Date: 2021-03-03T22:26:10+00:00

Actual source code: matrix.c
petsc-3.14.5 2021-03-03
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      1: /*
      2:    This is where the abstract matrix operations are defined
      3: */

      5: #include <petsc/private/matimpl.h>
      6: #include <petsc/private/isimpl.h>
      7: #include <petsc/private/vecimpl.h>

      9: /* Logging support */
     10: PetscClassId MAT_CLASSID;
     11: PetscClassId MAT_COLORING_CLASSID;
     12: PetscClassId MAT_FDCOLORING_CLASSID;
     13: PetscClassId MAT_TRANSPOSECOLORING_CLASSID;

     15: PetscLogEvent MAT_Mult, MAT_Mults, MAT_MultConstrained, MAT_MultAdd, MAT_MultTranspose;
     16: PetscLogEvent MAT_MultTransposeConstrained, MAT_MultTransposeAdd, MAT_Solve, MAT_Solves, MAT_SolveAdd, MAT_SolveTranspose, MAT_MatSolve,MAT_MatTrSolve;
     17: PetscLogEvent MAT_SolveTransposeAdd, MAT_SOR, MAT_ForwardSolve, MAT_BackwardSolve, MAT_LUFactor, MAT_LUFactorSymbolic;
     18: PetscLogEvent MAT_LUFactorNumeric, MAT_CholeskyFactor, MAT_CholeskyFactorSymbolic, MAT_CholeskyFactorNumeric, MAT_ILUFactor;
     19: PetscLogEvent MAT_ILUFactorSymbolic, MAT_ICCFactorSymbolic, MAT_Copy, MAT_Convert, MAT_Scale, MAT_AssemblyBegin;
     20: PetscLogEvent MAT_AssemblyEnd, MAT_SetValues, MAT_GetValues, MAT_GetRow, MAT_GetRowIJ, MAT_CreateSubMats, MAT_GetOrdering, MAT_RedundantMat, MAT_GetSeqNonzeroStructure;
     21: PetscLogEvent MAT_IncreaseOverlap, MAT_Partitioning, MAT_PartitioningND, MAT_Coarsen, MAT_ZeroEntries, MAT_Load, MAT_View, MAT_AXPY, MAT_FDColoringCreate;
     22: PetscLogEvent MAT_FDColoringSetUp, MAT_FDColoringApply,MAT_Transpose,MAT_FDColoringFunction, MAT_CreateSubMat;
     23: PetscLogEvent MAT_TransposeColoringCreate;
     24: PetscLogEvent MAT_MatMult, MAT_MatMultSymbolic, MAT_MatMultNumeric;
     25: PetscLogEvent MAT_PtAP, MAT_PtAPSymbolic, MAT_PtAPNumeric,MAT_RARt, MAT_RARtSymbolic, MAT_RARtNumeric;
     26: PetscLogEvent MAT_MatTransposeMult, MAT_MatTransposeMultSymbolic, MAT_MatTransposeMultNumeric;
     27: PetscLogEvent MAT_TransposeMatMult, MAT_TransposeMatMultSymbolic, MAT_TransposeMatMultNumeric;
     28: PetscLogEvent MAT_MatMatMult, MAT_MatMatMultSymbolic, MAT_MatMatMultNumeric;
     29: PetscLogEvent MAT_MultHermitianTranspose,MAT_MultHermitianTransposeAdd;
     30: PetscLogEvent MAT_Getsymtranspose, MAT_Getsymtransreduced, MAT_GetBrowsOfAcols;
     31: PetscLogEvent MAT_GetBrowsOfAocols, MAT_Getlocalmat, MAT_Getlocalmatcondensed, MAT_Seqstompi, MAT_Seqstompinum, MAT_Seqstompisym;
     32: PetscLogEvent MAT_Applypapt, MAT_Applypapt_numeric, MAT_Applypapt_symbolic, MAT_GetSequentialNonzeroStructure;
     33: PetscLogEvent MAT_GetMultiProcBlock;
     34: PetscLogEvent MAT_CUSPARSECopyToGPU, MAT_CUSPARSEGenerateTranspose, MAT_SetValuesBatch;
     35: PetscLogEvent MAT_ViennaCLCopyToGPU;
     36: PetscLogEvent MAT_DenseCopyToGPU, MAT_DenseCopyFromGPU;
     37: PetscLogEvent MAT_Merge,MAT_Residual,MAT_SetRandom;
     38: PetscLogEvent MAT_FactorFactS,MAT_FactorInvS;
     39: PetscLogEvent MATCOLORING_Apply,MATCOLORING_Comm,MATCOLORING_Local,MATCOLORING_ISCreate,MATCOLORING_SetUp,MATCOLORING_Weights;

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

     43: /*@
     44:    MatSetRandom - Sets all components of a matrix to random numbers. For sparse matrices that have been preallocated but not been assembled it randomly selects appropriate locations,
     45:                   for sparse matrices that already have locations it fills the locations with random numbers

     47:    Logically Collective on Mat

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

     54:    Output Parameter:
     55: .  x  - the matrix

     57:    Example of Usage:
     58: .vb
     59:      PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
     60:      MatSetRandom(x,rctx);
     61:      PetscRandomDestroy(rctx);
     62: .ve

     64:    Level: intermediate

     67: .seealso: MatZeroEntries(), MatSetValues(), PetscRandomCreate(), PetscRandomDestroy()
     68: @*/
     69: PetscErrorCode MatSetRandom(Mat x,PetscRandom rctx)
     70: {
     72:   PetscRandom    randObj = NULL;

     79:   if (!x->ops->setrandom) SETERRQ1(PetscObjectComm((PetscObject)x),PETSC_ERR_SUP,"Mat type %s",((PetscObject)x)->type_name);

     81:   if (!rctx) {
     82:     MPI_Comm comm;
     83:     PetscObjectGetComm((PetscObject)x,&comm);
     84:     PetscRandomCreate(comm,&randObj);
     85:     PetscRandomSetFromOptions(randObj);
     86:     rctx = randObj;
     87:   }

     89:   PetscLogEventBegin(MAT_SetRandom,x,rctx,0,0);
     90:   (*x->ops->setrandom)(x,rctx);
     91:   PetscLogEventEnd(MAT_SetRandom,x,rctx,0,0);

     93:   MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY);
     94:   MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY);
     95:   PetscRandomDestroy(&randObj);
     96:   return(0);
     97: }

     99: /*@
    100:    MatFactorGetErrorZeroPivot - returns the pivot value that was determined to be zero and the row it occurred in

    102:    Logically Collective on Mat

    104:    Input Parameters:
    105: .  mat - the factored matrix

    107:    Output Parameter:
    108: +  pivot - the pivot value computed
    109: -  row - the row that the zero pivot occurred. Note that this row must be interpreted carefully due to row reorderings and which processes
    110:          the share the matrix

    112:    Level: advanced

    114:    Notes:
    115:     This routine does not work for factorizations done with external packages.

    117:     This routine should only be called if MatGetFactorError() returns a value of MAT_FACTOR_NUMERIC_ZEROPIVOT

    119:     This can be called on non-factored matrices that come from, for example, matrices used in SOR.

    121: .seealso: MatZeroEntries(), MatFactor(), MatGetFactor(), MatLUFactorSymbolic(), MatCholeskyFactorSymbolic(), MatFactorClearError(), MatFactorGetErrorZeroPivot()
    122: @*/
    123: PetscErrorCode MatFactorGetErrorZeroPivot(Mat mat,PetscReal *pivot,PetscInt *row)
    124: {
    127:   *pivot = mat->factorerror_zeropivot_value;
    128:   *row   = mat->factorerror_zeropivot_row;
    129:   return(0);
    130: }

    132: /*@
    133:    MatFactorGetError - gets the error code from a factorization

    135:    Logically Collective on Mat

    137:    Input Parameters:
    138: .  mat - the factored matrix

    140:    Output Parameter:
    141: .  err  - the error code

    143:    Level: advanced

    145:    Notes:
    146:     This can be called on non-factored matrices that come from, for example, matrices used in SOR.

    148: .seealso: MatZeroEntries(), MatFactor(), MatGetFactor(), MatLUFactorSymbolic(), MatCholeskyFactorSymbolic(), MatFactorClearError(), MatFactorGetErrorZeroPivot()
    149: @*/
    150: PetscErrorCode MatFactorGetError(Mat mat,MatFactorError *err)
    151: {
    154:   *err = mat->factorerrortype;
    155:   return(0);
    156: }

    158: /*@
    159:    MatFactorClearError - clears the error code in a factorization

    161:    Logically Collective on Mat

    163:    Input Parameter:
    164: .  mat - the factored matrix

    166:    Level: developer

    168:    Notes:
    169:     This can be called on non-factored matrices that come from, for example, matrices used in SOR.

    171: .seealso: MatZeroEntries(), MatFactor(), MatGetFactor(), MatLUFactorSymbolic(), MatCholeskyFactorSymbolic(), MatFactorGetError(), MatFactorGetErrorZeroPivot()
    172: @*/
    173: PetscErrorCode MatFactorClearError(Mat mat)
    174: {
    177:   mat->factorerrortype             = MAT_FACTOR_NOERROR;
    178:   mat->factorerror_zeropivot_value = 0.0;
    179:   mat->factorerror_zeropivot_row   = 0;
    180:   return(0);
    181: }

    183: PETSC_INTERN PetscErrorCode MatFindNonzeroRowsOrCols_Basic(Mat mat,PetscBool cols,PetscReal tol,IS *nonzero)
    184: {
    185:   PetscErrorCode    ierr;
    186:   Vec               r,l;
    187:   const PetscScalar *al;
    188:   PetscInt          i,nz,gnz,N,n;

    191:   MatCreateVecs(mat,&r,&l);
    192:   if (!cols) { /* nonzero rows */
    193:     MatGetSize(mat,&N,NULL);
    194:     MatGetLocalSize(mat,&n,NULL);
    195:     VecSet(l,0.0);
    196:     VecSetRandom(r,NULL);
    197:     MatMult(mat,r,l);
    198:     VecGetArrayRead(l,&al);
    199:   } else { /* nonzero columns */
    200:     MatGetSize(mat,NULL,&N);
    201:     MatGetLocalSize(mat,NULL,&n);
    202:     VecSet(r,0.0);
    203:     VecSetRandom(l,NULL);
    204:     MatMultTranspose(mat,l,r);
    205:     VecGetArrayRead(r,&al);
    206:   }
    207:   if (tol <= 0.0) { for (i=0,nz=0;i<n;i++) if (al[i] != 0.0) nz++; }
    208:   else { for (i=0,nz=0;i<n;i++) if (PetscAbsScalar(al[i]) > tol) nz++; }
    209:   MPIU_Allreduce(&nz,&gnz,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)mat));
    210:   if (gnz != N) {
    211:     PetscInt *nzr;
    212:     PetscMalloc1(nz,&nzr);
    213:     if (nz) {
    214:       if (tol < 0) { for (i=0,nz=0;i<n;i++) if (al[i] != 0.0) nzr[nz++] = i; }
    215:       else { for (i=0,nz=0;i<n;i++) if (PetscAbsScalar(al[i]) > tol) nzr[nz++] = i; }
    216:     }
    217:     ISCreateGeneral(PetscObjectComm((PetscObject)mat),nz,nzr,PETSC_OWN_POINTER,nonzero);
    218:   } else *nonzero = NULL;
    219:   if (!cols) { /* nonzero rows */
    220:     VecRestoreArrayRead(l,&al);
    221:   } else {
    222:     VecRestoreArrayRead(r,&al);
    223:   }
    224:   VecDestroy(&l);
    225:   VecDestroy(&r);
    226:   return(0);
    227: }

    229: /*@
    230:       MatFindNonzeroRows - Locate all rows that are not completely zero in the matrix

    232:   Input Parameter:
    233: .    A  - the matrix

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

    238:   Notes:
    239:     keptrows is set to NULL if all rows are nonzero.

    241:   Level: intermediate

    243:  @*/
    244: PetscErrorCode MatFindNonzeroRows(Mat mat,IS *keptrows)
    245: {

    252:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    253:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    254:   if (!mat->ops->findnonzerorows) {
    255:     MatFindNonzeroRowsOrCols_Basic(mat,PETSC_FALSE,0.0,keptrows);
    256:   } else {
    257:     (*mat->ops->findnonzerorows)(mat,keptrows);
    258:   }
    259:   return(0);
    260: }

    262: /*@
    263:       MatFindZeroRows - Locate all rows that are completely zero in the matrix

    265:   Input Parameter:
    266: .    A  - the matrix

    268:   Output Parameter:
    269: .    zerorows - the rows that are completely zero

    271:   Notes:
    272:     zerorows is set to NULL if no rows are zero.

    274:   Level: intermediate

    276:  @*/
    277: PetscErrorCode MatFindZeroRows(Mat mat,IS *zerorows)
    278: {
    280:   IS keptrows;
    281:   PetscInt m, n;

    286:   MatFindNonzeroRows(mat, &keptrows);
    287:   /* MatFindNonzeroRows sets keptrows to NULL if there are no zero rows.
    288:      In keeping with this convention, we set zerorows to NULL if there are no zero
    289:      rows. */
    290:   if (keptrows == NULL) {
    291:     *zerorows = NULL;
    292:   } else {
    293:     MatGetOwnershipRange(mat,&m,&n);
    294:     ISComplement(keptrows,m,n,zerorows);
    295:     ISDestroy(&keptrows);
    296:   }
    297:   return(0);
    298: }

    300: /*@
    301:    MatGetDiagonalBlock - Returns the part of the matrix associated with the on-process coupling

    303:    Not Collective

    305:    Input Parameters:
    306: .   A - the matrix

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

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

    316:    Level: advanced

    318: @*/
    319: PetscErrorCode MatGetDiagonalBlock(Mat A,Mat *a)
    320: {

    327:   if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    328:   if (!A->ops->getdiagonalblock) {
    329:     PetscMPIInt size;
    330:     MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    331:     if (size == 1) {
    332:       *a = A;
    333:       return(0);
    334:     } else SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Not coded for matrix type %s",((PetscObject)A)->type_name);
    335:   }
    336:   (*A->ops->getdiagonalblock)(A,a);
    337:   return(0);
    338: }

    340: /*@
    341:    MatGetTrace - Gets the trace of a matrix. The sum of the diagonal entries.

    343:    Collective on Mat

    345:    Input Parameters:
    346: .  mat - the matrix

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

    351:    Level: advanced

    353: @*/
    354: PetscErrorCode MatGetTrace(Mat mat,PetscScalar *trace)
    355: {
    357:   Vec            diag;

    360:   MatCreateVecs(mat,&diag,NULL);
    361:   MatGetDiagonal(mat,diag);
    362:   VecSum(diag,trace);
    363:   VecDestroy(&diag);
    364:   return(0);
    365: }

    367: /*@
    368:    MatRealPart - Zeros out the imaginary part of the matrix

    370:    Logically Collective on Mat

    372:    Input Parameters:
    373: .  mat - the matrix

    375:    Level: advanced

    378: .seealso: MatImaginaryPart()
    379: @*/
    380: PetscErrorCode MatRealPart(Mat mat)
    381: {

    387:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    388:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    389:   if (!mat->ops->realpart) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    390:   MatCheckPreallocated(mat,1);
    391:   (*mat->ops->realpart)(mat);
    392:   return(0);
    393: }

    395: /*@C
    396:    MatGetGhosts - Get the global index of all ghost nodes defined by the sparse matrix

    398:    Collective on Mat

    400:    Input Parameter:
    401: .  mat - the matrix

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

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

    410:    Level: advanced

    412: @*/
    413: PetscErrorCode MatGetGhosts(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
    414: {

    420:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    421:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    422:   if (!mat->ops->getghosts) {
    423:     if (nghosts) *nghosts = 0;
    424:     if (ghosts) *ghosts = NULL;
    425:   } else {
    426:     (*mat->ops->getghosts)(mat,nghosts,ghosts);
    427:   }
    428:   return(0);
    429: }

    432: /*@
    433:    MatImaginaryPart - Moves the imaginary part of the matrix to the real part and zeros the imaginary part

    435:    Logically Collective on Mat

    437:    Input Parameters:
    438: .  mat - the matrix

    440:    Level: advanced

    443: .seealso: MatRealPart()
    444: @*/
    445: PetscErrorCode MatImaginaryPart(Mat mat)
    446: {

    452:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    453:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    454:   if (!mat->ops->imaginarypart) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    455:   MatCheckPreallocated(mat,1);
    456:   (*mat->ops->imaginarypart)(mat);
    457:   return(0);
    458: }

    460: /*@
    461:    MatMissingDiagonal - Determine if sparse matrix is missing a diagonal entry (or block entry for BAIJ matrices)

    463:    Not Collective

    465:    Input Parameter:
    466: .  mat - the matrix

    468:    Output Parameters:
    469: +  missing - is any diagonal missing
    470: -  dd - first diagonal entry that is missing (optional) on this process

    472:    Level: advanced

    475: .seealso: MatRealPart()
    476: @*/
    477: PetscErrorCode MatMissingDiagonal(Mat mat,PetscBool *missing,PetscInt *dd)
    478: {

    485:   if (!mat->assembled) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix %s",((PetscObject)mat)->type_name);
    486:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    487:   if (!mat->ops->missingdiagonal) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    488:   (*mat->ops->missingdiagonal)(mat,missing,dd);
    489:   return(0);
    490: }

    492: /*@C
    493:    MatGetRow - Gets a row of a matrix.  You MUST call MatRestoreRow()
    494:    for each row that you get to ensure that your application does
    495:    not bleed memory.

    497:    Not Collective

    499:    Input Parameters:
    500: +  mat - the matrix
    501: -  row - the row to get

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

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

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

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

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

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

    530:    Fortran Notes:
    531:    The calling sequence from Fortran is
    532: .vb
    533:    MatGetRow(matrix,row,ncols,cols,values,ierr)
    534:          Mat     matrix (input)
    535:          integer row    (input)
    536:          integer ncols  (output)
    537:          integer cols(maxcols) (output)
    538:          double precision (or double complex) values(maxcols) output
    539: .ve
    540:    where maxcols >= maximum nonzeros in any row of the matrix.

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

    547:    Level: advanced

    549: .seealso: MatRestoreRow(), MatSetValues(), MatGetValues(), MatCreateSubMatrices(), MatGetDiagonal()
    550: @*/
    551: PetscErrorCode MatGetRow(Mat mat,PetscInt row,PetscInt *ncols,const PetscInt *cols[],const PetscScalar *vals[])
    552: {
    554:   PetscInt       incols;

    559:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    560:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    561:   if (!mat->ops->getrow) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    562:   MatCheckPreallocated(mat,1);
    563:   PetscLogEventBegin(MAT_GetRow,mat,0,0,0);
    564:   (*mat->ops->getrow)(mat,row,&incols,(PetscInt**)cols,(PetscScalar**)vals);
    565:   if (ncols) *ncols = incols;
    566:   PetscLogEventEnd(MAT_GetRow,mat,0,0,0);
    567:   return(0);
    568: }

    570: /*@
    571:    MatConjugate - replaces the matrix values with their complex conjugates

    573:    Logically Collective on Mat

    575:    Input Parameters:
    576: .  mat - the matrix

    578:    Level: advanced

    580: .seealso:  VecConjugate()
    581: @*/
    582: PetscErrorCode MatConjugate(Mat mat)
    583: {
    584: #if defined(PETSC_USE_COMPLEX)

    589:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    590:   if (!mat->ops->conjugate) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not provided for matrix type %s, send email to petsc-maint@mcs.anl.gov",((PetscObject)mat)->type_name);
    591:   (*mat->ops->conjugate)(mat);
    592: #else
    594: #endif
    595:   return(0);
    596: }

    598: /*@C
    599:    MatRestoreRow - Frees any temporary space allocated by MatGetRow().

    601:    Not Collective

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

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

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

    616:    Fortran Notes:
    617:    The calling sequence from Fortran is
    618: .vb
    619:    MatRestoreRow(matrix,row,ncols,cols,values,ierr)
    620:       Mat     matrix (input)
    621:       integer row    (input)
    622:       integer ncols  (output)
    623:       integer cols(maxcols) (output)
    624:       double precision (or double complex) values(maxcols) output
    625: .ve
    626:    Where maxcols >= maximum nonzeros in any row of the matrix.

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

    631:    Level: advanced

    633: .seealso:  MatGetRow()
    634: @*/
    635: PetscErrorCode MatRestoreRow(Mat mat,PetscInt row,PetscInt *ncols,const PetscInt *cols[],const PetscScalar *vals[])
    636: {

    642:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    643:   if (!mat->ops->restorerow) return(0);
    644:   (*mat->ops->restorerow)(mat,row,ncols,(PetscInt **)cols,(PetscScalar **)vals);
    645:   if (ncols) *ncols = 0;
    646:   if (cols)  *cols = NULL;
    647:   if (vals)  *vals = NULL;
    648:   return(0);
    649: }

    651: /*@
    652:    MatGetRowUpperTriangular - Sets a flag to enable calls to MatGetRow() for matrix in MATSBAIJ format.
    653:    You should call MatRestoreRowUpperTriangular() after calling MatGetRow/MatRestoreRow() to disable the flag.

    655:    Not Collective

    657:    Input Parameters:
    658: .  mat - the matrix

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

    663:    Level: advanced

    665: .seealso: MatRestoreRowUpperTriangular()
    666: @*/
    667: PetscErrorCode MatGetRowUpperTriangular(Mat mat)
    668: {

    674:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    675:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    676:   MatCheckPreallocated(mat,1);
    677:   if (!mat->ops->getrowuppertriangular) return(0);
    678:   (*mat->ops->getrowuppertriangular)(mat);
    679:   return(0);
    680: }

    682: /*@
    683:    MatRestoreRowUpperTriangular - Disable calls to MatGetRow() for matrix in MATSBAIJ format.

    685:    Not Collective

    687:    Input Parameters:
    688: .  mat - the matrix

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

    694:    Level: advanced

    696: .seealso:  MatGetRowUpperTriangular()
    697: @*/
    698: PetscErrorCode MatRestoreRowUpperTriangular(Mat mat)
    699: {

    705:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    706:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    707:   MatCheckPreallocated(mat,1);
    708:   if (!mat->ops->restorerowuppertriangular) return(0);
    709:   (*mat->ops->restorerowuppertriangular)(mat);
    710:   return(0);
    711: }

    713: /*@C
    714:    MatSetOptionsPrefix - Sets the prefix used for searching for all
    715:    Mat options in the database.

    717:    Logically Collective on Mat

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

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

    727:    Level: advanced

    729: .seealso: MatSetFromOptions()
    730: @*/
    731: PetscErrorCode MatSetOptionsPrefix(Mat A,const char prefix[])
    732: {

    737:   PetscObjectSetOptionsPrefix((PetscObject)A,prefix);
    738:   return(0);
    739: }

    741: /*@C
    742:    MatAppendOptionsPrefix - Appends to the prefix used for searching for all
    743:    Mat options in the database.

    745:    Logically Collective on Mat

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

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

    755:    Level: advanced

    757: .seealso: MatGetOptionsPrefix()
    758: @*/
    759: PetscErrorCode MatAppendOptionsPrefix(Mat A,const char prefix[])
    760: {

    765:   PetscObjectAppendOptionsPrefix((PetscObject)A,prefix);
    766:   return(0);
    767: }

    769: /*@C
    770:    MatGetOptionsPrefix - Gets the prefix used for searching for all
    771:    Mat options in the database.

    773:    Not Collective

    775:    Input Parameter:
    776: .  A - the Mat context

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

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

    785:    Level: advanced

    787: .seealso: MatAppendOptionsPrefix()
    788: @*/
    789: PetscErrorCode MatGetOptionsPrefix(Mat A,const char *prefix[])
    790: {

    795:   PetscObjectGetOptionsPrefix((PetscObject)A,prefix);
    796:   return(0);
    797: }

    799: /*@
    800:    MatResetPreallocation - Reset mat to use the original nonzero pattern provided by users.

    802:    Collective on Mat

    804:    Input Parameters:
    805: .  A - the Mat context

    807:    Notes:
    808:    The allocated memory will be shrunk after calling MatAssembly with MAT_FINAL_ASSEMBLY. Users can reset the preallocation to access the original memory.
    809:    Currently support MPIAIJ and SEQAIJ.

    811:    Level: beginner

    813: .seealso: MatSeqAIJSetPreallocation(), MatMPIAIJSetPreallocation(), MatXAIJSetPreallocation()
    814: @*/
    815: PetscErrorCode MatResetPreallocation(Mat A)
    816: {

    822:   PetscUseMethod(A,"MatResetPreallocation_C",(Mat),(A));
    823:   return(0);
    824: }

    827: /*@
    828:    MatSetUp - Sets up the internal matrix data structures for later use.

    830:    Collective on Mat

    832:    Input Parameters:
    833: .  A - the Mat context

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

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

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

    842:    Level: beginner

    844: .seealso: MatCreate(), MatDestroy()
    845: @*/
    846: PetscErrorCode MatSetUp(Mat A)
    847: {
    848:   PetscMPIInt    size;

    853:   if (!((PetscObject)A)->type_name) {
    854:     MPI_Comm_size(PetscObjectComm((PetscObject)A), &size);
    855:     if (size == 1) {
    856:       MatSetType(A, MATSEQAIJ);
    857:     } else {
    858:       MatSetType(A, MATMPIAIJ);
    859:     }
    860:   }
    861:   if (!A->preallocated && A->ops->setup) {
    862:     PetscInfo(A,"Warning not preallocating matrix storage\n");
    863:     (*A->ops->setup)(A);
    864:   }
    865:   PetscLayoutSetUp(A->rmap);
    866:   PetscLayoutSetUp(A->cmap);
    867:   A->preallocated = PETSC_TRUE;
    868:   return(0);
    869: }

    871: #if defined(PETSC_HAVE_SAWS)
    872: #include <petscviewersaws.h>
    873: #endif

    875: /*@C
    876:    MatViewFromOptions - View from Options

    878:    Collective on Mat

    880:    Input Parameters:
    881: +  A - the Mat context
    882: .  obj - Optional object
    883: -  name - command line option

    885:    Level: intermediate
    886: .seealso:  Mat, MatView, PetscObjectViewFromOptions(), MatCreate()
    887: @*/
    888: PetscErrorCode  MatViewFromOptions(Mat A,PetscObject obj,const char name[])
    889: {

    894:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
    895:   return(0);
    896: }

    898: /*@C
    899:    MatView - Visualizes a matrix object.

    901:    Collective on Mat

    903:    Input Parameters:
    904: +  mat - the matrix
    905: -  viewer - visualization context

    907:   Notes:
    908:   The available visualization contexts include
    909: +    PETSC_VIEWER_STDOUT_SELF - for sequential matrices
    910: .    PETSC_VIEWER_STDOUT_WORLD - for parallel matrices created on PETSC_COMM_WORLD
    911: .    PETSC_VIEWER_STDOUT_(comm) - for matrices created on MPI communicator comm
    912: -     PETSC_VIEWER_DRAW_WORLD - graphical display of nonzero structure

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

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

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

    954:    Notes:
    955:     The ASCII viewers are only recommended for small matrices on at most a moderate number of processes,
    956:     the program will seemingly hang and take hours for larger matrices, for larger matrices one should use the binary format.

    958:     In the debugger you can do "call MatView(mat,0)" to display the matrix. (The same holds for any PETSc object viewer).

    960:     See the manual page for MatLoad() for the exact format of the binary file when the binary
    961:       viewer is used.

    963:       See share/petsc/matlab/PetscBinaryRead.m for a Matlab code that can read in the binary file when the binary
    964:       viewer is used and lib/petsc/bin/PetscBinaryIO.py for loading them into Python.

    966:       One can use '-mat_view draw -draw_pause -1' to pause the graphical display of matrix nonzero structure,
    967:       and then use the following mouse functions.
    968: + left mouse: zoom in
    969: . middle mouse: zoom out
    970: - right mouse: continue with the simulation

    972: .seealso: PetscViewerPushFormat(), PetscViewerASCIIOpen(), PetscViewerDrawOpen(),
    973:           PetscViewerSocketOpen(), PetscViewerBinaryOpen(), MatLoad()
    974: @*/
    975: PetscErrorCode MatView(Mat mat,PetscViewer viewer)
    976: {
    977:   PetscErrorCode    ierr;
    978:   PetscInt          rows,cols,rbs,cbs;
    979:   PetscBool         isascii,isstring,issaws;
    980:   PetscViewerFormat format;
    981:   PetscMPIInt       size;

    986:   if (!viewer) {PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)mat),&viewer);}
    989:   MatCheckPreallocated(mat,1);

    991:   PetscViewerGetFormat(viewer,&format);
    992:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    993:   if (size == 1 && format == PETSC_VIEWER_LOAD_BALANCE) return(0);

    995:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
    996:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    997:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSAWS,&issaws);
    998:   if ((!isascii || (format != PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL)) && mat->factortype) {
    999:     SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"No viewers for factored matrix except ASCII info or info_detail");
    1000:   }

    1002:   PetscLogEventBegin(MAT_View,mat,viewer,0,0);
    1003:   if (isascii) {
    1004:     if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ORDER,"Must call MatAssemblyBegin/End() before viewing matrix");
    1005:     PetscObjectPrintClassNamePrefixType((PetscObject)mat,viewer);
    1006:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1007:       MatNullSpace nullsp,transnullsp;

    1009:       PetscViewerASCIIPushTab(viewer);
    1010:       MatGetSize(mat,&rows,&cols);
    1011:       MatGetBlockSizes(mat,&rbs,&cbs);
    1012:       if (rbs != 1 || cbs != 1) {
    1013:         if (rbs != cbs) {PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D, rbs=%D, cbs=%D\n",rows,cols,rbs,cbs);}
    1014:         else            {PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D, bs=%D\n",rows,cols,rbs);}
    1015:       } else {
    1016:         PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D\n",rows,cols);
    1017:       }
    1018:       if (mat->factortype) {
    1019:         MatSolverType solver;
    1020:         MatFactorGetSolverType(mat,&solver);
    1021:         PetscViewerASCIIPrintf(viewer,"package used to perform factorization: %s\n",solver);
    1022:       }
    1023:       if (mat->ops->getinfo) {
    1024:         MatInfo info;
    1025:         MatGetInfo(mat,MAT_GLOBAL_SUM,&info);
    1026:         PetscViewerASCIIPrintf(viewer,"total: nonzeros=%.f, allocated nonzeros=%.f\n",info.nz_used,info.nz_allocated);
    1027:         if (!mat->factortype) {
    1028:           PetscViewerASCIIPrintf(viewer,"total number of mallocs used during MatSetValues calls=%D\n",(PetscInt)info.mallocs);
    1029:         }
    1030:       }
    1031:       MatGetNullSpace(mat,&nullsp);
    1032:       MatGetTransposeNullSpace(mat,&transnullsp);
    1033:       if (nullsp) {PetscViewerASCIIPrintf(viewer,"  has attached null space\n");}
    1034:       if (transnullsp && transnullsp != nullsp) {PetscViewerASCIIPrintf(viewer,"  has attached transposed null space\n");}
    1035:       MatGetNearNullSpace(mat,&nullsp);
    1036:       if (nullsp) {PetscViewerASCIIPrintf(viewer,"  has attached near null space\n");}
    1037:       PetscViewerASCIIPushTab(viewer);
    1038:       MatProductView(mat,viewer);
    1039:       PetscViewerASCIIPopTab(viewer);
    1040:     }
    1041:   } else if (issaws) {
    1042: #if defined(PETSC_HAVE_SAWS)
    1043:     PetscMPIInt rank;

    1045:     PetscObjectName((PetscObject)mat);
    1046:     MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
    1047:     if (!((PetscObject)mat)->amsmem && !rank) {
    1048:       PetscObjectViewSAWs((PetscObject)mat,viewer);
    1049:     }
    1050: #endif
    1051:   } else if (isstring) {
    1052:     const char *type;
    1053:     MatGetType(mat,&type);
    1054:     PetscViewerStringSPrintf(viewer," MatType: %-7.7s",type);
    1055:     if (mat->ops->view) {(*mat->ops->view)(mat,viewer);}
    1056:   }
    1057:   if ((format == PETSC_VIEWER_NATIVE || format == PETSC_VIEWER_LOAD_BALANCE) && mat->ops->viewnative) {
    1058:     PetscViewerASCIIPushTab(viewer);
    1059:     (*mat->ops->viewnative)(mat,viewer);
    1060:     PetscViewerASCIIPopTab(viewer);
    1061:   } else if (mat->ops->view) {
    1062:     PetscViewerASCIIPushTab(viewer);
    1063:     (*mat->ops->view)(mat,viewer);
    1064:     PetscViewerASCIIPopTab(viewer);
    1065:   }
    1066:   if (isascii) {
    1067:     PetscViewerGetFormat(viewer,&format);
    1068:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1069:       PetscViewerASCIIPopTab(viewer);
    1070:     }
    1071:   }
    1072:   PetscLogEventEnd(MAT_View,mat,viewer,0,0);
    1073:   return(0);
    1074: }

    1076: #if defined(PETSC_USE_DEBUG)
    1077: #include <../src/sys/totalview/tv_data_display.h>
    1078: PETSC_UNUSED static int TV_display_type(const struct _p_Mat *mat)
    1079: {
    1080:   TV_add_row("Local rows", "int", &mat->rmap->n);
    1081:   TV_add_row("Local columns", "int", &mat->cmap->n);
    1082:   TV_add_row("Global rows", "int", &mat->rmap->N);
    1083:   TV_add_row("Global columns", "int", &mat->cmap->N);
    1084:   TV_add_row("Typename", TV_ascii_string_type, ((PetscObject)mat)->type_name);
    1085:   return TV_format_OK;
    1086: }
    1087: #endif

    1089: /*@C
    1090:    MatLoad - Loads a matrix that has been stored in binary/HDF5 format
    1091:    with MatView().  The matrix format is determined from the options database.
    1092:    Generates a parallel MPI matrix if the communicator has more than one
    1093:    processor.  The default matrix type is AIJ.

    1095:    Collective on PetscViewer

    1097:    Input Parameters:
    1098: +  mat - the newly loaded matrix, this needs to have been created with MatCreate()
    1099:             or some related function before a call to MatLoad()
    1100: -  viewer - binary/HDF5 file viewer

    1102:    Options Database Keys:
    1103:    Used with block matrix formats (MATSEQBAIJ,  ...) to specify
    1104:    block size
    1105: .    -matload_block_size <bs>

    1107:    Level: beginner

    1109:    Notes:
    1110:    If the Mat type has not yet been given then MATAIJ is used, call MatSetFromOptions() on the
    1111:    Mat before calling this routine if you wish to set it from the options database.

    1113:    MatLoad() automatically loads into the options database any options
    1114:    given in the file filename.info where filename is the name of the file
    1115:    that was passed to the PetscViewerBinaryOpen(). The options in the info
    1116:    file will be ignored if you use the -viewer_binary_skip_info option.

    1118:    If the type or size of mat is not set before a call to MatLoad, PETSc
    1119:    sets the default matrix type AIJ and sets the local and global sizes.
    1120:    If type and/or size is already set, then the same are used.

    1122:    In parallel, each processor can load a subset of rows (or the
    1123:    entire matrix).  This routine is especially useful when a large
    1124:    matrix is stored on disk and only part of it is desired on each
    1125:    processor.  For example, a parallel solver may access only some of
    1126:    the rows from each processor.  The algorithm used here reads
    1127:    relatively small blocks of data rather than reading the entire
    1128:    matrix and then subsetting it.

    1130:    Viewer's PetscViewerType must be either PETSCVIEWERBINARY or PETSCVIEWERHDF5.
    1131:    Such viewer can be created using PetscViewerBinaryOpen()/PetscViewerHDF5Open(),
    1132:    or the sequence like
    1133: $    PetscViewer v;
    1134: $    PetscViewerCreate(PETSC_COMM_WORLD,&v);
    1135: $    PetscViewerSetType(v,PETSCVIEWERBINARY);
    1136: $    PetscViewerSetFromOptions(v);
    1137: $    PetscViewerFileSetMode(v,FILE_MODE_READ);
    1138: $    PetscViewerFileSetName(v,"datafile");
    1139:    The optional PetscViewerSetFromOptions() call allows to override PetscViewerSetType() using option
    1140: $ -viewer_type {binary,hdf5}

    1142:    See the example src/ksp/ksp/tutorials/ex27.c with the first approach,
    1143:    and src/mat/tutorials/ex10.c with the second approach.

    1145:    Notes about the PETSc binary format:
    1146:    In case of PETSCVIEWERBINARY, a native PETSc binary format is used. Each of the blocks
    1147:    is read onto rank 0 and then shipped to its destination rank, one after another.
    1148:    Multiple objects, both matrices and vectors, can be stored within the same file.
    1149:    Their PetscObject name is ignored; they are loaded in the order of their storage.

    1151:    Most users should not need to know the details of the binary storage
    1152:    format, since MatLoad() and MatView() completely hide these details.
    1153:    But for anyone who's interested, the standard binary matrix storage
    1154:    format is

    1156: $    PetscInt    MAT_FILE_CLASSID
    1157: $    PetscInt    number of rows
    1158: $    PetscInt    number of columns
    1159: $    PetscInt    total number of nonzeros
    1160: $    PetscInt    *number nonzeros in each row
    1161: $    PetscInt    *column indices of all nonzeros (starting index is zero)
    1162: $    PetscScalar *values of all nonzeros

    1164:    PETSc automatically does the byte swapping for
    1165: machines that store the bytes reversed, e.g.  DEC alpha, freebsd,
    1166: linux, Windows and the paragon; thus if you write your own binary
    1167: read/write routines you have to swap the bytes; see PetscBinaryRead()
    1168: and PetscBinaryWrite() to see how this may be done.

    1170:    Notes about the HDF5 (MATLAB MAT-File Version 7.3) format:
    1171:    In case of PETSCVIEWERHDF5, a parallel HDF5 reader is used.
    1172:    Each processor's chunk is loaded independently by its owning rank.
    1173:    Multiple objects, both matrices and vectors, can be stored within the same file.
    1174:    They are looked up by their PetscObject name.

    1176:    As the MATLAB MAT-File Version 7.3 format is also a HDF5 flavor, we decided to use
    1177:    by default the same structure and naming of the AIJ arrays and column count
    1178:    within the HDF5 file. This means that a MAT file saved with -v7.3 flag, e.g.
    1179: $    save example.mat A b -v7.3
    1180:    can be directly read by this routine (see Reference 1 for details).
    1181:    Note that depending on your MATLAB version, this format might be a default,
    1182:    otherwise you can set it as default in Preferences.

    1184:    Unless -nocompression flag is used to save the file in MATLAB,
    1185:    PETSc must be configured with ZLIB package.

    1187:    See also examples src/mat/tutorials/ex10.c and src/ksp/ksp/tutorials/ex27.c

    1189:    Current HDF5 (MAT-File) limitations:
    1190:    This reader currently supports only real MATSEQAIJ, MATMPIAIJ, MATSEQDENSE and MATMPIDENSE matrices.

    1192:    Corresponding MatView() is not yet implemented.

    1194:    The loaded matrix is actually a transpose of the original one in MATLAB,
    1195:    unless you push PETSC_VIEWER_HDF5_MAT format (see examples above).
    1196:    With this format, matrix is automatically transposed by PETSc,
    1197:    unless the matrix is marked as SPD or symmetric
    1198:    (see MatSetOption(), MAT_SPD, MAT_SYMMETRIC).

    1200:    References:
    1201: 1. MATLAB(R) Documentation, manual page of save(), https://www.mathworks.com/help/matlab/ref/save.html#btox10b-1-version

    1203: .seealso: PetscViewerBinaryOpen(), PetscViewerSetType(), MatView(), VecLoad()

    1205:  @*/
    1206: PetscErrorCode MatLoad(Mat mat,PetscViewer viewer)
    1207: {
    1209:   PetscBool      flg;

    1215:   if (!((PetscObject)mat)->type_name) {
    1216:     MatSetType(mat,MATAIJ);
    1217:   }

    1219:   flg  = PETSC_FALSE;
    1220:   PetscOptionsGetBool(((PetscObject)mat)->options,((PetscObject)mat)->prefix,"-matload_symmetric",&flg,NULL);
    1221:   if (flg) {
    1222:     MatSetOption(mat,MAT_SYMMETRIC,PETSC_TRUE);
    1223:     MatSetOption(mat,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
    1224:   }
    1225:   flg  = PETSC_FALSE;
    1226:   PetscOptionsGetBool(((PetscObject)mat)->options,((PetscObject)mat)->prefix,"-matload_spd",&flg,NULL);
    1227:   if (flg) {
    1228:     MatSetOption(mat,MAT_SPD,PETSC_TRUE);
    1229:   }

    1231:   if (!mat->ops->load) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatLoad is not supported for type %s",((PetscObject)mat)->type_name);
    1232:   PetscLogEventBegin(MAT_Load,mat,viewer,0,0);
    1233:   (*mat->ops->load)(mat,viewer);
    1234:   PetscLogEventEnd(MAT_Load,mat,viewer,0,0);
    1235:   return(0);
    1236: }

    1238: static PetscErrorCode MatDestroy_Redundant(Mat_Redundant **redundant)
    1239: {
    1241:   Mat_Redundant  *redund = *redundant;
    1242:   PetscInt       i;

    1245:   if (redund){
    1246:     if (redund->matseq) { /* via MatCreateSubMatrices()  */
    1247:       ISDestroy(&redund->isrow);
    1248:       ISDestroy(&redund->iscol);
    1249:       MatDestroySubMatrices(1,&redund->matseq);
    1250:     } else {
    1251:       PetscFree2(redund->send_rank,redund->recv_rank);
    1252:       PetscFree(redund->sbuf_j);
    1253:       PetscFree(redund->sbuf_a);
    1254:       for (i=0; i<redund->nrecvs; i++) {
    1255:         PetscFree(redund->rbuf_j[i]);
    1256:         PetscFree(redund->rbuf_a[i]);
    1257:       }
    1258:       PetscFree4(redund->sbuf_nz,redund->rbuf_nz,redund->rbuf_j,redund->rbuf_a);
    1259:     }

    1261:     if (redund->subcomm) {
    1262:       PetscCommDestroy(&redund->subcomm);
    1263:     }
    1264:     PetscFree(redund);
    1265:   }
    1266:   return(0);
    1267: }

    1269: /*@
    1270:    MatDestroy - Frees space taken by a matrix.

    1272:    Collective on Mat

    1274:    Input Parameter:
    1275: .  A - the matrix

    1277:    Level: beginner

    1279: @*/
    1280: PetscErrorCode MatDestroy(Mat *A)
    1281: {

    1285:   if (!*A) return(0);
    1287:   if (--((PetscObject)(*A))->refct > 0) {*A = NULL; return(0);}

    1289:   /* if memory was published with SAWs then destroy it */
    1290:   PetscObjectSAWsViewOff((PetscObject)*A);
    1291:   if ((*A)->ops->destroy) {
    1292:     (*(*A)->ops->destroy)(*A);
    1293:   }

    1295:   PetscFree((*A)->defaultvectype);
    1296:   PetscFree((*A)->bsizes);
    1297:   PetscFree((*A)->solvertype);
    1298:   MatDestroy_Redundant(&(*A)->redundant);
    1299:   MatProductClear(*A);
    1300:   MatNullSpaceDestroy(&(*A)->nullsp);
    1301:   MatNullSpaceDestroy(&(*A)->transnullsp);
    1302:   MatNullSpaceDestroy(&(*A)->nearnullsp);
    1303:   MatDestroy(&(*A)->schur);
    1304:   PetscLayoutDestroy(&(*A)->rmap);
    1305:   PetscLayoutDestroy(&(*A)->cmap);
    1306:   PetscHeaderDestroy(A);
    1307:   return(0);
    1308: }

    1310: /*@C
    1311:    MatSetValues - Inserts or adds a block of values into a matrix.
    1312:    These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
    1313:    MUST be called after all calls to MatSetValues() have been completed.

    1315:    Not Collective

    1317:    Input Parameters:
    1318: +  mat - the matrix
    1319: .  v - a logically two-dimensional array of values
    1320: .  m, idxm - the number of rows and their global indices
    1321: .  n, idxn - the number of columns and their global indices
    1322: -  addv - either ADD_VALUES or INSERT_VALUES, where
    1323:    ADD_VALUES adds values to any existing entries, and
    1324:    INSERT_VALUES replaces existing entries with new values

    1326:    Notes:
    1327:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
    1328:       MatSetUp() before using this routine

    1330:    By default the values, v, are row-oriented. See MatSetOption() for other options.

    1332:    Calls to MatSetValues() with the INSERT_VALUES and ADD_VALUES
    1333:    options cannot be mixed without intervening calls to the assembly
    1334:    routines.

    1336:    MatSetValues() uses 0-based row and column numbers in Fortran
    1337:    as well as in C.

    1339:    Negative indices may be passed in idxm and idxn, these rows and columns are
    1340:    simply ignored. This allows easily inserting element stiffness matrices
    1341:    with homogeneous Dirchlet boundary conditions that you don't want represented
    1342:    in the matrix.

    1344:    Efficiency Alert:
    1345:    The routine MatSetValuesBlocked() may offer much better efficiency
    1346:    for users of block sparse formats (MATSEQBAIJ and MATMPIBAIJ).

    1348:    Level: beginner

    1350:    Developer Notes:
    1351:     This is labeled with C so does not automatically generate Fortran stubs and interfaces
    1352:                     because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    1354: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
    1355:           InsertMode, INSERT_VALUES, ADD_VALUES
    1356: @*/
    1357: PetscErrorCode MatSetValues(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
    1358: {

    1364:   if (!m || !n) return(0); /* no values to insert */
    1367:   MatCheckPreallocated(mat,1);

    1369:   if (mat->insertmode == NOT_SET_VALUES) {
    1370:     mat->insertmode = addv;
    1371:   } else if (PetscUnlikely(mat->insertmode != addv)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
    1372:   if (PetscDefined(USE_DEBUG)) {
    1373:     PetscInt       i,j;

    1375:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1376:     if (!mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);

    1378:     for (i=0; i<m; i++) {
    1379:       for (j=0; j<n; j++) {
    1380:         if (mat->erroriffailure && PetscIsInfOrNanScalar(v[i*n+j]))
    1381: #if defined(PETSC_USE_COMPLEX)
    1382:           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]);
    1383: #else
    1384:           SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_FP,"Inserting %g at matrix entry (%D,%D)",(double)v[i*n+j],idxm[i],idxn[j]);
    1385: #endif
    1386:       }
    1387:     }
    1388:   }

    1390:   if (mat->assembled) {
    1391:     mat->was_assembled = PETSC_TRUE;
    1392:     mat->assembled     = PETSC_FALSE;
    1393:   }
    1394:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    1395:   (*mat->ops->setvalues)(mat,m,idxm,n,idxn,v,addv);
    1396:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    1397:   return(0);
    1398: }

    1401: /*@
    1402:    MatSetValuesRowLocal - Inserts a row (block row for BAIJ matrices) of nonzero
    1403:         values into a matrix

    1405:    Not Collective

    1407:    Input Parameters:
    1408: +  mat - the matrix
    1409: .  row - the (block) row to set
    1410: -  v - a logically two-dimensional array of values

    1412:    Notes:
    1413:    By the values, v, are column-oriented (for the block version) and sorted

    1415:    All the nonzeros in the row must be provided

    1417:    The matrix must have previously had its column indices set

    1419:    The row must belong to this process

    1421:    Level: intermediate

    1423: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
    1424:           InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues(), MatSetValuesRow(), MatSetLocalToGlobalMapping()
    1425: @*/
    1426: PetscErrorCode MatSetValuesRowLocal(Mat mat,PetscInt row,const PetscScalar v[])
    1427: {
    1429:   PetscInt       globalrow;

    1435:   ISLocalToGlobalMappingApply(mat->rmap->mapping,1,&row,&globalrow);
    1436:   MatSetValuesRow(mat,globalrow,v);
    1437:   return(0);
    1438: }

    1440: /*@
    1441:    MatSetValuesRow - Inserts a row (block row for BAIJ matrices) of nonzero
    1442:         values into a matrix

    1444:    Not Collective

    1446:    Input Parameters:
    1447: +  mat - the matrix
    1448: .  row - the (block) row to set
    1449: -  v - a logically two-dimensional (column major) array of values for  block matrices with blocksize larger than one, otherwise a one dimensional array of values

    1451:    Notes:
    1452:    The values, v, are column-oriented for the block version.

    1454:    All the nonzeros in the row must be provided

    1456:    THE MATRIX MUST HAVE PREVIOUSLY HAD ITS COLUMN INDICES SET. IT IS RARE THAT THIS ROUTINE IS USED, usually MatSetValues() is used.

    1458:    The row must belong to this process

    1460:    Level: advanced

    1462: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
    1463:           InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues()
    1464: @*/
    1465: PetscErrorCode MatSetValuesRow(Mat mat,PetscInt row,const PetscScalar v[])
    1466: {

    1472:   MatCheckPreallocated(mat,1);
    1474:   if (PetscUnlikely(mat->insertmode == ADD_VALUES)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add and insert values");
    1475:   if (PetscUnlikely(mat->factortype)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1476:   mat->insertmode = INSERT_VALUES;

    1478:   if (mat->assembled) {
    1479:     mat->was_assembled = PETSC_TRUE;
    1480:     mat->assembled     = PETSC_FALSE;
    1481:   }
    1482:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    1483:   if (!mat->ops->setvaluesrow) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    1484:   (*mat->ops->setvaluesrow)(mat,row,v);
    1485:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    1486:   return(0);
    1487: }

    1489: /*@
    1490:    MatSetValuesStencil - Inserts or adds a block of values into a matrix.
    1491:      Using structured grid indexing

    1493:    Not Collective

    1495:    Input Parameters:
    1496: +  mat - the matrix
    1497: .  m - number of rows being entered
    1498: .  idxm - grid coordinates (and component number when dof > 1) for matrix rows being entered
    1499: .  n - number of columns being entered
    1500: .  idxn - grid coordinates (and component number when dof > 1) for matrix columns being entered
    1501: .  v - a logically two-dimensional array of values
    1502: -  addv - either ADD_VALUES or INSERT_VALUES, where
    1503:    ADD_VALUES adds values to any existing entries, and
    1504:    INSERT_VALUES replaces existing entries with new values

    1506:    Notes:
    1507:    By default the values, v, are row-oriented.  See MatSetOption() for other options.

    1509:    Calls to MatSetValuesStencil() with the INSERT_VALUES and ADD_VALUES
    1510:    options cannot be mixed without intervening calls to the assembly
    1511:    routines.

    1513:    The grid coordinates are across the entire grid, not just the local portion

    1515:    MatSetValuesStencil() uses 0-based row and column numbers in Fortran
    1516:    as well as in C.

    1518:    For setting/accessing vector values via array coordinates you can use the DMDAVecGetArray() routine

    1520:    In order to use this routine you must either obtain the matrix with DMCreateMatrix()
    1521:    or call MatSetLocalToGlobalMapping() and MatSetStencil() first.

    1523:    The columns and rows in the stencil passed in MUST be contained within the
    1524:    ghost region of the given process as set with DMDACreateXXX() or MatSetStencil(). For example,
    1525:    if you create a DMDA with an overlap of one grid level and on a particular process its first
    1526:    local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
    1527:    first i index you can use in your column and row indices in MatSetStencil() is 5.

    1529:    In Fortran idxm and idxn should be declared as
    1530: $     MatStencil idxm(4,m),idxn(4,n)
    1531:    and the values inserted using
    1532: $    idxm(MatStencil_i,1) = i
    1533: $    idxm(MatStencil_j,1) = j
    1534: $    idxm(MatStencil_k,1) = k
    1535: $    idxm(MatStencil_c,1) = c
    1536:    etc

    1538:    For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    1539:    obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    1540:    etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    1541:    DM_BOUNDARY_PERIODIC boundary type.

    1543:    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
    1544:    a single value per point) you can skip filling those indices.

    1546:    Inspired by the structured grid interface to the HYPRE package
    1547:    (https://computation.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)

    1549:    Efficiency Alert:
    1550:    The routine MatSetValuesBlockedStencil() may offer much better efficiency
    1551:    for users of block sparse formats (MATSEQBAIJ and MATMPIBAIJ).

    1553:    Level: beginner

    1555: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
    1556:           MatSetValues(), MatSetValuesBlockedStencil(), MatSetStencil(), DMCreateMatrix(), DMDAVecGetArray(), MatStencil
    1557: @*/
    1558: PetscErrorCode MatSetValuesStencil(Mat mat,PetscInt m,const MatStencil idxm[],PetscInt n,const MatStencil idxn[],const PetscScalar v[],InsertMode addv)
    1559: {
    1561:   PetscInt       buf[8192],*bufm=NULL,*bufn=NULL,*jdxm,*jdxn;
    1562:   PetscInt       j,i,dim = mat->stencil.dim,*dims = mat->stencil.dims+1,tmp;
    1563:   PetscInt       *starts = mat->stencil.starts,*dxm = (PetscInt*)idxm,*dxn = (PetscInt*)idxn,sdim = dim - (1 - (PetscInt)mat->stencil.noc);

    1566:   if (!m || !n) return(0); /* no values to insert */

    1572:   if ((m+n) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    1573:     jdxm = buf; jdxn = buf+m;
    1574:   } else {
    1575:     PetscMalloc2(m,&bufm,n,&bufn);
    1576:     jdxm = bufm; jdxn = bufn;
    1577:   }
    1578:   for (i=0; i<m; i++) {
    1579:     for (j=0; j<3-sdim; j++) dxm++;
    1580:     tmp = *dxm++ - starts[0];
    1581:     for (j=0; j<dim-1; j++) {
    1582:       if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
    1583:       else                                       tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    1584:     }
    1585:     if (mat->stencil.noc) dxm++;
    1586:     jdxm[i] = tmp;
    1587:   }
    1588:   for (i=0; i<n; i++) {
    1589:     for (j=0; j<3-sdim; j++) dxn++;
    1590:     tmp = *dxn++ - starts[0];
    1591:     for (j=0; j<dim-1; j++) {
    1592:       if ((*dxn++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
    1593:       else                                       tmp = tmp*dims[j] + *(dxn-1) - starts[j+1];
    1594:     }
    1595:     if (mat->stencil.noc) dxn++;
    1596:     jdxn[i] = tmp;
    1597:   }
    1598:   MatSetValuesLocal(mat,m,jdxm,n,jdxn,v,addv);
    1599:   PetscFree2(bufm,bufn);
    1600:   return(0);
    1601: }

    1603: /*@
    1604:    MatSetValuesBlockedStencil - Inserts or adds a block of values into a matrix.
    1605:      Using structured grid indexing

    1607:    Not Collective

    1609:    Input Parameters:
    1610: +  mat - the matrix
    1611: .  m - number of rows being entered
    1612: .  idxm - grid coordinates for matrix rows being entered
    1613: .  n - number of columns being entered
    1614: .  idxn - grid coordinates for matrix columns being entered
    1615: .  v - a logically two-dimensional array of values
    1616: -  addv - either ADD_VALUES or INSERT_VALUES, where
    1617:    ADD_VALUES adds values to any existing entries, and
    1618:    INSERT_VALUES replaces existing entries with new values

    1620:    Notes:
    1621:    By default the values, v, are row-oriented and unsorted.
    1622:    See MatSetOption() for other options.

    1624:    Calls to MatSetValuesBlockedStencil() with the INSERT_VALUES and ADD_VALUES
    1625:    options cannot be mixed without intervening calls to the assembly
    1626:    routines.

    1628:    The grid coordinates are across the entire grid, not just the local portion

    1630:    MatSetValuesBlockedStencil() uses 0-based row and column numbers in Fortran
    1631:    as well as in C.

    1633:    For setting/accessing vector values via array coordinates you can use the DMDAVecGetArray() routine

    1635:    In order to use this routine you must either obtain the matrix with DMCreateMatrix()
    1636:    or call MatSetBlockSize(), MatSetLocalToGlobalMapping() and MatSetStencil() first.

    1638:    The columns and rows in the stencil passed in MUST be contained within the
    1639:    ghost region of the given process as set with DMDACreateXXX() or MatSetStencil(). For example,
    1640:    if you create a DMDA with an overlap of one grid level and on a particular process its first
    1641:    local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
    1642:    first i index you can use in your column and row indices in MatSetStencil() is 5.

    1644:    In Fortran idxm and idxn should be declared as
    1645: $     MatStencil idxm(4,m),idxn(4,n)
    1646:    and the values inserted using
    1647: $    idxm(MatStencil_i,1) = i
    1648: $    idxm(MatStencil_j,1) = j
    1649: $    idxm(MatStencil_k,1) = k
    1650:    etc

    1652:    Negative indices may be passed in idxm and idxn, these rows and columns are
    1653:    simply ignored. This allows easily inserting element stiffness matrices
    1654:    with homogeneous Dirchlet boundary conditions that you don't want represented
    1655:    in the matrix.

    1657:    Inspired by the structured grid interface to the HYPRE package
    1658:    (https://computation.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)

    1660:    Level: beginner

    1662: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
    1663:           MatSetValues(), MatSetValuesStencil(), MatSetStencil(), DMCreateMatrix(), DMDAVecGetArray(), MatStencil,
    1664:           MatSetBlockSize(), MatSetLocalToGlobalMapping()
    1665: @*/
    1666: PetscErrorCode MatSetValuesBlockedStencil(Mat mat,PetscInt m,const MatStencil idxm[],PetscInt n,const MatStencil idxn[],const PetscScalar v[],InsertMode addv)
    1667: {
    1669:   PetscInt       buf[8192],*bufm=NULL,*bufn=NULL,*jdxm,*jdxn;
    1670:   PetscInt       j,i,dim = mat->stencil.dim,*dims = mat->stencil.dims+1,tmp;
    1671:   PetscInt       *starts = mat->stencil.starts,*dxm = (PetscInt*)idxm,*dxn = (PetscInt*)idxn,sdim = dim - (1 - (PetscInt)mat->stencil.noc);

    1674:   if (!m || !n) return(0); /* no values to insert */

    1681:   if ((m+n) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    1682:     jdxm = buf; jdxn = buf+m;
    1683:   } else {
    1684:     PetscMalloc2(m,&bufm,n,&bufn);
    1685:     jdxm = bufm; jdxn = bufn;
    1686:   }
    1687:   for (i=0; i<m; i++) {
    1688:     for (j=0; j<3-sdim; j++) dxm++;
    1689:     tmp = *dxm++ - starts[0];
    1690:     for (j=0; j<sdim-1; j++) {
    1691:       if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
    1692:       else                                       tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    1693:     }
    1694:     dxm++;
    1695:     jdxm[i] = tmp;
    1696:   }
    1697:   for (i=0; i<n; i++) {
    1698:     for (j=0; j<3-sdim; j++) dxn++;
    1699:     tmp = *dxn++ - starts[0];
    1700:     for (j=0; j<sdim-1; j++) {
    1701:       if ((*dxn++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
    1702:       else                                       tmp = tmp*dims[j] + *(dxn-1) - starts[j+1];
    1703:     }
    1704:     dxn++;
    1705:     jdxn[i] = tmp;
    1706:   }
    1707:   MatSetValuesBlockedLocal(mat,m,jdxm,n,jdxn,v,addv);
    1708:   PetscFree2(bufm,bufn);
    1709:   return(0);
    1710: }

    1712: /*@
    1713:    MatSetStencil - Sets the grid information for setting values into a matrix via
    1714:         MatSetValuesStencil()

    1716:    Not Collective

    1718:    Input Parameters:
    1719: +  mat - the matrix
    1720: .  dim - dimension of the grid 1, 2, or 3
    1721: .  dims - number of grid points in x, y, and z direction, including ghost points on your processor
    1722: .  starts - starting point of ghost nodes on your processor in x, y, and z direction
    1723: -  dof - number of degrees of freedom per node

    1726:    Inspired by the structured grid interface to the HYPRE package
    1727:    (www.llnl.gov/CASC/hyper)

    1729:    For matrices generated with DMCreateMatrix() this routine is automatically called and so not needed by the
    1730:    user.

    1732:    Level: beginner

    1734: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
    1735:           MatSetValues(), MatSetValuesBlockedStencil(), MatSetValuesStencil()
    1736: @*/
    1737: PetscErrorCode MatSetStencil(Mat mat,PetscInt dim,const PetscInt dims[],const PetscInt starts[],PetscInt dof)
    1738: {
    1739:   PetscInt i;

    1746:   mat->stencil.dim = dim + (dof > 1);
    1747:   for (i=0; i<dim; i++) {
    1748:     mat->stencil.dims[i]   = dims[dim-i-1];      /* copy the values in backwards */
    1749:     mat->stencil.starts[i] = starts[dim-i-1];
    1750:   }
    1751:   mat->stencil.dims[dim]   = dof;
    1752:   mat->stencil.starts[dim] = 0;
    1753:   mat->stencil.noc         = (PetscBool)(dof == 1);
    1754:   return(0);
    1755: }

    1757: /*@C
    1758:    MatSetValuesBlocked - Inserts or adds a block of values into a matrix.

    1760:    Not Collective

    1762:    Input Parameters:
    1763: +  mat - the matrix
    1764: .  v - a logically two-dimensional array of values
    1765: .  m, idxm - the number of block rows and their global block indices
    1766: .  n, idxn - the number of block columns and their global block indices
    1767: -  addv - either ADD_VALUES or INSERT_VALUES, where
    1768:    ADD_VALUES adds values to any existing entries, and
    1769:    INSERT_VALUES replaces existing entries with new values

    1771:    Notes:
    1772:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call
    1773:    MatXXXXSetPreallocation() or MatSetUp() before using this routine.

    1775:    The m and n count the NUMBER of blocks in the row direction and column direction,
    1776:    NOT the total number of rows/columns; for example, if the block size is 2 and
    1777:    you are passing in values for rows 2,3,4,5  then m would be 2 (not 4).
    1778:    The values in idxm would be 1 2; that is the first index for each block divided by
    1779:    the block size.

    1781:    Note that you must call MatSetBlockSize() when constructing this matrix (before
    1782:    preallocating it).

    1784:    By default the values, v, are row-oriented, so the layout of
    1785:    v is the same as for MatSetValues(). See MatSetOption() for other options.

    1787:    Calls to MatSetValuesBlocked() with the INSERT_VALUES and ADD_VALUES
    1788:    options cannot be mixed without intervening calls to the assembly
    1789:    routines.

    1791:    MatSetValuesBlocked() uses 0-based row and column numbers in Fortran
    1792:    as well as in C.

    1794:    Negative indices may be passed in idxm and idxn, these rows and columns are
    1795:    simply ignored. This allows easily inserting element stiffness matrices
    1796:    with homogeneous Dirchlet boundary conditions that you don't want represented
    1797:    in the matrix.

    1799:    Each time an entry is set within a sparse matrix via MatSetValues(),
    1800:    internal searching must be done to determine where to place the
    1801:    data in the matrix storage space.  By instead inserting blocks of
    1802:    entries via MatSetValuesBlocked(), the overhead of matrix assembly is
    1803:    reduced.

    1805:    Example:
    1806: $   Suppose m=n=2 and block size(bs) = 2 The array is
    1807: $
    1808: $   1  2  | 3  4
    1809: $   5  6  | 7  8
    1810: $   - - - | - - -
    1811: $   9  10 | 11 12
    1812: $   13 14 | 15 16
    1813: $
    1814: $   v[] should be passed in like
    1815: $   v[] = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
    1816: $
    1817: $  If you are not using row oriented storage of v (that is you called MatSetOption(mat,MAT_ROW_ORIENTED,PETSC_FALSE)) then
    1818: $   v[] = [1,5,9,13,2,6,10,14,3,7,11,15,4,8,12,16]

    1820:    Level: intermediate

    1822: .seealso: MatSetBlockSize(), MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetValuesBlockedLocal()
    1823: @*/
    1824: PetscErrorCode MatSetValuesBlocked(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
    1825: {

    1831:   if (!m || !n) return(0); /* no values to insert */
    1835:   MatCheckPreallocated(mat,1);
    1836:   if (mat->insertmode == NOT_SET_VALUES) {
    1837:     mat->insertmode = addv;
    1838:   } else if (PetscUnlikely(mat->insertmode != addv)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
    1839:   if (PetscDefined(USE_DEBUG)) {
    1840:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1841:     if (!mat->ops->setvaluesblocked && !mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    1842:   }

    1844:   if (mat->assembled) {
    1845:     mat->was_assembled = PETSC_TRUE;
    1846:     mat->assembled     = PETSC_FALSE;
    1847:   }
    1848:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    1849:   if (mat->ops->setvaluesblocked) {
    1850:     (*mat->ops->setvaluesblocked)(mat,m,idxm,n,idxn,v,addv);
    1851:   } else {
    1852:     PetscInt buf[8192],*bufr=NULL,*bufc=NULL,*iidxm,*iidxn;
    1853:     PetscInt i,j,bs,cbs;
    1854:     MatGetBlockSizes(mat,&bs,&cbs);
    1855:     if (m*bs+n*cbs <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    1856:       iidxm = buf; iidxn = buf + m*bs;
    1857:     } else {
    1858:       PetscMalloc2(m*bs,&bufr,n*cbs,&bufc);
    1859:       iidxm = bufr; iidxn = bufc;
    1860:     }
    1861:     for (i=0; i<m; i++) {
    1862:       for (j=0; j<bs; j++) {
    1863:         iidxm[i*bs+j] = bs*idxm[i] + j;
    1864:       }
    1865:     }
    1866:     for (i=0; i<n; i++) {
    1867:       for (j=0; j<cbs; j++) {
    1868:         iidxn[i*cbs+j] = cbs*idxn[i] + j;
    1869:       }
    1870:     }
    1871:     MatSetValues(mat,m*bs,iidxm,n*cbs,iidxn,v,addv);
    1872:     PetscFree2(bufr,bufc);
    1873:   }
    1874:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    1875:   return(0);
    1876: }

    1878: /*@C
    1879:    MatGetValues - Gets a block of values from a matrix.

    1881:    Not Collective; can only return values that are owned by the give process

    1883:    Input Parameters:
    1884: +  mat - the matrix
    1885: .  v - a logically two-dimensional array for storing the values
    1886: .  m, idxm - the number of rows and their global indices
    1887: -  n, idxn - the number of columns and their global indices

    1889:    Notes:
    1890:      The user must allocate space (m*n PetscScalars) for the values, v.
    1891:      The values, v, are then returned in a row-oriented format,
    1892:      analogous to that used by default in MatSetValues().

    1894:      MatGetValues() uses 0-based row and column numbers in
    1895:      Fortran as well as in C.

    1897:      MatGetValues() requires that the matrix has been assembled
    1898:      with MatAssemblyBegin()/MatAssemblyEnd().  Thus, calls to
    1899:      MatSetValues() and MatGetValues() CANNOT be made in succession
    1900:      without intermediate matrix assembly.

    1902:      Negative row or column indices will be ignored and those locations in v[] will be
    1903:      left unchanged.

    1905:      For the standard row-based matrix formats, idxm[] can only contain rows owned by the requesting MPI rank.
    1906:      That is, rows with global index greater than or equal to restart and less than rend where restart and rend are obtainable
    1907:      from MatGetOwnershipRange(mat,&rstart,&rend).

    1909:    Level: advanced

    1911: .seealso: MatGetRow(), MatCreateSubMatrices(), MatSetValues(), MatGetOwnershipRange(), MatGetValuesLocal()
    1912: @*/
    1913: PetscErrorCode MatGetValues(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
    1914: {

    1920:   if (!m || !n) return(0);
    1924:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    1925:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1926:   if (!mat->ops->getvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    1927:   MatCheckPreallocated(mat,1);

    1929:   PetscLogEventBegin(MAT_GetValues,mat,0,0,0);
    1930:   (*mat->ops->getvalues)(mat,m,idxm,n,idxn,v);
    1931:   PetscLogEventEnd(MAT_GetValues,mat,0,0,0);
    1932:   return(0);
    1933: }

    1935: /*@C
    1936:    MatGetValuesLocal - retrieves values from certain locations in a matrix using the local numbering of the indices
    1937:      defined previously by MatSetLocalToGlobalMapping()

    1939:    Not Collective

    1941:    Input Parameters:
    1942: +  mat - the matrix
    1943: .  nrow, irow - number of rows and their local indices
    1944: -  ncol, icol - number of columns and their local indices

    1946:    Output Parameter:
    1947: .  y -  a logically two-dimensional array of values

    1949:    Notes:
    1950:      If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatSetLocalToGlobalMapping() before using this routine.

    1952:      This routine can only return values that are owned by the requesting MPI rank. That is, for standard matrix formats, rows that, in the global numbering,
    1953:      are greater than or equal to restart and less than rend where restart and rend are obtainable from MatGetOwnershipRange(mat,&rstart,&rend). One can
    1954:      determine if the resulting global row associated with the local row r is owned by the requesting MPI rank by applying the ISLocalToGlobalMapping set
    1955:      with MatSetLocalToGlobalMapping().

    1957:    Developer Notes:
    1958:       This is labelled with C so does not automatically generate Fortran stubs and interfaces
    1959:       because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    1961:    Level: advanced

    1963: .seealso:  MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetLocalToGlobalMapping(),
    1964:            MatSetValuesLocal(), MatGetValues()
    1965: @*/
    1966: PetscErrorCode MatGetValuesLocal(Mat mat,PetscInt nrow,const PetscInt irow[],PetscInt ncol,const PetscInt icol[],PetscScalar y[])
    1967: {

    1973:   MatCheckPreallocated(mat,1);
    1974:   if (!nrow || !ncol) return(0); /* no values to retrieve */
    1977:   if (PetscDefined(USE_DEBUG)) {
    1978:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1979:     if (!mat->ops->getvalueslocal && !mat->ops->getvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    1980:   }
    1981:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    1982:   PetscLogEventBegin(MAT_GetValues,mat,0,0,0);
    1983:   if (mat->ops->getvalueslocal) {
    1984:     (*mat->ops->getvalueslocal)(mat,nrow,irow,ncol,icol,y);
    1985:   } else {
    1986:     PetscInt buf[8192],*bufr=NULL,*bufc=NULL,*irowm,*icolm;
    1987:     if ((nrow+ncol) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    1988:       irowm = buf; icolm = buf+nrow;
    1989:     } else {
    1990:       PetscMalloc2(nrow,&bufr,ncol,&bufc);
    1991:       irowm = bufr; icolm = bufc;
    1992:     }
    1993:     if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatGetValuesLocal() cannot proceed without local-to-global row mapping (See MatSetLocalToGlobalMapping()).");
    1994:     if (!mat->cmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatGetValuesLocal() cannot proceed without local-to-global column mapping (See MatSetLocalToGlobalMapping()).");
    1995:     ISLocalToGlobalMappingApply(mat->rmap->mapping,nrow,irow,irowm);
    1996:     ISLocalToGlobalMappingApply(mat->cmap->mapping,ncol,icol,icolm);
    1997:     MatGetValues(mat,nrow,irowm,ncol,icolm,y);
    1998:     PetscFree2(bufr,bufc);
    1999:   }
    2000:   PetscLogEventEnd(MAT_GetValues,mat,0,0,0);
    2001:   return(0);
    2002: }

    2004: /*@
    2005:   MatSetValuesBatch - Adds (ADD_VALUES) many blocks of values into a matrix at once. The blocks must all be square and
    2006:   the same size. Currently, this can only be called once and creates the given matrix.

    2008:   Not Collective

    2010:   Input Parameters:
    2011: + mat - the matrix
    2012: . nb - the number of blocks
    2013: . bs - the number of rows (and columns) in each block
    2014: . rows - a concatenation of the rows for each block
    2015: - v - a concatenation of logically two-dimensional arrays of values

    2017:   Notes:
    2018:   In the future, we will extend this routine to handle rectangular blocks, and to allow multiple calls for a given matrix.

    2020:   Level: advanced

    2022: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
    2023:           InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues()
    2024: @*/
    2025: PetscErrorCode MatSetValuesBatch(Mat mat, PetscInt nb, PetscInt bs, PetscInt rows[], const PetscScalar v[])
    2026: {

    2034:   if (PetscUnlikelyDebug(mat->factortype)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

    2036:   PetscLogEventBegin(MAT_SetValuesBatch,mat,0,0,0);
    2037:   if (mat->ops->setvaluesbatch) {
    2038:     (*mat->ops->setvaluesbatch)(mat,nb,bs,rows,v);
    2039:   } else {
    2040:     PetscInt b;
    2041:     for (b = 0; b < nb; ++b) {
    2042:       MatSetValues(mat, bs, &rows[b*bs], bs, &rows[b*bs], &v[b*bs*bs], ADD_VALUES);
    2043:     }
    2044:   }
    2045:   PetscLogEventEnd(MAT_SetValuesBatch,mat,0,0,0);
    2046:   return(0);
    2047: }

    2049: /*@
    2050:    MatSetLocalToGlobalMapping - Sets a local-to-global numbering for use by
    2051:    the routine MatSetValuesLocal() to allow users to insert matrix entries
    2052:    using a local (per-processor) numbering.

    2054:    Not Collective

    2056:    Input Parameters:
    2057: +  x - the matrix
    2058: .  rmapping - row mapping created with ISLocalToGlobalMappingCreate()   or ISLocalToGlobalMappingCreateIS()
    2059: - cmapping - column mapping

    2061:    Level: intermediate

    2064: .seealso:  MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetValuesLocal(), MatGetValuesLocal()
    2065: @*/
    2066: PetscErrorCode MatSetLocalToGlobalMapping(Mat x,ISLocalToGlobalMapping rmapping,ISLocalToGlobalMapping cmapping)
    2067: {

    2076:   if (x->ops->setlocaltoglobalmapping) {
    2077:     (*x->ops->setlocaltoglobalmapping)(x,rmapping,cmapping);
    2078:   } else {
    2079:     PetscLayoutSetISLocalToGlobalMapping(x->rmap,rmapping);
    2080:     PetscLayoutSetISLocalToGlobalMapping(x->cmap,cmapping);
    2081:   }
    2082:   return(0);
    2083: }

    2086: /*@
    2087:    MatGetLocalToGlobalMapping - Gets the local-to-global numbering set by MatSetLocalToGlobalMapping()

    2089:    Not Collective

    2091:    Input Parameters:
    2092: .  A - the matrix

    2094:    Output Parameters:
    2095: + rmapping - row mapping
    2096: - cmapping - column mapping

    2098:    Level: advanced

    2101: .seealso:  MatSetValuesLocal()
    2102: @*/
    2103: PetscErrorCode MatGetLocalToGlobalMapping(Mat A,ISLocalToGlobalMapping *rmapping,ISLocalToGlobalMapping *cmapping)
    2104: {
    2110:   if (rmapping) *rmapping = A->rmap->mapping;
    2111:   if (cmapping) *cmapping = A->cmap->mapping;
    2112:   return(0);
    2113: }

    2115: /*@
    2116:    MatSetLayouts - Sets the PetscLayout objects for rows and columns of a matrix

    2118:    Logically Collective on A

    2120:    Input Parameters:
    2121: +  A - the matrix
    2122: . rmap - row layout
    2123: - cmap - column layout

    2125:    Level: advanced

    2127: .seealso:  MatCreateVecs(), MatGetLocalToGlobalMapping(), MatGetLayouts()
    2128: @*/
    2129: PetscErrorCode MatSetLayouts(Mat A,PetscLayout rmap,PetscLayout cmap)
    2130: {

    2136:   PetscLayoutReference(rmap,&A->rmap);
    2137:   PetscLayoutReference(cmap,&A->cmap);
    2138:   return(0);
    2139: }

    2141: /*@
    2142:    MatGetLayouts - Gets the PetscLayout objects for rows and columns

    2144:    Not Collective

    2146:    Input Parameters:
    2147: .  A - the matrix

    2149:    Output Parameters:
    2150: + rmap - row layout
    2151: - cmap - column layout

    2153:    Level: advanced

    2155: .seealso:  MatCreateVecs(), MatGetLocalToGlobalMapping(), MatSetLayouts()
    2156: @*/
    2157: PetscErrorCode MatGetLayouts(Mat A,PetscLayout *rmap,PetscLayout *cmap)
    2158: {
    2164:   if (rmap) *rmap = A->rmap;
    2165:   if (cmap) *cmap = A->cmap;
    2166:   return(0);
    2167: }

    2169: /*@C
    2170:    MatSetValuesLocal - Inserts or adds values into certain locations of a matrix,
    2171:    using a local numbering of the nodes.

    2173:    Not Collective

    2175:    Input Parameters:
    2176: +  mat - the matrix
    2177: .  nrow, irow - number of rows and their local indices
    2178: .  ncol, icol - number of columns and their local indices
    2179: .  y -  a logically two-dimensional array of values
    2180: -  addv - either INSERT_VALUES or ADD_VALUES, where
    2181:    ADD_VALUES adds values to any existing entries, and
    2182:    INSERT_VALUES replaces existing entries with new values

    2184:    Notes:
    2185:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
    2186:       MatSetUp() before using this routine

    2188:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatSetLocalToGlobalMapping() before using this routine

    2190:    Calls to MatSetValuesLocal() with the INSERT_VALUES and ADD_VALUES
    2191:    options cannot be mixed without intervening calls to the assembly
    2192:    routines.

    2194:    These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
    2195:    MUST be called after all calls to MatSetValuesLocal() have been completed.

    2197:    Level: intermediate

    2199:    Developer Notes:
    2200:     This is labeled with C so does not automatically generate Fortran stubs and interfaces
    2201:                     because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    2203: .seealso:  MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetLocalToGlobalMapping(),
    2204:            MatSetValueLocal(), MatGetValuesLocal()
    2205: @*/
    2206: PetscErrorCode MatSetValuesLocal(Mat mat,PetscInt nrow,const PetscInt irow[],PetscInt ncol,const PetscInt icol[],const PetscScalar y[],InsertMode addv)
    2207: {

    2213:   MatCheckPreallocated(mat,1);
    2214:   if (!nrow || !ncol) return(0); /* no values to insert */
    2217:   if (mat->insertmode == NOT_SET_VALUES) {
    2218:     mat->insertmode = addv;
    2219:   }
    2220:   else if (PetscUnlikely(mat->insertmode != addv)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
    2221:   if (PetscDefined(USE_DEBUG)) {
    2222:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2223:     if (!mat->ops->setvalueslocal && !mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    2224:   }

    2226:   if (mat->assembled) {
    2227:     mat->was_assembled = PETSC_TRUE;
    2228:     mat->assembled     = PETSC_FALSE;
    2229:   }
    2230:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    2231:   if (mat->ops->setvalueslocal) {
    2232:     (*mat->ops->setvalueslocal)(mat,nrow,irow,ncol,icol,y,addv);
    2233:   } else {
    2234:     PetscInt buf[8192],*bufr=NULL,*bufc=NULL,*irowm,*icolm;
    2235:     if ((nrow+ncol) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    2236:       irowm = buf; icolm = buf+nrow;
    2237:     } else {
    2238:       PetscMalloc2(nrow,&bufr,ncol,&bufc);
    2239:       irowm = bufr; icolm = bufc;
    2240:     }
    2241:     if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatSetValuesLocal() cannot proceed without local-to-global row mapping (See MatSetLocalToGlobalMapping()).");
    2242:     if (!mat->cmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatSetValuesLocal() cannot proceed without local-to-global column mapping (See MatSetLocalToGlobalMapping()).");
    2243:     ISLocalToGlobalMappingApply(mat->rmap->mapping,nrow,irow,irowm);
    2244:     ISLocalToGlobalMappingApply(mat->cmap->mapping,ncol,icol,icolm);
    2245:     MatSetValues(mat,nrow,irowm,ncol,icolm,y,addv);
    2246:     PetscFree2(bufr,bufc);
    2247:   }
    2248:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    2249:   return(0);
    2250: }

    2252: /*@C
    2253:    MatSetValuesBlockedLocal - Inserts or adds values into certain locations of a matrix,
    2254:    using a local ordering of the nodes a block at a time.

    2256:    Not Collective

    2258:    Input Parameters:
    2259: +  x - the matrix
    2260: .  nrow, irow - number of rows and their local indices
    2261: .  ncol, icol - number of columns and their local indices
    2262: .  y -  a logically two-dimensional array of values
    2263: -  addv - either INSERT_VALUES or ADD_VALUES, where
    2264:    ADD_VALUES adds values to any existing entries, and
    2265:    INSERT_VALUES replaces existing entries with new values

    2267:    Notes:
    2268:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
    2269:       MatSetUp() before using this routine

    2271:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatSetBlockSize() and MatSetLocalToGlobalMapping()
    2272:       before using this routineBefore calling MatSetValuesLocal(), the user must first set the

    2274:    Calls to MatSetValuesBlockedLocal() with the INSERT_VALUES and ADD_VALUES
    2275:    options cannot be mixed without intervening calls to the assembly
    2276:    routines.

    2278:    These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
    2279:    MUST be called after all calls to MatSetValuesBlockedLocal() have been completed.

    2281:    Level: intermediate

    2283:    Developer Notes:
    2284:     This is labeled with C so does not automatically generate Fortran stubs and interfaces
    2285:                     because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    2287: .seealso:  MatSetBlockSize(), MatSetLocalToGlobalMapping(), MatAssemblyBegin(), MatAssemblyEnd(),
    2288:            MatSetValuesLocal(),  MatSetValuesBlocked()
    2289: @*/
    2290: PetscErrorCode MatSetValuesBlockedLocal(Mat mat,PetscInt nrow,const PetscInt irow[],PetscInt ncol,const PetscInt icol[],const PetscScalar y[],InsertMode addv)
    2291: {

    2297:   MatCheckPreallocated(mat,1);
    2298:   if (!nrow || !ncol) return(0); /* no values to insert */
    2302:   if (mat->insertmode == NOT_SET_VALUES) {
    2303:     mat->insertmode = addv;
    2304:   } else if (PetscUnlikely(mat->insertmode != addv)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
    2305:   if (PetscDefined(USE_DEBUG)) {
    2306:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2307:     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);
    2308:   }

    2310:   if (mat->assembled) {
    2311:     mat->was_assembled = PETSC_TRUE;
    2312:     mat->assembled     = PETSC_FALSE;
    2313:   }
    2314:   if (PetscUnlikelyDebug(mat->rmap->mapping)) { /* Condition on the mapping existing, because MatSetValuesBlockedLocal_IS does not require it to be set. */
    2315:     PetscInt irbs, rbs;
    2316:     MatGetBlockSizes(mat, &rbs, NULL);
    2317:     ISLocalToGlobalMappingGetBlockSize(mat->rmap->mapping,&irbs);
    2318:     if (rbs != irbs) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Different row block sizes! mat %D, row l2g map %D",rbs,irbs);
    2319:   }
    2320:   if (PetscUnlikelyDebug(mat->cmap->mapping)) {
    2321:     PetscInt icbs, cbs;
    2322:     MatGetBlockSizes(mat,NULL,&cbs);
    2323:     ISLocalToGlobalMappingGetBlockSize(mat->cmap->mapping,&icbs);
    2324:     if (cbs != icbs) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Different col block sizes! mat %D, col l2g map %D",cbs,icbs);
    2325:   }
    2326:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    2327:   if (mat->ops->setvaluesblockedlocal) {
    2328:     (*mat->ops->setvaluesblockedlocal)(mat,nrow,irow,ncol,icol,y,addv);
    2329:   } else {
    2330:     PetscInt buf[8192],*bufr=NULL,*bufc=NULL,*irowm,*icolm;
    2331:     if ((nrow+ncol) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    2332:       irowm = buf; icolm = buf + nrow;
    2333:     } else {
    2334:       PetscMalloc2(nrow,&bufr,ncol,&bufc);
    2335:       irowm = bufr; icolm = bufc;
    2336:     }
    2337:     ISLocalToGlobalMappingApplyBlock(mat->rmap->mapping,nrow,irow,irowm);
    2338:     ISLocalToGlobalMappingApplyBlock(mat->cmap->mapping,ncol,icol,icolm);
    2339:     MatSetValuesBlocked(mat,nrow,irowm,ncol,icolm,y,addv);
    2340:     PetscFree2(bufr,bufc);
    2341:   }
    2342:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    2343:   return(0);
    2344: }

    2346: /*@
    2347:    MatMultDiagonalBlock - Computes the matrix-vector product, y = Dx. Where D is defined by the inode or block structure of the diagonal

    2349:    Collective on Mat

    2351:    Input Parameters:
    2352: +  mat - the matrix
    2353: -  x   - the vector to be multiplied

    2355:    Output Parameters:
    2356: .  y - the result

    2358:    Notes:
    2359:    The vectors x and y cannot be the same.  I.e., one cannot
    2360:    call MatMult(A,y,y).

    2362:    Level: developer

    2364: .seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    2365: @*/
    2366: PetscErrorCode MatMultDiagonalBlock(Mat mat,Vec x,Vec y)
    2367: {

    2376:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2377:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2378:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2379:   MatCheckPreallocated(mat,1);

    2381:   if (!mat->ops->multdiagonalblock) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s does not have a multiply defined",((PetscObject)mat)->type_name);
    2382:   (*mat->ops->multdiagonalblock)(mat,x,y);
    2383:   PetscObjectStateIncrease((PetscObject)y);
    2384:   return(0);
    2385: }

    2387: /* --------------------------------------------------------*/
    2388: /*@
    2389:    MatMult - Computes the matrix-vector product, y = Ax.

    2391:    Neighbor-wise Collective on Mat

    2393:    Input Parameters:
    2394: +  mat - the matrix
    2395: -  x   - the vector to be multiplied

    2397:    Output Parameters:
    2398: .  y - the result

    2400:    Notes:
    2401:    The vectors x and y cannot be the same.  I.e., one cannot
    2402:    call MatMult(A,y,y).

    2404:    Level: beginner

    2406: .seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    2407: @*/
    2408: PetscErrorCode MatMult(Mat mat,Vec x,Vec y)
    2409: {

    2417:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2418:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2419:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2420: #if !defined(PETSC_HAVE_CONSTRAINTS)
    2421:   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);
    2422:   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);
    2423:   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);
    2424: #endif
    2425:   VecSetErrorIfLocked(y,3);
    2426:   if (mat->erroriffailure) {VecValidValues(x,2,PETSC_TRUE);}
    2427:   MatCheckPreallocated(mat,1);

    2429:   VecLockReadPush(x);
    2430:   if (!mat->ops->mult) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s does not have a multiply defined",((PetscObject)mat)->type_name);
    2431:   PetscLogEventBegin(MAT_Mult,mat,x,y,0);
    2432:   (*mat->ops->mult)(mat,x,y);
    2433:   PetscLogEventEnd(MAT_Mult,mat,x,y,0);
    2434:   if (mat->erroriffailure) {VecValidValues(y,3,PETSC_FALSE);}
    2435:   VecLockReadPop(x);
    2436:   return(0);
    2437: }

    2439: /*@
    2440:    MatMultTranspose - Computes matrix transpose times a vector y = A^T * x.

    2442:    Neighbor-wise Collective on Mat

    2444:    Input Parameters:
    2445: +  mat - the matrix
    2446: -  x   - the vector to be multiplied

    2448:    Output Parameters:
    2449: .  y - the result

    2451:    Notes:
    2452:    The vectors x and y cannot be the same.  I.e., one cannot
    2453:    call MatMultTranspose(A,y,y).

    2455:    For complex numbers this does NOT compute the Hermitian (complex conjugate) transpose multiple,
    2456:    use MatMultHermitianTranspose()

    2458:    Level: beginner

    2460: .seealso: MatMult(), MatMultAdd(), MatMultTransposeAdd(), MatMultHermitianTranspose(), MatTranspose()
    2461: @*/
    2462: PetscErrorCode MatMultTranspose(Mat mat,Vec x,Vec y)
    2463: {
    2464:   PetscErrorCode (*op)(Mat,Vec,Vec)=NULL,ierr;

    2472:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2473:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2474:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2475: #if !defined(PETSC_HAVE_CONSTRAINTS)
    2476:   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);
    2477:   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);
    2478: #endif
    2479:   if (mat->erroriffailure) {VecValidValues(x,2,PETSC_TRUE);}
    2480:   MatCheckPreallocated(mat,1);

    2482:   if (!mat->ops->multtranspose) {
    2483:     if (mat->symmetric && mat->ops->mult) op = mat->ops->mult;
    2484:     if (!op) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s does not have a multiply transpose defined or is symmetric and does not have a multiply defined",((PetscObject)mat)->type_name);
    2485:   } else op = mat->ops->multtranspose;
    2486:   PetscLogEventBegin(MAT_MultTranspose,mat,x,y,0);
    2487:   VecLockReadPush(x);
    2488:   (*op)(mat,x,y);
    2489:   VecLockReadPop(x);
    2490:   PetscLogEventEnd(MAT_MultTranspose,mat,x,y,0);
    2491:   PetscObjectStateIncrease((PetscObject)y);
    2492:   if (mat->erroriffailure) {VecValidValues(y,3,PETSC_FALSE);}
    2493:   return(0);
    2494: }

    2496: /*@
    2497:    MatMultHermitianTranspose - Computes matrix Hermitian transpose times a vector.

    2499:    Neighbor-wise Collective on Mat

    2501:    Input Parameters:
    2502: +  mat - the matrix
    2503: -  x   - the vector to be multilplied

    2505:    Output Parameters:
    2506: .  y - the result

    2508:    Notes:
    2509:    The vectors x and y cannot be the same.  I.e., one cannot
    2510:    call MatMultHermitianTranspose(A,y,y).

    2512:    Also called the conjugate transpose, complex conjugate transpose, or adjoint.

    2514:    For real numbers MatMultTranspose() and MatMultHermitianTranspose() are identical.

    2516:    Level: beginner

    2518: .seealso: MatMult(), MatMultAdd(), MatMultHermitianTransposeAdd(), MatMultTranspose()
    2519: @*/
    2520: PetscErrorCode MatMultHermitianTranspose(Mat mat,Vec x,Vec y)
    2521: {

    2530:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2531:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2532:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2533: #if !defined(PETSC_HAVE_CONSTRAINTS)
    2534:   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);
    2535:   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);
    2536: #endif
    2537:   MatCheckPreallocated(mat,1);

    2539:   PetscLogEventBegin(MAT_MultHermitianTranspose,mat,x,y,0);
    2540: #if defined(PETSC_USE_COMPLEX)
    2541:   if (mat->ops->multhermitiantranspose || (mat->hermitian && mat->ops->mult)) {
    2542:     VecLockReadPush(x);
    2543:     if (mat->ops->multhermitiantranspose) {
    2544:       (*mat->ops->multhermitiantranspose)(mat,x,y);
    2545:     } else {
    2546:       (*mat->ops->mult)(mat,x,y);
    2547:     }
    2548:     VecLockReadPop(x);
    2549:   } else {
    2550:     Vec w;
    2551:     VecDuplicate(x,&w);
    2552:     VecCopy(x,w);
    2553:     VecConjugate(w);
    2554:     MatMultTranspose(mat,w,y);
    2555:     VecDestroy(&w);
    2556:     VecConjugate(y);
    2557:   }
    2558:   PetscObjectStateIncrease((PetscObject)y);
    2559: #else
    2560:   MatMultTranspose(mat,x,y);
    2561: #endif
    2562:   PetscLogEventEnd(MAT_MultHermitianTranspose,mat,x,y,0);
    2563:   return(0);
    2564: }

    2566: /*@
    2567:     MatMultAdd -  Computes v3 = v2 + A * v1.

    2569:     Neighbor-wise Collective on Mat

    2571:     Input Parameters:
    2572: +   mat - the matrix
    2573: -   v1, v2 - the vectors

    2575:     Output Parameters:
    2576: .   v3 - the result

    2578:     Notes:
    2579:     The vectors v1 and v3 cannot be the same.  I.e., one cannot
    2580:     call MatMultAdd(A,v1,v2,v1).

    2582:     Level: beginner

    2584: .seealso: MatMultTranspose(), MatMult(), MatMultTransposeAdd()
    2585: @*/
    2586: PetscErrorCode MatMultAdd(Mat mat,Vec v1,Vec v2,Vec v3)
    2587: {

    2597:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2598:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2599:   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);
    2600:   /* 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);
    2601:      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); */
    2602:   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);
    2603:   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);
    2604:   if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
    2605:   MatCheckPreallocated(mat,1);

    2607:   if (!mat->ops->multadd) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No MatMultAdd() for matrix type %s",((PetscObject)mat)->type_name);
    2608:   PetscLogEventBegin(MAT_MultAdd,mat,v1,v2,v3);
    2609:   VecLockReadPush(v1);
    2610:   (*mat->ops->multadd)(mat,v1,v2,v3);
    2611:   VecLockReadPop(v1);
    2612:   PetscLogEventEnd(MAT_MultAdd,mat,v1,v2,v3);
    2613:   PetscObjectStateIncrease((PetscObject)v3);
    2614:   return(0);
    2615: }

    2617: /*@
    2618:    MatMultTransposeAdd - Computes v3 = v2 + A' * v1.

    2620:    Neighbor-wise Collective on Mat

    2622:    Input Parameters:
    2623: +  mat - the matrix
    2624: -  v1, v2 - the vectors

    2626:    Output Parameters:
    2627: .  v3 - the result

    2629:    Notes:
    2630:    The vectors v1 and v3 cannot be the same.  I.e., one cannot
    2631:    call MatMultTransposeAdd(A,v1,v2,v1).

    2633:    Level: beginner

    2635: .seealso: MatMultTranspose(), MatMultAdd(), MatMult()
    2636: @*/
    2637: PetscErrorCode MatMultTransposeAdd(Mat mat,Vec v1,Vec v2,Vec v3)
    2638: {

    2648:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2649:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2650:   if (!mat->ops->multtransposeadd) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    2651:   if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
    2652:   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);
    2653:   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);
    2654:   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);
    2655:   MatCheckPreallocated(mat,1);

    2657:   PetscLogEventBegin(MAT_MultTransposeAdd,mat,v1,v2,v3);
    2658:   VecLockReadPush(v1);
    2659:   (*mat->ops->multtransposeadd)(mat,v1,v2,v3);
    2660:   VecLockReadPop(v1);
    2661:   PetscLogEventEnd(MAT_MultTransposeAdd,mat,v1,v2,v3);
    2662:   PetscObjectStateIncrease((PetscObject)v3);
    2663:   return(0);
    2664: }

    2666: /*@
    2667:    MatMultHermitianTransposeAdd - Computes v3 = v2 + A^H * v1.

    2669:    Neighbor-wise Collective on Mat

    2671:    Input Parameters:
    2672: +  mat - the matrix
    2673: -  v1, v2 - the vectors

    2675:    Output Parameters:
    2676: .  v3 - the result

    2678:    Notes:
    2679:    The vectors v1 and v3 cannot be the same.  I.e., one cannot
    2680:    call MatMultHermitianTransposeAdd(A,v1,v2,v1).

    2682:    Level: beginner

    2684: .seealso: MatMultHermitianTranspose(), MatMultTranspose(), MatMultAdd(), MatMult()
    2685: @*/
    2686: PetscErrorCode MatMultHermitianTransposeAdd(Mat mat,Vec v1,Vec v2,Vec v3)
    2687: {

    2697:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2698:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2699:   if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
    2700:   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);
    2701:   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);
    2702:   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);
    2703:   MatCheckPreallocated(mat,1);

    2705:   PetscLogEventBegin(MAT_MultHermitianTransposeAdd,mat,v1,v2,v3);
    2706:   VecLockReadPush(v1);
    2707:   if (mat->ops->multhermitiantransposeadd) {
    2708:     (*mat->ops->multhermitiantransposeadd)(mat,v1,v2,v3);
    2709:   } else {
    2710:     Vec w,z;
    2711:     VecDuplicate(v1,&w);
    2712:     VecCopy(v1,w);
    2713:     VecConjugate(w);
    2714:     VecDuplicate(v3,&z);
    2715:     MatMultTranspose(mat,w,z);
    2716:     VecDestroy(&w);
    2717:     VecConjugate(z);
    2718:     if (v2 != v3) {
    2719:       VecWAXPY(v3,1.0,v2,z);
    2720:     } else {
    2721:       VecAXPY(v3,1.0,z);
    2722:     }
    2723:     VecDestroy(&z);
    2724:   }
    2725:   VecLockReadPop(v1);
    2726:   PetscLogEventEnd(MAT_MultHermitianTransposeAdd,mat,v1,v2,v3);
    2727:   PetscObjectStateIncrease((PetscObject)v3);
    2728:   return(0);
    2729: }

    2731: /*@
    2732:    MatMultConstrained - The inner multiplication routine for a
    2733:    constrained matrix P^T A P.

    2735:    Neighbor-wise Collective on Mat

    2737:    Input Parameters:
    2738: +  mat - the matrix
    2739: -  x   - the vector to be multilplied

    2741:    Output Parameters:
    2742: .  y - the result

    2744:    Notes:
    2745:    The vectors x and y cannot be the same.  I.e., one cannot
    2746:    call MatMult(A,y,y).

    2748:    Level: beginner

    2750: .seealso: MatMult(), MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    2751: @*/
    2752: PetscErrorCode MatMultConstrained(Mat mat,Vec x,Vec y)
    2753: {

    2760:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2761:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2762:   if (x == y) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2763:   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);
    2764:   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);
    2765:   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);

    2767:   PetscLogEventBegin(MAT_MultConstrained,mat,x,y,0);
    2768:   VecLockReadPush(x);
    2769:   (*mat->ops->multconstrained)(mat,x,y);
    2770:   VecLockReadPop(x);
    2771:   PetscLogEventEnd(MAT_MultConstrained,mat,x,y,0);
    2772:   PetscObjectStateIncrease((PetscObject)y);
    2773:   return(0);
    2774: }

    2776: /*@
    2777:    MatMultTransposeConstrained - The inner multiplication routine for a
    2778:    constrained matrix P^T A^T P.

    2780:    Neighbor-wise Collective on Mat

    2782:    Input Parameters:
    2783: +  mat - the matrix
    2784: -  x   - the vector to be multilplied

    2786:    Output Parameters:
    2787: .  y - the result

    2789:    Notes:
    2790:    The vectors x and y cannot be the same.  I.e., one cannot
    2791:    call MatMult(A,y,y).

    2793:    Level: beginner

    2795: .seealso: MatMult(), MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    2796: @*/
    2797: PetscErrorCode MatMultTransposeConstrained(Mat mat,Vec x,Vec y)
    2798: {

    2805:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2806:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2807:   if (x == y) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2808:   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);
    2809:   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);

    2811:   PetscLogEventBegin(MAT_MultConstrained,mat,x,y,0);
    2812:   (*mat->ops->multtransposeconstrained)(mat,x,y);
    2813:   PetscLogEventEnd(MAT_MultConstrained,mat,x,y,0);
    2814:   PetscObjectStateIncrease((PetscObject)y);
    2815:   return(0);
    2816: }

    2818: /*@C
    2819:    MatGetFactorType - gets the type of factorization it is

    2821:    Not Collective

    2823:    Input Parameters:
    2824: .  mat - the matrix

    2826:    Output Parameters:
    2827: .  t - the type, one of MAT_FACTOR_NONE, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ILU, MAT_FACTOR_ICC,MAT_FACTOR_ILUDT

    2829:    Level: intermediate

    2831: .seealso: MatFactorType, MatGetFactor(), MatSetFactorType()
    2832: @*/
    2833: PetscErrorCode MatGetFactorType(Mat mat,MatFactorType *t)
    2834: {
    2839:   *t = mat->factortype;
    2840:   return(0);
    2841: }

    2843: /*@C
    2844:    MatSetFactorType - sets the type of factorization it is

    2846:    Logically Collective on Mat

    2848:    Input Parameters:
    2849: +  mat - the matrix
    2850: -  t - the type, one of MAT_FACTOR_NONE, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ILU, MAT_FACTOR_ICC,MAT_FACTOR_ILUDT

    2852:    Level: intermediate

    2854: .seealso: MatFactorType, MatGetFactor(), MatGetFactorType()
    2855: @*/
    2856: PetscErrorCode MatSetFactorType(Mat mat, MatFactorType t)
    2857: {
    2861:   mat->factortype = t;
    2862:   return(0);
    2863: }

    2865: /* ------------------------------------------------------------*/
    2866: /*@C
    2867:    MatGetInfo - Returns information about matrix storage (number of
    2868:    nonzeros, memory, etc.).

    2870:    Collective on Mat if MAT_GLOBAL_MAX or MAT_GLOBAL_SUM is used as the flag

    2872:    Input Parameters:
    2873: .  mat - the matrix

    2875:    Output Parameters:
    2876: +  flag - flag indicating the type of parameters to be returned
    2877:    (MAT_LOCAL - local matrix, MAT_GLOBAL_MAX - maximum over all processors,
    2878:    MAT_GLOBAL_SUM - sum over all processors)
    2879: -  info - matrix information context

    2881:    Notes:
    2882:    The MatInfo context contains a variety of matrix data, including
    2883:    number of nonzeros allocated and used, number of mallocs during
    2884:    matrix assembly, etc.  Additional information for factored matrices
    2885:    is provided (such as the fill ratio, number of mallocs during
    2886:    factorization, etc.).  Much of this info is printed to PETSC_STDOUT
    2887:    when using the runtime options
    2888: $       -info -mat_view ::ascii_info

    2890:    Example for C/C++ Users:
    2891:    See the file ${PETSC_DIR}/include/petscmat.h for a complete list of
    2892:    data within the MatInfo context.  For example,
    2893: .vb
    2894:       MatInfo info;
    2895:       Mat     A;
    2896:       double  mal, nz_a, nz_u;

    2898:       MatGetInfo(A,MAT_LOCAL,&info);
    2899:       mal  = info.mallocs;
    2900:       nz_a = info.nz_allocated;
    2901: .ve

    2903:    Example for Fortran Users:
    2904:    Fortran users should declare info as a double precision
    2905:    array of dimension MAT_INFO_SIZE, and then extract the parameters
    2906:    of interest.  See the file ${PETSC_DIR}/include/petsc/finclude/petscmat.h
    2907:    a complete list of parameter names.
    2908: .vb
    2909:       double  precision info(MAT_INFO_SIZE)
    2910:       double  precision mal, nz_a
    2911:       Mat     A
    2912:       integer ierr

    2914:       call MatGetInfo(A,MAT_LOCAL,info,ierr)
    2915:       mal = info(MAT_INFO_MALLOCS)
    2916:       nz_a = info(MAT_INFO_NZ_ALLOCATED)
    2917: .ve

    2919:     Level: intermediate

    2921:     Developer Note: fortran interface is not autogenerated as the f90
    2922:     interface defintion cannot be generated correctly [due to MatInfo]

    2924: .seealso: MatStashGetInfo()

    2926: @*/
    2927: PetscErrorCode MatGetInfo(Mat mat,MatInfoType flag,MatInfo *info)
    2928: {

    2935:   if (!mat->ops->getinfo) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    2936:   MatCheckPreallocated(mat,1);
    2937:   (*mat->ops->getinfo)(mat,flag,info);
    2938:   return(0);
    2939: }

    2941: /*
    2942:    This is used by external packages where it is not easy to get the info from the actual
    2943:    matrix factorization.
    2944: */
    2945: PetscErrorCode MatGetInfo_External(Mat A,MatInfoType flag,MatInfo *info)
    2946: {

    2950:   PetscMemzero(info,sizeof(MatInfo));
    2951:   return(0);
    2952: }

    2954: /* ----------------------------------------------------------*/

    2956: /*@C
    2957:    MatLUFactor - Performs in-place LU factorization of matrix.

    2959:    Collective on Mat

    2961:    Input Parameters:
    2962: +  mat - the matrix
    2963: .  row - row permutation
    2964: .  col - column permutation
    2965: -  info - options for factorization, includes
    2966: $          fill - expected fill as ratio of original fill.
    2967: $          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    2968: $                   Run with the option -info to determine an optimal value to use

    2970:    Notes:
    2971:    Most users should employ the simplified KSP interface for linear solvers
    2972:    instead of working directly with matrix algebra routines such as this.
    2973:    See, e.g., KSPCreate().

    2975:    This changes the state of the matrix to a factored matrix; it cannot be used
    2976:    for example with MatSetValues() unless one first calls MatSetUnfactored().

    2978:    Level: developer

    2980: .seealso: MatLUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor(),
    2981:           MatGetOrdering(), MatSetUnfactored(), MatFactorInfo, MatGetFactor()

    2983:     Developer Note: fortran interface is not autogenerated as the f90
    2984:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    2986: @*/
    2987: PetscErrorCode MatLUFactor(Mat mat,IS row,IS col,const MatFactorInfo *info)
    2988: {
    2990:   MatFactorInfo  tinfo;

    2998:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2999:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3000:   if (!mat->ops->lufactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3001:   MatCheckPreallocated(mat,1);
    3002:   if (!info) {
    3003:     MatFactorInfoInitialize(&tinfo);
    3004:     info = &tinfo;
    3005:   }

    3007:   PetscLogEventBegin(MAT_LUFactor,mat,row,col,0);
    3008:   (*mat->ops->lufactor)(mat,row,col,info);
    3009:   PetscLogEventEnd(MAT_LUFactor,mat,row,col,0);
    3010:   PetscObjectStateIncrease((PetscObject)mat);
    3011:   return(0);
    3012: }

    3014: /*@C
    3015:    MatILUFactor - Performs in-place ILU factorization of matrix.

    3017:    Collective on Mat

    3019:    Input Parameters:
    3020: +  mat - the matrix
    3021: .  row - row permutation
    3022: .  col - column permutation
    3023: -  info - structure containing
    3024: $      levels - number of levels of fill.
    3025: $      expected fill - as ratio of original fill.
    3026: $      1 or 0 - indicating force fill on diagonal (improves robustness for matrices
    3027:                 missing diagonal entries)

    3029:    Notes:
    3030:    Probably really in-place only when level of fill is zero, otherwise allocates
    3031:    new space to store factored matrix and deletes previous memory.

    3033:    Most users should employ the simplified KSP interface for linear solvers
    3034:    instead of working directly with matrix algebra routines such as this.
    3035:    See, e.g., KSPCreate().

    3037:    Level: developer

    3039: .seealso: MatILUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor(), MatFactorInfo

    3041:     Developer Note: fortran interface is not autogenerated as the f90
    3042:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3044: @*/
    3045: PetscErrorCode MatILUFactor(Mat mat,IS row,IS col,const MatFactorInfo *info)
    3046: {

    3055:   if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"matrix must be square");
    3056:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3057:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3058:   if (!mat->ops->ilufactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3059:   MatCheckPreallocated(mat,1);

    3061:   PetscLogEventBegin(MAT_ILUFactor,mat,row,col,0);
    3062:   (*mat->ops->ilufactor)(mat,row,col,info);
    3063:   PetscLogEventEnd(MAT_ILUFactor,mat,row,col,0);
    3064:   PetscObjectStateIncrease((PetscObject)mat);
    3065:   return(0);
    3066: }

    3068: /*@C
    3069:    MatLUFactorSymbolic - Performs symbolic LU factorization of matrix.
    3070:    Call this routine before calling MatLUFactorNumeric().

    3072:    Collective on Mat

    3074:    Input Parameters:
    3075: +  fact - the factor matrix obtained with MatGetFactor()
    3076: .  mat - the matrix
    3077: .  row, col - row and column permutations
    3078: -  info - options for factorization, includes
    3079: $          fill - expected fill as ratio of original fill.
    3080: $          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3081: $                   Run with the option -info to determine an optimal value to use

    3084:    Notes:
    3085:     See Users-Manual: ch_mat for additional information about choosing the fill factor for better efficiency.

    3087:    Most users should employ the simplified KSP interface for linear solvers
    3088:    instead of working directly with matrix algebra routines such as this.
    3089:    See, e.g., KSPCreate().

    3091:    Level: developer

    3093: .seealso: MatLUFactor(), MatLUFactorNumeric(), MatCholeskyFactor(), MatFactorInfo, MatFactorInfoInitialize()

    3095:     Developer Note: fortran interface is not autogenerated as the f90
    3096:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3098: @*/
    3099: PetscErrorCode MatLUFactorSymbolic(Mat fact,Mat mat,IS row,IS col,const MatFactorInfo *info)
    3100: {
    3102:   MatFactorInfo  tinfo;

    3111:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3112:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3113:   if (!(fact)->ops->lufactorsymbolic) {
    3114:     MatSolverType stype;
    3115:     MatFactorGetSolverType(fact,&stype);
    3116:     SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic LU using solver package %s",((PetscObject)mat)->type_name,stype);
    3117:   }
    3118:   MatCheckPreallocated(mat,2);
    3119:   if (!info) {
    3120:     MatFactorInfoInitialize(&tinfo);
    3121:     info = &tinfo;
    3122:   }

    3124:   PetscLogEventBegin(MAT_LUFactorSymbolic,mat,row,col,0);
    3125:   (fact->ops->lufactorsymbolic)(fact,mat,row,col,info);
    3126:   PetscLogEventEnd(MAT_LUFactorSymbolic,mat,row,col,0);
    3127:   PetscObjectStateIncrease((PetscObject)fact);
    3128:   return(0);
    3129: }

    3131: /*@C
    3132:    MatLUFactorNumeric - Performs numeric LU factorization of a matrix.
    3133:    Call this routine after first calling MatLUFactorSymbolic().

    3135:    Collective on Mat

    3137:    Input Parameters:
    3138: +  fact - the factor matrix obtained with MatGetFactor()
    3139: .  mat - the matrix
    3140: -  info - options for factorization

    3142:    Notes:
    3143:    See MatLUFactor() for in-place factorization.  See
    3144:    MatCholeskyFactorNumeric() for the symmetric, positive definite case.

    3146:    Most users should employ the simplified KSP interface for linear solvers
    3147:    instead of working directly with matrix algebra routines such as this.
    3148:    See, e.g., KSPCreate().

    3150:    Level: developer

    3152: .seealso: MatLUFactorSymbolic(), MatLUFactor(), MatCholeskyFactor()

    3154:     Developer Note: fortran interface is not autogenerated as the f90
    3155:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3157: @*/
    3158: PetscErrorCode MatLUFactorNumeric(Mat fact,Mat mat,const MatFactorInfo *info)
    3159: {
    3160:   MatFactorInfo  tinfo;

    3168:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3169:   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);

    3171:   if (!(fact)->ops->lufactornumeric) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s numeric LU",((PetscObject)mat)->type_name);
    3172:   MatCheckPreallocated(mat,2);
    3173:   if (!info) {
    3174:     MatFactorInfoInitialize(&tinfo);
    3175:     info = &tinfo;
    3176:   }

    3178:   PetscLogEventBegin(MAT_LUFactorNumeric,mat,fact,0,0);
    3179:   (fact->ops->lufactornumeric)(fact,mat,info);
    3180:   PetscLogEventEnd(MAT_LUFactorNumeric,mat,fact,0,0);
    3181:   MatViewFromOptions(fact,NULL,"-mat_factor_view");
    3182:   PetscObjectStateIncrease((PetscObject)fact);
    3183:   return(0);
    3184: }

    3186: /*@C
    3187:    MatCholeskyFactor - Performs in-place Cholesky factorization of a
    3188:    symmetric matrix.

    3190:    Collective on Mat

    3192:    Input Parameters:
    3193: +  mat - the matrix
    3194: .  perm - row and column permutations
    3195: -  f - expected fill as ratio of original fill

    3197:    Notes:
    3198:    See MatLUFactor() for the nonsymmetric case.  See also
    3199:    MatCholeskyFactorSymbolic(), and MatCholeskyFactorNumeric().

    3201:    Most users should employ the simplified KSP interface for linear solvers
    3202:    instead of working directly with matrix algebra routines such as this.
    3203:    See, e.g., KSPCreate().

    3205:    Level: developer

    3207: .seealso: MatLUFactor(), MatCholeskyFactorSymbolic(), MatCholeskyFactorNumeric()
    3208:           MatGetOrdering()

    3210:     Developer Note: fortran interface is not autogenerated as the f90
    3211:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3213: @*/
    3214: PetscErrorCode MatCholeskyFactor(Mat mat,IS perm,const MatFactorInfo *info)
    3215: {
    3217:   MatFactorInfo  tinfo;

    3224:   if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Matrix must be square");
    3225:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3226:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3227:   if (!mat->ops->choleskyfactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"In-place factorization for Mat type %s is not supported, try out-of-place factorization. See MatCholeskyFactorSymbolic/Numeric",((PetscObject)mat)->type_name);
    3228:   MatCheckPreallocated(mat,1);
    3229:   if (!info) {
    3230:     MatFactorInfoInitialize(&tinfo);
    3231:     info = &tinfo;
    3232:   }

    3234:   PetscLogEventBegin(MAT_CholeskyFactor,mat,perm,0,0);
    3235:   (*mat->ops->choleskyfactor)(mat,perm,info);
    3236:   PetscLogEventEnd(MAT_CholeskyFactor,mat,perm,0,0);
    3237:   PetscObjectStateIncrease((PetscObject)mat);
    3238:   return(0);
    3239: }

    3241: /*@C
    3242:    MatCholeskyFactorSymbolic - Performs symbolic Cholesky factorization
    3243:    of a symmetric matrix.

    3245:    Collective on Mat

    3247:    Input Parameters:
    3248: +  fact - the factor matrix obtained with MatGetFactor()
    3249: .  mat - the matrix
    3250: .  perm - row and column permutations
    3251: -  info - options for factorization, includes
    3252: $          fill - expected fill as ratio of original fill.
    3253: $          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3254: $                   Run with the option -info to determine an optimal value to use

    3256:    Notes:
    3257:    See MatLUFactorSymbolic() for the nonsymmetric case.  See also
    3258:    MatCholeskyFactor() and MatCholeskyFactorNumeric().

    3260:    Most users should employ the simplified KSP interface for linear solvers
    3261:    instead of working directly with matrix algebra routines such as this.
    3262:    See, e.g., KSPCreate().

    3264:    Level: developer

    3266: .seealso: MatLUFactorSymbolic(), MatCholeskyFactor(), MatCholeskyFactorNumeric()
    3267:           MatGetOrdering()

    3269:     Developer Note: fortran interface is not autogenerated as the f90
    3270:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3272: @*/
    3273: PetscErrorCode MatCholeskyFactorSymbolic(Mat fact,Mat mat,IS perm,const MatFactorInfo *info)
    3274: {
    3276:   MatFactorInfo  tinfo;

    3284:   if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Matrix must be square");
    3285:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3286:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3287:   if (!(fact)->ops->choleskyfactorsymbolic) {
    3288:     MatSolverType stype;
    3289:     MatFactorGetSolverType(fact,&stype);
    3290:     SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s symbolic factor Cholesky using solver package %s",((PetscObject)mat)->type_name,stype);
    3291:   }
    3292:   MatCheckPreallocated(mat,2);
    3293:   if (!info) {
    3294:     MatFactorInfoInitialize(&tinfo);
    3295:     info = &tinfo;
    3296:   }

    3298:   PetscLogEventBegin(MAT_CholeskyFactorSymbolic,mat,perm,0,0);
    3299:   (fact->ops->choleskyfactorsymbolic)(fact,mat,perm,info);
    3300:   PetscLogEventEnd(MAT_CholeskyFactorSymbolic,mat,perm,0,0);
    3301:   PetscObjectStateIncrease((PetscObject)fact);
    3302:   return(0);
    3303: }

    3305: /*@C
    3306:    MatCholeskyFactorNumeric - Performs numeric Cholesky factorization
    3307:    of a symmetric matrix. Call this routine after first calling
    3308:    MatCholeskyFactorSymbolic().

    3310:    Collective on Mat

    3312:    Input Parameters:
    3313: +  fact - the factor matrix obtained with MatGetFactor()
    3314: .  mat - the initial matrix
    3315: .  info - options for factorization
    3316: -  fact - the symbolic factor of mat

    3319:    Notes:
    3320:    Most users should employ the simplified KSP interface for linear solvers
    3321:    instead of working directly with matrix algebra routines such as this.
    3322:    See, e.g., KSPCreate().

    3324:    Level: developer

    3326: .seealso: MatCholeskyFactorSymbolic(), MatCholeskyFactor(), MatLUFactorNumeric()

    3328:     Developer Note: fortran interface is not autogenerated as the f90
    3329:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3331: @*/
    3332: PetscErrorCode MatCholeskyFactorNumeric(Mat fact,Mat mat,const MatFactorInfo *info)
    3333: {
    3334:   MatFactorInfo  tinfo;

    3342:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3343:   if (!(fact)->ops->choleskyfactornumeric) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s numeric factor Cholesky",((PetscObject)mat)->type_name);
    3344:   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);
    3345:   MatCheckPreallocated(mat,2);
    3346:   if (!info) {
    3347:     MatFactorInfoInitialize(&tinfo);
    3348:     info = &tinfo;
    3349:   }

    3351:   PetscLogEventBegin(MAT_CholeskyFactorNumeric,mat,fact,0,0);
    3352:   (fact->ops->choleskyfactornumeric)(fact,mat,info);
    3353:   PetscLogEventEnd(MAT_CholeskyFactorNumeric,mat,fact,0,0);
    3354:   MatViewFromOptions(fact,NULL,"-mat_factor_view");
    3355:   PetscObjectStateIncrease((PetscObject)fact);
    3356:   return(0);
    3357: }

    3359: /* ----------------------------------------------------------------*/
    3360: /*@
    3361:    MatSolve - Solves A x = b, given a factored matrix.

    3363:    Neighbor-wise Collective on Mat

    3365:    Input Parameters:
    3366: +  mat - the factored matrix
    3367: -  b - the right-hand-side vector

    3369:    Output Parameter:
    3370: .  x - the result vector

    3372:    Notes:
    3373:    The vectors b and x cannot be the same.  I.e., one cannot
    3374:    call MatSolve(A,x,x).

    3376:    Notes:
    3377:    Most users should employ the simplified KSP interface for linear solvers
    3378:    instead of working directly with matrix algebra routines such as this.
    3379:    See, e.g., KSPCreate().

    3381:    Level: developer

    3383: .seealso: MatSolveAdd(), MatSolveTranspose(), MatSolveTransposeAdd()
    3384: @*/
    3385: PetscErrorCode MatSolve(Mat mat,Vec b,Vec x)
    3386: {

    3396:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3397:   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);
    3398:   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);
    3399:   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);
    3400:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3401:   MatCheckPreallocated(mat,1);

    3403:   PetscLogEventBegin(MAT_Solve,mat,b,x,0);
    3404:   if (mat->factorerrortype) {
    3405:     PetscInfo1(mat,"MatFactorError %D\n",mat->factorerrortype);
    3406:     VecSetInf(x);
    3407:   } else {
    3408:     if (!mat->ops->solve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3409:     (*mat->ops->solve)(mat,b,x);
    3410:   }
    3411:   PetscLogEventEnd(MAT_Solve,mat,b,x,0);
    3412:   PetscObjectStateIncrease((PetscObject)x);
    3413:   return(0);
    3414: }

    3416: static PetscErrorCode MatMatSolve_Basic(Mat A,Mat B,Mat X,PetscBool trans)
    3417: {
    3419:   Vec            b,x;
    3420:   PetscInt       m,N,i;
    3421:   PetscScalar    *bb,*xx;

    3424:   MatDenseGetArrayRead(B,(const PetscScalar**)&bb);
    3425:   MatDenseGetArray(X,&xx);
    3426:   MatGetLocalSize(B,&m,NULL);  /* number local rows */
    3427:   MatGetSize(B,NULL,&N);       /* total columns in dense matrix */
    3428:   MatCreateVecs(A,&x,&b);
    3429:   for (i=0; i<N; i++) {
    3430:     VecPlaceArray(b,bb + i*m);
    3431:     VecPlaceArray(x,xx + i*m);
    3432:     if (trans) {
    3433:       MatSolveTranspose(A,b,x);
    3434:     } else {
    3435:       MatSolve(A,b,x);
    3436:     }
    3437:     VecResetArray(x);
    3438:     VecResetArray(b);
    3439:   }
    3440:   VecDestroy(&b);
    3441:   VecDestroy(&x);
    3442:   MatDenseRestoreArrayRead(B,(const PetscScalar**)&bb);
    3443:   MatDenseRestoreArray(X,&xx);
    3444:   return(0);
    3445: }

    3447: /*@
    3448:    MatMatSolve - Solves A X = B, given a factored matrix.

    3450:    Neighbor-wise Collective on Mat

    3452:    Input Parameters:
    3453: +  A - the factored matrix
    3454: -  B - the right-hand-side matrix MATDENSE (or sparse -- when using MUMPS)

    3456:    Output Parameter:
    3457: .  X - the result matrix (dense matrix)

    3459:    Notes:
    3460:    If B is a MATDENSE matrix then one can call MatMatSolve(A,B,B) except with MKL_CPARDISO;
    3461:    otherwise, B and X cannot be the same.

    3463:    Notes:
    3464:    Most users should usually employ the simplified KSP interface for linear solvers
    3465:    instead of working directly with matrix algebra routines such as this.
    3466:    See, e.g., KSPCreate(). However KSP can only solve for one vector (column of X)
    3467:    at a time.

    3469:    Level: developer

    3471: .seealso: MatMatSolveTranspose(), MatLUFactor(), MatCholeskyFactor()
    3472: @*/
    3473: PetscErrorCode MatMatSolve(Mat A,Mat B,Mat X)
    3474: {

    3484:   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);
    3485:   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);
    3486:   if (X->cmap->N != B->cmap->N) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Solution matrix must have same number of columns as rhs matrix");
    3487:   if (!A->rmap->N && !A->cmap->N) return(0);
    3488:   if (!A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    3489:   MatCheckPreallocated(A,1);

    3491:   PetscLogEventBegin(MAT_MatSolve,A,B,X,0);
    3492:   if (!A->ops->matsolve) {
    3493:     PetscInfo1(A,"Mat type %s using basic MatMatSolve\n",((PetscObject)A)->type_name);
    3494:     MatMatSolve_Basic(A,B,X,PETSC_FALSE);
    3495:   } else {
    3496:     (*A->ops->matsolve)(A,B,X);
    3497:   }
    3498:   PetscLogEventEnd(MAT_MatSolve,A,B,X,0);
    3499:   PetscObjectStateIncrease((PetscObject)X);
    3500:   return(0);
    3501: }

    3503: /*@
    3504:    MatMatSolveTranspose - Solves A^T X = B, given a factored matrix.

    3506:    Neighbor-wise Collective on Mat

    3508:    Input Parameters:
    3509: +  A - the factored matrix
    3510: -  B - the right-hand-side matrix  (dense matrix)

    3512:    Output Parameter:
    3513: .  X - the result matrix (dense matrix)

    3515:    Notes:
    3516:    The matrices B and X cannot be the same.  I.e., one cannot
    3517:    call MatMatSolveTranspose(A,X,X).

    3519:    Notes:
    3520:    Most users should usually employ the simplified KSP interface for linear solvers
    3521:    instead of working directly with matrix algebra routines such as this.
    3522:    See, e.g., KSPCreate(). However KSP can only solve for one vector (column of X)
    3523:    at a time.

    3525:    When using SuperLU_Dist or MUMPS as a parallel solver, PETSc will use their functionality to solve multiple right hand sides simultaneously.

    3527:    Level: developer

    3529: .seealso: MatMatSolve(), MatLUFactor(), MatCholeskyFactor()
    3530: @*/
    3531: PetscErrorCode MatMatSolveTranspose(Mat A,Mat B,Mat X)
    3532: {

    3542:   if (X == B) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_IDN,"X and B must be different matrices");
    3543:   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);
    3544:   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);
    3545:   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);
    3546:   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");
    3547:   if (!A->rmap->N && !A->cmap->N) return(0);
    3548:   if (!A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    3549:   MatCheckPreallocated(A,1);

    3551:   PetscLogEventBegin(MAT_MatSolve,A,B,X,0);
    3552:   if (!A->ops->matsolvetranspose) {
    3553:     PetscInfo1(A,"Mat type %s using basic MatMatSolveTranspose\n",((PetscObject)A)->type_name);
    3554:     MatMatSolve_Basic(A,B,X,PETSC_TRUE);
    3555:   } else {
    3556:     (*A->ops->matsolvetranspose)(A,B,X);
    3557:   }
    3558:   PetscLogEventEnd(MAT_MatSolve,A,B,X,0);
    3559:   PetscObjectStateIncrease((PetscObject)X);
    3560:   return(0);
    3561: }

    3563: /*@
    3564:    MatMatTransposeSolve - Solves A X = B^T, given a factored matrix.

    3566:    Neighbor-wise Collective on Mat

    3568:    Input Parameters:
    3569: +  A - the factored matrix
    3570: -  Bt - the transpose of right-hand-side matrix

    3572:    Output Parameter:
    3573: .  X - the result matrix (dense matrix)

    3575:    Notes:
    3576:    Most users should usually employ the simplified KSP interface for linear solvers
    3577:    instead of working directly with matrix algebra routines such as this.
    3578:    See, e.g., KSPCreate(). However KSP can only solve for one vector (column of X)
    3579:    at a time.

    3581:    For MUMPS, it only supports centralized sparse compressed column format on the host processor for right hand side matrix. User must create B^T in sparse compressed row format on the host processor and call MatMatTransposeSolve() to implement MUMPS' MatMatSolve().

    3583:    Level: developer

    3585: .seealso: MatMatSolve(), MatMatSolveTranspose(), MatLUFactor(), MatCholeskyFactor()
    3586: @*/
    3587: PetscErrorCode MatMatTransposeSolve(Mat A,Mat Bt,Mat X)
    3588: {

    3599:   if (X == Bt) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_IDN,"X and B must be different matrices");
    3600:   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);
    3601:   if (A->rmap->N != Bt->cmap->N) SETERRQ2(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_SIZ,"Mat A,Mat Bt: global dim %D %D",A->rmap->N,Bt->cmap->N);
    3602:   if (X->cmap->N < Bt->rmap->N) SETERRQ(PetscObjectComm((PetscObject)X),PETSC_ERR_ARG_SIZ,"Solution matrix must have same number of columns as row number of the rhs matrix");
    3603:   if (!A->rmap->N && !A->cmap->N) return(0);
    3604:   if (!A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    3605:   MatCheckPreallocated(A,1);

    3607:   if (!A->ops->mattransposesolve) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)A)->type_name);
    3608:   PetscLogEventBegin(MAT_MatTrSolve,A,Bt,X,0);
    3609:   (*A->ops->mattransposesolve)(A,Bt,X);
    3610:   PetscLogEventEnd(MAT_MatTrSolve,A,Bt,X,0);
    3611:   PetscObjectStateIncrease((PetscObject)X);
    3612:   return(0);
    3613: }

    3615: /*@
    3616:    MatForwardSolve - Solves L x = b, given a factored matrix, A = LU, or
    3617:                             U^T*D^(1/2) x = b, given a factored symmetric matrix, A = U^T*D*U,

    3619:    Neighbor-wise Collective on Mat

    3621:    Input Parameters:
    3622: +  mat - the factored matrix
    3623: -  b - the right-hand-side vector

    3625:    Output Parameter:
    3626: .  x - the result vector

    3628:    Notes:
    3629:    MatSolve() should be used for most applications, as it performs
    3630:    a forward solve followed by a backward solve.

    3632:    The vectors b and x cannot be the same,  i.e., one cannot
    3633:    call MatForwardSolve(A,x,x).

    3635:    For matrix in seqsbaij format with block size larger than 1,
    3636:    the diagonal blocks are not implemented as D = D^(1/2) * D^(1/2) yet.
    3637:    MatForwardSolve() solves U^T*D y = b, and
    3638:    MatBackwardSolve() solves U x = y.
    3639:    Thus they do not provide a symmetric preconditioner.

    3641:    Most users should employ the simplified KSP interface for linear solvers
    3642:    instead of working directly with matrix algebra routines such as this.
    3643:    See, e.g., KSPCreate().

    3645:    Level: developer

    3647: .seealso: MatSolve(), MatBackwardSolve()
    3648: @*/
    3649: PetscErrorCode MatForwardSolve(Mat mat,Vec b,Vec x)
    3650: {

    3660:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3661:   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);
    3662:   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);
    3663:   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);
    3664:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3665:   MatCheckPreallocated(mat,1);

    3667:   if (!mat->ops->forwardsolve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3668:   PetscLogEventBegin(MAT_ForwardSolve,mat,b,x,0);
    3669:   (*mat->ops->forwardsolve)(mat,b,x);
    3670:   PetscLogEventEnd(MAT_ForwardSolve,mat,b,x,0);
    3671:   PetscObjectStateIncrease((PetscObject)x);
    3672:   return(0);
    3673: }

    3675: /*@
    3676:    MatBackwardSolve - Solves U x = b, given a factored matrix, A = LU.
    3677:                              D^(1/2) U x = b, given a factored symmetric matrix, A = U^T*D*U,

    3679:    Neighbor-wise Collective on Mat

    3681:    Input Parameters:
    3682: +  mat - the factored matrix
    3683: -  b - the right-hand-side vector

    3685:    Output Parameter:
    3686: .  x - the result vector

    3688:    Notes:
    3689:    MatSolve() should be used for most applications, as it performs
    3690:    a forward solve followed by a backward solve.

    3692:    The vectors b and x cannot be the same.  I.e., one cannot
    3693:    call MatBackwardSolve(A,x,x).

    3695:    For matrix in seqsbaij format with block size larger than 1,
    3696:    the diagonal blocks are not implemented as D = D^(1/2) * D^(1/2) yet.
    3697:    MatForwardSolve() solves U^T*D y = b, and
    3698:    MatBackwardSolve() solves U x = y.
    3699:    Thus they do not provide a symmetric preconditioner.

    3701:    Most users should employ the simplified KSP interface for linear solvers
    3702:    instead of working directly with matrix algebra routines such as this.
    3703:    See, e.g., KSPCreate().

    3705:    Level: developer

    3707: .seealso: MatSolve(), MatForwardSolve()
    3708: @*/
    3709: PetscErrorCode MatBackwardSolve(Mat mat,Vec b,Vec x)
    3710: {

    3720:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3721:   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);
    3722:   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);
    3723:   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);
    3724:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3725:   MatCheckPreallocated(mat,1);

    3727:   if (!mat->ops->backwardsolve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3728:   PetscLogEventBegin(MAT_BackwardSolve,mat,b,x,0);
    3729:   (*mat->ops->backwardsolve)(mat,b,x);
    3730:   PetscLogEventEnd(MAT_BackwardSolve,mat,b,x,0);
    3731:   PetscObjectStateIncrease((PetscObject)x);
    3732:   return(0);
    3733: }

    3735: /*@
    3736:    MatSolveAdd - Computes x = y + inv(A)*b, given a factored matrix.

    3738:    Neighbor-wise Collective on Mat

    3740:    Input Parameters:
    3741: +  mat - the factored matrix
    3742: .  b - the right-hand-side vector
    3743: -  y - the vector to be added to

    3745:    Output Parameter:
    3746: .  x - the result vector

    3748:    Notes:
    3749:    The vectors b and x cannot be the same.  I.e., one cannot
    3750:    call MatSolveAdd(A,x,y,x).

    3752:    Most users should employ the simplified KSP interface for linear solvers
    3753:    instead of working directly with matrix algebra routines such as this.
    3754:    See, e.g., KSPCreate().

    3756:    Level: developer

    3758: .seealso: MatSolve(), MatSolveTranspose(), MatSolveTransposeAdd()
    3759: @*/
    3760: PetscErrorCode MatSolveAdd(Mat mat,Vec b,Vec y,Vec x)
    3761: {
    3762:   PetscScalar    one = 1.0;
    3763:   Vec            tmp;

    3775:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3776:   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);
    3777:   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);
    3778:   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);
    3779:   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);
    3780:   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);
    3781:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3782:    MatCheckPreallocated(mat,1);

    3784:   PetscLogEventBegin(MAT_SolveAdd,mat,b,x,y);
    3785:   if (mat->factorerrortype) {
    3786:     PetscInfo1(mat,"MatFactorError %D\n",mat->factorerrortype);
    3787:     VecSetInf(x);
    3788:   } else if (mat->ops->solveadd) {
    3789:     (*mat->ops->solveadd)(mat,b,y,x);
    3790:   } else {
    3791:     /* do the solve then the add manually */
    3792:     if (x != y) {
    3793:       MatSolve(mat,b,x);
    3794:       VecAXPY(x,one,y);
    3795:     } else {
    3796:       VecDuplicate(x,&tmp);
    3797:       PetscLogObjectParent((PetscObject)mat,(PetscObject)tmp);
    3798:       VecCopy(x,tmp);
    3799:       MatSolve(mat,b,x);
    3800:       VecAXPY(x,one,tmp);
    3801:       VecDestroy(&tmp);
    3802:     }
    3803:   }
    3804:   PetscLogEventEnd(MAT_SolveAdd,mat,b,x,y);
    3805:   PetscObjectStateIncrease((PetscObject)x);
    3806:   return(0);
    3807: }

    3809: /*@
    3810:    MatSolveTranspose - Solves A' x = b, given a factored matrix.

    3812:    Neighbor-wise Collective on Mat

    3814:    Input Parameters:
    3815: +  mat - the factored matrix
    3816: -  b - the right-hand-side vector

    3818:    Output Parameter:
    3819: .  x - the result vector

    3821:    Notes:
    3822:    The vectors b and x cannot be the same.  I.e., one cannot
    3823:    call MatSolveTranspose(A,x,x).

    3825:    Most users should employ the simplified KSP interface for linear solvers
    3826:    instead of working directly with matrix algebra routines such as this.
    3827:    See, e.g., KSPCreate().

    3829:    Level: developer

    3831: .seealso: MatSolve(), MatSolveAdd(), MatSolveTransposeAdd()
    3832: @*/
    3833: PetscErrorCode MatSolveTranspose(Mat mat,Vec b,Vec x)
    3834: {

    3844:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3845:   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);
    3846:   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);
    3847:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3848:   MatCheckPreallocated(mat,1);
    3849:   PetscLogEventBegin(MAT_SolveTranspose,mat,b,x,0);
    3850:   if (mat->factorerrortype) {
    3851:     PetscInfo1(mat,"MatFactorError %D\n",mat->factorerrortype);
    3852:     VecSetInf(x);
    3853:   } else {
    3854:     if (!mat->ops->solvetranspose) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s",((PetscObject)mat)->type_name);
    3855:     (*mat->ops->solvetranspose)(mat,b,x);
    3856:   }
    3857:   PetscLogEventEnd(MAT_SolveTranspose,mat,b,x,0);
    3858:   PetscObjectStateIncrease((PetscObject)x);
    3859:   return(0);
    3860: }

    3862: /*@
    3863:    MatSolveTransposeAdd - Computes x = y + inv(Transpose(A)) b, given a
    3864:                       factored matrix.

    3866:    Neighbor-wise Collective on Mat

    3868:    Input Parameters:
    3869: +  mat - the factored matrix
    3870: .  b - the right-hand-side vector
    3871: -  y - the vector to be added to

    3873:    Output Parameter:
    3874: .  x - the result vector

    3876:    Notes:
    3877:    The vectors b and x cannot be the same.  I.e., one cannot
    3878:    call MatSolveTransposeAdd(A,x,y,x).

    3880:    Most users should employ the simplified KSP interface for linear solvers
    3881:    instead of working directly with matrix algebra routines such as this.
    3882:    See, e.g., KSPCreate().

    3884:    Level: developer

    3886: .seealso: MatSolve(), MatSolveAdd(), MatSolveTranspose()
    3887: @*/
    3888: PetscErrorCode MatSolveTransposeAdd(Mat mat,Vec b,Vec y,Vec x)
    3889: {
    3890:   PetscScalar    one = 1.0;
    3892:   Vec            tmp;

    3903:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3904:   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);
    3905:   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);
    3906:   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);
    3907:   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);
    3908:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3909:    MatCheckPreallocated(mat,1);

    3911:   PetscLogEventBegin(MAT_SolveTransposeAdd,mat,b,x,y);
    3912:   if (mat->factorerrortype) {
    3913:     PetscInfo1(mat,"MatFactorError %D\n",mat->factorerrortype);
    3914:     VecSetInf(x);
    3915:   } else if (mat->ops->solvetransposeadd){
    3916:     (*mat->ops->solvetransposeadd)(mat,b,y,x);
    3917:   } else {
    3918:     /* do the solve then the add manually */
    3919:     if (x != y) {
    3920:       MatSolveTranspose(mat,b,x);
    3921:       VecAXPY(x,one,y);
    3922:     } else {
    3923:       VecDuplicate(x,&tmp);
    3924:       PetscLogObjectParent((PetscObject)mat,(PetscObject)tmp);
    3925:       VecCopy(x,tmp);
    3926:       MatSolveTranspose(mat,b,x);
    3927:       VecAXPY(x,one,tmp);
    3928:       VecDestroy(&tmp);
    3929:     }
    3930:   }
    3931:   PetscLogEventEnd(MAT_SolveTransposeAdd,mat,b,x,y);
    3932:   PetscObjectStateIncrease((PetscObject)x);
    3933:   return(0);
    3934: }
    3935: /* ----------------------------------------------------------------*/

    3937: /*@
    3938:    MatSOR - Computes relaxation (SOR, Gauss-Seidel) sweeps.

    3940:    Neighbor-wise Collective on Mat

    3942:    Input Parameters:
    3943: +  mat - the matrix
    3944: .  b - the right hand side
    3945: .  omega - the relaxation factor
    3946: .  flag - flag indicating the type of SOR (see below)
    3947: .  shift -  diagonal shift
    3948: .  its - the number of iterations
    3949: -  lits - the number of local iterations

    3951:    Output Parameters:
    3952: .  x - the solution (can contain an initial guess, use option SOR_ZERO_INITIAL_GUESS to indicate no guess)

    3954:    SOR Flags:
    3955: +     SOR_FORWARD_SWEEP - forward SOR
    3956: .     SOR_BACKWARD_SWEEP - backward SOR
    3957: .     SOR_SYMMETRIC_SWEEP - SSOR (symmetric SOR)
    3958: .     SOR_LOCAL_FORWARD_SWEEP - local forward SOR
    3959: .     SOR_LOCAL_BACKWARD_SWEEP - local forward SOR
    3960: .     SOR_LOCAL_SYMMETRIC_SWEEP - local SSOR
    3961: .     SOR_APPLY_UPPER, SOR_APPLY_LOWER - applies
    3962:          upper/lower triangular part of matrix to
    3963:          vector (with omega)
    3964: -     SOR_ZERO_INITIAL_GUESS - zero initial guess

    3966:    Notes:
    3967:    SOR_LOCAL_FORWARD_SWEEP, SOR_LOCAL_BACKWARD_SWEEP, and
    3968:    SOR_LOCAL_SYMMETRIC_SWEEP perform separate independent smoothings
    3969:    on each processor.

    3971:    Application programmers will not generally use MatSOR() directly,
    3972:    but instead will employ the KSP/PC interface.

    3974:    Notes:
    3975:     for BAIJ, SBAIJ, and AIJ matrices with Inodes this does a block SOR smoothing, otherwise it does a pointwise smoothing

    3977:    Notes for Advanced Users:
    3978:    The flags are implemented as bitwise inclusive or operations.
    3979:    For example, use (SOR_ZERO_INITIAL_GUESS | SOR_SYMMETRIC_SWEEP)
    3980:    to specify a zero initial guess for SSOR.

    3982:    Most users should employ the simplified KSP interface for linear solvers
    3983:    instead of working directly with matrix algebra routines such as this.
    3984:    See, e.g., KSPCreate().

    3986:    Vectors x and b CANNOT be the same

    3988:    Developer Note: We should add block SOR support for AIJ matrices with block size set to great than one and no inodes

    3990:    Level: developer

    3992: @*/
    3993: PetscErrorCode MatSOR(Mat mat,Vec b,PetscReal omega,MatSORType flag,PetscReal shift,PetscInt its,PetscInt lits,Vec x)
    3994: {

    4004:   if (!mat->ops->sor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4005:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4006:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4007:   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);
    4008:   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);
    4009:   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);
    4010:   if (its <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D positive",its);
    4011:   if (lits <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires local its %D positive",lits);
    4012:   if (b == x) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_IDN,"b and x vector cannot be the same");

    4014:   MatCheckPreallocated(mat,1);
    4015:   PetscLogEventBegin(MAT_SOR,mat,b,x,0);
    4016:   ierr =(*mat->ops->sor)(mat,b,omega,flag,shift,its,lits,x);
    4017:   PetscLogEventEnd(MAT_SOR,mat,b,x,0);
    4018:   PetscObjectStateIncrease((PetscObject)x);
    4019:   return(0);
    4020: }

    4022: /*
    4023:       Default matrix copy routine.
    4024: */
    4025: PetscErrorCode MatCopy_Basic(Mat A,Mat B,MatStructure str)
    4026: {
    4027:   PetscErrorCode    ierr;
    4028:   PetscInt          i,rstart = 0,rend = 0,nz;
    4029:   const PetscInt    *cwork;
    4030:   const PetscScalar *vwork;

    4033:   if (B->assembled) {
    4034:     MatZeroEntries(B);
    4035:   }
    4036:   if (str == SAME_NONZERO_PATTERN) {
    4037:     MatGetOwnershipRange(A,&rstart,&rend);
    4038:     for (i=rstart; i<rend; i++) {
    4039:       MatGetRow(A,i,&nz,&cwork,&vwork);
    4040:       MatSetValues(B,1,&i,nz,cwork,vwork,INSERT_VALUES);
    4041:       MatRestoreRow(A,i,&nz,&cwork,&vwork);
    4042:     }
    4043:   } else {
    4044:     MatAYPX(B,0.0,A,str);
    4045:   }
    4046:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    4047:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    4048:   return(0);
    4049: }

    4051: /*@
    4052:    MatCopy - Copies a matrix to another matrix.

    4054:    Collective on Mat

    4056:    Input Parameters:
    4057: +  A - the matrix
    4058: -  str - SAME_NONZERO_PATTERN or DIFFERENT_NONZERO_PATTERN

    4060:    Output Parameter:
    4061: .  B - where the copy is put

    4063:    Notes:
    4064:    If you use SAME_NONZERO_PATTERN then the two matrices had better have the
    4065:    same nonzero pattern or the routine will crash.

    4067:    MatCopy() copies the matrix entries of a matrix to another existing
    4068:    matrix (after first zeroing the second matrix).  A related routine is
    4069:    MatConvert(), which first creates a new matrix and then copies the data.

    4071:    Level: intermediate

    4073: .seealso: MatConvert(), MatDuplicate()

    4075: @*/
    4076: PetscErrorCode MatCopy(Mat A,Mat B,MatStructure str)
    4077: {
    4079:   PetscInt       i;

    4087:   MatCheckPreallocated(B,2);
    4088:   if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4089:   if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4090:   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);
    4091:   MatCheckPreallocated(A,1);
    4092:   if (A == B) return(0);

    4094:   PetscLogEventBegin(MAT_Copy,A,B,0,0);
    4095:   if (A->ops->copy) {
    4096:     (*A->ops->copy)(A,B,str);
    4097:   } else { /* generic conversion */
    4098:     MatCopy_Basic(A,B,str);
    4099:   }

    4101:   B->stencil.dim = A->stencil.dim;
    4102:   B->stencil.noc = A->stencil.noc;
    4103:   for (i=0; i<=A->stencil.dim; i++) {
    4104:     B->stencil.dims[i]   = A->stencil.dims[i];
    4105:     B->stencil.starts[i] = A->stencil.starts[i];
    4106:   }

    4108:   PetscLogEventEnd(MAT_Copy,A,B,0,0);
    4109:   PetscObjectStateIncrease((PetscObject)B);
    4110:   return(0);
    4111: }

    4113: /*@C
    4114:    MatConvert - Converts a matrix to another matrix, either of the same
    4115:    or different type.

    4117:    Collective on Mat

    4119:    Input Parameters:
    4120: +  mat - the matrix
    4121: .  newtype - new matrix type.  Use MATSAME to create a new matrix of the
    4122:    same type as the original matrix.
    4123: -  reuse - denotes if the destination matrix is to be created or reused.
    4124:    Use MAT_INPLACE_MATRIX for inplace conversion (that is when you want the input mat to be changed to contain the matrix in the new format), otherwise use
    4125:    MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX (can only be used after the first call was made with MAT_INITIAL_MATRIX, causes the matrix space in M to be reused).

    4127:    Output Parameter:
    4128: .  M - pointer to place new matrix

    4130:    Notes:
    4131:    MatConvert() first creates a new matrix and then copies the data from
    4132:    the first matrix.  A related routine is MatCopy(), which copies the matrix
    4133:    entries of one matrix to another already existing matrix context.

    4135:    Cannot be used to convert a sequential matrix to parallel or parallel to sequential,
    4136:    the MPI communicator of the generated matrix is always the same as the communicator
    4137:    of the input matrix.

    4139:    Level: intermediate

    4141: .seealso: MatCopy(), MatDuplicate()
    4142: @*/
    4143: PetscErrorCode MatConvert(Mat mat, MatType newtype,MatReuse reuse,Mat *M)
    4144: {
    4146:   PetscBool      sametype,issame,flg,issymmetric,ishermitian;
    4147:   char           convname[256],mtype[256];
    4148:   Mat            B;

    4154:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4155:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4156:   MatCheckPreallocated(mat,1);

    4158:   PetscOptionsGetString(((PetscObject)mat)->options,((PetscObject)mat)->prefix,"-matconvert_type",mtype,sizeof(mtype),&flg);
    4159:   if (flg) newtype = mtype;

    4161:   PetscObjectTypeCompare((PetscObject)mat,newtype,&sametype);
    4162:   PetscStrcmp(newtype,"same",&issame);
    4163:   if ((reuse == MAT_INPLACE_MATRIX) && (mat != *M)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"MAT_INPLACE_MATRIX requires same input and output matrix");
    4164:   if ((reuse == MAT_REUSE_MATRIX) && (mat == *M)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"MAT_REUSE_MATRIX means reuse matrix in final argument, perhaps you mean MAT_INPLACE_MATRIX");

    4166:   if ((reuse == MAT_INPLACE_MATRIX) && (issame || sametype)) {
    4167:     PetscInfo3(mat,"Early return for inplace %s %d %d\n",((PetscObject)mat)->type_name,sametype,issame);
    4168:     return(0);
    4169:   }

    4171:   /* Cache Mat options because some converter use MatHeaderReplace  */
    4172:   issymmetric = mat->symmetric;
    4173:   ishermitian = mat->hermitian;

    4175:   if ((sametype || issame) && (reuse==MAT_INITIAL_MATRIX) && mat->ops->duplicate) {
    4176:     PetscInfo3(mat,"Calling duplicate for initial matrix %s %d %d\n",((PetscObject)mat)->type_name,sametype,issame);
    4177:     (*mat->ops->duplicate)(mat,MAT_COPY_VALUES,M);
    4178:   } else {
    4179:     PetscErrorCode (*conv)(Mat, MatType,MatReuse,Mat*)=NULL;
    4180:     const char     *prefix[3] = {"seq","mpi",""};
    4181:     PetscInt       i;
    4182:     /*
    4183:        Order of precedence:
    4184:        0) See if newtype is a superclass of the current matrix.
    4185:        1) See if a specialized converter is known to the current matrix.
    4186:        2) See if a specialized converter is known to the desired matrix class.
    4187:        3) See if a good general converter is registered for the desired class
    4188:           (as of 6/27/03 only MATMPIADJ falls into this category).
    4189:        4) See if a good general converter is known for the current matrix.
    4190:        5) Use a really basic converter.
    4191:     */

    4193:     /* 0) See if newtype is a superclass of the current matrix.
    4194:           i.e mat is mpiaij and newtype is aij */
    4195:     for (i=0; i<2; i++) {
    4196:       PetscStrncpy(convname,prefix[i],sizeof(convname));
    4197:       PetscStrlcat(convname,newtype,sizeof(convname));
    4198:       PetscStrcmp(convname,((PetscObject)mat)->type_name,&flg);
    4199:       PetscInfo3(mat,"Check superclass %s %s -> %d\n",convname,((PetscObject)mat)->type_name,flg);
    4200:       if (flg) {
    4201:         if (reuse == MAT_INPLACE_MATRIX) {
    4202:           PetscInfo(mat,"Early return\n");
    4203:           return(0);
    4204:         } else if (reuse == MAT_INITIAL_MATRIX && mat->ops->duplicate) {
    4205:           PetscInfo(mat,"Calling MatDuplicate\n");
    4206:           (*mat->ops->duplicate)(mat,MAT_COPY_VALUES,M);
    4207:           return(0);
    4208:         } else if (reuse == MAT_REUSE_MATRIX && mat->ops->copy) {
    4209:           PetscInfo(mat,"Calling MatCopy\n");
    4210:           MatCopy(mat,*M,SAME_NONZERO_PATTERN);
    4211:           return(0);
    4212:         }
    4213:       }
    4214:     }
    4215:     /* 1) See if a specialized converter is known to the current matrix and the desired class */
    4216:     for (i=0; i<3; i++) {
    4217:       PetscStrncpy(convname,"MatConvert_",sizeof(convname));
    4218:       PetscStrlcat(convname,((PetscObject)mat)->type_name,sizeof(convname));
    4219:       PetscStrlcat(convname,"_",sizeof(convname));
    4220:       PetscStrlcat(convname,prefix[i],sizeof(convname));
    4221:       PetscStrlcat(convname,issame ? ((PetscObject)mat)->type_name : newtype,sizeof(convname));
    4222:       PetscStrlcat(convname,"_C",sizeof(convname));
    4223:       PetscObjectQueryFunction((PetscObject)mat,convname,&conv);
    4224:       PetscInfo3(mat,"Check specialized (1) %s (%s) -> %d\n",convname,((PetscObject)mat)->type_name,!!conv);
    4225:       if (conv) goto foundconv;
    4226:     }

    4228:     /* 2)  See if a specialized converter is known to the desired matrix class. */
    4229:     MatCreate(PetscObjectComm((PetscObject)mat),&B);
    4230:     MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->N,mat->cmap->N);
    4231:     MatSetType(B,newtype);
    4232:     for (i=0; i<3; i++) {
    4233:       PetscStrncpy(convname,"MatConvert_",sizeof(convname));
    4234:       PetscStrlcat(convname,((PetscObject)mat)->type_name,sizeof(convname));
    4235:       PetscStrlcat(convname,"_",sizeof(convname));
    4236:       PetscStrlcat(convname,prefix[i],sizeof(convname));
    4237:       PetscStrlcat(convname,newtype,sizeof(convname));
    4238:       PetscStrlcat(convname,"_C",sizeof(convname));
    4239:       PetscObjectQueryFunction((PetscObject)B,convname,&conv);
    4240:       PetscInfo3(mat,"Check specialized (2) %s (%s) -> %d\n",convname,((PetscObject)B)->type_name,!!conv);
    4241:       if (conv) {
    4242:         MatDestroy(&B);
    4243:         goto foundconv;
    4244:       }
    4245:     }

    4247:     /* 3) See if a good general converter is registered for the desired class */
    4248:     conv = B->ops->convertfrom;
    4249:     PetscInfo2(mat,"Check convertfrom (%s) -> %d\n",((PetscObject)B)->type_name,!!conv);
    4250:     MatDestroy(&B);
    4251:     if (conv) goto foundconv;

    4253:     /* 4) See if a good general converter is known for the current matrix */
    4254:     if (mat->ops->convert) conv = mat->ops->convert;

    4256:     PetscInfo2(mat,"Check general convert (%s) -> %d\n",((PetscObject)mat)->type_name,!!conv);
    4257:     if (conv) goto foundconv;

    4259:     /* 5) Use a really basic converter. */
    4260:     PetscInfo(mat,"Using MatConvert_Basic\n");
    4261:     conv = MatConvert_Basic;

    4263: foundconv:
    4264:     PetscLogEventBegin(MAT_Convert,mat,0,0,0);
    4265:     (*conv)(mat,newtype,reuse,M);
    4266:     if (mat->rmap->mapping && mat->cmap->mapping && !(*M)->rmap->mapping && !(*M)->cmap->mapping) {
    4267:       /* the block sizes must be same if the mappings are copied over */
    4268:       (*M)->rmap->bs = mat->rmap->bs;
    4269:       (*M)->cmap->bs = mat->cmap->bs;
    4270:       PetscObjectReference((PetscObject)mat->rmap->mapping);
    4271:       PetscObjectReference((PetscObject)mat->cmap->mapping);
    4272:       (*M)->rmap->mapping = mat->rmap->mapping;
    4273:       (*M)->cmap->mapping = mat->cmap->mapping;
    4274:     }
    4275:     (*M)->stencil.dim = mat->stencil.dim;
    4276:     (*M)->stencil.noc = mat->stencil.noc;
    4277:     for (i=0; i<=mat->stencil.dim; i++) {
    4278:       (*M)->stencil.dims[i]   = mat->stencil.dims[i];
    4279:       (*M)->stencil.starts[i] = mat->stencil.starts[i];
    4280:     }
    4281:     PetscLogEventEnd(MAT_Convert,mat,0,0,0);
    4282:   }
    4283:   PetscObjectStateIncrease((PetscObject)*M);

    4285:   /* Copy Mat options */
    4286:   if (issymmetric) {
    4287:     MatSetOption(*M,MAT_SYMMETRIC,PETSC_TRUE);
    4288:   }
    4289:   if (ishermitian) {
    4290:     MatSetOption(*M,MAT_HERMITIAN,PETSC_TRUE);
    4291:   }
    4292:   return(0);
    4293: }

    4295: /*@C
    4296:    MatFactorGetSolverType - Returns name of the package providing the factorization routines

    4298:    Not Collective

    4300:    Input Parameter:
    4301: .  mat - the matrix, must be a factored matrix

    4303:    Output Parameter:
    4304: .   type - the string name of the package (do not free this string)

    4306:    Notes:
    4307:       In Fortran you pass in a empty string and the package name will be copied into it.
    4308:     (Make sure the string is long enough)

    4310:    Level: intermediate

    4312: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatGetFactor()
    4313: @*/
    4314: PetscErrorCode MatFactorGetSolverType(Mat mat, MatSolverType *type)
    4315: {
    4316:   PetscErrorCode ierr, (*conv)(Mat,MatSolverType*);

    4321:   if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Only for factored matrix");
    4322:   PetscObjectQueryFunction((PetscObject)mat,"MatFactorGetSolverType_C",&conv);
    4323:   if (!conv) {
    4324:     *type = MATSOLVERPETSC;
    4325:   } else {
    4326:     (*conv)(mat,type);
    4327:   }
    4328:   return(0);
    4329: }

    4331: typedef struct _MatSolverTypeForSpecifcType* MatSolverTypeForSpecifcType;
    4332: struct _MatSolverTypeForSpecifcType {
    4333:   MatType                        mtype;
    4334:   PetscErrorCode                 (*createfactor[4])(Mat,MatFactorType,Mat*);
    4335:   MatSolverTypeForSpecifcType next;
    4336: };

    4338: typedef struct _MatSolverTypeHolder* MatSolverTypeHolder;
    4339: struct _MatSolverTypeHolder {
    4340:   char                        *name;
    4341:   MatSolverTypeForSpecifcType handlers;
    4342:   MatSolverTypeHolder         next;
    4343: };

    4345: static MatSolverTypeHolder MatSolverTypeHolders = NULL;

    4347: /*@C
    4348:    MatSolveTypeRegister - Registers a MatSolverType that works for a particular matrix type

    4350:    Input Parameters:
    4351: +    package - name of the package, for example petsc or superlu
    4352: .    mtype - the matrix type that works with this package
    4353: .    ftype - the type of factorization supported by the package
    4354: -    createfactor - routine that will create the factored matrix ready to be used

    4356:     Level: intermediate

    4358: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatGetFactor()
    4359: @*/
    4360: PetscErrorCode MatSolverTypeRegister(MatSolverType package,MatType mtype,MatFactorType ftype,PetscErrorCode (*createfactor)(Mat,MatFactorType,Mat*))
    4361: {
    4362:   PetscErrorCode              ierr;
    4363:   MatSolverTypeHolder         next = MatSolverTypeHolders,prev = NULL;
    4364:   PetscBool                   flg;
    4365:   MatSolverTypeForSpecifcType inext,iprev = NULL;

    4368:   MatInitializePackage();
    4369:   if (!next) {
    4370:     PetscNew(&MatSolverTypeHolders);
    4371:     PetscStrallocpy(package,&MatSolverTypeHolders->name);
    4372:     PetscNew(&MatSolverTypeHolders->handlers);
    4373:     PetscStrallocpy(mtype,(char **)&MatSolverTypeHolders->handlers->mtype);
    4374:     MatSolverTypeHolders->handlers->createfactor[(int)ftype-1] = createfactor;
    4375:     return(0);
    4376:   }
    4377:   while (next) {
    4378:     PetscStrcasecmp(package,next->name,&flg);
    4379:     if (flg) {
    4380:       if (!next->handlers) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MatSolverTypeHolder is missing handlers");
    4381:       inext = next->handlers;
    4382:       while (inext) {
    4383:         PetscStrcasecmp(mtype,inext->mtype,&flg);
    4384:         if (flg) {
    4385:           inext->createfactor[(int)ftype-1] = createfactor;
    4386:           return(0);
    4387:         }
    4388:         iprev = inext;
    4389:         inext = inext->next;
    4390:       }
    4391:       PetscNew(&iprev->next);
    4392:       PetscStrallocpy(mtype,(char **)&iprev->next->mtype);
    4393:       iprev->next->createfactor[(int)ftype-1] = createfactor;
    4394:       return(0);
    4395:     }
    4396:     prev = next;
    4397:     next = next->next;
    4398:   }
    4399:   PetscNew(&prev->next);
    4400:   PetscStrallocpy(package,&prev->next->name);
    4401:   PetscNew(&prev->next->handlers);
    4402:   PetscStrallocpy(mtype,(char **)&prev->next->handlers->mtype);
    4403:   prev->next->handlers->createfactor[(int)ftype-1] = createfactor;
    4404:   return(0);
    4405: }

    4407: /*@C
    4408:    MatSolveTypeGet - Gets the function that creates the factor matrix if it exist

    4410:    Input Parameters:
    4411: +    type - name of the package, for example petsc or superlu
    4412: .    ftype - the type of factorization supported by the type
    4413: -    mtype - the matrix type that works with this type

    4415:    Output Parameters:
    4416: +   foundtype - PETSC_TRUE if the type was registered
    4417: .   foundmtype - PETSC_TRUE if the type supports the requested mtype
    4418: -   createfactor - routine that will create the factored matrix ready to be used or NULL if not found

    4420:     Level: intermediate

    4422: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatSolvePackageRegister), MatGetFactor()
    4423: @*/
    4424: PetscErrorCode MatSolverTypeGet(MatSolverType type,MatType mtype,MatFactorType ftype,PetscBool *foundtype,PetscBool *foundmtype,PetscErrorCode (**createfactor)(Mat,MatFactorType,Mat*))
    4425: {
    4426:   PetscErrorCode              ierr;
    4427:   MatSolverTypeHolder         next = MatSolverTypeHolders;
    4428:   PetscBool                   flg;
    4429:   MatSolverTypeForSpecifcType inext;

    4432:   if (foundtype) *foundtype = PETSC_FALSE;
    4433:   if (foundmtype)   *foundmtype   = PETSC_FALSE;
    4434:   if (createfactor) *createfactor    = NULL;

    4436:   if (type) {
    4437:     while (next) {
    4438:       PetscStrcasecmp(type,next->name,&flg);
    4439:       if (flg) {
    4440:         if (foundtype) *foundtype = PETSC_TRUE;
    4441:         inext = next->handlers;
    4442:         while (inext) {
    4443:           PetscStrbeginswith(mtype,inext->mtype,&flg);
    4444:           if (flg) {
    4445:             if (foundmtype) *foundmtype = PETSC_TRUE;
    4446:             if (createfactor)  *createfactor  = inext->createfactor[(int)ftype-1];
    4447:             return(0);
    4448:           }
    4449:           inext = inext->next;
    4450:         }
    4451:       }
    4452:       next = next->next;
    4453:     }
    4454:   } else {
    4455:     while (next) {
    4456:       inext = next->handlers;
    4457:       while (inext) {
    4458:         PetscStrbeginswith(mtype,inext->mtype,&flg);
    4459:         if (flg && inext->createfactor[(int)ftype-1]) {
    4460:           if (foundtype) *foundtype = PETSC_TRUE;
    4461:           if (foundmtype)   *foundmtype   = PETSC_TRUE;
    4462:           if (createfactor) *createfactor = inext->createfactor[(int)ftype-1];
    4463:           return(0);
    4464:         }
    4465:         inext = inext->next;
    4466:       }
    4467:       next = next->next;
    4468:     }
    4469:   }
    4470:   return(0);
    4471: }

    4473: PetscErrorCode MatSolverTypeDestroy(void)
    4474: {
    4475:   PetscErrorCode              ierr;
    4476:   MatSolverTypeHolder         next = MatSolverTypeHolders,prev;
    4477:   MatSolverTypeForSpecifcType inext,iprev;

    4480:   while (next) {
    4481:     PetscFree(next->name);
    4482:     inext = next->handlers;
    4483:     while (inext) {
    4484:       PetscFree(inext->mtype);
    4485:       iprev = inext;
    4486:       inext = inext->next;
    4487:       PetscFree(iprev);
    4488:     }
    4489:     prev = next;
    4490:     next = next->next;
    4491:     PetscFree(prev);
    4492:   }
    4493:   MatSolverTypeHolders = NULL;
    4494:   return(0);
    4495: }

    4497: /*@C
    4498:    MatFactorGetUseOrdering - Indicates if the factorization uses the ordering provided in MatLUFactorSymbolic(), MatCholeskyFactorSymbolic()

    4500:    Logically Collective on Mat

    4502:    Input Parameters:
    4503: .  mat - the matrix

    4505:    Output Parameters:
    4506: .  flg - PETSC_TRUE if uses the ordering

    4508:    Notes:
    4509:       Most internal PETSc factorizations use the ordering past to the factorization routine but external
    4510:       packages do no, thus we want to skip the ordering when it is not needed.

    4512:    Level: developer

    4514: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatGetFactor(), MatLUFactorSymbolic(), MatCholeskyFactorSymbolic()
    4515: @*/
    4516: PetscErrorCode MatFactorGetUseOrdering(Mat mat, PetscBool *flg)
    4517: {
    4519:   *flg = mat->useordering;
    4520:   return(0);
    4521: }

    4523: /*@C
    4524:    MatGetFactor - Returns a matrix suitable to calls to MatXXFactorSymbolic()

    4526:    Collective on Mat

    4528:    Input Parameters:
    4529: +  mat - the matrix
    4530: .  type - name of solver type, for example, superlu, petsc (to use PETSc's default)
    4531: -  ftype - factor type, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ICC, MAT_FACTOR_ILU,

    4533:    Output Parameters:
    4534: .  f - the factor matrix used with MatXXFactorSymbolic() calls

    4536:    Notes:
    4537:       Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
    4538:      such as pastix, superlu, mumps etc.

    4540:       PETSc must have been ./configure to use the external solver, using the option --download-package

    4542:    Developer Notes:
    4543:       This should actually be called MatCreateFactor() since it creates a new factor object

    4545:    Level: intermediate

    4547: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatFactorGetUseOrdering(), MatSolverTypeRegister()
    4548: @*/
    4549: PetscErrorCode MatGetFactor(Mat mat, MatSolverType type,MatFactorType ftype,Mat *f)
    4550: {
    4551:   PetscErrorCode ierr,(*conv)(Mat,MatFactorType,Mat*);
    4552:   PetscBool      foundtype,foundmtype;

    4558:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4559:   MatCheckPreallocated(mat,1);

    4561:   MatSolverTypeGet(type,((PetscObject)mat)->type_name,ftype,&foundtype,&foundmtype,&conv);
    4562:   if (!foundtype) {
    4563:     if (type) {
    4564:       SETERRQ4(PetscObjectComm((PetscObject)mat),PETSC_ERR_MISSING_FACTOR,"Could not locate solver type %s for factorization type %s and matrix type %s. Perhaps you must ./configure with --download-%s",type,MatFactorTypes[ftype],((PetscObject)mat)->type_name,type);
    4565:     } else {
    4566:       SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_MISSING_FACTOR,"Could not locate a solver type for factorization type %s and matrix type %s.",MatFactorTypes[ftype],((PetscObject)mat)->type_name);
    4567:     }
    4568:   }
    4569:   if (!foundmtype) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_MISSING_FACTOR,"MatSolverType %s does not support matrix type %s",type,((PetscObject)mat)->type_name);
    4570:   if (!conv) SETERRQ3(PetscObjectComm((PetscObject)mat),PETSC_ERR_MISSING_FACTOR,"MatSolverType %s does not support factorization type %s for matrix type %s",type,MatFactorTypes[ftype],((PetscObject)mat)->type_name);

    4572:   (*conv)(mat,ftype,f);
    4573:   return(0);
    4574: }

    4576: /*@C
    4577:    MatGetFactorAvailable - Returns a a flag if matrix supports particular type and factor type

    4579:    Not Collective

    4581:    Input Parameters:
    4582: +  mat - the matrix
    4583: .  type - name of solver type, for example, superlu, petsc (to use PETSc's default)
    4584: -  ftype - factor type, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ICC, MAT_FACTOR_ILU,

    4586:    Output Parameter:
    4587: .    flg - PETSC_TRUE if the factorization is available

    4589:    Notes:
    4590:       Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
    4591:      such as pastix, superlu, mumps etc.

    4593:       PETSc must have been ./configure to use the external solver, using the option --download-package

    4595:    Developer Notes:
    4596:       This should actually be called MatCreateFactorAvailable() since MatGetFactor() creates a new factor object

    4598:    Level: intermediate

    4600: .seealso: MatCopy(), MatDuplicate(), MatGetFactor(), MatSolverTypeRegister()
    4601: @*/
    4602: PetscErrorCode MatGetFactorAvailable(Mat mat, MatSolverType type,MatFactorType ftype,PetscBool  *flg)
    4603: {
    4604:   PetscErrorCode ierr, (*gconv)(Mat,MatFactorType,Mat*);

    4610:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4611:   MatCheckPreallocated(mat,1);

    4613:   *flg = PETSC_FALSE;
    4614:   MatSolverTypeGet(type,((PetscObject)mat)->type_name,ftype,NULL,NULL,&gconv);
    4615:   if (gconv) {
    4616:     *flg = PETSC_TRUE;
    4617:   }
    4618:   return(0);
    4619: }

    4621: #include <petscdmtypes.h>

    4623: /*@
    4624:    MatDuplicate - Duplicates a matrix including the non-zero structure.

    4626:    Collective on Mat

    4628:    Input Parameters:
    4629: +  mat - the matrix
    4630: -  op - One of MAT_DO_NOT_COPY_VALUES, MAT_COPY_VALUES, or MAT_SHARE_NONZERO_PATTERN.
    4631:         See the manual page for MatDuplicateOption for an explanation of these options.

    4633:    Output Parameter:
    4634: .  M - pointer to place new matrix

    4636:    Level: intermediate

    4638:    Notes:
    4639:     You cannot change the nonzero pattern for the parent or child matrix if you use MAT_SHARE_NONZERO_PATTERN.
    4640:     When original mat is a product of matrix operation, e.g., an output of MatMatMult() or MatCreateSubMatrix(), only the simple matrix data structure of mat is duplicated and the internal data structures created for the reuse of previous matrix operations are not duplicated. User should not use MatDuplicate() to create new matrix M if M is intended to be reused as the product of matrix operation.

    4642: .seealso: MatCopy(), MatConvert(), MatDuplicateOption
    4643: @*/
    4644: PetscErrorCode MatDuplicate(Mat mat,MatDuplicateOption op,Mat *M)
    4645: {
    4647:   Mat            B;
    4648:   PetscInt       i;
    4649:   DM             dm;
    4650:   void           (*viewf)(void);

    4656:   if (op == MAT_COPY_VALUES && !mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MAT_COPY_VALUES not allowed for unassembled matrix");
    4657:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4658:   MatCheckPreallocated(mat,1);

    4660:   *M = NULL;
    4661:   if (!mat->ops->duplicate) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not written for matrix type %s\n",((PetscObject)mat)->type_name);
    4662:   PetscLogEventBegin(MAT_Convert,mat,0,0,0);
    4663:   (*mat->ops->duplicate)(mat,op,M);
    4664:   B    = *M;

    4666:   MatGetOperation(mat,MATOP_VIEW,&viewf);
    4667:   if (viewf) {
    4668:     MatSetOperation(B,MATOP_VIEW,viewf);
    4669:   }

    4671:   B->stencil.dim = mat->stencil.dim;
    4672:   B->stencil.noc = mat->stencil.noc;
    4673:   for (i=0; i<=mat->stencil.dim; i++) {
    4674:     B->stencil.dims[i]   = mat->stencil.dims[i];
    4675:     B->stencil.starts[i] = mat->stencil.starts[i];
    4676:   }

    4678:   B->nooffproczerorows = mat->nooffproczerorows;
    4679:   B->nooffprocentries  = mat->nooffprocentries;

    4681:   PetscObjectQuery((PetscObject) mat, "__PETSc_dm", (PetscObject*) &dm);
    4682:   if (dm) {
    4683:     PetscObjectCompose((PetscObject) B, "__PETSc_dm", (PetscObject) dm);
    4684:   }
    4685:   PetscLogEventEnd(MAT_Convert,mat,0,0,0);
    4686:   PetscObjectStateIncrease((PetscObject)B);
    4687:   return(0);
    4688: }

    4690: /*@
    4691:    MatGetDiagonal - Gets the diagonal of a matrix.

    4693:    Logically Collective on Mat

    4695:    Input Parameters:
    4696: +  mat - the matrix
    4697: -  v - the vector for storing the diagonal

    4699:    Output Parameter:
    4700: .  v - the diagonal of the matrix

    4702:    Level: intermediate

    4704:    Note:
    4705:    Currently only correct in parallel for square matrices.

    4707: .seealso: MatGetRow(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMaxAbs()
    4708: @*/
    4709: PetscErrorCode MatGetDiagonal(Mat mat,Vec v)
    4710: {

    4717:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4718:   if (!mat->ops->getdiagonal) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4719:   MatCheckPreallocated(mat,1);

    4721:   (*mat->ops->getdiagonal)(mat,v);
    4722:   PetscObjectStateIncrease((PetscObject)v);
    4723:   return(0);
    4724: }

    4726: /*@C
    4727:    MatGetRowMin - Gets the minimum value (of the real part) of each
    4728:         row of the matrix

    4730:    Logically Collective on Mat

    4732:    Input Parameters:
    4733: .  mat - the matrix

    4735:    Output Parameter:
    4736: +  v - the vector for storing the maximums
    4737: -  idx - the indices of the column found for each row (optional)

    4739:    Level: intermediate

    4741:    Notes:
    4742:     The result of this call are the same as if one converted the matrix to dense format
    4743:       and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    4745:     This code is only implemented for a couple of matrix formats.

    4747: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMaxAbs(),
    4748:           MatGetRowMax()
    4749: @*/
    4750: PetscErrorCode MatGetRowMin(Mat mat,Vec v,PetscInt idx[])
    4751: {

    4758:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");

    4760:   if (!mat->cmap->N) {
    4761:     VecSet(v,PETSC_MAX_REAL);
    4762:     if (idx) {
    4763:       PetscInt i,m = mat->rmap->n;
    4764:       for (i=0; i<m; i++) idx[i] = -1;
    4765:     }
    4766:   } else {
    4767:     if (!mat->ops->getrowmin) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4768:     MatCheckPreallocated(mat,1);
    4769:   }
    4770:   (*mat->ops->getrowmin)(mat,v,idx);
    4771:   PetscObjectStateIncrease((PetscObject)v);
    4772:   return(0);
    4773: }

    4775: /*@C
    4776:    MatGetRowMinAbs - Gets the minimum value (in absolute value) of each
    4777:         row of the matrix

    4779:    Logically Collective on Mat

    4781:    Input Parameters:
    4782: .  mat - the matrix

    4784:    Output Parameter:
    4785: +  v - the vector for storing the minimums
    4786: -  idx - the indices of the column found for each row (or NULL if not needed)

    4788:    Level: intermediate

    4790:    Notes:
    4791:     if a row is completely empty or has only 0.0 values then the idx[] value for that
    4792:     row is 0 (the first column).

    4794:     This code is only implemented for a couple of matrix formats.

    4796: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMax(), MatGetRowMaxAbs(), MatGetRowMin()
    4797: @*/
    4798: PetscErrorCode MatGetRowMinAbs(Mat mat,Vec v,PetscInt idx[])
    4799: {

    4806:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4807:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

    4809:   if (!mat->cmap->N) {
    4810:     VecSet(v,0.0);
    4811:     if (idx) {
    4812:       PetscInt i,m = mat->rmap->n;
    4813:       for (i=0; i<m; i++) idx[i] = -1;
    4814:     }
    4815:   } else {
    4816:     if (!mat->ops->getrowminabs) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4817:     MatCheckPreallocated(mat,1);
    4818:     if (idx) {PetscArrayzero(idx,mat->rmap->n);}
    4819:     (*mat->ops->getrowminabs)(mat,v,idx);
    4820:   }
    4821:   PetscObjectStateIncrease((PetscObject)v);
    4822:   return(0);
    4823: }

    4825: /*@C
    4826:    MatGetRowMax - Gets the maximum value (of the real part) of each
    4827:         row of the matrix

    4829:    Logically Collective on Mat

    4831:    Input Parameters:
    4832: .  mat - the matrix

    4834:    Output Parameter:
    4835: +  v - the vector for storing the maximums
    4836: -  idx - the indices of the column found for each row (optional)

    4838:    Level: intermediate

    4840:    Notes:
    4841:     The result of this call are the same as if one converted the matrix to dense format
    4842:       and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    4844:     This code is only implemented for a couple of matrix formats.

    4846: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMaxAbs(), MatGetRowMin()
    4847: @*/
    4848: PetscErrorCode MatGetRowMax(Mat mat,Vec v,PetscInt idx[])
    4849: {

    4856:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");

    4858:   if (!mat->cmap->N) {
    4859:     VecSet(v,PETSC_MIN_REAL);
    4860:     if (idx) {
    4861:       PetscInt i,m = mat->rmap->n;
    4862:       for (i=0; i<m; i++) idx[i] = -1;
    4863:     }
    4864:   } else {
    4865:     if (!mat->ops->getrowmax) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4866:     MatCheckPreallocated(mat,1);
    4867:     (*mat->ops->getrowmax)(mat,v,idx);
    4868:   }
    4869:   PetscObjectStateIncrease((PetscObject)v);
    4870:   return(0);
    4871: }

    4873: /*@C
    4874:    MatGetRowMaxAbs - Gets the maximum value (in absolute value) of each
    4875:         row of the matrix

    4877:    Logically Collective on Mat

    4879:    Input Parameters:
    4880: .  mat - the matrix

    4882:    Output Parameter:
    4883: +  v - the vector for storing the maximums
    4884: -  idx - the indices of the column found for each row (or NULL if not needed)

    4886:    Level: intermediate

    4888:    Notes:
    4889:     if a row is completely empty or has only 0.0 values then the idx[] value for that
    4890:     row is 0 (the first column).

    4892:     This code is only implemented for a couple of matrix formats.

    4894: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMax(), MatGetRowMin()
    4895: @*/
    4896: PetscErrorCode MatGetRowMaxAbs(Mat mat,Vec v,PetscInt idx[])
    4897: {

    4904:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");

    4906:   if (!mat->cmap->N) {
    4907:     VecSet(v,0.0);
    4908:     if (idx) {
    4909:       PetscInt i,m = mat->rmap->n;
    4910:       for (i=0; i<m; i++) idx[i] = -1;
    4911:     }
    4912:   } else {
    4913:     if (!mat->ops->getrowmaxabs) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4914:     MatCheckPreallocated(mat,1);
    4915:     if (idx) {PetscArrayzero(idx,mat->rmap->n);}
    4916:     (*mat->ops->getrowmaxabs)(mat,v,idx);
    4917:   }
    4918:   PetscObjectStateIncrease((PetscObject)v);
    4919:   return(0);
    4920: }

    4922: /*@
    4923:    MatGetRowSum - Gets the sum of each row of the matrix

    4925:    Logically or Neighborhood Collective on Mat

    4927:    Input Parameters:
    4928: .  mat - the matrix

    4930:    Output Parameter:
    4931: .  v - the vector for storing the sum of rows

    4933:    Level: intermediate

    4935:    Notes:
    4936:     This code is slow since it is not currently specialized for different formats

    4938: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMax(), MatGetRowMin()
    4939: @*/
    4940: PetscErrorCode MatGetRowSum(Mat mat, Vec v)
    4941: {
    4942:   Vec            ones;

    4949:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4950:   MatCheckPreallocated(mat,1);
    4951:   MatCreateVecs(mat,&ones,NULL);
    4952:   VecSet(ones,1.);
    4953:   MatMult(mat,ones,v);
    4954:   VecDestroy(&ones);
    4955:   return(0);
    4956: }

    4958: /*@
    4959:    MatTranspose - Computes an in-place or out-of-place transpose of a matrix.

    4961:    Collective on Mat

    4963:    Input Parameter:
    4964: +  mat - the matrix to transpose
    4965: -  reuse - either MAT_INITIAL_MATRIX, MAT_REUSE_MATRIX, or MAT_INPLACE_MATRIX

    4967:    Output Parameters:
    4968: .  B - the transpose

    4970:    Notes:
    4971:      If you use MAT_INPLACE_MATRIX then you must pass in &mat for B

    4973:      MAT_REUSE_MATRIX causes the B matrix from a previous call to this function with MAT_INITIAL_MATRIX to be used

    4975:      Consider using MatCreateTranspose() instead if you only need a matrix that behaves like the transpose, but don't need the storage to be changed.

    4977:    Level: intermediate

    4979: .seealso: MatMultTranspose(), MatMultTransposeAdd(), MatIsTranspose(), MatReuse
    4980: @*/
    4981: PetscErrorCode MatTranspose(Mat mat,MatReuse reuse,Mat *B)
    4982: {

    4988:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4989:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4990:   if (!mat->ops->transpose) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4991:   if (reuse == MAT_INPLACE_MATRIX && mat != *B) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"MAT_INPLACE_MATRIX requires last matrix to match first");
    4992:   if (reuse == MAT_REUSE_MATRIX && mat == *B) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Perhaps you mean MAT_INPLACE_MATRIX");
    4993:   MatCheckPreallocated(mat,1);

    4995:   PetscLogEventBegin(MAT_Transpose,mat,0,0,0);
    4996:   (*mat->ops->transpose)(mat,reuse,B);
    4997:   PetscLogEventEnd(MAT_Transpose,mat,0,0,0);
    4998:   if (B) {PetscObjectStateIncrease((PetscObject)*B);}
    4999:   return(0);
    5000: }

    5002: /*@
    5003:    MatIsTranspose - Test whether a matrix is another one's transpose,
    5004:         or its own, in which case it tests symmetry.

    5006:    Collective on Mat

    5008:    Input Parameter:
    5009: +  A - the matrix to test
    5010: -  B - the matrix to test against, this can equal the first parameter

    5012:    Output Parameters:
    5013: .  flg - the result

    5015:    Notes:
    5016:    Only available for SeqAIJ/MPIAIJ matrices. The sequential algorithm
    5017:    has a running time of the order of the number of nonzeros; the parallel
    5018:    test involves parallel copies of the block-offdiagonal parts of the matrix.

    5020:    Level: intermediate

    5022: .seealso: MatTranspose(), MatIsSymmetric(), MatIsHermitian()
    5023: @*/
    5024: PetscErrorCode MatIsTranspose(Mat A,Mat B,PetscReal tol,PetscBool  *flg)
    5025: {
    5026:   PetscErrorCode ierr,(*f)(Mat,Mat,PetscReal,PetscBool*),(*g)(Mat,Mat,PetscReal,PetscBool*);

    5032:   PetscObjectQueryFunction((PetscObject)A,"MatIsTranspose_C",&f);
    5033:   PetscObjectQueryFunction((PetscObject)B,"MatIsTranspose_C",&g);
    5034:   *flg = PETSC_FALSE;
    5035:   if (f && g) {
    5036:     if (f == g) {
    5037:       (*f)(A,B,tol,flg);
    5038:     } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_NOTSAMETYPE,"Matrices do not have the same comparator for symmetry test");
    5039:   } else {
    5040:     MatType mattype;
    5041:     if (!f) {
    5042:       MatGetType(A,&mattype);
    5043:     } else {
    5044:       MatGetType(B,&mattype);
    5045:     }
    5046:     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for transpose",mattype);
    5047:   }
    5048:   return(0);
    5049: }

    5051: /*@
    5052:    MatHermitianTranspose - Computes an in-place or out-of-place transpose of a matrix in complex conjugate.

    5054:    Collective on Mat

    5056:    Input Parameter:
    5057: +  mat - the matrix to transpose and complex conjugate
    5058: -  reuse - MAT_INITIAL_MATRIX to create a new matrix, MAT_INPLACE_MATRIX to reuse the first argument to store the transpose

    5060:    Output Parameters:
    5061: .  B - the Hermitian

    5063:    Level: intermediate

    5065: .seealso: MatTranspose(), MatMultTranspose(), MatMultTransposeAdd(), MatIsTranspose(), MatReuse
    5066: @*/
    5067: PetscErrorCode MatHermitianTranspose(Mat mat,MatReuse reuse,Mat *B)
    5068: {

    5072:   MatTranspose(mat,reuse,B);
    5073: #if defined(PETSC_USE_COMPLEX)
    5074:   MatConjugate(*B);
    5075: #endif
    5076:   return(0);
    5077: }

    5079: /*@
    5080:    MatIsHermitianTranspose - Test whether a matrix is another one's Hermitian transpose,

    5082:    Collective on Mat

    5084:    Input Parameter:
    5085: +  A - the matrix to test
    5086: -  B - the matrix to test against, this can equal the first parameter

    5088:    Output Parameters:
    5089: .  flg - the result

    5091:    Notes:
    5092:    Only available for SeqAIJ/MPIAIJ matrices. The sequential algorithm
    5093:    has a running time of the order of the number of nonzeros; the parallel
    5094:    test involves parallel copies of the block-offdiagonal parts of the matrix.

    5096:    Level: intermediate

    5098: .seealso: MatTranspose(), MatIsSymmetric(), MatIsHermitian(), MatIsTranspose()
    5099: @*/
    5100: PetscErrorCode MatIsHermitianTranspose(Mat A,Mat B,PetscReal tol,PetscBool  *flg)
    5101: {
    5102:   PetscErrorCode ierr,(*f)(Mat,Mat,PetscReal,PetscBool*),(*g)(Mat,Mat,PetscReal,PetscBool*);

    5108:   PetscObjectQueryFunction((PetscObject)A,"MatIsHermitianTranspose_C",&f);
    5109:   PetscObjectQueryFunction((PetscObject)B,"MatIsHermitianTranspose_C",&g);
    5110:   if (f && g) {
    5111:     if (f==g) {
    5112:       (*f)(A,B,tol,flg);
    5113:     } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_NOTSAMETYPE,"Matrices do not have the same comparator for Hermitian test");
    5114:   }
    5115:   return(0);
    5116: }

    5118: /*@
    5119:    MatPermute - Creates a new matrix with rows and columns permuted from the
    5120:    original.

    5122:    Collective on Mat

    5124:    Input Parameters:
    5125: +  mat - the matrix to permute
    5126: .  row - row permutation, each processor supplies only the permutation for its rows
    5127: -  col - column permutation, each processor supplies only the permutation for its columns

    5129:    Output Parameters:
    5130: .  B - the permuted matrix

    5132:    Level: advanced

    5134:    Note:
    5135:    The index sets map from row/col of permuted matrix to row/col of original matrix.
    5136:    The index sets should be on the same communicator as Mat and have the same local sizes.

    5138: .seealso: MatGetOrdering(), ISAllGather()

    5140: @*/
    5141: PetscErrorCode MatPermute(Mat mat,IS row,IS col,Mat *B)
    5142: {

    5151:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5152:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5153:   if (!mat->ops->permute) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatPermute not available for Mat type %s",((PetscObject)mat)->type_name);
    5154:   MatCheckPreallocated(mat,1);

    5156:   (*mat->ops->permute)(mat,row,col,B);
    5157:   PetscObjectStateIncrease((PetscObject)*B);
    5158:   return(0);
    5159: }

    5161: /*@
    5162:    MatEqual - Compares two matrices.

    5164:    Collective on Mat

    5166:    Input Parameters:
    5167: +  A - the first matrix
    5168: -  B - the second matrix

    5170:    Output Parameter:
    5171: .  flg - PETSC_TRUE if the matrices are equal; PETSC_FALSE otherwise.

    5173:    Level: intermediate

    5175: @*/
    5176: PetscErrorCode MatEqual(Mat A,Mat B,PetscBool  *flg)
    5177: {

    5187:   MatCheckPreallocated(B,2);
    5188:   if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5189:   if (!B->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5190:   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);
    5191:   if (!A->ops->equal) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)A)->type_name);
    5192:   if (!B->ops->equal) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)B)->type_name);
    5193:   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);
    5194:   MatCheckPreallocated(A,1);

    5196:   (*A->ops->equal)(A,B,flg);
    5197:   return(0);
    5198: }

    5200: /*@
    5201:    MatDiagonalScale - Scales a matrix on the left and right by diagonal
    5202:    matrices that are stored as vectors.  Either of the two scaling
    5203:    matrices can be NULL.

    5205:    Collective on Mat

    5207:    Input Parameters:
    5208: +  mat - the matrix to be scaled
    5209: .  l - the left scaling vector (or NULL)
    5210: -  r - the right scaling vector (or NULL)

    5212:    Notes:
    5213:    MatDiagonalScale() computes A = LAR, where
    5214:    L = a diagonal matrix (stored as a vector), R = a diagonal matrix (stored as a vector)
    5215:    The L scales the rows of the matrix, the R scales the columns of the matrix.

    5217:    Level: intermediate

    5220: .seealso: MatScale(), MatShift(), MatDiagonalSet()
    5221: @*/
    5222: PetscErrorCode MatDiagonalScale(Mat mat,Vec l,Vec r)
    5223: {

    5231:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5232:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5233:   MatCheckPreallocated(mat,1);
    5234:   if (!l && !r) return(0);

    5236:   if (!mat->ops->diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5237:   PetscLogEventBegin(MAT_Scale,mat,0,0,0);
    5238:   (*mat->ops->diagonalscale)(mat,l,r);
    5239:   PetscLogEventEnd(MAT_Scale,mat,0,0,0);
    5240:   PetscObjectStateIncrease((PetscObject)mat);
    5241:   return(0);
    5242: }

    5244: /*@
    5245:     MatScale - Scales all elements of a matrix by a given number.

    5247:     Logically Collective on Mat

    5249:     Input Parameters:
    5250: +   mat - the matrix to be scaled
    5251: -   a  - the scaling value

    5253:     Output Parameter:
    5254: .   mat - the scaled matrix

    5256:     Level: intermediate

    5258: .seealso: MatDiagonalScale()
    5259: @*/
    5260: PetscErrorCode MatScale(Mat mat,PetscScalar a)
    5261: {

    5267:   if (a != (PetscScalar)1.0 && !mat->ops->scale) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5268:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5269:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5271:   MatCheckPreallocated(mat,1);

    5273:   PetscLogEventBegin(MAT_Scale,mat,0,0,0);
    5274:   if (a != (PetscScalar)1.0) {
    5275:     (*mat->ops->scale)(mat,a);
    5276:     PetscObjectStateIncrease((PetscObject)mat);
    5277:   }
    5278:   PetscLogEventEnd(MAT_Scale,mat,0,0,0);
    5279:   return(0);
    5280: }

    5282: /*@
    5283:    MatNorm - Calculates various norms of a matrix.

    5285:    Collective on Mat

    5287:    Input Parameters:
    5288: +  mat - the matrix
    5289: -  type - the type of norm, NORM_1, NORM_FROBENIUS, NORM_INFINITY

    5291:    Output Parameters:
    5292: .  nrm - the resulting norm

    5294:    Level: intermediate

    5296: @*/
    5297: PetscErrorCode MatNorm(Mat mat,NormType type,PetscReal *nrm)
    5298: {

    5306:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5307:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5308:   if (!mat->ops->norm) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5309:   MatCheckPreallocated(mat,1);

    5311:   (*mat->ops->norm)(mat,type,nrm);
    5312:   return(0);
    5313: }

    5315: /*
    5316:      This variable is used to prevent counting of MatAssemblyBegin() that
    5317:    are called from within a MatAssemblyEnd().
    5318: */
    5319: static PetscInt MatAssemblyEnd_InUse = 0;
    5320: /*@
    5321:    MatAssemblyBegin - Begins assembling the matrix.  This routine should
    5322:    be called after completing all calls to MatSetValues().

    5324:    Collective on Mat

    5326:    Input Parameters:
    5327: +  mat - the matrix
    5328: -  type - type of assembly, either MAT_FLUSH_ASSEMBLY or MAT_FINAL_ASSEMBLY

    5330:    Notes:
    5331:    MatSetValues() generally caches the values.  The matrix is ready to
    5332:    use only after MatAssemblyBegin() and MatAssemblyEnd() have been called.
    5333:    Use MAT_FLUSH_ASSEMBLY when switching between ADD_VALUES and INSERT_VALUES
    5334:    in MatSetValues(); use MAT_FINAL_ASSEMBLY for the final assembly before
    5335:    using the matrix.

    5337:    ALL processes that share a matrix MUST call MatAssemblyBegin() and MatAssemblyEnd() the SAME NUMBER of times, and each time with the
    5338:    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
    5339:    a global collective operation requring all processes that share the matrix.

    5341:    Space for preallocated nonzeros that is not filled by a call to MatSetValues() or a related routine are compressed
    5342:    out by assembly. If you intend to use that extra space on a subsequent assembly, be sure to insert explicit zeros
    5343:    before MAT_FINAL_ASSEMBLY so the space is not compressed out.

    5345:    Level: beginner

    5347: .seealso: MatAssemblyEnd(), MatSetValues(), MatAssembled()
    5348: @*/
    5349: PetscErrorCode MatAssemblyBegin(Mat mat,MatAssemblyType type)
    5350: {

    5356:   MatCheckPreallocated(mat,1);
    5357:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix.\nDid you forget to call MatSetUnfactored()?");
    5358:   if (mat->assembled) {
    5359:     mat->was_assembled = PETSC_TRUE;
    5360:     mat->assembled     = PETSC_FALSE;
    5361:   }

    5363:   if (!MatAssemblyEnd_InUse) {
    5364:     PetscLogEventBegin(MAT_AssemblyBegin,mat,0,0,0);
    5365:     if (mat->ops->assemblybegin) {(*mat->ops->assemblybegin)(mat,type);}
    5366:     PetscLogEventEnd(MAT_AssemblyBegin,mat,0,0,0);
    5367:   } else if (mat->ops->assemblybegin) {
    5368:     (*mat->ops->assemblybegin)(mat,type);
    5369:   }
    5370:   return(0);
    5371: }

    5373: /*@
    5374:    MatAssembled - Indicates if a matrix has been assembled and is ready for
    5375:      use; for example, in matrix-vector product.

    5377:    Not Collective

    5379:    Input Parameter:
    5380: .  mat - the matrix

    5382:    Output Parameter:
    5383: .  assembled - PETSC_TRUE or PETSC_FALSE

    5385:    Level: advanced

    5387: .seealso: MatAssemblyEnd(), MatSetValues(), MatAssemblyBegin()
    5388: @*/
    5389: PetscErrorCode MatAssembled(Mat mat,PetscBool  *assembled)
    5390: {
    5394:   *assembled = mat->assembled;
    5395:   return(0);
    5396: }

    5398: /*@
    5399:    MatAssemblyEnd - Completes assembling the matrix.  This routine should
    5400:    be called after MatAssemblyBegin().

    5402:    Collective on Mat

    5404:    Input Parameters:
    5405: +  mat - the matrix
    5406: -  type - type of assembly, either MAT_FLUSH_ASSEMBLY or MAT_FINAL_ASSEMBLY

    5408:    Options Database Keys:
    5409: +  -mat_view ::ascii_info - Prints info on matrix at conclusion of MatEndAssembly()
    5410: .  -mat_view ::ascii_info_detail - Prints more detailed info
    5411: .  -mat_view - Prints matrix in ASCII format
    5412: .  -mat_view ::ascii_matlab - Prints matrix in Matlab format
    5413: .  -mat_view draw - PetscDraws nonzero structure of matrix, using MatView() and PetscDrawOpenX().
    5414: .  -display <name> - Sets display name (default is host)
    5415: .  -draw_pause <sec> - Sets number of seconds to pause after display
    5416: .  -mat_view socket - Sends matrix to socket, can be accessed from Matlab (See Users-Manual: ch_matlab)
    5417: .  -viewer_socket_machine <machine> - Machine to use for socket
    5418: .  -viewer_socket_port <port> - Port number to use for socket
    5419: -  -mat_view binary:filename[:append] - Save matrix to file in binary format

    5421:    Notes:
    5422:    MatSetValues() generally caches the values.  The matrix is ready to
    5423:    use only after MatAssemblyBegin() and MatAssemblyEnd() have been called.
    5424:    Use MAT_FLUSH_ASSEMBLY when switching between ADD_VALUES and INSERT_VALUES
    5425:    in MatSetValues(); use MAT_FINAL_ASSEMBLY for the final assembly before
    5426:    using the matrix.

    5428:    Space for preallocated nonzeros that is not filled by a call to MatSetValues() or a related routine are compressed
    5429:    out by assembly. If you intend to use that extra space on a subsequent assembly, be sure to insert explicit zeros
    5430:    before MAT_FINAL_ASSEMBLY so the space is not compressed out.

    5432:    Level: beginner

    5434: .seealso: MatAssemblyBegin(), MatSetValues(), PetscDrawOpenX(), PetscDrawCreate(), MatView(), MatAssembled(), PetscViewerSocketOpen()
    5435: @*/
    5436: PetscErrorCode MatAssemblyEnd(Mat mat,MatAssemblyType type)
    5437: {
    5438:   PetscErrorCode  ierr;
    5439:   static PetscInt inassm = 0;
    5440:   PetscBool       flg    = PETSC_FALSE;

    5446:   inassm++;
    5447:   MatAssemblyEnd_InUse++;
    5448:   if (MatAssemblyEnd_InUse == 1) { /* Do the logging only the first time through */
    5449:     PetscLogEventBegin(MAT_AssemblyEnd,mat,0,0,0);
    5450:     if (mat->ops->assemblyend) {
    5451:       (*mat->ops->assemblyend)(mat,type);
    5452:     }
    5453:     PetscLogEventEnd(MAT_AssemblyEnd,mat,0,0,0);
    5454:   } else if (mat->ops->assemblyend) {
    5455:     (*mat->ops->assemblyend)(mat,type);
    5456:   }

    5458:   /* Flush assembly is not a true assembly */
    5459:   if (type != MAT_FLUSH_ASSEMBLY) {
    5460:     mat->num_ass++;
    5461:     mat->assembled        = PETSC_TRUE;
    5462:     mat->ass_nonzerostate = mat->nonzerostate;
    5463:   }

    5465:   mat->insertmode = NOT_SET_VALUES;
    5466:   MatAssemblyEnd_InUse--;
    5467:   PetscObjectStateIncrease((PetscObject)mat);
    5468:   if (!mat->symmetric_eternal) {
    5469:     mat->symmetric_set              = PETSC_FALSE;
    5470:     mat->hermitian_set              = PETSC_FALSE;
    5471:     mat->structurally_symmetric_set = PETSC_FALSE;
    5472:   }
    5473:   if (inassm == 1 && type != MAT_FLUSH_ASSEMBLY) {
    5474:     MatViewFromOptions(mat,NULL,"-mat_view");

    5476:     if (mat->checksymmetryonassembly) {
    5477:       MatIsSymmetric(mat,mat->checksymmetrytol,&flg);
    5478:       if (flg) {
    5479:         PetscPrintf(PetscObjectComm((PetscObject)mat),"Matrix is symmetric (tolerance %g)\n",(double)mat->checksymmetrytol);
    5480:       } else {
    5481:         PetscPrintf(PetscObjectComm((PetscObject)mat),"Matrix is not symmetric (tolerance %g)\n",(double)mat->checksymmetrytol);
    5482:       }
    5483:     }
    5484:     if (mat->nullsp && mat->checknullspaceonassembly) {
    5485:       MatNullSpaceTest(mat->nullsp,mat,NULL);
    5486:     }
    5487:   }
    5488:   inassm--;
    5489:   return(0);
    5490: }

    5492: /*@
    5493:    MatSetOption - Sets a parameter option for a matrix. Some options
    5494:    may be specific to certain storage formats.  Some options
    5495:    determine how values will be inserted (or added). Sorted,
    5496:    row-oriented input will generally assemble the fastest. The default
    5497:    is row-oriented.

    5499:    Logically Collective on Mat for certain operations, such as MAT_SPD, not collective for MAT_ROW_ORIENTED, see MatOption

    5501:    Input Parameters:
    5502: +  mat - the matrix
    5503: .  option - the option, one of those listed below (and possibly others),
    5504: -  flg - turn the option on (PETSC_TRUE) or off (PETSC_FALSE)

    5506:   Options Describing Matrix Structure:
    5507: +    MAT_SPD - symmetric positive definite
    5508: .    MAT_SYMMETRIC - symmetric in terms of both structure and value
    5509: .    MAT_HERMITIAN - transpose is the complex conjugation
    5510: .    MAT_STRUCTURALLY_SYMMETRIC - symmetric nonzero structure
    5511: -    MAT_SYMMETRY_ETERNAL - if you would like the symmetry/Hermitian flag
    5512:                             you set to be kept with all future use of the matrix
    5513:                             including after MatAssemblyBegin/End() which could
    5514:                             potentially change the symmetry structure, i.e. you
    5515:                             KNOW the matrix will ALWAYS have the property you set.
    5516:                             Note that setting this flag alone implies nothing about whether the matrix is symmetric/Hermitian;
    5517:                             the relevant flags must be set independently.

    5520:    Options For Use with MatSetValues():
    5521:    Insert a logically dense subblock, which can be
    5522: .    MAT_ROW_ORIENTED - row-oriented (default)

    5524:    Note these options reflect the data you pass in with MatSetValues(); it has
    5525:    nothing to do with how the data is stored internally in the matrix
    5526:    data structure.

    5528:    When (re)assembling a matrix, we can restrict the input for
    5529:    efficiency/debugging purposes.  These options include:
    5530: +    MAT_NEW_NONZERO_LOCATIONS - additional insertions will be allowed if they generate a new nonzero (slow)
    5531: .    MAT_NEW_DIAGONALS - new diagonals will be allowed (for block diagonal format only)
    5532: .    MAT_IGNORE_OFF_PROC_ENTRIES - drops off-processor entries
    5533: .    MAT_NEW_NONZERO_LOCATION_ERR - generates an error for new matrix entry
    5534: .    MAT_USE_HASH_TABLE - uses a hash table to speed up matrix assembly
    5535: .    MAT_NO_OFF_PROC_ENTRIES - you know each process will only set values for its own rows, will generate an error if
    5536:         any process sets values for another process. This avoids all reductions in the MatAssembly routines and thus improves
    5537:         performance for very large process counts.
    5538: -    MAT_SUBSET_OFF_PROC_ENTRIES - you know that the first assembly after setting this flag will set a superset
    5539:         of the off-process entries required for all subsequent assemblies. This avoids a rendezvous step in the MatAssembly
    5540:         functions, instead sending only neighbor messages.

    5542:    Notes:
    5543:    Except for MAT_UNUSED_NONZERO_LOCATION_ERR and  MAT_ROW_ORIENTED all processes that share the matrix must pass the same value in flg!

    5545:    Some options are relevant only for particular matrix types and
    5546:    are thus ignored by others.  Other options are not supported by
    5547:    certain matrix types and will generate an error message if set.

    5549:    If using a Fortran 77 module to compute a matrix, one may need to
    5550:    use the column-oriented option (or convert to the row-oriented
    5551:    format).

    5553:    MAT_NEW_NONZERO_LOCATIONS set to PETSC_FALSE indicates that any add or insertion
    5554:    that would generate a new entry in the nonzero structure is instead
    5555:    ignored.  Thus, if memory has not alredy been allocated for this particular
    5556:    data, then the insertion is ignored. For dense matrices, in which
    5557:    the entire array is allocated, no entries are ever ignored.
    5558:    Set after the first MatAssemblyEnd(). If this option is set then the MatAssemblyBegin/End() processes has one less global reduction

    5560:    MAT_NEW_NONZERO_LOCATION_ERR set to PETSC_TRUE indicates that any add or insertion
    5561:    that would generate a new entry in the nonzero structure instead produces
    5562:    an error. (Currently supported for AIJ and BAIJ formats only.) If this option is set then the MatAssemblyBegin/End() processes has one less global reduction

    5564:    MAT_NEW_NONZERO_ALLOCATION_ERR set to PETSC_TRUE indicates that any add or insertion
    5565:    that would generate a new entry that has not been preallocated will
    5566:    instead produce an error. (Currently supported for AIJ and BAIJ formats
    5567:    only.) This is a useful flag when debugging matrix memory preallocation.
    5568:    If this option is set then the MatAssemblyBegin/End() processes has one less global reduction

    5570:    MAT_IGNORE_OFF_PROC_ENTRIES set to PETSC_TRUE indicates entries destined for
    5571:    other processors should be dropped, rather than stashed.
    5572:    This is useful if you know that the "owning" processor is also
    5573:    always generating the correct matrix entries, so that PETSc need
    5574:    not transfer duplicate entries generated on another processor.

    5576:    MAT_USE_HASH_TABLE indicates that a hash table be used to improve the
    5577:    searches during matrix assembly. When this flag is set, the hash table
    5578:    is created during the first Matrix Assembly. This hash table is
    5579:    used the next time through, during MatSetVaules()/MatSetVaulesBlocked()
    5580:    to improve the searching of indices. MAT_NEW_NONZERO_LOCATIONS flag
    5581:    should be used with MAT_USE_HASH_TABLE flag. This option is currently
    5582:    supported by MATMPIBAIJ format only.

    5584:    MAT_KEEP_NONZERO_PATTERN indicates when MatZeroRows() is called the zeroed entries
    5585:    are kept in the nonzero structure

    5587:    MAT_IGNORE_ZERO_ENTRIES - for AIJ/IS matrices this will stop zero values from creating
    5588:    a zero location in the matrix

    5590:    MAT_USE_INODES - indicates using inode version of the code - works with AIJ matrix types

    5592:    MAT_NO_OFF_PROC_ZERO_ROWS - you know each process will only zero its own rows. This avoids all reductions in the
    5593:         zero row routines and thus improves performance for very large process counts.

    5595:    MAT_IGNORE_LOWER_TRIANGULAR - For SBAIJ matrices will ignore any insertions you make in the lower triangular
    5596:         part of the matrix (since they should match the upper triangular part).

    5598:    MAT_SORTED_FULL - each process provides exactly its local rows; all column indices for a given row are passed in a
    5599:                      single call to MatSetValues(), preallocation is perfect, row oriented, INSERT_VALUES is used. Common
    5600:                      with finite difference schemes with non-periodic boundary conditions.
    5601:    Notes:
    5602:     Can only be called after MatSetSizes() and MatSetType() have been set.

    5604:    Level: intermediate

    5606: .seealso:  MatOption, Mat

    5608: @*/
    5609: PetscErrorCode MatSetOption(Mat mat,MatOption op,PetscBool flg)
    5610: {

    5616:   if (op > 0) {
    5619:   }

    5621:   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);
    5622:   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()");

    5624:   switch (op) {
    5625:   case MAT_NO_OFF_PROC_ENTRIES:
    5626:     mat->nooffprocentries = flg;
    5627:     return(0);
    5628:   case MAT_SUBSET_OFF_PROC_ENTRIES:
    5629:     mat->assembly_subset = flg;
    5630:     if (!mat->assembly_subset) { /* See the same logic in VecAssembly wrt VEC_SUBSET_OFF_PROC_ENTRIES */
    5631: #if !defined(PETSC_HAVE_MPIUNI)
    5632:       MatStashScatterDestroy_BTS(&mat->stash);
    5633: #endif
    5634:       mat->stash.first_assembly_done = PETSC_FALSE;
    5635:     }
    5636:     return(0);
    5637:   case MAT_NO_OFF_PROC_ZERO_ROWS:
    5638:     mat->nooffproczerorows = flg;
    5639:     return(0);
    5640:   case MAT_SPD:
    5641:     mat->spd_set = PETSC_TRUE;
    5642:     mat->spd     = flg;
    5643:     if (flg) {
    5644:       mat->symmetric                  = PETSC_TRUE;
    5645:       mat->structurally_symmetric     = PETSC_TRUE;
    5646:       mat->symmetric_set              = PETSC_TRUE;
    5647:       mat->structurally_symmetric_set = PETSC_TRUE;
    5648:     }
    5649:     break;
    5650:   case MAT_SYMMETRIC:
    5651:     mat->symmetric = flg;
    5652:     if (flg) mat->structurally_symmetric = PETSC_TRUE;
    5653:     mat->symmetric_set              = PETSC_TRUE;
    5654:     mat->structurally_symmetric_set = flg;
    5655: #if !defined(PETSC_USE_COMPLEX)
    5656:     mat->hermitian     = flg;
    5657:     mat->hermitian_set = PETSC_TRUE;
    5658: #endif
    5659:     break;
    5660:   case MAT_HERMITIAN:
    5661:     mat->hermitian = flg;
    5662:     if (flg) mat->structurally_symmetric = PETSC_TRUE;
    5663:     mat->hermitian_set              = PETSC_TRUE;
    5664:     mat->structurally_symmetric_set = flg;
    5665: #if !defined(PETSC_USE_COMPLEX)
    5666:     mat->symmetric     = flg;
    5667:     mat->symmetric_set = PETSC_TRUE;
    5668: #endif
    5669:     break;
    5670:   case MAT_STRUCTURALLY_SYMMETRIC:
    5671:     mat->structurally_symmetric     = flg;
    5672:     mat->structurally_symmetric_set = PETSC_TRUE;
    5673:     break;
    5674:   case MAT_SYMMETRY_ETERNAL:
    5675:     mat->symmetric_eternal = flg;
    5676:     break;
    5677:   case MAT_STRUCTURE_ONLY:
    5678:     mat->structure_only = flg;
    5679:     break;
    5680:   case MAT_SORTED_FULL:
    5681:     mat->sortedfull = flg;
    5682:     break;
    5683:   default:
    5684:     break;
    5685:   }
    5686:   if (mat->ops->setoption) {
    5687:     (*mat->ops->setoption)(mat,op,flg);
    5688:   }
    5689:   return(0);
    5690: }

    5692: /*@
    5693:    MatGetOption - Gets a parameter option that has been set for a matrix.

    5695:    Logically Collective on Mat for certain operations, such as MAT_SPD, not collective for MAT_ROW_ORIENTED, see MatOption

    5697:    Input Parameters:
    5698: +  mat - the matrix
    5699: -  option - the option, this only responds to certain options, check the code for which ones

    5701:    Output Parameter:
    5702: .  flg - turn the option on (PETSC_TRUE) or off (PETSC_FALSE)

    5704:     Notes:
    5705:     Can only be called after MatSetSizes() and MatSetType() have been set.

    5707:    Level: intermediate

    5709: .seealso:  MatOption, MatSetOption()

    5711: @*/
    5712: PetscErrorCode MatGetOption(Mat mat,MatOption op,PetscBool *flg)
    5713: {

    5718:   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);
    5719:   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()");

    5721:   switch (op) {
    5722:   case MAT_NO_OFF_PROC_ENTRIES:
    5723:     *flg = mat->nooffprocentries;
    5724:     break;
    5725:   case MAT_NO_OFF_PROC_ZERO_ROWS:
    5726:     *flg = mat->nooffproczerorows;
    5727:     break;
    5728:   case MAT_SYMMETRIC:
    5729:     *flg = mat->symmetric;
    5730:     break;
    5731:   case MAT_HERMITIAN:
    5732:     *flg = mat->hermitian;
    5733:     break;
    5734:   case MAT_STRUCTURALLY_SYMMETRIC:
    5735:     *flg = mat->structurally_symmetric;
    5736:     break;
    5737:   case MAT_SYMMETRY_ETERNAL:
    5738:     *flg = mat->symmetric_eternal;
    5739:     break;
    5740:   case MAT_SPD:
    5741:     *flg = mat->spd;
    5742:     break;
    5743:   default:
    5744:     break;
    5745:   }
    5746:   return(0);
    5747: }

    5749: /*@
    5750:    MatZeroEntries - Zeros all entries of a matrix.  For sparse matrices
    5751:    this routine retains the old nonzero structure.

    5753:    Logically Collective on Mat

    5755:    Input Parameters:
    5756: .  mat - the matrix

    5758:    Level: intermediate

    5760:    Notes:
    5761:     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.
    5762:    See the Performance chapter of the users manual for information on preallocating matrices.

    5764: .seealso: MatZeroRows()
    5765: @*/
    5766: PetscErrorCode MatZeroEntries(Mat mat)
    5767: {

    5773:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5774:   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");
    5775:   if (!mat->ops->zeroentries) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5776:   MatCheckPreallocated(mat,1);

    5778:   PetscLogEventBegin(MAT_ZeroEntries,mat,0,0,0);
    5779:   (*mat->ops->zeroentries)(mat);
    5780:   PetscLogEventEnd(MAT_ZeroEntries,mat,0,0,0);
    5781:   PetscObjectStateIncrease((PetscObject)mat);
    5782:   return(0);
    5783: }

    5785: /*@
    5786:    MatZeroRowsColumns - Zeros all entries (except possibly the main diagonal)
    5787:    of a set of rows and columns of a matrix.

    5789:    Collective on Mat

    5791:    Input Parameters:
    5792: +  mat - the matrix
    5793: .  numRows - the number of rows to remove
    5794: .  rows - the global row indices
    5795: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    5796: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    5797: -  b - optional vector of right hand side, that will be adjusted by provided solution

    5799:    Notes:
    5800:    This does not change the nonzero structure of the matrix, it merely zeros those entries in the matrix.

    5802:    The user can set a value in the diagonal entry (or for the AIJ and
    5803:    row formats can optionally remove the main diagonal entry from the
    5804:    nonzero structure as well, by passing 0.0 as the final argument).

    5806:    For the parallel case, all processes that share the matrix (i.e.,
    5807:    those in the communicator used for matrix creation) MUST call this
    5808:    routine, regardless of whether any rows being zeroed are owned by
    5809:    them.

    5811:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    5812:    list only rows local to itself).

    5814:    The option MAT_NO_OFF_PROC_ZERO_ROWS does not apply to this routine.

    5816:    Level: intermediate

    5818: .seealso: MatZeroRowsIS(), MatZeroRows(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    5819:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    5820: @*/
    5821: PetscErrorCode MatZeroRowsColumns(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
    5822: {

    5829:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5830:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5831:   if (!mat->ops->zerorowscolumns) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5832:   MatCheckPreallocated(mat,1);

    5834:   (*mat->ops->zerorowscolumns)(mat,numRows,rows,diag,x,b);
    5835:   MatViewFromOptions(mat,NULL,"-mat_view");
    5836:   PetscObjectStateIncrease((PetscObject)mat);
    5837:   return(0);
    5838: }

    5840: /*@
    5841:    MatZeroRowsColumnsIS - Zeros all entries (except possibly the main diagonal)
    5842:    of a set of rows and columns of a matrix.

    5844:    Collective on Mat

    5846:    Input Parameters:
    5847: +  mat - the matrix
    5848: .  is - the rows to zero
    5849: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    5850: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    5851: -  b - optional vector of right hand side, that will be adjusted by provided solution

    5853:    Notes:
    5854:    This does not change the nonzero structure of the matrix, it merely zeros those entries in the matrix.

    5856:    The user can set a value in the diagonal entry (or for the AIJ and
    5857:    row formats can optionally remove the main diagonal entry from the
    5858:    nonzero structure as well, by passing 0.0 as the final argument).

    5860:    For the parallel case, all processes that share the matrix (i.e.,
    5861:    those in the communicator used for matrix creation) MUST call this
    5862:    routine, regardless of whether any rows being zeroed are owned by
    5863:    them.

    5865:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    5866:    list only rows local to itself).

    5868:    The option MAT_NO_OFF_PROC_ZERO_ROWS does not apply to this routine.

    5870:    Level: intermediate

    5872: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    5873:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRows(), MatZeroRowsColumnsStencil()
    5874: @*/
    5875: PetscErrorCode MatZeroRowsColumnsIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
    5876: {
    5878:   PetscInt       numRows;
    5879:   const PetscInt *rows;

    5886:   ISGetLocalSize(is,&numRows);
    5887:   ISGetIndices(is,&rows);
    5888:   MatZeroRowsColumns(mat,numRows,rows,diag,x,b);
    5889:   ISRestoreIndices(is,&rows);
    5890:   return(0);
    5891: }

    5893: /*@
    5894:    MatZeroRows - Zeros all entries (except possibly the main diagonal)
    5895:    of a set of rows of a matrix.

    5897:    Collective on Mat

    5899:    Input Parameters:
    5900: +  mat - the matrix
    5901: .  numRows - the number of rows to remove
    5902: .  rows - the global row indices
    5903: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    5904: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    5905: -  b - optional vector of right hand side, that will be adjusted by provided solution

    5907:    Notes:
    5908:    For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
    5909:    but does not release memory.  For the dense and block diagonal
    5910:    formats this does not alter the nonzero structure.

    5912:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    5913:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    5914:    merely zeroed.

    5916:    The user can set a value in the diagonal entry (or for the AIJ and
    5917:    row formats can optionally remove the main diagonal entry from the
    5918:    nonzero structure as well, by passing 0.0 as the final argument).

    5920:    For the parallel case, all processes that share the matrix (i.e.,
    5921:    those in the communicator used for matrix creation) MUST call this
    5922:    routine, regardless of whether any rows being zeroed are owned by
    5923:    them.

    5925:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    5926:    list only rows local to itself).

    5928:    You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
    5929:    owns that are to be zeroed. This saves a global synchronization in the implementation.

    5931:    Level: intermediate

    5933: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    5934:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    5935: @*/
    5936: PetscErrorCode MatZeroRows(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
    5937: {

    5944:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5945:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5946:   if (!mat->ops->zerorows) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5947:   MatCheckPreallocated(mat,1);

    5949:   (*mat->ops->zerorows)(mat,numRows,rows,diag,x,b);
    5950:   MatViewFromOptions(mat,NULL,"-mat_view");
    5951:   PetscObjectStateIncrease((PetscObject)mat);
    5952:   return(0);
    5953: }

    5955: /*@
    5956:    MatZeroRowsIS - Zeros all entries (except possibly the main diagonal)
    5957:    of a set of rows of a matrix.

    5959:    Collective on Mat

    5961:    Input Parameters:
    5962: +  mat - the matrix
    5963: .  is - index set of rows to remove
    5964: .  diag - value put in all diagonals of eliminated rows
    5965: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    5966: -  b - optional vector of right hand side, that will be adjusted by provided solution

    5968:    Notes:
    5969:    For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
    5970:    but does not release memory.  For the dense and block diagonal
    5971:    formats this does not alter the nonzero structure.

    5973:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    5974:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    5975:    merely zeroed.

    5977:    The user can set a value in the diagonal entry (or for the AIJ and
    5978:    row formats can optionally remove the main diagonal entry from the
    5979:    nonzero structure as well, by passing 0.0 as the final argument).

    5981:    For the parallel case, all processes that share the matrix (i.e.,
    5982:    those in the communicator used for matrix creation) MUST call this
    5983:    routine, regardless of whether any rows being zeroed are owned by
    5984:    them.

    5986:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    5987:    list only rows local to itself).

    5989:    You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
    5990:    owns that are to be zeroed. This saves a global synchronization in the implementation.

    5992:    Level: intermediate

    5994: .seealso: MatZeroRows(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    5995:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    5996: @*/
    5997: PetscErrorCode MatZeroRowsIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
    5998: {
    5999:   PetscInt       numRows;
    6000:   const PetscInt *rows;

    6007:   ISGetLocalSize(is,&numRows);
    6008:   ISGetIndices(is,&rows);
    6009:   MatZeroRows(mat,numRows,rows,diag,x,b);
    6010:   ISRestoreIndices(is,&rows);
    6011:   return(0);
    6012: }

    6014: /*@
    6015:    MatZeroRowsStencil - Zeros all entries (except possibly the main diagonal)
    6016:    of a set of rows of a matrix. These rows must be local to the process.

    6018:    Collective on Mat

    6020:    Input Parameters:
    6021: +  mat - the matrix
    6022: .  numRows - the number of rows to remove
    6023: .  rows - the grid coordinates (and component number when dof > 1) for matrix rows
    6024: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6025: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6026: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6028:    Notes:
    6029:    For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
    6030:    but does not release memory.  For the dense and block diagonal
    6031:    formats this does not alter the nonzero structure.

    6033:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6034:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6035:    merely zeroed.

    6037:    The user can set a value in the diagonal entry (or for the AIJ and
    6038:    row formats can optionally remove the main diagonal entry from the
    6039:    nonzero structure as well, by passing 0.0 as the final argument).

    6041:    For the parallel case, all processes that share the matrix (i.e.,
    6042:    those in the communicator used for matrix creation) MUST call this
    6043:    routine, regardless of whether any rows being zeroed are owned by
    6044:    them.

    6046:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6047:    list only rows local to itself).

    6049:    The grid coordinates are across the entire grid, not just the local portion

    6051:    In Fortran idxm and idxn should be declared as
    6052: $     MatStencil idxm(4,m)
    6053:    and the values inserted using
    6054: $    idxm(MatStencil_i,1) = i
    6055: $    idxm(MatStencil_j,1) = j
    6056: $    idxm(MatStencil_k,1) = k
    6057: $    idxm(MatStencil_c,1) = c
    6058:    etc

    6060:    For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    6061:    obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    6062:    etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    6063:    DM_BOUNDARY_PERIODIC boundary type.

    6065:    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
    6066:    a single value per point) you can skip filling those indices.

    6068:    Level: intermediate

    6070: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsl(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6071:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6072: @*/
    6073: PetscErrorCode MatZeroRowsStencil(Mat mat,PetscInt numRows,const MatStencil rows[],PetscScalar diag,Vec x,Vec b)
    6074: {
    6075:   PetscInt       dim     = mat->stencil.dim;
    6076:   PetscInt       sdim    = dim - (1 - (PetscInt) mat->stencil.noc);
    6077:   PetscInt       *dims   = mat->stencil.dims+1;
    6078:   PetscInt       *starts = mat->stencil.starts;
    6079:   PetscInt       *dxm    = (PetscInt*) rows;
    6080:   PetscInt       *jdxm, i, j, tmp, numNewRows = 0;

    6088:   PetscMalloc1(numRows, &jdxm);
    6089:   for (i = 0; i < numRows; ++i) {
    6090:     /* Skip unused dimensions (they are ordered k, j, i, c) */
    6091:     for (j = 0; j < 3-sdim; ++j) dxm++;
    6092:     /* Local index in X dir */
    6093:     tmp = *dxm++ - starts[0];
    6094:     /* Loop over remaining dimensions */
    6095:     for (j = 0; j < dim-1; ++j) {
    6096:       /* If nonlocal, set index to be negative */
    6097:       if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = PETSC_MIN_INT;
    6098:       /* Update local index */
    6099:       else tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    6100:     }
    6101:     /* Skip component slot if necessary */
    6102:     if (mat->stencil.noc) dxm++;
    6103:     /* Local row number */
    6104:     if (tmp >= 0) {
    6105:       jdxm[numNewRows++] = tmp;
    6106:     }
    6107:   }
    6108:   MatZeroRowsLocal(mat,numNewRows,jdxm,diag,x,b);
    6109:   PetscFree(jdxm);
    6110:   return(0);
    6111: }

    6113: /*@
    6114:    MatZeroRowsColumnsStencil - Zeros all row and column entries (except possibly the main diagonal)
    6115:    of a set of rows and columns of a matrix.

    6117:    Collective on Mat

    6119:    Input Parameters:
    6120: +  mat - the matrix
    6121: .  numRows - the number of rows/columns to remove
    6122: .  rows - the grid coordinates (and component number when dof > 1) for matrix rows
    6123: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6124: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6125: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6127:    Notes:
    6128:    For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
    6129:    but does not release memory.  For the dense and block diagonal
    6130:    formats this does not alter the nonzero structure.

    6132:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6133:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6134:    merely zeroed.

    6136:    The user can set a value in the diagonal entry (or for the AIJ and
    6137:    row formats can optionally remove the main diagonal entry from the
    6138:    nonzero structure as well, by passing 0.0 as the final argument).

    6140:    For the parallel case, all processes that share the matrix (i.e.,
    6141:    those in the communicator used for matrix creation) MUST call this
    6142:    routine, regardless of whether any rows being zeroed are owned by
    6143:    them.

    6145:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6146:    list only rows local to itself, but the row/column numbers are given in local numbering).

    6148:    The grid coordinates are across the entire grid, not just the local portion

    6150:    In Fortran idxm and idxn should be declared as
    6151: $     MatStencil idxm(4,m)
    6152:    and the values inserted using
    6153: $    idxm(MatStencil_i,1) = i
    6154: $    idxm(MatStencil_j,1) = j
    6155: $    idxm(MatStencil_k,1) = k
    6156: $    idxm(MatStencil_c,1) = c
    6157:    etc

    6159:    For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    6160:    obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    6161:    etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    6162:    DM_BOUNDARY_PERIODIC boundary type.

    6164:    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
    6165:    a single value per point) you can skip filling those indices.

    6167:    Level: intermediate

    6169: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6170:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRows()
    6171: @*/
    6172: PetscErrorCode MatZeroRowsColumnsStencil(Mat mat,PetscInt numRows,const MatStencil rows[],PetscScalar diag,Vec x,Vec b)
    6173: {
    6174:   PetscInt       dim     = mat->stencil.dim;
    6175:   PetscInt       sdim    = dim - (1 - (PetscInt) mat->stencil.noc);
    6176:   PetscInt       *dims   = mat->stencil.dims+1;
    6177:   PetscInt       *starts = mat->stencil.starts;
    6178:   PetscInt       *dxm    = (PetscInt*) rows;
    6179:   PetscInt       *jdxm, i, j, tmp, numNewRows = 0;

    6187:   PetscMalloc1(numRows, &jdxm);
    6188:   for (i = 0; i < numRows; ++i) {
    6189:     /* Skip unused dimensions (they are ordered k, j, i, c) */
    6190:     for (j = 0; j < 3-sdim; ++j) dxm++;
    6191:     /* Local index in X dir */
    6192:     tmp = *dxm++ - starts[0];
    6193:     /* Loop over remaining dimensions */
    6194:     for (j = 0; j < dim-1; ++j) {
    6195:       /* If nonlocal, set index to be negative */
    6196:       if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = PETSC_MIN_INT;
    6197:       /* Update local index */
    6198:       else tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    6199:     }
    6200:     /* Skip component slot if necessary */
    6201:     if (mat->stencil.noc) dxm++;
    6202:     /* Local row number */
    6203:     if (tmp >= 0) {
    6204:       jdxm[numNewRows++] = tmp;
    6205:     }
    6206:   }
    6207:   MatZeroRowsColumnsLocal(mat,numNewRows,jdxm,diag,x,b);
    6208:   PetscFree(jdxm);
    6209:   return(0);
    6210: }

    6212: /*@C
    6213:    MatZeroRowsLocal - Zeros all entries (except possibly the main diagonal)
    6214:    of a set of rows of a matrix; using local numbering of rows.

    6216:    Collective on Mat

    6218:    Input Parameters:
    6219: +  mat - the matrix
    6220: .  numRows - the number of rows to remove
    6221: .  rows - the global row indices
    6222: .  diag - value put in all diagonals of eliminated rows
    6223: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6224: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6226:    Notes:
    6227:    Before calling MatZeroRowsLocal(), the user must first set the
    6228:    local-to-global mapping by calling MatSetLocalToGlobalMapping().

    6230:    For the AIJ matrix formats this removes the old nonzero structure,
    6231:    but does not release memory.  For the dense and block diagonal
    6232:    formats this does not alter the nonzero structure.

    6234:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6235:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6236:    merely zeroed.

    6238:    The user can set a value in the diagonal entry (or for the AIJ and
    6239:    row formats can optionally remove the main diagonal entry from the
    6240:    nonzero structure as well, by passing 0.0 as the final argument).

    6242:    You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
    6243:    owns that are to be zeroed. This saves a global synchronization in the implementation.

    6245:    Level: intermediate

    6247: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRows(), MatSetOption(),
    6248:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6249: @*/
    6250: PetscErrorCode MatZeroRowsLocal(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
    6251: {

    6258:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6259:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6260:   MatCheckPreallocated(mat,1);

    6262:   if (mat->ops->zerorowslocal) {
    6263:     (*mat->ops->zerorowslocal)(mat,numRows,rows,diag,x,b);
    6264:   } else {
    6265:     IS             is, newis;
    6266:     const PetscInt *newRows;

    6268:     if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Need to provide local to global mapping to matrix first");
    6269:     ISCreateGeneral(PETSC_COMM_SELF,numRows,rows,PETSC_COPY_VALUES,&is);
    6270:     ISLocalToGlobalMappingApplyIS(mat->rmap->mapping,is,&newis);
    6271:     ISGetIndices(newis,&newRows);
    6272:     (*mat->ops->zerorows)(mat,numRows,newRows,diag,x,b);
    6273:     ISRestoreIndices(newis,&newRows);
    6274:     ISDestroy(&newis);
    6275:     ISDestroy(&is);
    6276:   }
    6277:   PetscObjectStateIncrease((PetscObject)mat);
    6278:   return(0);
    6279: }

    6281: /*@
    6282:    MatZeroRowsLocalIS - Zeros all entries (except possibly the main diagonal)
    6283:    of a set of rows of a matrix; using local numbering of rows.

    6285:    Collective on Mat

    6287:    Input Parameters:
    6288: +  mat - the matrix
    6289: .  is - index set of rows to remove
    6290: .  diag - value put in all diagonals of eliminated rows
    6291: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6292: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6294:    Notes:
    6295:    Before calling MatZeroRowsLocalIS(), the user must first set the
    6296:    local-to-global mapping by calling MatSetLocalToGlobalMapping().

    6298:    For the AIJ matrix formats this removes the old nonzero structure,
    6299:    but does not release memory.  For the dense and block diagonal
    6300:    formats this does not alter the nonzero structure.

    6302:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6303:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6304:    merely zeroed.

    6306:    The user can set a value in the diagonal entry (or for the AIJ and
    6307:    row formats can optionally remove the main diagonal entry from the
    6308:    nonzero structure as well, by passing 0.0 as the final argument).

    6310:    You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
    6311:    owns that are to be zeroed. This saves a global synchronization in the implementation.

    6313:    Level: intermediate

    6315: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRows(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6316:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6317: @*/
    6318: PetscErrorCode MatZeroRowsLocalIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
    6319: {
    6321:   PetscInt       numRows;
    6322:   const PetscInt *rows;

    6328:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6329:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6330:   MatCheckPreallocated(mat,1);

    6332:   ISGetLocalSize(is,&numRows);
    6333:   ISGetIndices(is,&rows);
    6334:   MatZeroRowsLocal(mat,numRows,rows,diag,x,b);
    6335:   ISRestoreIndices(is,&rows);
    6336:   return(0);
    6337: }

    6339: /*@
    6340:    MatZeroRowsColumnsLocal - Zeros all entries (except possibly the main diagonal)
    6341:    of a set of rows and columns of a matrix; using local numbering of rows.

    6343:    Collective on Mat

    6345:    Input Parameters:
    6346: +  mat - the matrix
    6347: .  numRows - the number of rows to remove
    6348: .  rows - the global row indices
    6349: .  diag - value put in all diagonals of eliminated rows
    6350: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6351: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6353:    Notes:
    6354:    Before calling MatZeroRowsColumnsLocal(), the user must first set the
    6355:    local-to-global mapping by calling MatSetLocalToGlobalMapping().

    6357:    The user can set a value in the diagonal entry (or for the AIJ and
    6358:    row formats can optionally remove the main diagonal entry from the
    6359:    nonzero structure as well, by passing 0.0 as the final argument).

    6361:    Level: intermediate

    6363: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6364:           MatZeroRows(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6365: @*/
    6366: PetscErrorCode MatZeroRowsColumnsLocal(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
    6367: {
    6369:   IS             is, newis;
    6370:   const PetscInt *newRows;

    6376:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6377:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6378:   MatCheckPreallocated(mat,1);

    6380:   if (!mat->cmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Need to provide local to global mapping to matrix first");
    6381:   ISCreateGeneral(PETSC_COMM_SELF,numRows,rows,PETSC_COPY_VALUES,&is);
    6382:   ISLocalToGlobalMappingApplyIS(mat->cmap->mapping,is,&newis);
    6383:   ISGetIndices(newis,&newRows);
    6384:   (*mat->ops->zerorowscolumns)(mat,numRows,newRows,diag,x,b);
    6385:   ISRestoreIndices(newis,&newRows);
    6386:   ISDestroy(&newis);
    6387:   ISDestroy(&is);
    6388:   PetscObjectStateIncrease((PetscObject)mat);
    6389:   return(0);
    6390: }

    6392: /*@
    6393:    MatZeroRowsColumnsLocalIS - Zeros all entries (except possibly the main diagonal)
    6394:    of a set of rows and columns of a matrix; using local numbering of rows.

    6396:    Collective on Mat

    6398:    Input Parameters:
    6399: +  mat - the matrix
    6400: .  is - index set of rows to remove
    6401: .  diag - value put in all diagonals of eliminated rows
    6402: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6403: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6405:    Notes:
    6406:    Before calling MatZeroRowsColumnsLocalIS(), the user must first set the
    6407:    local-to-global mapping by calling MatSetLocalToGlobalMapping().

    6409:    The user can set a value in the diagonal entry (or for the AIJ and
    6410:    row formats can optionally remove the main diagonal entry from the
    6411:    nonzero structure as well, by passing 0.0 as the final argument).

    6413:    Level: intermediate

    6415: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6416:           MatZeroRowsColumnsLocal(), MatZeroRows(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6417: @*/
    6418: PetscErrorCode MatZeroRowsColumnsLocalIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
    6419: {
    6421:   PetscInt       numRows;
    6422:   const PetscInt *rows;

    6428:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6429:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6430:   MatCheckPreallocated(mat,1);

    6432:   ISGetLocalSize(is,&numRows);
    6433:   ISGetIndices(is,&rows);
    6434:   MatZeroRowsColumnsLocal(mat,numRows,rows,diag,x,b);
    6435:   ISRestoreIndices(is,&rows);
    6436:   return(0);
    6437: }

    6439: /*@C
    6440:    MatGetSize - Returns the numbers of rows and columns in a matrix.

    6442:    Not Collective

    6444:    Input Parameter:
    6445: .  mat - the matrix

    6447:    Output Parameters:
    6448: +  m - the number of global rows
    6449: -  n - the number of global columns

    6451:    Note: both output parameters can be NULL on input.

    6453:    Level: beginner

    6455: .seealso: MatGetLocalSize()
    6456: @*/
    6457: PetscErrorCode MatGetSize(Mat mat,PetscInt *m,PetscInt *n)
    6458: {
    6461:   if (m) *m = mat->rmap->N;
    6462:   if (n) *n = mat->cmap->N;
    6463:   return(0);
    6464: }

    6466: /*@C
    6467:    MatGetLocalSize - Returns the number of local rows and local columns
    6468:    of a matrix, that is the local size of the left and right vectors as returned by MatCreateVecs().

    6470:    Not Collective

    6472:    Input Parameters:
    6473: .  mat - the matrix

    6475:    Output Parameters:
    6476: +  m - the number of local rows
    6477: -  n - the number of local columns

    6479:    Note: both output parameters can be NULL on input.

    6481:    Level: beginner

    6483: .seealso: MatGetSize()
    6484: @*/
    6485: PetscErrorCode MatGetLocalSize(Mat mat,PetscInt *m,PetscInt *n)
    6486: {
    6491:   if (m) *m = mat->rmap->n;
    6492:   if (n) *n = mat->cmap->n;
    6493:   return(0);
    6494: }

    6496: /*@C
    6497:    MatGetOwnershipRangeColumn - Returns the range of matrix columns associated with rows of a vector one multiplies by that owned by
    6498:    this processor. (The columns of the "diagonal block")

    6500:    Not Collective, unless matrix has not been allocated, then collective on Mat

    6502:    Input Parameters:
    6503: .  mat - the matrix

    6505:    Output Parameters:
    6506: +  m - the global index of the first local column
    6507: -  n - one more than the global index of the last local column

    6509:    Notes:
    6510:     both output parameters can be NULL on input.

    6512:    Level: developer

    6514: .seealso:  MatGetOwnershipRange(), MatGetOwnershipRanges(), MatGetOwnershipRangesColumn()

    6516: @*/
    6517: PetscErrorCode MatGetOwnershipRangeColumn(Mat mat,PetscInt *m,PetscInt *n)
    6518: {
    6524:   MatCheckPreallocated(mat,1);
    6525:   if (m) *m = mat->cmap->rstart;
    6526:   if (n) *n = mat->cmap->rend;
    6527:   return(0);
    6528: }

    6530: /*@C
    6531:    MatGetOwnershipRange - Returns the range of matrix rows owned by
    6532:    this processor, assuming that the matrix is laid out with the first
    6533:    n1 rows on the first processor, the next n2 rows on the second, etc.
    6534:    For certain parallel layouts this range may not be well defined.

    6536:    Not Collective

    6538:    Input Parameters:
    6539: .  mat - the matrix

    6541:    Output Parameters:
    6542: +  m - the global index of the first local row
    6543: -  n - one more than the global index of the last local row

    6545:    Note: Both output parameters can be NULL on input.
    6546: $  This function requires that the matrix be preallocated. If you have not preallocated, consider using
    6547: $    PetscSplitOwnership(MPI_Comm comm, PetscInt *n, PetscInt *N)
    6548: $  and then MPI_Scan() to calculate prefix sums of the local sizes.

    6550:    Level: beginner

    6552: .seealso:   MatGetOwnershipRanges(), MatGetOwnershipRangeColumn(), MatGetOwnershipRangesColumn(), PetscSplitOwnership(), PetscSplitOwnershipBlock()

    6554: @*/
    6555: PetscErrorCode MatGetOwnershipRange(Mat mat,PetscInt *m,PetscInt *n)
    6556: {
    6562:   MatCheckPreallocated(mat,1);
    6563:   if (m) *m = mat->rmap->rstart;
    6564:   if (n) *n = mat->rmap->rend;
    6565:   return(0);
    6566: }

    6568: /*@C
    6569:    MatGetOwnershipRanges - Returns the range of matrix rows owned by
    6570:    each process

    6572:    Not Collective, unless matrix has not been allocated, then collective on Mat

    6574:    Input Parameters:
    6575: .  mat - the matrix

    6577:    Output Parameters:
    6578: .  ranges - start of each processors portion plus one more than the total length at the end

    6580:    Level: beginner

    6582: .seealso:   MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatGetOwnershipRangesColumn()

    6584: @*/
    6585: PetscErrorCode MatGetOwnershipRanges(Mat mat,const PetscInt **ranges)
    6586: {

    6592:   MatCheckPreallocated(mat,1);
    6593:   PetscLayoutGetRanges(mat->rmap,ranges);
    6594:   return(0);
    6595: }

    6597: /*@C
    6598:    MatGetOwnershipRangesColumn - Returns the range of matrix columns associated with rows of a vector one multiplies by that owned by
    6599:    this processor. (The columns of the "diagonal blocks" for each process)

    6601:    Not Collective, unless matrix has not been allocated, then collective on Mat

    6603:    Input Parameters:
    6604: .  mat - the matrix

    6606:    Output Parameters:
    6607: .  ranges - start of each processors portion plus one more then the total length at the end

    6609:    Level: beginner

    6611: .seealso:   MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatGetOwnershipRanges()

    6613: @*/
    6614: PetscErrorCode MatGetOwnershipRangesColumn(Mat mat,const PetscInt **ranges)
    6615: {

    6621:   MatCheckPreallocated(mat,1);
    6622:   PetscLayoutGetRanges(mat->cmap,ranges);
    6623:   return(0);
    6624: }

    6626: /*@C
    6627:    MatGetOwnershipIS - Get row and column ownership as index sets

    6629:    Not Collective

    6631:    Input Arguments:
    6632: .  A - matrix of type Elemental or ScaLAPACK

    6634:    Output Arguments:
    6635: +  rows - rows in which this process owns elements
    6636: -  cols - columns in which this process owns elements

    6638:    Level: intermediate

    6640: .seealso: MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatSetValues(), MATELEMENTAL
    6641: @*/
    6642: PetscErrorCode MatGetOwnershipIS(Mat A,IS *rows,IS *cols)
    6643: {
    6644:   PetscErrorCode ierr,(*f)(Mat,IS*,IS*);

    6647:   MatCheckPreallocated(A,1);
    6648:   PetscObjectQueryFunction((PetscObject)A,"MatGetOwnershipIS_C",&f);
    6649:   if (f) {
    6650:     (*f)(A,rows,cols);
    6651:   } else {   /* Create a standard row-based partition, each process is responsible for ALL columns in their row block */
    6652:     if (rows) {ISCreateStride(PETSC_COMM_SELF,A->rmap->n,A->rmap->rstart,1,rows);}
    6653:     if (cols) {ISCreateStride(PETSC_COMM_SELF,A->cmap->N,0,1,cols);}
    6654:   }
    6655:   return(0);
    6656: }

    6658: /*@C
    6659:    MatILUFactorSymbolic - Performs symbolic ILU factorization of a matrix.
    6660:    Uses levels of fill only, not drop tolerance. Use MatLUFactorNumeric()
    6661:    to complete the factorization.

    6663:    Collective on Mat

    6665:    Input Parameters:
    6666: +  mat - the matrix
    6667: .  row - row permutation
    6668: .  column - column permutation
    6669: -  info - structure containing
    6670: $      levels - number of levels of fill.
    6671: $      expected fill - as ratio of original fill.
    6672: $      1 or 0 - indicating force fill on diagonal (improves robustness for matrices
    6673:                 missing diagonal entries)

    6675:    Output Parameters:
    6676: .  fact - new matrix that has been symbolically factored

    6678:    Notes:
    6679:     See Users-Manual: ch_mat for additional information about choosing the fill factor for better efficiency.

    6681:    Most users should employ the simplified KSP interface for linear solvers
    6682:    instead of working directly with matrix algebra routines such as this.
    6683:    See, e.g., KSPCreate().

    6685:    Level: developer

    6687: .seealso: MatLUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor()
    6688:           MatGetOrdering(), MatFactorInfo

    6690:     Note: this uses the definition of level of fill as in Y. Saad, 2003

    6692:     Developer Note: fortran interface is not autogenerated as the f90
    6693:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    6695:    References:
    6696:      Y. Saad, Iterative methods for sparse linear systems Philadelphia: Society for Industrial and Applied Mathematics, 2003
    6697: @*/
    6698: PetscErrorCode MatILUFactorSymbolic(Mat fact,Mat mat,IS row,IS col,const MatFactorInfo *info)
    6699: {

    6709:   if (info->levels < 0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Levels of fill negative %D",(PetscInt)info->levels);
    6710:   if (info->fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Expected fill less than 1.0 %g",(double)info->fill);
    6711:   if (!fact->ops->ilufactorsymbolic) {
    6712:     MatSolverType stype;
    6713:     MatFactorGetSolverType(fact,&stype);
    6714:     SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic ILU using solver type %s",((PetscObject)mat)->type_name,stype);
    6715:   }
    6716:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6717:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6718:   MatCheckPreallocated(mat,2);

    6720:   PetscLogEventBegin(MAT_ILUFactorSymbolic,mat,row,col,0);
    6721:   (fact->ops->ilufactorsymbolic)(fact,mat,row,col,info);
    6722:   PetscLogEventEnd(MAT_ILUFactorSymbolic,mat,row,col,0);
    6723:   return(0);
    6724: }

    6726: /*@C
    6727:    MatICCFactorSymbolic - Performs symbolic incomplete
    6728:    Cholesky factorization for a symmetric matrix.  Use
    6729:    MatCholeskyFactorNumeric() to complete the factorization.

    6731:    Collective on Mat

    6733:    Input Parameters:
    6734: +  mat - the matrix
    6735: .  perm - row and column permutation
    6736: -  info - structure containing
    6737: $      levels - number of levels of fill.
    6738: $      expected fill - as ratio of original fill.

    6740:    Output Parameter:
    6741: .  fact - the factored matrix

    6743:    Notes:
    6744:    Most users should employ the KSP interface for linear solvers
    6745:    instead of working directly with matrix algebra routines such as this.
    6746:    See, e.g., KSPCreate().

    6748:    Level: developer

    6750: .seealso: MatCholeskyFactorNumeric(), MatCholeskyFactor(), MatFactorInfo

    6752:     Note: this uses the definition of level of fill as in Y. Saad, 2003

    6754:     Developer Note: fortran interface is not autogenerated as the f90
    6755:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    6757:    References:
    6758:      Y. Saad, Iterative methods for sparse linear systems Philadelphia: Society for Industrial and Applied Mathematics, 2003
    6759: @*/
    6760: PetscErrorCode MatICCFactorSymbolic(Mat fact,Mat mat,IS perm,const MatFactorInfo *info)
    6761: {

    6770:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6771:   if (info->levels < 0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Levels negative %D",(PetscInt) info->levels);
    6772:   if (info->fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Expected fill less than 1.0 %g",(double)info->fill);
    6773:   if (!(fact)->ops->iccfactorsymbolic) {
    6774:     MatSolverType stype;
    6775:     MatFactorGetSolverType(fact,&stype);
    6776:     SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic ICC using solver type %s",((PetscObject)mat)->type_name,stype);
    6777:   }
    6778:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6779:   MatCheckPreallocated(mat,2);

    6781:   PetscLogEventBegin(MAT_ICCFactorSymbolic,mat,perm,0,0);
    6782:   (fact->ops->iccfactorsymbolic)(fact,mat,perm,info);
    6783:   PetscLogEventEnd(MAT_ICCFactorSymbolic,mat,perm,0,0);
    6784:   return(0);
    6785: }

    6787: /*@C
    6788:    MatCreateSubMatrices - Extracts several submatrices from a matrix. If submat
    6789:    points to an array of valid matrices, they may be reused to store the new
    6790:    submatrices.

    6792:    Collective on Mat

    6794:    Input Parameters:
    6795: +  mat - the matrix
    6796: .  n   - the number of submatrixes to be extracted (on this processor, may be zero)
    6797: .  irow, icol - index sets of rows and columns to extract
    6798: -  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    6800:    Output Parameter:
    6801: .  submat - the array of submatrices

    6803:    Notes:
    6804:    MatCreateSubMatrices() can extract ONLY sequential submatrices
    6805:    (from both sequential and parallel matrices). Use MatCreateSubMatrix()
    6806:    to extract a parallel submatrix.

    6808:    Some matrix types place restrictions on the row and column
    6809:    indices, such as that they be sorted or that they be equal to each other.

    6811:    The index sets may not have duplicate entries.

    6813:    When extracting submatrices from a parallel matrix, each processor can
    6814:    form a different submatrix by setting the rows and columns of its
    6815:    individual index sets according to the local submatrix desired.

    6817:    When finished using the submatrices, the user should destroy
    6818:    them with MatDestroySubMatrices().

    6820:    MAT_REUSE_MATRIX can only be used when the nonzero structure of the
    6821:    original matrix has not changed from that last call to MatCreateSubMatrices().

    6823:    This routine creates the matrices in submat; you should NOT create them before
    6824:    calling it. It also allocates the array of matrix pointers submat.

    6826:    For BAIJ matrices the index sets must respect the block structure, that is if they
    6827:    request one row/column in a block, they must request all rows/columns that are in
    6828:    that block. For example, if the block size is 2 you cannot request just row 0 and
    6829:    column 0.

    6831:    Fortran Note:
    6832:    The Fortran interface is slightly different from that given below; it
    6833:    requires one to pass in  as submat a Mat (integer) array of size at least n+1.

    6835:    Level: advanced

    6838: .seealso: MatDestroySubMatrices(), MatCreateSubMatrix(), MatGetRow(), MatGetDiagonal(), MatReuse
    6839: @*/
    6840: PetscErrorCode MatCreateSubMatrices(Mat mat,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
    6841: {
    6843:   PetscInt       i;
    6844:   PetscBool      eq;

    6849:   if (n) {
    6854:   }
    6856:   if (n && scall == MAT_REUSE_MATRIX) {
    6859:   }
    6860:   if (!mat->ops->createsubmatrices) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    6861:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6862:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6863:   MatCheckPreallocated(mat,1);

    6865:   PetscLogEventBegin(MAT_CreateSubMats,mat,0,0,0);
    6866:   (*mat->ops->createsubmatrices)(mat,n,irow,icol,scall,submat);
    6867:   PetscLogEventEnd(MAT_CreateSubMats,mat,0,0,0);
    6868:   for (i=0; i<n; i++) {
    6869:     (*submat)[i]->factortype = MAT_FACTOR_NONE;  /* in case in place factorization was previously done on submatrix */
    6870:     ISEqualUnsorted(irow[i],icol[i],&eq);
    6871:     if (eq) {
    6872:       MatPropagateSymmetryOptions(mat,(*submat)[i]);
    6873:     }
    6874:   }
    6875:   return(0);
    6876: }

    6878: /*@C
    6879:    MatCreateSubMatricesMPI - Extracts MPI submatrices across a sub communicator of mat (by pairs of IS that may live on subcomms).

    6881:    Collective on Mat

    6883:    Input Parameters:
    6884: +  mat - the matrix
    6885: .  n   - the number of submatrixes to be extracted
    6886: .  irow, icol - index sets of rows and columns to extract
    6887: -  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    6889:    Output Parameter:
    6890: .  submat - the array of submatrices

    6892:    Level: advanced

    6895: .seealso: MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRow(), MatGetDiagonal(), MatReuse
    6896: @*/
    6897: PetscErrorCode MatCreateSubMatricesMPI(Mat mat,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
    6898: {
    6900:   PetscInt       i;
    6901:   PetscBool      eq;

    6906:   if (n) {
    6911:   }
    6913:   if (n && scall == MAT_REUSE_MATRIX) {
    6916:   }
    6917:   if (!mat->ops->createsubmatricesmpi) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    6918:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6919:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6920:   MatCheckPreallocated(mat,1);

    6922:   PetscLogEventBegin(MAT_CreateSubMats,mat,0,0,0);
    6923:   (*mat->ops->createsubmatricesmpi)(mat,n,irow,icol,scall,submat);
    6924:   PetscLogEventEnd(MAT_CreateSubMats,mat,0,0,0);
    6925:   for (i=0; i<n; i++) {
    6926:     ISEqualUnsorted(irow[i],icol[i],&eq);
    6927:     if (eq) {
    6928:       MatPropagateSymmetryOptions(mat,(*submat)[i]);
    6929:     }
    6930:   }
    6931:   return(0);
    6932: }

    6934: /*@C
    6935:    MatDestroyMatrices - Destroys an array of matrices.

    6937:    Collective on Mat

    6939:    Input Parameters:
    6940: +  n - the number of local matrices
    6941: -  mat - the matrices (note that this is a pointer to the array of matrices)

    6943:    Level: advanced

    6945:     Notes:
    6946:     Frees not only the matrices, but also the array that contains the matrices
    6947:            In Fortran will not free the array.

    6949: .seealso: MatCreateSubMatrices() MatDestroySubMatrices()
    6950: @*/
    6951: PetscErrorCode MatDestroyMatrices(PetscInt n,Mat *mat[])
    6952: {
    6954:   PetscInt       i;

    6957:   if (!*mat) return(0);
    6958:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Trying to destroy negative number of matrices %D",n);

    6961:   for (i=0; i<n; i++) {
    6962:     MatDestroy(&(*mat)[i]);
    6963:   }

    6965:   /* memory is allocated even if n = 0 */
    6966:   PetscFree(*mat);
    6967:   return(0);
    6968: }

    6970: /*@C
    6971:    MatDestroySubMatrices - Destroys a set of matrices obtained with MatCreateSubMatrices().

    6973:    Collective on Mat

    6975:    Input Parameters:
    6976: +  n - the number of local matrices
    6977: -  mat - the matrices (note that this is a pointer to the array of matrices, just to match the calling
    6978:                        sequence of MatCreateSubMatrices())

    6980:    Level: advanced

    6982:     Notes:
    6983:     Frees not only the matrices, but also the array that contains the matrices
    6984:            In Fortran will not free the array.

    6986: .seealso: MatCreateSubMatrices()
    6987: @*/
    6988: PetscErrorCode MatDestroySubMatrices(PetscInt n,Mat *mat[])
    6989: {
    6991:   Mat            mat0;

    6994:   if (!*mat) return(0);
    6995:   /* mat[] is an array of length n+1, see MatCreateSubMatrices_xxx() */
    6996:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Trying to destroy negative number of matrices %D",n);

    6999:   mat0 = (*mat)[0];
    7000:   if (mat0 && mat0->ops->destroysubmatrices) {
    7001:     (mat0->ops->destroysubmatrices)(n,mat);
    7002:   } else {
    7003:     MatDestroyMatrices(n,mat);
    7004:   }
    7005:   return(0);
    7006: }

    7008: /*@C
    7009:    MatGetSeqNonzeroStructure - Extracts the sequential nonzero structure from a matrix.

    7011:    Collective on Mat

    7013:    Input Parameters:
    7014: .  mat - the matrix

    7016:    Output Parameter:
    7017: .  matstruct - the sequential matrix with the nonzero structure of mat

    7019:   Level: intermediate

    7021: .seealso: MatDestroySeqNonzeroStructure(), MatCreateSubMatrices(), MatDestroyMatrices()
    7022: @*/
    7023: PetscErrorCode MatGetSeqNonzeroStructure(Mat mat,Mat *matstruct)
    7024: {

    7032:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7033:   MatCheckPreallocated(mat,1);

    7035:   if (!mat->ops->getseqnonzerostructure) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not for matrix type %s\n",((PetscObject)mat)->type_name);
    7036:   PetscLogEventBegin(MAT_GetSeqNonzeroStructure,mat,0,0,0);
    7037:   (*mat->ops->getseqnonzerostructure)(mat,matstruct);
    7038:   PetscLogEventEnd(MAT_GetSeqNonzeroStructure,mat,0,0,0);
    7039:   return(0);
    7040: }

    7042: /*@C
    7043:    MatDestroySeqNonzeroStructure - Destroys matrix obtained with MatGetSeqNonzeroStructure().

    7045:    Collective on Mat

    7047:    Input Parameters:
    7048: .  mat - the matrix (note that this is a pointer to the array of matrices, just to match the calling
    7049:                        sequence of MatGetSequentialNonzeroStructure())

    7051:    Level: advanced

    7053:     Notes:
    7054:     Frees not only the matrices, but also the array that contains the matrices

    7056: .seealso: MatGetSeqNonzeroStructure()
    7057: @*/
    7058: PetscErrorCode MatDestroySeqNonzeroStructure(Mat *mat)
    7059: {

    7064:   MatDestroy(mat);
    7065:   return(0);
    7066: }

    7068: /*@
    7069:    MatIncreaseOverlap - Given a set of submatrices indicated by index sets,
    7070:    replaces the index sets by larger ones that represent submatrices with
    7071:    additional overlap.

    7073:    Collective on Mat

    7075:    Input Parameters:
    7076: +  mat - the matrix
    7077: .  n   - the number of index sets
    7078: .  is  - the array of index sets (these index sets will changed during the call)
    7079: -  ov  - the additional overlap requested

    7081:    Options Database:
    7082: .  -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

    7084:    Level: developer

    7087: .seealso: MatCreateSubMatrices()
    7088: @*/
    7089: PetscErrorCode MatIncreaseOverlap(Mat mat,PetscInt n,IS is[],PetscInt ov)
    7090: {

    7096:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more domains, you have %D",n);
    7097:   if (n) {
    7100:   }
    7101:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    7102:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7103:   MatCheckPreallocated(mat,1);

    7105:   if (!ov) return(0);
    7106:   if (!mat->ops->increaseoverlap) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    7107:   PetscLogEventBegin(MAT_IncreaseOverlap,mat,0,0,0);
    7108:   (*mat->ops->increaseoverlap)(mat,n,is,ov);
    7109:   PetscLogEventEnd(MAT_IncreaseOverlap,mat,0,0,0);
    7110:   return(0);
    7111: }

    7114: PetscErrorCode MatIncreaseOverlapSplit_Single(Mat,IS*,PetscInt);

    7116: /*@
    7117:    MatIncreaseOverlapSplit - Given a set of submatrices indicated by index sets across
    7118:    a sub communicator, replaces the index sets by larger ones that represent submatrices with
    7119:    additional overlap.

    7121:    Collective on Mat

    7123:    Input Parameters:
    7124: +  mat - the matrix
    7125: .  n   - the number of index sets
    7126: .  is  - the array of index sets (these index sets will changed during the call)
    7127: -  ov  - the additional overlap requested

    7129:    Options Database:
    7130: .  -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

    7132:    Level: developer

    7135: .seealso: MatCreateSubMatrices()
    7136: @*/
    7137: PetscErrorCode MatIncreaseOverlapSplit(Mat mat,PetscInt n,IS is[],PetscInt ov)
    7138: {
    7139:   PetscInt       i;

    7145:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more domains, you have %D",n);
    7146:   if (n) {
    7149:   }
    7150:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    7151:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7152:   MatCheckPreallocated(mat,1);
    7153:   if (!ov) return(0);
    7154:   PetscLogEventBegin(MAT_IncreaseOverlap,mat,0,0,0);
    7155:   for (i=0; i<n; i++){
    7156:          MatIncreaseOverlapSplit_Single(mat,&is[i],ov);
    7157:   }
    7158:   PetscLogEventEnd(MAT_IncreaseOverlap,mat,0,0,0);
    7159:   return(0);
    7160: }

    7165: /*@
    7166:    MatGetBlockSize - Returns the matrix block size.

    7168:    Not Collective

    7170:    Input Parameter:
    7171: .  mat - the matrix

    7173:    Output Parameter:
    7174: .  bs - block size

    7176:    Notes:
    7177:     Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.

    7179:    If the block size has not been set yet this routine returns 1.

    7181:    Level: intermediate

    7183: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSizes()
    7184: @*/
    7185: PetscErrorCode MatGetBlockSize(Mat mat,PetscInt *bs)
    7186: {
    7190:   *bs = PetscAbs(mat->rmap->bs);
    7191:   return(0);
    7192: }

    7194: /*@
    7195:    MatGetBlockSizes - Returns the matrix block row and column sizes.

    7197:    Not Collective

    7199:    Input Parameter:
    7200: .  mat - the matrix

    7202:    Output Parameter:
    7203: +  rbs - row block size
    7204: -  cbs - column block size

    7206:    Notes:
    7207:     Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.
    7208:     If you pass a different block size for the columns than the rows, the row block size determines the square block storage.

    7210:    If a block size has not been set yet this routine returns 1.

    7212:    Level: intermediate

    7214: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSize(), MatSetBlockSizes()
    7215: @*/
    7216: PetscErrorCode MatGetBlockSizes(Mat mat,PetscInt *rbs, PetscInt *cbs)
    7217: {
    7222:   if (rbs) *rbs = PetscAbs(mat->rmap->bs);
    7223:   if (cbs) *cbs = PetscAbs(mat->cmap->bs);
    7224:   return(0);
    7225: }

    7227: /*@
    7228:    MatSetBlockSize - Sets the matrix block size.

    7230:    Logically Collective on Mat

    7232:    Input Parameters:
    7233: +  mat - the matrix
    7234: -  bs - block size

    7236:    Notes:
    7237:     Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.
    7238:     This must be called before MatSetUp() or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later.

    7240:     For MATMPIAIJ and MATSEQAIJ matrix formats, this function can be called at a later stage, provided that the specified block size
    7241:     is compatible with the matrix local sizes.

    7243:    Level: intermediate

    7245: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes(), MatGetBlockSizes()
    7246: @*/
    7247: PetscErrorCode MatSetBlockSize(Mat mat,PetscInt bs)
    7248: {

    7254:   MatSetBlockSizes(mat,bs,bs);
    7255:   return(0);
    7256: }

    7258: /*@
    7259:    MatSetVariableBlockSizes - Sets a diagonal blocks of the matrix that need not be of the same size

    7261:    Logically Collective on Mat

    7263:    Input Parameters:
    7264: +  mat - the matrix
    7265: .  nblocks - the number of blocks on this process
    7266: -  bsizes - the block sizes

    7268:    Notes:
    7269:     Currently used by PCVPBJACOBI for SeqAIJ matrices

    7271:    Level: intermediate

    7273: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes(), MatGetBlockSizes(), MatGetVariableBlockSizes()
    7274: @*/
    7275: PetscErrorCode MatSetVariableBlockSizes(Mat mat,PetscInt nblocks,PetscInt *bsizes)
    7276: {
    7278:   PetscInt       i,ncnt = 0, nlocal;

    7282:   if (nblocks < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number of local blocks must be great than or equal to zero");
    7283:   MatGetLocalSize(mat,&nlocal,NULL);
    7284:   for (i=0; i<nblocks; i++) ncnt += bsizes[i];
    7285:   if (ncnt != nlocal) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Sum of local block sizes %D does not equal local size of matrix %D",ncnt,nlocal);
    7286:   PetscFree(mat->bsizes);
    7287:   mat->nblocks = nblocks;
    7288:   PetscMalloc1(nblocks,&mat->bsizes);
    7289:   PetscArraycpy(mat->bsizes,bsizes,nblocks);
    7290:   return(0);
    7291: }

    7293: /*@C
    7294:    MatGetVariableBlockSizes - Gets a diagonal blocks of the matrix that need not be of the same size

    7296:    Logically Collective on Mat

    7298:    Input Parameters:
    7299: .  mat - the matrix

    7301:    Output Parameters:
    7302: +  nblocks - the number of blocks on this process
    7303: -  bsizes - the block sizes

    7305:    Notes: Currently not supported from Fortran

    7307:    Level: intermediate

    7309: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes(), MatGetBlockSizes(), MatSetVariableBlockSizes()
    7310: @*/
    7311: PetscErrorCode MatGetVariableBlockSizes(Mat mat,PetscInt *nblocks,const PetscInt **bsizes)
    7312: {
    7315:   *nblocks = mat->nblocks;
    7316:   *bsizes  = mat->bsizes;
    7317:   return(0);
    7318: }

    7320: /*@
    7321:    MatSetBlockSizes - Sets the matrix block row and column sizes.

    7323:    Logically Collective on Mat

    7325:    Input Parameters:
    7326: +  mat - the matrix
    7327: .  rbs - row block size
    7328: -  cbs - column block size

    7330:    Notes:
    7331:     Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.
    7332:     If you pass a different block size for the columns than the rows, the row block size determines the square block storage.
    7333:     This must be called before MatSetUp() or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later.

    7335:     For MATMPIAIJ and MATSEQAIJ matrix formats, this function can be called at a later stage, provided that the specified block sizes
    7336:     are compatible with the matrix local sizes.

    7338:     The row and column block size determine the blocksize of the "row" and "column" vectors returned by MatCreateVecs().

    7340:    Level: intermediate

    7342: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSize(), MatGetBlockSizes()
    7343: @*/
    7344: PetscErrorCode MatSetBlockSizes(Mat mat,PetscInt rbs,PetscInt cbs)
    7345: {

    7352:   if (mat->ops->setblocksizes) {
    7353:     (*mat->ops->setblocksizes)(mat,rbs,cbs);
    7354:   }
    7355:   if (mat->rmap->refcnt) {
    7356:     ISLocalToGlobalMapping l2g = NULL;
    7357:     PetscLayout            nmap = NULL;

    7359:     PetscLayoutDuplicate(mat->rmap,&nmap);
    7360:     if (mat->rmap->mapping) {
    7361:       ISLocalToGlobalMappingDuplicate(mat->rmap->mapping,&l2g);
    7362:     }
    7363:     PetscLayoutDestroy(&mat->rmap);
    7364:     mat->rmap = nmap;
    7365:     mat->rmap->mapping = l2g;
    7366:   }
    7367:   if (mat->cmap->refcnt) {
    7368:     ISLocalToGlobalMapping l2g = NULL;
    7369:     PetscLayout            nmap = NULL;

    7371:     PetscLayoutDuplicate(mat->cmap,&nmap);
    7372:     if (mat->cmap->mapping) {
    7373:       ISLocalToGlobalMappingDuplicate(mat->cmap->mapping,&l2g);
    7374:     }
    7375:     PetscLayoutDestroy(&mat->cmap);
    7376:     mat->cmap = nmap;
    7377:     mat->cmap->mapping = l2g;
    7378:   }
    7379:   PetscLayoutSetBlockSize(mat->rmap,rbs);
    7380:   PetscLayoutSetBlockSize(mat->cmap,cbs);
    7381:   return(0);
    7382: }

    7384: /*@
    7385:    MatSetBlockSizesFromMats - Sets the matrix block row and column sizes to match a pair of matrices

    7387:    Logically Collective on Mat

    7389:    Input Parameters:
    7390: +  mat - the matrix
    7391: .  fromRow - matrix from which to copy row block size
    7392: -  fromCol - matrix from which to copy column block size (can be same as fromRow)

    7394:    Level: developer

    7396: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes()
    7397: @*/
    7398: PetscErrorCode MatSetBlockSizesFromMats(Mat mat,Mat fromRow,Mat fromCol)
    7399: {

    7406:   if (fromRow->rmap->bs > 0) {PetscLayoutSetBlockSize(mat->rmap,fromRow->rmap->bs);}
    7407:   if (fromCol->cmap->bs > 0) {PetscLayoutSetBlockSize(mat->cmap,fromCol->cmap->bs);}
    7408:   return(0);
    7409: }

    7411: /*@
    7412:    MatResidual - Default routine to calculate the residual.

    7414:    Collective on Mat

    7416:    Input Parameters:
    7417: +  mat - the matrix
    7418: .  b   - the right-hand-side
    7419: -  x   - the approximate solution

    7421:    Output Parameter:
    7422: .  r - location to store the residual

    7424:    Level: developer

    7426: .seealso: PCMGSetResidual()
    7427: @*/
    7428: PetscErrorCode MatResidual(Mat mat,Vec b,Vec x,Vec r)
    7429: {

    7438:   MatCheckPreallocated(mat,1);
    7439:   PetscLogEventBegin(MAT_Residual,mat,0,0,0);
    7440:   if (!mat->ops->residual) {
    7441:     MatMult(mat,x,r);
    7442:     VecAYPX(r,-1.0,b);
    7443:   } else {
    7444:     (*mat->ops->residual)(mat,b,x,r);
    7445:   }
    7446:   PetscLogEventEnd(MAT_Residual,mat,0,0,0);
    7447:   return(0);
    7448: }

    7450: /*@C
    7451:     MatGetRowIJ - Returns the compressed row storage i and j indices for sequential matrices.

    7453:    Collective on Mat

    7455:     Input Parameters:
    7456: +   mat - the matrix
    7457: .   shift -  0 or 1 indicating we want the indices starting at 0 or 1
    7458: .   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be   symmetrized
    7459: -   inodecompressed - PETSC_TRUE or PETSC_FALSE  indicating if the nonzero structure of the
    7460:                  inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
    7461:                  always used.

    7463:     Output Parameters:
    7464: +   n - number of rows in the (possibly compressed) matrix
    7465: .   ia - the row pointers; that is ia[0] = 0, ia[row] = ia[row-1] + number of elements in that row of the matrix
    7466: .   ja - the column indices
    7467: -   done - indicates if the routine actually worked and returned appropriate ia[] and ja[] arrays; callers
    7468:            are responsible for handling the case when done == PETSC_FALSE and ia and ja are not set

    7470:     Level: developer

    7472:     Notes:
    7473:     You CANNOT change any of the ia[] or ja[] values.

    7475:     Use MatRestoreRowIJ() when you are finished accessing the ia[] and ja[] values.

    7477:     Fortran Notes:
    7478:     In Fortran use
    7479: $
    7480: $      PetscInt ia(1), ja(1)
    7481: $      PetscOffset iia, jja
    7482: $      call MatGetRowIJ(mat,shift,symmetric,inodecompressed,n,ia,iia,ja,jja,done,ierr)
    7483: $      ! Access the ith and jth entries via ia(iia + i) and ja(jja + j)

    7485:      or
    7486: $
    7487: $    PetscInt, pointer :: ia(:),ja(:)
    7488: $    call MatGetRowIJF90(mat,shift,symmetric,inodecompressed,n,ia,ja,done,ierr)
    7489: $    ! Access the ith and jth entries via ia(i) and ja(j)

    7491: .seealso: MatGetColumnIJ(), MatRestoreRowIJ(), MatSeqAIJGetArray()
    7492: @*/
    7493: PetscErrorCode MatGetRowIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    7494: {

    7504:   MatCheckPreallocated(mat,1);
    7505:   if (!mat->ops->getrowij) *done = PETSC_FALSE;
    7506:   else {
    7507:     *done = PETSC_TRUE;
    7508:     PetscLogEventBegin(MAT_GetRowIJ,mat,0,0,0);
    7509:     (*mat->ops->getrowij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);
    7510:     PetscLogEventEnd(MAT_GetRowIJ,mat,0,0,0);
    7511:   }
    7512:   return(0);
    7513: }

    7515: /*@C
    7516:     MatGetColumnIJ - Returns the compressed column storage i and j indices for sequential matrices.

    7518:     Collective on Mat

    7520:     Input Parameters:
    7521: +   mat - the matrix
    7522: .   shift - 1 or zero indicating we want the indices starting at 0 or 1
    7523: .   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
    7524:                 symmetrized
    7525: .   inodecompressed - PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
    7526:                  inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
    7527:                  always used.
    7528: .   n - number of columns in the (possibly compressed) matrix
    7529: .   ia - the column pointers; that is ia[0] = 0, ia[col] = i[col-1] + number of elements in that col of the matrix
    7530: -   ja - the row indices

    7532:     Output Parameters:
    7533: .   done - PETSC_TRUE or PETSC_FALSE, indicating whether the values have been returned

    7535:     Level: developer

    7537: .seealso: MatGetRowIJ(), MatRestoreColumnIJ()
    7538: @*/
    7539: PetscErrorCode MatGetColumnIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    7540: {

    7550:   MatCheckPreallocated(mat,1);
    7551:   if (!mat->ops->getcolumnij) *done = PETSC_FALSE;
    7552:   else {
    7553:     *done = PETSC_TRUE;
    7554:     (*mat->ops->getcolumnij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);
    7555:   }
    7556:   return(0);
    7557: }

    7559: /*@C
    7560:     MatRestoreRowIJ - Call after you are completed with the ia,ja indices obtained with
    7561:     MatGetRowIJ().

    7563:     Collective on Mat

    7565:     Input Parameters:
    7566: +   mat - the matrix
    7567: .   shift - 1 or zero indicating we want the indices starting at 0 or 1
    7568: .   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
    7569:                 symmetrized
    7570: .   inodecompressed -  PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
    7571:                  inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
    7572:                  always used.
    7573: .   n - size of (possibly compressed) matrix
    7574: .   ia - the row pointers
    7575: -   ja - the column indices

    7577:     Output Parameters:
    7578: .   done - PETSC_TRUE or PETSC_FALSE indicated that the values have been returned

    7580:     Note:
    7581:     This routine zeros out n, ia, and ja. This is to prevent accidental
    7582:     us of the array after it has been restored. If you pass NULL, it will
    7583:     not zero the pointers.  Use of ia or ja after MatRestoreRowIJ() is invalid.

    7585:     Level: developer

    7587: .seealso: MatGetRowIJ(), MatRestoreColumnIJ()
    7588: @*/
    7589: PetscErrorCode MatRestoreRowIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    7590: {

    7599:   MatCheckPreallocated(mat,1);

    7601:   if (!mat->ops->restorerowij) *done = PETSC_FALSE;
    7602:   else {
    7603:     *done = PETSC_TRUE;
    7604:     (*mat->ops->restorerowij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);
    7605:     if (n)  *n = 0;
    7606:     if (ia) *ia = NULL;
    7607:     if (ja) *ja = NULL;
    7608:   }
    7609:   return(0);
    7610: }

    7612: /*@C
    7613:     MatRestoreColumnIJ - Call after you are completed with the ia,ja indices obtained with
    7614:     MatGetColumnIJ().

    7616:     Collective on Mat

    7618:     Input Parameters:
    7619: +   mat - the matrix
    7620: .   shift - 1 or zero indicating we want the indices starting at 0 or 1
    7621: -   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
    7622:                 symmetrized
    7623: -   inodecompressed - PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
    7624:                  inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
    7625:                  always used.

    7627:     Output Parameters:
    7628: +   n - size of (possibly compressed) matrix
    7629: .   ia - the column pointers
    7630: .   ja - the row indices
    7631: -   done - PETSC_TRUE or PETSC_FALSE indicated that the values have been returned

    7633:     Level: developer

    7635: .seealso: MatGetColumnIJ(), MatRestoreRowIJ()
    7636: @*/
    7637: PetscErrorCode MatRestoreColumnIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    7638: {

    7647:   MatCheckPreallocated(mat,1);

    7649:   if (!mat->ops->restorecolumnij) *done = PETSC_FALSE;
    7650:   else {
    7651:     *done = PETSC_TRUE;
    7652:     (*mat->ops->restorecolumnij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);
    7653:     if (n)  *n = 0;
    7654:     if (ia) *ia = NULL;
    7655:     if (ja) *ja = NULL;
    7656:   }
    7657:   return(0);
    7658: }

    7660: /*@C
    7661:     MatColoringPatch -Used inside matrix coloring routines that
    7662:     use MatGetRowIJ() and/or MatGetColumnIJ().

    7664:     Collective on Mat

    7666:     Input Parameters:
    7667: +   mat - the matrix
    7668: .   ncolors - max color value
    7669: .   n   - number of entries in colorarray
    7670: -   colorarray - array indicating color for each column

    7672:     Output Parameters:
    7673: .   iscoloring - coloring generated using colorarray information

    7675:     Level: developer

    7677: .seealso: MatGetRowIJ(), MatGetColumnIJ()

    7679: @*/
    7680: PetscErrorCode MatColoringPatch(Mat mat,PetscInt ncolors,PetscInt n,ISColoringValue colorarray[],ISColoring *iscoloring)
    7681: {

    7689:   MatCheckPreallocated(mat,1);

    7691:   if (!mat->ops->coloringpatch) {
    7692:     ISColoringCreate(PetscObjectComm((PetscObject)mat),ncolors,n,colorarray,PETSC_OWN_POINTER,iscoloring);
    7693:   } else {
    7694:     (*mat->ops->coloringpatch)(mat,ncolors,n,colorarray,iscoloring);
    7695:   }
    7696:   return(0);
    7697: }

    7700: /*@
    7701:    MatSetUnfactored - Resets a factored matrix to be treated as unfactored.

    7703:    Logically Collective on Mat

    7705:    Input Parameter:
    7706: .  mat - the factored matrix to be reset

    7708:    Notes:
    7709:    This routine should be used only with factored matrices formed by in-place
    7710:    factorization via ILU(0) (or by in-place LU factorization for the MATSEQDENSE
    7711:    format).  This option can save memory, for example, when solving nonlinear
    7712:    systems with a matrix-free Newton-Krylov method and a matrix-based, in-place
    7713:    ILU(0) preconditioner.

    7715:    Note that one can specify in-place ILU(0) factorization by calling
    7716: .vb
    7717:      PCType(pc,PCILU);
    7718:      PCFactorSeUseInPlace(pc);
    7719: .ve
    7720:    or by using the options -pc_type ilu -pc_factor_in_place

    7722:    In-place factorization ILU(0) can also be used as a local
    7723:    solver for the blocks within the block Jacobi or additive Schwarz
    7724:    methods (runtime option: -sub_pc_factor_in_place).  See Users-Manual: ch_pc
    7725:    for details on setting local solver options.

    7727:    Most users should employ the simplified KSP interface for linear solvers
    7728:    instead of working directly with matrix algebra routines such as this.
    7729:    See, e.g., KSPCreate().

    7731:    Level: developer

    7733: .seealso: PCFactorSetUseInPlace(), PCFactorGetUseInPlace()

    7735: @*/
    7736: PetscErrorCode MatSetUnfactored(Mat mat)
    7737: {

    7743:   MatCheckPreallocated(mat,1);
    7744:   mat->factortype = MAT_FACTOR_NONE;
    7745:   if (!mat->ops->setunfactored) return(0);
    7746:   (*mat->ops->setunfactored)(mat);
    7747:   return(0);
    7748: }

    7750: /*MC
    7751:     MatDenseGetArrayF90 - Accesses a matrix array from Fortran90.

    7753:     Synopsis:
    7754:     MatDenseGetArrayF90(Mat x,{Scalar, pointer :: xx_v(:,:)},integer ierr)

    7756:     Not collective

    7758:     Input Parameter:
    7759: .   x - matrix

    7761:     Output Parameters:
    7762: +   xx_v - the Fortran90 pointer to the array
    7763: -   ierr - error code

    7765:     Example of Usage:
    7766: .vb
    7767:       PetscScalar, pointer xx_v(:,:)
    7768:       ....
    7769:       call MatDenseGetArrayF90(x,xx_v,ierr)
    7770:       a = xx_v(3)
    7771:       call MatDenseRestoreArrayF90(x,xx_v,ierr)
    7772: .ve

    7774:     Level: advanced

    7776: .seealso:  MatDenseRestoreArrayF90(), MatDenseGetArray(), MatDenseRestoreArray(), MatSeqAIJGetArrayF90()

    7778: M*/

    7780: /*MC
    7781:     MatDenseRestoreArrayF90 - Restores a matrix array that has been
    7782:     accessed with MatDenseGetArrayF90().

    7784:     Synopsis:
    7785:     MatDenseRestoreArrayF90(Mat x,{Scalar, pointer :: xx_v(:,:)},integer ierr)

    7787:     Not collective

    7789:     Input Parameters:
    7790: +   x - matrix
    7791: -   xx_v - the Fortran90 pointer to the array

    7793:     Output Parameter:
    7794: .   ierr - error code

    7796:     Example of Usage:
    7797: .vb
    7798:        PetscScalar, pointer xx_v(:,:)
    7799:        ....
    7800:        call MatDenseGetArrayF90(x,xx_v,ierr)
    7801:        a = xx_v(3)
    7802:        call MatDenseRestoreArrayF90(x,xx_v,ierr)
    7803: .ve

    7805:     Level: advanced

    7807: .seealso:  MatDenseGetArrayF90(), MatDenseGetArray(), MatDenseRestoreArray(), MatSeqAIJRestoreArrayF90()

    7809: M*/

    7812: /*MC
    7813:     MatSeqAIJGetArrayF90 - Accesses a matrix array from Fortran90.

    7815:     Synopsis:
    7816:     MatSeqAIJGetArrayF90(Mat x,{Scalar, pointer :: xx_v(:)},integer ierr)

    7818:     Not collective

    7820:     Input Parameter:
    7821: .   x - matrix

    7823:     Output Parameters:
    7824: +   xx_v - the Fortran90 pointer to the array
    7825: -   ierr - error code

    7827:     Example of Usage:
    7828: .vb
    7829:       PetscScalar, pointer xx_v(:)
    7830:       ....
    7831:       call MatSeqAIJGetArrayF90(x,xx_v,ierr)
    7832:       a = xx_v(3)
    7833:       call MatSeqAIJRestoreArrayF90(x,xx_v,ierr)
    7834: .ve

    7836:     Level: advanced

    7838: .seealso:  MatSeqAIJRestoreArrayF90(), MatSeqAIJGetArray(), MatSeqAIJRestoreArray(), MatDenseGetArrayF90()

    7840: M*/

    7842: /*MC
    7843:     MatSeqAIJRestoreArrayF90 - Restores a matrix array that has been
    7844:     accessed with MatSeqAIJGetArrayF90().

    7846:     Synopsis:
    7847:     MatSeqAIJRestoreArrayF90(Mat x,{Scalar, pointer :: xx_v(:)},integer ierr)

    7849:     Not collective

    7851:     Input Parameters:
    7852: +   x - matrix
    7853: -   xx_v - the Fortran90 pointer to the array

    7855:     Output Parameter:
    7856: .   ierr - error code

    7858:     Example of Usage:
    7859: .vb
    7860:        PetscScalar, pointer xx_v(:)
    7861:        ....
    7862:        call MatSeqAIJGetArrayF90(x,xx_v,ierr)
    7863:        a = xx_v(3)
    7864:        call MatSeqAIJRestoreArrayF90(x,xx_v,ierr)
    7865: .ve

    7867:     Level: advanced

    7869: .seealso:  MatSeqAIJGetArrayF90(), MatSeqAIJGetArray(), MatSeqAIJRestoreArray(), MatDenseRestoreArrayF90()

    7871: M*/

    7874: /*@
    7875:     MatCreateSubMatrix - Gets a single submatrix on the same number of processors
    7876:                       as the original matrix.

    7878:     Collective on Mat

    7880:     Input Parameters:
    7881: +   mat - the original matrix
    7882: .   isrow - parallel IS containing the rows this processor should obtain
    7883: .   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.
    7884: -   cll - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    7886:     Output Parameter:
    7887: .   newmat - the new submatrix, of the same type as the old

    7889:     Level: advanced

    7891:     Notes:
    7892:     The submatrix will be able to be multiplied with vectors using the same layout as iscol.

    7894:     Some matrix types place restrictions on the row and column indices, such
    7895:     as that they be sorted or that they be equal to each other.

    7897:     The index sets may not have duplicate entries.

    7899:       The first time this is called you should use a cll of MAT_INITIAL_MATRIX,
    7900:    the MatCreateSubMatrix() routine will create the newmat for you. Any additional calls
    7901:    to this routine with a mat of the same nonzero structure and with a call of MAT_REUSE_MATRIX
    7902:    will reuse the matrix generated the first time.  You should call MatDestroy() on newmat when
    7903:    you are finished using it.

    7905:     The communicator of the newly obtained matrix is ALWAYS the same as the communicator of
    7906:     the input matrix.

    7908:     If iscol is NULL then all columns are obtained (not supported in Fortran).

    7910:    Example usage:
    7911:    Consider the following 8x8 matrix with 34 non-zero values, that is
    7912:    assembled across 3 processors. Let's assume that proc0 owns 3 rows,
    7913:    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    7914:    as follows:

    7916: .vb
    7917:             1  2  0  |  0  3  0  |  0  4
    7918:     Proc0   0  5  6  |  7  0  0  |  8  0
    7919:             9  0 10  | 11  0  0  | 12  0
    7920:     -------------------------------------
    7921:            13  0 14  | 15 16 17  |  0  0
    7922:     Proc1   0 18  0  | 19 20 21  |  0  0
    7923:             0  0  0  | 22 23  0  | 24  0
    7924:     -------------------------------------
    7925:     Proc2  25 26 27  |  0  0 28  | 29  0
    7926:            30  0  0  | 31 32 33  |  0 34
    7927: .ve

    7929:     Suppose isrow = [0 1 | 4 | 6 7] and iscol = [1 2 | 3 4 5 | 6].  The resulting submatrix is

    7931: .vb
    7932:             2  0  |  0  3  0  |  0
    7933:     Proc0   5  6  |  7  0  0  |  8
    7934:     -------------------------------
    7935:     Proc1  18  0  | 19 20 21  |  0
    7936:     -------------------------------
    7937:     Proc2  26 27  |  0  0 28  | 29
    7938:             0  0  | 31 32 33  |  0
    7939: .ve

    7942: .seealso: MatCreateSubMatrices(), MatCreateSubMatricesMPI(), MatCreateSubMatrixVirtual(), MatSubMatrixVirtualUpdate()
    7943: @*/
    7944: PetscErrorCode MatCreateSubMatrix(Mat mat,IS isrow,IS iscol,MatReuse cll,Mat *newmat)
    7945: {
    7947:   PetscMPIInt    size;
    7948:   Mat            *local;
    7949:   IS             iscoltmp;
    7950:   PetscBool      flg;

    7959:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7960:   if (cll == MAT_IGNORE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Cannot use MAT_IGNORE_MATRIX");

    7962:   MatCheckPreallocated(mat,1);
    7963:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);

    7965:   if (!iscol || isrow == iscol) {
    7966:     PetscBool   stride;
    7967:     PetscMPIInt grabentirematrix = 0,grab;
    7968:     PetscObjectTypeCompare((PetscObject)isrow,ISSTRIDE,&stride);
    7969:     if (stride) {
    7970:       PetscInt first,step,n,rstart,rend;
    7971:       ISStrideGetInfo(isrow,&first,&step);
    7972:       if (step == 1) {
    7973:         MatGetOwnershipRange(mat,&rstart,&rend);
    7974:         if (rstart == first) {
    7975:           ISGetLocalSize(isrow,&n);
    7976:           if (n == rend-rstart) {
    7977:             grabentirematrix = 1;
    7978:           }
    7979:         }
    7980:       }
    7981:     }
    7982:     MPIU_Allreduce(&grabentirematrix,&grab,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));
    7983:     if (grab) {
    7984:       PetscInfo(mat,"Getting entire matrix as submatrix\n");
    7985:       if (cll == MAT_INITIAL_MATRIX) {
    7986:         *newmat = mat;
    7987:         PetscObjectReference((PetscObject)mat);
    7988:       }
    7989:       return(0);
    7990:     }
    7991:   }

    7993:   if (!iscol) {
    7994:     ISCreateStride(PetscObjectComm((PetscObject)mat),mat->cmap->n,mat->cmap->rstart,1,&iscoltmp);
    7995:   } else {
    7996:     iscoltmp = iscol;
    7997:   }

    7999:   /* if original matrix is on just one processor then use submatrix generated */
    8000:   if (mat->ops->createsubmatrices && !mat->ops->createsubmatrix && size == 1 && cll == MAT_REUSE_MATRIX) {
    8001:     MatCreateSubMatrices(mat,1,&isrow,&iscoltmp,MAT_REUSE_MATRIX,&newmat);
    8002:     goto setproperties;
    8003:   } else if (mat->ops->createsubmatrices && !mat->ops->createsubmatrix && size == 1) {
    8004:     MatCreateSubMatrices(mat,1,&isrow,&iscoltmp,MAT_INITIAL_MATRIX,&local);
    8005:     *newmat = *local;
    8006:     PetscFree(local);
    8007:     goto setproperties;
    8008:   } else if (!mat->ops->createsubmatrix) {
    8009:     /* Create a new matrix type that implements the operation using the full matrix */
    8010:     PetscLogEventBegin(MAT_CreateSubMat,mat,0,0,0);
    8011:     switch (cll) {
    8012:     case MAT_INITIAL_MATRIX:
    8013:       MatCreateSubMatrixVirtual(mat,isrow,iscoltmp,newmat);
    8014:       break;
    8015:     case MAT_REUSE_MATRIX:
    8016:       MatSubMatrixVirtualUpdate(*newmat,mat,isrow,iscoltmp);
    8017:       break;
    8018:     default: SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Invalid MatReuse, must be either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX");
    8019:     }
    8020:     PetscLogEventEnd(MAT_CreateSubMat,mat,0,0,0);
    8021:     goto setproperties;
    8022:   }

    8024:   if (!mat->ops->createsubmatrix) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    8025:   PetscLogEventBegin(MAT_CreateSubMat,mat,0,0,0);
    8026:   (*mat->ops->createsubmatrix)(mat,isrow,iscoltmp,cll,newmat);
    8027:   PetscLogEventEnd(MAT_CreateSubMat,mat,0,0,0);

    8029: setproperties:
    8030:   ISEqualUnsorted(isrow,iscoltmp,&flg);
    8031:   if (flg) {
    8032:     MatPropagateSymmetryOptions(mat,*newmat);
    8033:   }
    8034:   if (!iscol) {ISDestroy(&iscoltmp);}
    8035:   if (*newmat && cll == MAT_INITIAL_MATRIX) {PetscObjectStateIncrease((PetscObject)*newmat);}
    8036:   return(0);
    8037: }

    8039: /*@
    8040:    MatPropagateSymmetryOptions - Propagates symmetry options set on a matrix to another matrix

    8042:    Not Collective

    8044:    Input Parameters:
    8045: +  A - the matrix we wish to propagate options from
    8046: -  B - the matrix we wish to propagate options to

    8048:    Level: beginner

    8050:    Notes: Propagates the options associated to MAT_SYMMETRY_ETERNAL, MAT_STRUCTURALLY_SYMMETRIC, MAT_HERMITIAN, MAT_SPD and MAT_SYMMETRIC

    8052: .seealso: MatSetOption()
    8053: @*/
    8054: PetscErrorCode MatPropagateSymmetryOptions(Mat A, Mat B)
    8055: {

    8061:   if (A->symmetric_eternal) { /* symmetric_eternal does not have a corresponding *set flag */
    8062:     MatSetOption(B,MAT_SYMMETRY_ETERNAL,A->symmetric_eternal);
    8063:   }
    8064:   if (A->structurally_symmetric_set) {
    8065:     MatSetOption(B,MAT_STRUCTURALLY_SYMMETRIC,A->structurally_symmetric);
    8066:   }
    8067:   if (A->hermitian_set) {
    8068:     MatSetOption(B,MAT_HERMITIAN,A->hermitian);
    8069:   }
    8070:   if (A->spd_set) {
    8071:     MatSetOption(B,MAT_SPD,A->spd);
    8072:   }
    8073:   if (A->symmetric_set) {
    8074:     MatSetOption(B,MAT_SYMMETRIC,A->symmetric);
    8075:   }
    8076:   return(0);
    8077: }

    8079: /*@
    8080:    MatStashSetInitialSize - sets the sizes of the matrix stash, that is
    8081:    used during the assembly process to store values that belong to
    8082:    other processors.

    8084:    Not Collective

    8086:    Input Parameters:
    8087: +  mat   - the matrix
    8088: .  size  - the initial size of the stash.
    8089: -  bsize - the initial size of the block-stash(if used).

    8091:    Options Database Keys:
    8092: +   -matstash_initial_size <size> or <size0,size1,...sizep-1>
    8093: -   -matstash_block_initial_size <bsize>  or <bsize0,bsize1,...bsizep-1>

    8095:    Level: intermediate

    8097:    Notes:
    8098:      The block-stash is used for values set with MatSetValuesBlocked() while
    8099:      the stash is used for values set with MatSetValues()

    8101:      Run with the option -info and look for output of the form
    8102:      MatAssemblyBegin_MPIXXX:Stash has MM entries, uses nn mallocs.
    8103:      to determine the appropriate value, MM, to use for size and
    8104:      MatAssemblyBegin_MPIXXX:Block-Stash has BMM entries, uses nn mallocs.
    8105:      to determine the value, BMM to use for bsize

    8108: .seealso: MatAssemblyBegin(), MatAssemblyEnd(), Mat, MatStashGetInfo()

    8110: @*/
    8111: PetscErrorCode MatStashSetInitialSize(Mat mat,PetscInt size, PetscInt bsize)
    8112: {

    8118:   MatStashSetInitialSize_Private(&mat->stash,size);
    8119:   MatStashSetInitialSize_Private(&mat->bstash,bsize);
    8120:   return(0);
    8121: }

    8123: /*@
    8124:    MatInterpolateAdd - w = y + A*x or A'*x depending on the shape of
    8125:      the matrix

    8127:    Neighbor-wise Collective on Mat

    8129:    Input Parameters:
    8130: +  mat   - the matrix
    8131: .  x,y - the vectors
    8132: -  w - where the result is stored

    8134:    Level: intermediate

    8136:    Notes:
    8137:     w may be the same vector as y.

    8139:     This allows one to use either the restriction or interpolation (its transpose)
    8140:     matrix to do the interpolation

    8142: .seealso: MatMultAdd(), MatMultTransposeAdd(), MatRestrict()

    8144: @*/
    8145: PetscErrorCode MatInterpolateAdd(Mat A,Vec x,Vec y,Vec w)
    8146: {
    8148:   PetscInt       M,N,Ny;

    8156:   MatCheckPreallocated(A,1);
    8157:   MatGetSize(A,&M,&N);
    8158:   VecGetSize(y,&Ny);
    8159:   if (M == Ny) {
    8160:     MatMultAdd(A,x,y,w);
    8161:   } else {
    8162:     MatMultTransposeAdd(A,x,y,w);
    8163:   }
    8164:   return(0);
    8165: }

    8167: /*@
    8168:    MatInterpolate - y = A*x or A'*x depending on the shape of
    8169:      the matrix

    8171:    Neighbor-wise Collective on Mat

    8173:    Input Parameters:
    8174: +  mat   - the matrix
    8175: -  x,y - the vectors

    8177:    Level: intermediate

    8179:    Notes:
    8180:     This allows one to use either the restriction or interpolation (its transpose)
    8181:     matrix to do the interpolation

    8183: .seealso: MatMultAdd(), MatMultTransposeAdd(), MatRestrict()

    8185: @*/
    8186: PetscErrorCode MatInterpolate(Mat A,Vec x,Vec y)
    8187: {
    8189:   PetscInt       M,N,Ny;

    8196:   MatCheckPreallocated(A,1);
    8197:   MatGetSize(A,&M,&N);
    8198:   VecGetSize(y,&Ny);
    8199:   if (M == Ny) {
    8200:     MatMult(A,x,y);
    8201:   } else {
    8202:     MatMultTranspose(A,x,y);
    8203:   }
    8204:   return(0);
    8205: }

    8207: /*@
    8208:    MatRestrict - y = A*x or A'*x

    8210:    Neighbor-wise Collective on Mat

    8212:    Input Parameters:
    8213: +  mat   - the matrix
    8214: -  x,y - the vectors

    8216:    Level: intermediate

    8218:    Notes:
    8219:     This allows one to use either the restriction or interpolation (its transpose)
    8220:     matrix to do the restriction

    8222: .seealso: MatMultAdd(), MatMultTransposeAdd(), MatInterpolate()

    8224: @*/
    8225: PetscErrorCode MatRestrict(Mat A,Vec x,Vec y)
    8226: {
    8228:   PetscInt       M,N,Ny;

    8235:   MatCheckPreallocated(A,1);

    8237:   MatGetSize(A,&M,&N);
    8238:   VecGetSize(y,&Ny);
    8239:   if (M == Ny) {
    8240:     MatMult(A,x,y);
    8241:   } else {
    8242:     MatMultTranspose(A,x,y);
    8243:   }
    8244:   return(0);
    8245: }

    8247: /*@
    8248:    MatGetNullSpace - retrieves the null space of a matrix.

    8250:    Logically Collective on Mat

    8252:    Input Parameters:
    8253: +  mat - the matrix
    8254: -  nullsp - the null space object

    8256:    Level: developer

    8258: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatSetNullSpace()
    8259: @*/
    8260: PetscErrorCode MatGetNullSpace(Mat mat, MatNullSpace *nullsp)
    8261: {
    8265:   *nullsp = (mat->symmetric_set && mat->symmetric && !mat->nullsp) ? mat->transnullsp : mat->nullsp;
    8266:   return(0);
    8267: }

    8269: /*@
    8270:    MatSetNullSpace - attaches a null space to a matrix.

    8272:    Logically Collective on Mat

    8274:    Input Parameters:
    8275: +  mat - the matrix
    8276: -  nullsp - the null space object

    8278:    Level: advanced

    8280:    Notes:
    8281:       This null space is used by the linear solvers. Overwrites any previous null space that may have been attached

    8283:       For inconsistent singular systems (linear systems where the right hand side is not in the range of the operator) you also likely should
    8284:       call MatSetTransposeNullSpace(). This allows the linear system to be solved in a least squares sense.

    8286:       You can remove the null space by calling this routine with an nullsp of NULL

    8289:       The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
    8290:    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).
    8291:    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
    8292:    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
    8293:    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).

    8295:       Krylov solvers can produce the minimal norm solution to the least squares problem by utilizing MatNullSpaceRemove().

    8297:     If the matrix is known to be symmetric because it is an SBAIJ matrix or one as called MatSetOption(mat,MAT_SYMMETRIC or MAT_SYMMETRIC_ETERNAL,PETSC_TRUE); this
    8298:     routine also automatically calls MatSetTransposeNullSpace().

    8300: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatGetNullSpace(), MatSetTransposeNullSpace(), MatGetTransposeNullSpace(), MatNullSpaceRemove()
    8301: @*/
    8302: PetscErrorCode MatSetNullSpace(Mat mat,MatNullSpace nullsp)
    8303: {

    8309:   if (nullsp) {PetscObjectReference((PetscObject)nullsp);}
    8310:   MatNullSpaceDestroy(&mat->nullsp);
    8311:   mat->nullsp = nullsp;
    8312:   if (mat->symmetric_set && mat->symmetric) {
    8313:     MatSetTransposeNullSpace(mat,nullsp);
    8314:   }
    8315:   return(0);
    8316: }

    8318: /*@
    8319:    MatGetTransposeNullSpace - retrieves the null space of the transpose of a matrix.

    8321:    Logically Collective on Mat

    8323:    Input Parameters:
    8324: +  mat - the matrix
    8325: -  nullsp - the null space object

    8327:    Level: developer

    8329: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatSetTransposeNullSpace(), MatSetNullSpace(), MatGetNullSpace()
    8330: @*/
    8331: PetscErrorCode MatGetTransposeNullSpace(Mat mat, MatNullSpace *nullsp)
    8332: {
    8337:   *nullsp = (mat->symmetric_set && mat->symmetric && !mat->transnullsp) ? mat->nullsp : mat->transnullsp;
    8338:   return(0);
    8339: }

    8341: /*@
    8342:    MatSetTransposeNullSpace - attaches a null space to a matrix.

    8344:    Logically Collective on Mat

    8346:    Input Parameters:
    8347: +  mat - the matrix
    8348: -  nullsp - the null space object

    8350:    Level: advanced

    8352:    Notes:
    8353:       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.
    8354:       You must also call MatSetNullSpace()

    8357:       The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
    8358:    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).
    8359:    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
    8360:    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
    8361:    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).

    8363:       Krylov solvers can produce the minimal norm solution to the least squares problem by utilizing MatNullSpaceRemove().

    8365: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatGetNullSpace(), MatSetNullSpace(), MatGetTransposeNullSpace(), MatNullSpaceRemove()
    8366: @*/
    8367: PetscErrorCode MatSetTransposeNullSpace(Mat mat,MatNullSpace nullsp)
    8368: {

    8374:   if (nullsp) {PetscObjectReference((PetscObject)nullsp);}
    8375:   MatNullSpaceDestroy(&mat->transnullsp);
    8376:   mat->transnullsp = nullsp;
    8377:   return(0);
    8378: }

    8380: /*@
    8381:    MatSetNearNullSpace - attaches a null space to a matrix, which is often the null space (rigid body modes) of the operator without boundary conditions
    8382:         This null space will be used to provide near null space vectors to a multigrid preconditioner built from this matrix.

    8384:    Logically Collective on Mat

    8386:    Input Parameters:
    8387: +  mat - the matrix
    8388: -  nullsp - the null space object

    8390:    Level: advanced

    8392:    Notes:
    8393:       Overwrites any previous near null space that may have been attached

    8395:       You can remove the null space by calling this routine with an nullsp of NULL

    8397: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNullSpace(), MatNullSpaceCreateRigidBody(), MatGetNearNullSpace()
    8398: @*/
    8399: PetscErrorCode MatSetNearNullSpace(Mat mat,MatNullSpace nullsp)
    8400: {

    8407:   MatCheckPreallocated(mat,1);
    8408:   if (nullsp) {PetscObjectReference((PetscObject)nullsp);}
    8409:   MatNullSpaceDestroy(&mat->nearnullsp);
    8410:   mat->nearnullsp = nullsp;
    8411:   return(0);
    8412: }

    8414: /*@
    8415:    MatGetNearNullSpace - Get null space attached with MatSetNearNullSpace()

    8417:    Not Collective

    8419:    Input Parameter:
    8420: .  mat - the matrix

    8422:    Output Parameter:
    8423: .  nullsp - the null space object, NULL if not set

    8425:    Level: developer

    8427: .seealso: MatSetNearNullSpace(), MatGetNullSpace(), MatNullSpaceCreate()
    8428: @*/
    8429: PetscErrorCode MatGetNearNullSpace(Mat mat,MatNullSpace *nullsp)
    8430: {
    8435:   MatCheckPreallocated(mat,1);
    8436:   *nullsp = mat->nearnullsp;
    8437:   return(0);
    8438: }

    8440: /*@C
    8441:    MatICCFactor - Performs in-place incomplete Cholesky factorization of matrix.

    8443:    Collective on Mat

    8445:    Input Parameters:
    8446: +  mat - the matrix
    8447: .  row - row/column permutation
    8448: .  fill - expected fill factor >= 1.0
    8449: -  level - level of fill, for ICC(k)

    8451:    Notes:
    8452:    Probably really in-place only when level of fill is zero, otherwise allocates
    8453:    new space to store factored matrix and deletes previous memory.

    8455:    Most users should employ the simplified KSP interface for linear solvers
    8456:    instead of working directly with matrix algebra routines such as this.
    8457:    See, e.g., KSPCreate().

    8459:    Level: developer

    8462: .seealso: MatICCFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor()

    8464:     Developer Note: fortran interface is not autogenerated as the f90
    8465:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    8467: @*/
    8468: PetscErrorCode MatICCFactor(Mat mat,IS row,const MatFactorInfo *info)
    8469: {

    8477:   if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"matrix must be square");
    8478:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    8479:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    8480:   if (!mat->ops->iccfactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    8481:   MatCheckPreallocated(mat,1);
    8482:   (*mat->ops->iccfactor)(mat,row,info);
    8483:   PetscObjectStateIncrease((PetscObject)mat);
    8484:   return(0);
    8485: }

    8487: /*@
    8488:    MatDiagonalScaleLocal - Scales columns of a matrix given the scaling values including the
    8489:          ghosted ones.

    8491:    Not Collective

    8493:    Input Parameters:
    8494: +  mat - the matrix
    8495: -  diag = the diagonal values, including ghost ones

    8497:    Level: developer

    8499:    Notes:
    8500:     Works only for MPIAIJ and MPIBAIJ matrices

    8502: .seealso: MatDiagonalScale()
    8503: @*/
    8504: PetscErrorCode MatDiagonalScaleLocal(Mat mat,Vec diag)
    8505: {
    8507:   PetscMPIInt    size;

    8514:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Matrix must be already assembled");
    8515:   PetscLogEventBegin(MAT_Scale,mat,0,0,0);
    8516:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    8517:   if (size == 1) {
    8518:     PetscInt n,m;
    8519:     VecGetSize(diag,&n);
    8520:     MatGetSize(mat,NULL,&m);
    8521:     if (m == n) {
    8522:       MatDiagonalScale(mat,NULL,diag);
    8523:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only supported for sequential matrices when no ghost points/periodic conditions");
    8524:   } else {
    8525:     PetscUseMethod(mat,"MatDiagonalScaleLocal_C",(Mat,Vec),(mat,diag));
    8526:   }
    8527:   PetscLogEventEnd(MAT_Scale,mat,0,0,0);
    8528:   PetscObjectStateIncrease((PetscObject)mat);
    8529:   return(0);
    8530: }

    8532: /*@
    8533:    MatGetInertia - Gets the inertia from a factored matrix

    8535:    Collective on Mat

    8537:    Input Parameter:
    8538: .  mat - the matrix

    8540:    Output Parameters:
    8541: +   nneg - number of negative eigenvalues
    8542: .   nzero - number of zero eigenvalues
    8543: -   npos - number of positive eigenvalues

    8545:    Level: advanced

    8547:    Notes:
    8548:     Matrix must have been factored by MatCholeskyFactor()

    8551: @*/
    8552: PetscErrorCode MatGetInertia(Mat mat,PetscInt *nneg,PetscInt *nzero,PetscInt *npos)
    8553: {

    8559:   if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    8560:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Numeric factor mat is not assembled");
    8561:   if (!mat->ops->getinertia) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    8562:   (*mat->ops->getinertia)(mat,nneg,nzero,npos);
    8563:   return(0);
    8564: }

    8566: /* ----------------------------------------------------------------*/
    8567: /*@C
    8568:    MatSolves - Solves A x = b, given a factored matrix, for a collection of vectors

    8570:    Neighbor-wise Collective on Mats

    8572:    Input Parameters:
    8573: +  mat - the factored matrix
    8574: -  b - the right-hand-side vectors

    8576:    Output Parameter:
    8577: .  x - the result vectors

    8579:    Notes:
    8580:    The vectors b and x cannot be the same.  I.e., one cannot
    8581:    call MatSolves(A,x,x).

    8583:    Notes:
    8584:    Most users should employ the simplified KSP interface for linear solvers
    8585:    instead of working directly with matrix algebra routines such as this.
    8586:    See, e.g., KSPCreate().

    8588:    Level: developer

    8590: .seealso: MatSolveAdd(), MatSolveTranspose(), MatSolveTransposeAdd(), MatSolve()
    8591: @*/
    8592: PetscErrorCode MatSolves(Mat mat,Vecs b,Vecs x)
    8593: {

    8599:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    8600:   if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    8601:   if (!mat->rmap->N && !mat->cmap->N) return(0);

    8603:   if (!mat->ops->solves) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    8604:   MatCheckPreallocated(mat,1);
    8605:   PetscLogEventBegin(MAT_Solves,mat,0,0,0);
    8606:   (*mat->ops->solves)(mat,b,x);
    8607:   PetscLogEventEnd(MAT_Solves,mat,0,0,0);
    8608:   return(0);
    8609: }

    8611: /*@
    8612:    MatIsSymmetric - Test whether a matrix is symmetric

    8614:    Collective on Mat

    8616:    Input Parameter:
    8617: +  A - the matrix to test
    8618: -  tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact transpose)

    8620:    Output Parameters:
    8621: .  flg - the result

    8623:    Notes:
    8624:     For real numbers MatIsSymmetric() and MatIsHermitian() return identical results

    8626:    Level: intermediate

    8628: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetricKnown()
    8629: @*/
    8630: PetscErrorCode MatIsSymmetric(Mat A,PetscReal tol,PetscBool  *flg)
    8631: {

    8638:   if (!A->symmetric_set) {
    8639:     if (!A->ops->issymmetric) {
    8640:       MatType mattype;
    8641:       MatGetType(A,&mattype);
    8642:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for symmetric",mattype);
    8643:     }
    8644:     (*A->ops->issymmetric)(A,tol,flg);
    8645:     if (!tol) {
    8646:       MatSetOption(A,MAT_SYMMETRIC,*flg);
    8647:     }
    8648:   } else if (A->symmetric) {
    8649:     *flg = PETSC_TRUE;
    8650:   } else if (!tol) {
    8651:     *flg = PETSC_FALSE;
    8652:   } else {
    8653:     if (!A->ops->issymmetric) {
    8654:       MatType mattype;
    8655:       MatGetType(A,&mattype);
    8656:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for symmetric",mattype);
    8657:     }
    8658:     (*A->ops->issymmetric)(A,tol,flg);
    8659:   }
    8660:   return(0);
    8661: }

    8663: /*@
    8664:    MatIsHermitian - Test whether a matrix is Hermitian

    8666:    Collective on Mat

    8668:    Input Parameter:
    8669: +  A - the matrix to test
    8670: -  tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact Hermitian)

    8672:    Output Parameters:
    8673: .  flg - the result

    8675:    Level: intermediate

    8677: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(),
    8678:           MatIsSymmetricKnown(), MatIsSymmetric()
    8679: @*/
    8680: PetscErrorCode MatIsHermitian(Mat A,PetscReal tol,PetscBool  *flg)
    8681: {

    8688:   if (!A->hermitian_set) {
    8689:     if (!A->ops->ishermitian) {
    8690:       MatType mattype;
    8691:       MatGetType(A,&mattype);
    8692:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for hermitian",mattype);
    8693:     }
    8694:     (*A->ops->ishermitian)(A,tol,flg);
    8695:     if (!tol) {
    8696:       MatSetOption(A,MAT_HERMITIAN,*flg);
    8697:     }
    8698:   } else if (A->hermitian) {
    8699:     *flg = PETSC_TRUE;
    8700:   } else if (!tol) {
    8701:     *flg = PETSC_FALSE;
    8702:   } else {
    8703:     if (!A->ops->ishermitian) {
    8704:       MatType mattype;
    8705:       MatGetType(A,&mattype);
    8706:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for hermitian",mattype);
    8707:     }
    8708:     (*A->ops->ishermitian)(A,tol,flg);
    8709:   }
    8710:   return(0);
    8711: }

    8713: /*@
    8714:    MatIsSymmetricKnown - Checks the flag on the matrix to see if it is symmetric.

    8716:    Not Collective

    8718:    Input Parameter:
    8719: .  A - the matrix to check

    8721:    Output Parameters:
    8722: +  set - if the symmetric flag is set (this tells you if the next flag is valid)
    8723: -  flg - the result

    8725:    Level: advanced

    8727:    Note: Does not check the matrix values directly, so this may return unknown (set = PETSC_FALSE). Use MatIsSymmetric()
    8728:          if you want it explicitly checked

    8730: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetric()
    8731: @*/
    8732: PetscErrorCode MatIsSymmetricKnown(Mat A,PetscBool *set,PetscBool *flg)
    8733: {
    8738:   if (A->symmetric_set) {
    8739:     *set = PETSC_TRUE;
    8740:     *flg = A->symmetric;
    8741:   } else {
    8742:     *set = PETSC_FALSE;
    8743:   }
    8744:   return(0);
    8745: }

    8747: /*@
    8748:    MatIsHermitianKnown - Checks the flag on the matrix to see if it is hermitian.

    8750:    Not Collective

    8752:    Input Parameter:
    8753: .  A - the matrix to check

    8755:    Output Parameters:
    8756: +  set - if the hermitian flag is set (this tells you if the next flag is valid)
    8757: -  flg - the result

    8759:    Level: advanced

    8761:    Note: Does not check the matrix values directly, so this may return unknown (set = PETSC_FALSE). Use MatIsHermitian()
    8762:          if you want it explicitly checked

    8764: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetric()
    8765: @*/
    8766: PetscErrorCode MatIsHermitianKnown(Mat A,PetscBool *set,PetscBool *flg)
    8767: {
    8772:   if (A->hermitian_set) {
    8773:     *set = PETSC_TRUE;
    8774:     *flg = A->hermitian;
    8775:   } else {
    8776:     *set = PETSC_FALSE;
    8777:   }
    8778:   return(0);
    8779: }

    8781: /*@
    8782:    MatIsStructurallySymmetric - Test whether a matrix is structurally symmetric

    8784:    Collective on Mat

    8786:    Input Parameter:
    8787: .  A - the matrix to test

    8789:    Output Parameters:
    8790: .  flg - the result

    8792:    Level: intermediate

    8794: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsSymmetric(), MatSetOption()
    8795: @*/
    8796: PetscErrorCode MatIsStructurallySymmetric(Mat A,PetscBool *flg)
    8797: {

    8803:   if (!A->structurally_symmetric_set) {
    8804:     if (!A->ops->isstructurallysymmetric) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Matrix of type %s does not support checking for structural symmetric",((PetscObject)A)->type_name);
    8805:     (*A->ops->isstructurallysymmetric)(A,flg);
    8806:     MatSetOption(A,MAT_STRUCTURALLY_SYMMETRIC,*flg);
    8807:   } else *flg = A->structurally_symmetric;
    8808:   return(0);
    8809: }

    8811: /*@
    8812:    MatStashGetInfo - Gets how many values are currently in the matrix stash, i.e. need
    8813:        to be communicated to other processors during the MatAssemblyBegin/End() process

    8815:     Not collective

    8817:    Input Parameter:
    8818: .   vec - the vector

    8820:    Output Parameters:
    8821: +   nstash   - the size of the stash
    8822: .   reallocs - the number of additional mallocs incurred.
    8823: .   bnstash   - the size of the block stash
    8824: -   breallocs - the number of additional mallocs incurred.in the block stash

    8826:    Level: advanced

    8828: .seealso: MatAssemblyBegin(), MatAssemblyEnd(), Mat, MatStashSetInitialSize()

    8830: @*/
    8831: PetscErrorCode MatStashGetInfo(Mat mat,PetscInt *nstash,PetscInt *reallocs,PetscInt *bnstash,PetscInt *breallocs)
    8832: {

    8836:   MatStashGetInfo_Private(&mat->stash,nstash,reallocs);
    8837:   MatStashGetInfo_Private(&mat->bstash,bnstash,breallocs);
    8838:   return(0);
    8839: }

    8841: /*@C
    8842:    MatCreateVecs - Get vector(s) compatible with the matrix, i.e. with the same
    8843:      parallel layout

    8845:    Collective on Mat

    8847:    Input Parameter:
    8848: .  mat - the matrix

    8850:    Output Parameter:
    8851: +   right - (optional) vector that the matrix can be multiplied against
    8852: -   left - (optional) vector that the matrix vector product can be stored in

    8854:    Notes:
    8855:     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().

    8857:   Notes:
    8858:     These are new vectors which are not owned by the Mat, they should be destroyed in VecDestroy() when no longer needed

    8860:   Level: advanced

    8862: .seealso: MatCreate(), VecDestroy()
    8863: @*/
    8864: PetscErrorCode MatCreateVecs(Mat mat,Vec *right,Vec *left)
    8865: {

    8871:   if (mat->ops->getvecs) {
    8872:     (*mat->ops->getvecs)(mat,right,left);
    8873:   } else {
    8874:     PetscInt rbs,cbs;
    8875:     MatGetBlockSizes(mat,&rbs,&cbs);
    8876:     if (right) {
    8877:       if (mat->cmap->n < 0) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"PetscLayout for columns not yet setup");
    8878:       VecCreate(PetscObjectComm((PetscObject)mat),right);
    8879:       VecSetSizes(*right,mat->cmap->n,PETSC_DETERMINE);
    8880:       VecSetBlockSize(*right,cbs);
    8881:       VecSetType(*right,mat->defaultvectype);
    8882:       PetscLayoutReference(mat->cmap,&(*right)->map);
    8883:     }
    8884:     if (left) {
    8885:       if (mat->rmap->n < 0) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"PetscLayout for rows not yet setup");
    8886:       VecCreate(PetscObjectComm((PetscObject)mat),left);
    8887:       VecSetSizes(*left,mat->rmap->n,PETSC_DETERMINE);
    8888:       VecSetBlockSize(*left,rbs);
    8889:       VecSetType(*left,mat->defaultvectype);
    8890:       PetscLayoutReference(mat->rmap,&(*left)->map);
    8891:     }
    8892:   }
    8893:   return(0);
    8894: }

    8896: /*@C
    8897:    MatFactorInfoInitialize - Initializes a MatFactorInfo data structure
    8898:      with default values.

    8900:    Not Collective

    8902:    Input Parameters:
    8903: .    info - the MatFactorInfo data structure

    8906:    Notes:
    8907:     The solvers are generally used through the KSP and PC objects, for example
    8908:           PCLU, PCILU, PCCHOLESKY, PCICC

    8910:    Level: developer

    8912: .seealso: MatFactorInfo

    8914:     Developer Note: fortran interface is not autogenerated as the f90
    8915:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    8917: @*/

    8919: PetscErrorCode MatFactorInfoInitialize(MatFactorInfo *info)
    8920: {

    8924:   PetscMemzero(info,sizeof(MatFactorInfo));
    8925:   return(0);
    8926: }

    8928: /*@
    8929:    MatFactorSetSchurIS - Set indices corresponding to the Schur complement you wish to have computed

    8931:    Collective on Mat

    8933:    Input Parameters:
    8934: +  mat - the factored matrix
    8935: -  is - the index set defining the Schur indices (0-based)

    8937:    Notes:
    8938:     Call MatFactorSolveSchurComplement() or MatFactorSolveSchurComplementTranspose() after this call to solve a Schur complement system.

    8940:    You can call MatFactorGetSchurComplement() or MatFactorCreateSchurComplement() after this call.

    8942:    Level: developer

    8944: .seealso: MatGetFactor(), MatFactorGetSchurComplement(), MatFactorRestoreSchurComplement(), MatFactorCreateSchurComplement(), MatFactorSolveSchurComplement(),
    8945:           MatFactorSolveSchurComplementTranspose(), MatFactorSolveSchurComplement()

    8947: @*/
    8948: PetscErrorCode MatFactorSetSchurIS(Mat mat,IS is)
    8949: {
    8950:   PetscErrorCode ierr,(*f)(Mat,IS);

    8958:   if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Only for factored matrix");
    8959:   PetscObjectQueryFunction((PetscObject)mat,"MatFactorSetSchurIS_C",&f);
    8960:   if (!f) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"The selected MatSolverType does not support Schur complement computation. You should use MATSOLVERMUMPS or MATSOLVERMKL_PARDISO");
    8961:   MatDestroy(&mat->schur);
    8962:   (*f)(mat,is);
    8963:   if (!mat->schur) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_PLIB,"Schur complement has not been created");
    8964:   return(0);
    8965: }

    8967: /*@
    8968:   MatFactorCreateSchurComplement - Create a Schur complement matrix object using Schur data computed during the factorization step

    8970:    Logically Collective on Mat

    8972:    Input Parameters:
    8973: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    8974: .  S - location where to return the Schur complement, can be NULL
    8975: -  status - the status of the Schur complement matrix, can be NULL

    8977:    Notes:
    8978:    You must call MatFactorSetSchurIS() before calling this routine.

    8980:    The routine provides a copy of the Schur matrix stored within the solver data structures.
    8981:    The caller must destroy the object when it is no longer needed.
    8982:    If MatFactorInvertSchurComplement() has been called, the routine gets back the inverse.

    8984:    Use MatFactorGetSchurComplement() to get access to the Schur complement matrix inside the factored matrix instead of making a copy of it (which this function does)

    8986:    Developer Notes:
    8987:     The reason this routine exists is because the representation of the Schur complement within the factor matrix may be different than a standard PETSc
    8988:    matrix representation and we normally do not want to use the time or memory to make a copy as a regular PETSc matrix.

    8990:    See MatCreateSchurComplement() or MatGetSchurComplement() for ways to create virtual or approximate Schur complements.

    8992:    Level: advanced

    8994:    References:

    8996: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorGetSchurComplement(), MatFactorSchurStatus
    8997: @*/
    8998: PetscErrorCode MatFactorCreateSchurComplement(Mat F,Mat* S,MatFactorSchurStatus* status)
    8999: {

    9006:   if (S) {
    9007:     PetscErrorCode (*f)(Mat,Mat*);

    9009:     PetscObjectQueryFunction((PetscObject)F,"MatFactorCreateSchurComplement_C",&f);
    9010:     if (f) {
    9011:       (*f)(F,S);
    9012:     } else {
    9013:       MatDuplicate(F->schur,MAT_COPY_VALUES,S);
    9014:     }
    9015:   }
    9016:   if (status) *status = F->schur_status;
    9017:   return(0);
    9018: }

    9020: /*@
    9021:   MatFactorGetSchurComplement - Gets access to a Schur complement matrix using the current Schur data within a factored matrix

    9023:    Logically Collective on Mat

    9025:    Input Parameters:
    9026: +  F - the factored matrix obtained by calling MatGetFactor()
    9027: .  *S - location where to return the Schur complement, can be NULL
    9028: -  status - the status of the Schur complement matrix, can be NULL

    9030:    Notes:
    9031:    You must call MatFactorSetSchurIS() before calling this routine.

    9033:    Schur complement mode is currently implemented for sequential matrices.
    9034:    The routine returns a the Schur Complement stored within the data strutures of the solver.
    9035:    If MatFactorInvertSchurComplement() has previously been called, the returned matrix is actually the inverse of the Schur complement.
    9036:    The returned matrix should not be destroyed; the caller should call MatFactorRestoreSchurComplement() when the object is no longer needed.

    9038:    Use MatFactorCreateSchurComplement() to create a copy of the Schur complement matrix that is within a factored matrix

    9040:    See MatCreateSchurComplement() or MatGetSchurComplement() for ways to create virtual or approximate Schur complements.

    9042:    Level: advanced

    9044:    References:

    9046: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorRestoreSchurComplement(), MatFactorCreateSchurComplement(), MatFactorSchurStatus
    9047: @*/
    9048: PetscErrorCode MatFactorGetSchurComplement(Mat F,Mat* S,MatFactorSchurStatus* status)
    9049: {
    9054:   if (S) *S = F->schur;
    9055:   if (status) *status = F->schur_status;
    9056:   return(0);
    9057: }

    9059: /*@
    9060:   MatFactorRestoreSchurComplement - Restore the Schur complement matrix object obtained from a call to MatFactorGetSchurComplement

    9062:    Logically Collective on Mat

    9064:    Input Parameters:
    9065: +  F - the factored matrix obtained by calling MatGetFactor()
    9066: .  *S - location where the Schur complement is stored
    9067: -  status - the status of the Schur complement matrix (see MatFactorSchurStatus)

    9069:    Notes:

    9071:    Level: advanced

    9073:    References:

    9075: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorRestoreSchurComplement(), MatFactorCreateSchurComplement(), MatFactorSchurStatus
    9076: @*/
    9077: PetscErrorCode MatFactorRestoreSchurComplement(Mat F,Mat* S,MatFactorSchurStatus status)
    9078: {

    9083:   if (S) {
    9085:     *S = NULL;
    9086:   }
    9087:   F->schur_status = status;
    9088:   MatFactorUpdateSchurStatus_Private(F);
    9089:   return(0);
    9090: }

    9092: /*@
    9093:   MatFactorSolveSchurComplementTranspose - Solve the transpose of the Schur complement system computed during the factorization step

    9095:    Logically Collective on Mat

    9097:    Input Parameters:
    9098: +  F - the factored matrix obtained by calling MatGetFactor()
    9099: .  rhs - location where the right hand side of the Schur complement system is stored
    9100: -  sol - location where the solution of the Schur complement system has to be returned

    9102:    Notes:
    9103:    The sizes of the vectors should match the size of the Schur complement

    9105:    Must be called after MatFactorSetSchurIS()

    9107:    Level: advanced

    9109:    References:

    9111: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorSolveSchurComplement()
    9112: @*/
    9113: PetscErrorCode MatFactorSolveSchurComplementTranspose(Mat F, Vec rhs, Vec sol)
    9114: {

    9126:   MatFactorFactorizeSchurComplement(F);
    9127:   switch (F->schur_status) {
    9128:   case MAT_FACTOR_SCHUR_FACTORED:
    9129:     MatSolveTranspose(F->schur,rhs,sol);
    9130:     break;
    9131:   case MAT_FACTOR_SCHUR_INVERTED:
    9132:     MatMultTranspose(F->schur,rhs,sol);
    9133:     break;
    9134:   default:
    9135:     SETERRQ1(PetscObjectComm((PetscObject)F),PETSC_ERR_SUP,"Unhandled MatFactorSchurStatus %D",F->schur_status);
    9136:   }
    9137:   return(0);
    9138: }

    9140: /*@
    9141:   MatFactorSolveSchurComplement - Solve the Schur complement system computed during the factorization step

    9143:    Logically Collective on Mat

    9145:    Input Parameters:
    9146: +  F - the factored matrix obtained by calling MatGetFactor()
    9147: .  rhs - location where the right hand side of the Schur complement system is stored
    9148: -  sol - location where the solution of the Schur complement system has to be returned

    9150:    Notes:
    9151:    The sizes of the vectors should match the size of the Schur complement

    9153:    Must be called after MatFactorSetSchurIS()

    9155:    Level: advanced

    9157:    References:

    9159: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorSolveSchurComplementTranspose()
    9160: @*/
    9161: PetscErrorCode MatFactorSolveSchurComplement(Mat F, Vec rhs, Vec sol)
    9162: {

    9174:   MatFactorFactorizeSchurComplement(F);
    9175:   switch (F->schur_status) {
    9176:   case MAT_FACTOR_SCHUR_FACTORED:
    9177:     MatSolve(F->schur,rhs,sol);
    9178:     break;
    9179:   case MAT_FACTOR_SCHUR_INVERTED:
    9180:     MatMult(F->schur,rhs,sol);
    9181:     break;
    9182:   default:
    9183:     SETERRQ1(PetscObjectComm((PetscObject)F),PETSC_ERR_SUP,"Unhandled MatFactorSchurStatus %D",F->schur_status);
    9184:   }
    9185:   return(0);
    9186: }

    9188: /*@
    9189:   MatFactorInvertSchurComplement - Invert the Schur complement matrix computed during the factorization step

    9191:    Logically Collective on Mat

    9193:    Input Parameters:
    9194: .  F - the factored matrix obtained by calling MatGetFactor()

    9196:    Notes:
    9197:     Must be called after MatFactorSetSchurIS().

    9199:    Call MatFactorGetSchurComplement() or  MatFactorCreateSchurComplement() AFTER this call to actually compute the inverse and get access to it.

    9201:    Level: advanced

    9203:    References:

    9205: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorGetSchurComplement(), MatFactorCreateSchurComplement()
    9206: @*/
    9207: PetscErrorCode MatFactorInvertSchurComplement(Mat F)
    9208: {

    9214:   if (F->schur_status == MAT_FACTOR_SCHUR_INVERTED) return(0);
    9215:   MatFactorFactorizeSchurComplement(F);
    9216:   MatFactorInvertSchurComplement_Private(F);
    9217:   F->schur_status = MAT_FACTOR_SCHUR_INVERTED;
    9218:   return(0);
    9219: }

    9221: /*@
    9222:   MatFactorFactorizeSchurComplement - Factorize the Schur complement matrix computed during the factorization step

    9224:    Logically Collective on Mat

    9226:    Input Parameters:
    9227: .  F - the factored matrix obtained by calling MatGetFactor()

    9229:    Notes:
    9230:     Must be called after MatFactorSetSchurIS().

    9232:    Level: advanced

    9234:    References:

    9236: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorInvertSchurComplement()
    9237: @*/
    9238: PetscErrorCode MatFactorFactorizeSchurComplement(Mat F)
    9239: {

    9245:   if (F->schur_status == MAT_FACTOR_SCHUR_INVERTED || F->schur_status == MAT_FACTOR_SCHUR_FACTORED) return(0);
    9246:   MatFactorFactorizeSchurComplement_Private(F);
    9247:   F->schur_status = MAT_FACTOR_SCHUR_FACTORED;
    9248:   return(0);
    9249: }

    9251: /*@
    9252:    MatPtAP - Creates the matrix product C = P^T * A * P

    9254:    Neighbor-wise Collective on Mat

    9256:    Input Parameters:
    9257: +  A - the matrix
    9258: .  P - the projection matrix
    9259: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9260: -  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(P)), use PETSC_DEFAULT if you do not have a good estimate
    9261:           if the result is a dense matrix this is irrelevent

    9263:    Output Parameters:
    9264: .  C - the product matrix

    9266:    Notes:
    9267:    C will be created and must be destroyed by the user with MatDestroy().

    9269:    For matrix types without special implementation the function fallbacks to MatMatMult() followed by MatTransposeMatMult().

    9271:    Level: intermediate

    9273: .seealso: MatMatMult(), MatRARt()
    9274: @*/
    9275: PetscErrorCode MatPtAP(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
    9276: {

    9280:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*C,5);
    9281:   if (scall == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");

    9283:   if (scall == MAT_INITIAL_MATRIX) {
    9284:     MatProductCreate(A,P,NULL,C);
    9285:     MatProductSetType(*C,MATPRODUCT_PtAP);
    9286:     MatProductSetAlgorithm(*C,"default");
    9287:     MatProductSetFill(*C,fill);

    9289:     (*C)->product->api_user = PETSC_TRUE;
    9290:     MatProductSetFromOptions(*C);
    9291:     if (!(*C)->ops->productsymbolic) SETERRQ3(PetscObjectComm((PetscObject)(*C)),PETSC_ERR_SUP,"MatProduct %s not supported for A %s and P %s",MatProductTypes[MATPRODUCT_PtAP],((PetscObject)A)->type_name,((PetscObject)P)->type_name);
    9292:     MatProductSymbolic(*C);
    9293:   } else { /* scall == MAT_REUSE_MATRIX */
    9294:     MatProductReplaceMats(A,P,NULL,*C);
    9295:   }

    9297:   MatProductNumeric(*C);
    9298:   if (A->symmetric_set && A->symmetric) {
    9299:     MatSetOption(*C,MAT_SYMMETRIC,PETSC_TRUE);
    9300:   }
    9301:   return(0);
    9302: }

    9304: /*@
    9305:    MatRARt - Creates the matrix product C = R * A * R^T

    9307:    Neighbor-wise Collective on Mat

    9309:    Input Parameters:
    9310: +  A - the matrix
    9311: .  R - the projection matrix
    9312: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9313: -  fill - expected fill as ratio of nnz(C)/nnz(A), use PETSC_DEFAULT if you do not have a good estimate
    9314:           if the result is a dense matrix this is irrelevent

    9316:    Output Parameters:
    9317: .  C - the product matrix

    9319:    Notes:
    9320:    C will be created and must be destroyed by the user with MatDestroy().

    9322:    This routine is currently only implemented for pairs of AIJ matrices and classes
    9323:    which inherit from AIJ. Due to PETSc sparse matrix block row distribution among processes,
    9324:    parallel MatRARt is implemented via explicit transpose of R, which could be very expensive.
    9325:    We recommend using MatPtAP().

    9327:    Level: intermediate

    9329: .seealso: MatMatMult(), MatPtAP()
    9330: @*/
    9331: PetscErrorCode MatRARt(Mat A,Mat R,MatReuse scall,PetscReal fill,Mat *C)
    9332: {

    9336:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*C,5);
    9337:   if (scall == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");

    9339:   if (scall == MAT_INITIAL_MATRIX) {
    9340:     MatProductCreate(A,R,NULL,C);
    9341:     MatProductSetType(*C,MATPRODUCT_RARt);
    9342:     MatProductSetAlgorithm(*C,"default");
    9343:     MatProductSetFill(*C,fill);

    9345:     (*C)->product->api_user = PETSC_TRUE;
    9346:     MatProductSetFromOptions(*C);
    9347:     if (!(*C)->ops->productsymbolic) SETERRQ3(PetscObjectComm((PetscObject)(*C)),PETSC_ERR_SUP,"MatProduct %s not supported for A %s and R %s",MatProductTypes[MATPRODUCT_RARt],((PetscObject)A)->type_name,((PetscObject)R)->type_name);
    9348:     MatProductSymbolic(*C);
    9349:   } else { /* scall == MAT_REUSE_MATRIX */
    9350:     MatProductReplaceMats(A,R,NULL,*C);
    9351:   }

    9353:   MatProductNumeric(*C);
    9354:   if (A->symmetric_set && A->symmetric) {
    9355:     MatSetOption(*C,MAT_SYMMETRIC,PETSC_TRUE);
    9356:   }
    9357:   return(0);
    9358: }

    9361: static PetscErrorCode MatProduct_Private(Mat A,Mat B,MatReuse scall,PetscReal fill,MatProductType ptype, Mat *C)
    9362: {

    9366:   if (scall == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");

    9368:   if (scall == MAT_INITIAL_MATRIX) {
    9369:     PetscInfo1(A,"Calling MatProduct API with MAT_INITIAL_MATRIX and product type %s\n",MatProductTypes[ptype]);
    9370:     MatProductCreate(A,B,NULL,C);
    9371:     MatProductSetType(*C,ptype);
    9372:     MatProductSetAlgorithm(*C,MATPRODUCTALGORITHM_DEFAULT);
    9373:     MatProductSetFill(*C,fill);

    9375:     (*C)->product->api_user = PETSC_TRUE;
    9376:     MatProductSetFromOptions(*C);
    9377:     MatProductSymbolic(*C);
    9378:   } else { /* scall == MAT_REUSE_MATRIX */
    9379:     Mat_Product *product = (*C)->product;

    9381:     PetscInfo2(A,"Calling MatProduct API with MAT_REUSE_MATRIX %s product present and product type %s\n",product ? "with" : "without",MatProductTypes[ptype]);
    9382:     if (!product) {
    9383:       /* user provide the dense matrix *C without calling MatProductCreate() */
    9384:       PetscBool isdense;

    9386:       PetscObjectBaseTypeCompareAny((PetscObject)(*C),&isdense,MATSEQDENSE,MATMPIDENSE,"");
    9387:       if (isdense) {
    9388:         /* user wants to reuse an assembled dense matrix */
    9389:         /* Create product -- see MatCreateProduct() */
    9390:         MatProductCreate_Private(A,B,NULL,*C);
    9391:         product = (*C)->product;
    9392:         product->fill     = fill;
    9393:         product->api_user = PETSC_TRUE;
    9394:         product->clear    = PETSC_TRUE;

    9396:         MatProductSetType(*C,ptype);
    9397:         MatProductSetFromOptions(*C);
    9398:         if (!(*C)->ops->productsymbolic) SETERRQ3(PetscObjectComm((PetscObject)(*C)),PETSC_ERR_SUP,"MatProduct %s not supported for %s and %s",MatProductTypes[ptype],((PetscObject)A)->type_name,((PetscObject)B)->type_name);
    9399:         MatProductSymbolic(*C);
    9400:       } else SETERRQ(PetscObjectComm((PetscObject)(*C)),PETSC_ERR_SUP,"Call MatProductCreate() first");
    9401:     } else { /* user may change input matrices A or B when REUSE */
    9402:       MatProductReplaceMats(A,B,NULL,*C);
    9403:     }
    9404:   }
    9405:   MatProductNumeric(*C);
    9406:   return(0);
    9407: }

    9409: /*@
    9410:    MatMatMult - Performs Matrix-Matrix Multiplication C=A*B.

    9412:    Neighbor-wise Collective on Mat

    9414:    Input Parameters:
    9415: +  A - the left matrix
    9416: .  B - the right matrix
    9417: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9418: -  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if you do not have a good estimate
    9419:           if the result is a dense matrix this is irrelevent

    9421:    Output Parameters:
    9422: .  C - the product matrix

    9424:    Notes:
    9425:    Unless scall is MAT_REUSE_MATRIX C will be created.

    9427:    MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call and C was obtained from a previous
    9428:    call to this function with MAT_INITIAL_MATRIX.

    9430:    To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value actually needed.

    9432:    If you have many matrices with the same non-zero structure to multiply, you should use MatProductCreate()/MatProductSymbolic(C)/ReplaceMats(), and call MatProductNumeric() repeatedly.

    9434:    In the special case where matrix B (and hence C) are dense you can create the correctly sized matrix C yourself and then call this routine with MAT_REUSE_MATRIX, rather than first having MatMatMult() create it for you. You can NEVER do this if the matrix C is sparse.

    9436:    Level: intermediate

    9438: .seealso: MatTransposeMatMult(), MatMatTransposeMult(), MatPtAP()
    9439: @*/
    9440: PetscErrorCode MatMatMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    9441: {

    9445:   MatProduct_Private(A,B,scall,fill,MATPRODUCT_AB,C);
    9446:   return(0);
    9447: }

    9449: /*@
    9450:    MatMatTransposeMult - Performs Matrix-Matrix Multiplication C=A*B^T.

    9452:    Neighbor-wise Collective on Mat

    9454:    Input Parameters:
    9455: +  A - the left matrix
    9456: .  B - the right matrix
    9457: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9458: -  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if not known

    9460:    Output Parameters:
    9461: .  C - the product matrix

    9463:    Notes:
    9464:    C will be created if MAT_INITIAL_MATRIX and must be destroyed by the user with MatDestroy().

    9466:    MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call

    9468:   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    9469:    actually needed.

    9471:    This routine is currently only implemented for pairs of SeqAIJ matrices, for the SeqDense class,
    9472:    and for pairs of MPIDense matrices.

    9474:    Options Database Keys:
    9475: .  -matmattransmult_mpidense_mpidense_via {allgatherv,cyclic} - Choose between algorthims for MPIDense matrices: the
    9476:                                                                 first redundantly copies the transposed B matrix on each process and requiers O(log P) communication complexity;
    9477:                                                                 the second never stores more than one portion of the B matrix at a time by requires O(P) communication complexity.

    9479:    Level: intermediate

    9481: .seealso: MatMatMult(), MatTransposeMatMult() MatPtAP()
    9482: @*/
    9483: PetscErrorCode MatMatTransposeMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    9484: {

    9488:   MatProduct_Private(A,B,scall,fill,MATPRODUCT_ABt,C);
    9489:   return(0);
    9490: }

    9492: /*@
    9493:    MatTransposeMatMult - Performs Matrix-Matrix Multiplication C=A^T*B.

    9495:    Neighbor-wise Collective on Mat

    9497:    Input Parameters:
    9498: +  A - the left matrix
    9499: .  B - the right matrix
    9500: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9501: -  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if not known

    9503:    Output Parameters:
    9504: .  C - the product matrix

    9506:    Notes:
    9507:    C will be created if MAT_INITIAL_MATRIX and must be destroyed by the user with MatDestroy().

    9509:    MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call.

    9511:   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    9512:    actually needed.

    9514:    This routine is currently implemented for pairs of AIJ matrices and pairs of SeqDense matrices and classes
    9515:    which inherit from SeqAIJ.  C will be of same type as the input matrices.

    9517:    Level: intermediate

    9519: .seealso: MatMatMult(), MatMatTransposeMult(), MatPtAP()
    9520: @*/
    9521: PetscErrorCode MatTransposeMatMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    9522: {

    9526:   MatProduct_Private(A,B,scall,fill,MATPRODUCT_AtB,C);
    9527:   return(0);
    9528: }

    9530: /*@
    9531:    MatMatMatMult - Performs Matrix-Matrix-Matrix Multiplication D=A*B*C.

    9533:    Neighbor-wise Collective on Mat

    9535:    Input Parameters:
    9536: +  A - the left matrix
    9537: .  B - the middle matrix
    9538: .  C - the right matrix
    9539: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9540: -  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
    9541:           if the result is a dense matrix this is irrelevent

    9543:    Output Parameters:
    9544: .  D - the product matrix

    9546:    Notes:
    9547:    Unless scall is MAT_REUSE_MATRIX D will be created.

    9549:    MAT_REUSE_MATRIX can only be used if the matrices A, B and C have the same nonzero pattern as in the previous call

    9551:    To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    9552:    actually needed.

    9554:    If you have many matrices with the same non-zero structure to multiply, you
    9555:    should use MAT_REUSE_MATRIX in all calls but the first or

    9557:    Level: intermediate

    9559: .seealso: MatMatMult, MatPtAP()
    9560: @*/
    9561: PetscErrorCode MatMatMatMult(Mat A,Mat B,Mat C,MatReuse scall,PetscReal fill,Mat *D)
    9562: {

    9566:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*D,6);
    9567:   if (scall == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");

    9569:   if (scall == MAT_INITIAL_MATRIX) {
    9570:     MatProductCreate(A,B,C,D);
    9571:     MatProductSetType(*D,MATPRODUCT_ABC);
    9572:     MatProductSetAlgorithm(*D,"default");
    9573:     MatProductSetFill(*D,fill);

    9575:     (*D)->product->api_user = PETSC_TRUE;
    9576:     MatProductSetFromOptions(*D);
    9577:     if (!(*D)->ops->productsymbolic) SETERRQ4(PetscObjectComm((PetscObject)(*D)),PETSC_ERR_SUP,"MatProduct %s not supported for A %s, B %s and C %s",MatProductTypes[MATPRODUCT_ABC],((PetscObject)A)->type_name,((PetscObject)B)->type_name,((PetscObject)C)->type_name);
    9578:     MatProductSymbolic(*D);
    9579:   } else { /* user may change input matrices when REUSE */
    9580:     MatProductReplaceMats(A,B,C,*D);
    9581:   }
    9582:   MatProductNumeric(*D);
    9583:   return(0);
    9584: }

    9586: /*@
    9587:    MatCreateRedundantMatrix - Create redundant matrices and put them into processors of subcommunicators.

    9589:    Collective on Mat

    9591:    Input Parameters:
    9592: +  mat - the matrix
    9593: .  nsubcomm - the number of subcommunicators (= number of redundant parallel or sequential matrices)
    9594: .  subcomm - MPI communicator split from the communicator where mat resides in (or MPI_COMM_NULL if nsubcomm is used)
    9595: -  reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    9597:    Output Parameter:
    9598: .  matredundant - redundant matrix

    9600:    Notes:
    9601:    MAT_REUSE_MATRIX can only be used when the nonzero structure of the
    9602:    original matrix has not changed from that last call to MatCreateRedundantMatrix().

    9604:    This routine creates the duplicated matrices in subcommunicators; you should NOT create them before
    9605:    calling it.

    9607:    Level: advanced

    9610: .seealso: MatDestroy()
    9611: @*/
    9612: PetscErrorCode MatCreateRedundantMatrix(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,MatReuse reuse,Mat *matredundant)
    9613: {
    9615:   MPI_Comm       comm;
    9616:   PetscMPIInt    size;
    9617:   PetscInt       mloc_sub,nloc_sub,rstart,rend,M=mat->rmap->N,N=mat->cmap->N,bs=mat->rmap->bs;
    9618:   Mat_Redundant  *redund=NULL;
    9619:   PetscSubcomm   psubcomm=NULL;
    9620:   MPI_Comm       subcomm_in=subcomm;
    9621:   Mat            *matseq;
    9622:   IS             isrow,iscol;
    9623:   PetscBool      newsubcomm=PETSC_FALSE;

    9627:   if (nsubcomm && reuse == MAT_REUSE_MATRIX) {
    9630:   }

    9632:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    9633:   if (size == 1 || nsubcomm == 1) {
    9634:     if (reuse == MAT_INITIAL_MATRIX) {
    9635:       MatDuplicate(mat,MAT_COPY_VALUES,matredundant);
    9636:     } else {
    9637:       if (*matredundant == mat) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"MAT_REUSE_MATRIX means reuse the matrix passed in as the final argument, not the original matrix");
    9638:       MatCopy(mat,*matredundant,SAME_NONZERO_PATTERN);
    9639:     }
    9640:     return(0);
    9641:   }

    9643:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    9644:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    9645:   MatCheckPreallocated(mat,1);

    9647:   PetscLogEventBegin(MAT_RedundantMat,mat,0,0,0);
    9648:   if (subcomm_in == MPI_COMM_NULL && reuse == MAT_INITIAL_MATRIX) { /* get subcomm if user does not provide subcomm */
    9649:     /* create psubcomm, then get subcomm */
    9650:     PetscObjectGetComm((PetscObject)mat,&comm);
    9651:     MPI_Comm_size(comm,&size);
    9652:     if (nsubcomm < 1 || nsubcomm > size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"nsubcomm must between 1 and %D",size);

    9654:     PetscSubcommCreate(comm,&psubcomm);
    9655:     PetscSubcommSetNumber(psubcomm,nsubcomm);
    9656:     PetscSubcommSetType(psubcomm,PETSC_SUBCOMM_CONTIGUOUS);
    9657:     PetscSubcommSetFromOptions(psubcomm);
    9658:     PetscCommDuplicate(PetscSubcommChild(psubcomm),&subcomm,NULL);
    9659:     newsubcomm = PETSC_TRUE;
    9660:     PetscSubcommDestroy(&psubcomm);
    9661:   }

    9663:   /* get isrow, iscol and a local sequential matrix matseq[0] */
    9664:   if (reuse == MAT_INITIAL_MATRIX) {
    9665:     mloc_sub = PETSC_DECIDE;
    9666:     nloc_sub = PETSC_DECIDE;
    9667:     if (bs < 1) {
    9668:       PetscSplitOwnership(subcomm,&mloc_sub,&M);
    9669:       PetscSplitOwnership(subcomm,&nloc_sub,&N);
    9670:     } else {
    9671:       PetscSplitOwnershipBlock(subcomm,bs,&mloc_sub,&M);
    9672:       PetscSplitOwnershipBlock(subcomm,bs,&nloc_sub,&N);
    9673:     }
    9674:     MPI_Scan(&mloc_sub,&rend,1,MPIU_INT,MPI_SUM,subcomm);
    9675:     rstart = rend - mloc_sub;
    9676:     ISCreateStride(PETSC_COMM_SELF,mloc_sub,rstart,1,&isrow);
    9677:     ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol);
    9678:   } else { /* reuse == MAT_REUSE_MATRIX */
    9679:     if (*matredundant == mat) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"MAT_REUSE_MATRIX means reuse the matrix passed in as the final argument, not the original matrix");
    9680:     /* retrieve subcomm */
    9681:     PetscObjectGetComm((PetscObject)(*matredundant),&subcomm);
    9682:     redund = (*matredundant)->redundant;
    9683:     isrow  = redund->isrow;
    9684:     iscol  = redund->iscol;
    9685:     matseq = redund->matseq;
    9686:   }
    9687:   MatCreateSubMatrices(mat,1,&isrow,&iscol,reuse,&matseq);

    9689:   /* get matredundant over subcomm */
    9690:   if (reuse == MAT_INITIAL_MATRIX) {
    9691:     MatCreateMPIMatConcatenateSeqMat(subcomm,matseq[0],nloc_sub,reuse,matredundant);

    9693:     /* create a supporting struct and attach it to C for reuse */
    9694:     PetscNewLog(*matredundant,&redund);
    9695:     (*matredundant)->redundant = redund;
    9696:     redund->isrow              = isrow;
    9697:     redund->iscol              = iscol;
    9698:     redund->matseq             = matseq;
    9699:     if (newsubcomm) {
    9700:       redund->subcomm          = subcomm;
    9701:     } else {
    9702:       redund->subcomm          = MPI_COMM_NULL;
    9703:     }
    9704:   } else {
    9705:     MatCreateMPIMatConcatenateSeqMat(subcomm,matseq[0],PETSC_DECIDE,reuse,matredundant);
    9706:   }
    9707:   PetscLogEventEnd(MAT_RedundantMat,mat,0,0,0);
    9708:   return(0);
    9709: }

    9711: /*@C
    9712:    MatGetMultiProcBlock - Create multiple [bjacobi] 'parallel submatrices' from
    9713:    a given 'mat' object. Each submatrix can span multiple procs.

    9715:    Collective on Mat

    9717:    Input Parameters:
    9718: +  mat - the matrix
    9719: .  subcomm - the subcommunicator obtained by com_split(comm)
    9720: -  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    9722:    Output Parameter:
    9723: .  subMat - 'parallel submatrices each spans a given subcomm

    9725:   Notes:
    9726:   The submatrix partition across processors is dictated by 'subComm' a
    9727:   communicator obtained by com_split(comm). The comm_split
    9728:   is not restriced to be grouped with consecutive original ranks.

    9730:   Due the comm_split() usage, the parallel layout of the submatrices
    9731:   map directly to the layout of the original matrix [wrt the local
    9732:   row,col partitioning]. So the original 'DiagonalMat' naturally maps
    9733:   into the 'DiagonalMat' of the subMat, hence it is used directly from
    9734:   the subMat. However the offDiagMat looses some columns - and this is
    9735:   reconstructed with MatSetValues()

    9737:   Level: advanced

    9740: .seealso: MatCreateSubMatrices()
    9741: @*/
    9742: PetscErrorCode   MatGetMultiProcBlock(Mat mat, MPI_Comm subComm, MatReuse scall,Mat *subMat)
    9743: {
    9745:   PetscMPIInt    commsize,subCommSize;

    9748:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&commsize);
    9749:   MPI_Comm_size(subComm,&subCommSize);
    9750:   if (subCommSize > commsize) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"CommSize %D < SubCommZize %D",commsize,subCommSize);

    9752:   if (scall == MAT_REUSE_MATRIX && *subMat == mat) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"MAT_REUSE_MATRIX means reuse the matrix passed in as the final argument, not the original matrix");
    9753:   PetscLogEventBegin(MAT_GetMultiProcBlock,mat,0,0,0);
    9754:   (*mat->ops->getmultiprocblock)(mat,subComm,scall,subMat);
    9755:   PetscLogEventEnd(MAT_GetMultiProcBlock,mat,0,0,0);
    9756:   return(0);
    9757: }

    9759: /*@
    9760:    MatGetLocalSubMatrix - Gets a reference to a submatrix specified in local numbering

    9762:    Not Collective

    9764:    Input Arguments:
    9765: +  mat - matrix to extract local submatrix from
    9766: .  isrow - local row indices for submatrix
    9767: -  iscol - local column indices for submatrix

    9769:    Output Arguments:
    9770: .  submat - the submatrix

    9772:    Level: intermediate

    9774:    Notes:
    9775:    The submat should be returned with MatRestoreLocalSubMatrix().

    9777:    Depending on the format of mat, the returned submat may not implement MatMult().  Its communicator may be
    9778:    the same as mat, it may be PETSC_COMM_SELF, or some other subcomm of mat's.

    9780:    The submat always implements MatSetValuesLocal().  If isrow and iscol have the same block size, then
    9781:    MatSetValuesBlockedLocal() will also be implemented.

    9783:    The mat must have had a ISLocalToGlobalMapping provided to it with MatSetLocalToGlobalMapping(). Note that
    9784:    matrices obtained with DMCreateMatrix() generally already have the local to global mapping provided.

    9786: .seealso: MatRestoreLocalSubMatrix(), MatCreateLocalRef(), MatSetLocalToGlobalMapping()
    9787: @*/
    9788: PetscErrorCode MatGetLocalSubMatrix(Mat mat,IS isrow,IS iscol,Mat *submat)
    9789: {

    9798:   if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Matrix must have local to global mapping provided before this call");

    9800:   if (mat->ops->getlocalsubmatrix) {
    9801:     (*mat->ops->getlocalsubmatrix)(mat,isrow,iscol,submat);
    9802:   } else {
    9803:     MatCreateLocalRef(mat,isrow,iscol,submat);
    9804:   }
    9805:   return(0);
    9806: }

    9808: /*@
    9809:    MatRestoreLocalSubMatrix - Restores a reference to a submatrix specified in local numbering

    9811:    Not Collective

    9813:    Input Arguments:
    9814:    mat - matrix to extract local submatrix from
    9815:    isrow - local row indices for submatrix
    9816:    iscol - local column indices for submatrix
    9817:    submat - the submatrix

    9819:    Level: intermediate

    9821: .seealso: MatGetLocalSubMatrix()
    9822: @*/
    9823: PetscErrorCode MatRestoreLocalSubMatrix(Mat mat,IS isrow,IS iscol,Mat *submat)
    9824: {

    9833:   if (*submat) {
    9835:   }

    9837:   if (mat->ops->restorelocalsubmatrix) {
    9838:     (*mat->ops->restorelocalsubmatrix)(mat,isrow,iscol,submat);
    9839:   } else {
    9840:     MatDestroy(submat);
    9841:   }
    9842:   *submat = NULL;
    9843:   return(0);
    9844: }

    9846: /* --------------------------------------------------------*/
    9847: /*@
    9848:    MatFindZeroDiagonals - Finds all the rows of a matrix that have zero or no diagonal entry in the matrix

    9850:    Collective on Mat

    9852:    Input Parameter:
    9853: .  mat - the matrix

    9855:    Output Parameter:
    9856: .  is - if any rows have zero diagonals this contains the list of them

    9858:    Level: developer

    9860: .seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    9861: @*/
    9862: PetscErrorCode MatFindZeroDiagonals(Mat mat,IS *is)
    9863: {

    9869:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    9870:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

    9872:   if (!mat->ops->findzerodiagonals) {
    9873:     Vec                diag;
    9874:     const PetscScalar *a;
    9875:     PetscInt          *rows;
    9876:     PetscInt           rStart, rEnd, r, nrow = 0;

    9878:     MatCreateVecs(mat, &diag, NULL);
    9879:     MatGetDiagonal(mat, diag);
    9880:     MatGetOwnershipRange(mat, &rStart, &rEnd);
    9881:     VecGetArrayRead(diag, &a);
    9882:     for (r = 0; r < rEnd-rStart; ++r) if (a[r] == 0.0) ++nrow;
    9883:     PetscMalloc1(nrow, &rows);
    9884:     nrow = 0;
    9885:     for (r = 0; r < rEnd-rStart; ++r) if (a[r] == 0.0) rows[nrow++] = r+rStart;
    9886:     VecRestoreArrayRead(diag, &a);
    9887:     VecDestroy(&diag);
    9888:     ISCreateGeneral(PetscObjectComm((PetscObject) mat), nrow, rows, PETSC_OWN_POINTER, is);
    9889:   } else {
    9890:     (*mat->ops->findzerodiagonals)(mat, is);
    9891:   }
    9892:   return(0);
    9893: }

    9895: /*@
    9896:    MatFindOffBlockDiagonalEntries - Finds all the rows of a matrix that have entries outside of the main diagonal block (defined by the matrix block size)

    9898:    Collective on Mat

    9900:    Input Parameter:
    9901: .  mat - the matrix

    9903:    Output Parameter:
    9904: .  is - contains the list of rows with off block diagonal entries

    9906:    Level: developer

    9908: .seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    9909: @*/
    9910: PetscErrorCode MatFindOffBlockDiagonalEntries(Mat mat,IS *is)
    9911: {

    9917:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    9918:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

    9920:   if (!mat->ops->findoffblockdiagonalentries) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s does not have a find off block diagonal entries defined",((PetscObject)mat)->type_name);
    9921:   (*mat->ops->findoffblockdiagonalentries)(mat,is);
    9922:   return(0);
    9923: }

    9925: /*@C
    9926:   MatInvertBlockDiagonal - Inverts the block diagonal entries.

    9928:   Collective on Mat

    9930:   Input Parameters:
    9931: . mat - the matrix

    9933:   Output Parameters:
    9934: . values - the block inverses in column major order (FORTRAN-like)

    9936:    Note:
    9937:    This routine is not available from Fortran.

    9939:   Level: advanced

    9941: .seealso: MatInvertBockDiagonalMat
    9942: @*/
    9943: PetscErrorCode MatInvertBlockDiagonal(Mat mat,const PetscScalar **values)
    9944: {

    9949:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    9950:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    9951:   if (!mat->ops->invertblockdiagonal) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for type %s",((PetscObject)mat)->type_name);
    9952:   (*mat->ops->invertblockdiagonal)(mat,values);
    9953:   return(0);
    9954: }

    9956: /*@C
    9957:   MatInvertVariableBlockDiagonal - Inverts the block diagonal entries.

    9959:   Collective on Mat

    9961:   Input Parameters:
    9962: + mat - the matrix
    9963: . nblocks - the number of blocks
    9964: - bsizes - the size of each block

    9966:   Output Parameters:
    9967: . values - the block inverses in column major order (FORTRAN-like)

    9969:    Note:
    9970:    This routine is not available from Fortran.

    9972:   Level: advanced

    9974: .seealso: MatInvertBockDiagonal()
    9975: @*/
    9976: PetscErrorCode MatInvertVariableBlockDiagonal(Mat mat,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *values)
    9977: {

    9982:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    9983:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    9984:   if (!mat->ops->invertvariableblockdiagonal) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for type",((PetscObject)mat)->type_name);
    9985:   (*mat->ops->invertvariableblockdiagonal)(mat,nblocks,bsizes,values);
    9986:   return(0);
    9987: }

    9989: /*@
    9990:   MatInvertBlockDiagonalMat - set matrix C to be the inverted block diagonal of matrix A

    9992:   Collective on Mat

    9994:   Input Parameters:
    9995: . A - the matrix

    9997:   Output Parameters:
    9998: . C - matrix with inverted block diagonal of A.  This matrix should be created and may have its type set.

    10000:   Notes: the blocksize of the matrix is used to determine the blocks on the diagonal of C

    10002:   Level: advanced

    10004: .seealso: MatInvertBockDiagonal()
    10005: @*/
    10006: PetscErrorCode MatInvertBlockDiagonalMat(Mat A,Mat C)
    10007: {
    10008:   PetscErrorCode     ierr;
    10009:   const PetscScalar *vals;
    10010:   PetscInt          *dnnz;
    10011:   PetscInt           M,N,m,n,rstart,rend,bs,i,j;

    10014:   MatInvertBlockDiagonal(A,&vals);
    10015:   MatGetBlockSize(A,&bs);
    10016:   MatGetSize(A,&M,&N);
    10017:   MatGetLocalSize(A,&m,&n);
    10018:   MatSetSizes(C,m,n,M,N);
    10019:   MatSetBlockSize(C,bs);
    10020:   PetscMalloc1(m/bs,&dnnz);
    10021:   for (j = 0; j < m/bs; j++) dnnz[j] = 1;
    10022:   MatXAIJSetPreallocation(C,bs,dnnz,NULL,NULL,NULL);
    10023:   PetscFree(dnnz);
    10024:   MatGetOwnershipRange(C,&rstart,&rend);
    10025:   MatSetOption(C,MAT_ROW_ORIENTED,PETSC_FALSE);
    10026:   for (i = rstart/bs; i < rend/bs; i++) {
    10027:     MatSetValuesBlocked(C,1,&i,1,&i,&vals[(i-rstart/bs)*bs*bs],INSERT_VALUES);
    10028:   }
    10029:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    10030:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    10031:   MatSetOption(C,MAT_ROW_ORIENTED,PETSC_TRUE);
    10032:   return(0);
    10033: }

    10035: /*@C
    10036:     MatTransposeColoringDestroy - Destroys a coloring context for matrix product C=A*B^T that was created
    10037:     via MatTransposeColoringCreate().

    10039:     Collective on MatTransposeColoring

    10041:     Input Parameter:
    10042: .   c - coloring context

    10044:     Level: intermediate

    10046: .seealso: MatTransposeColoringCreate()
    10047: @*/
    10048: PetscErrorCode MatTransposeColoringDestroy(MatTransposeColoring *c)
    10049: {
    10050:   PetscErrorCode       ierr;
    10051:   MatTransposeColoring matcolor=*c;

    10054:   if (!matcolor) return(0);
    10055:   if (--((PetscObject)matcolor)->refct > 0) {matcolor = NULL; return(0);}

    10057:   PetscFree3(matcolor->ncolumns,matcolor->nrows,matcolor->colorforrow);
    10058:   PetscFree(matcolor->rows);
    10059:   PetscFree(matcolor->den2sp);
    10060:   PetscFree(matcolor->colorforcol);
    10061:   PetscFree(matcolor->columns);
    10062:   if (matcolor->brows>0) {
    10063:     PetscFree(matcolor->lstart);
    10064:   }
    10065:   PetscHeaderDestroy(c);
    10066:   return(0);
    10067: }

    10069: /*@C
    10070:     MatTransColoringApplySpToDen - Given a symbolic matrix product C=A*B^T for which
    10071:     a MatTransposeColoring context has been created, computes a dense B^T by Apply
    10072:     MatTransposeColoring to sparse B.

    10074:     Collective on MatTransposeColoring

    10076:     Input Parameters:
    10077: +   B - sparse matrix B
    10078: .   Btdense - symbolic dense matrix B^T
    10079: -   coloring - coloring context created with MatTransposeColoringCreate()

    10081:     Output Parameter:
    10082: .   Btdense - dense matrix B^T

    10084:     Level: advanced

    10086:      Notes:
    10087:     These are used internally for some implementations of MatRARt()

    10089: .seealso: MatTransposeColoringCreate(), MatTransposeColoringDestroy(), MatTransColoringApplyDenToSp()

    10091: @*/
    10092: PetscErrorCode MatTransColoringApplySpToDen(MatTransposeColoring coloring,Mat B,Mat Btdense)
    10093: {

    10101:   if (!B->ops->transcoloringapplysptoden) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for this matrix type %s",((PetscObject)B)->type_name);
    10102:   (B->ops->transcoloringapplysptoden)(coloring,B,Btdense);
    10103:   return(0);
    10104: }

    10106: /*@C
    10107:     MatTransColoringApplyDenToSp - Given a symbolic matrix product Csp=A*B^T for which
    10108:     a MatTransposeColoring context has been created and a dense matrix Cden=A*Btdense
    10109:     in which Btdens is obtained from MatTransColoringApplySpToDen(), recover sparse matrix
    10110:     Csp from Cden.

    10112:     Collective on MatTransposeColoring

    10114:     Input Parameters:
    10115: +   coloring - coloring context created with MatTransposeColoringCreate()
    10116: -   Cden - matrix product of a sparse matrix and a dense matrix Btdense

    10118:     Output Parameter:
    10119: .   Csp - sparse matrix

    10121:     Level: advanced

    10123:      Notes:
    10124:     These are used internally for some implementations of MatRARt()

    10126: .seealso: MatTransposeColoringCreate(), MatTransposeColoringDestroy(), MatTransColoringApplySpToDen()

    10128: @*/
    10129: PetscErrorCode MatTransColoringApplyDenToSp(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
    10130: {

    10138:   if (!Csp->ops->transcoloringapplydentosp) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for this matrix type %s",((PetscObject)Csp)->type_name);
    10139:   (Csp->ops->transcoloringapplydentosp)(matcoloring,Cden,Csp);
    10140:   MatAssemblyBegin(Csp,MAT_FINAL_ASSEMBLY);
    10141:   MatAssemblyEnd(Csp,MAT_FINAL_ASSEMBLY);
    10142:   return(0);
    10143: }

    10145: /*@C
    10146:    MatTransposeColoringCreate - Creates a matrix coloring context for matrix product C=A*B^T.

    10148:    Collective on Mat

    10150:    Input Parameters:
    10151: +  mat - the matrix product C
    10152: -  iscoloring - the coloring of the matrix; usually obtained with MatColoringCreate() or DMCreateColoring()

    10154:     Output Parameter:
    10155: .   color - the new coloring context

    10157:     Level: intermediate

    10159: .seealso: MatTransposeColoringDestroy(),  MatTransColoringApplySpToDen(),
    10160:            MatTransColoringApplyDenToSp()
    10161: @*/
    10162: PetscErrorCode MatTransposeColoringCreate(Mat mat,ISColoring iscoloring,MatTransposeColoring *color)
    10163: {
    10164:   MatTransposeColoring c;
    10165:   MPI_Comm             comm;
    10166:   PetscErrorCode       ierr;

    10169:   PetscLogEventBegin(MAT_TransposeColoringCreate,mat,0,0,0);
    10170:   PetscObjectGetComm((PetscObject)mat,&comm);
    10171:   PetscHeaderCreate(c,MAT_TRANSPOSECOLORING_CLASSID,"MatTransposeColoring","Matrix product C=A*B^T via coloring","Mat",comm,MatTransposeColoringDestroy,NULL);

    10173:   c->ctype = iscoloring->ctype;
    10174:   if (mat->ops->transposecoloringcreate) {
    10175:     (*mat->ops->transposecoloringcreate)(mat,iscoloring,c);
    10176:   } else SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Code not yet written for matrix type %s",((PetscObject)mat)->type_name);

    10178:   *color = c;
    10179:   PetscLogEventEnd(MAT_TransposeColoringCreate,mat,0,0,0);
    10180:   return(0);
    10181: }

    10183: /*@
    10184:       MatGetNonzeroState - Returns a 64 bit integer representing the current state of nonzeros in the matrix. If the
    10185:         matrix has had no new nonzero locations added to the matrix since the previous call then the value will be the
    10186:         same, otherwise it will be larger

    10188:      Not Collective

    10190:   Input Parameter:
    10191: .    A  - the matrix

    10193:   Output Parameter:
    10194: .    state - the current state

    10196:   Notes:
    10197:     You can only compare states from two different calls to the SAME matrix, you cannot compare calls between
    10198:          different matrices

    10200:   Level: intermediate

    10202: @*/
    10203: PetscErrorCode MatGetNonzeroState(Mat mat,PetscObjectState *state)
    10204: {
    10207:   *state = mat->nonzerostate;
    10208:   return(0);
    10209: }

    10211: /*@
    10212:       MatCreateMPIMatConcatenateSeqMat - Creates a single large PETSc matrix by concatenating sequential
    10213:                  matrices from each processor

    10215:     Collective

    10217:    Input Parameters:
    10218: +    comm - the communicators the parallel matrix will live on
    10219: .    seqmat - the input sequential matrices
    10220: .    n - number of local columns (or PETSC_DECIDE)
    10221: -    reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    10223:    Output Parameter:
    10224: .    mpimat - the parallel matrix generated

    10226:     Level: advanced

    10228:    Notes:
    10229:     The number of columns of the matrix in EACH processor MUST be the same.

    10231: @*/
    10232: PetscErrorCode MatCreateMPIMatConcatenateSeqMat(MPI_Comm comm,Mat seqmat,PetscInt n,MatReuse reuse,Mat *mpimat)
    10233: {

    10237:   if (!seqmat->ops->creatempimatconcatenateseqmat) SETERRQ1(PetscObjectComm((PetscObject)seqmat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)seqmat)->type_name);
    10238:   if (reuse == MAT_REUSE_MATRIX && seqmat == *mpimat) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"MAT_REUSE_MATRIX means reuse the matrix passed in as the final argument, not the original matrix");

    10240:   PetscLogEventBegin(MAT_Merge,seqmat,0,0,0);
    10241:   (*seqmat->ops->creatempimatconcatenateseqmat)(comm,seqmat,n,reuse,mpimat);
    10242:   PetscLogEventEnd(MAT_Merge,seqmat,0,0,0);
    10243:   return(0);
    10244: }

    10246: /*@
    10247:      MatSubdomainsCreateCoalesce - Creates index subdomains by coalescing adjacent
    10248:                  ranks' ownership ranges.

    10250:     Collective on A

    10252:    Input Parameters:
    10253: +    A   - the matrix to create subdomains from
    10254: -    N   - requested number of subdomains

    10257:    Output Parameters:
    10258: +    n   - number of subdomains resulting on this rank
    10259: -    iss - IS list with indices of subdomains on this rank

    10261:     Level: advanced

    10263:     Notes:
    10264:     number of subdomains must be smaller than the communicator size
    10265: @*/
    10266: PetscErrorCode MatSubdomainsCreateCoalesce(Mat A,PetscInt N,PetscInt *n,IS *iss[])
    10267: {
    10268:   MPI_Comm        comm,subcomm;
    10269:   PetscMPIInt     size,rank,color;
    10270:   PetscInt        rstart,rend,k;
    10271:   PetscErrorCode  ierr;

    10274:   PetscObjectGetComm((PetscObject)A,&comm);
    10275:   MPI_Comm_size(comm,&size);
    10276:   MPI_Comm_rank(comm,&rank);
    10277:   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);
    10278:   *n = 1;
    10279:   k = ((PetscInt)size)/N + ((PetscInt)size%N>0); /* There are up to k ranks to a color */
    10280:   color = rank/k;
    10281:   MPI_Comm_split(comm,color,rank,&subcomm);
    10282:   PetscMalloc1(1,iss);
    10283:   MatGetOwnershipRange(A,&rstart,&rend);
    10284:   ISCreateStride(subcomm,rend-rstart,rstart,1,iss[0]);
    10285:   MPI_Comm_free(&subcomm);
    10286:   return(0);
    10287: }

    10289: /*@
    10290:    MatGalerkin - Constructs the coarse grid problem via Galerkin projection.

    10292:    If the interpolation and restriction operators are the same, uses MatPtAP.
    10293:    If they are not the same, use MatMatMatMult.

    10295:    Once the coarse grid problem is constructed, correct for interpolation operators
    10296:    that are not of full rank, which can legitimately happen in the case of non-nested
    10297:    geometric multigrid.

    10299:    Input Parameters:
    10300: +  restrct - restriction operator
    10301: .  dA - fine grid matrix
    10302: .  interpolate - interpolation operator
    10303: .  reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    10304: -  fill - expected fill, use PETSC_DEFAULT if you do not have a good estimate

    10306:    Output Parameters:
    10307: .  A - the Galerkin coarse matrix

    10309:    Options Database Key:
    10310: .  -pc_mg_galerkin <both,pmat,mat,none>

    10312:    Level: developer

    10314: .seealso: MatPtAP(), MatMatMatMult()
    10315: @*/
    10316: PetscErrorCode  MatGalerkin(Mat restrct, Mat dA, Mat interpolate, MatReuse reuse, PetscReal fill, Mat *A)
    10317: {
    10319:   IS             zerorows;
    10320:   Vec            diag;

    10323:   if (reuse == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");
    10324:   /* Construct the coarse grid matrix */
    10325:   if (interpolate == restrct) {
    10326:     MatPtAP(dA,interpolate,reuse,fill,A);
    10327:   } else {
    10328:     MatMatMatMult(restrct,dA,interpolate,reuse,fill,A);
    10329:   }

    10331:   /* If the interpolation matrix is not of full rank, A will have zero rows.
    10332:      This can legitimately happen in the case of non-nested geometric multigrid.
    10333:      In that event, we set the rows of the matrix to the rows of the identity,
    10334:      ignoring the equations (as the RHS will also be zero). */

    10336:   MatFindZeroRows(*A, &zerorows);

    10338:   if (zerorows != NULL) { /* if there are any zero rows */
    10339:     MatCreateVecs(*A, &diag, NULL);
    10340:     MatGetDiagonal(*A, diag);
    10341:     VecISSet(diag, zerorows, 1.0);
    10342:     MatDiagonalSet(*A, diag, INSERT_VALUES);
    10343:     VecDestroy(&diag);
    10344:     ISDestroy(&zerorows);
    10345:   }
    10346:   return(0);
    10347: }

    10349: /*@C
    10350:     MatSetOperation - Allows user to set a matrix operation for any matrix type

    10352:    Logically Collective on Mat

    10354:     Input Parameters:
    10355: +   mat - the matrix
    10356: .   op - the name of the operation
    10357: -   f - the function that provides the operation

    10359:    Level: developer

    10361:     Usage:
    10362: $      extern PetscErrorCode usermult(Mat,Vec,Vec);
    10363: $      MatCreateXXX(comm,...&A);
    10364: $      MatSetOperation(A,MATOP_MULT,(void(*)(void))usermult);

    10366:     Notes:
    10367:     See the file include/petscmat.h for a complete list of matrix
    10368:     operations, which all have the form MATOP_<OPERATION>, where
    10369:     <OPERATION> is the name (in all capital letters) of the
    10370:     user interface routine (e.g., MatMult() -> MATOP_MULT).

    10372:     All user-provided functions (except for MATOP_DESTROY) should have the same calling
    10373:     sequence as the usual matrix interface routines, since they
    10374:     are intended to be accessed via the usual matrix interface
    10375:     routines, e.g.,
    10376: $       MatMult(Mat,Vec,Vec) -> usermult(Mat,Vec,Vec)

    10378:     In particular each function MUST return an error code of 0 on success and
    10379:     nonzero on failure.

    10381:     This routine is distinct from MatShellSetOperation() in that it can be called on any matrix type.

    10383: .seealso: MatGetOperation(), MatCreateShell(), MatShellSetContext(), MatShellSetOperation()
    10384: @*/
    10385: PetscErrorCode MatSetOperation(Mat mat,MatOperation op,void (*f)(void))
    10386: {
    10389:   if (op == MATOP_VIEW && !mat->ops->viewnative && f != (void (*)(void))(mat->ops->view)) {
    10390:     mat->ops->viewnative = mat->ops->view;
    10391:   }
    10392:   (((void(**)(void))mat->ops)[op]) = f;
    10393:   return(0);
    10394: }

    10396: /*@C
    10397:     MatGetOperation - Gets a matrix operation for any matrix type.

    10399:     Not Collective

    10401:     Input Parameters:
    10402: +   mat - the matrix
    10403: -   op - the name of the operation

    10405:     Output Parameter:
    10406: .   f - the function that provides the operation

    10408:     Level: developer

    10410:     Usage:
    10411: $      PetscErrorCode (*usermult)(Mat,Vec,Vec);
    10412: $      MatGetOperation(A,MATOP_MULT,(void(**)(void))&usermult);

    10414:     Notes:
    10415:     See the file include/petscmat.h for a complete list of matrix
    10416:     operations, which all have the form MATOP_<OPERATION>, where
    10417:     <OPERATION> is the name (in all capital letters) of the
    10418:     user interface routine (e.g., MatMult() -> MATOP_MULT).

    10420:     This routine is distinct from MatShellGetOperation() in that it can be called on any matrix type.

    10422: .seealso: MatSetOperation(), MatCreateShell(), MatShellGetContext(), MatShellGetOperation()
    10423: @*/
    10424: PetscErrorCode MatGetOperation(Mat mat,MatOperation op,void(**f)(void))
    10425: {
    10428:   *f = (((void (**)(void))mat->ops)[op]);
    10429:   return(0);
    10430: }

    10432: /*@
    10433:     MatHasOperation - Determines whether the given matrix supports the particular
    10434:     operation.

    10436:    Not Collective

    10438:    Input Parameters:
    10439: +  mat - the matrix
    10440: -  op - the operation, for example, MATOP_GET_DIAGONAL

    10442:    Output Parameter:
    10443: .  has - either PETSC_TRUE or PETSC_FALSE

    10445:    Level: advanced

    10447:    Notes:
    10448:    See the file include/petscmat.h for a complete list of matrix
    10449:    operations, which all have the form MATOP_<OPERATION>, where
    10450:    <OPERATION> is the name (in all capital letters) of the
    10451:    user-level routine.  E.g., MatNorm() -> MATOP_NORM.

    10453: .seealso: MatCreateShell()
    10454: @*/
    10455: PetscErrorCode MatHasOperation(Mat mat,MatOperation op,PetscBool *has)
    10456: {

    10461:   /* symbolic product can be set before matrix type */
    10464:   if (mat->ops->hasoperation) {
    10465:     (*mat->ops->hasoperation)(mat,op,has);
    10466:   } else {
    10467:     if (((void**)mat->ops)[op]) *has =  PETSC_TRUE;
    10468:     else {
    10469:       *has = PETSC_FALSE;
    10470:       if (op == MATOP_CREATE_SUBMATRIX) {
    10471:         PetscMPIInt size;

    10473:         MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    10474:         if (size == 1) {
    10475:           MatHasOperation(mat,MATOP_CREATE_SUBMATRICES,has);
    10476:         }
    10477:       }
    10478:     }
    10479:   }
    10480:   return(0);
    10481: }

    10483: /*@
    10484:     MatHasCongruentLayouts - Determines whether the rows and columns layouts
    10485:     of the matrix are congruent

    10487:    Collective on mat

    10489:    Input Parameters:
    10490: .  mat - the matrix

    10492:    Output Parameter:
    10493: .  cong - either PETSC_TRUE or PETSC_FALSE

    10495:    Level: beginner

    10497:    Notes:

    10499: .seealso: MatCreate(), MatSetSizes()
    10500: @*/
    10501: PetscErrorCode MatHasCongruentLayouts(Mat mat,PetscBool *cong)
    10502: {

    10509:   if (!mat->rmap || !mat->cmap) {
    10510:     *cong = mat->rmap == mat->cmap ? PETSC_TRUE : PETSC_FALSE;
    10511:     return(0);
    10512:   }
    10513:   if (mat->congruentlayouts == PETSC_DECIDE) { /* first time we compare rows and cols layouts */
    10514:     PetscLayoutCompare(mat->rmap,mat->cmap,cong);
    10515:     if (*cong) mat->congruentlayouts = 1;
    10516:     else       mat->congruentlayouts = 0;
    10517:   } else *cong = mat->congruentlayouts ? PETSC_TRUE : PETSC_FALSE;
    10518:   return(0);
    10519: }

    10521: PetscErrorCode MatSetInf(Mat A)
    10522: {

    10526:   if (!A->ops->setinf) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"No support for this operation for this matrix type");
    10527:   (*A->ops->setinf)(A);
    10528:   return(0);
    10529: }