocal"
/*@C
   MatZeroRowsColumnsLocal - Zeros all entries (except possibly the main diagonal)
   of a set of rows and columns of a matrix; using local numbering of rows.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  numRows - the number of rows to remove
.  rows - the global row indices
.  diag - value put in all diagonals of eliminated rows
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   Before calling MatZeroRowsColumnsLocal(), the user must first set the
   local-to-global mapping by calling MatSetLocalToGlobalMapping().

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   Level: intermediate

   Concepts: matrices^zeroing

.seealso: MatZeroRows(), MatZeroRowsLocalIS(), MatZeroEntries(), MatZeroRows(), MatSetLocalToGlobalMapping
@*/
PetscErrorCode  MatZeroRowsColumnsLocal(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
{
  PetscErrorCode ierr;
  IS             is, newis;
  const PetscInt *newRows;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (numRows) PetscValidIntPointer(rows,3);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  if (!mat->cmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Need to provide local to global mapping to matrix first");
  ierr = ISCreateGeneral(PETSC_COMM_SELF,numRows,rows,PETSC_COPY_VALUES,&is);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingApplyIS(mat->cmap->mapping,is,&newis);CHKERRQ(ierr);
  ierr = ISGetIndices(newis,&newRows);CHKERRQ(ierr);
  ierr = (*mat->ops->zerorowscolumns)(mat,numRows,newRows,diag,x,b);CHKERRQ(ierr);
  ierr = ISRestoreIndices(newis,&newRows);CHKERRQ(ierr);
  ierr = ISDestroy(&newis);CHKERRQ(ierr);
  ierr = ISDestroy(&is);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUSP)
  if (mat->valid_GPU_matrix != PETSC_CUSP_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_CUSP_CPU;
  }
#endif
#if defined(PETSC_HAVE_VIENNACL)
  if (mat->valid_GPU_matrix != PETSC_VIENNACL_UNALLOCATED) {
    mat->valid_GPU_matrix = PETSC_VIENNACL_CPU;
  }
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatZeroRowsColumnsLocalIS"
/*@C
   MatZeroRowsColumnsLocalIS - Zeros all entries (except possibly the main diagonal)
   of a set of rows and columns of a matrix; using local numbering of rows.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  is - index set of rows to remove
.  diag - value put in all diagonals of eliminated rows
.  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
-  b - optional vector of right hand side, that will be adjusted by provided solution

   Notes:
   Before calling MatZeroRowsColumnsLocalIS(), the user must first set the
   local-to-global mapping by calling MatSetLocalToGlobalMapping().

   The user can set a value in the diagonal entry (or for the AIJ and
   row formats can optionally remove the main diagonal entry from the
   nonzero structure as well, by passing 0.0 as the final argument).

   Level: intermediate

   Concepts: matrices^zeroing

.seealso: MatZeroRows(), MatZeroRowsLocal(), MatZeroEntries(), MatZeroRows(), MatSetLocalToGlobalMapping
@*/
PetscErrorCode  MatZeroRowsColumnsLocalIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
{
  PetscErrorCode ierr;
  PetscInt       numRows;
  const PetscInt *rows;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(is,IS_CLASSID,2);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  ierr = ISGetLocalSize(is,&numRows);CHKERRQ(ierr);
  ierr = ISGetIndices(is,&rows);CHKERRQ(ierr);
  ierr = MatZeroRowsColumnsLocal(mat,numRows,rows,diag,x,b);CHKERRQ(ierr);
  ierr = ISRestoreIndices(is,&rows);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetSize"
/*@
   MatGetSize - Returns the numbers of rows and columns in a matrix.

   Not Collective

   Input Parameter:
.  mat - the matrix

   Output Parameters:
+  m - the number of global rows
-  n - the number of global columns

   Note: both output parameters can be NULL on input.

   Level: beginner

   Concepts: matrices^size

.seealso: MatGetLocalSize()
@*/
PetscErrorCode  MatGetSize(Mat mat,PetscInt *m,PetscInt *n)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (m) *m = mat->rmap->N;
  if (n) *n = mat->cmap->N;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetLocalSize"
/*@
   MatGetLocalSize - Returns the number of rows and columns in a matrix
   stored locally.  This information may be implementation dependent, so
   use with care.

   Not Collective

   Input Parameters:
.  mat - the matrix

   Output Parameters:
+  m - the number of local rows
-  n - the number of local columns

   Note: both output parameters can be NULL on input.

   Level: beginner

   Concepts: matrices^local size

.seealso: MatGetSize()
@*/
PetscErrorCode  MatGetLocalSize(Mat mat,PetscInt *m,PetscInt *n)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (m) PetscValidIntPointer(m,2);
  if (n) PetscValidIntPointer(n,3);
  if (m) *m = mat->rmap->n;
  if (n) *n = mat->cmap->n;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetOwnershipRangeColumn"
/*@
   MatGetOwnershipRangeColumn - Returns the range of matrix columns associated with rows of a vector one multiplies by that owned by
   this processor. (The columns of the "diagonal block")

   Not Collective, unless matrix has not been allocated, then collective on Mat

   Input Parameters:
.  mat - the matrix

   Output Parameters:
+  m - the global index of the first local column
-  n - one more than the global index of the last local column

   Notes: both output parameters can be NULL on input.

   Level: developer

   Concepts: matrices^column ownership

.seealso:  MatGetOwnershipRange(), MatGetOwnershipRanges(), MatGetOwnershipRangesColumn()

@*/
PetscErrorCode  MatGetOwnershipRangeColumn(Mat mat,PetscInt *m,PetscInt *n)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (m) PetscValidIntPointer(m,2);
  if (n) PetscValidIntPointer(n,3);
  MatCheckPreallocated(mat,1);
  if (m) *m = mat->cmap->rstart;
  if (n) *n = mat->cmap->rend;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetOwnershipRange"
/*@
   MatGetOwnershipRange - Returns the range of matrix rows owned by
   this processor, assuming that the matrix is laid out with the first
   n1 rows on the first processor, the next n2 rows on the second, etc.
   For certain parallel layouts this range may not be well defined.

   Not Collective

   Input Parameters:
.  mat - the matrix

   Output Parameters:
+  m - the global index of the first local row
-  n - one more than the global index of the last local row

   Note: Both output parameters can be NULL on input.
$  This function requires that the matrix be preallocated. If you have not preallocated, consider using
$    PetscSplitOwnership(MPI_Comm comm, PetscInt *n, PetscInt *N)
$  and then MPI_Scan() to calculate prefix sums of the local sizes.

   Level: beginner

   Concepts: matrices^row ownership

.seealso:   MatGetOwnershipRanges(), MatGetOwnershipRangeColumn(), MatGetOwnershipRangesColumn(), PetscSplitOwnership(), PetscSplitOwnershipBlock()

@*/
PetscErrorCode  MatGetOwnershipRange(Mat mat,PetscInt *m,PetscInt *n)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (m) PetscValidIntPointer(m,2);
  if (n) PetscValidIntPointer(n,3);
  MatCheckPreallocated(mat,1);
  if (m) *m = mat->rmap->rstart;
  if (n) *n = mat->rmap->rend;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetOwnershipRanges"
/*@C
   MatGetOwnershipRanges - Returns the range of matrix rows owned by
   each process

   Not Collective, unless matrix has not been allocated, then collective on Mat

   Input Parameters:
.  mat - the matrix

   Output Parameters:
.  ranges - start of each processors portion plus one more then the total length at the end

   Level: beginner

   Concepts: matrices^row ownership

.seealso:   MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatGetOwnershipRangesColumn()

@*/
PetscErrorCode  MatGetOwnershipRanges(Mat mat,const PetscInt **ranges)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  ierr = PetscLayoutGetRanges(mat->rmap,ranges);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetOwnershipRangesColumn"
/*@C
   MatGetOwnershipRangesColumn - Returns the range of matrix columns associated with rows of a vector one multiplies by that owned by
   this processor. (The columns of the "diagonal blocks" for each process)

   Not Collective, unless matrix has not been allocated, then collective on Mat

   Input Parameters:
.  mat - the matrix

   Output Parameters:
.  ranges - start of each processors portion plus one more then the total length at the end

   Level: beginner

   Concepts: matrices^column ownership

.seealso:   MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatGetOwnershipRanges()

@*/
PetscErrorCode  MatGetOwnershipRangesColumn(Mat mat,const PetscInt **ranges)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  ierr = PetscLayoutGetRanges(mat->cmap,ranges);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetOwnershipIS"
/*@C
   MatGetOwnershipIS - Get row and column ownership as index sets

   Not Collective

   Input Arguments:
.  A - matrix of type Elemental

   Output Arguments:
+  rows - rows in which this process owns elements
.  cols - columns in which this process owns elements

   Level: intermediate

.seealso: MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatSetValues(), MATELEMENTAL, MatSetValues()
@*/
PetscErrorCode MatGetOwnershipIS(Mat A,IS *rows,IS *cols)
{
  PetscErrorCode ierr,(*f)(Mat,IS*,IS*);

  PetscFunctionBegin;
  MatCheckPreallocated(A,1);
  ierr = PetscObjectQueryFunction((PetscObject)A,"MatGetOwnershipIS_C",&f);CHKERRQ(ierr);
  if (f) {
    ierr = (*f)(A,rows,cols);CHKERRQ(ierr);
  } else {   /* Create a standard row-based partition, each process is responsible for ALL columns in their row block */
    if (rows) {ierr = ISCreateStride(PETSC_COMM_SELF,A->rmap->n,A->rmap->rstart,1,rows);CHKERRQ(ierr);}
    if (cols) {ierr = ISCreateStride(PETSC_COMM_SELF,A->cmap->N,0,1,cols);CHKERRQ(ierr);}
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatILUFactorSymbolic"
/*@C
   MatILUFactorSymbolic - Performs symbolic ILU factorization of a matrix.
   Uses levels of fill only, not drop tolerance. Use MatLUFactorNumeric()
   to complete the factorization.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  row - row permutation
.  column - column permutation
-  info - structure containing
$      levels - number of levels of fill.
$      expected fill - as ratio of original fill.
$      1 or 0 - indicating force fill on diagonal (improves robustness for matrices
                missing diagonal entries)

   Output Parameters:
.  fact - new matrix that has been symbolically factored

   Notes: See Users-Manual: ch_mat for additional information about choosing the fill factor for better efficiency.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

  Concepts: matrices^symbolic LU factorization
  Concepts: matrices^factorization
  Concepts: LU^symbolic factorization

.seealso: MatLUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor()
          MatGetOrdering(), MatFactorInfo

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatILUFactorSymbolic(Mat fact,Mat mat,IS row,IS col,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(row,IS_CLASSID,2);
  PetscValidHeaderSpecific(col,IS_CLASSID,3);
  PetscValidPointer(info,4);
  PetscValidPointer(fact,5);
  if (info->levels < 0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Levels of fill negative %D",(PetscInt)info->levels);
  if (info->fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Expected fill less than 1.0 %g",(double)info->fill);
  if (!(fact)->ops->ilufactorsymbolic) {
    const MatSolverPackage spackage;
    ierr = MatFactorGetSolverPackage(fact,&spackage);CHKERRQ(ierr);
    SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic ILU using solver package %s",((PetscObject)mat)->type_name,spackage);
  }
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,2);

  ierr = PetscLogEventBegin(MAT_ILUFactorSymbolic,mat,row,col,0);CHKERRQ(ierr);
  ierr = (fact->ops->ilufactorsymbolic)(fact,mat,row,col,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_ILUFactorSymbolic,mat,row,col,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatICCFactorSymbolic"
/*@C
   MatICCFactorSymbolic - Performs symbolic incomplete
   Cholesky factorization for a symmetric matrix.  Use
   MatCholeskyFactorNumeric() to complete the factorization.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  perm - row and column permutation
-  info - structure containing
$      levels - number of levels of fill.
$      expected fill - as ratio of original fill.

   Output Parameter:
.  fact - the factored matrix

   Notes:
   Most users should employ the KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

  Concepts: matrices^symbolic incomplete Cholesky factorization
  Concepts: matrices^factorization
  Concepts: Cholsky^symbolic factorization

.seealso: MatCholeskyFactorNumeric(), MatCholeskyFactor(), MatFactorInfo

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatICCFactorSymbolic(Mat fact,Mat mat,IS perm,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(perm,IS_CLASSID,2);
  PetscValidPointer(info,3);
  PetscValidPointer(fact,4);
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (info->levels < 0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Levels negative %D",(PetscInt) info->levels);
  if (info->fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Expected fill less than 1.0 %g",(double)info->fill);
  if (!(fact)->ops->iccfactorsymbolic) {
    const MatSolverPackage spackage;
    ierr = MatFactorGetSolverPackage(fact,&spackage);CHKERRQ(ierr);
    SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic ICC using solver package %s",((PetscObject)mat)->type_name,spackage);
  }
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  MatCheckPreallocated(mat,2);

  ierr = PetscLogEventBegin(MAT_ICCFactorSymbolic,mat,perm,0,0);CHKERRQ(ierr);
  ierr = (fact->ops->iccfactorsymbolic)(fact,mat,perm,info);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_ICCFactorSymbolic,mat,perm,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetSubMatrices"
/*@C
   MatGetSubMatrices - Extracts several submatrices from a matrix. If submat
   points to an array of valid matrices, they may be reused to store the new
   submatrices.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  n   - the number of submatrixes to be extracted (on this processor, may be zero)
.  irow, icol - index sets of rows and columns to extract
-  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

   Output Parameter:
.  submat - the array of submatrices

   Notes:
   MatGetSubMatrices() can extract ONLY sequential submatrices
   (from both sequential and parallel matrices). Use MatGetSubMatrix()
   to extract a parallel submatrix.

   Some matrix types place restrictions on the row and column
   indices, such as that they be sorted or that they be equal to each other.

   The index sets may not have duplicate entries.

   When extracting submatrices from a parallel matrix, each processor can
   form a different submatrix by setting the rows and columns of its
   individual index sets according to the local submatrix desired.

   When finished using the submatrices, the user should destroy
   them with MatDestroyMatrices().

   MAT_REUSE_MATRIX can only be used when the nonzero structure of the
   original matrix has not changed from that last call to MatGetSubMatrices().

   This routine creates the matrices in submat; you should NOT create them before
   calling it. It also allocates the array of matrix pointers submat.

   For BAIJ matrices the index sets must respect the block structure, that is if they
   request one row/column in a block, they must request all rows/columns that are in
   that block. For example, if the block size is 2 you cannot request just row 0 and
   column 0.

   Fortran Note:
   The Fortran interface is slightly different from that given below; it
   requires one to pass in  as submat a Mat (integer) array of size at least m.

   Level: advanced

   Concepts: matrices^accessing submatrices
   Concepts: submatrices

.seealso: MatDestroyMatrices(), MatGetSubMatrix(), MatGetRow(), MatGetDiagonal(), MatReuse
@*/
PetscErrorCode  MatGetSubMatrices(Mat mat,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
{
  PetscErrorCode ierr;
  PetscInt       i;
  PetscBool      eq;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (n) {
    PetscValidPointer(irow,3);
    PetscValidHeaderSpecific(*irow,IS_CLASSID,3);
    PetscValidPointer(icol,4);
    PetscValidHeaderSpecific(*icol,IS_CLASSID,4);
  }
  PetscValidPointer(submat,6);
  if (n && scall == MAT_REUSE_MATRIX) {
    PetscValidPointer(*submat,6);
    PetscValidHeaderSpecific(**submat,MAT_CLASSID,6);
  }
  if (!mat->ops->getsubmatrices) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_GetSubMatrices,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->getsubmatrices)(mat,n,irow,icol,scall,submat);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_GetSubMatrices,mat,0,0,0);CHKERRQ(ierr);
  for (i=0; i<n; i++) {
    (*submat)[i]->factortype = MAT_FACTOR_NONE;  /* in case in place factorization was previously done on submatrix */
    if (mat->symmetric || mat->structurally_symmetric || mat->hermitian) {
      ierr = ISEqual(irow[i],icol[i],&eq);CHKERRQ(ierr);
      if (eq) {
        if (mat->symmetric) {
          ierr = MatSetOption((*submat)[i],MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
        } else if (mat->hermitian) {
          ierr = MatSetOption((*submat)[i],MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
        } else if (mat->structurally_symmetric) {
          ierr = MatSetOption((*submat)[i],MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
        }
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetSubMatricesMPI"
PetscErrorCode  MatGetSubMatricesMPI(Mat mat,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
{
  PetscErrorCode ierr;
  PetscInt       i;
  PetscBool      eq;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (n) {
    PetscValidPointer(irow,3);
    PetscValidHeaderSpecific(*irow,IS_CLASSID,3);
    PetscValidPointer(icol,4);
    PetscValidHeaderSpecific(*icol,IS_CLASSID,4);
  }
  PetscValidPointer(submat,6);
  if (n && scall == MAT_REUSE_MATRIX) {
    PetscValidPointer(*submat,6);
    PetscValidHeaderSpecific(**submat,MAT_CLASSID,6);
  }
  if (!mat->ops->getsubmatricesmpi) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_GetSubMatrices,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->getsubmatricesmpi)(mat,n,irow,icol,scall,submat);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_GetSubMatrices,mat,0,0,0);CHKERRQ(ierr);
  for (i=0; i<n; i++) {
    if (mat->symmetric || mat->structurally_symmetric || mat->hermitian) {
      ierr = ISEqual(irow[i],icol[i],&eq);CHKERRQ(ierr);
      if (eq) {
        if (mat->symmetric) {
          ierr = MatSetOption((*submat)[i],MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
        } else if (mat->hermitian) {
          ierr = MatSetOption((*submat)[i],MAT_HERMITIAN,PETSC_TRUE);CHKERRQ(ierr);
        } else if (mat->structurally_symmetric) {
          ierr = MatSetOption((*submat)[i],MAT_STRUCTURALLY_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
        }
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroyMatrices"
/*@C
   MatDestroyMatrices - Destroys a set of matrices obtained with MatGetSubMatrices().

   Collective on Mat

   Input Parameters:
+  n - the number of local matrices
-  mat - the matrices (note that this is a pointer to the array of matrices, just to match the calling
                       sequence of MatGetSubMatrices())

   Level: advanced

    Notes: Frees not only the matrices, but also the array that contains the matrices
           In Fortran will not free the array.

.seealso: MatGetSubMatrices()
@*/
PetscErrorCode  MatDestroyMatrices(PetscInt n,Mat *mat[])
{
  PetscErrorCode ierr;
  PetscInt       i;

  PetscFunctionBegin;
  if (!*mat) PetscFunctionReturn(0);
  if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Trying to destroy negative number of matrices %D",n);
  PetscValidPointer(mat,2);
  for (i=0; i<n; i++) {
    ierr = MatDestroy(&(*mat)[i]);CHKERRQ(ierr);
  }
  /* memory is allocated even if n = 0 */
  ierr = PetscFree(*mat);CHKERRQ(ierr);
  *mat = NULL;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetSeqNonzeroStructure"
/*@C
   MatGetSeqNonzeroStructure - Extracts the sequential nonzero structure from a matrix.

   Collective on Mat

   Input Parameters:
.  mat - the matrix

   Output Parameter:
.  matstruct - the sequential matrix with the nonzero structure of mat

  Level: intermediate

.seealso: MatDestroySeqNonzeroStructure(), MatGetSubMatrices(), MatDestroyMatrices()
@*/
PetscErrorCode  MatGetSeqNonzeroStructure(Mat mat,Mat *matstruct)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidPointer(matstruct,2);

  PetscValidType(mat,1);
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  if (!mat->ops->getseqnonzerostructure) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not for matrix type %s\n",((PetscObject)mat)->type_name);
  ierr = PetscLogEventBegin(MAT_GetSeqNonzeroStructure,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->getseqnonzerostructure)(mat,matstruct);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_GetSeqNonzeroStructure,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroySeqNonzeroStructure"
/*@C
   MatDestroySeqNonzeroStructure - Destroys matrix obtained with MatGetSeqNonzeroStructure().

   Collective on Mat

   Input Parameters:
.  mat - the matrix (note that this is a pointer to the array of matrices, just to match the calling
                       sequence of MatGetSequentialNonzeroStructure())

   Level: advanced

    Notes: Frees not only the matrices, but also the array that contains the matrices

.seealso: MatGetSeqNonzeroStructure()
@*/
PetscErrorCode  MatDestroySeqNonzeroStructure(Mat *mat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidPointer(mat,1);
  ierr = MatDestroy(mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatIncreaseOverlap"
/*@
   MatIncreaseOverlap - Given a set of submatrices indicated by index sets,
   replaces the index sets by larger ones that represent submatrices with
   additional overlap.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  n   - the number of index sets
.  is  - the array of index sets (these index sets will changed during the call)
-  ov  - the additional overlap requested

   Options Database:
.  -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

   Level: developer

   Concepts: overlap
   Concepts: ASM^computing overlap

.seealso: MatGetSubMatrices()
@*/
PetscErrorCode  MatIncreaseOverlap(Mat mat,PetscInt n,IS is[],PetscInt ov)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more domains, you have %D",n);
  if (n) {
    PetscValidPointer(is,3);
    PetscValidHeaderSpecific(*is,IS_CLASSID,3);
  }
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  if (!ov) PetscFunctionReturn(0);
  if (!mat->ops->increaseoverlap) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  ierr = PetscLogEventBegin(MAT_IncreaseOverlap,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->increaseoverlap)(mat,n,is,ov);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_IncreaseOverlap,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


static PetscErrorCode  MatIncreaseOverlapSplit_Single(Mat mat,IS *is,PetscInt ov);

#undef __FUNCT__
#define __FUNCT__ "MatIncreaseOverlapSplit"
/*@
   MatIncreaseOverlapSplit - Given a set of submatrices indicated by index sets across
   a sub communicator, replaces the index sets by larger ones that represent submatrices with
   additional overlap.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  n   - the number of index sets
.  is  - the array of index sets (these index sets will changed during the call)
-  ov  - the additional overlap requested

   Options Database:
.  -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

   Level: developer

   Concepts: overlap
   Concepts: ASM^computing overlap

.seealso: MatGetSubMatrices()
@*/
PetscErrorCode  MatIncreaseOverlapSplit(Mat mat,PetscInt n,IS is[],PetscInt ov)
{
  PetscInt       i;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more domains, you have %D",n);
  if (n) {
    PetscValidPointer(is,3);
    PetscValidHeaderSpecific(*is,IS_CLASSID,3);
  }
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);
  if (!ov) PetscFunctionReturn(0);
  ierr = PetscLogEventBegin(MAT_IncreaseOverlap,mat,0,0,0);CHKERRQ(ierr);
  for(i=0; i<n; i++){
	ierr =  MatIncreaseOverlapSplit_Single(mat,&is[i],ov);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_IncreaseOverlap,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*
 * where should we put this function????
 * all functions in this file are interfaces
 * */
static PetscErrorCode  MatIncreaseOverlapSplit_Single(Mat mat,IS *is,PetscInt ov)
{
  PetscInt         i,local,nindx,current,*indices_sc,*indices_ov,localsize,*localsizes_sc,localsize_tmp;
  PetscInt         *indices_ov_rd,nroots,nleaves,*localoffsets,*indices_recv;
  const PetscInt   *ranges,*indices;
  PetscMPIInt      gsize,grank,srank,ssize,issamecomm,*granks,k,*sources_sc,*sources_sc_rd;
  IS               is_sc,allis_sc,partitioning;
  MPI_Comm         gcomm,scomm;
  PetscSF          sf;
  PetscSFNode      *remote;
  Mat              smat;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)*is,&scomm);CHKERRQ(ierr);
  /*increase overlap on each individual subdomain*/
  ierr = (*mat->ops->increaseoverlap)(mat,1,is,ov);CHKERRQ(ierr);
  /*remove duplicate entrices belonging to the same subcomm */
  ierr = PetscObjectGetComm((PetscObject)mat,&gcomm);CHKERRQ(ierr);
  ierr = MPI_Comm_compare(gcomm,scomm,&issamecomm);CHKERRQ(ierr);
  /* if subcomm is the same as the global comm,
   * user does not want to use subcomm
   * */
  if(issamecomm!=MPI_IDENT) PetscFunctionReturn(0);
  /* if subcomm is petsc_comm_self,
   * user also does not care subcomm
   * */
  ierr = MPI_Comm_compare(scomm,PETSC_COMM_SELF,&issamecomm);CHKERRQ(ierr);
  if(issamecomm!=MPI_IDENT) PetscFunctionReturn(0);
  /*global rank, size */
  ierr = MPI_Comm_rank(gcomm,&grank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(gcomm,&gsize);CHKERRQ(ierr);
  /*local rank, size in a subcomm */
  ierr = MPI_Comm_rank(scomm,&srank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(scomm,&ssize);CHKERRQ(ierr);
  /*create a new IS based on subcomm
   * since the old IS is often petsc_comm_self
   * */
  ierr = ISGetLocalSize(*is,&nindx);CHKERRQ(ierr);
  ierr = PetscCalloc1(nindx,&indices_sc);CHKERRQ(ierr);
  ierr = ISGetIndices(*is,&indices);CHKERRQ(ierr);
  ierr = PetscMemcpy(indices_sc,indices,sizeof(PetscInt)*nindx);CHKERRQ(ierr);
  ierr = ISRestoreIndices(*is,&indices);CHKERRQ(ierr);
  ierr = ISCreateGeneral(scomm,nindx,indices_sc,PETSC_OWN_POINTER,&is_sc);CHKERRQ(ierr);
  /*gather all indices */
  ierr = ISAllGather(is_sc,&allis_sc);CHKERRQ(ierr);
  ierr = ISDestroy(&is_sc);CHKERRQ(ierr);
  /* gather lolcal sizes */
  ierr = PetscMalloc1(ssize,&localsizes_sc);CHKERRQ(ierr);
  ierr = MPI_Gather(&nindx,MPIU_INT,localsizes_sc,MPIU_INT,1,scomm);CHKERRQ(ierr);
  /*only root does these computation */
  if(!srank){
   ierr = ISGetLocalSize(allis_sc,&localsize);CHKERRQ(ierr);
   ierr = PetscCalloc2(localsize,&indices_ov,localsize,&sources_sc);CHKERRQ(ierr);
   ierr = PetscCalloc2(localsize,&indices_ov_rd,localsize,&sources_sc_rd);CHKERRQ(ierr);
   ierr = ISGetIndices(allis_sc,&indices_sc);CHKERRQ(ierr);
   ierr = PetscMemcpy(indices_ov,indices_sc,sizeof(PetscInt)*localsize);CHKERRQ(ierr);
   ierr = ISDestroy(&allis_sc);CHKERRQ(ierr);
   localsize_tmp = 0;
   for(k=0; k<ssize; k++){
     for(i=0; i<localsizes_sc[k]; i++){
       sources_sc[localsize_tmp++] = k;
     }
   }
   ierr = PetscSortIntWithArray(localsize,indices_ov,sources_sc);CHKERRQ(ierr);
   localsize_tmp = 1;
   ierr = PetscMemzero(localsizes_sc,sizeof(PetscInt)*ssize);CHKERRQ(ierr);
   /*initialize the first entities*/
   if(localsize){
	 indices_ov_rd[0] = indices_ov[0];
	 sources_sc_rd[0] = sources_sc[0];
	 localsizes_sc[sources_sc[0]]++;
   }
   /*remove duplicate integers */
   for(i=1; i<localsize; i++){
	 if(indices_ov[i] != indices_ov[i-1]){
	   indices_ov_rd[localsize_tmp]   = indices_ov[i];
	   sources_sc_rd[localsize_tmp++] = sources_sc[i];
	   localsizes_sc[sources_sc[i]]++;
	 }
   }
   ierr = PetscFree2(indices_ov,sources_sc);CHKERRQ(ierr);
   ierr = PetscCalloc1(ssize+1,localoffsets);CHKERRQ(ierr);
   for(k=0; k<ssize; k++){
	 localoffsets[k+1] = localoffsets[k] + localsizes_sc[i];
   }
   /*build a star forest to send data back */
   nleaves = localoffsets[ssize];
   nroot   = localsizes_sc[srank];
   ierr = PetscCalloc1(nleaves,&remote);CHKERRQ(ierr);
   for(i=0; i<nleaves; i++){
	 remote[i].rank  = sources_sc[i];
	 remote[i].index = localoffsets[sources_sc[i]]++;
   }
  }else{
   ierr = ISDestroy(&allis_sc);CHKERRQ(ierr);
   nleaves = 0;
   indices_ov_rd = 0;
  }
  /*scatter sizes to everybody */
  ierr = MPI_Scatter(localsizes_sc,1, MPIU_INT,&nroots,1, MPIU_INT,0,scomm);CHKERRQ(ierr);
  ierr = PetscCalloc1(nroots,&indices_recv);CHKERRQ(ierr);
  /*set data back to every body */
  ierr = PetscSFCreate(scomm,&sf);CHKERRQ(ierr);
  ierr = PetscSFSetType(sf,petscsfb);CHKERRQ(ierr);
  ierr = PetscSFSetType(sf,PETSCSFBASIC);CHKERRQ(ierr);
  ierr = PetscSFSetFromOptions(sf);CHKERRQ(ierr);
  ierr = PetscSFSetGraph(sf,nroots,nleaves,PETSC_NULL,PETSC_OWN_POINTER,remote,PETSC_OWN_POINTER);CHKERRQ(ierr);
  ierr = PetscSFReduceBegin(sf,MPIU_INT,&indices_ov_rd,indices_recv,MPI_REPLACE);CHKERRQ(ierr);
  ierr = PetscSFReduceEnd(sf,MPIU_INT,&indices_ov_rd,indices_recv,MPI_REPLACE);CHKERRQ(ierr);
  /*create a indexset*/
  ierr = ISCreate(scomm,&is_sc);CHKERRQ(ierr);
  /*create a index set for cols */
  ierr = ISAllGather(is_sc,&allis_sc);CHKERRQ(ierr);
  /*reparition */
  /*construct a parallel submatrix */
  ierr = MatGetSubMatricesMPI(mat,1,is_sc,allis_sc,MAT_INITIAL_MATRIX,&smat);CHKERRQ(ierr);
  /* we do not need it any more */
  ierr = ISDestroy(&is_sc);CHKERRQ(ierr);
  ierr = ISDestroy(&allis_sc);CHKERRQ(ierr);
  /*create a partitioner to repartition the submatrix*/
  ierr = MatPartitioningCreate(scomm,&part);CHKERRQ(ierr);
  ierr = MatPartitioningSetAdjacency(part,smat);CHKERRQ(ierr);
#if PETSC_HAVE_PARMETIS
  ierr = MatPartitioningSetType(part,PARMETIS);CHKERRQ(ierr);
  /*try to use reparition function, instead of partition function */
  ierr = MatPartitioningParmetisSetRepartition(part);CHKERRQ(ierr);
#else
  SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"please install parmetis using --download-parmetis \n");
#endif
  /* apply partition */
  ierr = MatPartitioningApply(part,&partitioning);CHKERRQ(ierr);
  /* get local rows including  overlap */
  ierr = ISBuildTwoSided(partitioning,is);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatGetBlockSize"
/*@
   MatGetBlockSize - Returns the matrix block size.

   Not Collective

   Input Parameter:
.  mat - the matrix

   Output Parameter:
.  bs - block size

   Notes:
    Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.

   If the block size has not been set yet this routine returns 1.

   Level: intermediate

   Concepts: matrices^block size

.seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSizes()
@*/
PetscErrorCode  MatGetBlockSize(Mat mat,PetscInt *bs)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidIntPointer(bs,2);
  *bs = PetscAbs(mat->rmap->bs);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetBlockSizes"
/*@
   MatGetBlockSizes - Returns the matrix block row and column sizes.

   Not Collective

   Input Parameter:
.  mat - the matrix

   Output Parameter:
.  rbs - row block size
.  cbs - coumn block size

   Notes:
    Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.
    If you pass a different block size for the columns than the rows, the row block size determines the square block storage.

   If a block size has not been set yet this routine returns 1.

   Level: intermediate

   Concepts: matrices^block size

.seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSize(), MatSetBlockSizes()
@*/
PetscErrorCode  MatGetBlockSizes(Mat mat,PetscInt *rbs, PetscInt *cbs)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (rbs) PetscValidIntPointer(rbs,2);
  if (cbs) PetscValidIntPointer(cbs,3);
  if (rbs) *rbs = PetscAbs(mat->rmap->bs);
  if (cbs) *cbs = PetscAbs(mat->cmap->bs);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetBlockSize"
/*@
   MatSetBlockSize - Sets the matrix block size.

   Logically Collective on Mat

   Input Parameters:
+  mat - the matrix
-  bs - block size

   Notes:
    Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.

     This must be called before MatSetUp() or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later

   Level: intermediate

   Concepts: matrices^block size

.seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes(), MatGetBlockSizes()
@*/
PetscErrorCode  MatSetBlockSize(Mat mat,PetscInt bs)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidLogicalCollectiveInt(mat,bs,2);
  ierr = PetscLayoutSetBlockSize(mat->rmap,bs);CHKERRQ(ierr);
  ierr = PetscLayoutSetBlockSize(mat->cmap,bs);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetBlockSizes"
/*@
   MatSetBlockSizes - Sets the matrix block row and column sizes.

   Logically Collective on Mat

   Input Parameters:
+  mat - the matrix
-  rbs - row block size
-  cbs - column block size

   Notes:
    Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.
    If you pass a different block size for the columns than the rows, the row block size determines the square block storage.

    This must be called before MatSetUp() or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later

    The row and column block size determine the blocksize of the "row" and "column" vectors returned by MatCreateVecs().

   Level: intermediate

   Concepts: matrices^block size

.seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSize(), MatGetBlockSizes()
@*/
PetscErrorCode  MatSetBlockSizes(Mat mat,PetscInt rbs,PetscInt cbs)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidLogicalCollectiveInt(mat,rbs,2);
  PetscValidLogicalCollectiveInt(mat,cbs,3);
  ierr = PetscLayoutSetBlockSize(mat->rmap,rbs);CHKERRQ(ierr);
  ierr = PetscLayoutSetBlockSize(mat->cmap,cbs);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetBlockSizesFromMats"
/*@
   MatSetBlockSizesFromMats - Sets the matrix block row and column sizes to match a pair of matrices

   Logically Collective on Mat

   Input Parameters:
+  mat - the matrix
.  fromRow - matrix from which to copy row block size
-  fromCol - matrix from which to copy column block size (can be same as fromRow)

   Level: developer

   Concepts: matrices^block size

.seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes()
@*/
PetscErrorCode  MatSetBlockSizesFromMats(Mat mat,Mat fromRow,Mat fromCol)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(fromRow,MAT_CLASSID,2);
  PetscValidHeaderSpecific(fromCol,MAT_CLASSID,3);
  if (fromRow->rmap->bs > 0) {ierr = PetscLayoutSetBlockSize(mat->rmap,fromRow->rmap->bs);CHKERRQ(ierr);}
  if (fromCol->cmap->bs > 0) {ierr = PetscLayoutSetBlockSize(mat->cmap,fromCol->cmap->bs);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatResidual"
/*@
   MatResidual - Default routine to calculate the residual.

   Collective on Mat and Vec

   Input Parameters:
+  mat - the matrix
.  b   - the right-hand-side
-  x   - the approximate solution

   Output Parameter:
.  r - location to store the residual

   Level: developer

.keywords: MG, default, multigrid, residual

.seealso: PCMGSetResidual()
@*/
PetscErrorCode  MatResidual(Mat mat,Vec b,Vec x,Vec r)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(b,VEC_CLASSID,2);
  PetscValidHeaderSpecific(x,VEC_CLASSID,3);
  PetscValidHeaderSpecific(r,VEC_CLASSID,4);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  ierr  = PetscLogEventBegin(MAT_Residual,mat,0,0,0);CHKERRQ(ierr);
  if (!mat->ops->residual) {
    ierr = MatMult(mat,x,r);CHKERRQ(ierr);
    ierr = VecAYPX(r,-1.0,b);CHKERRQ(ierr);
  } else {
    ierr  = (*mat->ops->residual)(mat,b,x,r);CHKERRQ(ierr);
  }
  ierr  = PetscLogEventEnd(MAT_Residual,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetRowIJ"
/*@C
    MatGetRowIJ - Returns the compressed row storage i and j indices for sequential matrices.

   Collective on Mat

    Input Parameters:
+   mat - the matrix
.   shift -  0 or 1 indicating we want the indices starting at 0 or 1
.   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be   symmetrized
-   inodecompressed - PETSC_TRUE or PETSC_FALSE  indicating if the nonzero structure of the
                 inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
                 always used.

    Output Parameters:
+   n - number of rows in the (possibly compressed) matrix
.   ia - the row pointers [of length n+1]
.   ja - the column indices
-   done - indicates if the routine actually worked and returned appropriate ia[] and ja[] arrays; callers
           are responsible for handling the case when done == PETSC_FALSE and ia and ja are not set

    Level: developer

    Notes: You CANNOT change any of the ia[] or ja[] values.

           Use MatRestoreRowIJ() when you are finished accessing the ia[] and ja[] values

    Fortran Node

           In Fortran use
$           PetscInt ia(1), ja(1)
$           PetscOffset iia, jja
$      call MatGetRowIJ(mat,shift,symmetric,inodecompressed,n,ia,iia,ja,jja,done,ierr)
$
$          or
$
$           PetscScalar, pointer :: xx_v(:)
$    call  MatGetRowIJF90(mat,shift,symmetric,inodecompressed,n,ia,ja,done,ierr)


       Acess the ith and jth entries via ia(iia + i) and ja(jja + j)

.seealso: MatGetColumnIJ(), MatRestoreRowIJ(), MatSeqAIJGetArray()
@*/
PetscErrorCode MatGetRowIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidIntPointer(n,4);
  if (ia) PetscValidIntPointer(ia,5);
  if (ja) PetscValidIntPointer(ja,6);
  PetscValidIntPointer(done,7);
  MatCheckPreallocated(mat,1);
  if (!mat->ops->getrowij) *done = PETSC_FALSE;
  else {
    *done = PETSC_TRUE;
    ierr  = PetscLogEventBegin(MAT_GetRowIJ,mat,0,0,0);CHKERRQ(ierr);
    ierr  = (*mat->ops->getrowij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);CHKERRQ(ierr);
    ierr  = PetscLogEventEnd(MAT_GetRowIJ,mat,0,0,0);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetColumnIJ"
/*@C
    MatGetColumnIJ - Returns the compressed column storage i and j indices for sequential matrices.

    Collective on Mat

    Input Parameters:
+   mat - the matrix
.   shift - 1 or zero indicating we want the indices starting at 0 or 1
.   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
                symmetrized
.   inodecompressed - PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
                 inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
                 always used.
.   n - number of columns in the (possibly compressed) matrix
.   ia - the column pointers
-   ja - the row indices

    Output Parameters:
.   done - PETSC_TRUE or PETSC_FALSE, indicating whether the values have been returned

    Note:
    This routine zeros out n, ia, and ja. This is to prevent accidental
    us of the array after it has been restored. If you pass NULL, it will
    not zero the pointers.  Use of ia or ja after MatRestoreColumnIJ() is invalid.

    Level: developer

.seealso: MatGetRowIJ(), MatRestoreColumnIJ()
@*/
PetscErrorCode MatGetColumnIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidIntPointer(n,4);
  if (ia) PetscValidIntPointer(ia,5);
  if (ja) PetscValidIntPointer(ja,6);
  PetscValidIntPointer(done,7);
  MatCheckPreallocated(mat,1);
  if (!mat->ops->getcolumnij) *done = PETSC_FALSE;
  else {
    *done = PETSC_TRUE;
    ierr  = (*mat->ops->getcolumnij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRestoreRowIJ"
/*@C
    MatRestoreRowIJ - Call after you are completed with the ia,ja indices obtained with
    MatGetRowIJ().

    Collective on Mat

    Input Parameters:
+   mat - the matrix
.   shift - 1 or zero indicating we want the indices starting at 0 or 1
.   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
                symmetrized
.   inodecompressed -  PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
                 inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
                 always used.
.   n - size of (possibly compressed) matrix
.   ia - the row pointers
-   ja - the column indices

    Output Parameters:
.   done - PETSC_TRUE or PETSC_FALSE indicated that the values have been returned

    Note:
    This routine zeros out n, ia, and ja. This is to prevent accidental
    us of the array after it has been restored. If you pass NULL, it will
    not zero the pointers.  Use of ia or ja after MatRestoreRowIJ() is invalid.

    Level: developer

.seealso: MatGetRowIJ(), MatRestoreColumnIJ()
@*/
PetscErrorCode MatRestoreRowIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (ia) PetscValidIntPointer(ia,5);
  if (ja) PetscValidIntPointer(ja,6);
  PetscValidIntPointer(done,7);
  MatCheckPreallocated(mat,1);

  if (!mat->ops->restorerowij) *done = PETSC_FALSE;
  else {
    *done = PETSC_TRUE;
    ierr  = (*mat->ops->restorerowij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);CHKERRQ(ierr);
    if (n)  *n = 0;
    if (ia) *ia = NULL;
    if (ja) *ja = NULL;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRestoreColumnIJ"
/*@C
    MatRestoreColumnIJ - Call after you are completed with the ia,ja indices obtained with
    MatGetColumnIJ().

    Collective on Mat

    Input Parameters:
+   mat - the matrix
.   shift - 1 or zero indicating we want the indices starting at 0 or 1
-   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
                symmetrized
-   inodecompressed - PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
                 inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
                 always used.

    Output Parameters:
+   n - size of (possibly compressed) matrix
.   ia - the column pointers
.   ja - the row indices
-   done - PETSC_TRUE or PETSC_FALSE indicated that the values have been returned

    Level: developer

.seealso: MatGetColumnIJ(), MatRestoreRowIJ()
@*/
PetscErrorCode MatRestoreColumnIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (ia) PetscValidIntPointer(ia,5);
  if (ja) PetscValidIntPointer(ja,6);
  PetscValidIntPointer(done,7);
  MatCheckPreallocated(mat,1);

  if (!mat->ops->restorecolumnij) *done = PETSC_FALSE;
  else {
    *done = PETSC_TRUE;
    ierr  = (*mat->ops->restorecolumnij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);CHKERRQ(ierr);
    if (n)  *n = 0;
    if (ia) *ia = NULL;
    if (ja) *ja = NULL;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatColoringPatch"
/*@C
    MatColoringPatch -Used inside matrix coloring routines that
    use MatGetRowIJ() and/or MatGetColumnIJ().

    Collective on Mat

    Input Parameters:
+   mat - the matrix
.   ncolors - max color value
.   n   - number of entries in colorarray
-   colorarray - array indicating color for each column

    Output Parameters:
.   iscoloring - coloring generated using colorarray information

    Level: developer

.seealso: MatGetRowIJ(), MatGetColumnIJ()

@*/
PetscErrorCode  MatColoringPatch(Mat mat,PetscInt ncolors,PetscInt n,ISColoringValue colorarray[],ISColoring *iscoloring)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidIntPointer(colorarray,4);
  PetscValidPointer(iscoloring,5);
  MatCheckPreallocated(mat,1);

  if (!mat->ops->coloringpatch) {
    ierr = ISColoringCreate(PetscObjectComm((PetscObject)mat),ncolors,n,colorarray,PETSC_OWN_POINTER,iscoloring);CHKERRQ(ierr);
  } else {
    ierr = (*mat->ops->coloringpatch)(mat,ncolors,n,colorarray,iscoloring);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}


#undef __FUNCT__
#define __FUNCT__ "MatSetUnfactored"
/*@
   MatSetUnfactored - Resets a factored matrix to be treated as unfactored.

   Logically Collective on Mat

   Input Parameter:
.  mat - the factored matrix to be reset

   Notes:
   This routine should be used only with factored matrices formed by in-place
   factorization via ILU(0) (or by in-place LU factorization for the MATSEQDENSE
   format).  This option can save memory, for example, when solving nonlinear
   systems with a matrix-free Newton-Krylov method and a matrix-based, in-place
   ILU(0) preconditioner.

   Note that one can specify in-place ILU(0) factorization by calling
.vb
     PCType(pc,PCILU);
     PCFactorSeUseInPlace(pc);
.ve
   or by using the options -pc_type ilu -pc_factor_in_place

   In-place factorization ILU(0) can also be used as a local
   solver for the blocks within the block Jacobi or additive Schwarz
   methods (runtime option: -sub_pc_factor_in_place).  See Users-Manual: ch_pc
   for details on setting local solver options.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

.seealso: PCFactorSetUseInPlace(), PCFactorGetUseInPlace()

   Concepts: matrices^unfactored

@*/
PetscErrorCode  MatSetUnfactored(Mat mat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  mat->factortype = MAT_FACTOR_NONE;
  if (!mat->ops->setunfactored) PetscFunctionReturn(0);
  ierr = (*mat->ops->setunfactored)(mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*MC
    MatDenseGetArrayF90 - Accesses a matrix array from Fortran90.

    Synopsis:
    MatDenseGetArrayF90(Mat x,{Scalar, pointer :: xx_v(:,:)},integer ierr)

    Not collective

    Input Parameter:
.   x - matrix

    Output Parameters:
+   xx_v - the Fortran90 pointer to the array
-   ierr - error code

    Example of Usage:
.vb
      PetscScalar, pointer xx_v(:,:)
      ....
      call MatDenseGetArrayF90(x,xx_v,ierr)
      a = xx_v(3)
      call MatDenseRestoreArrayF90(x,xx_v,ierr)
.ve

    Level: advanced

.seealso:  MatDenseRestoreArrayF90(), MatDenseGetArray(), MatDenseRestoreArray(), MatSeqAIJGetArrayF90()

    Concepts: matrices^accessing array

M*/

/*MC
    MatDenseRestoreArrayF90 - Restores a matrix array that has been
    accessed with MatDenseGetArrayF90().

    Synopsis:
    MatDenseRestoreArrayF90(Mat x,{Scalar, pointer :: xx_v(:)},integer ierr)

    Not collective

    Input Parameters:
+   x - matrix
-   xx_v - the Fortran90 pointer to the array

    Output Parameter:
.   ierr - error code

    Example of Usage:
.vb
       PetscScalar, pointer xx_v(:)
       ....
       call MatDenseGetArrayF90(x,xx_v,ierr)
       a = xx_v(3)
       call MatDenseRestoreArrayF90(x,xx_v,ierr)
.ve

    Level: advanced

.seealso:  MatDenseGetArrayF90(), MatDenseGetArray(), MatDenseRestoreArray(), MatSeqAIJRestoreArrayF90()

M*/


/*MC
    MatSeqAIJGetArrayF90 - Accesses a matrix array from Fortran90.

    Synopsis:
    MatSeqAIJGetArrayF90(Mat x,{Scalar, pointer :: xx_v(:,:)},integer ierr)

    Not collective

    Input Parameter:
.   x - matrix

    Output Parameters:
+   xx_v - the Fortran90 pointer to the array
-   ierr - error code

    Example of Usage:
.vb
      PetscScalar, pointer xx_v(:,:)
      ....
      call MatSeqAIJGetArrayF90(x,xx_v,ierr)
      a = xx_v(3)
      call MatSeqAIJRestoreArrayF90(x,xx_v,ierr)
.ve

    Level: advanced

.seealso:  MatSeqAIJRestoreArrayF90(), MatSeqAIJGetArray(), MatSeqAIJRestoreArray(), MatDenseGetArrayF90()

    Concepts: matrices^accessing array

M*/

/*MC
    MatSeqAIJRestoreArrayF90 - Restores a matrix array that has been
    accessed with MatSeqAIJGetArrayF90().

    Synopsis:
    MatSeqAIJRestoreArrayF90(Mat x,{Scalar, pointer :: xx_v(:)},integer ierr)

    Not collective

    Input Parameters:
+   x - matrix
-   xx_v - the Fortran90 pointer to the array

    Output Parameter:
.   ierr - error code

    Example of Usage:
.vb
       PetscScalar, pointer xx_v(:)
       ....
       call MatSeqAIJGetArrayF90(x,xx_v,ierr)
       a = xx_v(3)
       call MatSeqAIJRestoreArrayF90(x,xx_v,ierr)
.ve

    Level: advanced

.seealso:  MatSeqAIJGetArrayF90(), MatSeqAIJGetArray(), MatSeqAIJRestoreArray(), MatDenseRestoreArrayF90()

M*/


#undef __FUNCT__
#define __FUNCT__ "MatGetSubMatrix"
/*@
    MatGetSubMatrix - Gets a single submatrix on the same number of processors
                      as the original matrix.

    Collective on Mat

    Input Parameters:
+   mat - the original matrix
.   isrow - parallel IS containing the rows this processor should obtain
.   iscol - parallel IS containing all columns you wish to keep. Each process should list the columns that will be in IT's "diagonal part" in the new matrix.
-   cll - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    Output Parameter:
.   newmat - the new submatrix, of the same type as the old

    Level: advanced

    Notes:
    The submatrix will be able to be multiplied with vectors using the same layout as iscol.

    Some matrix types place restrictions on the row and column indices, such
    as that they be sorted or that they be equal to each other.

    The index sets may not have duplicate entries.

      The first time this is called you should use a cll of MAT_INITIAL_MATRIX,
   the MatGetSubMatrix() routine will create the newmat for you. Any additional calls
   to this routine with a mat of the same nonzero structure and with a call of MAT_REUSE_MATRIX
   will reuse the matrix generated the first time.  You should call MatDestroy() on newmat when
   you are finished using it.

    The communicator of the newly obtained matrix is ALWAYS the same as the communicator of
    the input matrix.

    If iscol is NULL then all columns are obtained (not supported in Fortran).

   Example usage:
   Consider the following 8x8 matrix with 34 non-zero values, that is
   assembled across 3 processors. Let's assume that proc0 owns 3 rows,
   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
   as follows:

.vb
            1  2  0  |  0  3  0  |  0  4
    Proc0   0  5  6  |  7  0  0  |  8  0
            9  0 10  | 11  0  0  | 12  0
    -------------------------------------
           13  0 14  | 15 16 17  |  0  0
    Proc1   0 18  0  | 19 20 21  |  0  0
            0  0  0  | 22 23  0  | 24  0
    -------------------------------------
    Proc2  25 26 27  |  0  0 28  | 29  0
           30  0  0  | 31 32 33  |  0 34
.ve

    Suppose isrow = [0 1 | 4 | 6 7] and iscol = [1 2 | 3 4 5 | 6].  The resulting submatrix is

.vb
            2  0  |  0  3  0  |  0
    Proc0   5  6  |  7  0  0  |  8
    -------------------------------
    Proc1  18  0  | 19 20 21  |  0
    -------------------------------
    Proc2  26 27  |  0  0 28  | 29
            0  0  | 31 32 33  |  0
.ve


    Concepts: matrices^submatrices

.seealso: MatGetSubMatrices()
@*/
PetscErrorCode  MatGetSubMatrix(Mat mat,IS isrow,IS iscol,MatReuse cll,Mat *newmat)
{
  PetscErrorCode ierr;
  PetscMPIInt    size;
  Mat            *local;
  IS             iscoltmp;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(isrow,IS_CLASSID,2);
  if (iscol) PetscValidHeaderSpecific(iscol,IS_CLASSID,3);
  PetscValidPointer(newmat,5);
  if (cll == MAT_REUSE_MATRIX) PetscValidHeaderSpecific(*newmat,MAT_CLASSID,5);
  PetscValidType(mat,1);
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (cll == MAT_IGNORE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Cannot use MAT_IGNORE_MATRIX");

  MatCheckPreallocated(mat,1);
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);

  if (!iscol || isrow == iscol) {
    PetscBool   stride;
    PetscMPIInt grabentirematrix = 0,grab;
    ierr = PetscObjectTypeCompare((PetscObject)isrow,ISSTRIDE,&stride);CHKERRQ(ierr);
    if (stride) {
      PetscInt first,step,n,rstart,rend;
      ierr = ISStrideGetInfo(isrow,&first,&step);CHKERRQ(ierr);
      if (step == 1) {
        ierr = MatGetOwnershipRange(mat,&rstart,&rend);CHKERRQ(ierr);
        if (rstart == first) {
          ierr = ISGetLocalSize(isrow,&n);CHKERRQ(ierr);
          if (n == rend-rstart) {
            grabentirematrix = 1;
          }
        }
      }
    }
    ierr = MPI_Allreduce(&grabentirematrix,&grab,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
    if (grab) {
      ierr = PetscInfo(mat,"Getting entire matrix as submatrix\n");CHKERRQ(ierr);
      if (cll == MAT_INITIAL_MATRIX) {
        *newmat = mat;
        ierr    = PetscObjectReference((PetscObject)mat);CHKERRQ(ierr);
      }
      PetscFunctionReturn(0);
    }
  }

  if (!iscol) {
    ierr = ISCreateStride(PetscObjectComm((PetscObject)mat),mat->cmap->n,mat->cmap->rstart,1,&iscoltmp);CHKERRQ(ierr);
  } else {
    iscoltmp = iscol;
  }

  /* if original matrix is on just one processor then use submatrix generated */
  if (mat->ops->getsubmatrices && !mat->ops->getsubmatrix && size == 1 && cll == MAT_REUSE_MATRIX) {
    ierr = MatGetSubMatrices(mat,1,&isrow,&iscoltmp,MAT_REUSE_MATRIX,&newmat);CHKERRQ(ierr);
    if (!iscol) {ierr = ISDestroy(&iscoltmp);CHKERRQ(ierr);}
    PetscFunctionReturn(0);
  } else if (mat->ops->getsubmatrices && !mat->ops->getsubmatrix && size == 1) {
    ierr    = MatGetSubMatrices(mat,1,&isrow,&iscoltmp,MAT_INITIAL_MATRIX,&local);CHKERRQ(ierr);
    *newmat = *local;
    ierr    = PetscFree(local);CHKERRQ(ierr);
    if (!iscol) {ierr = ISDestroy(&iscoltmp);CHKERRQ(ierr);}
    PetscFunctionReturn(0);
  } else if (!mat->ops->getsubmatrix) {
    /* Create a new matrix type that implements the operation using the full matrix */
    ierr = PetscLogEventBegin(MAT_GetSubMatrix,mat,0,0,0);CHKERRQ(ierr);
    switch (cll) {
    case MAT_INITIAL_MATRIX:
      ierr = MatCreateSubMatrix(mat,isrow,iscoltmp,newmat);CHKERRQ(ierr);
      break;
    case MAT_REUSE_MATRIX:
      ierr = MatSubMatrixUpdate(*newmat,mat,isrow,iscoltmp);CHKERRQ(ierr);
      break;
    default: SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Invalid MatReuse, must be either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX");
    }
    ierr = PetscLogEventEnd(MAT_GetSubMatrix,mat,0,0,0);CHKERRQ(ierr);
    if (!iscol) {ierr = ISDestroy(&iscoltmp);CHKERRQ(ierr);}
    PetscFunctionReturn(0);
  }

  if (!mat->ops->getsubmatrix) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  ierr = PetscLogEventBegin(MAT_GetSubMatrix,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->getsubmatrix)(mat,isrow,iscoltmp,cll,newmat);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_GetSubMatrix,mat,0,0,0);CHKERRQ(ierr);
  if (!iscol) {ierr = ISDestroy(&iscoltmp);CHKERRQ(ierr);}
  if (*newmat && cll == MAT_INITIAL_MATRIX) {ierr = PetscObjectStateIncrease((PetscObject)*newmat);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatStashSetInitialSize"
/*@
   MatStashSetInitialSize - sets the sizes of the matrix stash, that is
   used during the assembly process to store values that belong to
   other processors.

   Not Collective

   Input Parameters:
+  mat   - the matrix
.  size  - the initial size of the stash.
-  bsize - the initial size of the block-stash(if used).

   Options Database Keys:
+   -matstash_initial_size <size> or <size0,size1,...sizep-1>
-   -matstash_block_initial_size <bsize>  or <bsize0,bsize1,...bsizep-1>

   Level: intermediate

   Notes:
     The block-stash is used for values set with MatSetValuesBlocked() while
     the stash is used for values set with MatSetValues()

     Run with the option -info and look for output of the form
     MatAssemblyBegin_MPIXXX:Stash has MM entries, uses nn mallocs.
     to determine the appropriate value, MM, to use for size and
     MatAssemblyBegin_MPIXXX:Block-Stash has BMM entries, uses nn mallocs.
     to determine the value, BMM to use for bsize

   Concepts: stash^setting matrix size
   Concepts: matrices^stash

.seealso: MatAssemblyBegin(), MatAssemblyEnd(), Mat, MatStashGetInfo()

@*/
PetscErrorCode  MatStashSetInitialSize(Mat mat,PetscInt size, PetscInt bsize)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  ierr = MatStashSetInitialSize_Private(&mat->stash,size);CHKERRQ(ierr);
  ierr = MatStashSetInitialSize_Private(&mat->bstash,bsize);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatInterpolateAdd"
/*@
   MatInterpolateAdd - w = y + A*x or A'*x depending on the shape of
     the matrix

   Neighbor-wise Collective on Mat

   Input Parameters:
+  mat   - the matrix
.  x,y - the vectors
-  w - where the result is stored

   Level: intermediate

   Notes:
    w may be the same vector as y.

    This allows one to use either the restriction or interpolation (its transpose)
    matrix to do the interpolation

    Concepts: interpolation

.seealso: MatMultAdd(), MatMultTransposeAdd(), MatRestrict()

@*/
PetscErrorCode  MatInterpolateAdd(Mat A,Vec x,Vec y,Vec w)
{
  PetscErrorCode ierr;
  PetscInt       M,N,Ny;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);
  PetscValidHeaderSpecific(w,VEC_CLASSID,4);
  PetscValidType(A,1);
  MatCheckPreallocated(A,1);
  ierr = MatGetSize(A,&M,&N);CHKERRQ(ierr);
  ierr = VecGetSize(y,&Ny);CHKERRQ(ierr);
  if (M == Ny) {
    ierr = MatMultAdd(A,x,y,w);CHKERRQ(ierr);
  } else {
    ierr = MatMultTransposeAdd(A,x,y,w);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatInterpolate"
/*@
   MatInterpolate - y = A*x or A'*x depending on the shape of
     the matrix

   Neighbor-wise Collective on Mat

   Input Parameters:
+  mat   - the matrix
-  x,y - the vectors

   Level: intermediate

   Notes:
    This allows one to use either the restriction or interpolation (its transpose)
    matrix to do the interpolation

   Concepts: matrices^interpolation

.seealso: MatMultAdd(), MatMultTransposeAdd(), MatRestrict()

@*/
PetscErrorCode  MatInterpolate(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  PetscInt       M,N,Ny;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);
  PetscValidType(A,1);
  MatCheckPreallocated(A,1);
  ierr = MatGetSize(A,&M,&N);CHKERRQ(ierr);
  ierr = VecGetSize(y,&Ny);CHKERRQ(ierr);
  if (M == Ny) {
    ierr = MatMult(A,x,y);CHKERRQ(ierr);
  } else {
    ierr = MatMultTranspose(A,x,y);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRestrict"
/*@
   MatRestrict - y = A*x or A'*x

   Neighbor-wise Collective on Mat

   Input Parameters:
+  mat   - the matrix
-  x,y - the vectors

   Level: intermediate

   Notes:
    This allows one to use either the restriction or interpolation (its transpose)
    matrix to do the restriction

   Concepts: matrices^restriction

.seealso: MatMultAdd(), MatMultTransposeAdd(), MatInterpolate()

@*/
PetscErrorCode  MatRestrict(Mat A,Vec x,Vec y)
{
  PetscErrorCode ierr;
  PetscInt       M,N,Ny;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidHeaderSpecific(x,VEC_CLASSID,2);
  PetscValidHeaderSpecific(y,VEC_CLASSID,3);
  PetscValidType(A,1);
  MatCheckPreallocated(A,1);

  ierr = MatGetSize(A,&M,&N);CHKERRQ(ierr);
  ierr = VecGetSize(y,&Ny);CHKERRQ(ierr);
  if (M == Ny) {
    ierr = MatMult(A,x,y);CHKERRQ(ierr);
  } else {
    ierr = MatMultTranspose(A,x,y);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetNullSpace"
/*@
   MatGetNullSpace - retrieves the null space to a matrix.

   Logically Collective on Mat and MatNullSpace

   Input Parameters:
+  mat - the matrix
-  nullsp - the null space object

   Level: developer

   Notes:
      This null space is used by solvers. Overwrites any previous null space that may have been attached

   Concepts: null space^attaching to matrix

.seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace()
@*/
PetscErrorCode MatGetNullSpace(Mat mat, MatNullSpace *nullsp)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(nullsp,2);
  *nullsp = mat->nullsp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetNullSpace"
/*@
   MatSetNullSpace - attaches a null space to a matrix.

   Logically Collective on Mat and MatNullSpace

   Input Parameters:
+  mat - the matrix
-  nullsp - the null space object

   Level: advanced

   Notes:
      This null space is used by the linear solvers. Overwrites any previous null space that may have been attached

      For inconsistent singular systems (linear systems where the right hand side is not in the range of the operator) you also likely should
      call MatSetTransposeNullSpace(). This allows the linear system to be solved in a least squares sense.


      The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
   the domain of a matrix A (from R^n to R^m (m rows, n columns) R^n = the direct sum of the null space of A, n(A), + the range of A^T, R(A^T).
   Similarly R^m = direct sum n(A^T) + R(A).  Hence the linear system A x = b has a solution only if b in R(A) (or correspondingly b is orthogonal to
   n(A^T)) and if x is a solution then x + alpha n(A) is a solution for any alpha. The minimum norm solution is orthogonal to n(A). For problems without a solution
   the solution that minimizes the norm of the residual (the least squares solution) can be obtained by solving A x = \hat{b} where \hat{b} is b orthogonalized to the n(A^T).

      Krylov solvers can produce the minimal norm solution to the least squares problem by utilizing MatNullSpaceRemove().

   Concepts: null space^attaching to matrix

.seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatGetNullSpace(), MatSetTransposeNullSpace(), MatGetTransposeNullSpace(), MatNullSpaceRemove()
@*/
PetscErrorCode  MatSetNullSpace(Mat mat,MatNullSpace nullsp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(nullsp,MAT_NULLSPACE_CLASSID,2);
  MatCheckPreallocated(mat,1);
  ierr = PetscObjectReference((PetscObject)nullsp);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&mat->nullsp);CHKERRQ(ierr);
  mat->nullsp = nullsp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetTransposeNullSpace"
/*@
   MatGetTransposeNullSpace - retrieves the null space to a matrix.

   Logically Collective on Mat and MatNullSpace

   Input Parameters:
+  mat - the matrix
-  nullsp - the null space object

   Level: developer

   Notes:
      This null space is used by solvers. Overwrites any previous null space that may have been attached

   Concepts: null space^attaching to matrix

.seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace()
@*/
PetscErrorCode MatGetTransposeNullSpace(Mat mat, MatNullSpace *nullsp)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(nullsp,2);
  *nullsp = mat->transnullsp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetTransposeNullSpace"
/*@
   MatSetTransposeNullSpace - attaches a null space to a matrix.

   Logically Collective on Mat and MatNullSpace

   Input Parameters:
+  mat - the matrix
-  nullsp - the null space object

   Level: advanced

   Notes:
      For inconsistent singular systems (linear systems where the right hand side is not in the range of the operator) this allows the linear system to be solved in a least squares sense.
      You must also call MatSetNullSpace()


      The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
   the domain of a matrix A (from R^n to R^m (m rows, n columns) R^n = the direct sum of the null space of A, n(A), + the range of A^T, R(A^T).
   Similarly R^m = direct sum n(A^T) + R(A).  Hence the linear system A x = b has a solution only if b in R(A) (or correspondingly b is orthogonal to
   n(A^T)) and if x is a solution then x + alpha n(A) is a solution for any alpha. The minimum norm solution is orthogonal to n(A). For problems without a solution
   the solution that minimizes the norm of the residual (the least squares solution) can be obtained by solving A x = \hat{b} where \hat{b} is b orthogonalized to the n(A^T).

      Krylov solvers can produce the minimal norm solution to the least squares problem by utilizing MatNullSpaceRemove().

   Concepts: null space^attaching to matrix

.seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatGetNullSpace(), MatSetNullSpace(), MatGetNullSpace(), MatNullSpaceRemove()
@*/
PetscErrorCode  MatSetTransposeNullSpace(Mat mat,MatNullSpace nullsp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(nullsp,MAT_NULLSPACE_CLASSID,2);
  MatCheckPreallocated(mat,1);
  ierr = PetscObjectReference((PetscObject)nullsp);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&mat->transnullsp);CHKERRQ(ierr);
  mat->transnullsp = nullsp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetNearNullSpace"
/*@
   MatSetNearNullSpace - attaches a null space to a matrix.
        This null space will be used to provide near null space vectors to a multigrid preconditioner built from this matrix.

   Logically Collective on Mat and MatNullSpace

   Input Parameters:
+  mat - the matrix
-  nullsp - the null space object

   Level: advanced

   Notes:
      Overwrites any previous near null space that may have been attached

   Concepts: null space^attaching to matrix

.seealso: MatCreate(), MatNullSpaceCreate(), MatSetNullSpace()
@*/
PetscErrorCode MatSetNearNullSpace(Mat mat,MatNullSpace nullsp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidHeaderSpecific(nullsp,MAT_NULLSPACE_CLASSID,2);
  MatCheckPreallocated(mat,1);
  ierr = PetscObjectReference((PetscObject)nullsp);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&mat->nearnullsp);CHKERRQ(ierr);

  mat->nearnullsp = nullsp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetNearNullSpace"
/*@
   MatGetNearNullSpace -Get null space attached with MatSetNearNullSpace()

   Not Collective

   Input Parameters:
.  mat - the matrix

   Output Parameters:
.  nullsp - the null space object, NULL if not set

   Level: developer

   Concepts: null space^attaching to matrix

.seealso: MatSetNearNullSpace(), MatGetNullSpace()
@*/
PetscErrorCode MatGetNearNullSpace(Mat mat,MatNullSpace *nullsp)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(nullsp,2);
  MatCheckPreallocated(mat,1);
  *nullsp = mat->nearnullsp;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatICCFactor"
/*@C
   MatICCFactor - Performs in-place incomplete Cholesky factorization of matrix.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  row - row/column permutation
.  fill - expected fill factor >= 1.0
-  level - level of fill, for ICC(k)

   Notes:
   Probably really in-place only when level of fill is zero, otherwise allocates
   new space to store factored matrix and deletes previous memory.

   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^incomplete Cholesky factorization
   Concepts: Cholesky factorization

.seealso: MatICCFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor()

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/
PetscErrorCode  MatICCFactor(Mat mat,IS row,const MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (row) PetscValidHeaderSpecific(row,IS_CLASSID,2);
  PetscValidPointer(info,3);
  if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"matrix must be square");
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->iccfactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  ierr = (*mat->ops->iccfactor)(mat,row,info);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValuesAdifor"
/*@
   MatSetValuesAdifor - Sets values computed with automatic differentiation into a matrix.

   Not Collective

   Input Parameters:
+  mat - the matrix
.  nl - leading dimension of v
-  v - the values compute with ADIFOR

   Level: developer

   Notes:
     Must call MatSetColoring() before using this routine. Also this matrix must already
     have its nonzero pattern determined.

.seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
          MatSetValues(), MatSetColoring()
@*/
PetscErrorCode  MatSetValuesAdifor(Mat mat,PetscInt nl,void *v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  PetscValidPointer(v,3);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Matrix must be already assembled");
  ierr = PetscLogEventBegin(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
  if (!mat->ops->setvaluesadifor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  ierr = (*mat->ops->setvaluesadifor)(mat,nl,v);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_SetValues,mat,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDiagonalScaleLocal"
/*@
   MatDiagonalScaleLocal - Scales columns of a matrix given the scaling values including the
         ghosted ones.

   Not Collective

   Input Parameters:
+  mat - the matrix
-  diag = the diagonal values, including ghost ones

   Level: developer

   Notes: Works only for MPIAIJ and MPIBAIJ matrices

.seealso: MatDiagonalScale()
@*/
PetscErrorCode  MatDiagonalScaleLocal(Mat mat,Vec diag)
{
  PetscErrorCode ierr;
  PetscMPIInt    size;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(diag,VEC_CLASSID,2);
  PetscValidType(mat,1);

  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Matrix must be already assembled");
  ierr = PetscLogEventBegin(MAT_Scale,mat,0,0,0);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
  if (size == 1) {
    PetscInt n,m;
    ierr = VecGetSize(diag,&n);CHKERRQ(ierr);
    ierr = MatGetSize(mat,0,&m);CHKERRQ(ierr);
    if (m == n) {
      ierr = MatDiagonalScale(mat,0,diag);CHKERRQ(ierr);
    } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only supported for sequential matrices when no ghost points/periodic conditions");
  } else {
    ierr = PetscUseMethod(mat,"MatDiagonalScaleLocal_C",(Mat,Vec),(mat,diag));CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_Scale,mat,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectStateIncrease((PetscObject)mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetInertia"
/*@
   MatGetInertia - Gets the inertia from a factored matrix

   Collective on Mat

   Input Parameter:
.  mat - the matrix

   Output Parameters:
+   nneg - number of negative eigenvalues
.   nzero - number of zero eigenvalues
-   npos - number of positive eigenvalues

   Level: advanced

   Notes: Matrix must have been factored by MatCholeskyFactor()


@*/
PetscErrorCode  MatGetInertia(Mat mat,PetscInt *nneg,PetscInt *nzero,PetscInt *npos)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Numeric factor mat is not assembled");
  if (!mat->ops->getinertia) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  ierr = (*mat->ops->getinertia)(mat,nneg,nzero,npos);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "MatSolves"
/*@C
   MatSolves - Solves A x = b, given a factored matrix, for a collection of vectors

   Neighbor-wise Collective on Mat and Vecs

   Input Parameters:
+  mat - the factored matrix
-  b - the right-hand-side vectors

   Output Parameter:
.  x - the result vectors

   Notes:
   The vectors b and x cannot be the same.  I.e., one cannot
   call MatSolves(A,x,x).

   Notes:
   Most users should employ the simplified KSP interface for linear solvers
   instead of working directly with matrix algebra routines such as this.
   See, e.g., KSPCreate().

   Level: developer

   Concepts: matrices^triangular solves

.seealso: MatSolveAdd(), MatSolveTranspose(), MatSolveTransposeAdd(), MatSolve()
@*/
PetscErrorCode  MatSolves(Mat mat,Vecs b,Vecs x)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
  if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
  if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(0);

  if (!mat->ops->solves) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
  MatCheckPreallocated(mat,1);
  ierr = PetscLogEventBegin(MAT_Solves,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->solves)(mat,b,x);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_Solves,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatIsSymmetric"
/*@
   MatIsSymmetric - Test whether a matrix is symmetric

   Collective on Mat

   Input Parameter:
+  A - the matrix to test
-  tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact transpose)

   Output Parameters:
.  flg - the result

   Notes: For real numbers MatIsSymmetric() and MatIsHermitian() return identical results

   Level: intermediate

   Concepts: matrix^symmetry

.seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetricKnown()
@*/
PetscErrorCode  MatIsSymmetric(Mat A,PetscReal tol,PetscBool  *flg)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidPointer(flg,2);

  if (!A->symmetric_set) {
    if (!A->ops->issymmetric) {
      MatType mattype;
      ierr = MatGetType(A,&mattype);CHKERRQ(ierr);
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type <%s> does not support checking for symmetric",mattype);
    }
    ierr = (*A->ops->issymmetric)(A,tol,flg);CHKERRQ(ierr);
    if (!tol) {
      A->symmetric_set = PETSC_TRUE;
      A->symmetric     = *flg;
      if (A->symmetric) {
        A->structurally_symmetric_set = PETSC_TRUE;
        A->structurally_symmetric     = PETSC_TRUE;
      }
    }
  } else if (A->symmetric) {
    *flg = PETSC_TRUE;
  } else if (!tol) {
    *flg = PETSC_FALSE;
  } else {
    if (!A->ops->issymmetric) {
      MatType mattype;
      ierr = MatGetType(A,&mattype);CHKERRQ(ierr);
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type <%s> does not support checking for symmetric",mattype);
    }
    ierr = (*A->ops->issymmetric)(A,tol,flg);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatIsHermitian"
/*@
   MatIsHermitian - Test whether a matrix is Hermitian

   Collective on Mat

   Input Parameter:
+  A - the matrix to test
-  tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact Hermitian)

   Output Parameters:
.  flg - the result

   Level: intermediate

   Concepts: matrix^symmetry

.seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(),
          MatIsSymmetricKnown(), MatIsSymmetric()
@*/
PetscErrorCode  MatIsHermitian(Mat A,PetscReal tol,PetscBool  *flg)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidPointer(flg,2);

  if (!A->hermitian_set) {
    if (!A->ops->ishermitian) {
      MatType mattype;
      ierr = MatGetType(A,&mattype);CHKERRQ(ierr);
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type <%s> does not support checking for hermitian",mattype);
    }
    ierr = (*A->ops->ishermitian)(A,tol,flg);CHKERRQ(ierr);
    if (!tol) {
      A->hermitian_set = PETSC_TRUE;
      A->hermitian     = *flg;
      if (A->hermitian) {
        A->structurally_symmetric_set = PETSC_TRUE;
        A->structurally_symmetric     = PETSC_TRUE;
      }
    }
  } else if (A->hermitian) {
    *flg = PETSC_TRUE;
  } else if (!tol) {
    *flg = PETSC_FALSE;
  } else {
    if (!A->ops->ishermitian) {
      MatType mattype;
      ierr = MatGetType(A,&mattype);CHKERRQ(ierr);
      SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type <%s> does not support checking for hermitian",mattype);
    }
    ierr = (*A->ops->ishermitian)(A,tol,flg);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatIsSymmetricKnown"
/*@
   MatIsSymmetricKnown - Checks the flag on the matrix to see if it is symmetric.

   Not Collective

   Input Parameter:
.  A - the matrix to check

   Output Parameters:
+  set - if the symmetric flag is set (this tells you if the next flag is valid)
-  flg - the result

   Level: advanced

   Concepts: matrix^symmetry

   Note: Does not check the matrix values directly, so this may return unknown (set = PETSC_FALSE). Use MatIsSymmetric()
         if you want it explicitly checked

.seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetric()
@*/
PetscErrorCode  MatIsSymmetricKnown(Mat A,PetscBool  *set,PetscBool  *flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidPointer(set,2);
  PetscValidPointer(flg,3);
  if (A->symmetric_set) {
    *set = PETSC_TRUE;
    *flg = A->symmetric;
  } else {
    *set = PETSC_FALSE;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatIsHermitianKnown"
/*@
   MatIsHermitianKnown - Checks the flag on the matrix to see if it is hermitian.

   Not Collective

   Input Parameter:
.  A - the matrix to check

   Output Parameters:
+  set - if the hermitian flag is set (this tells you if the next flag is valid)
-  flg - the result

   Level: advanced

   Concepts: matrix^symmetry

   Note: Does not check the matrix values directly, so this may return unknown (set = PETSC_FALSE). Use MatIsHermitian()
         if you want it explicitly checked

.seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetric()
@*/
PetscErrorCode  MatIsHermitianKnown(Mat A,PetscBool  *set,PetscBool  *flg)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidPointer(set,2);
  PetscValidPointer(flg,3);
  if (A->hermitian_set) {
    *set = PETSC_TRUE;
    *flg = A->hermitian;
  } else {
    *set = PETSC_FALSE;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatIsStructurallySymmetric"
/*@
   MatIsStructurallySymmetric - Test whether a matrix is structurally symmetric

   Collective on Mat

   Input Parameter:
.  A - the matrix to test

   Output Parameters:
.  flg - the result

   Level: intermediate

   Concepts: matrix^symmetry

.seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsSymmetric(), MatSetOption()
@*/
PetscErrorCode  MatIsStructurallySymmetric(Mat A,PetscBool  *flg)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidPointer(flg,2);
  if (!A->structurally_symmetric_set) {
    if (!A->ops->isstructurallysymmetric) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Matrix does not support checking for structural symmetric");
    ierr = (*A->ops->isstructurallysymmetric)(A,&A->structurally_symmetric);CHKERRQ(ierr);

    A->structurally_symmetric_set = PETSC_TRUE;
  }
  *flg = A->structurally_symmetric;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatStashGetInfo"
extern PetscErrorCode MatStashGetInfo_Private(MatStash*,PetscInt*,PetscInt*);
/*@
   MatStashGetInfo - Gets how many values are currently in the matrix stash, i.e. need
       to be communicated to other processors during the MatAssemblyBegin/End() process

    Not collective

   Input Parameter:
.   vec - the vector

   Output Parameters:
+   nstash   - the size of the stash
.   reallocs - the number of additional mallocs incurred.
.   bnstash   - the size of the block stash
-   breallocs - the number of additional mallocs incurred.in the block stash

   Level: advanced

.seealso: MatAssemblyBegin(), MatAssemblyEnd(), Mat, MatStashSetInitialSize()

@*/
PetscErrorCode  MatStashGetInfo(Mat mat,PetscInt *nstash,PetscInt *reallocs,PetscInt *bnstash,PetscInt *breallocs)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatStashGetInfo_Private(&mat->stash,nstash,reallocs);CHKERRQ(ierr);
  ierr = MatStashGetInfo_Private(&mat->bstash,bnstash,breallocs);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCreateVecs"
/*@C
   MatCreateVecs - Get vector(s) compatible with the matrix, i.e. with the same
     parallel layout

   Collective on Mat

   Input Parameter:
.  mat - the matrix

   Output Parameter:
+   right - (optional) vector that the matrix can be multiplied against
-   left - (optional) vector that the matrix vector product can be stored in

   Notes:
    The blocksize of the returned vectors is determined by the row and column block sizes set with MatSetBlockSizes() or the single blocksize (same for both) set by MatSetBlockSize().

  Notes: These are new vectors which are not owned by the Mat, they should be destroyed in VecDestroy() when no longer needed

  Level: advanced

.seealso: MatCreate(), VecDestroy()
@*/
PetscErrorCode  MatCreateVecs(Mat mat,Vec *right,Vec *left)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  MatCheckPreallocated(mat,1);
  if (mat->ops->getvecs) {
    ierr = (*mat->ops->getvecs)(mat,right,left);CHKERRQ(ierr);
  } else {
    PetscMPIInt size;
    PetscInt    rbs,cbs;
    ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size);CHKERRQ(ierr);
    ierr = MatGetBlockSizes(mat,&rbs,&cbs);CHKERRQ(ierr);
    if (right) {
      ierr = VecCreate(PetscObjectComm((PetscObject)mat),right);CHKERRQ(ierr);
      ierr = VecSetSizes(*right,mat->cmap->n,PETSC_DETERMINE);CHKERRQ(ierr);
      ierr = VecSetBlockSize(*right,cbs);CHKERRQ(ierr);
      ierr = VecSetType(*right,VECSTANDARD);CHKERRQ(ierr);
      ierr = PetscLayoutReference(mat->cmap,&(*right)->map);CHKERRQ(ierr);
    }
    if (left) {
      ierr = VecCreate(PetscObjectComm((PetscObject)mat),left);CHKERRQ(ierr);
      ierr = VecSetSizes(*left,mat->rmap->n,PETSC_DETERMINE);CHKERRQ(ierr);
      ierr = VecSetBlockSize(*left,rbs);CHKERRQ(ierr);
      ierr = VecSetType(*left,VECSTANDARD);CHKERRQ(ierr);
      ierr = PetscLayoutReference(mat->rmap,&(*left)->map);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFactorInfoInitialize"
/*@C
   MatFactorInfoInitialize - Initializes a MatFactorInfo data structure
     with default values.

   Not Collective

   Input Parameters:
.    info - the MatFactorInfo data structure


   Notes: The solvers are generally used through the KSP and PC objects, for example
          PCLU, PCILU, PCCHOLESKY, PCICC

   Level: developer

.seealso: MatFactorInfo

    Developer Note: fortran interface is not autogenerated as the f90
    interface defintion cannot be generated correctly [due to MatFactorInfo]

@*/

PetscErrorCode  MatFactorInfoInitialize(MatFactorInfo *info)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscMemzero(info,sizeof(MatFactorInfo));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPtAP"
/*@
   MatPtAP - Creates the matrix product C = P^T * A * P

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the matrix
.  P - the projection matrix
.  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
-  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(P))

   Output Parameters:
.  C - the product matrix

   Notes:
   C will be created and must be destroyed by the user with MatDestroy().

   This routine is currently only implemented for pairs of AIJ matrices and classes
   which inherit from AIJ.

   Level: intermediate

.seealso: MatPtAPSymbolic(), MatPtAPNumeric(), MatMatMult(), MatRARt()
@*/
PetscErrorCode  MatPtAP(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;
  PetscErrorCode (*fA)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*fP)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*ptap)(Mat,Mat,MatReuse,PetscReal,Mat*)=NULL;
  PetscBool      viatranspose=PETSC_FALSE,viamatmatmatmult=PETSC_FALSE;

  PetscFunctionBegin;
  ierr = PetscOptionsGetBool(((PetscObject)A)->prefix,"-matptap_viatranspose",&viatranspose,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(((PetscObject)A)->prefix,"-matptap_viamatmatmatmult",&viamatmatmatmult,NULL);CHKERRQ(ierr);

  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  MatCheckPreallocated(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(P,MAT_CLASSID,2);
  PetscValidType(P,2);
  MatCheckPreallocated(P,2);
  if (!P->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (P->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  if (P->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",P->rmap->N,A->cmap->N);
  if (fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be >= 1.0",(double)fill);

  if (scall == MAT_REUSE_MATRIX) {
    PetscValidPointer(*C,5);
    PetscValidHeaderSpecific(*C,MAT_CLASSID,5);
    if (viatranspose || viamatmatmatmult) {
      Mat Pt;
      ierr = MatTranspose(P,MAT_INITIAL_MATRIX,&Pt);CHKERRQ(ierr);
      if (viamatmatmatmult) {
        ierr = MatMatMatMult(Pt,A,P,scall,fill,C);CHKERRQ(ierr);
      } else {
        Mat AP;
        ierr = MatMatMult(A,P,MAT_INITIAL_MATRIX,fill,&AP);CHKERRQ(ierr);
        ierr = MatMatMult(Pt,AP,scall,fill,C);CHKERRQ(ierr);
        ierr = MatDestroy(&AP);CHKERRQ(ierr);
      }
      ierr = MatDestroy(&Pt);CHKERRQ(ierr);
    } else {
      ierr = PetscLogEventBegin(MAT_PtAP,A,P,0,0);CHKERRQ(ierr);
      ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
      ierr = (*(*C)->ops->ptapnumeric)(A,P,*C);CHKERRQ(ierr);
      ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
      ierr = PetscLogEventEnd(MAT_PtAP,A,P,0,0);CHKERRQ(ierr);
    }
    PetscFunctionReturn(0);
  }

  if (fill == PETSC_DEFAULT || fill == PETSC_DECIDE) fill = 2.0;
  if (fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be >= 1.0",(double)fill);

  fA = A->ops->ptap;
  fP = P->ops->ptap;
  if (fP == fA) {
    if (!fA) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatPtAP not supported for A of type %s",((PetscObject)A)->type_name);
    ptap = fA;
  } else {
    /* dispatch based on the type of A and P from their PetscObject's PetscFunctionLists. */
    char ptapname[256];
    ierr = PetscStrcpy(ptapname,"MatPtAP_");CHKERRQ(ierr);
    ierr = PetscStrcat(ptapname,((PetscObject)A)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(ptapname,"_");CHKERRQ(ierr);
    ierr = PetscStrcat(ptapname,((PetscObject)P)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(ptapname,"_C");CHKERRQ(ierr); /* e.g., ptapname = "MatPtAP_seqdense_seqaij_C" */
    ierr = PetscObjectQueryFunction((PetscObject)P,ptapname,&ptap);CHKERRQ(ierr);
    if (!ptap) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"MatPtAP requires A, %s, to be compatible with P, %s",((PetscObject)A)->type_name,((PetscObject)P)->type_name);
  }

  if (viatranspose || viamatmatmatmult) {
    Mat Pt;
    ierr = MatTranspose(P,MAT_INITIAL_MATRIX,&Pt);CHKERRQ(ierr);
    if (viamatmatmatmult) {
      ierr = MatMatMatMult(Pt,A,P,scall,fill,C);CHKERRQ(ierr);
      ierr = PetscInfo(*C,"MatPtAP via MatMatMatMult\n");CHKERRQ(ierr);
    } else {
      Mat AP;
      ierr = MatMatMult(A,P,MAT_INITIAL_MATRIX,fill,&AP);CHKERRQ(ierr);
      ierr = MatMatMult(Pt,AP,scall,fill,C);CHKERRQ(ierr);
      ierr = MatDestroy(&AP);CHKERRQ(ierr);
      ierr = PetscInfo(*C,"MatPtAP via MatTranspose and MatMatMult\n");CHKERRQ(ierr);
    }
    ierr = MatDestroy(&Pt);CHKERRQ(ierr);
  } else {
    ierr = PetscLogEventBegin(MAT_PtAP,A,P,0,0);CHKERRQ(ierr);
    ierr = (*ptap)(A,P,scall,fill,C);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_PtAP,A,P,0,0);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPtAPNumeric"
/*@
   MatPtAPNumeric - Computes the matrix product C = P^T * A * P

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the matrix
-  P - the projection matrix

   Output Parameters:
.  C - the product matrix

   Notes:
   C must have been created by calling MatPtAPSymbolic and must be destroyed by
   the user using MatDeatroy().

   This routine is currently only implemented for pairs of AIJ matrices and classes
   which inherit from AIJ.  C will be of type MATAIJ.

   Level: intermediate

.seealso: MatPtAP(), MatPtAPSymbolic(), MatMatMultNumeric()
@*/
PetscErrorCode  MatPtAPNumeric(Mat A,Mat P,Mat C)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(P,MAT_CLASSID,2);
  PetscValidType(P,2);
  MatCheckPreallocated(P,2);
  if (!P->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (P->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(C,MAT_CLASSID,3);
  PetscValidType(C,3);
  MatCheckPreallocated(C,3);
  if (C->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (P->cmap->N!=C->rmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",P->cmap->N,C->rmap->N);
  if (P->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",P->rmap->N,A->cmap->N);
  if (A->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %D != %D",A->rmap->N,A->cmap->N);
  if (P->cmap->N!=C->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",P->cmap->N,C->cmap->N);
  MatCheckPreallocated(A,1);

  ierr = PetscLogEventBegin(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
  ierr = (*C->ops->ptapnumeric)(A,P,C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_PtAPNumeric,A,P,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPtAPSymbolic"
/*@
   MatPtAPSymbolic - Creates the (i,j) structure of the matrix product C = P^T * A * P

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the matrix
-  P - the projection matrix

   Output Parameters:
.  C - the (i,j) structure of the product matrix

   Notes:
   C will be created and must be destroyed by the user with MatDestroy().

   This routine is currently only implemented for pairs of SeqAIJ matrices and classes
   which inherit from SeqAIJ.  C will be of type MATSEQAIJ.  The product is computed using
   this (i,j) structure by calling MatPtAPNumeric().

   Level: intermediate

.seealso: MatPtAP(), MatPtAPNumeric(), MatMatMultSymbolic()
@*/
PetscErrorCode  MatPtAPSymbolic(Mat A,Mat P,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (fill <1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be >= 1.0",(double)fill);
  PetscValidHeaderSpecific(P,MAT_CLASSID,2);
  PetscValidType(P,2);
  MatCheckPreallocated(P,2);
  if (!P->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (P->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidPointer(C,3);

  if (P->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",P->rmap->N,A->cmap->N);
  if (A->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %D != %D",A->rmap->N,A->cmap->N);
  MatCheckPreallocated(A,1);
  ierr = PetscLogEventBegin(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);
  ierr = (*A->ops->ptapsymbolic)(A,P,fill,C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_PtAPSymbolic,A,P,0,0);CHKERRQ(ierr);

  /* ierr = MatSetBlockSize(*C,A->rmap->bs);CHKERRQ(ierr); NO! this is not always true -ma */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRARt"
/*@
   MatRARt - Creates the matrix product C = R * A * R^T

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the matrix
.  R - the projection matrix
.  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
-  fill - expected fill as ratio of nnz(C)/nnz(A)

   Output Parameters:
.  C - the product matrix

   Notes:
   C will be created and must be destroyed by the user with MatDestroy().

   This routine is currently only implemented for pairs of AIJ matrices and classes
   which inherit from AIJ.

   Level: intermediate

.seealso: MatRARtSymbolic(), MatRARtNumeric(), MatMatMult(), MatPtAP()
@*/
PetscErrorCode  MatRARt(Mat A,Mat R,MatReuse scall,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(R,MAT_CLASSID,2);
  PetscValidType(R,2);
  MatCheckPreallocated(R,2);
  if (!R->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (R->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidPointer(C,3);
  if (R->cmap->N!=A->rmap->N) SETERRQ2(PetscObjectComm((PetscObject)R),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",R->cmap->N,A->rmap->N);
  if (fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be >= 1.0",(double)fill);
  MatCheckPreallocated(A,1);

  if (!A->ops->rart) {
    MatType mattype;
    ierr = MatGetType(A,&mattype);CHKERRQ(ierr);
    SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Matrix of type <%s> does not support RARt",mattype);
  }
  ierr = PetscLogEventBegin(MAT_RARt,A,R,0,0);CHKERRQ(ierr);
  ierr = (*A->ops->rart)(A,R,scall,fill,C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_RARt,A,R,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRARtNumeric"
/*@
   MatRARtNumeric - Computes the matrix product C = R * A * R^T

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the matrix
-  R - the projection matrix

   Output Parameters:
.  C - the product matrix

   Notes:
   C must have been created by calling MatRARtSymbolic and must be destroyed by
   the user using MatDeatroy().

   This routine is currently only implemented for pairs of AIJ matrices and classes
   which inherit from AIJ.  C will be of type MATAIJ.

   Level: intermediate

.seealso: MatRARt(), MatRARtSymbolic(), MatMatMultNumeric()
@*/
PetscErrorCode  MatRARtNumeric(Mat A,Mat R,Mat C)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(R,MAT_CLASSID,2);
  PetscValidType(R,2);
  MatCheckPreallocated(R,2);
  if (!R->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (R->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(C,MAT_CLASSID,3);
  PetscValidType(C,3);
  MatCheckPreallocated(C,3);
  if (C->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (R->rmap->N!=C->rmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",R->rmap->N,C->rmap->N);
  if (R->cmap->N!=A->rmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",R->cmap->N,A->rmap->N);
  if (A->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %D != %D",A->rmap->N,A->cmap->N);
  if (R->rmap->N!=C->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",R->rmap->N,C->cmap->N);
  MatCheckPreallocated(A,1);

  ierr = PetscLogEventBegin(MAT_RARtNumeric,A,R,0,0);CHKERRQ(ierr);
  ierr = (*A->ops->rartnumeric)(A,R,C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_RARtNumeric,A,R,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRARtSymbolic"
/*@
   MatRARtSymbolic - Creates the (i,j) structure of the matrix product C = R * A * R^T

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the matrix
-  R - the projection matrix

   Output Parameters:
.  C - the (i,j) structure of the product matrix

   Notes:
   C will be created and must be destroyed by the user with MatDestroy().

   This routine is currently only implemented for pairs of SeqAIJ matrices and classes
   which inherit from SeqAIJ.  C will be of type MATSEQAIJ.  The product is computed using
   this (i,j) structure by calling MatRARtNumeric().

   Level: intermediate

.seealso: MatRARt(), MatRARtNumeric(), MatMatMultSymbolic()
@*/
PetscErrorCode  MatRARtSymbolic(Mat A,Mat R,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (fill <1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be >= 1.0",(double)fill);
  PetscValidHeaderSpecific(R,MAT_CLASSID,2);
  PetscValidType(R,2);
  MatCheckPreallocated(R,2);
  if (!R->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (R->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidPointer(C,3);

  if (R->cmap->N!=A->rmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",R->cmap->N,A->rmap->N);
  if (A->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix 'A' must be square, %D != %D",A->rmap->N,A->cmap->N);
  MatCheckPreallocated(A,1);
  ierr = PetscLogEventBegin(MAT_RARtSymbolic,A,R,0,0);CHKERRQ(ierr);
  ierr = (*A->ops->rartsymbolic)(A,R,fill,C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_RARtSymbolic,A,R,0,0);CHKERRQ(ierr);

  ierr = MatSetBlockSizes(*C,PetscAbs(R->rmap->bs),PetscAbs(R->rmap->bs));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMult"
/*@
   MatMatMult - Performs Matrix-Matrix Multiplication C=A*B.

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the left matrix
.  B - the right matrix
.  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
-  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if you do not have a good estimate
          if the result is a dense matrix this is irrelevent

   Output Parameters:
.  C - the product matrix

   Notes:
   Unless scall is MAT_REUSE_MATRIX C will be created.

   MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call

   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
   actually needed.

   If you have many matrices with the same non-zero structure to multiply, you
   should either
$   1) use MAT_REUSE_MATRIX in all calls but the first or
$   2) call MatMatMultSymbolic() once and then MatMatMultNumeric() for each product needed

   Level: intermediate

.seealso: MatMatMultSymbolic(), MatMatMultNumeric(), MatTransposeMatMult(),  MatMatTransposeMult(), MatPtAP()
@*/
PetscErrorCode  MatMatMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;
  PetscErrorCode (*fA)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*fB)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*mult)(Mat,Mat,MatReuse,PetscReal,Mat*)=NULL;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  MatCheckPreallocated(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidType(B,2);
  MatCheckPreallocated(B,2);
  if (!B->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (B->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidPointer(C,3);
  if (B->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",B->rmap->N,A->cmap->N);
  if (scall == MAT_REUSE_MATRIX) {
    PetscValidPointer(*C,5);
    PetscValidHeaderSpecific(*C,MAT_CLASSID,5);
    ierr = PetscLogEventBegin(MAT_MatMult,A,B,0,0);CHKERRQ(ierr);
    ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
    ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_MatMult,A,B,0,0);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (fill == PETSC_DEFAULT || fill == PETSC_DECIDE) fill = 2.0;
  if (fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be >= 1.0",(double)fill);

  fA = A->ops->matmult;
  fB = B->ops->matmult;
  if (fB == fA) {
    if (!fB) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatMatMult not supported for B of type %s",((PetscObject)B)->type_name);
    mult = fB;
  } else {
    /* dispatch based on the type of A and B from their PetscObject's PetscFunctionLists. */
    char multname[256];
    ierr = PetscStrcpy(multname,"MatMatMult_");CHKERRQ(ierr);
    ierr = PetscStrcat(multname,((PetscObject)A)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(multname,"_");CHKERRQ(ierr);
    ierr = PetscStrcat(multname,((PetscObject)B)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(multname,"_C");CHKERRQ(ierr); /* e.g., multname = "MatMatMult_seqdense_seqaij_C" */
    ierr = PetscObjectQueryFunction((PetscObject)B,multname,&mult);CHKERRQ(ierr);
    if (!mult) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"MatMatMult requires A, %s, to be compatible with B, %s",((PetscObject)A)->type_name,((PetscObject)B)->type_name);
  }
  ierr = PetscLogEventBegin(MAT_MatMult,A,B,0,0);CHKERRQ(ierr);
  ierr = (*mult)(A,B,scall,fill,C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MatMult,A,B,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMultSymbolic"
/*@
   MatMatMultSymbolic - Performs construction, preallocation, and computes the ij structure
   of the matrix-matrix product C=A*B.  Call this routine before calling MatMatMultNumeric().

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the left matrix
.  B - the right matrix
-  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if you do not have a good estimate,
      if C is a dense matrix this is irrelevent

   Output Parameters:
.  C - the product matrix

   Notes:
   Unless scall is MAT_REUSE_MATRIX C will be created.

   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
   actually needed.

   This routine is currently implemented for
    - pairs of AIJ matrices and classes which inherit from AIJ, C will be of type AIJ
    - pairs of AIJ (A) and Dense (B) matrix, C will be of type Dense.
    - pairs of Dense (A) and AIJ (B) matrix, C will be of type Dense.

   Level: intermediate

   Developers Note: There are ways to estimate the number of nonzeros in the resulting product, see for example, http://arxiv.org/abs/1006.4173
     We should incorporate them into PETSc.

.seealso: MatMatMult(), MatMatMultNumeric()
@*/
PetscErrorCode  MatMatMultSymbolic(Mat A,Mat B,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;
  PetscErrorCode (*Asymbolic)(Mat,Mat,PetscReal,Mat*);
  PetscErrorCode (*Bsymbolic)(Mat,Mat,PetscReal,Mat*);
  PetscErrorCode (*symbolic)(Mat,Mat,PetscReal,Mat*)=NULL;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidType(B,2);
  MatCheckPreallocated(B,2);
  if (!B->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (B->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidPointer(C,3);

  if (B->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",B->rmap->N,A->cmap->N);
  if (fill == PETSC_DEFAULT) fill = 2.0;
  if (fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be > 1.0",(double)fill);
  MatCheckPreallocated(A,1);

  Asymbolic = A->ops->matmultsymbolic;
  Bsymbolic = B->ops->matmultsymbolic;
  if (Asymbolic == Bsymbolic) {
    if (!Bsymbolic) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"C=A*B not implemented for B of type %s",((PetscObject)B)->type_name);
    symbolic = Bsymbolic;
  } else { /* dispatch based on the type of A and B */
    char symbolicname[256];
    ierr = PetscStrcpy(symbolicname,"MatMatMultSymbolic_");CHKERRQ(ierr);
    ierr = PetscStrcat(symbolicname,((PetscObject)A)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(symbolicname,"_");CHKERRQ(ierr);
    ierr = PetscStrcat(symbolicname,((PetscObject)B)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(symbolicname,"_C");CHKERRQ(ierr);
    ierr = PetscObjectQueryFunction((PetscObject)B,symbolicname,&symbolic);CHKERRQ(ierr);
    if (!symbolic) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"MatMatMultSymbolic requires A, %s, to be compatible with B, %s",((PetscObject)A)->type_name,((PetscObject)B)->type_name);
  }
  ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
  ierr = (*symbolic)(A,B,fill,C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMultNumeric"
/*@
   MatMatMultNumeric - Performs the numeric matrix-matrix product.
   Call this routine after first calling MatMatMultSymbolic().

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the left matrix
-  B - the right matrix

   Output Parameters:
.  C - the product matrix, which was created by from MatMatMultSymbolic() or a call to MatMatMult().

   Notes:
   C must have been created with MatMatMultSymbolic().

   This routine is currently implemented for
    - pairs of AIJ matrices and classes which inherit from AIJ, C will be of type MATAIJ.
    - pairs of AIJ (A) and Dense (B) matrix, C will be of type Dense.
    - pairs of Dense (A) and AIJ (B) matrix, C will be of type Dense.

   Level: intermediate

.seealso: MatMatMult(), MatMatMultSymbolic()
@*/
PetscErrorCode  MatMatMultNumeric(Mat A,Mat B,Mat C)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatMatMult(A,B,MAT_REUSE_MATRIX,0.0,&C);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatTransposeMult"
/*@
   MatMatTransposeMult - Performs Matrix-Matrix Multiplication C=A*B^T.

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the left matrix
.  B - the right matrix
.  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
-  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if not known

   Output Parameters:
.  C - the product matrix

   Notes:
   C will be created if MAT_INITIAL_MATRIX and must be destroyed by the user with MatDestroy().

   MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call

  To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
   actually needed.

   This routine is currently only implemented for pairs of SeqAIJ matrices.  C will be of type MATSEQAIJ.

   Level: intermediate

.seealso: MatMatTransposeMultSymbolic(), MatMatTransposeMultNumeric(), MatMatMult(), MatTransposeMatMult() MatPtAP()
@*/
PetscErrorCode  MatMatTransposeMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;
  PetscErrorCode (*fA)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*fB)(Mat,Mat,MatReuse,PetscReal,Mat*);

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidType(B,2);
  MatCheckPreallocated(B,2);
  if (!B->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (B->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidPointer(C,3);
  if (B->cmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, AN %D != BN %D",A->cmap->N,B->cmap->N);
  if (fill == PETSC_DEFAULT || fill == PETSC_DECIDE) fill = 2.0;
  if (fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be > 1.0",(double)fill);
  MatCheckPreallocated(A,1);

  fA = A->ops->mattransposemult;
  if (!fA) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatMatTransposeMult not supported for A of type %s",((PetscObject)A)->type_name);
  fB = B->ops->mattransposemult;
  if (!fB) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatMatTransposeMult not supported for B of type %s",((PetscObject)B)->type_name);
  if (fB!=fA) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"MatMatTransposeMult requires A, %s, to be compatible with B, %s",((PetscObject)A)->type_name,((PetscObject)B)->type_name);

  ierr = PetscLogEventBegin(MAT_MatTransposeMult,A,B,0,0);CHKERRQ(ierr);
  if (scall == MAT_INITIAL_MATRIX) {
    ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
    ierr = (*A->ops->mattransposemultsymbolic)(A,B,fill,C);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
  }
  ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
  ierr = (*A->ops->mattransposemultnumeric)(A,B,*C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MatTransposeMult,A,B,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatTransposeMatMult"
/*@
   MatTransposeMatMult - Performs Matrix-Matrix Multiplication C=A^T*B.

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the left matrix
.  B - the right matrix
.  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
-  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if not known

   Output Parameters:
.  C - the product matrix

   Notes:
   C will be created if MAT_INITIAL_MATRIX and must be destroyed by the user with MatDestroy().

   MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call

  To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
   actually needed.

   This routine is currently implemented for pairs of AIJ matrices and pairs of SeqDense matrices and classes
   which inherit from SeqAIJ.  C will be of same type as the input matrices.

   Level: intermediate

.seealso: MatTransposeMatMultSymbolic(), MatTransposeMatMultNumeric(), MatMatMult(), MatMatTransposeMult(), MatPtAP()
@*/
PetscErrorCode  MatTransposeMatMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
{
  PetscErrorCode ierr;
  PetscErrorCode (*fA)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*fB)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*transposematmult)(Mat,Mat,MatReuse,PetscReal,Mat*) = NULL;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidType(B,2);
  MatCheckPreallocated(B,2);
  if (!B->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (B->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidPointer(C,3);
  if (B->rmap->N!=A->rmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",B->rmap->N,A->rmap->N);
  if (fill == PETSC_DEFAULT || fill == PETSC_DECIDE) fill = 2.0;
  if (fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be > 1.0",(double)fill);
  MatCheckPreallocated(A,1);

  fA = A->ops->transposematmult;
  fB = B->ops->transposematmult;
  if (fB==fA) {
    if (!fA) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatTransposeMatMult not supported for A of type %s",((PetscObject)A)->type_name);
    transposematmult = fA;
  } else {
    /* dispatch based on the type of A and B from their PetscObject's PetscFunctionLists. */
    char multname[256];
    ierr = PetscStrcpy(multname,"MatTransposeMatMult_");CHKERRQ(ierr);
    ierr = PetscStrcat(multname,((PetscObject)A)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(multname,"_");CHKERRQ(ierr);
    ierr = PetscStrcat(multname,((PetscObject)B)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(multname,"_C");CHKERRQ(ierr); /* e.g., multname = "MatMatMult_seqdense_seqaij_C" */
    ierr = PetscObjectQueryFunction((PetscObject)B,multname,&transposematmult);CHKERRQ(ierr);
    if (!transposematmult) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"MatTransposeMatMult requires A, %s, to be compatible with B, %s",((PetscObject)A)->type_name,((PetscObject)B)->type_name);
  }
  ierr = PetscLogEventBegin(MAT_TransposeMatMult,A,B,0,0);CHKERRQ(ierr);
  ierr = (*transposematmult)(A,B,scall,fill,C);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_TransposeMatMult,A,B,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMatMatMult"
/*@
   MatMatMatMult - Performs Matrix-Matrix-Matrix Multiplication D=A*B*C.

   Neighbor-wise Collective on Mat

   Input Parameters:
+  A - the left matrix
.  B - the middle matrix
.  C - the right matrix
.  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
-  fill - expected fill as ratio of nnz(D)/(nnz(A) + nnz(B)+nnz(C)), use PETSC_DEFAULT if you do not have a good estimate
          if the result is a dense matrix this is irrelevent

   Output Parameters:
.  D - the product matrix

   Notes:
   Unless scall is MAT_REUSE_MATRIX D will be created.

   MAT_REUSE_MATRIX can only be used if the matrices A, B and C have the same nonzero pattern as in the previous call

   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
   actually needed.

   If you have many matrices with the same non-zero structure to multiply, you
   should either
$   1) use MAT_REUSE_MATRIX in all calls but the first or
$   2) call MatMatMatMultSymbolic() once and then MatMatMatMultNumeric() for each product needed

   Level: intermediate

.seealso: MatMatMult, MatPtAP()
@*/
PetscErrorCode  MatMatMatMult(Mat A,Mat B,Mat C,MatReuse scall,PetscReal fill,Mat *D)
{
  PetscErrorCode ierr;
  PetscErrorCode (*fA)(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*fB)(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*fC)(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*mult)(Mat,Mat,Mat,MatReuse,PetscReal,Mat*)=NULL;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A,MAT_CLASSID,1);
  PetscValidType(A,1);
  MatCheckPreallocated(A,1);
  if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(B,MAT_CLASSID,2);
  PetscValidType(B,2);
  MatCheckPreallocated(B,2);
  if (!B->assembled) SETERRQ(PetscObjectComm((PetscObject)B),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (B->factortype) SETERRQ(PetscObjectComm((PetscObject)B),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  PetscValidHeaderSpecific(C,MAT_CLASSID,3);
  PetscValidPointer(C,3);
  MatCheckPreallocated(C,3);
  if (!C->assembled) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (C->factortype) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (B->rmap->N!=A->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)B),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",B->rmap->N,A->cmap->N);
  if (C->rmap->N!=B->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_SIZ,"Matrix dimensions are incompatible, %D != %D",C->rmap->N,B->cmap->N);
  if (scall == MAT_REUSE_MATRIX) {
    PetscValidPointer(*D,6);
    PetscValidHeaderSpecific(*D,MAT_CLASSID,6);
    ierr = PetscLogEventBegin(MAT_MatMatMult,A,B,0,0);CHKERRQ(ierr);
    ierr = (*(*D)->ops->matmatmult)(A,B,C,scall,fill,D);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_MatMatMult,A,B,0,0);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (fill == PETSC_DEFAULT || fill == PETSC_DECIDE) fill = 2.0;
  if (fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Expected fill=%g must be >= 1.0",(double)fill);

  fA = A->ops->matmatmult;
  fB = B->ops->matmatmult;
  fC = C->ops->matmatmult;
  if (fA == fB && fA == fC) {
    if (!fA) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatMatMatMult not supported for A of type %s",((PetscObject)A)->type_name);
    mult = fA;
  } else {
    /* dispatch based on the type of A, B and C from their PetscObject's PetscFunctionLists. */
    char multname[256];
    ierr = PetscStrcpy(multname,"MatMatMatMult_");CHKERRQ(ierr);
    ierr = PetscStrcat(multname,((PetscObject)A)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(multname,"_");CHKERRQ(ierr);
    ierr = PetscStrcat(multname,((PetscObject)B)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(multname,"_");CHKERRQ(ierr);
    ierr = PetscStrcat(multname,((PetscObject)C)->type_name);CHKERRQ(ierr);
    ierr = PetscStrcat(multname,"_C");CHKERRQ(ierr);
    ierr = PetscObjectQueryFunction((PetscObject)B,multname,&mult);CHKERRQ(ierr);
    if (!mult) SETERRQ3(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"MatMatMatMult requires A, %s, to be compatible with B, %s, C, %s",((PetscObject)A)->type_name,((PetscObject)B)->type_name,((PetscObject)C)->type_name);
  }
  ierr = PetscLogEventBegin(MAT_MatMatMult,A,B,0,0);CHKERRQ(ierr);
  ierr = (*mult)(A,B,C,scall,fill,D);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_MatMatMult,A,B,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCreateRedundantMatrix"
/*@C
   MatCreateRedundantMatrix - Create redundant matrices and put them into processors of subcommunicators.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  nsubcomm - the number of subcommunicators (= number of redundant parallel or sequential matrices)
.  subcomm - MPI communicator split from the communicator where mat resides in (or MPI_COMM_NULL if nsubcomm is used)
-  reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

   Output Parameter:
.  matredundant - redundant matrix

   Notes:
   MAT_REUSE_MATRIX can only be used when the nonzero structure of the
   original matrix has not changed from that last call to MatCreateRedundantMatrix().

   This routine creates the duplicated matrices in subcommunicators; you should NOT create them before
   calling it.

   Level: advanced

   Concepts: subcommunicator
   Concepts: duplicate matrix

.seealso: MatDestroy()
@*/
PetscErrorCode MatCreateRedundantMatrix(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,MatReuse reuse,Mat *matredundant)
{
  PetscErrorCode ierr;
  MPI_Comm       comm;
  PetscMPIInt    size;
  PetscInt       mloc_sub,rstart,rend,M=mat->rmap->N,N=mat->cmap->N,bs=mat->rmap->bs;
  Mat_Redundant  *redund=NULL;
  PetscSubcomm   psubcomm=NULL;
  MPI_Comm       subcomm_in=subcomm;
  Mat            *matseq;
  IS             isrow,iscol;
  PetscBool      newsubcomm=PETSC_FALSE;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
  if (size == 1 || nsubcomm == 1) {
    if (reuse == MAT_INITIAL_MATRIX) {
      ierr = MatDuplicate(mat,MAT_COPY_VALUES,matredundant);CHKERRQ(ierr);
    } else {
      ierr = MatCopy(mat,*matredundant,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
    }
    PetscFunctionReturn(0);
  }

  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (nsubcomm && reuse == MAT_REUSE_MATRIX) {
    PetscValidPointer(*matredundant,5);
    PetscValidHeaderSpecific(*matredundant,MAT_CLASSID,5);
  }
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  MatCheckPreallocated(mat,1);

  ierr = PetscLogEventBegin(MAT_RedundantMat,mat,0,0,0);CHKERRQ(ierr);
  if (subcomm_in == MPI_COMM_NULL && reuse == MAT_INITIAL_MATRIX) { /* get subcomm if user does not provide subcomm */
    /* create psubcomm, then get subcomm */
    ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
    ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
    if (nsubcomm < 1 || nsubcomm > size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"nsubcomm must between 1 and %D",size);

    ierr = PetscSubcommCreate(comm,&psubcomm);CHKERRQ(ierr);
    ierr = PetscSubcommSetNumber(psubcomm,nsubcomm);CHKERRQ(ierr);
    ierr = PetscSubcommSetType(psubcomm,PETSC_SUBCOMM_CONTIGUOUS);CHKERRQ(ierr);
    ierr = PetscSubcommSetFromOptions(psubcomm);CHKERRQ(ierr);
    ierr = PetscCommDuplicate(PetscSubcommChild(psubcomm),&subcomm,NULL);CHKERRQ(ierr);
    newsubcomm = PETSC_TRUE;
    ierr = PetscSubcommDestroy(&psubcomm);CHKERRQ(ierr);
  }

  /* get isrow, iscol and a local sequential matrix matseq[0] */
  if (reuse == MAT_INITIAL_MATRIX) {
    mloc_sub = PETSC_DECIDE;
    if (bs < 1) {
      ierr = PetscSplitOwnership(subcomm,&mloc_sub,&M);CHKERRQ(ierr);
    } else {
      ierr = PetscSplitOwnershipBlock(subcomm,bs,&mloc_sub,&M);CHKERRQ(ierr);
    }
    ierr = MPI_Scan(&mloc_sub,&rend,1,MPIU_INT,MPI_SUM,subcomm);CHKERRQ(ierr);
    rstart = rend - mloc_sub;
    ierr = ISCreateStride(PETSC_COMM_SELF,mloc_sub,rstart,1,&isrow);CHKERRQ(ierr);
    ierr = ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol);CHKERRQ(ierr);
  } else { /* reuse == MAT_REUSE_MATRIX */
    /* retrieve subcomm */
    ierr = PetscObjectGetComm((PetscObject)(*matredundant),&subcomm);CHKERRQ(ierr);
    redund = (*matredundant)->redundant;
    isrow  = redund->isrow;
    iscol  = redund->iscol;
    matseq = redund->matseq;
  }
  ierr = MatGetSubMatrices(mat,1,&isrow,&iscol,reuse,&matseq);CHKERRQ(ierr);

  /* get matredundant over subcomm */
  if (reuse == MAT_INITIAL_MATRIX) {
    ierr = MatCreateMPIMatConcatenateSeqMat(subcomm,matseq[0],mloc_sub,reuse,matredundant);CHKERRQ(ierr);

    /* create a supporting struct and attach it to C for reuse */
    ierr = PetscNewLog(*matredundant,&redund);CHKERRQ(ierr);
    (*matredundant)->redundant = redund;
    redund->isrow              = isrow;
    redund->iscol              = iscol;
    redund->matseq             = matseq;
    if (newsubcomm) {
      redund->subcomm          = subcomm;
    } else {
      redund->subcomm          = MPI_COMM_NULL;
    }
  } else {
    ierr = MatCreateMPIMatConcatenateSeqMat(subcomm,matseq[0],PETSC_DECIDE,reuse,matredundant);CHKERRQ(ierr);
  }
  ierr = PetscLogEventEnd(MAT_RedundantMat,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetMultiProcBlock"
/*@C
   MatGetMultiProcBlock - Create multiple [bjacobi] 'parallel submatrices' from
   a given 'mat' object. Each submatrix can span multiple procs.

   Collective on Mat

   Input Parameters:
+  mat - the matrix
.  subcomm - the subcommunicator obtained by com_split(comm)
-  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

   Output Parameter:
.  subMat - 'parallel submatrices each spans a given subcomm

  Notes:
  The submatrix partition across processors is dictated by 'subComm' a
  communicator obtained by com_split(comm). The comm_split
  is not restriced to be grouped with consecutive original ranks.

  Due the comm_split() usage, the parallel layout of the submatrices
  map directly to the layout of the original matrix [wrt the local
  row,col partitioning]. So the original 'DiagonalMat' naturally maps
  into the 'DiagonalMat' of the subMat, hence it is used directly from
  the subMat. However the offDiagMat looses some columns - and this is
  reconstructed with MatSetValues()

  Level: advanced

  Concepts: subcommunicator
  Concepts: submatrices

.seealso: MatGetSubMatrices()
@*/
PetscErrorCode   MatGetMultiProcBlock(Mat mat, MPI_Comm subComm, MatReuse scall,Mat *subMat)
{
  PetscErrorCode ierr;
  PetscMPIInt    commsize,subCommSize;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&commsize);CHKERRQ(ierr);
  ierr = MPI_Comm_size(subComm,&subCommSize);CHKERRQ(ierr);
  if (subCommSize > commsize) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"CommSize %D < SubCommZize %D",commsize,subCommSize);

  ierr = PetscLogEventBegin(MAT_GetMultiProcBlock,mat,0,0,0);CHKERRQ(ierr);
  ierr = (*mat->ops->getmultiprocblock)(mat,subComm,scall,subMat);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_GetMultiProcBlock,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetLocalSubMatrix"
/*@
   MatGetLocalSubMatrix - Gets a reference to a submatrix specified in local numbering

   Not Collective

   Input Arguments:
   mat - matrix to extract local submatrix from
   isrow - local row indices for submatrix
   iscol - local column indices for submatrix

   Output Arguments:
   submat - the submatrix

   Level: intermediate

   Notes:
   The submat should be returned with MatRestoreLocalSubMatrix().

   Depending on the format of mat, the returned submat may not implement MatMult().  Its communicator may be
   the same as mat, it may be PETSC_COMM_SELF, or some other subcomm of mat's.

   The submat always implements MatSetValuesLocal().  If isrow and iscol have the same block size, then
   MatSetValuesBlockedLocal() will also be implemented.

.seealso: MatRestoreLocalSubMatrix(), MatCreateLocalRef()
@*/
PetscErrorCode  MatGetLocalSubMatrix(Mat mat,IS isrow,IS iscol,Mat *submat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(isrow,IS_CLASSID,2);
  PetscValidHeaderSpecific(iscol,IS_CLASSID,3);
  PetscCheckSameComm(isrow,2,iscol,3);
  PetscValidPointer(submat,4);

  if (mat->ops->getlocalsubmatrix) {
    ierr = (*mat->ops->getlocalsubmatrix)(mat,isrow,iscol,submat);CHKERRQ(ierr);
  } else {
    ierr = MatCreateLocalRef(mat,isrow,iscol,submat);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatRestoreLocalSubMatrix"
/*@
   MatRestoreLocalSubMatrix - Restores a reference to a submatrix specified in local numbering

   Not Collective

   Input Arguments:
   mat - matrix to extract local submatrix from
   isrow - local row indices for submatrix
   iscol - local column indices for submatrix
   submat - the submatrix

   Level: intermediate

.seealso: MatGetLocalSubMatrix()
@*/
PetscErrorCode  MatRestoreLocalSubMatrix(Mat mat,IS isrow,IS iscol,Mat *submat)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidHeaderSpecific(isrow,IS_CLASSID,2);
  PetscValidHeaderSpecific(iscol,IS_CLASSID,3);
  PetscCheckSameComm(isrow,2,iscol,3);
  PetscValidPointer(submat,4);
  if (*submat) {
    PetscValidHeaderSpecific(*submat,MAT_CLASSID,4);
  }

  if (mat->ops->restorelocalsubmatrix) {
    ierr = (*mat->ops->restorelocalsubmatrix)(mat,isrow,iscol,submat);CHKERRQ(ierr);
  } else {
    ierr = MatDestroy(submat);CHKERRQ(ierr);
  }
  *submat = NULL;
  PetscFunctionReturn(0);
}

/* --------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "MatFindZeroDiagonals"
/*@
   MatFindZeroDiagonals - Finds all the rows of a matrix that have zero or no entry in the matrix

   Collective on Mat

   Input Parameter:
.  mat - the matrix

   Output Parameter:
.  is - if any rows have zero diagonals this contains the list of them

   Level: developer

   Concepts: matrix-vector product

.seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
@*/
PetscErrorCode  MatFindZeroDiagonals(Mat mat,IS *is)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  if (!mat->ops->findzerodiagonals) {
    Vec                diag;
    const PetscScalar *a;
    PetscInt          *rows;
    PetscInt           rStart, rEnd, r, nrow = 0;

    ierr = MatCreateVecs(mat, &diag, NULL);CHKERRQ(ierr);
    ierr = MatGetDiagonal(mat, diag);CHKERRQ(ierr);
    ierr = MatGetOwnershipRange(mat, &rStart, &rEnd);CHKERRQ(ierr);
    ierr = VecGetArrayRead(diag, &a);CHKERRQ(ierr);
    for (r = 0; r < rEnd-rStart; ++r) if (a[r] == 0.0) ++nrow;
    ierr = PetscMalloc1(nrow, &rows);CHKERRQ(ierr);
    nrow = 0;
    for (r = 0; r < rEnd-rStart; ++r) if (a[r] == 0.0) rows[nrow++] = r+rStart;
    ierr = VecRestoreArrayRead(diag, &a);CHKERRQ(ierr);
    ierr = VecDestroy(&diag);CHKERRQ(ierr);
    ierr = ISCreateGeneral(PetscObjectComm((PetscObject) mat), nrow, rows, PETSC_OWN_POINTER, is);CHKERRQ(ierr);
  } else {
    ierr = (*mat->ops->findzerodiagonals)(mat, is);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFindOffBlockDiagonalEntries"
/*@
   MatFindOffBlockDiagonalEntries - Finds all the rows of a matrix that have entries outside of the main diagonal block (defined by the matrix block size)

   Collective on Mat

   Input Parameter:
.  mat - the matrix

   Output Parameter:
.  is - contains the list of rows with off block diagonal entries

   Level: developer

   Concepts: matrix-vector product

.seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
@*/
PetscErrorCode  MatFindOffBlockDiagonalEntries(Mat mat,IS *is)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  PetscValidType(mat,1);
  if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

  if (!mat->ops->findoffblockdiagonalentries) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"This matrix type does not have a find off block diagonal entries defined");
  ierr = (*mat->ops->findoffblockdiagonalentries)(mat,is);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatInvertBlockDiagonal"
/*@C
  MatInvertBlockDiagonal - Inverts the block diagonal entries.

  Collective on Mat

  Input Parameters:
. mat - the matrix

  Output Parameters:
. values - the block inverses in column major order (FORTRAN-like)

   Note:
   This routine is not available from Fortran.

  Level: advanced
@*/
PetscErrorCode MatInvertBlockDiagonal(Mat mat,const PetscScalar **values)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
  if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
  if (!mat->ops->invertblockdiagonal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported");
  ierr = (*mat->ops->invertblockdiagonal)(mat,values);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatTransposeColoringDestroy"
/*@C
    MatTransposeColoringDestroy - Destroys a coloring context for matrix product C=A*B^T that was created
    via MatTransposeColoringCreate().

    Collective on MatTransposeColoring

    Input Parameter:
.   c - coloring context

    Level: intermediate

.seealso: MatTransposeColoringCreate()
@*/
PetscErrorCode  MatTransposeColoringDestroy(MatTransposeColoring *c)
{
  PetscErrorCode       ierr;
  MatTransposeColoring matcolor=*c;

  PetscFunctionBegin;
  if (!matcolor) PetscFunctionReturn(0);
  if (--((PetscObject)matcolor)->refct > 0) {matcolor = 0; PetscFunctionReturn(0);}

  ierr = PetscFree3(matcolor->ncolumns,matcolor->nrows,matcolor->colorforrow);CHKERRQ(ierr);
  ierr = PetscFree(matcolor->rows);CHKERRQ(ierr);
  ierr = PetscFree(matcolor->den2sp);CHKERRQ(ierr);
  ierr = PetscFree(matcolor->colorforcol);CHKERRQ(ierr);
  ierr = PetscFree(matcolor->columns);CHKERRQ(ierr);
  if (matcolor->brows>0) {
    ierr = PetscFree(matcolor->lstart);CHKERRQ(ierr);
  }
  ierr = PetscHeaderDestroy(c);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatTransColoringApplySpToDen"
/*@C
    MatTransColoringApplySpToDen - Given a symbolic matrix product C=A*B^T for which
    a MatTransposeColoring context has been created, computes a dense B^T by Apply
    MatTransposeColoring to sparse B.

    Collective on MatTransposeColoring

    Input Parameters:
+   B - sparse matrix B
.   Btdense - symbolic dense matrix B^T
-   coloring - coloring context created with MatTransposeColoringCreate()

    Output Parameter:
.   Btdense - dense matrix B^T

    Options Database Keys:
+    -mat_transpose_coloring_view - Activates basic viewing or coloring
.    -mat_transpose_coloring_view_draw - Activates drawing of coloring
-    -mat_transpose_coloring_view_info - Activates viewing of coloring info

    Level: intermediate

.seealso: MatTransposeColoringCreate(), MatTransposeColoringDestroy()

.keywords: coloring
@*/
PetscErrorCode MatTransColoringApplySpToDen(MatTransposeColoring coloring,Mat B,Mat Btdense)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(B,MAT_CLASSID,1);
  PetscValidHeaderSpecific(Btdense,MAT_CLASSID,2);
  PetscValidHeaderSpecific(coloring,MAT_TRANSPOSECOLORING_CLASSID,3);

  if (!B->ops->transcoloringapplysptoden) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for this matrix type %s",((PetscObject)B)->type_name);
  ierr = (B->ops->transcoloringapplysptoden)(coloring,B,Btdense);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatTransColoringApplyDenToSp"
/*@C
    MatTransColoringApplyDenToSp - Given a symbolic matrix product Csp=A*B^T for which
    a MatTransposeColoring context has been created and a dense matrix Cden=A*Btdense
    in which Btdens is obtained from MatTransColoringApplySpToDen(), recover sparse matrix
    Csp from Cden.

    Collective on MatTransposeColoring

    Input Parameters:
+   coloring - coloring context created with MatTransposeColoringCreate()
-   Cden - matrix product of a sparse matrix and a dense matrix Btdense

    Output Parameter:
.   Csp - sparse matrix

    Options Database Keys:
+    -mat_multtranspose_coloring_view - Activates basic viewing or coloring
.    -mat_multtranspose_coloring_view_draw - Activates drawing of coloring
-    -mat_multtranspose_coloring_view_info - Activates viewing of coloring info

    Level: intermediate

.seealso: MatTransposeColoringCreate(), MatTransposeColoringDestroy(), MatTransColoringApplySpToDen()

.keywords: coloring
@*/
PetscErrorCode MatTransColoringApplyDenToSp(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(matcoloring,MAT_TRANSPOSECOLORING_CLASSID,1);
  PetscValidHeaderSpecific(Cden,MAT_CLASSID,2);
  PetscValidHeaderSpecific(Csp,MAT_CLASSID,3);

  if (!Csp->ops->transcoloringapplydentosp) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for this matrix type %s",((PetscObject)Csp)->type_name);
  ierr = (Csp->ops->transcoloringapplydentosp)(matcoloring,Cden,Csp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatTransposeColoringCreate"
/*@C
   MatTransposeColoringCreate - Creates a matrix coloring context for matrix product C=A*B^T.

   Collective on Mat

   Input Parameters:
+  mat - the matrix product C
-  iscoloring - the coloring of the matrix; usually obtained with MatColoringCreate() or DMCreateColoring()

    Output Parameter:
.   color - the new coloring context

    Level: intermediate

.seealso: MatTransposeColoringDestroy(), MatTransposeColoringSetFromOptions(), MatTransColoringApplySpToDen(),
           MatTransColoringApplyDenToSp(), MatTransposeColoringView(),
@*/
PetscErrorCode  MatTransposeColoringCreate(Mat mat,ISColoring iscoloring,MatTransposeColoring *color)
{
  MatTransposeColoring c;
  MPI_Comm             comm;
  PetscErrorCode       ierr;

  PetscFunctionBegin;
  ierr = PetscLogEventBegin(MAT_TransposeColoringCreate,mat,0,0,0);CHKERRQ(ierr);
  ierr = PetscObjectGetComm((PetscObject)mat,&comm);CHKERRQ(ierr);
  ierr = PetscHeaderCreate(c,MAT_TRANSPOSECOLORING_CLASSID,"MatTransposeColoring","Matrix product C=A*B^T via coloring","Mat",comm,MatTransposeColoringDestroy,NULL);CHKERRQ(ierr);

  c->ctype = iscoloring->ctype;
  if (mat->ops->transposecoloringcreate) {
    ierr = (*mat->ops->transposecoloringcreate)(mat,iscoloring,c);CHKERRQ(ierr);
  } else SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Code not yet written for this matrix type");

  *color = c;
  ierr   = PetscLogEventEnd(MAT_TransposeColoringCreate,mat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetNonzeroState"
/*@
      MatGetNonzeroState - Returns a 64 bit integer representing the current state of nonzeros in the matrix. If the
        matrix has had no new nonzero locations added to the matrix since the previous call then the value will be the
        same, otherwise it will be larger

     Not Collective

  Input Parameter:
.    A  - the matrix

  Output Parameter:
.    state - the current state

  Notes: You can only compare states from two different calls to the SAME matrix, you cannot compare calls between
         different matrices

  Level: intermediate

@*/
PetscErrorCode MatGetNonzeroState(Mat mat,PetscObjectState *state)
{
  PetscFunctionBegin;
  PetscValidHeaderSpecific(mat,MAT_CLASSID,1);
  *state = mat->nonzerostate;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCreateMPIMatConcatenateSeqMat"
/*@
      MatCreateMPIMatConcatenateSeqMat - Creates a single large PETSc matrix by concatenating sequential
                 matrices from each processor

    Collective on MPI_Comm

   Input Parameters:
+    comm - the communicators the parallel matrix will live on
.    seqmat - the input sequential matrices
.    n - number of local columns (or PETSC_DECIDE)
-    reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

   Output Parameter:
.    mpimat - the parallel matrix generated

    Level: advanced

   Notes: The number of columns of the matrix in EACH processor MUST be the same.

@*/
PetscErrorCode MatCreateMPIMatConcatenateSeqMat(MPI_Comm comm,Mat seqmat,PetscInt n,MatReuse reuse,Mat *mpimat)
{
  PetscErrorCode ierr;
  PetscMPIInt    size;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  if (size == 1) {
    if (reuse == MAT_INITIAL_MATRIX) {
      ierr = MatDuplicate(seqmat,MAT_COPY_VALUES,mpimat);CHKERRQ(ierr);
    } else {
      ierr = MatCopy(seqmat,*mpimat,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
    }
    PetscFunctionReturn(0);
  }

  if (!seqmat->ops->creatempimatconcatenateseqmat) SETERRQ1(PetscObjectComm((PetscObject)seqmat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)seqmat)->type_name);
  ierr = PetscLogEventBegin(MAT_Merge,seqmat,0,0,0);CHKERRQ(ierr);
  ierr = (*seqmat->ops->creatempimatconcatenateseqmat)(comm,seqmat,n,reuse,mpimat);CHKERRQ(ierr);
  ierr = PetscLogEventEnd(MAT_Merge,seqmat,0,0,0);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSubdomainsCreateCoalesce"
/*@
     MatSubdomainsCreateCoalesce - Creates index subdomains by coalescing adjacent
                 ranks' ownership ranges.

    Collective on A

   Input Parameters:
+    A   - the matrix to create subdomains from
-    N   - requested number of subdomains


   Output Parameters:
+    n   - number of subdomains resulting on this rank
-    iss - IS list with indices of subdomains on this rank

    Level: advanced

    Notes: number of subdomains must be smaller than the communicator size
@*/
PetscErrorCode  MatSubdomainsCreateCoalesce(Mat A,PetscInt N,PetscInt *n,IS *iss[])
{
  MPI_Comm        comm,subcomm;
  PetscMPIInt     size,rank,color,subsize,subrank;
  PetscInt        rstart,rend,k;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)A,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
  if (N < 1 || N >= (PetscInt)size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"number of subdomains must be > 0 and < %D, got N = %D",size,N);
  *n = 1;
  k = ((PetscInt)size)/N + ((PetscInt)size%N>0); /* There are up to k ranks to a color */
  color = rank/k;
  ierr = MPI_Comm_split(comm,color,rank,&subcomm);CHKERRQ(ierr);
  ierr = MPI_Comm_size(subcomm,&subsize);CHKERRQ(ierr);
  ierr = MPI_Comm_size(subcomm,&subrank);CHKERRQ(ierr);
  ierr = PetscMalloc1(1,iss);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(A,&rstart,&rend);CHKERRQ(ierr);
  ierr = ISCreateStride(subcomm,rend-rstart,rstart,1,*iss);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}