Actual source code: matrix.c

      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_QRFactorNumeric, MAT_QRFactorSymbolic, MAT_QRFactor;
     21: PetscLogEvent MAT_AssemblyEnd, MAT_SetValues, MAT_GetValues, MAT_GetRow, MAT_GetRowIJ, MAT_CreateSubMats, MAT_GetOrdering, MAT_RedundantMat, MAT_GetSeqNonzeroStructure;
     22: PetscLogEvent MAT_IncreaseOverlap, MAT_Partitioning, MAT_PartitioningND, MAT_Coarsen, MAT_ZeroEntries, MAT_Load, MAT_View, MAT_AXPY, MAT_FDColoringCreate;
     23: PetscLogEvent MAT_FDColoringSetUp, MAT_FDColoringApply,MAT_Transpose,MAT_FDColoringFunction, MAT_CreateSubMat;
     24: PetscLogEvent MAT_TransposeColoringCreate;
     25: PetscLogEvent MAT_MatMult, MAT_MatMultSymbolic, MAT_MatMultNumeric;
     26: PetscLogEvent MAT_PtAP, MAT_PtAPSymbolic, MAT_PtAPNumeric,MAT_RARt, MAT_RARtSymbolic, MAT_RARtNumeric;
     27: PetscLogEvent MAT_MatTransposeMult, MAT_MatTransposeMultSymbolic, MAT_MatTransposeMultNumeric;
     28: PetscLogEvent MAT_TransposeMatMult, MAT_TransposeMatMultSymbolic, MAT_TransposeMatMultNumeric;
     29: PetscLogEvent MAT_MatMatMult, MAT_MatMatMultSymbolic, MAT_MatMatMultNumeric;
     30: PetscLogEvent MAT_MultHermitianTranspose,MAT_MultHermitianTransposeAdd;
     31: PetscLogEvent MAT_Getsymtranspose, MAT_Getsymtransreduced, MAT_GetBrowsOfAcols;
     32: PetscLogEvent MAT_GetBrowsOfAocols, MAT_Getlocalmat, MAT_Getlocalmatcondensed, MAT_Seqstompi, MAT_Seqstompinum, MAT_Seqstompisym;
     33: PetscLogEvent MAT_Applypapt, MAT_Applypapt_numeric, MAT_Applypapt_symbolic, MAT_GetSequentialNonzeroStructure;
     34: PetscLogEvent MAT_GetMultiProcBlock;
     35: PetscLogEvent MAT_CUSPARSECopyToGPU, MAT_CUSPARSECopyFromGPU, MAT_CUSPARSEGenerateTranspose, MAT_CUSPARSESolveAnalysis;
     36: PetscLogEvent MAT_PreallCOO, MAT_SetVCOO;
     37: PetscLogEvent MAT_SetValuesBatch;
     38: PetscLogEvent MAT_ViennaCLCopyToGPU;
     39: PetscLogEvent MAT_DenseCopyToGPU, MAT_DenseCopyFromGPU;
     40: PetscLogEvent MAT_Merge,MAT_Residual,MAT_SetRandom;
     41: PetscLogEvent MAT_FactorFactS,MAT_FactorInvS;
     42: PetscLogEvent MATCOLORING_Apply,MATCOLORING_Comm,MATCOLORING_Local,MATCOLORING_ISCreate,MATCOLORING_SetUp,MATCOLORING_Weights;

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

     46: /*@
     47:    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,
     48:                   for sparse matrices that already have locations it fills the locations with random numbers

     50:    Logically Collective on Mat

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

     57:    Output Parameter:
     58: .  x  - the matrix

     60:    Example of Usage:
     61: .vb
     62:      PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
     63:      MatSetRandom(x,rctx);
     64:      PetscRandomDestroy(rctx);
     65: .ve

     67:    Level: intermediate

     70: .seealso: MatZeroEntries(), MatSetValues(), PetscRandomCreate(), PetscRandomDestroy()
     71: @*/
     72: PetscErrorCode MatSetRandom(Mat x,PetscRandom rctx)
     73: {
     75:   PetscRandom    randObj = NULL;

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

     84:   if (!rctx) {
     85:     MPI_Comm comm;
     86:     PetscObjectGetComm((PetscObject)x,&comm);
     87:     PetscRandomCreate(comm,&randObj);
     88:     PetscRandomSetFromOptions(randObj);
     89:     rctx = randObj;
     90:   }

     92:   PetscLogEventBegin(MAT_SetRandom,x,rctx,0,0);
     93:   (*x->ops->setrandom)(x,rctx);
     94:   PetscLogEventEnd(MAT_SetRandom,x,rctx,0,0);

     96:   MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY);
     97:   MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY);
     98:   PetscRandomDestroy(&randObj);
     99:   return(0);
    100: }

    102: /*@
    103:    MatFactorGetErrorZeroPivot - returns the pivot value that was determined to be zero and the row it occurred in

    105:    Logically Collective on Mat

    107:    Input Parameters:
    108: .  mat - the factored matrix

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

    115:    Level: advanced

    117:    Notes:
    118:     This routine does not work for factorizations done with external packages.

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

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

    124: .seealso: MatZeroEntries(), MatFactor(), MatGetFactor(), MatLUFactorSymbolic(), MatCholeskyFactorSymbolic(), MatFactorClearError(), MatFactorGetErrorZeroPivot()
    125: @*/
    126: PetscErrorCode MatFactorGetErrorZeroPivot(Mat mat,PetscReal *pivot,PetscInt *row)
    127: {
    130:   *pivot = mat->factorerror_zeropivot_value;
    131:   *row   = mat->factorerror_zeropivot_row;
    132:   return(0);
    133: }

    135: /*@
    136:    MatFactorGetError - gets the error code from a factorization

    138:    Logically Collective on Mat

    140:    Input Parameters:
    141: .  mat - the factored matrix

    143:    Output Parameter:
    144: .  err  - the error code

    146:    Level: advanced

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

    151: .seealso: MatZeroEntries(), MatFactor(), MatGetFactor(), MatLUFactorSymbolic(), MatCholeskyFactorSymbolic(), MatFactorClearError(), MatFactorGetErrorZeroPivot()
    152: @*/
    153: PetscErrorCode MatFactorGetError(Mat mat,MatFactorError *err)
    154: {
    157:   *err = mat->factorerrortype;
    158:   return(0);
    159: }

    161: /*@
    162:    MatFactorClearError - clears the error code in a factorization

    164:    Logically Collective on Mat

    166:    Input Parameter:
    167: .  mat - the factored matrix

    169:    Level: developer

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

    174: .seealso: MatZeroEntries(), MatFactor(), MatGetFactor(), MatLUFactorSymbolic(), MatCholeskyFactorSymbolic(), MatFactorGetError(), MatFactorGetErrorZeroPivot()
    175: @*/
    176: PetscErrorCode MatFactorClearError(Mat mat)
    177: {
    180:   mat->factorerrortype             = MAT_FACTOR_NOERROR;
    181:   mat->factorerror_zeropivot_value = 0.0;
    182:   mat->factorerror_zeropivot_row   = 0;
    183:   return(0);
    184: }

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

    194:   MatCreateVecs(mat,&r,&l);
    195:   if (!cols) { /* nonzero rows */
    196:     MatGetSize(mat,&N,NULL);
    197:     MatGetLocalSize(mat,&n,NULL);
    198:     VecSet(l,0.0);
    199:     VecSetRandom(r,NULL);
    200:     MatMult(mat,r,l);
    201:     VecGetArrayRead(l,&al);
    202:   } else { /* nonzero columns */
    203:     MatGetSize(mat,NULL,&N);
    204:     MatGetLocalSize(mat,NULL,&n);
    205:     VecSet(r,0.0);
    206:     VecSetRandom(l,NULL);
    207:     MatMultTranspose(mat,l,r);
    208:     VecGetArrayRead(r,&al);
    209:   }
    210:   if (tol <= 0.0) { for (i=0,nz=0;i<n;i++) if (al[i] != 0.0) nz++; }
    211:   else { for (i=0,nz=0;i<n;i++) if (PetscAbsScalar(al[i]) > tol) nz++; }
    212:   MPIU_Allreduce(&nz,&gnz,1,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)mat));
    213:   if (gnz != N) {
    214:     PetscInt *nzr;
    215:     PetscMalloc1(nz,&nzr);
    216:     if (nz) {
    217:       if (tol < 0) { for (i=0,nz=0;i<n;i++) if (al[i] != 0.0) nzr[nz++] = i; }
    218:       else { for (i=0,nz=0;i<n;i++) if (PetscAbsScalar(al[i]) > tol) nzr[nz++] = i; }
    219:     }
    220:     ISCreateGeneral(PetscObjectComm((PetscObject)mat),nz,nzr,PETSC_OWN_POINTER,nonzero);
    221:   } else *nonzero = NULL;
    222:   if (!cols) { /* nonzero rows */
    223:     VecRestoreArrayRead(l,&al);
    224:   } else {
    225:     VecRestoreArrayRead(r,&al);
    226:   }
    227:   VecDestroy(&l);
    228:   VecDestroy(&r);
    229:   return(0);
    230: }

    232: /*@
    233:       MatFindNonzeroRows - Locate all rows that are not completely zero in the matrix

    235:   Input Parameter:
    236: .    A  - the matrix

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

    241:   Notes:
    242:     keptrows is set to NULL if all rows are nonzero.

    244:   Level: intermediate

    246:  @*/
    247: PetscErrorCode MatFindNonzeroRows(Mat mat,IS *keptrows)
    248: {

    255:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    256:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    257:   if (!mat->ops->findnonzerorows) {
    258:     MatFindNonzeroRowsOrCols_Basic(mat,PETSC_FALSE,0.0,keptrows);
    259:   } else {
    260:     (*mat->ops->findnonzerorows)(mat,keptrows);
    261:   }
    262:   return(0);
    263: }

    265: /*@
    266:       MatFindZeroRows - Locate all rows that are completely zero in the matrix

    268:   Input Parameter:
    269: .    A  - the matrix

    271:   Output Parameter:
    272: .    zerorows - the rows that are completely zero

    274:   Notes:
    275:     zerorows is set to NULL if no rows are zero.

    277:   Level: intermediate

    279:  @*/
    280: PetscErrorCode MatFindZeroRows(Mat mat,IS *zerorows)
    281: {
    283:   IS keptrows;
    284:   PetscInt m, n;

    289:   MatFindNonzeroRows(mat, &keptrows);
    290:   /* MatFindNonzeroRows sets keptrows to NULL if there are no zero rows.
    291:      In keeping with this convention, we set zerorows to NULL if there are no zero
    292:      rows. */
    293:   if (keptrows == NULL) {
    294:     *zerorows = NULL;
    295:   } else {
    296:     MatGetOwnershipRange(mat,&m,&n);
    297:     ISComplement(keptrows,m,n,zerorows);
    298:     ISDestroy(&keptrows);
    299:   }
    300:   return(0);
    301: }

    303: /*@
    304:    MatGetDiagonalBlock - Returns the part of the matrix associated with the on-process coupling

    306:    Not Collective

    308:    Input Parameters:
    309: .   A - the matrix

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

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

    319:    Level: advanced

    321: @*/
    322: PetscErrorCode MatGetDiagonalBlock(Mat A,Mat *a)
    323: {

    330:   if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    331:   if (!A->ops->getdiagonalblock) {
    332:     PetscMPIInt size;
    333:     MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    334:     if (size == 1) {
    335:       *a = A;
    336:       return(0);
    337:     } else SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Not coded for matrix type %s",((PetscObject)A)->type_name);
    338:   }
    339:   (*A->ops->getdiagonalblock)(A,a);
    340:   return(0);
    341: }

    343: /*@
    344:    MatGetTrace - Gets the trace of a matrix. The sum of the diagonal entries.

    346:    Collective on Mat

    348:    Input Parameters:
    349: .  mat - the matrix

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

    354:    Level: advanced

    356: @*/
    357: PetscErrorCode MatGetTrace(Mat mat,PetscScalar *trace)
    358: {
    360:   Vec            diag;

    363:   MatCreateVecs(mat,&diag,NULL);
    364:   MatGetDiagonal(mat,diag);
    365:   VecSum(diag,trace);
    366:   VecDestroy(&diag);
    367:   return(0);
    368: }

    370: /*@
    371:    MatRealPart - Zeros out the imaginary part of the matrix

    373:    Logically Collective on Mat

    375:    Input Parameters:
    376: .  mat - the matrix

    378:    Level: advanced

    381: .seealso: MatImaginaryPart()
    382: @*/
    383: PetscErrorCode MatRealPart(Mat mat)
    384: {

    390:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    391:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    392:   if (!mat->ops->realpart) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    393:   MatCheckPreallocated(mat,1);
    394:   (*mat->ops->realpart)(mat);
    395:   return(0);
    396: }

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

    401:    Collective on Mat

    403:    Input Parameter:
    404: .  mat - the matrix

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

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

    413:    Level: advanced

    415: @*/
    416: PetscErrorCode MatGetGhosts(Mat mat,PetscInt *nghosts,const PetscInt *ghosts[])
    417: {

    423:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    424:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    425:   if (!mat->ops->getghosts) {
    426:     if (nghosts) *nghosts = 0;
    427:     if (ghosts) *ghosts = NULL;
    428:   } else {
    429:     (*mat->ops->getghosts)(mat,nghosts,ghosts);
    430:   }
    431:   return(0);
    432: }

    435: /*@
    436:    MatImaginaryPart - Moves the imaginary part of the matrix to the real part and zeros the imaginary part

    438:    Logically Collective on Mat

    440:    Input Parameters:
    441: .  mat - the matrix

    443:    Level: advanced

    446: .seealso: MatRealPart()
    447: @*/
    448: PetscErrorCode MatImaginaryPart(Mat mat)
    449: {

    455:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    456:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    457:   if (!mat->ops->imaginarypart) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    458:   MatCheckPreallocated(mat,1);
    459:   (*mat->ops->imaginarypart)(mat);
    460:   return(0);
    461: }

    463: /*@
    464:    MatMissingDiagonal - Determine if sparse matrix is missing a diagonal entry (or block entry for BAIJ matrices)

    466:    Not Collective

    468:    Input Parameter:
    469: .  mat - the matrix

    471:    Output Parameters:
    472: +  missing - is any diagonal missing
    473: -  dd - first diagonal entry that is missing (optional) on this process

    475:    Level: advanced

    478: .seealso: MatRealPart()
    479: @*/
    480: PetscErrorCode MatMissingDiagonal(Mat mat,PetscBool *missing,PetscInt *dd)
    481: {

    488:   if (!mat->assembled) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix %s",((PetscObject)mat)->type_name);
    489:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    490:   if (!mat->ops->missingdiagonal) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    491:   (*mat->ops->missingdiagonal)(mat,missing,dd);
    492:   return(0);
    493: }

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

    500:    Not Collective

    502:    Input Parameters:
    503: +  mat - the matrix
    504: -  row - the row to get

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

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

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

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

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

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

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

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

    550:    Level: advanced

    552: .seealso: MatRestoreRow(), MatSetValues(), MatGetValues(), MatCreateSubMatrices(), MatGetDiagonal()
    553: @*/
    554: PetscErrorCode MatGetRow(Mat mat,PetscInt row,PetscInt *ncols,const PetscInt *cols[],const PetscScalar *vals[])
    555: {
    557:   PetscInt       incols;

    562:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    563:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    564:   if (!mat->ops->getrow) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    565:   MatCheckPreallocated(mat,1);
    566:   if (row < mat->rmap->rstart || row >= mat->rmap->rend) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Only for local rows, %D not in [%D,%D)",row,mat->rmap->rstart,mat->rmap->rend);
    567:   PetscLogEventBegin(MAT_GetRow,mat,0,0,0);
    568:   (*mat->ops->getrow)(mat,row,&incols,(PetscInt**)cols,(PetscScalar**)vals);
    569:   if (ncols) *ncols = incols;
    570:   PetscLogEventEnd(MAT_GetRow,mat,0,0,0);
    571:   return(0);
    572: }

    574: /*@
    575:    MatConjugate - replaces the matrix values with their complex conjugates

    577:    Logically Collective on Mat

    579:    Input Parameters:
    580: .  mat - the matrix

    582:    Level: advanced

    584: .seealso:  VecConjugate()
    585: @*/
    586: PetscErrorCode MatConjugate(Mat mat)
    587: {
    588: #if defined(PETSC_USE_COMPLEX)

    593:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    594:   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);
    595:   (*mat->ops->conjugate)(mat);
    596: #else
    598: #endif
    599:   return(0);
    600: }

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

    605:    Not Collective

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

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

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

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

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

    635:    Level: advanced

    637: .seealso:  MatGetRow()
    638: @*/
    639: PetscErrorCode MatRestoreRow(Mat mat,PetscInt row,PetscInt *ncols,const PetscInt *cols[],const PetscScalar *vals[])
    640: {

    646:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    647:   if (!mat->ops->restorerow) return(0);
    648:   (*mat->ops->restorerow)(mat,row,ncols,(PetscInt **)cols,(PetscScalar **)vals);
    649:   if (ncols) *ncols = 0;
    650:   if (cols)  *cols = NULL;
    651:   if (vals)  *vals = NULL;
    652:   return(0);
    653: }

    655: /*@
    656:    MatGetRowUpperTriangular - Sets a flag to enable calls to MatGetRow() for matrix in MATSBAIJ format.
    657:    You should call MatRestoreRowUpperTriangular() after calling MatGetRow/MatRestoreRow() to disable the flag.

    659:    Not Collective

    661:    Input Parameters:
    662: .  mat - the matrix

    664:    Notes:
    665:    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.

    667:    Level: advanced

    669: .seealso: MatRestoreRowUpperTriangular()
    670: @*/
    671: PetscErrorCode MatGetRowUpperTriangular(Mat mat)
    672: {

    678:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    679:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    680:   MatCheckPreallocated(mat,1);
    681:   if (!mat->ops->getrowuppertriangular) return(0);
    682:   (*mat->ops->getrowuppertriangular)(mat);
    683:   return(0);
    684: }

    686: /*@
    687:    MatRestoreRowUpperTriangular - Disable calls to MatGetRow() for matrix in MATSBAIJ format.

    689:    Not Collective

    691:    Input Parameters:
    692: .  mat - the matrix

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

    698:    Level: advanced

    700: .seealso:  MatGetRowUpperTriangular()
    701: @*/
    702: PetscErrorCode MatRestoreRowUpperTriangular(Mat mat)
    703: {

    709:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    710:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    711:   MatCheckPreallocated(mat,1);
    712:   if (!mat->ops->restorerowuppertriangular) return(0);
    713:   (*mat->ops->restorerowuppertriangular)(mat);
    714:   return(0);
    715: }

    717: /*@C
    718:    MatSetOptionsPrefix - Sets the prefix used for searching for all
    719:    Mat options in the database.

    721:    Logically Collective on Mat

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

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

    731:    Level: advanced

    733: .seealso: MatSetFromOptions()
    734: @*/
    735: PetscErrorCode MatSetOptionsPrefix(Mat A,const char prefix[])
    736: {

    741:   PetscObjectSetOptionsPrefix((PetscObject)A,prefix);
    742:   return(0);
    743: }

    745: /*@C
    746:    MatAppendOptionsPrefix - Appends to the prefix used for searching for all
    747:    Mat options in the database.

    749:    Logically Collective on Mat

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

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

    759:    Level: advanced

    761: .seealso: MatGetOptionsPrefix()
    762: @*/
    763: PetscErrorCode MatAppendOptionsPrefix(Mat A,const char prefix[])
    764: {

    769:   PetscObjectAppendOptionsPrefix((PetscObject)A,prefix);
    770:   return(0);
    771: }

    773: /*@C
    774:    MatGetOptionsPrefix - Gets the prefix used for searching for all
    775:    Mat options in the database.

    777:    Not Collective

    779:    Input Parameter:
    780: .  A - the Mat context

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

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

    789:    Level: advanced

    791: .seealso: MatAppendOptionsPrefix()
    792: @*/
    793: PetscErrorCode MatGetOptionsPrefix(Mat A,const char *prefix[])
    794: {

    799:   PetscObjectGetOptionsPrefix((PetscObject)A,prefix);
    800:   return(0);
    801: }

    803: /*@
    804:    MatResetPreallocation - Reset mat to use the original nonzero pattern provided by users.

    806:    Collective on Mat

    808:    Input Parameters:
    809: .  A - the Mat context

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

    815:    Level: beginner

    817: .seealso: MatSeqAIJSetPreallocation(), MatMPIAIJSetPreallocation(), MatXAIJSetPreallocation()
    818: @*/
    819: PetscErrorCode MatResetPreallocation(Mat A)
    820: {

    826:   PetscUseMethod(A,"MatResetPreallocation_C",(Mat),(A));
    827:   return(0);
    828: }

    831: /*@
    832:    MatSetUp - Sets up the internal matrix data structures for later use.

    834:    Collective on Mat

    836:    Input Parameters:
    837: .  A - the Mat context

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

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

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

    846:    Level: beginner

    848: .seealso: MatCreate(), MatDestroy()
    849: @*/
    850: PetscErrorCode MatSetUp(Mat A)
    851: {
    852:   PetscMPIInt    size;

    857:   if (!((PetscObject)A)->type_name) {
    858:     MPI_Comm_size(PetscObjectComm((PetscObject)A), &size);
    859:     if (size == 1) {
    860:       MatSetType(A, MATSEQAIJ);
    861:     } else {
    862:       MatSetType(A, MATMPIAIJ);
    863:     }
    864:   }
    865:   if (!A->preallocated && A->ops->setup) {
    866:     PetscInfo(A,"Warning not preallocating matrix storage\n");
    867:     (*A->ops->setup)(A);
    868:   }
    869:   PetscLayoutSetUp(A->rmap);
    870:   PetscLayoutSetUp(A->cmap);
    871:   A->preallocated = PETSC_TRUE;
    872:   return(0);
    873: }

    875: #if defined(PETSC_HAVE_SAWS)
    876: #include <petscviewersaws.h>
    877: #endif

    879: /*@C
    880:    MatViewFromOptions - View from Options

    882:    Collective on Mat

    884:    Input Parameters:
    885: +  A - the Mat context
    886: .  obj - Optional object
    887: -  name - command line option

    889:    Level: intermediate
    890: .seealso:  Mat, MatView, PetscObjectViewFromOptions(), MatCreate()
    891: @*/
    892: PetscErrorCode  MatViewFromOptions(Mat A,PetscObject obj,const char name[])
    893: {

    898:   PetscObjectViewFromOptions((PetscObject)A,obj,name);
    899:   return(0);
    900: }

    902: /*@C
    903:    MatView - Visualizes a matrix object.

    905:    Collective on Mat

    907:    Input Parameters:
    908: +  mat - the matrix
    909: -  viewer - visualization context

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

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

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

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

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

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

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

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

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

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

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

    995:   PetscViewerGetFormat(viewer,&format);
    996:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    997:   if (size == 1 && format == PETSC_VIEWER_LOAD_BALANCE) return(0);

    999:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
    1000:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&isascii);
    1001:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSAWS,&issaws);
    1002:   if ((!isascii || (format != PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL)) && mat->factortype) {
    1003:     SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"No viewers for factored matrix except ASCII info or info_detail");
    1004:   }

    1006:   PetscLogEventBegin(MAT_View,mat,viewer,0,0);
    1007:   if (isascii) {
    1008:     if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ORDER,"Must call MatAssemblyBegin/End() before viewing matrix");
    1009:     PetscObjectPrintClassNamePrefixType((PetscObject)mat,viewer);
    1010:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1011:       MatNullSpace nullsp,transnullsp;

    1013:       PetscViewerASCIIPushTab(viewer);
    1014:       MatGetSize(mat,&rows,&cols);
    1015:       MatGetBlockSizes(mat,&rbs,&cbs);
    1016:       if (rbs != 1 || cbs != 1) {
    1017:         if (rbs != cbs) {PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D, rbs=%D, cbs=%D\n",rows,cols,rbs,cbs);}
    1018:         else            {PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D, bs=%D\n",rows,cols,rbs);}
    1019:       } else {
    1020:         PetscViewerASCIIPrintf(viewer,"rows=%D, cols=%D\n",rows,cols);
    1021:       }
    1022:       if (mat->factortype) {
    1023:         MatSolverType solver;
    1024:         MatFactorGetSolverType(mat,&solver);
    1025:         PetscViewerASCIIPrintf(viewer,"package used to perform factorization: %s\n",solver);
    1026:       }
    1027:       if (mat->ops->getinfo) {
    1028:         MatInfo info;
    1029:         MatGetInfo(mat,MAT_GLOBAL_SUM,&info);
    1030:         PetscViewerASCIIPrintf(viewer,"total: nonzeros=%.f, allocated nonzeros=%.f\n",info.nz_used,info.nz_allocated);
    1031:         if (!mat->factortype) {
    1032:           PetscViewerASCIIPrintf(viewer,"total number of mallocs used during MatSetValues calls=%D\n",(PetscInt)info.mallocs);
    1033:         }
    1034:       }
    1035:       MatGetNullSpace(mat,&nullsp);
    1036:       MatGetTransposeNullSpace(mat,&transnullsp);
    1037:       if (nullsp) {PetscViewerASCIIPrintf(viewer,"  has attached null space\n");}
    1038:       if (transnullsp && transnullsp != nullsp) {PetscViewerASCIIPrintf(viewer,"  has attached transposed null space\n");}
    1039:       MatGetNearNullSpace(mat,&nullsp);
    1040:       if (nullsp) {PetscViewerASCIIPrintf(viewer,"  has attached near null space\n");}
    1041:       PetscViewerASCIIPushTab(viewer);
    1042:       MatProductView(mat,viewer);
    1043:       PetscViewerASCIIPopTab(viewer);
    1044:     }
    1045:   } else if (issaws) {
    1046: #if defined(PETSC_HAVE_SAWS)
    1047:     PetscMPIInt rank;

    1049:     PetscObjectName((PetscObject)mat);
    1050:     MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
    1051:     if (!((PetscObject)mat)->amsmem && !rank) {
    1052:       PetscObjectViewSAWs((PetscObject)mat,viewer);
    1053:     }
    1054: #endif
    1055:   } else if (isstring) {
    1056:     const char *type;
    1057:     MatGetType(mat,&type);
    1058:     PetscViewerStringSPrintf(viewer," MatType: %-7.7s",type);
    1059:     if (mat->ops->view) {(*mat->ops->view)(mat,viewer);}
    1060:   }
    1061:   if ((format == PETSC_VIEWER_NATIVE || format == PETSC_VIEWER_LOAD_BALANCE) && mat->ops->viewnative) {
    1062:     PetscViewerASCIIPushTab(viewer);
    1063:     (*mat->ops->viewnative)(mat,viewer);
    1064:     PetscViewerASCIIPopTab(viewer);
    1065:   } else if (mat->ops->view) {
    1066:     PetscViewerASCIIPushTab(viewer);
    1067:     (*mat->ops->view)(mat,viewer);
    1068:     PetscViewerASCIIPopTab(viewer);
    1069:   }
    1070:   if (isascii) {
    1071:     PetscViewerGetFormat(viewer,&format);
    1072:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1073:       PetscViewerASCIIPopTab(viewer);
    1074:     }
    1075:   }
    1076:   PetscLogEventEnd(MAT_View,mat,viewer,0,0);
    1077:   return(0);
    1078: }

    1080: #if defined(PETSC_USE_DEBUG)
    1081: #include <../src/sys/totalview/tv_data_display.h>
    1082: PETSC_UNUSED static int TV_display_type(const struct _p_Mat *mat)
    1083: {
    1084:   TV_add_row("Local rows", "int", &mat->rmap->n);
    1085:   TV_add_row("Local columns", "int", &mat->cmap->n);
    1086:   TV_add_row("Global rows", "int", &mat->rmap->N);
    1087:   TV_add_row("Global columns", "int", &mat->cmap->N);
    1088:   TV_add_row("Typename", TV_ascii_string_type, ((PetscObject)mat)->type_name);
    1089:   return TV_format_OK;
    1090: }
    1091: #endif

    1093: /*@C
    1094:    MatLoad - Loads a matrix that has been stored in binary/HDF5 format
    1095:    with MatView().  The matrix format is determined from the options database.
    1096:    Generates a parallel MPI matrix if the communicator has more than one
    1097:    processor.  The default matrix type is AIJ.

    1099:    Collective on PetscViewer

    1101:    Input Parameters:
    1102: +  mat - the newly loaded matrix, this needs to have been created with MatCreate()
    1103:             or some related function before a call to MatLoad()
    1104: -  viewer - binary/HDF5 file viewer

    1106:    Options Database Keys:
    1107:    Used with block matrix formats (MATSEQBAIJ,  ...) to specify
    1108:    block size
    1109: .    -matload_block_size <bs>

    1111:    Level: beginner

    1113:    Notes:
    1114:    If the Mat type has not yet been given then MATAIJ is used, call MatSetFromOptions() on the
    1115:    Mat before calling this routine if you wish to set it from the options database.

    1117:    MatLoad() automatically loads into the options database any options
    1118:    given in the file filename.info where filename is the name of the file
    1119:    that was passed to the PetscViewerBinaryOpen(). The options in the info
    1120:    file will be ignored if you use the -viewer_binary_skip_info option.

    1122:    If the type or size of mat is not set before a call to MatLoad, PETSc
    1123:    sets the default matrix type AIJ and sets the local and global sizes.
    1124:    If type and/or size is already set, then the same are used.

    1126:    In parallel, each processor can load a subset of rows (or the
    1127:    entire matrix).  This routine is especially useful when a large
    1128:    matrix is stored on disk and only part of it is desired on each
    1129:    processor.  For example, a parallel solver may access only some of
    1130:    the rows from each processor.  The algorithm used here reads
    1131:    relatively small blocks of data rather than reading the entire
    1132:    matrix and then subsetting it.

    1134:    Viewer's PetscViewerType must be either PETSCVIEWERBINARY or PETSCVIEWERHDF5.
    1135:    Such viewer can be created using PetscViewerBinaryOpen()/PetscViewerHDF5Open(),
    1136:    or the sequence like
    1137: $    PetscViewer v;
    1138: $    PetscViewerCreate(PETSC_COMM_WORLD,&v);
    1139: $    PetscViewerSetType(v,PETSCVIEWERBINARY);
    1140: $    PetscViewerSetFromOptions(v);
    1141: $    PetscViewerFileSetMode(v,FILE_MODE_READ);
    1142: $    PetscViewerFileSetName(v,"datafile");
    1143:    The optional PetscViewerSetFromOptions() call allows to override PetscViewerSetType() using option
    1144: $ -viewer_type {binary,hdf5}

    1146:    See the example src/ksp/ksp/tutorials/ex27.c with the first approach,
    1147:    and src/mat/tutorials/ex10.c with the second approach.

    1149:    Notes about the PETSc binary format:
    1150:    In case of PETSCVIEWERBINARY, a native PETSc binary format is used. Each of the blocks
    1151:    is read onto rank 0 and then shipped to its destination rank, one after another.
    1152:    Multiple objects, both matrices and vectors, can be stored within the same file.
    1153:    Their PetscObject name is ignored; they are loaded in the order of their storage.

    1155:    Most users should not need to know the details of the binary storage
    1156:    format, since MatLoad() and MatView() completely hide these details.
    1157:    But for anyone who's interested, the standard binary matrix storage
    1158:    format is

    1160: $    PetscInt    MAT_FILE_CLASSID
    1161: $    PetscInt    number of rows
    1162: $    PetscInt    number of columns
    1163: $    PetscInt    total number of nonzeros
    1164: $    PetscInt    *number nonzeros in each row
    1165: $    PetscInt    *column indices of all nonzeros (starting index is zero)
    1166: $    PetscScalar *values of all nonzeros

    1168:    PETSc automatically does the byte swapping for
    1169: machines that store the bytes reversed, e.g.  DEC alpha, freebsd,
    1170: linux, Windows and the paragon; thus if you write your own binary
    1171: read/write routines you have to swap the bytes; see PetscBinaryRead()
    1172: and PetscBinaryWrite() to see how this may be done.

    1174:    Notes about the HDF5 (MATLAB MAT-File Version 7.3) format:
    1175:    In case of PETSCVIEWERHDF5, a parallel HDF5 reader is used.
    1176:    Each processor's chunk is loaded independently by its owning rank.
    1177:    Multiple objects, both matrices and vectors, can be stored within the same file.
    1178:    They are looked up by their PetscObject name.

    1180:    As the MATLAB MAT-File Version 7.3 format is also a HDF5 flavor, we decided to use
    1181:    by default the same structure and naming of the AIJ arrays and column count
    1182:    within the HDF5 file. This means that a MAT file saved with -v7.3 flag, e.g.
    1183: $    save example.mat A b -v7.3
    1184:    can be directly read by this routine (see Reference 1 for details).
    1185:    Note that depending on your MATLAB version, this format might be a default,
    1186:    otherwise you can set it as default in Preferences.

    1188:    Unless -nocompression flag is used to save the file in MATLAB,
    1189:    PETSc must be configured with ZLIB package.

    1191:    See also examples src/mat/tutorials/ex10.c and src/ksp/ksp/tutorials/ex27.c

    1193:    Current HDF5 (MAT-File) limitations:
    1194:    This reader currently supports only real MATSEQAIJ, MATMPIAIJ, MATSEQDENSE and MATMPIDENSE matrices.

    1196:    Corresponding MatView() is not yet implemented.

    1198:    The loaded matrix is actually a transpose of the original one in MATLAB,
    1199:    unless you push PETSC_VIEWER_HDF5_MAT format (see examples above).
    1200:    With this format, matrix is automatically transposed by PETSc,
    1201:    unless the matrix is marked as SPD or symmetric
    1202:    (see MatSetOption(), MAT_SPD, MAT_SYMMETRIC).

    1204:    References:
    1205: 1. MATLAB(R) Documentation, manual page of save(), https://www.mathworks.com/help/matlab/ref/save.html#btox10b-1-version

    1207: .seealso: PetscViewerBinaryOpen(), PetscViewerSetType(), MatView(), VecLoad()

    1209:  @*/
    1210: PetscErrorCode MatLoad(Mat mat,PetscViewer viewer)
    1211: {
    1213:   PetscBool      flg;

    1219:   if (!((PetscObject)mat)->type_name) {
    1220:     MatSetType(mat,MATAIJ);
    1221:   }

    1223:   flg  = PETSC_FALSE;
    1224:   PetscOptionsGetBool(((PetscObject)mat)->options,((PetscObject)mat)->prefix,"-matload_symmetric",&flg,NULL);
    1225:   if (flg) {
    1226:     MatSetOption(mat,MAT_SYMMETRIC,PETSC_TRUE);
    1227:     MatSetOption(mat,MAT_SYMMETRY_ETERNAL,PETSC_TRUE);
    1228:   }
    1229:   flg  = PETSC_FALSE;
    1230:   PetscOptionsGetBool(((PetscObject)mat)->options,((PetscObject)mat)->prefix,"-matload_spd",&flg,NULL);
    1231:   if (flg) {
    1232:     MatSetOption(mat,MAT_SPD,PETSC_TRUE);
    1233:   }

    1235:   if (!mat->ops->load) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatLoad is not supported for type %s",((PetscObject)mat)->type_name);
    1236:   PetscLogEventBegin(MAT_Load,mat,viewer,0,0);
    1237:   (*mat->ops->load)(mat,viewer);
    1238:   PetscLogEventEnd(MAT_Load,mat,viewer,0,0);
    1239:   return(0);
    1240: }

    1242: static PetscErrorCode MatDestroy_Redundant(Mat_Redundant **redundant)
    1243: {
    1245:   Mat_Redundant  *redund = *redundant;
    1246:   PetscInt       i;

    1249:   if (redund){
    1250:     if (redund->matseq) { /* via MatCreateSubMatrices()  */
    1251:       ISDestroy(&redund->isrow);
    1252:       ISDestroy(&redund->iscol);
    1253:       MatDestroySubMatrices(1,&redund->matseq);
    1254:     } else {
    1255:       PetscFree2(redund->send_rank,redund->recv_rank);
    1256:       PetscFree(redund->sbuf_j);
    1257:       PetscFree(redund->sbuf_a);
    1258:       for (i=0; i<redund->nrecvs; i++) {
    1259:         PetscFree(redund->rbuf_j[i]);
    1260:         PetscFree(redund->rbuf_a[i]);
    1261:       }
    1262:       PetscFree4(redund->sbuf_nz,redund->rbuf_nz,redund->rbuf_j,redund->rbuf_a);
    1263:     }

    1265:     if (redund->subcomm) {
    1266:       PetscCommDestroy(&redund->subcomm);
    1267:     }
    1268:     PetscFree(redund);
    1269:   }
    1270:   return(0);
    1271: }

    1273: /*@C
    1274:    MatDestroy - Frees space taken by a matrix.

    1276:    Collective on Mat

    1278:    Input Parameter:
    1279: .  A - the matrix

    1281:    Level: beginner

    1283: @*/
    1284: PetscErrorCode MatDestroy(Mat *A)
    1285: {

    1289:   if (!*A) return(0);
    1291:   if (--((PetscObject)(*A))->refct > 0) {*A = NULL; return(0);}

    1293:   /* if memory was published with SAWs then destroy it */
    1294:   PetscObjectSAWsViewOff((PetscObject)*A);
    1295:   if ((*A)->ops->destroy) {
    1296:     (*(*A)->ops->destroy)(*A);
    1297:   }

    1299:   PetscFree((*A)->defaultvectype);
    1300:   PetscFree((*A)->bsizes);
    1301:   PetscFree((*A)->solvertype);
    1302:   MatDestroy_Redundant(&(*A)->redundant);
    1303:   MatProductClear(*A);
    1304:   MatNullSpaceDestroy(&(*A)->nullsp);
    1305:   MatNullSpaceDestroy(&(*A)->transnullsp);
    1306:   MatNullSpaceDestroy(&(*A)->nearnullsp);
    1307:   MatDestroy(&(*A)->schur);
    1308:   PetscLayoutDestroy(&(*A)->rmap);
    1309:   PetscLayoutDestroy(&(*A)->cmap);
    1310:   PetscHeaderDestroy(A);
    1311:   return(0);
    1312: }

    1314: /*@C
    1315:    MatSetValues - Inserts or adds a block of values into a matrix.
    1316:    These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
    1317:    MUST be called after all calls to MatSetValues() have been completed.

    1319:    Not Collective

    1321:    Input Parameters:
    1322: +  mat - the matrix
    1323: .  v - a logically two-dimensional array of values
    1324: .  m, idxm - the number of rows and their global indices
    1325: .  n, idxn - the number of columns and their global indices
    1326: -  addv - either ADD_VALUES or INSERT_VALUES, where
    1327:    ADD_VALUES adds values to any existing entries, and
    1328:    INSERT_VALUES replaces existing entries with new values

    1330:    Notes:
    1331:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
    1332:       MatSetUp() before using this routine

    1334:    By default the values, v, are row-oriented. See MatSetOption() for other options.

    1336:    Calls to MatSetValues() with the INSERT_VALUES and ADD_VALUES
    1337:    options cannot be mixed without intervening calls to the assembly
    1338:    routines.

    1340:    MatSetValues() uses 0-based row and column numbers in Fortran
    1341:    as well as in C.

    1343:    Negative indices may be passed in idxm and idxn, these rows and columns are
    1344:    simply ignored. This allows easily inserting element stiffness matrices
    1345:    with homogeneous Dirchlet boundary conditions that you don't want represented
    1346:    in the matrix.

    1348:    Efficiency Alert:
    1349:    The routine MatSetValuesBlocked() may offer much better efficiency
    1350:    for users of block sparse formats (MATSEQBAIJ and MATMPIBAIJ).

    1352:    Level: beginner

    1354:    Developer Notes:
    1355:     This is labeled with C so does not automatically generate Fortran stubs and interfaces
    1356:                     because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    1358: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
    1359:           InsertMode, INSERT_VALUES, ADD_VALUES
    1360: @*/
    1361: PetscErrorCode MatSetValues(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
    1362: {

    1368:   if (!m || !n) return(0); /* no values to insert */
    1371:   MatCheckPreallocated(mat,1);

    1373:   if (mat->insertmode == NOT_SET_VALUES) {
    1374:     mat->insertmode = addv;
    1375:   } else if (PetscUnlikely(mat->insertmode != addv)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
    1376:   if (PetscDefined(USE_DEBUG)) {
    1377:     PetscInt       i,j;

    1379:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1380:     if (!mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);

    1382:     for (i=0; i<m; i++) {
    1383:       for (j=0; j<n; j++) {
    1384:         if (mat->erroriffailure && PetscIsInfOrNanScalar(v[i*n+j]))
    1385: #if defined(PETSC_USE_COMPLEX)
    1386:           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]);
    1387: #else
    1388:           SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_FP,"Inserting %g at matrix entry (%D,%D)",(double)v[i*n+j],idxm[i],idxn[j]);
    1389: #endif
    1390:       }
    1391:     }
    1392:     for (i=0; i<m; i++) if (idxm[i] >= mat->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot insert in row %D, maximum is %D",idxm[i],mat->rmap->N-1);
    1393:     for (i=0; i<n; i++) if (idxn[i] >= mat->cmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot insert in column %D, maximum is %D",idxn[i],mat->cmap->N-1);
    1394:   }

    1396:   if (mat->assembled) {
    1397:     mat->was_assembled = PETSC_TRUE;
    1398:     mat->assembled     = PETSC_FALSE;
    1399:   }
    1400:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    1401:   (*mat->ops->setvalues)(mat,m,idxm,n,idxn,v,addv);
    1402:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    1403:   return(0);
    1404: }

    1407: /*@
    1408:    MatSetValuesRowLocal - Inserts a row (block row for BAIJ matrices) of nonzero
    1409:         values into a matrix

    1411:    Not Collective

    1413:    Input Parameters:
    1414: +  mat - the matrix
    1415: .  row - the (block) row to set
    1416: -  v - a logically two-dimensional array of values

    1418:    Notes:
    1419:    By the values, v, are column-oriented (for the block version) and sorted

    1421:    All the nonzeros in the row must be provided

    1423:    The matrix must have previously had its column indices set

    1425:    The row must belong to this process

    1427:    Level: intermediate

    1429: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
    1430:           InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues(), MatSetValuesRow(), MatSetLocalToGlobalMapping()
    1431: @*/
    1432: PetscErrorCode MatSetValuesRowLocal(Mat mat,PetscInt row,const PetscScalar v[])
    1433: {
    1435:   PetscInt       globalrow;

    1441:   ISLocalToGlobalMappingApply(mat->rmap->mapping,1,&row,&globalrow);
    1442:   MatSetValuesRow(mat,globalrow,v);
    1443:   return(0);
    1444: }

    1446: /*@
    1447:    MatSetValuesRow - Inserts a row (block row for BAIJ matrices) of nonzero
    1448:         values into a matrix

    1450:    Not Collective

    1452:    Input Parameters:
    1453: +  mat - the matrix
    1454: .  row - the (block) row to set
    1455: -  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

    1457:    Notes:
    1458:    The values, v, are column-oriented for the block version.

    1460:    All the nonzeros in the row must be provided

    1462:    THE MATRIX MUST HAVE PREVIOUSLY HAD ITS COLUMN INDICES SET. IT IS RARE THAT THIS ROUTINE IS USED, usually MatSetValues() is used.

    1464:    The row must belong to this process

    1466:    Level: advanced

    1468: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
    1469:           InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues()
    1470: @*/
    1471: PetscErrorCode MatSetValuesRow(Mat mat,PetscInt row,const PetscScalar v[])
    1472: {

    1478:   MatCheckPreallocated(mat,1);
    1480:   if (PetscUnlikely(mat->insertmode == ADD_VALUES)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add and insert values");
    1481:   if (PetscUnlikely(mat->factortype)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1482:   mat->insertmode = INSERT_VALUES;

    1484:   if (mat->assembled) {
    1485:     mat->was_assembled = PETSC_TRUE;
    1486:     mat->assembled     = PETSC_FALSE;
    1487:   }
    1488:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    1489:   if (!mat->ops->setvaluesrow) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    1490:   (*mat->ops->setvaluesrow)(mat,row,v);
    1491:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    1492:   return(0);
    1493: }

    1495: /*@
    1496:    MatSetValuesStencil - Inserts or adds a block of values into a matrix.
    1497:      Using structured grid indexing

    1499:    Not Collective

    1501:    Input Parameters:
    1502: +  mat - the matrix
    1503: .  m - number of rows being entered
    1504: .  idxm - grid coordinates (and component number when dof > 1) for matrix rows being entered
    1505: .  n - number of columns being entered
    1506: .  idxn - grid coordinates (and component number when dof > 1) for matrix columns being entered
    1507: .  v - a logically two-dimensional array of values
    1508: -  addv - either ADD_VALUES or INSERT_VALUES, where
    1509:    ADD_VALUES adds values to any existing entries, and
    1510:    INSERT_VALUES replaces existing entries with new values

    1512:    Notes:
    1513:    By default the values, v, are row-oriented.  See MatSetOption() for other options.

    1515:    Calls to MatSetValuesStencil() with the INSERT_VALUES and ADD_VALUES
    1516:    options cannot be mixed without intervening calls to the assembly
    1517:    routines.

    1519:    The grid coordinates are across the entire grid, not just the local portion

    1521:    MatSetValuesStencil() uses 0-based row and column numbers in Fortran
    1522:    as well as in C.

    1524:    For setting/accessing vector values via array coordinates you can use the DMDAVecGetArray() routine

    1526:    In order to use this routine you must either obtain the matrix with DMCreateMatrix()
    1527:    or call MatSetLocalToGlobalMapping() and MatSetStencil() first.

    1529:    The columns and rows in the stencil passed in MUST be contained within the
    1530:    ghost region of the given process as set with DMDACreateXXX() or MatSetStencil(). For example,
    1531:    if you create a DMDA with an overlap of one grid level and on a particular process its first
    1532:    local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
    1533:    first i index you can use in your column and row indices in MatSetStencil() is 5.

    1535:    In Fortran idxm and idxn should be declared as
    1536: $     MatStencil idxm(4,m),idxn(4,n)
    1537:    and the values inserted using
    1538: $    idxm(MatStencil_i,1) = i
    1539: $    idxm(MatStencil_j,1) = j
    1540: $    idxm(MatStencil_k,1) = k
    1541: $    idxm(MatStencil_c,1) = c
    1542:    etc

    1544:    For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    1545:    obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    1546:    etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    1547:    DM_BOUNDARY_PERIODIC boundary type.

    1549:    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
    1550:    a single value per point) you can skip filling those indices.

    1552:    Inspired by the structured grid interface to the HYPRE package
    1553:    (https://computation.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)

    1555:    Efficiency Alert:
    1556:    The routine MatSetValuesBlockedStencil() may offer much better efficiency
    1557:    for users of block sparse formats (MATSEQBAIJ and MATMPIBAIJ).

    1559:    Level: beginner

    1561: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
    1562:           MatSetValues(), MatSetValuesBlockedStencil(), MatSetStencil(), DMCreateMatrix(), DMDAVecGetArray(), MatStencil
    1563: @*/
    1564: PetscErrorCode MatSetValuesStencil(Mat mat,PetscInt m,const MatStencil idxm[],PetscInt n,const MatStencil idxn[],const PetscScalar v[],InsertMode addv)
    1565: {
    1567:   PetscInt       buf[8192],*bufm=NULL,*bufn=NULL,*jdxm,*jdxn;
    1568:   PetscInt       j,i,dim = mat->stencil.dim,*dims = mat->stencil.dims+1,tmp;
    1569:   PetscInt       *starts = mat->stencil.starts,*dxm = (PetscInt*)idxm,*dxn = (PetscInt*)idxn,sdim = dim - (1 - (PetscInt)mat->stencil.noc);

    1572:   if (!m || !n) return(0); /* no values to insert */

    1578:   if ((m+n) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    1579:     jdxm = buf; jdxn = buf+m;
    1580:   } else {
    1581:     PetscMalloc2(m,&bufm,n,&bufn);
    1582:     jdxm = bufm; jdxn = bufn;
    1583:   }
    1584:   for (i=0; i<m; i++) {
    1585:     for (j=0; j<3-sdim; j++) dxm++;
    1586:     tmp = *dxm++ - starts[0];
    1587:     for (j=0; j<dim-1; j++) {
    1588:       if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
    1589:       else                                       tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    1590:     }
    1591:     if (mat->stencil.noc) dxm++;
    1592:     jdxm[i] = tmp;
    1593:   }
    1594:   for (i=0; i<n; i++) {
    1595:     for (j=0; j<3-sdim; j++) dxn++;
    1596:     tmp = *dxn++ - starts[0];
    1597:     for (j=0; j<dim-1; j++) {
    1598:       if ((*dxn++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
    1599:       else                                       tmp = tmp*dims[j] + *(dxn-1) - starts[j+1];
    1600:     }
    1601:     if (mat->stencil.noc) dxn++;
    1602:     jdxn[i] = tmp;
    1603:   }
    1604:   MatSetValuesLocal(mat,m,jdxm,n,jdxn,v,addv);
    1605:   PetscFree2(bufm,bufn);
    1606:   return(0);
    1607: }

    1609: /*@
    1610:    MatSetValuesBlockedStencil - Inserts or adds a block of values into a matrix.
    1611:      Using structured grid indexing

    1613:    Not Collective

    1615:    Input Parameters:
    1616: +  mat - the matrix
    1617: .  m - number of rows being entered
    1618: .  idxm - grid coordinates for matrix rows being entered
    1619: .  n - number of columns being entered
    1620: .  idxn - grid coordinates for matrix columns being entered
    1621: .  v - a logically two-dimensional array of values
    1622: -  addv - either ADD_VALUES or INSERT_VALUES, where
    1623:    ADD_VALUES adds values to any existing entries, and
    1624:    INSERT_VALUES replaces existing entries with new values

    1626:    Notes:
    1627:    By default the values, v, are row-oriented and unsorted.
    1628:    See MatSetOption() for other options.

    1630:    Calls to MatSetValuesBlockedStencil() with the INSERT_VALUES and ADD_VALUES
    1631:    options cannot be mixed without intervening calls to the assembly
    1632:    routines.

    1634:    The grid coordinates are across the entire grid, not just the local portion

    1636:    MatSetValuesBlockedStencil() uses 0-based row and column numbers in Fortran
    1637:    as well as in C.

    1639:    For setting/accessing vector values via array coordinates you can use the DMDAVecGetArray() routine

    1641:    In order to use this routine you must either obtain the matrix with DMCreateMatrix()
    1642:    or call MatSetBlockSize(), MatSetLocalToGlobalMapping() and MatSetStencil() first.

    1644:    The columns and rows in the stencil passed in MUST be contained within the
    1645:    ghost region of the given process as set with DMDACreateXXX() or MatSetStencil(). For example,
    1646:    if you create a DMDA with an overlap of one grid level and on a particular process its first
    1647:    local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
    1648:    first i index you can use in your column and row indices in MatSetStencil() is 5.

    1650:    In Fortran idxm and idxn should be declared as
    1651: $     MatStencil idxm(4,m),idxn(4,n)
    1652:    and the values inserted using
    1653: $    idxm(MatStencil_i,1) = i
    1654: $    idxm(MatStencil_j,1) = j
    1655: $    idxm(MatStencil_k,1) = k
    1656:    etc

    1658:    Negative indices may be passed in idxm and idxn, these rows and columns are
    1659:    simply ignored. This allows easily inserting element stiffness matrices
    1660:    with homogeneous Dirchlet boundary conditions that you don't want represented
    1661:    in the matrix.

    1663:    Inspired by the structured grid interface to the HYPRE package
    1664:    (https://computation.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)

    1666:    Level: beginner

    1668: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
    1669:           MatSetValues(), MatSetValuesStencil(), MatSetStencil(), DMCreateMatrix(), DMDAVecGetArray(), MatStencil,
    1670:           MatSetBlockSize(), MatSetLocalToGlobalMapping()
    1671: @*/
    1672: PetscErrorCode MatSetValuesBlockedStencil(Mat mat,PetscInt m,const MatStencil idxm[],PetscInt n,const MatStencil idxn[],const PetscScalar v[],InsertMode addv)
    1673: {
    1675:   PetscInt       buf[8192],*bufm=NULL,*bufn=NULL,*jdxm,*jdxn;
    1676:   PetscInt       j,i,dim = mat->stencil.dim,*dims = mat->stencil.dims+1,tmp;
    1677:   PetscInt       *starts = mat->stencil.starts,*dxm = (PetscInt*)idxm,*dxn = (PetscInt*)idxn,sdim = dim - (1 - (PetscInt)mat->stencil.noc);

    1680:   if (!m || !n) return(0); /* no values to insert */

    1687:   if ((m+n) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    1688:     jdxm = buf; jdxn = buf+m;
    1689:   } else {
    1690:     PetscMalloc2(m,&bufm,n,&bufn);
    1691:     jdxm = bufm; jdxn = bufn;
    1692:   }
    1693:   for (i=0; i<m; i++) {
    1694:     for (j=0; j<3-sdim; j++) dxm++;
    1695:     tmp = *dxm++ - starts[0];
    1696:     for (j=0; j<sdim-1; j++) {
    1697:       if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
    1698:       else                                       tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    1699:     }
    1700:     dxm++;
    1701:     jdxm[i] = tmp;
    1702:   }
    1703:   for (i=0; i<n; i++) {
    1704:     for (j=0; j<3-sdim; j++) dxn++;
    1705:     tmp = *dxn++ - starts[0];
    1706:     for (j=0; j<sdim-1; j++) {
    1707:       if ((*dxn++ - starts[j+1]) < 0 || tmp < 0) tmp = -1;
    1708:       else                                       tmp = tmp*dims[j] + *(dxn-1) - starts[j+1];
    1709:     }
    1710:     dxn++;
    1711:     jdxn[i] = tmp;
    1712:   }
    1713:   MatSetValuesBlockedLocal(mat,m,jdxm,n,jdxn,v,addv);
    1714:   PetscFree2(bufm,bufn);
    1715:   return(0);
    1716: }

    1718: /*@
    1719:    MatSetStencil - Sets the grid information for setting values into a matrix via
    1720:         MatSetValuesStencil()

    1722:    Not Collective

    1724:    Input Parameters:
    1725: +  mat - the matrix
    1726: .  dim - dimension of the grid 1, 2, or 3
    1727: .  dims - number of grid points in x, y, and z direction, including ghost points on your processor
    1728: .  starts - starting point of ghost nodes on your processor in x, y, and z direction
    1729: -  dof - number of degrees of freedom per node

    1732:    Inspired by the structured grid interface to the HYPRE package
    1733:    (www.llnl.gov/CASC/hyper)

    1735:    For matrices generated with DMCreateMatrix() this routine is automatically called and so not needed by the
    1736:    user.

    1738:    Level: beginner

    1740: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal()
    1741:           MatSetValues(), MatSetValuesBlockedStencil(), MatSetValuesStencil()
    1742: @*/
    1743: PetscErrorCode MatSetStencil(Mat mat,PetscInt dim,const PetscInt dims[],const PetscInt starts[],PetscInt dof)
    1744: {
    1745:   PetscInt i;

    1752:   mat->stencil.dim = dim + (dof > 1);
    1753:   for (i=0; i<dim; i++) {
    1754:     mat->stencil.dims[i]   = dims[dim-i-1];      /* copy the values in backwards */
    1755:     mat->stencil.starts[i] = starts[dim-i-1];
    1756:   }
    1757:   mat->stencil.dims[dim]   = dof;
    1758:   mat->stencil.starts[dim] = 0;
    1759:   mat->stencil.noc         = (PetscBool)(dof == 1);
    1760:   return(0);
    1761: }

    1763: /*@C
    1764:    MatSetValuesBlocked - Inserts or adds a block of values into a matrix.

    1766:    Not Collective

    1768:    Input Parameters:
    1769: +  mat - the matrix
    1770: .  v - a logically two-dimensional array of values
    1771: .  m, idxm - the number of block rows and their global block indices
    1772: .  n, idxn - the number of block columns and their global block indices
    1773: -  addv - either ADD_VALUES or INSERT_VALUES, where
    1774:    ADD_VALUES adds values to any existing entries, and
    1775:    INSERT_VALUES replaces existing entries with new values

    1777:    Notes:
    1778:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call
    1779:    MatXXXXSetPreallocation() or MatSetUp() before using this routine.

    1781:    The m and n count the NUMBER of blocks in the row direction and column direction,
    1782:    NOT the total number of rows/columns; for example, if the block size is 2 and
    1783:    you are passing in values for rows 2,3,4,5  then m would be 2 (not 4).
    1784:    The values in idxm would be 1 2; that is the first index for each block divided by
    1785:    the block size.

    1787:    Note that you must call MatSetBlockSize() when constructing this matrix (before
    1788:    preallocating it).

    1790:    By default the values, v, are row-oriented, so the layout of
    1791:    v is the same as for MatSetValues(). See MatSetOption() for other options.

    1793:    Calls to MatSetValuesBlocked() with the INSERT_VALUES and ADD_VALUES
    1794:    options cannot be mixed without intervening calls to the assembly
    1795:    routines.

    1797:    MatSetValuesBlocked() uses 0-based row and column numbers in Fortran
    1798:    as well as in C.

    1800:    Negative indices may be passed in idxm and idxn, these rows and columns are
    1801:    simply ignored. This allows easily inserting element stiffness matrices
    1802:    with homogeneous Dirchlet boundary conditions that you don't want represented
    1803:    in the matrix.

    1805:    Each time an entry is set within a sparse matrix via MatSetValues(),
    1806:    internal searching must be done to determine where to place the
    1807:    data in the matrix storage space.  By instead inserting blocks of
    1808:    entries via MatSetValuesBlocked(), the overhead of matrix assembly is
    1809:    reduced.

    1811:    Example:
    1812: $   Suppose m=n=2 and block size(bs) = 2 The array is
    1813: $
    1814: $   1  2  | 3  4
    1815: $   5  6  | 7  8
    1816: $   - - - | - - -
    1817: $   9  10 | 11 12
    1818: $   13 14 | 15 16
    1819: $
    1820: $   v[] should be passed in like
    1821: $   v[] = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
    1822: $
    1823: $  If you are not using row oriented storage of v (that is you called MatSetOption(mat,MAT_ROW_ORIENTED,PETSC_FALSE)) then
    1824: $   v[] = [1,5,9,13,2,6,10,14,3,7,11,15,4,8,12,16]

    1826:    Level: intermediate

    1828: .seealso: MatSetBlockSize(), MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetValuesBlockedLocal()
    1829: @*/
    1830: PetscErrorCode MatSetValuesBlocked(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],const PetscScalar v[],InsertMode addv)
    1831: {

    1837:   if (!m || !n) return(0); /* no values to insert */
    1841:   MatCheckPreallocated(mat,1);
    1842:   if (mat->insertmode == NOT_SET_VALUES) {
    1843:     mat->insertmode = addv;
    1844:   } else if (PetscUnlikely(mat->insertmode != addv)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
    1845:   if (PetscDefined(USE_DEBUG)) {
    1846:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1847:     if (!mat->ops->setvaluesblocked && !mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    1848:   }
    1849:   if (PetscDefined(USE_DEBUG)) {
    1850:     PetscInt rbs,cbs,M,N,i;
    1851:     MatGetBlockSizes(mat,&rbs,&cbs);
    1852:     MatGetSize(mat,&M,&N);
    1853:     for (i=0; i<m; i++) {
    1854:       if (idxm[i]*rbs >= M) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row block index %D (index %D) greater than row length %D",i,idxm[i],M);
    1855:     }
    1856:     for (i=0; i<n; i++) {
    1857:       if (idxn[i]*cbs >= N) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column block index %D (index %D) great than column length %D",i,idxn[i],N);
    1858:     }
    1859:   }
    1860:   if (mat->assembled) {
    1861:     mat->was_assembled = PETSC_TRUE;
    1862:     mat->assembled     = PETSC_FALSE;
    1863:   }
    1864:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    1865:   if (mat->ops->setvaluesblocked) {
    1866:     (*mat->ops->setvaluesblocked)(mat,m,idxm,n,idxn,v,addv);
    1867:   } else {
    1868:     PetscInt buf[8192],*bufr=NULL,*bufc=NULL,*iidxm,*iidxn;
    1869:     PetscInt i,j,bs,cbs;
    1870:     MatGetBlockSizes(mat,&bs,&cbs);
    1871:     if (m*bs+n*cbs <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    1872:       iidxm = buf; iidxn = buf + m*bs;
    1873:     } else {
    1874:       PetscMalloc2(m*bs,&bufr,n*cbs,&bufc);
    1875:       iidxm = bufr; iidxn = bufc;
    1876:     }
    1877:     for (i=0; i<m; i++) {
    1878:       for (j=0; j<bs; j++) {
    1879:         iidxm[i*bs+j] = bs*idxm[i] + j;
    1880:       }
    1881:     }
    1882:     for (i=0; i<n; i++) {
    1883:       for (j=0; j<cbs; j++) {
    1884:         iidxn[i*cbs+j] = cbs*idxn[i] + j;
    1885:       }
    1886:     }
    1887:     MatSetValues(mat,m*bs,iidxm,n*cbs,iidxn,v,addv);
    1888:     PetscFree2(bufr,bufc);
    1889:   }
    1890:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    1891:   return(0);
    1892: }

    1894: /*@C
    1895:    MatGetValues - Gets a block of values from a matrix.

    1897:    Not Collective; can only return values that are owned by the give process

    1899:    Input Parameters:
    1900: +  mat - the matrix
    1901: .  v - a logically two-dimensional array for storing the values
    1902: .  m, idxm - the number of rows and their global indices
    1903: -  n, idxn - the number of columns and their global indices

    1905:    Notes:
    1906:      The user must allocate space (m*n PetscScalars) for the values, v.
    1907:      The values, v, are then returned in a row-oriented format,
    1908:      analogous to that used by default in MatSetValues().

    1910:      MatGetValues() uses 0-based row and column numbers in
    1911:      Fortran as well as in C.

    1913:      MatGetValues() requires that the matrix has been assembled
    1914:      with MatAssemblyBegin()/MatAssemblyEnd().  Thus, calls to
    1915:      MatSetValues() and MatGetValues() CANNOT be made in succession
    1916:      without intermediate matrix assembly.

    1918:      Negative row or column indices will be ignored and those locations in v[] will be
    1919:      left unchanged.

    1921:      For the standard row-based matrix formats, idxm[] can only contain rows owned by the requesting MPI rank.
    1922:      That is, rows with global index greater than or equal to restart and less than rend where restart and rend are obtainable
    1923:      from MatGetOwnershipRange(mat,&rstart,&rend).

    1925:    Level: advanced

    1927: .seealso: MatGetRow(), MatCreateSubMatrices(), MatSetValues(), MatGetOwnershipRange(), MatGetValuesLocal()
    1928: @*/
    1929: PetscErrorCode MatGetValues(Mat mat,PetscInt m,const PetscInt idxm[],PetscInt n,const PetscInt idxn[],PetscScalar v[])
    1930: {

    1936:   if (!m || !n) return(0);
    1940:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    1941:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1942:   if (!mat->ops->getvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    1943:   MatCheckPreallocated(mat,1);

    1945:   PetscLogEventBegin(MAT_GetValues,mat,0,0,0);
    1946:   (*mat->ops->getvalues)(mat,m,idxm,n,idxn,v);
    1947:   PetscLogEventEnd(MAT_GetValues,mat,0,0,0);
    1948:   return(0);
    1949: }

    1951: /*@C
    1952:    MatGetValuesLocal - retrieves values from certain locations in a matrix using the local numbering of the indices
    1953:      defined previously by MatSetLocalToGlobalMapping()

    1955:    Not Collective

    1957:    Input Parameters:
    1958: +  mat - the matrix
    1959: .  nrow, irow - number of rows and their local indices
    1960: -  ncol, icol - number of columns and their local indices

    1962:    Output Parameter:
    1963: .  y -  a logically two-dimensional array of values

    1965:    Notes:
    1966:      If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatSetLocalToGlobalMapping() before using this routine.

    1968:      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,
    1969:      are greater than or equal to restart and less than rend where restart and rend are obtainable from MatGetOwnershipRange(mat,&rstart,&rend). One can
    1970:      determine if the resulting global row associated with the local row r is owned by the requesting MPI rank by applying the ISLocalToGlobalMapping set
    1971:      with MatSetLocalToGlobalMapping().

    1973:    Developer Notes:
    1974:       This is labelled with C so does not automatically generate Fortran stubs and interfaces
    1975:       because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    1977:    Level: advanced

    1979: .seealso:  MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetLocalToGlobalMapping(),
    1980:            MatSetValuesLocal(), MatGetValues()
    1981: @*/
    1982: PetscErrorCode MatGetValuesLocal(Mat mat,PetscInt nrow,const PetscInt irow[],PetscInt ncol,const PetscInt icol[],PetscScalar y[])
    1983: {

    1989:   MatCheckPreallocated(mat,1);
    1990:   if (!nrow || !ncol) return(0); /* no values to retrieve */
    1993:   if (PetscDefined(USE_DEBUG)) {
    1994:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    1995:     if (!mat->ops->getvalueslocal && !mat->ops->getvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    1996:   }
    1997:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    1998:   PetscLogEventBegin(MAT_GetValues,mat,0,0,0);
    1999:   if (mat->ops->getvalueslocal) {
    2000:     (*mat->ops->getvalueslocal)(mat,nrow,irow,ncol,icol,y);
    2001:   } else {
    2002:     PetscInt buf[8192],*bufr=NULL,*bufc=NULL,*irowm,*icolm;
    2003:     if ((nrow+ncol) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    2004:       irowm = buf; icolm = buf+nrow;
    2005:     } else {
    2006:       PetscMalloc2(nrow,&bufr,ncol,&bufc);
    2007:       irowm = bufr; icolm = bufc;
    2008:     }
    2009:     if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatGetValuesLocal() cannot proceed without local-to-global row mapping (See MatSetLocalToGlobalMapping()).");
    2010:     if (!mat->cmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatGetValuesLocal() cannot proceed without local-to-global column mapping (See MatSetLocalToGlobalMapping()).");
    2011:     ISLocalToGlobalMappingApply(mat->rmap->mapping,nrow,irow,irowm);
    2012:     ISLocalToGlobalMappingApply(mat->cmap->mapping,ncol,icol,icolm);
    2013:     MatGetValues(mat,nrow,irowm,ncol,icolm,y);
    2014:     PetscFree2(bufr,bufc);
    2015:   }
    2016:   PetscLogEventEnd(MAT_GetValues,mat,0,0,0);
    2017:   return(0);
    2018: }

    2020: /*@
    2021:   MatSetValuesBatch - Adds (ADD_VALUES) many blocks of values into a matrix at once. The blocks must all be square and
    2022:   the same size. Currently, this can only be called once and creates the given matrix.

    2024:   Not Collective

    2026:   Input Parameters:
    2027: + mat - the matrix
    2028: . nb - the number of blocks
    2029: . bs - the number of rows (and columns) in each block
    2030: . rows - a concatenation of the rows for each block
    2031: - v - a concatenation of logically two-dimensional arrays of values

    2033:   Notes:
    2034:   In the future, we will extend this routine to handle rectangular blocks, and to allow multiple calls for a given matrix.

    2036:   Level: advanced

    2038: .seealso: MatSetOption(), MatAssemblyBegin(), MatAssemblyEnd(), MatSetValuesBlocked(), MatSetValuesLocal(),
    2039:           InsertMode, INSERT_VALUES, ADD_VALUES, MatSetValues()
    2040: @*/
    2041: PetscErrorCode MatSetValuesBatch(Mat mat, PetscInt nb, PetscInt bs, PetscInt rows[], const PetscScalar v[])
    2042: {

    2050:   if (PetscUnlikelyDebug(mat->factortype)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

    2052:   PetscLogEventBegin(MAT_SetValuesBatch,mat,0,0,0);
    2053:   if (mat->ops->setvaluesbatch) {
    2054:     (*mat->ops->setvaluesbatch)(mat,nb,bs,rows,v);
    2055:   } else {
    2056:     PetscInt b;
    2057:     for (b = 0; b < nb; ++b) {
    2058:       MatSetValues(mat, bs, &rows[b*bs], bs, &rows[b*bs], &v[b*bs*bs], ADD_VALUES);
    2059:     }
    2060:   }
    2061:   PetscLogEventEnd(MAT_SetValuesBatch,mat,0,0,0);
    2062:   return(0);
    2063: }

    2065: /*@
    2066:    MatSetLocalToGlobalMapping - Sets a local-to-global numbering for use by
    2067:    the routine MatSetValuesLocal() to allow users to insert matrix entries
    2068:    using a local (per-processor) numbering.

    2070:    Not Collective

    2072:    Input Parameters:
    2073: +  x - the matrix
    2074: .  rmapping - row mapping created with ISLocalToGlobalMappingCreate()   or ISLocalToGlobalMappingCreateIS()
    2075: - cmapping - column mapping

    2077:    Level: intermediate

    2080: .seealso:  MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetValuesLocal(), MatGetValuesLocal()
    2081: @*/
    2082: PetscErrorCode MatSetLocalToGlobalMapping(Mat x,ISLocalToGlobalMapping rmapping,ISLocalToGlobalMapping cmapping)
    2083: {

    2092:   if (x->ops->setlocaltoglobalmapping) {
    2093:     (*x->ops->setlocaltoglobalmapping)(x,rmapping,cmapping);
    2094:   } else {
    2095:     PetscLayoutSetISLocalToGlobalMapping(x->rmap,rmapping);
    2096:     PetscLayoutSetISLocalToGlobalMapping(x->cmap,cmapping);
    2097:   }
    2098:   return(0);
    2099: }

    2102: /*@
    2103:    MatGetLocalToGlobalMapping - Gets the local-to-global numbering set by MatSetLocalToGlobalMapping()

    2105:    Not Collective

    2107:    Input Parameters:
    2108: .  A - the matrix

    2110:    Output Parameters:
    2111: + rmapping - row mapping
    2112: - cmapping - column mapping

    2114:    Level: advanced

    2117: .seealso:  MatSetValuesLocal()
    2118: @*/
    2119: PetscErrorCode MatGetLocalToGlobalMapping(Mat A,ISLocalToGlobalMapping *rmapping,ISLocalToGlobalMapping *cmapping)
    2120: {
    2126:   if (rmapping) *rmapping = A->rmap->mapping;
    2127:   if (cmapping) *cmapping = A->cmap->mapping;
    2128:   return(0);
    2129: }

    2131: /*@
    2132:    MatSetLayouts - Sets the PetscLayout objects for rows and columns of a matrix

    2134:    Logically Collective on A

    2136:    Input Parameters:
    2137: +  A - the matrix
    2138: . rmap - row layout
    2139: - cmap - column layout

    2141:    Level: advanced

    2143: .seealso:  MatCreateVecs(), MatGetLocalToGlobalMapping(), MatGetLayouts()
    2144: @*/
    2145: PetscErrorCode MatSetLayouts(Mat A,PetscLayout rmap,PetscLayout cmap)
    2146: {

    2152:   PetscLayoutReference(rmap,&A->rmap);
    2153:   PetscLayoutReference(cmap,&A->cmap);
    2154:   return(0);
    2155: }

    2157: /*@
    2158:    MatGetLayouts - Gets the PetscLayout objects for rows and columns

    2160:    Not Collective

    2162:    Input Parameters:
    2163: .  A - the matrix

    2165:    Output Parameters:
    2166: + rmap - row layout
    2167: - cmap - column layout

    2169:    Level: advanced

    2171: .seealso:  MatCreateVecs(), MatGetLocalToGlobalMapping(), MatSetLayouts()
    2172: @*/
    2173: PetscErrorCode MatGetLayouts(Mat A,PetscLayout *rmap,PetscLayout *cmap)
    2174: {
    2180:   if (rmap) *rmap = A->rmap;
    2181:   if (cmap) *cmap = A->cmap;
    2182:   return(0);
    2183: }

    2185: /*@C
    2186:    MatSetValuesLocal - Inserts or adds values into certain locations of a matrix,
    2187:    using a local numbering of the nodes.

    2189:    Not Collective

    2191:    Input Parameters:
    2192: +  mat - the matrix
    2193: .  nrow, irow - number of rows and their local indices
    2194: .  ncol, icol - number of columns and their local indices
    2195: .  y -  a logically two-dimensional array of values
    2196: -  addv - either INSERT_VALUES or ADD_VALUES, where
    2197:    ADD_VALUES adds values to any existing entries, and
    2198:    INSERT_VALUES replaces existing entries with new values

    2200:    Notes:
    2201:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
    2202:       MatSetUp() before using this routine

    2204:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatSetLocalToGlobalMapping() before using this routine

    2206:    Calls to MatSetValuesLocal() with the INSERT_VALUES and ADD_VALUES
    2207:    options cannot be mixed without intervening calls to the assembly
    2208:    routines.

    2210:    These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
    2211:    MUST be called after all calls to MatSetValuesLocal() have been completed.

    2213:    Level: intermediate

    2215:    Developer Notes:
    2216:     This is labeled with C so does not automatically generate Fortran stubs and interfaces
    2217:                     because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    2219: .seealso:  MatAssemblyBegin(), MatAssemblyEnd(), MatSetValues(), MatSetLocalToGlobalMapping(),
    2220:            MatSetValueLocal(), MatGetValuesLocal()
    2221: @*/
    2222: PetscErrorCode MatSetValuesLocal(Mat mat,PetscInt nrow,const PetscInt irow[],PetscInt ncol,const PetscInt icol[],const PetscScalar y[],InsertMode addv)
    2223: {

    2229:   MatCheckPreallocated(mat,1);
    2230:   if (!nrow || !ncol) return(0); /* no values to insert */
    2233:   if (mat->insertmode == NOT_SET_VALUES) {
    2234:     mat->insertmode = addv;
    2235:   }
    2236:   else if (PetscUnlikely(mat->insertmode != addv)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
    2237:   if (PetscDefined(USE_DEBUG)) {
    2238:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2239:     if (!mat->ops->setvalueslocal && !mat->ops->setvalues) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    2240:   }

    2242:   if (mat->assembled) {
    2243:     mat->was_assembled = PETSC_TRUE;
    2244:     mat->assembled     = PETSC_FALSE;
    2245:   }
    2246:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    2247:   if (mat->ops->setvalueslocal) {
    2248:     (*mat->ops->setvalueslocal)(mat,nrow,irow,ncol,icol,y,addv);
    2249:   } else {
    2250:     PetscInt buf[8192],*bufr=NULL,*bufc=NULL,*irowm,*icolm;
    2251:     if ((nrow+ncol) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    2252:       irowm = buf; icolm = buf+nrow;
    2253:     } else {
    2254:       PetscMalloc2(nrow,&bufr,ncol,&bufc);
    2255:       irowm = bufr; icolm = bufc;
    2256:     }
    2257:     if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatSetValuesLocal() cannot proceed without local-to-global row mapping (See MatSetLocalToGlobalMapping()).");
    2258:     if (!mat->cmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MatSetValuesLocal() cannot proceed without local-to-global column mapping (See MatSetLocalToGlobalMapping()).");
    2259:     ISLocalToGlobalMappingApply(mat->rmap->mapping,nrow,irow,irowm);
    2260:     ISLocalToGlobalMappingApply(mat->cmap->mapping,ncol,icol,icolm);
    2261:     MatSetValues(mat,nrow,irowm,ncol,icolm,y,addv);
    2262:     PetscFree2(bufr,bufc);
    2263:   }
    2264:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    2265:   return(0);
    2266: }

    2268: /*@C
    2269:    MatSetValuesBlockedLocal - Inserts or adds values into certain locations of a matrix,
    2270:    using a local ordering of the nodes a block at a time.

    2272:    Not Collective

    2274:    Input Parameters:
    2275: +  x - the matrix
    2276: .  nrow, irow - number of rows and their local indices
    2277: .  ncol, icol - number of columns and their local indices
    2278: .  y -  a logically two-dimensional array of values
    2279: -  addv - either INSERT_VALUES or ADD_VALUES, where
    2280:    ADD_VALUES adds values to any existing entries, and
    2281:    INSERT_VALUES replaces existing entries with new values

    2283:    Notes:
    2284:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatXXXXSetPreallocation() or
    2285:       MatSetUp() before using this routine

    2287:    If you create the matrix yourself (that is not with a call to DMCreateMatrix()) then you MUST call MatSetBlockSize() and MatSetLocalToGlobalMapping()
    2288:       before using this routineBefore calling MatSetValuesLocal(), the user must first set the

    2290:    Calls to MatSetValuesBlockedLocal() with the INSERT_VALUES and ADD_VALUES
    2291:    options cannot be mixed without intervening calls to the assembly
    2292:    routines.

    2294:    These values may be cached, so MatAssemblyBegin() and MatAssemblyEnd()
    2295:    MUST be called after all calls to MatSetValuesBlockedLocal() have been completed.

    2297:    Level: intermediate

    2299:    Developer Notes:
    2300:     This is labeled with C so does not automatically generate Fortran stubs and interfaces
    2301:                     because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    2303: .seealso:  MatSetBlockSize(), MatSetLocalToGlobalMapping(), MatAssemblyBegin(), MatAssemblyEnd(),
    2304:            MatSetValuesLocal(),  MatSetValuesBlocked()
    2305: @*/
    2306: PetscErrorCode MatSetValuesBlockedLocal(Mat mat,PetscInt nrow,const PetscInt irow[],PetscInt ncol,const PetscInt icol[],const PetscScalar y[],InsertMode addv)
    2307: {

    2313:   MatCheckPreallocated(mat,1);
    2314:   if (!nrow || !ncol) return(0); /* no values to insert */
    2318:   if (mat->insertmode == NOT_SET_VALUES) {
    2319:     mat->insertmode = addv;
    2320:   } else if (PetscUnlikely(mat->insertmode != addv)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Cannot mix add values and insert values");
    2321:   if (PetscDefined(USE_DEBUG)) {
    2322:     if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2323:     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);
    2324:   }

    2326:   if (mat->assembled) {
    2327:     mat->was_assembled = PETSC_TRUE;
    2328:     mat->assembled     = PETSC_FALSE;
    2329:   }
    2330:   if (PetscUnlikelyDebug(mat->rmap->mapping)) { /* Condition on the mapping existing, because MatSetValuesBlockedLocal_IS does not require it to be set. */
    2331:     PetscInt irbs, rbs;
    2332:     MatGetBlockSizes(mat, &rbs, NULL);
    2333:     ISLocalToGlobalMappingGetBlockSize(mat->rmap->mapping,&irbs);
    2334:     if (rbs != irbs) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Different row block sizes! mat %D, row l2g map %D",rbs,irbs);
    2335:   }
    2336:   if (PetscUnlikelyDebug(mat->cmap->mapping)) {
    2337:     PetscInt icbs, cbs;
    2338:     MatGetBlockSizes(mat,NULL,&cbs);
    2339:     ISLocalToGlobalMappingGetBlockSize(mat->cmap->mapping,&icbs);
    2340:     if (cbs != icbs) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Different col block sizes! mat %D, col l2g map %D",cbs,icbs);
    2341:   }
    2342:   PetscLogEventBegin(MAT_SetValues,mat,0,0,0);
    2343:   if (mat->ops->setvaluesblockedlocal) {
    2344:     (*mat->ops->setvaluesblockedlocal)(mat,nrow,irow,ncol,icol,y,addv);
    2345:   } else {
    2346:     PetscInt buf[8192],*bufr=NULL,*bufc=NULL,*irowm,*icolm;
    2347:     if ((nrow+ncol) <= (PetscInt)(sizeof(buf)/sizeof(PetscInt))) {
    2348:       irowm = buf; icolm = buf + nrow;
    2349:     } else {
    2350:       PetscMalloc2(nrow,&bufr,ncol,&bufc);
    2351:       irowm = bufr; icolm = bufc;
    2352:     }
    2353:     ISLocalToGlobalMappingApplyBlock(mat->rmap->mapping,nrow,irow,irowm);
    2354:     ISLocalToGlobalMappingApplyBlock(mat->cmap->mapping,ncol,icol,icolm);
    2355:     MatSetValuesBlocked(mat,nrow,irowm,ncol,icolm,y,addv);
    2356:     PetscFree2(bufr,bufc);
    2357:   }
    2358:   PetscLogEventEnd(MAT_SetValues,mat,0,0,0);
    2359:   return(0);
    2360: }

    2362: /*@
    2363:    MatMultDiagonalBlock - Computes the matrix-vector product, y = Dx. Where D is defined by the inode or block structure of the diagonal

    2365:    Collective on Mat

    2367:    Input Parameters:
    2368: +  mat - the matrix
    2369: -  x   - the vector to be multiplied

    2371:    Output Parameters:
    2372: .  y - the result

    2374:    Notes:
    2375:    The vectors x and y cannot be the same.  I.e., one cannot
    2376:    call MatMult(A,y,y).

    2378:    Level: developer

    2380: .seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    2381: @*/
    2382: PetscErrorCode MatMultDiagonalBlock(Mat mat,Vec x,Vec y)
    2383: {

    2392:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2393:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2394:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2395:   MatCheckPreallocated(mat,1);

    2397:   if (!mat->ops->multdiagonalblock) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s does not have a multiply defined",((PetscObject)mat)->type_name);
    2398:   (*mat->ops->multdiagonalblock)(mat,x,y);
    2399:   PetscObjectStateIncrease((PetscObject)y);
    2400:   return(0);
    2401: }

    2403: /* --------------------------------------------------------*/
    2404: /*@
    2405:    MatMult - Computes the matrix-vector product, y = Ax.

    2407:    Neighbor-wise Collective on Mat

    2409:    Input Parameters:
    2410: +  mat - the matrix
    2411: -  x   - the vector to be multiplied

    2413:    Output Parameters:
    2414: .  y - the result

    2416:    Notes:
    2417:    The vectors x and y cannot be the same.  I.e., one cannot
    2418:    call MatMult(A,y,y).

    2420:    Level: beginner

    2422: .seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    2423: @*/
    2424: PetscErrorCode MatMult(Mat mat,Vec x,Vec y)
    2425: {

    2433:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2434:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2435:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2436:   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);
    2437:   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);
    2438:   if (mat->cmap->n != x->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: local dim %D %D",mat->cmap->n,x->map->n);
    2439:   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);
    2440:   VecSetErrorIfLocked(y,3);
    2441:   if (mat->erroriffailure) {VecValidValues(x,2,PETSC_TRUE);}
    2442:   MatCheckPreallocated(mat,1);

    2444:   VecLockReadPush(x);
    2445:   if (!mat->ops->mult) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s does not have a multiply defined",((PetscObject)mat)->type_name);
    2446:   PetscLogEventBegin(MAT_Mult,mat,x,y,0);
    2447:   (*mat->ops->mult)(mat,x,y);
    2448:   PetscLogEventEnd(MAT_Mult,mat,x,y,0);
    2449:   if (mat->erroriffailure) {VecValidValues(y,3,PETSC_FALSE);}
    2450:   VecLockReadPop(x);
    2451:   return(0);
    2452: }

    2454: /*@
    2455:    MatMultTranspose - Computes matrix transpose times a vector y = A^T * x.

    2457:    Neighbor-wise Collective on Mat

    2459:    Input Parameters:
    2460: +  mat - the matrix
    2461: -  x   - the vector to be multiplied

    2463:    Output Parameters:
    2464: .  y - the result

    2466:    Notes:
    2467:    The vectors x and y cannot be the same.  I.e., one cannot
    2468:    call MatMultTranspose(A,y,y).

    2470:    For complex numbers this does NOT compute the Hermitian (complex conjugate) transpose multiple,
    2471:    use MatMultHermitianTranspose()

    2473:    Level: beginner

    2475: .seealso: MatMult(), MatMultAdd(), MatMultTransposeAdd(), MatMultHermitianTranspose(), MatTranspose()
    2476: @*/
    2477: PetscErrorCode MatMultTranspose(Mat mat,Vec x,Vec y)
    2478: {
    2479:   PetscErrorCode (*op)(Mat,Vec,Vec)=NULL,ierr;

    2487:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2488:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2489:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2490:   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);
    2491:   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);
    2492:   if (mat->cmap->n != y->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: local dim %D %D",mat->cmap->n,y->map->n);
    2493:   if (mat->rmap->n != x->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: local dim %D %D",mat->rmap->n,x->map->n);
    2494:   if (mat->erroriffailure) {VecValidValues(x,2,PETSC_TRUE);}
    2495:   MatCheckPreallocated(mat,1);

    2497:   if (!mat->ops->multtranspose) {
    2498:     if (mat->symmetric && mat->ops->mult) op = mat->ops->mult;
    2499:     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);
    2500:   } else op = mat->ops->multtranspose;
    2501:   PetscLogEventBegin(MAT_MultTranspose,mat,x,y,0);
    2502:   VecLockReadPush(x);
    2503:   (*op)(mat,x,y);
    2504:   VecLockReadPop(x);
    2505:   PetscLogEventEnd(MAT_MultTranspose,mat,x,y,0);
    2506:   PetscObjectStateIncrease((PetscObject)y);
    2507:   if (mat->erroriffailure) {VecValidValues(y,3,PETSC_FALSE);}
    2508:   return(0);
    2509: }

    2511: /*@
    2512:    MatMultHermitianTranspose - Computes matrix Hermitian transpose times a vector.

    2514:    Neighbor-wise Collective on Mat

    2516:    Input Parameters:
    2517: +  mat - the matrix
    2518: -  x   - the vector to be multilplied

    2520:    Output Parameters:
    2521: .  y - the result

    2523:    Notes:
    2524:    The vectors x and y cannot be the same.  I.e., one cannot
    2525:    call MatMultHermitianTranspose(A,y,y).

    2527:    Also called the conjugate transpose, complex conjugate transpose, or adjoint.

    2529:    For real numbers MatMultTranspose() and MatMultHermitianTranspose() are identical.

    2531:    Level: beginner

    2533: .seealso: MatMult(), MatMultAdd(), MatMultHermitianTransposeAdd(), MatMultTranspose()
    2534: @*/
    2535: PetscErrorCode MatMultHermitianTranspose(Mat mat,Vec x,Vec y)
    2536: {

    2545:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2546:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2547:   if (x == y) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2548:   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);
    2549:   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);
    2550:   if (mat->cmap->n != y->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec y: local dim %D %D",mat->cmap->n,y->map->n);
    2551:   if (mat->rmap->n != x->map->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec x: local dim %D %D",mat->rmap->n,x->map->n);
    2552:   MatCheckPreallocated(mat,1);

    2554:   PetscLogEventBegin(MAT_MultHermitianTranspose,mat,x,y,0);
    2555: #if defined(PETSC_USE_COMPLEX)
    2556:   if (mat->ops->multhermitiantranspose || (mat->hermitian && mat->ops->mult)) {
    2557:     VecLockReadPush(x);
    2558:     if (mat->ops->multhermitiantranspose) {
    2559:       (*mat->ops->multhermitiantranspose)(mat,x,y);
    2560:     } else {
    2561:       (*mat->ops->mult)(mat,x,y);
    2562:     }
    2563:     VecLockReadPop(x);
    2564:   } else {
    2565:     Vec w;
    2566:     VecDuplicate(x,&w);
    2567:     VecCopy(x,w);
    2568:     VecConjugate(w);
    2569:     MatMultTranspose(mat,w,y);
    2570:     VecDestroy(&w);
    2571:     VecConjugate(y);
    2572:   }
    2573:   PetscObjectStateIncrease((PetscObject)y);
    2574: #else
    2575:   MatMultTranspose(mat,x,y);
    2576: #endif
    2577:   PetscLogEventEnd(MAT_MultHermitianTranspose,mat,x,y,0);
    2578:   return(0);
    2579: }

    2581: /*@
    2582:     MatMultAdd -  Computes v3 = v2 + A * v1.

    2584:     Neighbor-wise Collective on Mat

    2586:     Input Parameters:
    2587: +   mat - the matrix
    2588: -   v1, v2 - the vectors

    2590:     Output Parameters:
    2591: .   v3 - the result

    2593:     Notes:
    2594:     The vectors v1 and v3 cannot be the same.  I.e., one cannot
    2595:     call MatMultAdd(A,v1,v2,v1).

    2597:     Level: beginner

    2599: .seealso: MatMultTranspose(), MatMult(), MatMultTransposeAdd()
    2600: @*/
    2601: PetscErrorCode MatMultAdd(Mat mat,Vec v1,Vec v2,Vec v3)
    2602: {

    2612:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2613:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2614:   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);
    2615:   /* 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);
    2616:      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); */
    2617:   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);
    2618:   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);
    2619:   if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
    2620:   MatCheckPreallocated(mat,1);

    2622:   if (!mat->ops->multadd) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"No MatMultAdd() for matrix type %s",((PetscObject)mat)->type_name);
    2623:   PetscLogEventBegin(MAT_MultAdd,mat,v1,v2,v3);
    2624:   VecLockReadPush(v1);
    2625:   (*mat->ops->multadd)(mat,v1,v2,v3);
    2626:   VecLockReadPop(v1);
    2627:   PetscLogEventEnd(MAT_MultAdd,mat,v1,v2,v3);
    2628:   PetscObjectStateIncrease((PetscObject)v3);
    2629:   return(0);
    2630: }

    2632: /*@
    2633:    MatMultTransposeAdd - Computes v3 = v2 + A' * v1.

    2635:    Neighbor-wise Collective on Mat

    2637:    Input Parameters:
    2638: +  mat - the matrix
    2639: -  v1, v2 - the vectors

    2641:    Output Parameters:
    2642: .  v3 - the result

    2644:    Notes:
    2645:    The vectors v1 and v3 cannot be the same.  I.e., one cannot
    2646:    call MatMultTransposeAdd(A,v1,v2,v1).

    2648:    Level: beginner

    2650: .seealso: MatMultTranspose(), MatMultAdd(), MatMult()
    2651: @*/
    2652: PetscErrorCode MatMultTransposeAdd(Mat mat,Vec v1,Vec v2,Vec v3)
    2653: {

    2663:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2664:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2665:   if (!mat->ops->multtransposeadd) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    2666:   if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
    2667:   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);
    2668:   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);
    2669:   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);
    2670:   MatCheckPreallocated(mat,1);

    2672:   PetscLogEventBegin(MAT_MultTransposeAdd,mat,v1,v2,v3);
    2673:   VecLockReadPush(v1);
    2674:   (*mat->ops->multtransposeadd)(mat,v1,v2,v3);
    2675:   VecLockReadPop(v1);
    2676:   PetscLogEventEnd(MAT_MultTransposeAdd,mat,v1,v2,v3);
    2677:   PetscObjectStateIncrease((PetscObject)v3);
    2678:   return(0);
    2679: }

    2681: /*@
    2682:    MatMultHermitianTransposeAdd - Computes v3 = v2 + A^H * v1.

    2684:    Neighbor-wise Collective on Mat

    2686:    Input Parameters:
    2687: +  mat - the matrix
    2688: -  v1, v2 - the vectors

    2690:    Output Parameters:
    2691: .  v3 - the result

    2693:    Notes:
    2694:    The vectors v1 and v3 cannot be the same.  I.e., one cannot
    2695:    call MatMultHermitianTransposeAdd(A,v1,v2,v1).

    2697:    Level: beginner

    2699: .seealso: MatMultHermitianTranspose(), MatMultTranspose(), MatMultAdd(), MatMult()
    2700: @*/
    2701: PetscErrorCode MatMultHermitianTransposeAdd(Mat mat,Vec v1,Vec v2,Vec v3)
    2702: {

    2712:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2713:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2714:   if (v1 == v3) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"v1 and v3 must be different vectors");
    2715:   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);
    2716:   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);
    2717:   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);
    2718:   MatCheckPreallocated(mat,1);

    2720:   PetscLogEventBegin(MAT_MultHermitianTransposeAdd,mat,v1,v2,v3);
    2721:   VecLockReadPush(v1);
    2722:   if (mat->ops->multhermitiantransposeadd) {
    2723:     (*mat->ops->multhermitiantransposeadd)(mat,v1,v2,v3);
    2724:   } else {
    2725:     Vec w,z;
    2726:     VecDuplicate(v1,&w);
    2727:     VecCopy(v1,w);
    2728:     VecConjugate(w);
    2729:     VecDuplicate(v3,&z);
    2730:     MatMultTranspose(mat,w,z);
    2731:     VecDestroy(&w);
    2732:     VecConjugate(z);
    2733:     if (v2 != v3) {
    2734:       VecWAXPY(v3,1.0,v2,z);
    2735:     } else {
    2736:       VecAXPY(v3,1.0,z);
    2737:     }
    2738:     VecDestroy(&z);
    2739:   }
    2740:   VecLockReadPop(v1);
    2741:   PetscLogEventEnd(MAT_MultHermitianTransposeAdd,mat,v1,v2,v3);
    2742:   PetscObjectStateIncrease((PetscObject)v3);
    2743:   return(0);
    2744: }

    2746: /*@
    2747:    MatMultConstrained - The inner multiplication routine for a
    2748:    constrained matrix P^T A P.

    2750:    Neighbor-wise Collective on Mat

    2752:    Input Parameters:
    2753: +  mat - the matrix
    2754: -  x   - the vector to be multilplied

    2756:    Output Parameters:
    2757: .  y - the result

    2759:    Notes:
    2760:    The vectors x and y cannot be the same.  I.e., one cannot
    2761:    call MatMult(A,y,y).

    2763:    Level: beginner

    2765: .seealso: MatMult(), MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    2766: @*/
    2767: PetscErrorCode MatMultConstrained(Mat mat,Vec x,Vec y)
    2768: {

    2775:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2776:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2777:   if (x == y) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2778:   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);
    2779:   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);
    2780:   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);

    2782:   PetscLogEventBegin(MAT_MultConstrained,mat,x,y,0);
    2783:   VecLockReadPush(x);
    2784:   (*mat->ops->multconstrained)(mat,x,y);
    2785:   VecLockReadPop(x);
    2786:   PetscLogEventEnd(MAT_MultConstrained,mat,x,y,0);
    2787:   PetscObjectStateIncrease((PetscObject)y);
    2788:   return(0);
    2789: }

    2791: /*@
    2792:    MatMultTransposeConstrained - The inner multiplication routine for a
    2793:    constrained matrix P^T A^T P.

    2795:    Neighbor-wise Collective on Mat

    2797:    Input Parameters:
    2798: +  mat - the matrix
    2799: -  x   - the vector to be multilplied

    2801:    Output Parameters:
    2802: .  y - the result

    2804:    Notes:
    2805:    The vectors x and y cannot be the same.  I.e., one cannot
    2806:    call MatMult(A,y,y).

    2808:    Level: beginner

    2810: .seealso: MatMult(), MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    2811: @*/
    2812: PetscErrorCode MatMultTransposeConstrained(Mat mat,Vec x,Vec y)
    2813: {

    2820:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    2821:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    2822:   if (x == y) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"x and y must be different vectors");
    2823:   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);
    2824:   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);

    2826:   PetscLogEventBegin(MAT_MultConstrained,mat,x,y,0);
    2827:   (*mat->ops->multtransposeconstrained)(mat,x,y);
    2828:   PetscLogEventEnd(MAT_MultConstrained,mat,x,y,0);
    2829:   PetscObjectStateIncrease((PetscObject)y);
    2830:   return(0);
    2831: }

    2833: /*@C
    2834:    MatGetFactorType - gets the type of factorization it is

    2836:    Not Collective

    2838:    Input Parameters:
    2839: .  mat - the matrix

    2841:    Output Parameters:
    2842: .  t - the type, one of MAT_FACTOR_NONE, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ILU, MAT_FACTOR_ICC,MAT_FACTOR_ILUDT

    2844:    Level: intermediate

    2846: .seealso: MatFactorType, MatGetFactor(), MatSetFactorType()
    2847: @*/
    2848: PetscErrorCode MatGetFactorType(Mat mat,MatFactorType *t)
    2849: {
    2854:   *t = mat->factortype;
    2855:   return(0);
    2856: }

    2858: /*@C
    2859:    MatSetFactorType - sets the type of factorization it is

    2861:    Logically Collective on Mat

    2863:    Input Parameters:
    2864: +  mat - the matrix
    2865: -  t - the type, one of MAT_FACTOR_NONE, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ILU, MAT_FACTOR_ICC,MAT_FACTOR_ILUDT

    2867:    Level: intermediate

    2869: .seealso: MatFactorType, MatGetFactor(), MatGetFactorType()
    2870: @*/
    2871: PetscErrorCode MatSetFactorType(Mat mat, MatFactorType t)
    2872: {
    2876:   mat->factortype = t;
    2877:   return(0);
    2878: }

    2880: /* ------------------------------------------------------------*/
    2881: /*@C
    2882:    MatGetInfo - Returns information about matrix storage (number of
    2883:    nonzeros, memory, etc.).

    2885:    Collective on Mat if MAT_GLOBAL_MAX or MAT_GLOBAL_SUM is used as the flag

    2887:    Input Parameters:
    2888: .  mat - the matrix

    2890:    Output Parameters:
    2891: +  flag - flag indicating the type of parameters to be returned
    2892:    (MAT_LOCAL - local matrix, MAT_GLOBAL_MAX - maximum over all processors,
    2893:    MAT_GLOBAL_SUM - sum over all processors)
    2894: -  info - matrix information context

    2896:    Notes:
    2897:    The MatInfo context contains a variety of matrix data, including
    2898:    number of nonzeros allocated and used, number of mallocs during
    2899:    matrix assembly, etc.  Additional information for factored matrices
    2900:    is provided (such as the fill ratio, number of mallocs during
    2901:    factorization, etc.).  Much of this info is printed to PETSC_STDOUT
    2902:    when using the runtime options
    2903: $       -info -mat_view ::ascii_info

    2905:    Example for C/C++ Users:
    2906:    See the file ${PETSC_DIR}/include/petscmat.h for a complete list of
    2907:    data within the MatInfo context.  For example,
    2908: .vb
    2909:       MatInfo info;
    2910:       Mat     A;
    2911:       double  mal, nz_a, nz_u;

    2913:       MatGetInfo(A,MAT_LOCAL,&info);
    2914:       mal  = info.mallocs;
    2915:       nz_a = info.nz_allocated;
    2916: .ve

    2918:    Example for Fortran Users:
    2919:    Fortran users should declare info as a double precision
    2920:    array of dimension MAT_INFO_SIZE, and then extract the parameters
    2921:    of interest.  See the file ${PETSC_DIR}/include/petsc/finclude/petscmat.h
    2922:    a complete list of parameter names.
    2923: .vb
    2924:       double  precision info(MAT_INFO_SIZE)
    2925:       double  precision mal, nz_a
    2926:       Mat     A
    2927:       integer ierr

    2929:       call MatGetInfo(A,MAT_LOCAL,info,ierr)
    2930:       mal = info(MAT_INFO_MALLOCS)
    2931:       nz_a = info(MAT_INFO_NZ_ALLOCATED)
    2932: .ve

    2934:     Level: intermediate

    2936:     Developer Note: fortran interface is not autogenerated as the f90
    2937:     interface defintion cannot be generated correctly [due to MatInfo]

    2939: .seealso: MatStashGetInfo()

    2941: @*/
    2942: PetscErrorCode MatGetInfo(Mat mat,MatInfoType flag,MatInfo *info)
    2943: {

    2950:   if (!mat->ops->getinfo) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    2951:   MatCheckPreallocated(mat,1);
    2952:   (*mat->ops->getinfo)(mat,flag,info);
    2953:   return(0);
    2954: }

    2956: /*
    2957:    This is used by external packages where it is not easy to get the info from the actual
    2958:    matrix factorization.
    2959: */
    2960: PetscErrorCode MatGetInfo_External(Mat A,MatInfoType flag,MatInfo *info)
    2961: {

    2965:   PetscMemzero(info,sizeof(MatInfo));
    2966:   return(0);
    2967: }

    2969: /* ----------------------------------------------------------*/

    2971: /*@C
    2972:    MatLUFactor - Performs in-place LU factorization of matrix.

    2974:    Collective on Mat

    2976:    Input Parameters:
    2977: +  mat - the matrix
    2978: .  row - row permutation
    2979: .  col - column permutation
    2980: -  info - options for factorization, includes
    2981: $          fill - expected fill as ratio of original fill.
    2982: $          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    2983: $                   Run with the option -info to determine an optimal value to use

    2985:    Notes:
    2986:    Most users should employ the simplified KSP interface for linear solvers
    2987:    instead of working directly with matrix algebra routines such as this.
    2988:    See, e.g., KSPCreate().

    2990:    This changes the state of the matrix to a factored matrix; it cannot be used
    2991:    for example with MatSetValues() unless one first calls MatSetUnfactored().

    2993:    Level: developer

    2995: .seealso: MatLUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor(),
    2996:           MatGetOrdering(), MatSetUnfactored(), MatFactorInfo, MatGetFactor()

    2998:     Developer Note: fortran interface is not autogenerated as the f90
    2999:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3001: @*/
    3002: PetscErrorCode MatLUFactor(Mat mat,IS row,IS col,const MatFactorInfo *info)
    3003: {
    3005:   MatFactorInfo  tinfo;

    3013:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3014:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3015:   if (!mat->ops->lufactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3016:   MatCheckPreallocated(mat,1);
    3017:   if (!info) {
    3018:     MatFactorInfoInitialize(&tinfo);
    3019:     info = &tinfo;
    3020:   }

    3022:   PetscLogEventBegin(MAT_LUFactor,mat,row,col,0);
    3023:   (*mat->ops->lufactor)(mat,row,col,info);
    3024:   PetscLogEventEnd(MAT_LUFactor,mat,row,col,0);
    3025:   PetscObjectStateIncrease((PetscObject)mat);
    3026:   return(0);
    3027: }

    3029: /*@C
    3030:    MatILUFactor - Performs in-place ILU factorization of matrix.

    3032:    Collective on Mat

    3034:    Input Parameters:
    3035: +  mat - the matrix
    3036: .  row - row permutation
    3037: .  col - column permutation
    3038: -  info - structure containing
    3039: $      levels - number of levels of fill.
    3040: $      expected fill - as ratio of original fill.
    3041: $      1 or 0 - indicating force fill on diagonal (improves robustness for matrices
    3042:                 missing diagonal entries)

    3044:    Notes:
    3045:    Probably really in-place only when level of fill is zero, otherwise allocates
    3046:    new space to store factored matrix and deletes previous memory.

    3048:    Most users should employ the simplified KSP interface for linear solvers
    3049:    instead of working directly with matrix algebra routines such as this.
    3050:    See, e.g., KSPCreate().

    3052:    Level: developer

    3054: .seealso: MatILUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor(), MatFactorInfo

    3056:     Developer Note: fortran interface is not autogenerated as the f90
    3057:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3059: @*/
    3060: PetscErrorCode MatILUFactor(Mat mat,IS row,IS col,const MatFactorInfo *info)
    3061: {

    3070:   if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"matrix must be square");
    3071:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3072:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3073:   if (!mat->ops->ilufactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3074:   MatCheckPreallocated(mat,1);

    3076:   PetscLogEventBegin(MAT_ILUFactor,mat,row,col,0);
    3077:   (*mat->ops->ilufactor)(mat,row,col,info);
    3078:   PetscLogEventEnd(MAT_ILUFactor,mat,row,col,0);
    3079:   PetscObjectStateIncrease((PetscObject)mat);
    3080:   return(0);
    3081: }

    3083: /*@C
    3084:    MatLUFactorSymbolic - Performs symbolic LU factorization of matrix.
    3085:    Call this routine before calling MatLUFactorNumeric().

    3087:    Collective on Mat

    3089:    Input Parameters:
    3090: +  fact - the factor matrix obtained with MatGetFactor()
    3091: .  mat - the matrix
    3092: .  row, col - row and column permutations
    3093: -  info - options for factorization, includes
    3094: $          fill - expected fill as ratio of original fill.
    3095: $          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3096: $                   Run with the option -info to determine an optimal value to use

    3099:    Notes:
    3100:     See Users-Manual: ch_mat for additional information about choosing the fill factor for better efficiency.

    3102:    Most users should employ the simplified KSP interface for linear solvers
    3103:    instead of working directly with matrix algebra routines such as this.
    3104:    See, e.g., KSPCreate().

    3106:    Level: developer

    3108: .seealso: MatLUFactor(), MatLUFactorNumeric(), MatCholeskyFactor(), MatFactorInfo, MatFactorInfoInitialize()

    3110:     Developer Note: fortran interface is not autogenerated as the f90
    3111:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3113: @*/
    3114: PetscErrorCode MatLUFactorSymbolic(Mat fact,Mat mat,IS row,IS col,const MatFactorInfo *info)
    3115: {
    3117:   MatFactorInfo  tinfo;

    3126:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3127:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3128:   if (!(fact)->ops->lufactorsymbolic) {
    3129:     MatSolverType stype;
    3130:     MatFactorGetSolverType(fact,&stype);
    3131:     SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic LU using solver package %s",((PetscObject)mat)->type_name,stype);
    3132:   }
    3133:   MatCheckPreallocated(mat,2);
    3134:   if (!info) {
    3135:     MatFactorInfoInitialize(&tinfo);
    3136:     info = &tinfo;
    3137:   }

    3139:   PetscLogEventBegin(MAT_LUFactorSymbolic,mat,row,col,0);
    3140:   (fact->ops->lufactorsymbolic)(fact,mat,row,col,info);
    3141:   PetscLogEventEnd(MAT_LUFactorSymbolic,mat,row,col,0);
    3142:   PetscObjectStateIncrease((PetscObject)fact);
    3143:   return(0);
    3144: }

    3146: /*@C
    3147:    MatLUFactorNumeric - Performs numeric LU factorization of a matrix.
    3148:    Call this routine after first calling MatLUFactorSymbolic().

    3150:    Collective on Mat

    3152:    Input Parameters:
    3153: +  fact - the factor matrix obtained with MatGetFactor()
    3154: .  mat - the matrix
    3155: -  info - options for factorization

    3157:    Notes:
    3158:    See MatLUFactor() for in-place factorization.  See
    3159:    MatCholeskyFactorNumeric() for the symmetric, positive definite case.

    3161:    Most users should employ the simplified KSP interface for linear solvers
    3162:    instead of working directly with matrix algebra routines such as this.
    3163:    See, e.g., KSPCreate().

    3165:    Level: developer

    3167: .seealso: MatLUFactorSymbolic(), MatLUFactor(), MatCholeskyFactor()

    3169:     Developer Note: fortran interface is not autogenerated as the f90
    3170:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3172: @*/
    3173: PetscErrorCode MatLUFactorNumeric(Mat fact,Mat mat,const MatFactorInfo *info)
    3174: {
    3175:   MatFactorInfo  tinfo;

    3183:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3184:   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);

    3186:   if (!(fact)->ops->lufactornumeric) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s numeric LU",((PetscObject)mat)->type_name);
    3187:   MatCheckPreallocated(mat,2);
    3188:   if (!info) {
    3189:     MatFactorInfoInitialize(&tinfo);
    3190:     info = &tinfo;
    3191:   }

    3193:   PetscLogEventBegin(MAT_LUFactorNumeric,mat,fact,0,0);
    3194:   (fact->ops->lufactornumeric)(fact,mat,info);
    3195:   PetscLogEventEnd(MAT_LUFactorNumeric,mat,fact,0,0);
    3196:   MatViewFromOptions(fact,NULL,"-mat_factor_view");
    3197:   PetscObjectStateIncrease((PetscObject)fact);
    3198:   return(0);
    3199: }

    3201: /*@C
    3202:    MatCholeskyFactor - Performs in-place Cholesky factorization of a
    3203:    symmetric matrix.

    3205:    Collective on Mat

    3207:    Input Parameters:
    3208: +  mat - the matrix
    3209: .  perm - row and column permutations
    3210: -  f - expected fill as ratio of original fill

    3212:    Notes:
    3213:    See MatLUFactor() for the nonsymmetric case.  See also
    3214:    MatCholeskyFactorSymbolic(), and MatCholeskyFactorNumeric().

    3216:    Most users should employ the simplified KSP interface for linear solvers
    3217:    instead of working directly with matrix algebra routines such as this.
    3218:    See, e.g., KSPCreate().

    3220:    Level: developer

    3222: .seealso: MatLUFactor(), MatCholeskyFactorSymbolic(), MatCholeskyFactorNumeric()
    3223:           MatGetOrdering()

    3225:     Developer Note: fortran interface is not autogenerated as the f90
    3226:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3228: @*/
    3229: PetscErrorCode MatCholeskyFactor(Mat mat,IS perm,const MatFactorInfo *info)
    3230: {
    3232:   MatFactorInfo  tinfo;

    3239:   if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Matrix must be square");
    3240:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3241:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3242:   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);
    3243:   MatCheckPreallocated(mat,1);
    3244:   if (!info) {
    3245:     MatFactorInfoInitialize(&tinfo);
    3246:     info = &tinfo;
    3247:   }

    3249:   PetscLogEventBegin(MAT_CholeskyFactor,mat,perm,0,0);
    3250:   (*mat->ops->choleskyfactor)(mat,perm,info);
    3251:   PetscLogEventEnd(MAT_CholeskyFactor,mat,perm,0,0);
    3252:   PetscObjectStateIncrease((PetscObject)mat);
    3253:   return(0);
    3254: }

    3256: /*@C
    3257:    MatCholeskyFactorSymbolic - Performs symbolic Cholesky factorization
    3258:    of a symmetric matrix.

    3260:    Collective on Mat

    3262:    Input Parameters:
    3263: +  fact - the factor matrix obtained with MatGetFactor()
    3264: .  mat - the matrix
    3265: .  perm - row and column permutations
    3266: -  info - options for factorization, includes
    3267: $          fill - expected fill as ratio of original fill.
    3268: $          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3269: $                   Run with the option -info to determine an optimal value to use

    3271:    Notes:
    3272:    See MatLUFactorSymbolic() for the nonsymmetric case.  See also
    3273:    MatCholeskyFactor() and MatCholeskyFactorNumeric().

    3275:    Most users should employ the simplified KSP interface for linear solvers
    3276:    instead of working directly with matrix algebra routines such as this.
    3277:    See, e.g., KSPCreate().

    3279:    Level: developer

    3281: .seealso: MatLUFactorSymbolic(), MatCholeskyFactor(), MatCholeskyFactorNumeric()
    3282:           MatGetOrdering()

    3284:     Developer Note: fortran interface is not autogenerated as the f90
    3285:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3287: @*/
    3288: PetscErrorCode MatCholeskyFactorSymbolic(Mat fact,Mat mat,IS perm,const MatFactorInfo *info)
    3289: {
    3291:   MatFactorInfo  tinfo;

    3299:   if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"Matrix must be square");
    3300:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3301:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3302:   if (!(fact)->ops->choleskyfactorsymbolic) {
    3303:     MatSolverType stype;
    3304:     MatFactorGetSolverType(fact,&stype);
    3305:     SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s symbolic factor Cholesky using solver package %s",((PetscObject)mat)->type_name,stype);
    3306:   }
    3307:   MatCheckPreallocated(mat,2);
    3308:   if (!info) {
    3309:     MatFactorInfoInitialize(&tinfo);
    3310:     info = &tinfo;
    3311:   }

    3313:   PetscLogEventBegin(MAT_CholeskyFactorSymbolic,mat,perm,0,0);
    3314:   (fact->ops->choleskyfactorsymbolic)(fact,mat,perm,info);
    3315:   PetscLogEventEnd(MAT_CholeskyFactorSymbolic,mat,perm,0,0);
    3316:   PetscObjectStateIncrease((PetscObject)fact);
    3317:   return(0);
    3318: }

    3320: /*@C
    3321:    MatCholeskyFactorNumeric - Performs numeric Cholesky factorization
    3322:    of a symmetric matrix. Call this routine after first calling
    3323:    MatCholeskyFactorSymbolic().

    3325:    Collective on Mat

    3327:    Input Parameters:
    3328: +  fact - the factor matrix obtained with MatGetFactor()
    3329: .  mat - the initial matrix
    3330: .  info - options for factorization
    3331: -  fact - the symbolic factor of mat

    3334:    Notes:
    3335:    Most users should employ the simplified KSP interface for linear solvers
    3336:    instead of working directly with matrix algebra routines such as this.
    3337:    See, e.g., KSPCreate().

    3339:    Level: developer

    3341: .seealso: MatCholeskyFactorSymbolic(), MatCholeskyFactor(), MatLUFactorNumeric()

    3343:     Developer Note: fortran interface is not autogenerated as the f90
    3344:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3346: @*/
    3347: PetscErrorCode MatCholeskyFactorNumeric(Mat fact,Mat mat,const MatFactorInfo *info)
    3348: {
    3349:   MatFactorInfo  tinfo;

    3357:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3358:   if (!(fact)->ops->choleskyfactornumeric) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s numeric factor Cholesky",((PetscObject)mat)->type_name);
    3359:   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);
    3360:   MatCheckPreallocated(mat,2);
    3361:   if (!info) {
    3362:     MatFactorInfoInitialize(&tinfo);
    3363:     info = &tinfo;
    3364:   }

    3366:   PetscLogEventBegin(MAT_CholeskyFactorNumeric,mat,fact,0,0);
    3367:   (fact->ops->choleskyfactornumeric)(fact,mat,info);
    3368:   PetscLogEventEnd(MAT_CholeskyFactorNumeric,mat,fact,0,0);
    3369:   MatViewFromOptions(fact,NULL,"-mat_factor_view");
    3370:   PetscObjectStateIncrease((PetscObject)fact);
    3371:   return(0);
    3372: }

    3374: /*@
    3375:    MatQRFactor - Performs in-place QR factorization of matrix.

    3377:    Collective on Mat

    3379:    Input Parameters:
    3380: +  mat - the matrix
    3381: .  col - column permutation
    3382: -  info - options for factorization, includes
    3383: $          fill - expected fill as ratio of original fill.
    3384: $          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3385: $                   Run with the option -info to determine an optimal value to use

    3387:    Notes:
    3388:    Most users should employ the simplified KSP interface for linear solvers
    3389:    instead of working directly with matrix algebra routines such as this.
    3390:    See, e.g., KSPCreate().

    3392:    This changes the state of the matrix to a factored matrix; it cannot be used
    3393:    for example with MatSetValues() unless one first calls MatSetUnfactored().

    3395:    Level: developer

    3397: .seealso: MatQRFactorSymbolic(), MatQRFactorNumeric(), MatLUFactor(),
    3398:           MatSetUnfactored(), MatFactorInfo, MatGetFactor()

    3400:     Developer Note: fortran interface is not autogenerated as the f90
    3401:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3403: @*/
    3404: PetscErrorCode MatQRFactor(Mat mat, IS col, const MatFactorInfo *info)
    3405: {

    3413:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3414:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3415:   MatCheckPreallocated(mat,1);
    3416:   PetscLogEventBegin(MAT_QRFactor,mat,col,0,0);
    3417:   PetscUseMethod(mat,"MatQRFactor_C", (Mat,IS,const MatFactorInfo*), (mat, col, info));
    3418:   PetscLogEventEnd(MAT_QRFactor,mat,col,0,0);
    3419:   PetscObjectStateIncrease((PetscObject)mat);
    3420:   return(0);
    3421: }

    3423: /*@
    3424:    MatQRFactorSymbolic - Performs symbolic QR factorization of matrix.
    3425:    Call this routine before calling MatQRFactorNumeric().

    3427:    Collective on Mat

    3429:    Input Parameters:
    3430: +  fact - the factor matrix obtained with MatGetFactor()
    3431: .  mat - the matrix
    3432: .  col - column permutation
    3433: -  info - options for factorization, includes
    3434: $          fill - expected fill as ratio of original fill.
    3435: $          dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3436: $                   Run with the option -info to determine an optimal value to use

    3438:    Most users should employ the simplified KSP interface for linear solvers
    3439:    instead of working directly with matrix algebra routines such as this.
    3440:    See, e.g., KSPCreate().

    3442:    Level: developer

    3444: .seealso: MatQRFactor(), MatQRFactorNumeric(), MatLUFactor(), MatFactorInfo, MatFactorInfoInitialize()

    3446:     Developer Note: fortran interface is not autogenerated as the f90
    3447:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3449: @*/
    3450: PetscErrorCode MatQRFactorSymbolic(Mat fact,Mat mat,IS col,const MatFactorInfo *info)
    3451: {
    3453:   MatFactorInfo  tinfo;

    3461:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3462:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    3463:   MatCheckPreallocated(mat,2);
    3464:   if (!info) {
    3465:     MatFactorInfoInitialize(&tinfo);
    3466:     info = &tinfo;
    3467:   }

    3469:   PetscLogEventBegin(MAT_QRFactorSymbolic,fact,mat,col,0);
    3470:   PetscUseMethod(fact,"MatQRFactorSymbolic_C", (Mat,Mat,IS,const MatFactorInfo*), (fact, mat, col, info));
    3471:   PetscLogEventEnd(MAT_QRFactorSymbolic,fact,mat,col,0);
    3472:   PetscObjectStateIncrease((PetscObject)fact);
    3473:   return(0);
    3474: }

    3476: /*@
    3477:    MatQRFactorNumeric - Performs numeric QR factorization of a matrix.
    3478:    Call this routine after first calling MatQRFactorSymbolic().

    3480:    Collective on Mat

    3482:    Input Parameters:
    3483: +  fact - the factor matrix obtained with MatGetFactor()
    3484: .  mat - the matrix
    3485: -  info - options for factorization

    3487:    Notes:
    3488:    See MatQRFactor() for in-place factorization.

    3490:    Most users should employ the simplified KSP interface for linear solvers
    3491:    instead of working directly with matrix algebra routines such as this.
    3492:    See, e.g., KSPCreate().

    3494:    Level: developer

    3496: .seealso: MatQRFactorSymbolic(), MatLUFactor()

    3498:     Developer Note: fortran interface is not autogenerated as the f90
    3499:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    3501: @*/
    3502: PetscErrorCode MatQRFactorNumeric(Mat fact,Mat mat,const MatFactorInfo *info)
    3503: {
    3504:   MatFactorInfo  tinfo;

    3512:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    3513:   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);

    3515:   MatCheckPreallocated(mat,2);
    3516:   if (!info) {
    3517:     MatFactorInfoInitialize(&tinfo);
    3518:     info = &tinfo;
    3519:   }

    3521:   PetscLogEventBegin(MAT_QRFactorNumeric,mat,fact,0,0);
    3522:   PetscUseMethod(fact,"MatQRFactorNumeric_C", (Mat,Mat,const MatFactorInfo*), (fact, mat, info));
    3523:   PetscLogEventEnd(MAT_QRFactorNumeric,mat,fact,0,0);
    3524:   MatViewFromOptions(fact,NULL,"-mat_factor_view");
    3525:   PetscObjectStateIncrease((PetscObject)fact);
    3526:   return(0);
    3527: }

    3529: /* ----------------------------------------------------------------*/
    3530: /*@
    3531:    MatSolve - Solves A x = b, given a factored matrix.

    3533:    Neighbor-wise Collective on Mat

    3535:    Input Parameters:
    3536: +  mat - the factored matrix
    3537: -  b - the right-hand-side vector

    3539:    Output Parameter:
    3540: .  x - the result vector

    3542:    Notes:
    3543:    The vectors b and x cannot be the same.  I.e., one cannot
    3544:    call MatSolve(A,x,x).

    3546:    Notes:
    3547:    Most users should employ the simplified KSP interface for linear solvers
    3548:    instead of working directly with matrix algebra routines such as this.
    3549:    See, e.g., KSPCreate().

    3551:    Level: developer

    3553: .seealso: MatSolveAdd(), MatSolveTranspose(), MatSolveTransposeAdd()
    3554: @*/
    3555: PetscErrorCode MatSolve(Mat mat,Vec b,Vec x)
    3556: {

    3566:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3567:   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);
    3568:   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);
    3569:   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);
    3570:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3571:   MatCheckPreallocated(mat,1);

    3573:   PetscLogEventBegin(MAT_Solve,mat,b,x,0);
    3574:   if (mat->factorerrortype) {
    3575:     PetscInfo1(mat,"MatFactorError %D\n",mat->factorerrortype);
    3576:     VecSetInf(x);
    3577:   } else {
    3578:     if (!mat->ops->solve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3579:     (*mat->ops->solve)(mat,b,x);
    3580:   }
    3581:   PetscLogEventEnd(MAT_Solve,mat,b,x,0);
    3582:   PetscObjectStateIncrease((PetscObject)x);
    3583:   return(0);
    3584: }

    3586: static PetscErrorCode MatMatSolve_Basic(Mat A,Mat B,Mat X,PetscBool trans)
    3587: {
    3589:   Vec            b,x;
    3590:   PetscInt       m,N,i;
    3591:   PetscScalar    *bb,*xx;
    3592:   PetscErrorCode (*f)(Mat,Vec,Vec);

    3595:   if (A->factorerrortype) {
    3596:     PetscInfo1(A,"MatFactorError %D\n",A->factorerrortype);
    3597:     MatSetInf(X);
    3598:     return(0);
    3599:   }
    3600:   f = trans ? A->ops->solvetranspose : A->ops->solve;
    3601:   if (!f) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)A)->type_name);

    3603:   MatDenseGetArrayRead(B,(const PetscScalar**)&bb);
    3604:   MatDenseGetArray(X,&xx);
    3605:   MatGetLocalSize(B,&m,NULL);  /* number local rows */
    3606:   MatGetSize(B,NULL,&N);       /* total columns in dense matrix */
    3607:   MatCreateVecs(A,&x,&b);
    3608:   for (i=0; i<N; i++) {
    3609:     VecPlaceArray(b,bb + i*m);
    3610:     VecPlaceArray(x,xx + i*m);
    3611:     (*f)(A,b,x);
    3612:     VecResetArray(x);
    3613:     VecResetArray(b);
    3614:   }
    3615:   VecDestroy(&b);
    3616:   VecDestroy(&x);
    3617:   MatDenseRestoreArrayRead(B,(const PetscScalar**)&bb);
    3618:   MatDenseRestoreArray(X,&xx);
    3619:   return(0);
    3620: }

    3622: /*@
    3623:    MatMatSolve - Solves A X = B, given a factored matrix.

    3625:    Neighbor-wise Collective on Mat

    3627:    Input Parameters:
    3628: +  A - the factored matrix
    3629: -  B - the right-hand-side matrix MATDENSE (or sparse -- when using MUMPS)

    3631:    Output Parameter:
    3632: .  X - the result matrix (dense matrix)

    3634:    Notes:
    3635:    If B is a MATDENSE matrix then one can call MatMatSolve(A,B,B) except with MKL_CPARDISO;
    3636:    otherwise, B and X cannot be the same.

    3638:    Notes:
    3639:    Most users should usually employ the simplified KSP interface for linear solvers
    3640:    instead of working directly with matrix algebra routines such as this.
    3641:    See, e.g., KSPCreate(). However KSP can only solve for one vector (column of X)
    3642:    at a time.

    3644:    Level: developer

    3646: .seealso: MatMatSolveTranspose(), MatLUFactor(), MatCholeskyFactor()
    3647: @*/
    3648: PetscErrorCode MatMatSolve(Mat A,Mat B,Mat X)
    3649: {

    3659:   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);
    3660:   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);
    3661:   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");
    3662:   if (!A->rmap->N && !A->cmap->N) return(0);
    3663:   if (!A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    3664:   MatCheckPreallocated(A,1);

    3666:   PetscLogEventBegin(MAT_MatSolve,A,B,X,0);
    3667:   if (!A->ops->matsolve) {
    3668:     PetscInfo1(A,"Mat type %s using basic MatMatSolve\n",((PetscObject)A)->type_name);
    3669:     MatMatSolve_Basic(A,B,X,PETSC_FALSE);
    3670:   } else {
    3671:     (*A->ops->matsolve)(A,B,X);
    3672:   }
    3673:   PetscLogEventEnd(MAT_MatSolve,A,B,X,0);
    3674:   PetscObjectStateIncrease((PetscObject)X);
    3675:   return(0);
    3676: }

    3678: /*@
    3679:    MatMatSolveTranspose - Solves A^T X = B, given a factored matrix.

    3681:    Neighbor-wise Collective on Mat

    3683:    Input Parameters:
    3684: +  A - the factored matrix
    3685: -  B - the right-hand-side matrix  (dense matrix)

    3687:    Output Parameter:
    3688: .  X - the result matrix (dense matrix)

    3690:    Notes:
    3691:    The matrices B and X cannot be the same.  I.e., one cannot
    3692:    call MatMatSolveTranspose(A,X,X).

    3694:    Notes:
    3695:    Most users should usually employ the simplified KSP interface for linear solvers
    3696:    instead of working directly with matrix algebra routines such as this.
    3697:    See, e.g., KSPCreate(). However KSP can only solve for one vector (column of X)
    3698:    at a time.

    3700:    When using SuperLU_Dist or MUMPS as a parallel solver, PETSc will use their functionality to solve multiple right hand sides simultaneously.

    3702:    Level: developer

    3704: .seealso: MatMatSolve(), MatLUFactor(), MatCholeskyFactor()
    3705: @*/
    3706: PetscErrorCode MatMatSolveTranspose(Mat A,Mat B,Mat X)
    3707: {

    3717:   if (X == B) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_IDN,"X and B must be different matrices");
    3718:   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);
    3719:   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);
    3720:   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);
    3721:   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");
    3722:   if (!A->rmap->N && !A->cmap->N) return(0);
    3723:   if (!A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    3724:   MatCheckPreallocated(A,1);

    3726:   PetscLogEventBegin(MAT_MatSolve,A,B,X,0);
    3727:   if (!A->ops->matsolvetranspose) {
    3728:     PetscInfo1(A,"Mat type %s using basic MatMatSolveTranspose\n",((PetscObject)A)->type_name);
    3729:     MatMatSolve_Basic(A,B,X,PETSC_TRUE);
    3730:   } else {
    3731:     (*A->ops->matsolvetranspose)(A,B,X);
    3732:   }
    3733:   PetscLogEventEnd(MAT_MatSolve,A,B,X,0);
    3734:   PetscObjectStateIncrease((PetscObject)X);
    3735:   return(0);
    3736: }

    3738: /*@
    3739:    MatMatTransposeSolve - Solves A X = B^T, given a factored matrix.

    3741:    Neighbor-wise Collective on Mat

    3743:    Input Parameters:
    3744: +  A - the factored matrix
    3745: -  Bt - the transpose of right-hand-side matrix

    3747:    Output Parameter:
    3748: .  X - the result matrix (dense matrix)

    3750:    Notes:
    3751:    Most users should usually employ the simplified KSP interface for linear solvers
    3752:    instead of working directly with matrix algebra routines such as this.
    3753:    See, e.g., KSPCreate(). However KSP can only solve for one vector (column of X)
    3754:    at a time.

    3756:    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().

    3758:    Level: developer

    3760: .seealso: MatMatSolve(), MatMatSolveTranspose(), MatLUFactor(), MatCholeskyFactor()
    3761: @*/
    3762: PetscErrorCode MatMatTransposeSolve(Mat A,Mat Bt,Mat X)
    3763: {

    3774:   if (X == Bt) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_IDN,"X and B must be different matrices");
    3775:   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);
    3776:   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);
    3777:   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");
    3778:   if (!A->rmap->N && !A->cmap->N) return(0);
    3779:   if (!A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    3780:   MatCheckPreallocated(A,1);

    3782:   if (!A->ops->mattransposesolve) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)A)->type_name);
    3783:   PetscLogEventBegin(MAT_MatTrSolve,A,Bt,X,0);
    3784:   (*A->ops->mattransposesolve)(A,Bt,X);
    3785:   PetscLogEventEnd(MAT_MatTrSolve,A,Bt,X,0);
    3786:   PetscObjectStateIncrease((PetscObject)X);
    3787:   return(0);
    3788: }

    3790: /*@
    3791:    MatForwardSolve - Solves L x = b, given a factored matrix, A = LU, or
    3792:                             U^T*D^(1/2) x = b, given a factored symmetric matrix, A = U^T*D*U,

    3794:    Neighbor-wise Collective on Mat

    3796:    Input Parameters:
    3797: +  mat - the factored matrix
    3798: -  b - the right-hand-side vector

    3800:    Output Parameter:
    3801: .  x - the result vector

    3803:    Notes:
    3804:    MatSolve() should be used for most applications, as it performs
    3805:    a forward solve followed by a backward solve.

    3807:    The vectors b and x cannot be the same,  i.e., one cannot
    3808:    call MatForwardSolve(A,x,x).

    3810:    For matrix in seqsbaij format with block size larger than 1,
    3811:    the diagonal blocks are not implemented as D = D^(1/2) * D^(1/2) yet.
    3812:    MatForwardSolve() solves U^T*D y = b, and
    3813:    MatBackwardSolve() solves U x = y.
    3814:    Thus they do not provide a symmetric preconditioner.

    3816:    Most users should employ the simplified KSP interface for linear solvers
    3817:    instead of working directly with matrix algebra routines such as this.
    3818:    See, e.g., KSPCreate().

    3820:    Level: developer

    3822: .seealso: MatSolve(), MatBackwardSolve()
    3823: @*/
    3824: PetscErrorCode MatForwardSolve(Mat mat,Vec b,Vec x)
    3825: {

    3835:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3836:   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);
    3837:   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);
    3838:   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);
    3839:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3840:   MatCheckPreallocated(mat,1);

    3842:   if (!mat->ops->forwardsolve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3843:   PetscLogEventBegin(MAT_ForwardSolve,mat,b,x,0);
    3844:   (*mat->ops->forwardsolve)(mat,b,x);
    3845:   PetscLogEventEnd(MAT_ForwardSolve,mat,b,x,0);
    3846:   PetscObjectStateIncrease((PetscObject)x);
    3847:   return(0);
    3848: }

    3850: /*@
    3851:    MatBackwardSolve - Solves U x = b, given a factored matrix, A = LU.
    3852:                              D^(1/2) U x = b, given a factored symmetric matrix, A = U^T*D*U,

    3854:    Neighbor-wise Collective on Mat

    3856:    Input Parameters:
    3857: +  mat - the factored matrix
    3858: -  b - the right-hand-side vector

    3860:    Output Parameter:
    3861: .  x - the result vector

    3863:    Notes:
    3864:    MatSolve() should be used for most applications, as it performs
    3865:    a forward solve followed by a backward solve.

    3867:    The vectors b and x cannot be the same.  I.e., one cannot
    3868:    call MatBackwardSolve(A,x,x).

    3870:    For matrix in seqsbaij format with block size larger than 1,
    3871:    the diagonal blocks are not implemented as D = D^(1/2) * D^(1/2) yet.
    3872:    MatForwardSolve() solves U^T*D y = b, and
    3873:    MatBackwardSolve() solves U x = y.
    3874:    Thus they do not provide a symmetric preconditioner.

    3876:    Most users should employ the simplified KSP interface for linear solvers
    3877:    instead of working directly with matrix algebra routines such as this.
    3878:    See, e.g., KSPCreate().

    3880:    Level: developer

    3882: .seealso: MatSolve(), MatForwardSolve()
    3883: @*/
    3884: PetscErrorCode MatBackwardSolve(Mat mat,Vec b,Vec x)
    3885: {

    3895:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3896:   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);
    3897:   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);
    3898:   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);
    3899:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3900:   MatCheckPreallocated(mat,1);

    3902:   if (!mat->ops->backwardsolve) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    3903:   PetscLogEventBegin(MAT_BackwardSolve,mat,b,x,0);
    3904:   (*mat->ops->backwardsolve)(mat,b,x);
    3905:   PetscLogEventEnd(MAT_BackwardSolve,mat,b,x,0);
    3906:   PetscObjectStateIncrease((PetscObject)x);
    3907:   return(0);
    3908: }

    3910: /*@
    3911:    MatSolveAdd - Computes x = y + inv(A)*b, given a factored matrix.

    3913:    Neighbor-wise Collective on Mat

    3915:    Input Parameters:
    3916: +  mat - the factored matrix
    3917: .  b - the right-hand-side vector
    3918: -  y - the vector to be added to

    3920:    Output Parameter:
    3921: .  x - the result vector

    3923:    Notes:
    3924:    The vectors b and x cannot be the same.  I.e., one cannot
    3925:    call MatSolveAdd(A,x,y,x).

    3927:    Most users should employ the simplified KSP interface for linear solvers
    3928:    instead of working directly with matrix algebra routines such as this.
    3929:    See, e.g., KSPCreate().

    3931:    Level: developer

    3933: .seealso: MatSolve(), MatSolveTranspose(), MatSolveTransposeAdd()
    3934: @*/
    3935: PetscErrorCode MatSolveAdd(Mat mat,Vec b,Vec y,Vec x)
    3936: {
    3937:   PetscScalar    one = 1.0;
    3938:   Vec            tmp;

    3950:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    3951:   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);
    3952:   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);
    3953:   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);
    3954:   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);
    3955:   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);
    3956:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    3957:    MatCheckPreallocated(mat,1);

    3959:   PetscLogEventBegin(MAT_SolveAdd,mat,b,x,y);
    3960:   if (mat->factorerrortype) {
    3961:     PetscInfo1(mat,"MatFactorError %D\n",mat->factorerrortype);
    3962:     VecSetInf(x);
    3963:   } else if (mat->ops->solveadd) {
    3964:     (*mat->ops->solveadd)(mat,b,y,x);
    3965:   } else {
    3966:     /* do the solve then the add manually */
    3967:     if (x != y) {
    3968:       MatSolve(mat,b,x);
    3969:       VecAXPY(x,one,y);
    3970:     } else {
    3971:       VecDuplicate(x,&tmp);
    3972:       PetscLogObjectParent((PetscObject)mat,(PetscObject)tmp);
    3973:       VecCopy(x,tmp);
    3974:       MatSolve(mat,b,x);
    3975:       VecAXPY(x,one,tmp);
    3976:       VecDestroy(&tmp);
    3977:     }
    3978:   }
    3979:   PetscLogEventEnd(MAT_SolveAdd,mat,b,x,y);
    3980:   PetscObjectStateIncrease((PetscObject)x);
    3981:   return(0);
    3982: }

    3984: /*@
    3985:    MatSolveTranspose - Solves A' x = b, given a factored matrix.

    3987:    Neighbor-wise Collective on Mat

    3989:    Input Parameters:
    3990: +  mat - the factored matrix
    3991: -  b - the right-hand-side vector

    3993:    Output Parameter:
    3994: .  x - the result vector

    3996:    Notes:
    3997:    The vectors b and x cannot be the same.  I.e., one cannot
    3998:    call MatSolveTranspose(A,x,x).

    4000:    Most users should employ the simplified KSP interface for linear solvers
    4001:    instead of working directly with matrix algebra routines such as this.
    4002:    See, e.g., KSPCreate().

    4004:    Level: developer

    4006: .seealso: MatSolve(), MatSolveAdd(), MatSolveTransposeAdd()
    4007: @*/
    4008: PetscErrorCode MatSolveTranspose(Mat mat,Vec b,Vec x)
    4009: {

    4019:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    4020:   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);
    4021:   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);
    4022:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    4023:   MatCheckPreallocated(mat,1);
    4024:   PetscLogEventBegin(MAT_SolveTranspose,mat,b,x,0);
    4025:   if (mat->factorerrortype) {
    4026:     PetscInfo1(mat,"MatFactorError %D\n",mat->factorerrortype);
    4027:     VecSetInf(x);
    4028:   } else {
    4029:     if (!mat->ops->solvetranspose) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s",((PetscObject)mat)->type_name);
    4030:     (*mat->ops->solvetranspose)(mat,b,x);
    4031:   }
    4032:   PetscLogEventEnd(MAT_SolveTranspose,mat,b,x,0);
    4033:   PetscObjectStateIncrease((PetscObject)x);
    4034:   return(0);
    4035: }

    4037: /*@
    4038:    MatSolveTransposeAdd - Computes x = y + inv(Transpose(A)) b, given a
    4039:                       factored matrix.

    4041:    Neighbor-wise Collective on Mat

    4043:    Input Parameters:
    4044: +  mat - the factored matrix
    4045: .  b - the right-hand-side vector
    4046: -  y - the vector to be added to

    4048:    Output Parameter:
    4049: .  x - the result vector

    4051:    Notes:
    4052:    The vectors b and x cannot be the same.  I.e., one cannot
    4053:    call MatSolveTransposeAdd(A,x,y,x).

    4055:    Most users should employ the simplified KSP interface for linear solvers
    4056:    instead of working directly with matrix algebra routines such as this.
    4057:    See, e.g., KSPCreate().

    4059:    Level: developer

    4061: .seealso: MatSolve(), MatSolveAdd(), MatSolveTranspose()
    4062: @*/
    4063: PetscErrorCode MatSolveTransposeAdd(Mat mat,Vec b,Vec y,Vec x)
    4064: {
    4065:   PetscScalar    one = 1.0;
    4067:   Vec            tmp;

    4078:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    4079:   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);
    4080:   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);
    4081:   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);
    4082:   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);
    4083:   if (!mat->rmap->N && !mat->cmap->N) return(0);
    4084:    MatCheckPreallocated(mat,1);

    4086:   PetscLogEventBegin(MAT_SolveTransposeAdd,mat,b,x,y);
    4087:   if (mat->factorerrortype) {
    4088:     PetscInfo1(mat,"MatFactorError %D\n",mat->factorerrortype);
    4089:     VecSetInf(x);
    4090:   } else if (mat->ops->solvetransposeadd){
    4091:     (*mat->ops->solvetransposeadd)(mat,b,y,x);
    4092:   } else {
    4093:     /* do the solve then the add manually */
    4094:     if (x != y) {
    4095:       MatSolveTranspose(mat,b,x);
    4096:       VecAXPY(x,one,y);
    4097:     } else {
    4098:       VecDuplicate(x,&tmp);
    4099:       PetscLogObjectParent((PetscObject)mat,(PetscObject)tmp);
    4100:       VecCopy(x,tmp);
    4101:       MatSolveTranspose(mat,b,x);
    4102:       VecAXPY(x,one,tmp);
    4103:       VecDestroy(&tmp);
    4104:     }
    4105:   }
    4106:   PetscLogEventEnd(MAT_SolveTransposeAdd,mat,b,x,y);
    4107:   PetscObjectStateIncrease((PetscObject)x);
    4108:   return(0);
    4109: }
    4110: /* ----------------------------------------------------------------*/

    4112: /*@
    4113:    MatSOR - Computes relaxation (SOR, Gauss-Seidel) sweeps.

    4115:    Neighbor-wise Collective on Mat

    4117:    Input Parameters:
    4118: +  mat - the matrix
    4119: .  b - the right hand side
    4120: .  omega - the relaxation factor
    4121: .  flag - flag indicating the type of SOR (see below)
    4122: .  shift -  diagonal shift
    4123: .  its - the number of iterations
    4124: -  lits - the number of local iterations

    4126:    Output Parameters:
    4127: .  x - the solution (can contain an initial guess, use option SOR_ZERO_INITIAL_GUESS to indicate no guess)

    4129:    SOR Flags:
    4130: +     SOR_FORWARD_SWEEP - forward SOR
    4131: .     SOR_BACKWARD_SWEEP - backward SOR
    4132: .     SOR_SYMMETRIC_SWEEP - SSOR (symmetric SOR)
    4133: .     SOR_LOCAL_FORWARD_SWEEP - local forward SOR
    4134: .     SOR_LOCAL_BACKWARD_SWEEP - local forward SOR
    4135: .     SOR_LOCAL_SYMMETRIC_SWEEP - local SSOR
    4136: .     SOR_APPLY_UPPER, SOR_APPLY_LOWER - applies
    4137:          upper/lower triangular part of matrix to
    4138:          vector (with omega)
    4139: -     SOR_ZERO_INITIAL_GUESS - zero initial guess

    4141:    Notes:
    4142:    SOR_LOCAL_FORWARD_SWEEP, SOR_LOCAL_BACKWARD_SWEEP, and
    4143:    SOR_LOCAL_SYMMETRIC_SWEEP perform separate independent smoothings
    4144:    on each processor.

    4146:    Application programmers will not generally use MatSOR() directly,
    4147:    but instead will employ the KSP/PC interface.

    4149:    Notes:
    4150:     for BAIJ, SBAIJ, and AIJ matrices with Inodes this does a block SOR smoothing, otherwise it does a pointwise smoothing

    4152:    Notes for Advanced Users:
    4153:    The flags are implemented as bitwise inclusive or operations.
    4154:    For example, use (SOR_ZERO_INITIAL_GUESS | SOR_SYMMETRIC_SWEEP)
    4155:    to specify a zero initial guess for SSOR.

    4157:    Most users should employ the simplified KSP interface for linear solvers
    4158:    instead of working directly with matrix algebra routines such as this.
    4159:    See, e.g., KSPCreate().

    4161:    Vectors x and b CANNOT be the same

    4163:    Developer Note: We should add block SOR support for AIJ matrices with block size set to great than one and no inodes

    4165:    Level: developer

    4167: @*/
    4168: PetscErrorCode MatSOR(Mat mat,Vec b,PetscReal omega,MatSORType flag,PetscReal shift,PetscInt its,PetscInt lits,Vec x)
    4169: {

    4179:   if (!mat->ops->sor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4180:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4181:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4182:   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);
    4183:   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);
    4184:   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);
    4185:   if (its <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D positive",its);
    4186:   if (lits <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires local its %D positive",lits);
    4187:   if (b == x) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_IDN,"b and x vector cannot be the same");

    4189:   MatCheckPreallocated(mat,1);
    4190:   PetscLogEventBegin(MAT_SOR,mat,b,x,0);
    4191:   ierr =(*mat->ops->sor)(mat,b,omega,flag,shift,its,lits,x);
    4192:   PetscLogEventEnd(MAT_SOR,mat,b,x,0);
    4193:   PetscObjectStateIncrease((PetscObject)x);
    4194:   return(0);
    4195: }

    4197: /*
    4198:       Default matrix copy routine.
    4199: */
    4200: PetscErrorCode MatCopy_Basic(Mat A,Mat B,MatStructure str)
    4201: {
    4202:   PetscErrorCode    ierr;
    4203:   PetscInt          i,rstart = 0,rend = 0,nz;
    4204:   const PetscInt    *cwork;
    4205:   const PetscScalar *vwork;

    4208:   if (B->assembled) {
    4209:     MatZeroEntries(B);
    4210:   }
    4211:   if (str == SAME_NONZERO_PATTERN) {
    4212:     MatGetOwnershipRange(A,&rstart,&rend);
    4213:     for (i=rstart; i<rend; i++) {
    4214:       MatGetRow(A,i,&nz,&cwork,&vwork);
    4215:       MatSetValues(B,1,&i,nz,cwork,vwork,INSERT_VALUES);
    4216:       MatRestoreRow(A,i,&nz,&cwork,&vwork);
    4217:     }
    4218:   } else {
    4219:     MatAYPX(B,0.0,A,str);
    4220:   }
    4221:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    4222:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    4223:   return(0);
    4224: }

    4226: /*@
    4227:    MatCopy - Copies a matrix to another matrix.

    4229:    Collective on Mat

    4231:    Input Parameters:
    4232: +  A - the matrix
    4233: -  str - SAME_NONZERO_PATTERN or DIFFERENT_NONZERO_PATTERN

    4235:    Output Parameter:
    4236: .  B - where the copy is put

    4238:    Notes:
    4239:    If you use SAME_NONZERO_PATTERN then the two matrices must have the same nonzero pattern or the routine will crash.

    4241:    MatCopy() copies the matrix entries of a matrix to another existing
    4242:    matrix (after first zeroing the second matrix).  A related routine is
    4243:    MatConvert(), which first creates a new matrix and then copies the data.

    4245:    Level: intermediate

    4247: .seealso: MatConvert(), MatDuplicate()

    4249: @*/
    4250: PetscErrorCode MatCopy(Mat A,Mat B,MatStructure str)
    4251: {
    4253:   PetscInt       i;

    4261:   MatCheckPreallocated(B,2);
    4262:   if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4263:   if (A->factortype) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4264:   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);
    4265:   MatCheckPreallocated(A,1);
    4266:   if (A == B) return(0);

    4268:   PetscLogEventBegin(MAT_Copy,A,B,0,0);
    4269:   if (A->ops->copy) {
    4270:     (*A->ops->copy)(A,B,str);
    4271:   } else { /* generic conversion */
    4272:     MatCopy_Basic(A,B,str);
    4273:   }

    4275:   B->stencil.dim = A->stencil.dim;
    4276:   B->stencil.noc = A->stencil.noc;
    4277:   for (i=0; i<=A->stencil.dim; i++) {
    4278:     B->stencil.dims[i]   = A->stencil.dims[i];
    4279:     B->stencil.starts[i] = A->stencil.starts[i];
    4280:   }

    4282:   PetscLogEventEnd(MAT_Copy,A,B,0,0);
    4283:   PetscObjectStateIncrease((PetscObject)B);
    4284:   return(0);
    4285: }

    4287: /*@C
    4288:    MatConvert - Converts a matrix to another matrix, either of the same
    4289:    or different type.

    4291:    Collective on Mat

    4293:    Input Parameters:
    4294: +  mat - the matrix
    4295: .  newtype - new matrix type.  Use MATSAME to create a new matrix of the
    4296:    same type as the original matrix.
    4297: -  reuse - denotes if the destination matrix is to be created or reused.
    4298:    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
    4299:    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).

    4301:    Output Parameter:
    4302: .  M - pointer to place new matrix

    4304:    Notes:
    4305:    MatConvert() first creates a new matrix and then copies the data from
    4306:    the first matrix.  A related routine is MatCopy(), which copies the matrix
    4307:    entries of one matrix to another already existing matrix context.

    4309:    Cannot be used to convert a sequential matrix to parallel or parallel to sequential,
    4310:    the MPI communicator of the generated matrix is always the same as the communicator
    4311:    of the input matrix.

    4313:    Level: intermediate

    4315: .seealso: MatCopy(), MatDuplicate()
    4316: @*/
    4317: PetscErrorCode MatConvert(Mat mat, MatType newtype,MatReuse reuse,Mat *M)
    4318: {
    4320:   PetscBool      sametype,issame,flg,issymmetric,ishermitian;
    4321:   char           convname[256],mtype[256];
    4322:   Mat            B;

    4328:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4329:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4330:   MatCheckPreallocated(mat,1);

    4332:   PetscOptionsGetString(((PetscObject)mat)->options,((PetscObject)mat)->prefix,"-matconvert_type",mtype,sizeof(mtype),&flg);
    4333:   if (flg) newtype = mtype;

    4335:   PetscObjectTypeCompare((PetscObject)mat,newtype,&sametype);
    4336:   PetscStrcmp(newtype,"same",&issame);
    4337:   if ((reuse == MAT_INPLACE_MATRIX) && (mat != *M)) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"MAT_INPLACE_MATRIX requires same input and output matrix");
    4338:   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");

    4340:   if ((reuse == MAT_INPLACE_MATRIX) && (issame || sametype)) {
    4341:     PetscInfo3(mat,"Early return for inplace %s %d %d\n",((PetscObject)mat)->type_name,sametype,issame);
    4342:     return(0);
    4343:   }

    4345:   /* Cache Mat options because some converter use MatHeaderReplace  */
    4346:   issymmetric = mat->symmetric;
    4347:   ishermitian = mat->hermitian;

    4349:   if ((sametype || issame) && (reuse==MAT_INITIAL_MATRIX) && mat->ops->duplicate) {
    4350:     PetscInfo3(mat,"Calling duplicate for initial matrix %s %d %d\n",((PetscObject)mat)->type_name,sametype,issame);
    4351:     (*mat->ops->duplicate)(mat,MAT_COPY_VALUES,M);
    4352:   } else {
    4353:     PetscErrorCode (*conv)(Mat, MatType,MatReuse,Mat*)=NULL;
    4354:     const char     *prefix[3] = {"seq","mpi",""};
    4355:     PetscInt       i;
    4356:     /*
    4357:        Order of precedence:
    4358:        0) See if newtype is a superclass of the current matrix.
    4359:        1) See if a specialized converter is known to the current matrix.
    4360:        2) See if a specialized converter is known to the desired matrix class.
    4361:        3) See if a good general converter is registered for the desired class
    4362:           (as of 6/27/03 only MATMPIADJ falls into this category).
    4363:        4) See if a good general converter is known for the current matrix.
    4364:        5) Use a really basic converter.
    4365:     */

    4367:     /* 0) See if newtype is a superclass of the current matrix.
    4368:           i.e mat is mpiaij and newtype is aij */
    4369:     for (i=0; i<2; i++) {
    4370:       PetscStrncpy(convname,prefix[i],sizeof(convname));
    4371:       PetscStrlcat(convname,newtype,sizeof(convname));
    4372:       PetscStrcmp(convname,((PetscObject)mat)->type_name,&flg);
    4373:       PetscInfo3(mat,"Check superclass %s %s -> %d\n",convname,((PetscObject)mat)->type_name,flg);
    4374:       if (flg) {
    4375:         if (reuse == MAT_INPLACE_MATRIX) {
    4376:           PetscInfo(mat,"Early return\n");
    4377:           return(0);
    4378:         } else if (reuse == MAT_INITIAL_MATRIX && mat->ops->duplicate) {
    4379:           PetscInfo(mat,"Calling MatDuplicate\n");
    4380:           (*mat->ops->duplicate)(mat,MAT_COPY_VALUES,M);
    4381:           return(0);
    4382:         } else if (reuse == MAT_REUSE_MATRIX && mat->ops->copy) {
    4383:           PetscInfo(mat,"Calling MatCopy\n");
    4384:           MatCopy(mat,*M,SAME_NONZERO_PATTERN);
    4385:           return(0);
    4386:         }
    4387:       }
    4388:     }
    4389:     /* 1) See if a specialized converter is known to the current matrix and the desired class */
    4390:     for (i=0; i<3; i++) {
    4391:       PetscStrncpy(convname,"MatConvert_",sizeof(convname));
    4392:       PetscStrlcat(convname,((PetscObject)mat)->type_name,sizeof(convname));
    4393:       PetscStrlcat(convname,"_",sizeof(convname));
    4394:       PetscStrlcat(convname,prefix[i],sizeof(convname));
    4395:       PetscStrlcat(convname,issame ? ((PetscObject)mat)->type_name : newtype,sizeof(convname));
    4396:       PetscStrlcat(convname,"_C",sizeof(convname));
    4397:       PetscObjectQueryFunction((PetscObject)mat,convname,&conv);
    4398:       PetscInfo3(mat,"Check specialized (1) %s (%s) -> %d\n",convname,((PetscObject)mat)->type_name,!!conv);
    4399:       if (conv) goto foundconv;
    4400:     }

    4402:     /* 2)  See if a specialized converter is known to the desired matrix class. */
    4403:     MatCreate(PetscObjectComm((PetscObject)mat),&B);
    4404:     MatSetSizes(B,mat->rmap->n,mat->cmap->n,mat->rmap->N,mat->cmap->N);
    4405:     MatSetType(B,newtype);
    4406:     for (i=0; i<3; i++) {
    4407:       PetscStrncpy(convname,"MatConvert_",sizeof(convname));
    4408:       PetscStrlcat(convname,((PetscObject)mat)->type_name,sizeof(convname));
    4409:       PetscStrlcat(convname,"_",sizeof(convname));
    4410:       PetscStrlcat(convname,prefix[i],sizeof(convname));
    4411:       PetscStrlcat(convname,newtype,sizeof(convname));
    4412:       PetscStrlcat(convname,"_C",sizeof(convname));
    4413:       PetscObjectQueryFunction((PetscObject)B,convname,&conv);
    4414:       PetscInfo3(mat,"Check specialized (2) %s (%s) -> %d\n",convname,((PetscObject)B)->type_name,!!conv);
    4415:       if (conv) {
    4416:         MatDestroy(&B);
    4417:         goto foundconv;
    4418:       }
    4419:     }

    4421:     /* 3) See if a good general converter is registered for the desired class */
    4422:     conv = B->ops->convertfrom;
    4423:     PetscInfo2(mat,"Check convertfrom (%s) -> %d\n",((PetscObject)B)->type_name,!!conv);
    4424:     MatDestroy(&B);
    4425:     if (conv) goto foundconv;

    4427:     /* 4) See if a good general converter is known for the current matrix */
    4428:     if (mat->ops->convert) conv = mat->ops->convert;

    4430:     PetscInfo2(mat,"Check general convert (%s) -> %d\n",((PetscObject)mat)->type_name,!!conv);
    4431:     if (conv) goto foundconv;

    4433:     /* 5) Use a really basic converter. */
    4434:     PetscInfo(mat,"Using MatConvert_Basic\n");
    4435:     conv = MatConvert_Basic;

    4437: foundconv:
    4438:     PetscLogEventBegin(MAT_Convert,mat,0,0,0);
    4439:     (*conv)(mat,newtype,reuse,M);
    4440:     if (mat->rmap->mapping && mat->cmap->mapping && !(*M)->rmap->mapping && !(*M)->cmap->mapping) {
    4441:       /* the block sizes must be same if the mappings are copied over */
    4442:       (*M)->rmap->bs = mat->rmap->bs;
    4443:       (*M)->cmap->bs = mat->cmap->bs;
    4444:       PetscObjectReference((PetscObject)mat->rmap->mapping);
    4445:       PetscObjectReference((PetscObject)mat->cmap->mapping);
    4446:       (*M)->rmap->mapping = mat->rmap->mapping;
    4447:       (*M)->cmap->mapping = mat->cmap->mapping;
    4448:     }
    4449:     (*M)->stencil.dim = mat->stencil.dim;
    4450:     (*M)->stencil.noc = mat->stencil.noc;
    4451:     for (i=0; i<=mat->stencil.dim; i++) {
    4452:       (*M)->stencil.dims[i]   = mat->stencil.dims[i];
    4453:       (*M)->stencil.starts[i] = mat->stencil.starts[i];
    4454:     }
    4455:     PetscLogEventEnd(MAT_Convert,mat,0,0,0);
    4456:   }
    4457:   PetscObjectStateIncrease((PetscObject)*M);

    4459:   /* Copy Mat options */
    4460:   if (issymmetric) {
    4461:     MatSetOption(*M,MAT_SYMMETRIC,PETSC_TRUE);
    4462:   }
    4463:   if (ishermitian) {
    4464:     MatSetOption(*M,MAT_HERMITIAN,PETSC_TRUE);
    4465:   }
    4466:   return(0);
    4467: }

    4469: /*@C
    4470:    MatFactorGetSolverType - Returns name of the package providing the factorization routines

    4472:    Not Collective

    4474:    Input Parameter:
    4475: .  mat - the matrix, must be a factored matrix

    4477:    Output Parameter:
    4478: .   type - the string name of the package (do not free this string)

    4480:    Notes:
    4481:       In Fortran you pass in a empty string and the package name will be copied into it.
    4482:     (Make sure the string is long enough)

    4484:    Level: intermediate

    4486: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatGetFactor()
    4487: @*/
    4488: PetscErrorCode MatFactorGetSolverType(Mat mat, MatSolverType *type)
    4489: {
    4490:   PetscErrorCode ierr, (*conv)(Mat,MatSolverType*);

    4495:   if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Only for factored matrix");
    4496:   PetscObjectQueryFunction((PetscObject)mat,"MatFactorGetSolverType_C",&conv);
    4497:   if (!conv) {
    4498:     *type = MATSOLVERPETSC;
    4499:   } else {
    4500:     (*conv)(mat,type);
    4501:   }
    4502:   return(0);
    4503: }

    4505: typedef struct _MatSolverTypeForSpecifcType* MatSolverTypeForSpecifcType;
    4506: struct _MatSolverTypeForSpecifcType {
    4507:   MatType                        mtype;
    4508:   PetscErrorCode                 (*createfactor[MAT_FACTOR_NUM_TYPES])(Mat,MatFactorType,Mat*);
    4509:   MatSolverTypeForSpecifcType next;
    4510: };

    4512: typedef struct _MatSolverTypeHolder* MatSolverTypeHolder;
    4513: struct _MatSolverTypeHolder {
    4514:   char                        *name;
    4515:   MatSolverTypeForSpecifcType handlers;
    4516:   MatSolverTypeHolder         next;
    4517: };

    4519: static MatSolverTypeHolder MatSolverTypeHolders = NULL;

    4521: /*@C
    4522:    MatSolverTypeRegister - Registers a MatSolverType that works for a particular matrix type

    4524:    Input Parameters:
    4525: +    package - name of the package, for example petsc or superlu
    4526: .    mtype - the matrix type that works with this package
    4527: .    ftype - the type of factorization supported by the package
    4528: -    createfactor - routine that will create the factored matrix ready to be used

    4530:     Level: intermediate

    4532: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatGetFactor()
    4533: @*/
    4534: PetscErrorCode MatSolverTypeRegister(MatSolverType package,MatType mtype,MatFactorType ftype,PetscErrorCode (*createfactor)(Mat,MatFactorType,Mat*))
    4535: {
    4536:   PetscErrorCode              ierr;
    4537:   MatSolverTypeHolder         next = MatSolverTypeHolders,prev = NULL;
    4538:   PetscBool                   flg;
    4539:   MatSolverTypeForSpecifcType inext,iprev = NULL;

    4542:   MatInitializePackage();
    4543:   if (!next) {
    4544:     PetscNew(&MatSolverTypeHolders);
    4545:     PetscStrallocpy(package,&MatSolverTypeHolders->name);
    4546:     PetscNew(&MatSolverTypeHolders->handlers);
    4547:     PetscStrallocpy(mtype,(char **)&MatSolverTypeHolders->handlers->mtype);
    4548:     MatSolverTypeHolders->handlers->createfactor[(int)ftype-1] = createfactor;
    4549:     return(0);
    4550:   }
    4551:   while (next) {
    4552:     PetscStrcasecmp(package,next->name,&flg);
    4553:     if (flg) {
    4554:       if (!next->handlers) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"MatSolverTypeHolder is missing handlers");
    4555:       inext = next->handlers;
    4556:       while (inext) {
    4557:         PetscStrcasecmp(mtype,inext->mtype,&flg);
    4558:         if (flg) {
    4559:           inext->createfactor[(int)ftype-1] = createfactor;
    4560:           return(0);
    4561:         }
    4562:         iprev = inext;
    4563:         inext = inext->next;
    4564:       }
    4565:       PetscNew(&iprev->next);
    4566:       PetscStrallocpy(mtype,(char **)&iprev->next->mtype);
    4567:       iprev->next->createfactor[(int)ftype-1] = createfactor;
    4568:       return(0);
    4569:     }
    4570:     prev = next;
    4571:     next = next->next;
    4572:   }
    4573:   PetscNew(&prev->next);
    4574:   PetscStrallocpy(package,&prev->next->name);
    4575:   PetscNew(&prev->next->handlers);
    4576:   PetscStrallocpy(mtype,(char **)&prev->next->handlers->mtype);
    4577:   prev->next->handlers->createfactor[(int)ftype-1] = createfactor;
    4578:   return(0);
    4579: }

    4581: /*@C
    4582:    MatSolveTypeGet - Gets the function that creates the factor matrix if it exist

    4584:    Input Parameters:
    4585: +    type - name of the package, for example petsc or superlu
    4586: .    ftype - the type of factorization supported by the type
    4587: -    mtype - the matrix type that works with this type

    4589:    Output Parameters:
    4590: +   foundtype - PETSC_TRUE if the type was registered
    4591: .   foundmtype - PETSC_TRUE if the type supports the requested mtype
    4592: -   createfactor - routine that will create the factored matrix ready to be used or NULL if not found

    4594:     Level: intermediate

    4596: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatSolverTypeRegister(), MatGetFactor()
    4597: @*/
    4598: PetscErrorCode MatSolverTypeGet(MatSolverType type,MatType mtype,MatFactorType ftype,PetscBool *foundtype,PetscBool *foundmtype,PetscErrorCode (**createfactor)(Mat,MatFactorType,Mat*))
    4599: {
    4600:   PetscErrorCode              ierr;
    4601:   MatSolverTypeHolder         next = MatSolverTypeHolders;
    4602:   PetscBool                   flg;
    4603:   MatSolverTypeForSpecifcType inext;

    4606:   if (foundtype) *foundtype = PETSC_FALSE;
    4607:   if (foundmtype)   *foundmtype   = PETSC_FALSE;
    4608:   if (createfactor) *createfactor    = NULL;

    4610:   if (type) {
    4611:     while (next) {
    4612:       PetscStrcasecmp(type,next->name,&flg);
    4613:       if (flg) {
    4614:         if (foundtype) *foundtype = PETSC_TRUE;
    4615:         inext = next->handlers;
    4616:         while (inext) {
    4617:           PetscStrbeginswith(mtype,inext->mtype,&flg);
    4618:           if (flg) {
    4619:             if (foundmtype) *foundmtype = PETSC_TRUE;
    4620:             if (createfactor)  *createfactor  = inext->createfactor[(int)ftype-1];
    4621:             return(0);
    4622:           }
    4623:           inext = inext->next;
    4624:         }
    4625:       }
    4626:       next = next->next;
    4627:     }
    4628:   } else {
    4629:     while (next) {
    4630:       inext = next->handlers;
    4631:       while (inext) {
    4632:         PetscStrcmp(mtype,inext->mtype,&flg);
    4633:         if (flg && inext->createfactor[(int)ftype-1]) {
    4634:           if (foundtype) *foundtype = PETSC_TRUE;
    4635:           if (foundmtype)   *foundmtype   = PETSC_TRUE;
    4636:           if (createfactor) *createfactor = inext->createfactor[(int)ftype-1];
    4637:           return(0);
    4638:         }
    4639:         inext = inext->next;
    4640:       }
    4641:       next = next->next;
    4642:     }
    4643:     /* try with base classes inext->mtype */
    4644:     next = MatSolverTypeHolders;
    4645:     while (next) {
    4646:       inext = next->handlers;
    4647:       while (inext) {
    4648:         PetscStrbeginswith(mtype,inext->mtype,&flg);
    4649:         if (flg && inext->createfactor[(int)ftype-1]) {
    4650:           if (foundtype) *foundtype = PETSC_TRUE;
    4651:           if (foundmtype)   *foundmtype   = PETSC_TRUE;
    4652:           if (createfactor) *createfactor = inext->createfactor[(int)ftype-1];
    4653:           return(0);
    4654:         }
    4655:         inext = inext->next;
    4656:       }
    4657:       next = next->next;
    4658:     }
    4659:   }
    4660:   return(0);
    4661: }

    4663: PetscErrorCode MatSolverTypeDestroy(void)
    4664: {
    4665:   PetscErrorCode              ierr;
    4666:   MatSolverTypeHolder         next = MatSolverTypeHolders,prev;
    4667:   MatSolverTypeForSpecifcType inext,iprev;

    4670:   while (next) {
    4671:     PetscFree(next->name);
    4672:     inext = next->handlers;
    4673:     while (inext) {
    4674:       PetscFree(inext->mtype);
    4675:       iprev = inext;
    4676:       inext = inext->next;
    4677:       PetscFree(iprev);
    4678:     }
    4679:     prev = next;
    4680:     next = next->next;
    4681:     PetscFree(prev);
    4682:   }
    4683:   MatSolverTypeHolders = NULL;
    4684:   return(0);
    4685: }

    4687: /*@C
    4688:    MatFactorGetUseOrdering - Indicates if the factorization uses the ordering provided in MatLUFactorSymbolic(), MatCholeskyFactorSymbolic()

    4690:    Logically Collective on Mat

    4692:    Input Parameters:
    4693: .  mat - the matrix

    4695:    Output Parameters:
    4696: .  flg - PETSC_TRUE if uses the ordering

    4698:    Notes:
    4699:       Most internal PETSc factorizations use the ordering past to the factorization routine but external
    4700:       packages do no, thus we want to skip the ordering when it is not needed.

    4702:    Level: developer

    4704: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatGetFactor(), MatLUFactorSymbolic(), MatCholeskyFactorSymbolic()
    4705: @*/
    4706: PetscErrorCode MatFactorGetUseOrdering(Mat mat, PetscBool *flg)
    4707: {
    4709:   *flg = mat->useordering;
    4710:   return(0);
    4711: }

    4713: /*@C
    4714:    MatGetFactor - Returns a matrix suitable to calls to MatXXFactorSymbolic()

    4716:    Collective on Mat

    4718:    Input Parameters:
    4719: +  mat - the matrix
    4720: .  type - name of solver type, for example, superlu, petsc (to use PETSc's default)
    4721: -  ftype - factor type, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ICC, MAT_FACTOR_ILU,

    4723:    Output Parameters:
    4724: .  f - the factor matrix used with MatXXFactorSymbolic() calls

    4726:    Notes:
    4727:       Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
    4728:      such as pastix, superlu, mumps etc.

    4730:       PETSc must have been ./configure to use the external solver, using the option --download-package

    4732:    Developer Notes:
    4733:       This should actually be called MatCreateFactor() since it creates a new factor object

    4735:    Level: intermediate

    4737: .seealso: MatCopy(), MatDuplicate(), MatGetFactorAvailable(), MatFactorGetUseOrdering(), MatSolverTypeRegister()
    4738: @*/
    4739: PetscErrorCode MatGetFactor(Mat mat, MatSolverType type,MatFactorType ftype,Mat *f)
    4740: {
    4741:   PetscErrorCode ierr,(*conv)(Mat,MatFactorType,Mat*);
    4742:   PetscBool      foundtype,foundmtype;

    4748:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4749:   MatCheckPreallocated(mat,1);

    4751:   MatSolverTypeGet(type,((PetscObject)mat)->type_name,ftype,&foundtype,&foundmtype,&conv);
    4752:   if (!foundtype) {
    4753:     if (type) {
    4754:       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);
    4755:     } else {
    4756:       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);
    4757:     }
    4758:   }
    4759:   if (!foundmtype) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_MISSING_FACTOR,"MatSolverType %s does not support matrix type %s",type,((PetscObject)mat)->type_name);
    4760:   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);

    4762:   (*conv)(mat,ftype,f);
    4763:   return(0);
    4764: }

    4766: /*@C
    4767:    MatGetFactorAvailable - Returns a a flag if matrix supports particular type and factor type

    4769:    Not Collective

    4771:    Input Parameters:
    4772: +  mat - the matrix
    4773: .  type - name of solver type, for example, superlu, petsc (to use PETSc's default)
    4774: -  ftype - factor type, MAT_FACTOR_LU, MAT_FACTOR_CHOLESKY, MAT_FACTOR_ICC, MAT_FACTOR_ILU,

    4776:    Output Parameter:
    4777: .    flg - PETSC_TRUE if the factorization is available

    4779:    Notes:
    4780:       Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
    4781:      such as pastix, superlu, mumps etc.

    4783:       PETSc must have been ./configure to use the external solver, using the option --download-package

    4785:    Developer Notes:
    4786:       This should actually be called MatCreateFactorAvailable() since MatGetFactor() creates a new factor object

    4788:    Level: intermediate

    4790: .seealso: MatCopy(), MatDuplicate(), MatGetFactor(), MatSolverTypeRegister()
    4791: @*/
    4792: PetscErrorCode MatGetFactorAvailable(Mat mat, MatSolverType type,MatFactorType ftype,PetscBool  *flg)
    4793: {
    4794:   PetscErrorCode ierr, (*gconv)(Mat,MatFactorType,Mat*);

    4800:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4801:   MatCheckPreallocated(mat,1);

    4803:   *flg = PETSC_FALSE;
    4804:   MatSolverTypeGet(type,((PetscObject)mat)->type_name,ftype,NULL,NULL,&gconv);
    4805:   if (gconv) {
    4806:     *flg = PETSC_TRUE;
    4807:   }
    4808:   return(0);
    4809: }

    4811: #include <petscdmtypes.h>

    4813: /*@
    4814:    MatDuplicate - Duplicates a matrix including the non-zero structure.

    4816:    Collective on Mat

    4818:    Input Parameters:
    4819: +  mat - the matrix
    4820: -  op - One of MAT_DO_NOT_COPY_VALUES, MAT_COPY_VALUES, or MAT_SHARE_NONZERO_PATTERN.
    4821:         See the manual page for MatDuplicateOption for an explanation of these options.

    4823:    Output Parameter:
    4824: .  M - pointer to place new matrix

    4826:    Level: intermediate

    4828:    Notes:
    4829:     You cannot change the nonzero pattern for the parent or child matrix if you use MAT_SHARE_NONZERO_PATTERN.
    4830:     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.

    4832: .seealso: MatCopy(), MatConvert(), MatDuplicateOption
    4833: @*/
    4834: PetscErrorCode MatDuplicate(Mat mat,MatDuplicateOption op,Mat *M)
    4835: {
    4837:   Mat            B;
    4838:   PetscInt       i;
    4839:   DM             dm;
    4840:   void           (*viewf)(void);

    4846:   if (op == MAT_COPY_VALUES && !mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"MAT_COPY_VALUES not allowed for unassembled matrix");
    4847:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    4848:   MatCheckPreallocated(mat,1);

    4850:   *M = NULL;
    4851:   if (!mat->ops->duplicate) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not written for matrix type %s\n",((PetscObject)mat)->type_name);
    4852:   PetscLogEventBegin(MAT_Convert,mat,0,0,0);
    4853:   (*mat->ops->duplicate)(mat,op,M);
    4854:   B    = *M;

    4856:   MatGetOperation(mat,MATOP_VIEW,&viewf);
    4857:   if (viewf) {
    4858:     MatSetOperation(B,MATOP_VIEW,viewf);
    4859:   }

    4861:   B->stencil.dim = mat->stencil.dim;
    4862:   B->stencil.noc = mat->stencil.noc;
    4863:   for (i=0; i<=mat->stencil.dim; i++) {
    4864:     B->stencil.dims[i]   = mat->stencil.dims[i];
    4865:     B->stencil.starts[i] = mat->stencil.starts[i];
    4866:   }

    4868:   B->nooffproczerorows = mat->nooffproczerorows;
    4869:   B->nooffprocentries  = mat->nooffprocentries;

    4871:   PetscObjectQuery((PetscObject) mat, "__PETSc_dm", (PetscObject*) &dm);
    4872:   if (dm) {
    4873:     PetscObjectCompose((PetscObject) B, "__PETSc_dm", (PetscObject) dm);
    4874:   }
    4875:   PetscLogEventEnd(MAT_Convert,mat,0,0,0);
    4876:   PetscObjectStateIncrease((PetscObject)B);
    4877:   return(0);
    4878: }

    4880: /*@
    4881:    MatGetDiagonal - Gets the diagonal of a matrix.

    4883:    Logically Collective on Mat

    4885:    Input Parameters:
    4886: +  mat - the matrix
    4887: -  v - the vector for storing the diagonal

    4889:    Output Parameter:
    4890: .  v - the diagonal of the matrix

    4892:    Level: intermediate

    4894:    Note:
    4895:    Currently only correct in parallel for square matrices.

    4897: .seealso: MatGetRow(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMaxAbs()
    4898: @*/
    4899: PetscErrorCode MatGetDiagonal(Mat mat,Vec v)
    4900: {

    4907:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4908:   if (!mat->ops->getdiagonal) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4909:   MatCheckPreallocated(mat,1);

    4911:   (*mat->ops->getdiagonal)(mat,v);
    4912:   PetscObjectStateIncrease((PetscObject)v);
    4913:   return(0);
    4914: }

    4916: /*@C
    4917:    MatGetRowMin - Gets the minimum value (of the real part) of each
    4918:         row of the matrix

    4920:    Logically Collective on Mat

    4922:    Input Parameters:
    4923: .  mat - the matrix

    4925:    Output Parameter:
    4926: +  v - the vector for storing the maximums
    4927: -  idx - the indices of the column found for each row (optional)

    4929:    Level: intermediate

    4931:    Notes:
    4932:     The result of this call are the same as if one converted the matrix to dense format
    4933:       and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    4935:     This code is only implemented for a couple of matrix formats.

    4937: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMaxAbs(),
    4938:           MatGetRowMax()
    4939: @*/
    4940: PetscErrorCode MatGetRowMin(Mat mat,Vec v,PetscInt idx[])
    4941: {

    4948:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");

    4950:   if (!mat->cmap->N) {
    4951:     VecSet(v,PETSC_MAX_REAL);
    4952:     if (idx) {
    4953:       PetscInt i,m = mat->rmap->n;
    4954:       for (i=0; i<m; i++) idx[i] = -1;
    4955:     }
    4956:   } else {
    4957:     if (!mat->ops->getrowmin) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    4958:     MatCheckPreallocated(mat,1);
    4959:   }
    4960:   (*mat->ops->getrowmin)(mat,v,idx);
    4961:   PetscObjectStateIncrease((PetscObject)v);
    4962:   return(0);
    4963: }

    4965: /*@C
    4966:    MatGetRowMinAbs - Gets the minimum value (in absolute value) of each
    4967:         row of the matrix

    4969:    Logically Collective on Mat

    4971:    Input Parameters:
    4972: .  mat - the matrix

    4974:    Output Parameter:
    4975: +  v - the vector for storing the minimums
    4976: -  idx - the indices of the column found for each row (or NULL if not needed)

    4978:    Level: intermediate

    4980:    Notes:
    4981:     if a row is completely empty or has only 0.0 values then the idx[] value for that
    4982:     row is 0 (the first column).

    4984:     This code is only implemented for a couple of matrix formats.

    4986: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMax(), MatGetRowMaxAbs(), MatGetRowMin()
    4987: @*/
    4988: PetscErrorCode MatGetRowMinAbs(Mat mat,Vec v,PetscInt idx[])
    4989: {

    4996:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    4997:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

    4999:   if (!mat->cmap->N) {
    5000:     VecSet(v,0.0);
    5001:     if (idx) {
    5002:       PetscInt i,m = mat->rmap->n;
    5003:       for (i=0; i<m; i++) idx[i] = -1;
    5004:     }
    5005:   } else {
    5006:     if (!mat->ops->getrowminabs) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5007:     MatCheckPreallocated(mat,1);
    5008:     if (idx) {PetscArrayzero(idx,mat->rmap->n);}
    5009:     (*mat->ops->getrowminabs)(mat,v,idx);
    5010:   }
    5011:   PetscObjectStateIncrease((PetscObject)v);
    5012:   return(0);
    5013: }

    5015: /*@C
    5016:    MatGetRowMax - Gets the maximum value (of the real part) of each
    5017:         row of the matrix

    5019:    Logically Collective on Mat

    5021:    Input Parameters:
    5022: .  mat - the matrix

    5024:    Output Parameter:
    5025: +  v - the vector for storing the maximums
    5026: -  idx - the indices of the column found for each row (optional)

    5028:    Level: intermediate

    5030:    Notes:
    5031:     The result of this call are the same as if one converted the matrix to dense format
    5032:       and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    5034:     This code is only implemented for a couple of matrix formats.

    5036: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMaxAbs(), MatGetRowMin()
    5037: @*/
    5038: PetscErrorCode MatGetRowMax(Mat mat,Vec v,PetscInt idx[])
    5039: {

    5046:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");

    5048:   if (!mat->cmap->N) {
    5049:     VecSet(v,PETSC_MIN_REAL);
    5050:     if (idx) {
    5051:       PetscInt i,m = mat->rmap->n;
    5052:       for (i=0; i<m; i++) idx[i] = -1;
    5053:     }
    5054:   } else {
    5055:     if (!mat->ops->getrowmax) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5056:     MatCheckPreallocated(mat,1);
    5057:     (*mat->ops->getrowmax)(mat,v,idx);
    5058:   }
    5059:   PetscObjectStateIncrease((PetscObject)v);
    5060:   return(0);
    5061: }

    5063: /*@C
    5064:    MatGetRowMaxAbs - Gets the maximum value (in absolute value) of each
    5065:         row of the matrix

    5067:    Logically Collective on Mat

    5069:    Input Parameters:
    5070: .  mat - the matrix

    5072:    Output Parameter:
    5073: +  v - the vector for storing the maximums
    5074: -  idx - the indices of the column found for each row (or NULL if not needed)

    5076:    Level: intermediate

    5078:    Notes:
    5079:     if a row is completely empty or has only 0.0 values then the idx[] value for that
    5080:     row is 0 (the first column).

    5082:     This code is only implemented for a couple of matrix formats.

    5084: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMax(), MatGetRowMin()
    5085: @*/
    5086: PetscErrorCode MatGetRowMaxAbs(Mat mat,Vec v,PetscInt idx[])
    5087: {

    5094:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");

    5096:   if (!mat->cmap->N) {
    5097:     VecSet(v,0.0);
    5098:     if (idx) {
    5099:       PetscInt i,m = mat->rmap->n;
    5100:       for (i=0; i<m; i++) idx[i] = -1;
    5101:     }
    5102:   } else {
    5103:     if (!mat->ops->getrowmaxabs) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5104:     MatCheckPreallocated(mat,1);
    5105:     if (idx) {PetscArrayzero(idx,mat->rmap->n);}
    5106:     (*mat->ops->getrowmaxabs)(mat,v,idx);
    5107:   }
    5108:   PetscObjectStateIncrease((PetscObject)v);
    5109:   return(0);
    5110: }

    5112: /*@
    5113:    MatGetRowSum - Gets the sum of each row of the matrix

    5115:    Logically or Neighborhood Collective on Mat

    5117:    Input Parameters:
    5118: .  mat - the matrix

    5120:    Output Parameter:
    5121: .  v - the vector for storing the sum of rows

    5123:    Level: intermediate

    5125:    Notes:
    5126:     This code is slow since it is not currently specialized for different formats

    5128: .seealso: MatGetDiagonal(), MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRowMax(), MatGetRowMin()
    5129: @*/
    5130: PetscErrorCode MatGetRowSum(Mat mat, Vec v)
    5131: {
    5132:   Vec            ones;

    5139:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5140:   MatCheckPreallocated(mat,1);
    5141:   MatCreateVecs(mat,&ones,NULL);
    5142:   VecSet(ones,1.);
    5143:   MatMult(mat,ones,v);
    5144:   VecDestroy(&ones);
    5145:   return(0);
    5146: }

    5148: /*@
    5149:    MatTranspose - Computes an in-place or out-of-place transpose of a matrix.

    5151:    Collective on Mat

    5153:    Input Parameters:
    5154: +  mat - the matrix to transpose
    5155: -  reuse - either MAT_INITIAL_MATRIX, MAT_REUSE_MATRIX, or MAT_INPLACE_MATRIX

    5157:    Output Parameter:
    5158: .  B - the transpose

    5160:    Notes:
    5161:      If you use MAT_INPLACE_MATRIX then you must pass in &mat for B

    5163:      MAT_REUSE_MATRIX causes the B matrix from a previous call to this function with MAT_INITIAL_MATRIX to be used

    5165:      Consider using MatCreateTranspose() instead if you only need a matrix that behaves like the transpose, but don't need the storage to be changed.

    5167:    Level: intermediate

    5169: .seealso: MatMultTranspose(), MatMultTransposeAdd(), MatIsTranspose(), MatReuse
    5170: @*/
    5171: PetscErrorCode MatTranspose(Mat mat,MatReuse reuse,Mat *B)
    5172: {

    5178:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5179:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5180:   if (!mat->ops->transpose) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5181:   if (reuse == MAT_INPLACE_MATRIX && mat != *B) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"MAT_INPLACE_MATRIX requires last matrix to match first");
    5182:   if (reuse == MAT_REUSE_MATRIX && mat == *B) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Perhaps you mean MAT_INPLACE_MATRIX");
    5183:   MatCheckPreallocated(mat,1);

    5185:   PetscLogEventBegin(MAT_Transpose,mat,0,0,0);
    5186:   (*mat->ops->transpose)(mat,reuse,B);
    5187:   PetscLogEventEnd(MAT_Transpose,mat,0,0,0);
    5188:   if (B) {PetscObjectStateIncrease((PetscObject)*B);}
    5189:   return(0);
    5190: }

    5192: /*@
    5193:    MatIsTranspose - Test whether a matrix is another one's transpose,
    5194:         or its own, in which case it tests symmetry.

    5196:    Collective on Mat

    5198:    Input Parameter:
    5199: +  A - the matrix to test
    5200: -  B - the matrix to test against, this can equal the first parameter

    5202:    Output Parameters:
    5203: .  flg - the result

    5205:    Notes:
    5206:    Only available for SeqAIJ/MPIAIJ matrices. The sequential algorithm
    5207:    has a running time of the order of the number of nonzeros; the parallel
    5208:    test involves parallel copies of the block-offdiagonal parts of the matrix.

    5210:    Level: intermediate

    5212: .seealso: MatTranspose(), MatIsSymmetric(), MatIsHermitian()
    5213: @*/
    5214: PetscErrorCode MatIsTranspose(Mat A,Mat B,PetscReal tol,PetscBool  *flg)
    5215: {
    5216:   PetscErrorCode ierr,(*f)(Mat,Mat,PetscReal,PetscBool*),(*g)(Mat,Mat,PetscReal,PetscBool*);

    5222:   PetscObjectQueryFunction((PetscObject)A,"MatIsTranspose_C",&f);
    5223:   PetscObjectQueryFunction((PetscObject)B,"MatIsTranspose_C",&g);
    5224:   *flg = PETSC_FALSE;
    5225:   if (f && g) {
    5226:     if (f == g) {
    5227:       (*f)(A,B,tol,flg);
    5228:     } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_NOTSAMETYPE,"Matrices do not have the same comparator for symmetry test");
    5229:   } else {
    5230:     MatType mattype;
    5231:     if (!f) {
    5232:       MatGetType(A,&mattype);
    5233:     } else {
    5234:       MatGetType(B,&mattype);
    5235:     }
    5236:     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for transpose",mattype);
    5237:   }
    5238:   return(0);
    5239: }

    5241: /*@
    5242:    MatHermitianTranspose - Computes an in-place or out-of-place transpose of a matrix in complex conjugate.

    5244:    Collective on Mat

    5246:    Input Parameters:
    5247: +  mat - the matrix to transpose and complex conjugate
    5248: -  reuse - either MAT_INITIAL_MATRIX, MAT_REUSE_MATRIX, or MAT_INPLACE_MATRIX

    5250:    Output Parameter:
    5251: .  B - the Hermitian

    5253:    Level: intermediate

    5255: .seealso: MatTranspose(), MatMultTranspose(), MatMultTransposeAdd(), MatIsTranspose(), MatReuse
    5256: @*/
    5257: PetscErrorCode MatHermitianTranspose(Mat mat,MatReuse reuse,Mat *B)
    5258: {

    5262:   MatTranspose(mat,reuse,B);
    5263: #if defined(PETSC_USE_COMPLEX)
    5264:   MatConjugate(*B);
    5265: #endif
    5266:   return(0);
    5267: }

    5269: /*@
    5270:    MatIsHermitianTranspose - Test whether a matrix is another one's Hermitian transpose,

    5272:    Collective on Mat

    5274:    Input Parameter:
    5275: +  A - the matrix to test
    5276: -  B - the matrix to test against, this can equal the first parameter

    5278:    Output Parameters:
    5279: .  flg - the result

    5281:    Notes:
    5282:    Only available for SeqAIJ/MPIAIJ matrices. The sequential algorithm
    5283:    has a running time of the order of the number of nonzeros; the parallel
    5284:    test involves parallel copies of the block-offdiagonal parts of the matrix.

    5286:    Level: intermediate

    5288: .seealso: MatTranspose(), MatIsSymmetric(), MatIsHermitian(), MatIsTranspose()
    5289: @*/
    5290: PetscErrorCode MatIsHermitianTranspose(Mat A,Mat B,PetscReal tol,PetscBool  *flg)
    5291: {
    5292:   PetscErrorCode ierr,(*f)(Mat,Mat,PetscReal,PetscBool*),(*g)(Mat,Mat,PetscReal,PetscBool*);

    5298:   PetscObjectQueryFunction((PetscObject)A,"MatIsHermitianTranspose_C",&f);
    5299:   PetscObjectQueryFunction((PetscObject)B,"MatIsHermitianTranspose_C",&g);
    5300:   if (f && g) {
    5301:     if (f==g) {
    5302:       (*f)(A,B,tol,flg);
    5303:     } else SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_NOTSAMETYPE,"Matrices do not have the same comparator for Hermitian test");
    5304:   }
    5305:   return(0);
    5306: }

    5308: /*@
    5309:    MatPermute - Creates a new matrix with rows and columns permuted from the
    5310:    original.

    5312:    Collective on Mat

    5314:    Input Parameters:
    5315: +  mat - the matrix to permute
    5316: .  row - row permutation, each processor supplies only the permutation for its rows
    5317: -  col - column permutation, each processor supplies only the permutation for its columns

    5319:    Output Parameters:
    5320: .  B - the permuted matrix

    5322:    Level: advanced

    5324:    Note:
    5325:    The index sets map from row/col of permuted matrix to row/col of original matrix.
    5326:    The index sets should be on the same communicator as Mat and have the same local sizes.

    5328:    Developer Note:
    5329:      If you want to implement MatPermute for a matrix type, and your approach doesn't
    5330:      exploit the fact that row and col are permutations, consider implementing the
    5331:      more general MatCreateSubMatrix() instead.

    5333: .seealso: MatGetOrdering(), ISAllGather()

    5335: @*/
    5336: PetscErrorCode MatPermute(Mat mat,IS row,IS col,Mat *B)
    5337: {

    5348:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5349:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5350:   if (!mat->ops->permute && !mat->ops->createsubmatrix) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatPermute not available for Mat type %s",((PetscObject)mat)->type_name);
    5351:   MatCheckPreallocated(mat,1);

    5353:   if (mat->ops->permute) {
    5354:     (*mat->ops->permute)(mat,row,col,B);
    5355:     PetscObjectStateIncrease((PetscObject)*B);
    5356:   } else {
    5357:     MatCreateSubMatrix(mat, row, col, MAT_INITIAL_MATRIX, B);
    5358:   }
    5359:   return(0);
    5360: }

    5362: /*@
    5363:    MatEqual - Compares two matrices.

    5365:    Collective on Mat

    5367:    Input Parameters:
    5368: +  A - the first matrix
    5369: -  B - the second matrix

    5371:    Output Parameter:
    5372: .  flg - PETSC_TRUE if the matrices are equal; PETSC_FALSE otherwise.

    5374:    Level: intermediate

    5376: @*/
    5377: PetscErrorCode MatEqual(Mat A,Mat B,PetscBool  *flg)
    5378: {

    5388:   MatCheckPreallocated(B,2);
    5389:   if (!A->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5390:   if (!B->assembled) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5391:   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);
    5392:   if (!A->ops->equal) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)A)->type_name);
    5393:   if (!B->ops->equal) SETERRQ1(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Mat type %s",((PetscObject)B)->type_name);
    5394:   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);
    5395:   MatCheckPreallocated(A,1);

    5397:   (*A->ops->equal)(A,B,flg);
    5398:   return(0);
    5399: }

    5401: /*@
    5402:    MatDiagonalScale - Scales a matrix on the left and right by diagonal
    5403:    matrices that are stored as vectors.  Either of the two scaling
    5404:    matrices can be NULL.

    5406:    Collective on Mat

    5408:    Input Parameters:
    5409: +  mat - the matrix to be scaled
    5410: .  l - the left scaling vector (or NULL)
    5411: -  r - the right scaling vector (or NULL)

    5413:    Notes:
    5414:    MatDiagonalScale() computes A = LAR, where
    5415:    L = a diagonal matrix (stored as a vector), R = a diagonal matrix (stored as a vector)
    5416:    The L scales the rows of the matrix, the R scales the columns of the matrix.

    5418:    Level: intermediate

    5421: .seealso: MatScale(), MatShift(), MatDiagonalSet()
    5422: @*/
    5423: PetscErrorCode MatDiagonalScale(Mat mat,Vec l,Vec r)
    5424: {

    5432:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5433:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5434:   MatCheckPreallocated(mat,1);
    5435:   if (!l && !r) return(0);

    5437:   if (!mat->ops->diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5438:   PetscLogEventBegin(MAT_Scale,mat,0,0,0);
    5439:   (*mat->ops->diagonalscale)(mat,l,r);
    5440:   PetscLogEventEnd(MAT_Scale,mat,0,0,0);
    5441:   PetscObjectStateIncrease((PetscObject)mat);
    5442:   return(0);
    5443: }

    5445: /*@
    5446:     MatScale - Scales all elements of a matrix by a given number.

    5448:     Logically Collective on Mat

    5450:     Input Parameters:
    5451: +   mat - the matrix to be scaled
    5452: -   a  - the scaling value

    5454:     Output Parameter:
    5455: .   mat - the scaled matrix

    5457:     Level: intermediate

    5459: .seealso: MatDiagonalScale()
    5460: @*/
    5461: PetscErrorCode MatScale(Mat mat,PetscScalar a)
    5462: {

    5468:   if (a != (PetscScalar)1.0 && !mat->ops->scale) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5469:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5470:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5472:   MatCheckPreallocated(mat,1);

    5474:   PetscLogEventBegin(MAT_Scale,mat,0,0,0);
    5475:   if (a != (PetscScalar)1.0) {
    5476:     (*mat->ops->scale)(mat,a);
    5477:     PetscObjectStateIncrease((PetscObject)mat);
    5478:   }
    5479:   PetscLogEventEnd(MAT_Scale,mat,0,0,0);
    5480:   return(0);
    5481: }

    5483: /*@
    5484:    MatNorm - Calculates various norms of a matrix.

    5486:    Collective on Mat

    5488:    Input Parameters:
    5489: +  mat - the matrix
    5490: -  type - the type of norm, NORM_1, NORM_FROBENIUS, NORM_INFINITY

    5492:    Output Parameters:
    5493: .  nrm - the resulting norm

    5495:    Level: intermediate

    5497: @*/
    5498: PetscErrorCode MatNorm(Mat mat,NormType type,PetscReal *nrm)
    5499: {

    5507:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    5508:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5509:   if (!mat->ops->norm) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5510:   MatCheckPreallocated(mat,1);

    5512:   (*mat->ops->norm)(mat,type,nrm);
    5513:   return(0);
    5514: }

    5516: /*
    5517:      This variable is used to prevent counting of MatAssemblyBegin() that
    5518:    are called from within a MatAssemblyEnd().
    5519: */
    5520: static PetscInt MatAssemblyEnd_InUse = 0;
    5521: /*@
    5522:    MatAssemblyBegin - Begins assembling the matrix.  This routine should
    5523:    be called after completing all calls to MatSetValues().

    5525:    Collective on Mat

    5527:    Input Parameters:
    5528: +  mat - the matrix
    5529: -  type - type of assembly, either MAT_FLUSH_ASSEMBLY or MAT_FINAL_ASSEMBLY

    5531:    Notes:
    5532:    MatSetValues() generally caches the values.  The matrix is ready to
    5533:    use only after MatAssemblyBegin() and MatAssemblyEnd() have been called.
    5534:    Use MAT_FLUSH_ASSEMBLY when switching between ADD_VALUES and INSERT_VALUES
    5535:    in MatSetValues(); use MAT_FINAL_ASSEMBLY for the final assembly before
    5536:    using the matrix.

    5538:    ALL processes that share a matrix MUST call MatAssemblyBegin() and MatAssemblyEnd() the SAME NUMBER of times, and each time with the
    5539:    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
    5540:    a global collective operation requring all processes that share the matrix.

    5542:    Space for preallocated nonzeros that is not filled by a call to MatSetValues() or a related routine are compressed
    5543:    out by assembly. If you intend to use that extra space on a subsequent assembly, be sure to insert explicit zeros
    5544:    before MAT_FINAL_ASSEMBLY so the space is not compressed out.

    5546:    Level: beginner

    5548: .seealso: MatAssemblyEnd(), MatSetValues(), MatAssembled()
    5549: @*/
    5550: PetscErrorCode MatAssemblyBegin(Mat mat,MatAssemblyType type)
    5551: {

    5557:   MatCheckPreallocated(mat,1);
    5558:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix.\nDid you forget to call MatSetUnfactored()?");
    5559:   if (mat->assembled) {
    5560:     mat->was_assembled = PETSC_TRUE;
    5561:     mat->assembled     = PETSC_FALSE;
    5562:   }

    5564:   if (!MatAssemblyEnd_InUse) {
    5565:     PetscLogEventBegin(MAT_AssemblyBegin,mat,0,0,0);
    5566:     if (mat->ops->assemblybegin) {(*mat->ops->assemblybegin)(mat,type);}
    5567:     PetscLogEventEnd(MAT_AssemblyBegin,mat,0,0,0);
    5568:   } else if (mat->ops->assemblybegin) {
    5569:     (*mat->ops->assemblybegin)(mat,type);
    5570:   }
    5571:   return(0);
    5572: }

    5574: /*@
    5575:    MatAssembled - Indicates if a matrix has been assembled and is ready for
    5576:      use; for example, in matrix-vector product.

    5578:    Not Collective

    5580:    Input Parameter:
    5581: .  mat - the matrix

    5583:    Output Parameter:
    5584: .  assembled - PETSC_TRUE or PETSC_FALSE

    5586:    Level: advanced

    5588: .seealso: MatAssemblyEnd(), MatSetValues(), MatAssemblyBegin()
    5589: @*/
    5590: PetscErrorCode MatAssembled(Mat mat,PetscBool  *assembled)
    5591: {
    5595:   *assembled = mat->assembled;
    5596:   return(0);
    5597: }

    5599: /*@
    5600:    MatAssemblyEnd - Completes assembling the matrix.  This routine should
    5601:    be called after MatAssemblyBegin().

    5603:    Collective on Mat

    5605:    Input Parameters:
    5606: +  mat - the matrix
    5607: -  type - type of assembly, either MAT_FLUSH_ASSEMBLY or MAT_FINAL_ASSEMBLY

    5609:    Options Database Keys:
    5610: +  -mat_view ::ascii_info - Prints info on matrix at conclusion of MatEndAssembly()
    5611: .  -mat_view ::ascii_info_detail - Prints more detailed info
    5612: .  -mat_view - Prints matrix in ASCII format
    5613: .  -mat_view ::ascii_matlab - Prints matrix in Matlab format
    5614: .  -mat_view draw - PetscDraws nonzero structure of matrix, using MatView() and PetscDrawOpenX().
    5615: .  -display <name> - Sets display name (default is host)
    5616: .  -draw_pause <sec> - Sets number of seconds to pause after display
    5617: .  -mat_view socket - Sends matrix to socket, can be accessed from Matlab (See Users-Manual: ch_matlab)
    5618: .  -viewer_socket_machine <machine> - Machine to use for socket
    5619: .  -viewer_socket_port <port> - Port number to use for socket
    5620: -  -mat_view binary:filename[:append] - Save matrix to file in binary format

    5622:    Notes:
    5623:    MatSetValues() generally caches the values.  The matrix is ready to
    5624:    use only after MatAssemblyBegin() and MatAssemblyEnd() have been called.
    5625:    Use MAT_FLUSH_ASSEMBLY when switching between ADD_VALUES and INSERT_VALUES
    5626:    in MatSetValues(); use MAT_FINAL_ASSEMBLY for the final assembly before
    5627:    using the matrix.

    5629:    Space for preallocated nonzeros that is not filled by a call to MatSetValues() or a related routine are compressed
    5630:    out by assembly. If you intend to use that extra space on a subsequent assembly, be sure to insert explicit zeros
    5631:    before MAT_FINAL_ASSEMBLY so the space is not compressed out.

    5633:    Level: beginner

    5635: .seealso: MatAssemblyBegin(), MatSetValues(), PetscDrawOpenX(), PetscDrawCreate(), MatView(), MatAssembled(), PetscViewerSocketOpen()
    5636: @*/
    5637: PetscErrorCode MatAssemblyEnd(Mat mat,MatAssemblyType type)
    5638: {
    5639:   PetscErrorCode  ierr;
    5640:   static PetscInt inassm = 0;
    5641:   PetscBool       flg    = PETSC_FALSE;

    5647:   inassm++;
    5648:   MatAssemblyEnd_InUse++;
    5649:   if (MatAssemblyEnd_InUse == 1) { /* Do the logging only the first time through */
    5650:     PetscLogEventBegin(MAT_AssemblyEnd,mat,0,0,0);
    5651:     if (mat->ops->assemblyend) {
    5652:       (*mat->ops->assemblyend)(mat,type);
    5653:     }
    5654:     PetscLogEventEnd(MAT_AssemblyEnd,mat,0,0,0);
    5655:   } else if (mat->ops->assemblyend) {
    5656:     (*mat->ops->assemblyend)(mat,type);
    5657:   }

    5659:   /* Flush assembly is not a true assembly */
    5660:   if (type != MAT_FLUSH_ASSEMBLY) {
    5661:     mat->num_ass++;
    5662:     mat->assembled        = PETSC_TRUE;
    5663:     mat->ass_nonzerostate = mat->nonzerostate;
    5664:   }

    5666:   mat->insertmode = NOT_SET_VALUES;
    5667:   MatAssemblyEnd_InUse--;
    5668:   PetscObjectStateIncrease((PetscObject)mat);
    5669:   if (!mat->symmetric_eternal) {
    5670:     mat->symmetric_set              = PETSC_FALSE;
    5671:     mat->hermitian_set              = PETSC_FALSE;
    5672:     mat->structurally_symmetric_set = PETSC_FALSE;
    5673:   }
    5674:   if (inassm == 1 && type != MAT_FLUSH_ASSEMBLY) {
    5675:     MatViewFromOptions(mat,NULL,"-mat_view");

    5677:     if (mat->checksymmetryonassembly) {
    5678:       MatIsSymmetric(mat,mat->checksymmetrytol,&flg);
    5679:       if (flg) {
    5680:         PetscPrintf(PetscObjectComm((PetscObject)mat),"Matrix is symmetric (tolerance %g)\n",(double)mat->checksymmetrytol);
    5681:       } else {
    5682:         PetscPrintf(PetscObjectComm((PetscObject)mat),"Matrix is not symmetric (tolerance %g)\n",(double)mat->checksymmetrytol);
    5683:       }
    5684:     }
    5685:     if (mat->nullsp && mat->checknullspaceonassembly) {
    5686:       MatNullSpaceTest(mat->nullsp,mat,NULL);
    5687:     }
    5688:   }
    5689:   inassm--;
    5690:   return(0);
    5691: }

    5693: /*@
    5694:    MatSetOption - Sets a parameter option for a matrix. Some options
    5695:    may be specific to certain storage formats.  Some options
    5696:    determine how values will be inserted (or added). Sorted,
    5697:    row-oriented input will generally assemble the fastest. The default
    5698:    is row-oriented.

    5700:    Logically Collective on Mat for certain operations, such as MAT_SPD, not collective for MAT_ROW_ORIENTED, see MatOption

    5702:    Input Parameters:
    5703: +  mat - the matrix
    5704: .  option - the option, one of those listed below (and possibly others),
    5705: -  flg - turn the option on (PETSC_TRUE) or off (PETSC_FALSE)

    5707:   Options Describing Matrix Structure:
    5708: +    MAT_SPD - symmetric positive definite
    5709: .    MAT_SYMMETRIC - symmetric in terms of both structure and value
    5710: .    MAT_HERMITIAN - transpose is the complex conjugation
    5711: .    MAT_STRUCTURALLY_SYMMETRIC - symmetric nonzero structure
    5712: -    MAT_SYMMETRY_ETERNAL - if you would like the symmetry/Hermitian flag
    5713:                             you set to be kept with all future use of the matrix
    5714:                             including after MatAssemblyBegin/End() which could
    5715:                             potentially change the symmetry structure, i.e. you
    5716:                             KNOW the matrix will ALWAYS have the property you set.
    5717:                             Note that setting this flag alone implies nothing about whether the matrix is symmetric/Hermitian;
    5718:                             the relevant flags must be set independently.

    5721:    Options For Use with MatSetValues():
    5722:    Insert a logically dense subblock, which can be
    5723: .    MAT_ROW_ORIENTED - row-oriented (default)

    5725:    Note these options reflect the data you pass in with MatSetValues(); it has
    5726:    nothing to do with how the data is stored internally in the matrix
    5727:    data structure.

    5729:    When (re)assembling a matrix, we can restrict the input for
    5730:    efficiency/debugging purposes.  These options include:
    5731: +    MAT_NEW_NONZERO_LOCATIONS - additional insertions will be allowed if they generate a new nonzero (slow)
    5732: .    MAT_FORCE_DIAGONAL_ENTRIES - forces diagonal entries to be allocated
    5733: .    MAT_IGNORE_OFF_PROC_ENTRIES - drops off-processor entries
    5734: .    MAT_NEW_NONZERO_LOCATION_ERR - generates an error for new matrix entry
    5735: .    MAT_USE_HASH_TABLE - uses a hash table to speed up matrix assembly
    5736: .    MAT_NO_OFF_PROC_ENTRIES - you know each process will only set values for its own rows, will generate an error if
    5737:         any process sets values for another process. This avoids all reductions in the MatAssembly routines and thus improves
    5738:         performance for very large process counts.
    5739: -    MAT_SUBSET_OFF_PROC_ENTRIES - you know that the first assembly after setting this flag will set a superset
    5740:         of the off-process entries required for all subsequent assemblies. This avoids a rendezvous step in the MatAssembly
    5741:         functions, instead sending only neighbor messages.

    5743:    Notes:
    5744:    Except for MAT_UNUSED_NONZERO_LOCATION_ERR and  MAT_ROW_ORIENTED all processes that share the matrix must pass the same value in flg!

    5746:    Some options are relevant only for particular matrix types and
    5747:    are thus ignored by others.  Other options are not supported by
    5748:    certain matrix types and will generate an error message if set.

    5750:    If using a Fortran 77 module to compute a matrix, one may need to
    5751:    use the column-oriented option (or convert to the row-oriented
    5752:    format).

    5754:    MAT_NEW_NONZERO_LOCATIONS set to PETSC_FALSE indicates that any add or insertion
    5755:    that would generate a new entry in the nonzero structure is instead
    5756:    ignored.  Thus, if memory has not alredy been allocated for this particular
    5757:    data, then the insertion is ignored. For dense matrices, in which
    5758:    the entire array is allocated, no entries are ever ignored.
    5759:    Set after the first MatAssemblyEnd(). If this option is set then the MatAssemblyBegin/End() processes has one less global reduction

    5761:    MAT_NEW_NONZERO_LOCATION_ERR set to PETSC_TRUE indicates that any add or insertion
    5762:    that would generate a new entry in the nonzero structure instead produces
    5763:    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

    5765:    MAT_NEW_NONZERO_ALLOCATION_ERR set to PETSC_TRUE indicates that any add or insertion
    5766:    that would generate a new entry that has not been preallocated will
    5767:    instead produce an error. (Currently supported for AIJ and BAIJ formats
    5768:    only.) This is a useful flag when debugging matrix memory preallocation.
    5769:    If this option is set then the MatAssemblyBegin/End() processes has one less global reduction

    5771:    MAT_IGNORE_OFF_PROC_ENTRIES set to PETSC_TRUE indicates entries destined for
    5772:    other processors should be dropped, rather than stashed.
    5773:    This is useful if you know that the "owning" processor is also
    5774:    always generating the correct matrix entries, so that PETSc need
    5775:    not transfer duplicate entries generated on another processor.

    5777:    MAT_USE_HASH_TABLE indicates that a hash table be used to improve the
    5778:    searches during matrix assembly. When this flag is set, the hash table
    5779:    is created during the first Matrix Assembly. This hash table is
    5780:    used the next time through, during MatSetVaules()/MatSetVaulesBlocked()
    5781:    to improve the searching of indices. MAT_NEW_NONZERO_LOCATIONS flag
    5782:    should be used with MAT_USE_HASH_TABLE flag. This option is currently
    5783:    supported by MATMPIBAIJ format only.

    5785:    MAT_KEEP_NONZERO_PATTERN indicates when MatZeroRows() is called the zeroed entries
    5786:    are kept in the nonzero structure

    5788:    MAT_IGNORE_ZERO_ENTRIES - for AIJ/IS matrices this will stop zero values from creating
    5789:    a zero location in the matrix

    5791:    MAT_USE_INODES - indicates using inode version of the code - works with AIJ matrix types

    5793:    MAT_NO_OFF_PROC_ZERO_ROWS - you know each process will only zero its own rows. This avoids all reductions in the
    5794:         zero row routines and thus improves performance for very large process counts.

    5796:    MAT_IGNORE_LOWER_TRIANGULAR - For SBAIJ matrices will ignore any insertions you make in the lower triangular
    5797:         part of the matrix (since they should match the upper triangular part).

    5799:    MAT_SORTED_FULL - each process provides exactly its local rows; all column indices for a given row are passed in a
    5800:                      single call to MatSetValues(), preallocation is perfect, row oriented, INSERT_VALUES is used. Common
    5801:                      with finite difference schemes with non-periodic boundary conditions.

    5803:    Level: intermediate

    5805: .seealso:  MatOption, Mat

    5807: @*/
    5808: PetscErrorCode MatSetOption(Mat mat,MatOption op,PetscBool flg)
    5809: {

    5814:   if (op > 0) {
    5817:   }

    5819:   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);

    5821:   switch (op) {
    5822:   case MAT_FORCE_DIAGONAL_ENTRIES:
    5823:     mat->force_diagonals = flg;
    5824:     return(0);
    5825:   case MAT_NO_OFF_PROC_ENTRIES:
    5826:     mat->nooffprocentries = flg;
    5827:     return(0);
    5828:   case MAT_SUBSET_OFF_PROC_ENTRIES:
    5829:     mat->assembly_subset = flg;
    5830:     if (!mat->assembly_subset) { /* See the same logic in VecAssembly wrt VEC_SUBSET_OFF_PROC_ENTRIES */
    5831: #if !defined(PETSC_HAVE_MPIUNI)
    5832:       MatStashScatterDestroy_BTS(&mat->stash);
    5833: #endif
    5834:       mat->stash.first_assembly_done = PETSC_FALSE;
    5835:     }
    5836:     return(0);
    5837:   case MAT_NO_OFF_PROC_ZERO_ROWS:
    5838:     mat->nooffproczerorows = flg;
    5839:     return(0);
    5840:   case MAT_SPD:
    5841:     mat->spd_set = PETSC_TRUE;
    5842:     mat->spd     = flg;
    5843:     if (flg) {
    5844:       mat->symmetric                  = PETSC_TRUE;
    5845:       mat->structurally_symmetric     = PETSC_TRUE;
    5846:       mat->symmetric_set              = PETSC_TRUE;
    5847:       mat->structurally_symmetric_set = PETSC_TRUE;
    5848:     }
    5849:     break;
    5850:   case MAT_SYMMETRIC:
    5851:     mat->symmetric = flg;
    5852:     if (flg) mat->structurally_symmetric = PETSC_TRUE;
    5853:     mat->symmetric_set              = PETSC_TRUE;
    5854:     mat->structurally_symmetric_set = flg;
    5855: #if !defined(PETSC_USE_COMPLEX)
    5856:     mat->hermitian     = flg;
    5857:     mat->hermitian_set = PETSC_TRUE;
    5858: #endif
    5859:     break;
    5860:   case MAT_HERMITIAN:
    5861:     mat->hermitian = flg;
    5862:     if (flg) mat->structurally_symmetric = PETSC_TRUE;
    5863:     mat->hermitian_set              = PETSC_TRUE;
    5864:     mat->structurally_symmetric_set = flg;
    5865: #if !defined(PETSC_USE_COMPLEX)
    5866:     mat->symmetric     = flg;
    5867:     mat->symmetric_set = PETSC_TRUE;
    5868: #endif
    5869:     break;
    5870:   case MAT_STRUCTURALLY_SYMMETRIC:
    5871:     mat->structurally_symmetric     = flg;
    5872:     mat->structurally_symmetric_set = PETSC_TRUE;
    5873:     break;
    5874:   case MAT_SYMMETRY_ETERNAL:
    5875:     mat->symmetric_eternal = flg;
    5876:     break;
    5877:   case MAT_STRUCTURE_ONLY:
    5878:     mat->structure_only = flg;
    5879:     break;
    5880:   case MAT_SORTED_FULL:
    5881:     mat->sortedfull = flg;
    5882:     break;
    5883:   default:
    5884:     break;
    5885:   }
    5886:   if (mat->ops->setoption) {
    5887:     (*mat->ops->setoption)(mat,op,flg);
    5888:   }
    5889:   return(0);
    5890: }

    5892: /*@
    5893:    MatGetOption - Gets a parameter option that has been set for a matrix.

    5895:    Logically Collective on Mat for certain operations, such as MAT_SPD, not collective for MAT_ROW_ORIENTED, see MatOption

    5897:    Input Parameters:
    5898: +  mat - the matrix
    5899: -  option - the option, this only responds to certain options, check the code for which ones

    5901:    Output Parameter:
    5902: .  flg - turn the option on (PETSC_TRUE) or off (PETSC_FALSE)

    5904:     Notes:
    5905:     Can only be called after MatSetSizes() and MatSetType() have been set.

    5907:    Level: intermediate

    5909: .seealso:  MatOption, MatSetOption()

    5911: @*/
    5912: PetscErrorCode MatGetOption(Mat mat,MatOption op,PetscBool *flg)
    5913: {

    5918:   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);
    5919:   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()");

    5921:   switch (op) {
    5922:   case MAT_NO_OFF_PROC_ENTRIES:
    5923:     *flg = mat->nooffprocentries;
    5924:     break;
    5925:   case MAT_NO_OFF_PROC_ZERO_ROWS:
    5926:     *flg = mat->nooffproczerorows;
    5927:     break;
    5928:   case MAT_SYMMETRIC:
    5929:     *flg = mat->symmetric;
    5930:     break;
    5931:   case MAT_HERMITIAN:
    5932:     *flg = mat->hermitian;
    5933:     break;
    5934:   case MAT_STRUCTURALLY_SYMMETRIC:
    5935:     *flg = mat->structurally_symmetric;
    5936:     break;
    5937:   case MAT_SYMMETRY_ETERNAL:
    5938:     *flg = mat->symmetric_eternal;
    5939:     break;
    5940:   case MAT_SPD:
    5941:     *flg = mat->spd;
    5942:     break;
    5943:   default:
    5944:     break;
    5945:   }
    5946:   return(0);
    5947: }

    5949: /*@
    5950:    MatZeroEntries - Zeros all entries of a matrix.  For sparse matrices
    5951:    this routine retains the old nonzero structure.

    5953:    Logically Collective on Mat

    5955:    Input Parameters:
    5956: .  mat - the matrix

    5958:    Level: intermediate

    5960:    Notes:
    5961:     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.
    5962:    See the Performance chapter of the users manual for information on preallocating matrices.

    5964: .seealso: MatZeroRows()
    5965: @*/
    5966: PetscErrorCode MatZeroEntries(Mat mat)
    5967: {

    5973:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    5974:   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");
    5975:   if (!mat->ops->zeroentries) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    5976:   MatCheckPreallocated(mat,1);

    5978:   PetscLogEventBegin(MAT_ZeroEntries,mat,0,0,0);
    5979:   (*mat->ops->zeroentries)(mat);
    5980:   PetscLogEventEnd(MAT_ZeroEntries,mat,0,0,0);
    5981:   PetscObjectStateIncrease((PetscObject)mat);
    5982:   return(0);
    5983: }

    5985: /*@
    5986:    MatZeroRowsColumns - Zeros all entries (except possibly the main diagonal)
    5987:    of a set of rows and columns of a matrix.

    5989:    Collective on Mat

    5991:    Input Parameters:
    5992: +  mat - the matrix
    5993: .  numRows - the number of rows to remove
    5994: .  rows - the global row indices
    5995: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    5996: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    5997: -  b - optional vector of right hand side, that will be adjusted by provided solution

    5999:    Notes:
    6000:    This does not change the nonzero structure of the matrix, it merely zeros those entries in the matrix.

    6002:    The user can set a value in the diagonal entry (or for the AIJ and
    6003:    row formats can optionally remove the main diagonal entry from the
    6004:    nonzero structure as well, by passing 0.0 as the final argument).

    6006:    For the parallel case, all processes that share the matrix (i.e.,
    6007:    those in the communicator used for matrix creation) MUST call this
    6008:    routine, regardless of whether any rows being zeroed are owned by
    6009:    them.

    6011:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6012:    list only rows local to itself).

    6014:    The option MAT_NO_OFF_PROC_ZERO_ROWS does not apply to this routine.

    6016:    Level: intermediate

    6018: .seealso: MatZeroRowsIS(), MatZeroRows(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6019:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6020: @*/
    6021: PetscErrorCode MatZeroRowsColumns(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
    6022: {

    6029:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6030:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6031:   if (!mat->ops->zerorowscolumns) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    6032:   MatCheckPreallocated(mat,1);

    6034:   (*mat->ops->zerorowscolumns)(mat,numRows,rows,diag,x,b);
    6035:   MatViewFromOptions(mat,NULL,"-mat_view");
    6036:   PetscObjectStateIncrease((PetscObject)mat);
    6037:   return(0);
    6038: }

    6040: /*@
    6041:    MatZeroRowsColumnsIS - Zeros all entries (except possibly the main diagonal)
    6042:    of a set of rows and columns of a matrix.

    6044:    Collective on Mat

    6046:    Input Parameters:
    6047: +  mat - the matrix
    6048: .  is - the rows to zero
    6049: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6050: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6051: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6053:    Notes:
    6054:    This does not change the nonzero structure of the matrix, it merely zeros those entries in the matrix.

    6056:    The user can set a value in the diagonal entry (or for the AIJ and
    6057:    row formats can optionally remove the main diagonal entry from the
    6058:    nonzero structure as well, by passing 0.0 as the final argument).

    6060:    For the parallel case, all processes that share the matrix (i.e.,
    6061:    those in the communicator used for matrix creation) MUST call this
    6062:    routine, regardless of whether any rows being zeroed are owned by
    6063:    them.

    6065:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6066:    list only rows local to itself).

    6068:    The option MAT_NO_OFF_PROC_ZERO_ROWS does not apply to this routine.

    6070:    Level: intermediate

    6072: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6073:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRows(), MatZeroRowsColumnsStencil()
    6074: @*/
    6075: PetscErrorCode MatZeroRowsColumnsIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
    6076: {
    6078:   PetscInt       numRows;
    6079:   const PetscInt *rows;

    6086:   ISGetLocalSize(is,&numRows);
    6087:   ISGetIndices(is,&rows);
    6088:   MatZeroRowsColumns(mat,numRows,rows,diag,x,b);
    6089:   ISRestoreIndices(is,&rows);
    6090:   return(0);
    6091: }

    6093: /*@
    6094:    MatZeroRows - Zeros all entries (except possibly the main diagonal)
    6095:    of a set of rows of a matrix.

    6097:    Collective on Mat

    6099:    Input Parameters:
    6100: +  mat - the matrix
    6101: .  numRows - the number of rows to remove
    6102: .  rows - the global row indices
    6103: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6104: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6105: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6107:    Notes:
    6108:    For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
    6109:    but does not release memory.  For the dense and block diagonal
    6110:    formats this does not alter the nonzero structure.

    6112:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6113:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6114:    merely zeroed.

    6116:    The user can set a value in the diagonal entry (or for the AIJ and
    6117:    row formats can optionally remove the main diagonal entry from the
    6118:    nonzero structure as well, by passing 0.0 as the final argument).

    6120:    For the parallel case, all processes that share the matrix (i.e.,
    6121:    those in the communicator used for matrix creation) MUST call this
    6122:    routine, regardless of whether any rows being zeroed are owned by
    6123:    them.

    6125:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6126:    list only rows local to itself).

    6128:    You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
    6129:    owns that are to be zeroed. This saves a global synchronization in the implementation.

    6131:    Level: intermediate

    6133: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6134:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6135: @*/
    6136: PetscErrorCode MatZeroRows(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
    6137: {

    6144:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6145:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6146:   if (!mat->ops->zerorows) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    6147:   MatCheckPreallocated(mat,1);

    6149:   (*mat->ops->zerorows)(mat,numRows,rows,diag,x,b);
    6150:   MatViewFromOptions(mat,NULL,"-mat_view");
    6151:   PetscObjectStateIncrease((PetscObject)mat);
    6152:   return(0);
    6153: }

    6155: /*@
    6156:    MatZeroRowsIS - Zeros all entries (except possibly the main diagonal)
    6157:    of a set of rows of a matrix.

    6159:    Collective on Mat

    6161:    Input Parameters:
    6162: +  mat - the matrix
    6163: .  is - index set of rows to remove (if NULL then no row is removed)
    6164: .  diag - value put in all diagonals of eliminated rows
    6165: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6166: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6168:    Notes:
    6169:    For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
    6170:    but does not release memory.  For the dense and block diagonal
    6171:    formats this does not alter the nonzero structure.

    6173:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6174:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6175:    merely zeroed.

    6177:    The user can set a value in the diagonal entry (or for the AIJ and
    6178:    row formats can optionally remove the main diagonal entry from the
    6179:    nonzero structure as well, by passing 0.0 as the final argument).

    6181:    For the parallel case, all processes that share the matrix (i.e.,
    6182:    those in the communicator used for matrix creation) MUST call this
    6183:    routine, regardless of whether any rows being zeroed are owned by
    6184:    them.

    6186:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6187:    list only rows local to itself).

    6189:    You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
    6190:    owns that are to be zeroed. This saves a global synchronization in the implementation.

    6192:    Level: intermediate

    6194: .seealso: MatZeroRows(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6195:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6196: @*/
    6197: PetscErrorCode MatZeroRowsIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
    6198: {
    6199:   PetscInt       numRows = 0;
    6200:   const PetscInt *rows = NULL;

    6206:   if (is) {
    6208:     ISGetLocalSize(is,&numRows);
    6209:     ISGetIndices(is,&rows);
    6210:   }
    6211:   MatZeroRows(mat,numRows,rows,diag,x,b);
    6212:   if (is) {
    6213:     ISRestoreIndices(is,&rows);
    6214:   }
    6215:   return(0);
    6216: }

    6218: /*@
    6219:    MatZeroRowsStencil - Zeros all entries (except possibly the main diagonal)
    6220:    of a set of rows of a matrix. These rows must be local to the process.

    6222:    Collective on Mat

    6224:    Input Parameters:
    6225: +  mat - the matrix
    6226: .  numRows - the number of rows to remove
    6227: .  rows - the grid coordinates (and component number when dof > 1) for matrix rows
    6228: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6229: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6230: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6232:    Notes:
    6233:    For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
    6234:    but does not release memory.  For the dense and block diagonal
    6235:    formats this does not alter the nonzero structure.

    6237:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6238:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6239:    merely zeroed.

    6241:    The user can set a value in the diagonal entry (or for the AIJ and
    6242:    row formats can optionally remove the main diagonal entry from the
    6243:    nonzero structure as well, by passing 0.0 as the final argument).

    6245:    For the parallel case, all processes that share the matrix (i.e.,
    6246:    those in the communicator used for matrix creation) MUST call this
    6247:    routine, regardless of whether any rows being zeroed are owned by
    6248:    them.

    6250:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6251:    list only rows local to itself).

    6253:    The grid coordinates are across the entire grid, not just the local portion

    6255:    In Fortran idxm and idxn should be declared as
    6256: $     MatStencil idxm(4,m)
    6257:    and the values inserted using
    6258: $    idxm(MatStencil_i,1) = i
    6259: $    idxm(MatStencil_j,1) = j
    6260: $    idxm(MatStencil_k,1) = k
    6261: $    idxm(MatStencil_c,1) = c
    6262:    etc

    6264:    For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    6265:    obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    6266:    etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    6267:    DM_BOUNDARY_PERIODIC boundary type.

    6269:    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
    6270:    a single value per point) you can skip filling those indices.

    6272:    Level: intermediate

    6274: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsl(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6275:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6276: @*/
    6277: PetscErrorCode MatZeroRowsStencil(Mat mat,PetscInt numRows,const MatStencil rows[],PetscScalar diag,Vec x,Vec b)
    6278: {
    6279:   PetscInt       dim     = mat->stencil.dim;
    6280:   PetscInt       sdim    = dim - (1 - (PetscInt) mat->stencil.noc);
    6281:   PetscInt       *dims   = mat->stencil.dims+1;
    6282:   PetscInt       *starts = mat->stencil.starts;
    6283:   PetscInt       *dxm    = (PetscInt*) rows;
    6284:   PetscInt       *jdxm, i, j, tmp, numNewRows = 0;

    6292:   PetscMalloc1(numRows, &jdxm);
    6293:   for (i = 0; i < numRows; ++i) {
    6294:     /* Skip unused dimensions (they are ordered k, j, i, c) */
    6295:     for (j = 0; j < 3-sdim; ++j) dxm++;
    6296:     /* Local index in X dir */
    6297:     tmp = *dxm++ - starts[0];
    6298:     /* Loop over remaining dimensions */
    6299:     for (j = 0; j < dim-1; ++j) {
    6300:       /* If nonlocal, set index to be negative */
    6301:       if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = PETSC_MIN_INT;
    6302:       /* Update local index */
    6303:       else tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    6304:     }
    6305:     /* Skip component slot if necessary */
    6306:     if (mat->stencil.noc) dxm++;
    6307:     /* Local row number */
    6308:     if (tmp >= 0) {
    6309:       jdxm[numNewRows++] = tmp;
    6310:     }
    6311:   }
    6312:   MatZeroRowsLocal(mat,numNewRows,jdxm,diag,x,b);
    6313:   PetscFree(jdxm);
    6314:   return(0);
    6315: }

    6317: /*@
    6318:    MatZeroRowsColumnsStencil - Zeros all row and column entries (except possibly the main diagonal)
    6319:    of a set of rows and columns of a matrix.

    6321:    Collective on Mat

    6323:    Input Parameters:
    6324: +  mat - the matrix
    6325: .  numRows - the number of rows/columns to remove
    6326: .  rows - the grid coordinates (and component number when dof > 1) for matrix rows
    6327: .  diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6328: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6329: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6331:    Notes:
    6332:    For the AIJ and BAIJ matrix formats this removes the old nonzero structure,
    6333:    but does not release memory.  For the dense and block diagonal
    6334:    formats this does not alter the nonzero structure.

    6336:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6337:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6338:    merely zeroed.

    6340:    The user can set a value in the diagonal entry (or for the AIJ and
    6341:    row formats can optionally remove the main diagonal entry from the
    6342:    nonzero structure as well, by passing 0.0 as the final argument).

    6344:    For the parallel case, all processes that share the matrix (i.e.,
    6345:    those in the communicator used for matrix creation) MUST call this
    6346:    routine, regardless of whether any rows being zeroed are owned by
    6347:    them.

    6349:    Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6350:    list only rows local to itself, but the row/column numbers are given in local numbering).

    6352:    The grid coordinates are across the entire grid, not just the local portion

    6354:    In Fortran idxm and idxn should be declared as
    6355: $     MatStencil idxm(4,m)
    6356:    and the values inserted using
    6357: $    idxm(MatStencil_i,1) = i
    6358: $    idxm(MatStencil_j,1) = j
    6359: $    idxm(MatStencil_k,1) = k
    6360: $    idxm(MatStencil_c,1) = c
    6361:    etc

    6363:    For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    6364:    obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    6365:    etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    6366:    DM_BOUNDARY_PERIODIC boundary type.

    6368:    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
    6369:    a single value per point) you can skip filling those indices.

    6371:    Level: intermediate

    6373: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6374:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRows()
    6375: @*/
    6376: PetscErrorCode MatZeroRowsColumnsStencil(Mat mat,PetscInt numRows,const MatStencil rows[],PetscScalar diag,Vec x,Vec b)
    6377: {
    6378:   PetscInt       dim     = mat->stencil.dim;
    6379:   PetscInt       sdim    = dim - (1 - (PetscInt) mat->stencil.noc);
    6380:   PetscInt       *dims   = mat->stencil.dims+1;
    6381:   PetscInt       *starts = mat->stencil.starts;
    6382:   PetscInt       *dxm    = (PetscInt*) rows;
    6383:   PetscInt       *jdxm, i, j, tmp, numNewRows = 0;

    6391:   PetscMalloc1(numRows, &jdxm);
    6392:   for (i = 0; i < numRows; ++i) {
    6393:     /* Skip unused dimensions (they are ordered k, j, i, c) */
    6394:     for (j = 0; j < 3-sdim; ++j) dxm++;
    6395:     /* Local index in X dir */
    6396:     tmp = *dxm++ - starts[0];
    6397:     /* Loop over remaining dimensions */
    6398:     for (j = 0; j < dim-1; ++j) {
    6399:       /* If nonlocal, set index to be negative */
    6400:       if ((*dxm++ - starts[j+1]) < 0 || tmp < 0) tmp = PETSC_MIN_INT;
    6401:       /* Update local index */
    6402:       else tmp = tmp*dims[j] + *(dxm-1) - starts[j+1];
    6403:     }
    6404:     /* Skip component slot if necessary */
    6405:     if (mat->stencil.noc) dxm++;
    6406:     /* Local row number */
    6407:     if (tmp >= 0) {
    6408:       jdxm[numNewRows++] = tmp;
    6409:     }
    6410:   }
    6411:   MatZeroRowsColumnsLocal(mat,numNewRows,jdxm,diag,x,b);
    6412:   PetscFree(jdxm);
    6413:   return(0);
    6414: }

    6416: /*@C
    6417:    MatZeroRowsLocal - Zeros all entries (except possibly the main diagonal)
    6418:    of a set of rows of a matrix; using local numbering of rows.

    6420:    Collective on Mat

    6422:    Input Parameters:
    6423: +  mat - the matrix
    6424: .  numRows - the number of rows to remove
    6425: .  rows - the local row indices
    6426: .  diag - value put in all diagonals of eliminated rows
    6427: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6428: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6430:    Notes:
    6431:    Before calling MatZeroRowsLocal(), the user must first set the
    6432:    local-to-global mapping by calling MatSetLocalToGlobalMapping().

    6434:    For the AIJ matrix formats this removes the old nonzero structure,
    6435:    but does not release memory.  For the dense and block diagonal
    6436:    formats this does not alter the nonzero structure.

    6438:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6439:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6440:    merely zeroed.

    6442:    The user can set a value in the diagonal entry (or for the AIJ and
    6443:    row formats can optionally remove the main diagonal entry from the
    6444:    nonzero structure as well, by passing 0.0 as the final argument).

    6446:    You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
    6447:    owns that are to be zeroed. This saves a global synchronization in the implementation.

    6449:    Level: intermediate

    6451: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRows(), MatSetOption(),
    6452:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6453: @*/
    6454: PetscErrorCode MatZeroRowsLocal(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
    6455: {

    6462:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6463:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6464:   MatCheckPreallocated(mat,1);

    6466:   if (mat->ops->zerorowslocal) {
    6467:     (*mat->ops->zerorowslocal)(mat,numRows,rows,diag,x,b);
    6468:   } else {
    6469:     IS             is, newis;
    6470:     const PetscInt *newRows;

    6472:     if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Need to provide local to global mapping to matrix first");
    6473:     ISCreateGeneral(PETSC_COMM_SELF,numRows,rows,PETSC_COPY_VALUES,&is);
    6474:     ISLocalToGlobalMappingApplyIS(mat->rmap->mapping,is,&newis);
    6475:     ISGetIndices(newis,&newRows);
    6476:     (*mat->ops->zerorows)(mat,numRows,newRows,diag,x,b);
    6477:     ISRestoreIndices(newis,&newRows);
    6478:     ISDestroy(&newis);
    6479:     ISDestroy(&is);
    6480:   }
    6481:   PetscObjectStateIncrease((PetscObject)mat);
    6482:   return(0);
    6483: }

    6485: /*@
    6486:    MatZeroRowsLocalIS - Zeros all entries (except possibly the main diagonal)
    6487:    of a set of rows of a matrix; using local numbering of rows.

    6489:    Collective on Mat

    6491:    Input Parameters:
    6492: +  mat - the matrix
    6493: .  is - index set of rows to remove
    6494: .  diag - value put in all diagonals of eliminated rows
    6495: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6496: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6498:    Notes:
    6499:    Before calling MatZeroRowsLocalIS(), the user must first set the
    6500:    local-to-global mapping by calling MatSetLocalToGlobalMapping().

    6502:    For the AIJ matrix formats this removes the old nonzero structure,
    6503:    but does not release memory.  For the dense and block diagonal
    6504:    formats this does not alter the nonzero structure.

    6506:    If the option MatSetOption(mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE) the nonzero structure
    6507:    of the matrix is not changed (even for AIJ and BAIJ matrices) the values are
    6508:    merely zeroed.

    6510:    The user can set a value in the diagonal entry (or for the AIJ and
    6511:    row formats can optionally remove the main diagonal entry from the
    6512:    nonzero structure as well, by passing 0.0 as the final argument).

    6514:    You can call MatSetOption(mat,MAT_NO_OFF_PROC_ZERO_ROWS,PETSC_TRUE) if each process indicates only rows it
    6515:    owns that are to be zeroed. This saves a global synchronization in the implementation.

    6517:    Level: intermediate

    6519: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRows(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6520:           MatZeroRowsColumnsLocal(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6521: @*/
    6522: PetscErrorCode MatZeroRowsLocalIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
    6523: {
    6525:   PetscInt       numRows;
    6526:   const PetscInt *rows;

    6532:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6533:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6534:   MatCheckPreallocated(mat,1);

    6536:   ISGetLocalSize(is,&numRows);
    6537:   ISGetIndices(is,&rows);
    6538:   MatZeroRowsLocal(mat,numRows,rows,diag,x,b);
    6539:   ISRestoreIndices(is,&rows);
    6540:   return(0);
    6541: }

    6543: /*@
    6544:    MatZeroRowsColumnsLocal - Zeros all entries (except possibly the main diagonal)
    6545:    of a set of rows and columns of a matrix; using local numbering of rows.

    6547:    Collective on Mat

    6549:    Input Parameters:
    6550: +  mat - the matrix
    6551: .  numRows - the number of rows to remove
    6552: .  rows - the global row indices
    6553: .  diag - value put in all diagonals of eliminated rows
    6554: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6555: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6557:    Notes:
    6558:    Before calling MatZeroRowsColumnsLocal(), the user must first set the
    6559:    local-to-global mapping by calling MatSetLocalToGlobalMapping().

    6561:    The user can set a value in the diagonal entry (or for the AIJ and
    6562:    row formats can optionally remove the main diagonal entry from the
    6563:    nonzero structure as well, by passing 0.0 as the final argument).

    6565:    Level: intermediate

    6567: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6568:           MatZeroRows(), MatZeroRowsColumnsLocalIS(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6569: @*/
    6570: PetscErrorCode MatZeroRowsColumnsLocal(Mat mat,PetscInt numRows,const PetscInt rows[],PetscScalar diag,Vec x,Vec b)
    6571: {
    6573:   IS             is, newis;
    6574:   const PetscInt *newRows;

    6580:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6581:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6582:   MatCheckPreallocated(mat,1);

    6584:   if (!mat->cmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Need to provide local to global mapping to matrix first");
    6585:   ISCreateGeneral(PETSC_COMM_SELF,numRows,rows,PETSC_COPY_VALUES,&is);
    6586:   ISLocalToGlobalMappingApplyIS(mat->cmap->mapping,is,&newis);
    6587:   ISGetIndices(newis,&newRows);
    6588:   (*mat->ops->zerorowscolumns)(mat,numRows,newRows,diag,x,b);
    6589:   ISRestoreIndices(newis,&newRows);
    6590:   ISDestroy(&newis);
    6591:   ISDestroy(&is);
    6592:   PetscObjectStateIncrease((PetscObject)mat);
    6593:   return(0);
    6594: }

    6596: /*@
    6597:    MatZeroRowsColumnsLocalIS - Zeros all entries (except possibly the main diagonal)
    6598:    of a set of rows and columns of a matrix; using local numbering of rows.

    6600:    Collective on Mat

    6602:    Input Parameters:
    6603: +  mat - the matrix
    6604: .  is - index set of rows to remove
    6605: .  diag - value put in all diagonals of eliminated rows
    6606: .  x - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6607: -  b - optional vector of right hand side, that will be adjusted by provided solution

    6609:    Notes:
    6610:    Before calling MatZeroRowsColumnsLocalIS(), the user must first set the
    6611:    local-to-global mapping by calling MatSetLocalToGlobalMapping().

    6613:    The user can set a value in the diagonal entry (or for the AIJ and
    6614:    row formats can optionally remove the main diagonal entry from the
    6615:    nonzero structure as well, by passing 0.0 as the final argument).

    6617:    Level: intermediate

    6619: .seealso: MatZeroRowsIS(), MatZeroRowsColumns(), MatZeroRowsLocalIS(), MatZeroRowsStencil(), MatZeroEntries(), MatZeroRowsLocal(), MatSetOption(),
    6620:           MatZeroRowsColumnsLocal(), MatZeroRows(), MatZeroRowsColumnsIS(), MatZeroRowsColumnsStencil()
    6621: @*/
    6622: PetscErrorCode MatZeroRowsColumnsLocalIS(Mat mat,IS is,PetscScalar diag,Vec x,Vec b)
    6623: {
    6625:   PetscInt       numRows;
    6626:   const PetscInt *rows;

    6632:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6633:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6634:   MatCheckPreallocated(mat,1);

    6636:   ISGetLocalSize(is,&numRows);
    6637:   ISGetIndices(is,&rows);
    6638:   MatZeroRowsColumnsLocal(mat,numRows,rows,diag,x,b);
    6639:   ISRestoreIndices(is,&rows);
    6640:   return(0);
    6641: }

    6643: /*@C
    6644:    MatGetSize - Returns the numbers of rows and columns in a matrix.

    6646:    Not Collective

    6648:    Input Parameter:
    6649: .  mat - the matrix

    6651:    Output Parameters:
    6652: +  m - the number of global rows
    6653: -  n - the number of global columns

    6655:    Note: both output parameters can be NULL on input.

    6657:    Level: beginner

    6659: .seealso: MatGetLocalSize()
    6660: @*/
    6661: PetscErrorCode MatGetSize(Mat mat,PetscInt *m,PetscInt *n)
    6662: {
    6665:   if (m) *m = mat->rmap->N;
    6666:   if (n) *n = mat->cmap->N;
    6667:   return(0);
    6668: }

    6670: /*@C
    6671:    MatGetLocalSize - Returns the number of local rows and local columns
    6672:    of a matrix, that is the local size of the left and right vectors as returned by MatCreateVecs().

    6674:    Not Collective

    6676:    Input Parameters:
    6677: .  mat - the matrix

    6679:    Output Parameters:
    6680: +  m - the number of local rows
    6681: -  n - the number of local columns

    6683:    Note: both output parameters can be NULL on input.

    6685:    Level: beginner

    6687: .seealso: MatGetSize()
    6688: @*/
    6689: PetscErrorCode MatGetLocalSize(Mat mat,PetscInt *m,PetscInt *n)
    6690: {
    6695:   if (m) *m = mat->rmap->n;
    6696:   if (n) *n = mat->cmap->n;
    6697:   return(0);
    6698: }

    6700: /*@C
    6701:    MatGetOwnershipRangeColumn - Returns the range of matrix columns associated with rows of a vector one multiplies by that owned by
    6702:    this processor. (The columns of the "diagonal block")

    6704:    Not Collective, unless matrix has not been allocated, then collective on Mat

    6706:    Input Parameters:
    6707: .  mat - the matrix

    6709:    Output Parameters:
    6710: +  m - the global index of the first local column
    6711: -  n - one more than the global index of the last local column

    6713:    Notes:
    6714:     both output parameters can be NULL on input.

    6716:    Level: developer

    6718: .seealso:  MatGetOwnershipRange(), MatGetOwnershipRanges(), MatGetOwnershipRangesColumn()

    6720: @*/
    6721: PetscErrorCode MatGetOwnershipRangeColumn(Mat mat,PetscInt *m,PetscInt *n)
    6722: {
    6728:   MatCheckPreallocated(mat,1);
    6729:   if (m) *m = mat->cmap->rstart;
    6730:   if (n) *n = mat->cmap->rend;
    6731:   return(0);
    6732: }

    6734: /*@C
    6735:    MatGetOwnershipRange - Returns the range of matrix rows owned by
    6736:    this processor, assuming that the matrix is laid out with the first
    6737:    n1 rows on the first processor, the next n2 rows on the second, etc.
    6738:    For certain parallel layouts this range may not be well defined.

    6740:    Not Collective

    6742:    Input Parameters:
    6743: .  mat - the matrix

    6745:    Output Parameters:
    6746: +  m - the global index of the first local row
    6747: -  n - one more than the global index of the last local row

    6749:    Note: Both output parameters can be NULL on input.
    6750: $  This function requires that the matrix be preallocated. If you have not preallocated, consider using
    6751: $    PetscSplitOwnership(MPI_Comm comm, PetscInt *n, PetscInt *N)
    6752: $  and then MPI_Scan() to calculate prefix sums of the local sizes.

    6754:    Level: beginner

    6756: .seealso:   MatGetOwnershipRanges(), MatGetOwnershipRangeColumn(), MatGetOwnershipRangesColumn(), PetscSplitOwnership(), PetscSplitOwnershipBlock()

    6758: @*/
    6759: PetscErrorCode MatGetOwnershipRange(Mat mat,PetscInt *m,PetscInt *n)
    6760: {
    6766:   MatCheckPreallocated(mat,1);
    6767:   if (m) *m = mat->rmap->rstart;
    6768:   if (n) *n = mat->rmap->rend;
    6769:   return(0);
    6770: }

    6772: /*@C
    6773:    MatGetOwnershipRanges - Returns the range of matrix rows owned by
    6774:    each process

    6776:    Not Collective, unless matrix has not been allocated, then collective on Mat

    6778:    Input Parameters:
    6779: .  mat - the matrix

    6781:    Output Parameters:
    6782: .  ranges - start of each processors portion plus one more than the total length at the end

    6784:    Level: beginner

    6786: .seealso:   MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatGetOwnershipRangesColumn()

    6788: @*/
    6789: PetscErrorCode MatGetOwnershipRanges(Mat mat,const PetscInt **ranges)
    6790: {

    6796:   MatCheckPreallocated(mat,1);
    6797:   PetscLayoutGetRanges(mat->rmap,ranges);
    6798:   return(0);
    6799: }

    6801: /*@C
    6802:    MatGetOwnershipRangesColumn - Returns the range of matrix columns associated with rows of a vector one multiplies by that owned by
    6803:    this processor. (The columns of the "diagonal blocks" for each process)

    6805:    Not Collective, unless matrix has not been allocated, then collective on Mat

    6807:    Input Parameters:
    6808: .  mat - the matrix

    6810:    Output Parameters:
    6811: .  ranges - start of each processors portion plus one more then the total length at the end

    6813:    Level: beginner

    6815: .seealso:   MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatGetOwnershipRanges()

    6817: @*/
    6818: PetscErrorCode MatGetOwnershipRangesColumn(Mat mat,const PetscInt **ranges)
    6819: {

    6825:   MatCheckPreallocated(mat,1);
    6826:   PetscLayoutGetRanges(mat->cmap,ranges);
    6827:   return(0);
    6828: }

    6830: /*@C
    6831:    MatGetOwnershipIS - Get row and column ownership as index sets

    6833:    Not Collective

    6835:    Input Arguments:
    6836: .  A - matrix of type Elemental or ScaLAPACK

    6838:    Output Arguments:
    6839: +  rows - rows in which this process owns elements
    6840: -  cols - columns in which this process owns elements

    6842:    Level: intermediate

    6844: .seealso: MatGetOwnershipRange(), MatGetOwnershipRangeColumn(), MatSetValues(), MATELEMENTAL
    6845: @*/
    6846: PetscErrorCode MatGetOwnershipIS(Mat A,IS *rows,IS *cols)
    6847: {
    6848:   PetscErrorCode ierr,(*f)(Mat,IS*,IS*);

    6851:   MatCheckPreallocated(A,1);
    6852:   PetscObjectQueryFunction((PetscObject)A,"MatGetOwnershipIS_C",&f);
    6853:   if (f) {
    6854:     (*f)(A,rows,cols);
    6855:   } else {   /* Create a standard row-based partition, each process is responsible for ALL columns in their row block */
    6856:     if (rows) {ISCreateStride(PETSC_COMM_SELF,A->rmap->n,A->rmap->rstart,1,rows);}
    6857:     if (cols) {ISCreateStride(PETSC_COMM_SELF,A->cmap->N,0,1,cols);}
    6858:   }
    6859:   return(0);
    6860: }

    6862: /*@C
    6863:    MatILUFactorSymbolic - Performs symbolic ILU factorization of a matrix.
    6864:    Uses levels of fill only, not drop tolerance. Use MatLUFactorNumeric()
    6865:    to complete the factorization.

    6867:    Collective on Mat

    6869:    Input Parameters:
    6870: +  mat - the matrix
    6871: .  row - row permutation
    6872: .  column - column permutation
    6873: -  info - structure containing
    6874: $      levels - number of levels of fill.
    6875: $      expected fill - as ratio of original fill.
    6876: $      1 or 0 - indicating force fill on diagonal (improves robustness for matrices
    6877:                 missing diagonal entries)

    6879:    Output Parameters:
    6880: .  fact - new matrix that has been symbolically factored

    6882:    Notes:
    6883:     See Users-Manual: ch_mat for additional information about choosing the fill factor for better efficiency.

    6885:    Most users should employ the simplified KSP interface for linear solvers
    6886:    instead of working directly with matrix algebra routines such as this.
    6887:    See, e.g., KSPCreate().

    6889:    Level: developer

    6891: .seealso: MatLUFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor()
    6892:           MatGetOrdering(), MatFactorInfo

    6894:     Note: this uses the definition of level of fill as in Y. Saad, 2003

    6896:     Developer Note: fortran interface is not autogenerated as the f90
    6897:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    6899:    References:
    6900:      Y. Saad, Iterative methods for sparse linear systems Philadelphia: Society for Industrial and Applied Mathematics, 2003
    6901: @*/
    6902: PetscErrorCode MatILUFactorSymbolic(Mat fact,Mat mat,IS row,IS col,const MatFactorInfo *info)
    6903: {

    6913:   if (info->levels < 0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Levels of fill negative %D",(PetscInt)info->levels);
    6914:   if (info->fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Expected fill less than 1.0 %g",(double)info->fill);
    6915:   if (!fact->ops->ilufactorsymbolic) {
    6916:     MatSolverType stype;
    6917:     MatFactorGetSolverType(fact,&stype);
    6918:     SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic ILU using solver type %s",((PetscObject)mat)->type_name,stype);
    6919:   }
    6920:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6921:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6922:   MatCheckPreallocated(mat,2);

    6924:   PetscLogEventBegin(MAT_ILUFactorSymbolic,mat,row,col,0);
    6925:   (fact->ops->ilufactorsymbolic)(fact,mat,row,col,info);
    6926:   PetscLogEventEnd(MAT_ILUFactorSymbolic,mat,row,col,0);
    6927:   return(0);
    6928: }

    6930: /*@C
    6931:    MatICCFactorSymbolic - Performs symbolic incomplete
    6932:    Cholesky factorization for a symmetric matrix.  Use
    6933:    MatCholeskyFactorNumeric() to complete the factorization.

    6935:    Collective on Mat

    6937:    Input Parameters:
    6938: +  mat - the matrix
    6939: .  perm - row and column permutation
    6940: -  info - structure containing
    6941: $      levels - number of levels of fill.
    6942: $      expected fill - as ratio of original fill.

    6944:    Output Parameter:
    6945: .  fact - the factored matrix

    6947:    Notes:
    6948:    Most users should employ the KSP interface for linear solvers
    6949:    instead of working directly with matrix algebra routines such as this.
    6950:    See, e.g., KSPCreate().

    6952:    Level: developer

    6954: .seealso: MatCholeskyFactorNumeric(), MatCholeskyFactor(), MatFactorInfo

    6956:     Note: this uses the definition of level of fill as in Y. Saad, 2003

    6958:     Developer Note: fortran interface is not autogenerated as the f90
    6959:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    6961:    References:
    6962:      Y. Saad, Iterative methods for sparse linear systems Philadelphia: Society for Industrial and Applied Mathematics, 2003
    6963: @*/
    6964: PetscErrorCode MatICCFactorSymbolic(Mat fact,Mat mat,IS perm,const MatFactorInfo *info)
    6965: {

    6974:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    6975:   if (info->levels < 0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Levels negative %D",(PetscInt) info->levels);
    6976:   if (info->fill < 1.0) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Expected fill less than 1.0 %g",(double)info->fill);
    6977:   if (!(fact)->ops->iccfactorsymbolic) {
    6978:     MatSolverType stype;
    6979:     MatFactorGetSolverType(fact,&stype);
    6980:     SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Matrix type %s symbolic ICC using solver type %s",((PetscObject)mat)->type_name,stype);
    6981:   }
    6982:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    6983:   MatCheckPreallocated(mat,2);

    6985:   PetscLogEventBegin(MAT_ICCFactorSymbolic,mat,perm,0,0);
    6986:   (fact->ops->iccfactorsymbolic)(fact,mat,perm,info);
    6987:   PetscLogEventEnd(MAT_ICCFactorSymbolic,mat,perm,0,0);
    6988:   return(0);
    6989: }

    6991: /*@C
    6992:    MatCreateSubMatrices - Extracts several submatrices from a matrix. If submat
    6993:    points to an array of valid matrices, they may be reused to store the new
    6994:    submatrices.

    6996:    Collective on Mat

    6998:    Input Parameters:
    6999: +  mat - the matrix
    7000: .  n   - the number of submatrixes to be extracted (on this processor, may be zero)
    7001: .  irow, icol - index sets of rows and columns to extract
    7002: -  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    7004:    Output Parameter:
    7005: .  submat - the array of submatrices

    7007:    Notes:
    7008:    MatCreateSubMatrices() can extract ONLY sequential submatrices
    7009:    (from both sequential and parallel matrices). Use MatCreateSubMatrix()
    7010:    to extract a parallel submatrix.

    7012:    Some matrix types place restrictions on the row and column
    7013:    indices, such as that they be sorted or that they be equal to each other.

    7015:    The index sets may not have duplicate entries.

    7017:    When extracting submatrices from a parallel matrix, each processor can
    7018:    form a different submatrix by setting the rows and columns of its
    7019:    individual index sets according to the local submatrix desired.

    7021:    When finished using the submatrices, the user should destroy
    7022:    them with MatDestroySubMatrices().

    7024:    MAT_REUSE_MATRIX can only be used when the nonzero structure of the
    7025:    original matrix has not changed from that last call to MatCreateSubMatrices().

    7027:    This routine creates the matrices in submat; you should NOT create them before
    7028:    calling it. It also allocates the array of matrix pointers submat.

    7030:    For BAIJ matrices the index sets must respect the block structure, that is if they
    7031:    request one row/column in a block, they must request all rows/columns that are in
    7032:    that block. For example, if the block size is 2 you cannot request just row 0 and
    7033:    column 0.

    7035:    Fortran Note:
    7036:    The Fortran interface is slightly different from that given below; it
    7037:    requires one to pass in  as submat a Mat (integer) array of size at least n+1.

    7039:    Level: advanced

    7042: .seealso: MatDestroySubMatrices(), MatCreateSubMatrix(), MatGetRow(), MatGetDiagonal(), MatReuse
    7043: @*/
    7044: PetscErrorCode MatCreateSubMatrices(Mat mat,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
    7045: {
    7047:   PetscInt       i;
    7048:   PetscBool      eq;

    7053:   if (n) {
    7058:   }
    7060:   if (n && scall == MAT_REUSE_MATRIX) {
    7063:   }
    7064:   if (!mat->ops->createsubmatrices) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    7065:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    7066:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7067:   MatCheckPreallocated(mat,1);

    7069:   PetscLogEventBegin(MAT_CreateSubMats,mat,0,0,0);
    7070:   (*mat->ops->createsubmatrices)(mat,n,irow,icol,scall,submat);
    7071:   PetscLogEventEnd(MAT_CreateSubMats,mat,0,0,0);
    7072:   for (i=0; i<n; i++) {
    7073:     (*submat)[i]->factortype = MAT_FACTOR_NONE;  /* in case in place factorization was previously done on submatrix */
    7074:     ISEqualUnsorted(irow[i],icol[i],&eq);
    7075:     if (eq) {
    7076:       MatPropagateSymmetryOptions(mat,(*submat)[i]);
    7077:     }
    7078:   }
    7079:   return(0);
    7080: }

    7082: /*@C
    7083:    MatCreateSubMatricesMPI - Extracts MPI submatrices across a sub communicator of mat (by pairs of IS that may live on subcomms).

    7085:    Collective on Mat

    7087:    Input Parameters:
    7088: +  mat - the matrix
    7089: .  n   - the number of submatrixes to be extracted
    7090: .  irow, icol - index sets of rows and columns to extract
    7091: -  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    7093:    Output Parameter:
    7094: .  submat - the array of submatrices

    7096:    Level: advanced

    7099: .seealso: MatCreateSubMatrices(), MatCreateSubMatrix(), MatGetRow(), MatGetDiagonal(), MatReuse
    7100: @*/
    7101: PetscErrorCode MatCreateSubMatricesMPI(Mat mat,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
    7102: {
    7104:   PetscInt       i;
    7105:   PetscBool      eq;

    7110:   if (n) {
    7115:   }
    7117:   if (n && scall == MAT_REUSE_MATRIX) {
    7120:   }
    7121:   if (!mat->ops->createsubmatricesmpi) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    7122:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    7123:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7124:   MatCheckPreallocated(mat,1);

    7126:   PetscLogEventBegin(MAT_CreateSubMats,mat,0,0,0);
    7127:   (*mat->ops->createsubmatricesmpi)(mat,n,irow,icol,scall,submat);
    7128:   PetscLogEventEnd(MAT_CreateSubMats,mat,0,0,0);
    7129:   for (i=0; i<n; i++) {
    7130:     ISEqualUnsorted(irow[i],icol[i],&eq);
    7131:     if (eq) {
    7132:       MatPropagateSymmetryOptions(mat,(*submat)[i]);
    7133:     }
    7134:   }
    7135:   return(0);
    7136: }

    7138: /*@C
    7139:    MatDestroyMatrices - Destroys an array of matrices.

    7141:    Collective on Mat

    7143:    Input Parameters:
    7144: +  n - the number of local matrices
    7145: -  mat - the matrices (note that this is a pointer to the array of matrices)

    7147:    Level: advanced

    7149:     Notes:
    7150:     Frees not only the matrices, but also the array that contains the matrices
    7151:            In Fortran will not free the array.

    7153: .seealso: MatCreateSubMatrices() MatDestroySubMatrices()
    7154: @*/
    7155: PetscErrorCode MatDestroyMatrices(PetscInt n,Mat *mat[])
    7156: {
    7158:   PetscInt       i;

    7161:   if (!*mat) return(0);
    7162:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Trying to destroy negative number of matrices %D",n);

    7165:   for (i=0; i<n; i++) {
    7166:     MatDestroy(&(*mat)[i]);
    7167:   }

    7169:   /* memory is allocated even if n = 0 */
    7170:   PetscFree(*mat);
    7171:   return(0);
    7172: }

    7174: /*@C
    7175:    MatDestroySubMatrices - Destroys a set of matrices obtained with MatCreateSubMatrices().

    7177:    Collective on Mat

    7179:    Input Parameters:
    7180: +  n - the number of local matrices
    7181: -  mat - the matrices (note that this is a pointer to the array of matrices, just to match the calling
    7182:                        sequence of MatCreateSubMatrices())

    7184:    Level: advanced

    7186:     Notes:
    7187:     Frees not only the matrices, but also the array that contains the matrices
    7188:            In Fortran will not free the array.

    7190: .seealso: MatCreateSubMatrices()
    7191: @*/
    7192: PetscErrorCode MatDestroySubMatrices(PetscInt n,Mat *mat[])
    7193: {
    7195:   Mat            mat0;

    7198:   if (!*mat) return(0);
    7199:   /* mat[] is an array of length n+1, see MatCreateSubMatrices_xxx() */
    7200:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Trying to destroy negative number of matrices %D",n);

    7203:   mat0 = (*mat)[0];
    7204:   if (mat0 && mat0->ops->destroysubmatrices) {
    7205:     (mat0->ops->destroysubmatrices)(n,mat);
    7206:   } else {
    7207:     MatDestroyMatrices(n,mat);
    7208:   }
    7209:   return(0);
    7210: }

    7212: /*@C
    7213:    MatGetSeqNonzeroStructure - Extracts the sequential nonzero structure from a matrix.

    7215:    Collective on Mat

    7217:    Input Parameters:
    7218: .  mat - the matrix

    7220:    Output Parameter:
    7221: .  matstruct - the sequential matrix with the nonzero structure of mat

    7223:   Level: intermediate

    7225: .seealso: MatDestroySeqNonzeroStructure(), MatCreateSubMatrices(), MatDestroyMatrices()
    7226: @*/
    7227: PetscErrorCode MatGetSeqNonzeroStructure(Mat mat,Mat *matstruct)
    7228: {

    7236:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7237:   MatCheckPreallocated(mat,1);

    7239:   if (!mat->ops->getseqnonzerostructure) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Not for matrix type %s\n",((PetscObject)mat)->type_name);
    7240:   PetscLogEventBegin(MAT_GetSeqNonzeroStructure,mat,0,0,0);
    7241:   (*mat->ops->getseqnonzerostructure)(mat,matstruct);
    7242:   PetscLogEventEnd(MAT_GetSeqNonzeroStructure,mat,0,0,0);
    7243:   return(0);
    7244: }

    7246: /*@C
    7247:    MatDestroySeqNonzeroStructure - Destroys matrix obtained with MatGetSeqNonzeroStructure().

    7249:    Collective on Mat

    7251:    Input Parameters:
    7252: .  mat - the matrix (note that this is a pointer to the array of matrices, just to match the calling
    7253:                        sequence of MatGetSequentialNonzeroStructure())

    7255:    Level: advanced

    7257:     Notes:
    7258:     Frees not only the matrices, but also the array that contains the matrices

    7260: .seealso: MatGetSeqNonzeroStructure()
    7261: @*/
    7262: PetscErrorCode MatDestroySeqNonzeroStructure(Mat *mat)
    7263: {

    7268:   MatDestroy(mat);
    7269:   return(0);
    7270: }

    7272: /*@
    7273:    MatIncreaseOverlap - Given a set of submatrices indicated by index sets,
    7274:    replaces the index sets by larger ones that represent submatrices with
    7275:    additional overlap.

    7277:    Collective on Mat

    7279:    Input Parameters:
    7280: +  mat - the matrix
    7281: .  n   - the number of index sets
    7282: .  is  - the array of index sets (these index sets will changed during the call)
    7283: -  ov  - the additional overlap requested

    7285:    Options Database:
    7286: .  -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

    7288:    Level: developer

    7291: .seealso: MatCreateSubMatrices()
    7292: @*/
    7293: PetscErrorCode MatIncreaseOverlap(Mat mat,PetscInt n,IS is[],PetscInt ov)
    7294: {

    7300:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more domains, you have %D",n);
    7301:   if (n) {
    7304:   }
    7305:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    7306:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7307:   MatCheckPreallocated(mat,1);

    7309:   if (!ov) return(0);
    7310:   if (!mat->ops->increaseoverlap) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    7311:   PetscLogEventBegin(MAT_IncreaseOverlap,mat,0,0,0);
    7312:   (*mat->ops->increaseoverlap)(mat,n,is,ov);
    7313:   PetscLogEventEnd(MAT_IncreaseOverlap,mat,0,0,0);
    7314:   return(0);
    7315: }

    7318: PetscErrorCode MatIncreaseOverlapSplit_Single(Mat,IS*,PetscInt);

    7320: /*@
    7321:    MatIncreaseOverlapSplit - Given a set of submatrices indicated by index sets across
    7322:    a sub communicator, replaces the index sets by larger ones that represent submatrices with
    7323:    additional overlap.

    7325:    Collective on Mat

    7327:    Input Parameters:
    7328: +  mat - the matrix
    7329: .  n   - the number of index sets
    7330: .  is  - the array of index sets (these index sets will changed during the call)
    7331: -  ov  - the additional overlap requested

    7333:    Options Database:
    7334: .  -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

    7336:    Level: developer

    7339: .seealso: MatCreateSubMatrices()
    7340: @*/
    7341: PetscErrorCode MatIncreaseOverlapSplit(Mat mat,PetscInt n,IS is[],PetscInt ov)
    7342: {
    7343:   PetscInt       i;

    7349:   if (n < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Must have one or more domains, you have %D",n);
    7350:   if (n) {
    7353:   }
    7354:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    7355:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    7356:   MatCheckPreallocated(mat,1);
    7357:   if (!ov) return(0);
    7358:   PetscLogEventBegin(MAT_IncreaseOverlap,mat,0,0,0);
    7359:   for (i=0; i<n; i++){
    7360:          MatIncreaseOverlapSplit_Single(mat,&is[i],ov);
    7361:   }
    7362:   PetscLogEventEnd(MAT_IncreaseOverlap,mat,0,0,0);
    7363:   return(0);
    7364: }

    7369: /*@
    7370:    MatGetBlockSize - Returns the matrix block size.

    7372:    Not Collective

    7374:    Input Parameter:
    7375: .  mat - the matrix

    7377:    Output Parameter:
    7378: .  bs - block size

    7380:    Notes:
    7381:     Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.

    7383:    If the block size has not been set yet this routine returns 1.

    7385:    Level: intermediate

    7387: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSizes()
    7388: @*/
    7389: PetscErrorCode MatGetBlockSize(Mat mat,PetscInt *bs)
    7390: {
    7394:   *bs = PetscAbs(mat->rmap->bs);
    7395:   return(0);
    7396: }

    7398: /*@
    7399:    MatGetBlockSizes - Returns the matrix block row and column sizes.

    7401:    Not Collective

    7403:    Input Parameter:
    7404: .  mat - the matrix

    7406:    Output Parameter:
    7407: +  rbs - row block size
    7408: -  cbs - column block size

    7410:    Notes:
    7411:     Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.
    7412:     If you pass a different block size for the columns than the rows, the row block size determines the square block storage.

    7414:    If a block size has not been set yet this routine returns 1.

    7416:    Level: intermediate

    7418: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSize(), MatSetBlockSizes()
    7419: @*/
    7420: PetscErrorCode MatGetBlockSizes(Mat mat,PetscInt *rbs, PetscInt *cbs)
    7421: {
    7426:   if (rbs) *rbs = PetscAbs(mat->rmap->bs);
    7427:   if (cbs) *cbs = PetscAbs(mat->cmap->bs);
    7428:   return(0);
    7429: }

    7431: /*@
    7432:    MatSetBlockSize - Sets the matrix block size.

    7434:    Logically Collective on Mat

    7436:    Input Parameters:
    7437: +  mat - the matrix
    7438: -  bs - block size

    7440:    Notes:
    7441:     Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.
    7442:     This must be called before MatSetUp() or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later.

    7444:     For MATMPIAIJ and MATSEQAIJ matrix formats, this function can be called at a later stage, provided that the specified block size
    7445:     is compatible with the matrix local sizes.

    7447:    Level: intermediate

    7449: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes(), MatGetBlockSizes()
    7450: @*/
    7451: PetscErrorCode MatSetBlockSize(Mat mat,PetscInt bs)
    7452: {

    7458:   MatSetBlockSizes(mat,bs,bs);
    7459:   return(0);
    7460: }

    7462: /*@
    7463:    MatSetVariableBlockSizes - Sets a diagonal blocks of the matrix that need not be of the same size

    7465:    Logically Collective on Mat

    7467:    Input Parameters:
    7468: +  mat - the matrix
    7469: .  nblocks - the number of blocks on this process
    7470: -  bsizes - the block sizes

    7472:    Notes:
    7473:     Currently used by PCVPBJACOBI for SeqAIJ matrices

    7475:    Level: intermediate

    7477: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes(), MatGetBlockSizes(), MatGetVariableBlockSizes()
    7478: @*/
    7479: PetscErrorCode MatSetVariableBlockSizes(Mat mat,PetscInt nblocks,PetscInt *bsizes)
    7480: {
    7482:   PetscInt       i,ncnt = 0, nlocal;

    7486:   if (nblocks < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number of local blocks must be great than or equal to zero");
    7487:   MatGetLocalSize(mat,&nlocal,NULL);
    7488:   for (i=0; i<nblocks; i++) ncnt += bsizes[i];
    7489:   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);
    7490:   PetscFree(mat->bsizes);
    7491:   mat->nblocks = nblocks;
    7492:   PetscMalloc1(nblocks,&mat->bsizes);
    7493:   PetscArraycpy(mat->bsizes,bsizes,nblocks);
    7494:   return(0);
    7495: }

    7497: /*@C
    7498:    MatGetVariableBlockSizes - Gets a diagonal blocks of the matrix that need not be of the same size

    7500:    Logically Collective on Mat

    7502:    Input Parameters:
    7503: .  mat - the matrix

    7505:    Output Parameters:
    7506: +  nblocks - the number of blocks on this process
    7507: -  bsizes - the block sizes

    7509:    Notes: Currently not supported from Fortran

    7511:    Level: intermediate

    7513: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes(), MatGetBlockSizes(), MatSetVariableBlockSizes()
    7514: @*/
    7515: PetscErrorCode MatGetVariableBlockSizes(Mat mat,PetscInt *nblocks,const PetscInt **bsizes)
    7516: {
    7519:   *nblocks = mat->nblocks;
    7520:   *bsizes  = mat->bsizes;
    7521:   return(0);
    7522: }

    7524: /*@
    7525:    MatSetBlockSizes - Sets the matrix block row and column sizes.

    7527:    Logically Collective on Mat

    7529:    Input Parameters:
    7530: +  mat - the matrix
    7531: .  rbs - row block size
    7532: -  cbs - column block size

    7534:    Notes:
    7535:     Block row formats are MATSEQBAIJ, MATMPIBAIJ, MATSEQSBAIJ, MATMPISBAIJ. These formats ALWAYS have square block storage in the matrix.
    7536:     If you pass a different block size for the columns than the rows, the row block size determines the square block storage.
    7537:     This must be called before MatSetUp() or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later.

    7539:     For MATMPIAIJ and MATSEQAIJ matrix formats, this function can be called at a later stage, provided that the specified block sizes
    7540:     are compatible with the matrix local sizes.

    7542:     The row and column block size determine the blocksize of the "row" and "column" vectors returned by MatCreateVecs().

    7544:    Level: intermediate

    7546: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSize(), MatGetBlockSizes()
    7547: @*/
    7548: PetscErrorCode MatSetBlockSizes(Mat mat,PetscInt rbs,PetscInt cbs)
    7549: {

    7556:   if (mat->ops->setblocksizes) {
    7557:     (*mat->ops->setblocksizes)(mat,rbs,cbs);
    7558:   }
    7559:   if (mat->rmap->refcnt) {
    7560:     ISLocalToGlobalMapping l2g = NULL;
    7561:     PetscLayout            nmap = NULL;

    7563:     PetscLayoutDuplicate(mat->rmap,&nmap);
    7564:     if (mat->rmap->mapping) {
    7565:       ISLocalToGlobalMappingDuplicate(mat->rmap->mapping,&l2g);
    7566:     }
    7567:     PetscLayoutDestroy(&mat->rmap);
    7568:     mat->rmap = nmap;
    7569:     mat->rmap->mapping = l2g;
    7570:   }
    7571:   if (mat->cmap->refcnt) {
    7572:     ISLocalToGlobalMapping l2g = NULL;
    7573:     PetscLayout            nmap = NULL;

    7575:     PetscLayoutDuplicate(mat->cmap,&nmap);
    7576:     if (mat->cmap->mapping) {
    7577:       ISLocalToGlobalMappingDuplicate(mat->cmap->mapping,&l2g);
    7578:     }
    7579:     PetscLayoutDestroy(&mat->cmap);
    7580:     mat->cmap = nmap;
    7581:     mat->cmap->mapping = l2g;
    7582:   }
    7583:   PetscLayoutSetBlockSize(mat->rmap,rbs);
    7584:   PetscLayoutSetBlockSize(mat->cmap,cbs);
    7585:   return(0);
    7586: }

    7588: /*@
    7589:    MatSetBlockSizesFromMats - Sets the matrix block row and column sizes to match a pair of matrices

    7591:    Logically Collective on Mat

    7593:    Input Parameters:
    7594: +  mat - the matrix
    7595: .  fromRow - matrix from which to copy row block size
    7596: -  fromCol - matrix from which to copy column block size (can be same as fromRow)

    7598:    Level: developer

    7600: .seealso: MatCreateSeqBAIJ(), MatCreateBAIJ(), MatGetBlockSize(), MatSetBlockSizes()
    7601: @*/
    7602: PetscErrorCode MatSetBlockSizesFromMats(Mat mat,Mat fromRow,Mat fromCol)
    7603: {

    7610:   if (fromRow->rmap->bs > 0) {PetscLayoutSetBlockSize(mat->rmap,fromRow->rmap->bs);}
    7611:   if (fromCol->cmap->bs > 0) {PetscLayoutSetBlockSize(mat->cmap,fromCol->cmap->bs);}
    7612:   return(0);
    7613: }

    7615: /*@
    7616:    MatResidual - Default routine to calculate the residual.

    7618:    Collective on Mat

    7620:    Input Parameters:
    7621: +  mat - the matrix
    7622: .  b   - the right-hand-side
    7623: -  x   - the approximate solution

    7625:    Output Parameter:
    7626: .  r - location to store the residual

    7628:    Level: developer

    7630: .seealso: PCMGSetResidual()
    7631: @*/
    7632: PetscErrorCode MatResidual(Mat mat,Vec b,Vec x,Vec r)
    7633: {

    7642:   MatCheckPreallocated(mat,1);
    7643:   PetscLogEventBegin(MAT_Residual,mat,0,0,0);
    7644:   if (!mat->ops->residual) {
    7645:     MatMult(mat,x,r);
    7646:     VecAYPX(r,-1.0,b);
    7647:   } else {
    7648:     (*mat->ops->residual)(mat,b,x,r);
    7649:   }
    7650:   PetscLogEventEnd(MAT_Residual,mat,0,0,0);
    7651:   return(0);
    7652: }

    7654: /*@C
    7655:     MatGetRowIJ - Returns the compressed row storage i and j indices for sequential matrices.

    7657:    Collective on Mat

    7659:     Input Parameters:
    7660: +   mat - the matrix
    7661: .   shift -  0 or 1 indicating we want the indices starting at 0 or 1
    7662: .   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be   symmetrized
    7663: -   inodecompressed - PETSC_TRUE or PETSC_FALSE  indicating if the nonzero structure of the
    7664:                  inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
    7665:                  always used.

    7667:     Output Parameters:
    7668: +   n - number of rows in the (possibly compressed) matrix
    7669: .   ia - the row pointers; that is ia[0] = 0, ia[row] = ia[row-1] + number of elements in that row of the matrix
    7670: .   ja - the column indices
    7671: -   done - indicates if the routine actually worked and returned appropriate ia[] and ja[] arrays; callers
    7672:            are responsible for handling the case when done == PETSC_FALSE and ia and ja are not set

    7674:     Level: developer

    7676:     Notes:
    7677:     You CANNOT change any of the ia[] or ja[] values.

    7679:     Use MatRestoreRowIJ() when you are finished accessing the ia[] and ja[] values.

    7681:     Fortran Notes:
    7682:     In Fortran use
    7683: $
    7684: $      PetscInt ia(1), ja(1)
    7685: $      PetscOffset iia, jja
    7686: $      call MatGetRowIJ(mat,shift,symmetric,inodecompressed,n,ia,iia,ja,jja,done,ierr)
    7687: $      ! Access the ith and jth entries via ia(iia + i) and ja(jja + j)

    7689:      or
    7690: $
    7691: $    PetscInt, pointer :: ia(:),ja(:)
    7692: $    call MatGetRowIJF90(mat,shift,symmetric,inodecompressed,n,ia,ja,done,ierr)
    7693: $    ! Access the ith and jth entries via ia(i) and ja(j)

    7695: .seealso: MatGetColumnIJ(), MatRestoreRowIJ(), MatSeqAIJGetArray()
    7696: @*/
    7697: PetscErrorCode MatGetRowIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    7698: {

    7708:   MatCheckPreallocated(mat,1);
    7709:   if (!mat->ops->getrowij) *done = PETSC_FALSE;
    7710:   else {
    7711:     *done = PETSC_TRUE;
    7712:     PetscLogEventBegin(MAT_GetRowIJ,mat,0,0,0);
    7713:     (*mat->ops->getrowij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);
    7714:     PetscLogEventEnd(MAT_GetRowIJ,mat,0,0,0);
    7715:   }
    7716:   return(0);
    7717: }

    7719: /*@C
    7720:     MatGetColumnIJ - Returns the compressed column storage i and j indices for sequential matrices.

    7722:     Collective on Mat

    7724:     Input Parameters:
    7725: +   mat - the matrix
    7726: .   shift - 1 or zero indicating we want the indices starting at 0 or 1
    7727: .   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
    7728:                 symmetrized
    7729: .   inodecompressed - PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
    7730:                  inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
    7731:                  always used.
    7732: .   n - number of columns in the (possibly compressed) matrix
    7733: .   ia - the column pointers; that is ia[0] = 0, ia[col] = i[col-1] + number of elements in that col of the matrix
    7734: -   ja - the row indices

    7736:     Output Parameters:
    7737: .   done - PETSC_TRUE or PETSC_FALSE, indicating whether the values have been returned

    7739:     Level: developer

    7741: .seealso: MatGetRowIJ(), MatRestoreColumnIJ()
    7742: @*/
    7743: PetscErrorCode MatGetColumnIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    7744: {

    7754:   MatCheckPreallocated(mat,1);
    7755:   if (!mat->ops->getcolumnij) *done = PETSC_FALSE;
    7756:   else {
    7757:     *done = PETSC_TRUE;
    7758:     (*mat->ops->getcolumnij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);
    7759:   }
    7760:   return(0);
    7761: }

    7763: /*@C
    7764:     MatRestoreRowIJ - Call after you are completed with the ia,ja indices obtained with
    7765:     MatGetRowIJ().

    7767:     Collective on Mat

    7769:     Input Parameters:
    7770: +   mat - the matrix
    7771: .   shift - 1 or zero indicating we want the indices starting at 0 or 1
    7772: .   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
    7773:                 symmetrized
    7774: .   inodecompressed -  PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
    7775:                  inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
    7776:                  always used.
    7777: .   n - size of (possibly compressed) matrix
    7778: .   ia - the row pointers
    7779: -   ja - the column indices

    7781:     Output Parameters:
    7782: .   done - PETSC_TRUE or PETSC_FALSE indicated that the values have been returned

    7784:     Note:
    7785:     This routine zeros out n, ia, and ja. This is to prevent accidental
    7786:     us of the array after it has been restored. If you pass NULL, it will
    7787:     not zero the pointers.  Use of ia or ja after MatRestoreRowIJ() is invalid.

    7789:     Level: developer

    7791: .seealso: MatGetRowIJ(), MatRestoreColumnIJ()
    7792: @*/
    7793: PetscErrorCode MatRestoreRowIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    7794: {

    7803:   MatCheckPreallocated(mat,1);

    7805:   if (!mat->ops->restorerowij) *done = PETSC_FALSE;
    7806:   else {
    7807:     *done = PETSC_TRUE;
    7808:     (*mat->ops->restorerowij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);
    7809:     if (n)  *n = 0;
    7810:     if (ia) *ia = NULL;
    7811:     if (ja) *ja = NULL;
    7812:   }
    7813:   return(0);
    7814: }

    7816: /*@C
    7817:     MatRestoreColumnIJ - Call after you are completed with the ia,ja indices obtained with
    7818:     MatGetColumnIJ().

    7820:     Collective on Mat

    7822:     Input Parameters:
    7823: +   mat - the matrix
    7824: .   shift - 1 or zero indicating we want the indices starting at 0 or 1
    7825: -   symmetric - PETSC_TRUE or PETSC_FALSE indicating the matrix data structure should be
    7826:                 symmetrized
    7827: -   inodecompressed - PETSC_TRUE or PETSC_FALSE indicating if the nonzero structure of the
    7828:                  inodes or the nonzero elements is wanted. For BAIJ matrices the compressed version is
    7829:                  always used.

    7831:     Output Parameters:
    7832: +   n - size of (possibly compressed) matrix
    7833: .   ia - the column pointers
    7834: .   ja - the row indices
    7835: -   done - PETSC_TRUE or PETSC_FALSE indicated that the values have been returned

    7837:     Level: developer

    7839: .seealso: MatGetColumnIJ(), MatRestoreRowIJ()
    7840: @*/
    7841: PetscErrorCode MatRestoreColumnIJ(Mat mat,PetscInt shift,PetscBool symmetric,PetscBool inodecompressed,PetscInt *n,const PetscInt *ia[],const PetscInt *ja[],PetscBool  *done)
    7842: {

    7851:   MatCheckPreallocated(mat,1);

    7853:   if (!mat->ops->restorecolumnij) *done = PETSC_FALSE;
    7854:   else {
    7855:     *done = PETSC_TRUE;
    7856:     (*mat->ops->restorecolumnij)(mat,shift,symmetric,inodecompressed,n,ia,ja,done);
    7857:     if (n)  *n = 0;
    7858:     if (ia) *ia = NULL;
    7859:     if (ja) *ja = NULL;
    7860:   }
    7861:   return(0);
    7862: }

    7864: /*@C
    7865:     MatColoringPatch -Used inside matrix coloring routines that
    7866:     use MatGetRowIJ() and/or MatGetColumnIJ().

    7868:     Collective on Mat

    7870:     Input Parameters:
    7871: +   mat - the matrix
    7872: .   ncolors - max color value
    7873: .   n   - number of entries in colorarray
    7874: -   colorarray - array indicating color for each column

    7876:     Output Parameters:
    7877: .   iscoloring - coloring generated using colorarray information

    7879:     Level: developer

    7881: .seealso: MatGetRowIJ(), MatGetColumnIJ()

    7883: @*/
    7884: PetscErrorCode MatColoringPatch(Mat mat,PetscInt ncolors,PetscInt n,ISColoringValue colorarray[],ISColoring *iscoloring)
    7885: {

    7893:   MatCheckPreallocated(mat,1);

    7895:   if (!mat->ops->coloringpatch) {
    7896:     ISColoringCreate(PetscObjectComm((PetscObject)mat),ncolors,n,colorarray,PETSC_OWN_POINTER,iscoloring);
    7897:   } else {
    7898:     (*mat->ops->coloringpatch)(mat,ncolors,n,colorarray,iscoloring);
    7899:   }
    7900:   return(0);
    7901: }

    7904: /*@
    7905:    MatSetUnfactored - Resets a factored matrix to be treated as unfactored.

    7907:    Logically Collective on Mat

    7909:    Input Parameter:
    7910: .  mat - the factored matrix to be reset

    7912:    Notes:
    7913:    This routine should be used only with factored matrices formed by in-place
    7914:    factorization via ILU(0) (or by in-place LU factorization for the MATSEQDENSE
    7915:    format).  This option can save memory, for example, when solving nonlinear
    7916:    systems with a matrix-free Newton-Krylov method and a matrix-based, in-place
    7917:    ILU(0) preconditioner.

    7919:    Note that one can specify in-place ILU(0) factorization by calling
    7920: .vb
    7921:      PCType(pc,PCILU);
    7922:      PCFactorSeUseInPlace(pc);
    7923: .ve
    7924:    or by using the options -pc_type ilu -pc_factor_in_place

    7926:    In-place factorization ILU(0) can also be used as a local
    7927:    solver for the blocks within the block Jacobi or additive Schwarz
    7928:    methods (runtime option: -sub_pc_factor_in_place).  See Users-Manual: ch_pc
    7929:    for details on setting local solver options.

    7931:    Most users should employ the simplified KSP interface for linear solvers
    7932:    instead of working directly with matrix algebra routines such as this.
    7933:    See, e.g., KSPCreate().

    7935:    Level: developer

    7937: .seealso: PCFactorSetUseInPlace(), PCFactorGetUseInPlace()

    7939: @*/
    7940: PetscErrorCode MatSetUnfactored(Mat mat)
    7941: {

    7947:   MatCheckPreallocated(mat,1);
    7948:   mat->factortype = MAT_FACTOR_NONE;
    7949:   if (!mat->ops->setunfactored) return(0);
    7950:   (*mat->ops->setunfactored)(mat);
    7951:   return(0);
    7952: }

    7954: /*MC
    7955:     MatDenseGetArrayF90 - Accesses a matrix array from Fortran90.

    7957:     Synopsis:
    7958:     MatDenseGetArrayF90(Mat x,{Scalar, pointer :: xx_v(:,:)},integer ierr)

    7960:     Not collective

    7962:     Input Parameter:
    7963: .   x - matrix

    7965:     Output Parameters:
    7966: +   xx_v - the Fortran90 pointer to the array
    7967: -   ierr - error code

    7969:     Example of Usage:
    7970: .vb
    7971:       PetscScalar, pointer xx_v(:,:)
    7972:       ....
    7973:       call MatDenseGetArrayF90(x,xx_v,ierr)
    7974:       a = xx_v(3)
    7975:       call MatDenseRestoreArrayF90(x,xx_v,ierr)
    7976: .ve

    7978:     Level: advanced

    7980: .seealso:  MatDenseRestoreArrayF90(), MatDenseGetArray(), MatDenseRestoreArray(), MatSeqAIJGetArrayF90()

    7982: M*/

    7984: /*MC
    7985:     MatDenseRestoreArrayF90 - Restores a matrix array that has been
    7986:     accessed with MatDenseGetArrayF90().

    7988:     Synopsis:
    7989:     MatDenseRestoreArrayF90(Mat x,{Scalar, pointer :: xx_v(:,:)},integer ierr)

    7991:     Not collective

    7993:     Input Parameters:
    7994: +   x - matrix
    7995: -   xx_v - the Fortran90 pointer to the array

    7997:     Output Parameter:
    7998: .   ierr - error code

    8000:     Example of Usage:
    8001: .vb
    8002:        PetscScalar, pointer xx_v(:,:)
    8003:        ....
    8004:        call MatDenseGetArrayF90(x,xx_v,ierr)
    8005:        a = xx_v(3)
    8006:        call MatDenseRestoreArrayF90(x,xx_v,ierr)
    8007: .ve

    8009:     Level: advanced

    8011: .seealso:  MatDenseGetArrayF90(), MatDenseGetArray(), MatDenseRestoreArray(), MatSeqAIJRestoreArrayF90()

    8013: M*/

    8016: /*MC
    8017:     MatSeqAIJGetArrayF90 - Accesses a matrix array from Fortran90.

    8019:     Synopsis:
    8020:     MatSeqAIJGetArrayF90(Mat x,{Scalar, pointer :: xx_v(:)},integer ierr)

    8022:     Not collective

    8024:     Input Parameter:
    8025: .   x - matrix

    8027:     Output Parameters:
    8028: +   xx_v - the Fortran90 pointer to the array
    8029: -   ierr - error code

    8031:     Example of Usage:
    8032: .vb
    8033:       PetscScalar, pointer xx_v(:)
    8034:       ....
    8035:       call MatSeqAIJGetArrayF90(x,xx_v,ierr)
    8036:       a = xx_v(3)
    8037:       call MatSeqAIJRestoreArrayF90(x,xx_v,ierr)
    8038: .ve

    8040:     Level: advanced

    8042: .seealso:  MatSeqAIJRestoreArrayF90(), MatSeqAIJGetArray(), MatSeqAIJRestoreArray(), MatDenseGetArrayF90()

    8044: M*/

    8046: /*MC
    8047:     MatSeqAIJRestoreArrayF90 - Restores a matrix array that has been
    8048:     accessed with MatSeqAIJGetArrayF90().

    8050:     Synopsis:
    8051:     MatSeqAIJRestoreArrayF90(Mat x,{Scalar, pointer :: xx_v(:)},integer ierr)

    8053:     Not collective

    8055:     Input Parameters:
    8056: +   x - matrix
    8057: -   xx_v - the Fortran90 pointer to the array

    8059:     Output Parameter:
    8060: .   ierr - error code

    8062:     Example of Usage:
    8063: .vb
    8064:        PetscScalar, pointer xx_v(:)
    8065:        ....
    8066:        call MatSeqAIJGetArrayF90(x,xx_v,ierr)
    8067:        a = xx_v(3)
    8068:        call MatSeqAIJRestoreArrayF90(x,xx_v,ierr)
    8069: .ve

    8071:     Level: advanced

    8073: .seealso:  MatSeqAIJGetArrayF90(), MatSeqAIJGetArray(), MatSeqAIJRestoreArray(), MatDenseRestoreArrayF90()

    8075: M*/

    8078: /*@
    8079:     MatCreateSubMatrix - Gets a single submatrix on the same number of processors
    8080:                       as the original matrix.

    8082:     Collective on Mat

    8084:     Input Parameters:
    8085: +   mat - the original matrix
    8086: .   isrow - parallel IS containing the rows this processor should obtain
    8087: .   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.
    8088: -   cll - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    8090:     Output Parameter:
    8091: .   newmat - the new submatrix, of the same type as the old

    8093:     Level: advanced

    8095:     Notes:
    8096:     The submatrix will be able to be multiplied with vectors using the same layout as iscol.

    8098:     Some matrix types place restrictions on the row and column indices, such
    8099:     as that they be sorted or that they be equal to each other.

    8101:     The index sets may not have duplicate entries.

    8103:       The first time this is called you should use a cll of MAT_INITIAL_MATRIX,
    8104:    the MatCreateSubMatrix() routine will create the newmat for you. Any additional calls
    8105:    to this routine with a mat of the same nonzero structure and with a call of MAT_REUSE_MATRIX
    8106:    will reuse the matrix generated the first time.  You should call MatDestroy() on newmat when
    8107:    you are finished using it.

    8109:     The communicator of the newly obtained matrix is ALWAYS the same as the communicator of
    8110:     the input matrix.

    8112:     If iscol is NULL then all columns are obtained (not supported in Fortran).

    8114:    Example usage:
    8115:    Consider the following 8x8 matrix with 34 non-zero values, that is
    8116:    assembled across 3 processors. Let's assume that proc0 owns 3 rows,
    8117:    proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    8118:    as follows:

    8120: .vb
    8121:             1  2  0  |  0  3  0  |  0  4
    8122:     Proc0   0  5  6  |  7  0  0  |  8  0
    8123:             9  0 10  | 11  0  0  | 12  0
    8124:     -------------------------------------
    8125:            13  0 14  | 15 16 17  |  0  0
    8126:     Proc1   0 18  0  | 19 20 21  |  0  0
    8127:             0  0  0  | 22 23  0  | 24  0
    8128:     -------------------------------------
    8129:     Proc2  25 26 27  |  0  0 28  | 29  0
    8130:            30  0  0  | 31 32 33  |  0 34
    8131: .ve

    8133:     Suppose isrow = [0 1 | 4 | 6 7] and iscol = [1 2 | 3 4 5 | 6].  The resulting submatrix is

    8135: .vb
    8136:             2  0  |  0  3  0  |  0
    8137:     Proc0   5  6  |  7  0  0  |  8
    8138:     -------------------------------
    8139:     Proc1  18  0  | 19 20 21  |  0
    8140:     -------------------------------
    8141:     Proc2  26 27  |  0  0 28  | 29
    8142:             0  0  | 31 32 33  |  0
    8143: .ve

    8146: .seealso: MatCreateSubMatrices(), MatCreateSubMatricesMPI(), MatCreateSubMatrixVirtual(), MatSubMatrixVirtualUpdate()
    8147: @*/
    8148: PetscErrorCode MatCreateSubMatrix(Mat mat,IS isrow,IS iscol,MatReuse cll,Mat *newmat)
    8149: {
    8151:   PetscMPIInt    size;
    8152:   Mat            *local;
    8153:   IS             iscoltmp;
    8154:   PetscBool      flg;

    8163:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    8164:   if (cll == MAT_IGNORE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Cannot use MAT_IGNORE_MATRIX");

    8166:   MatCheckPreallocated(mat,1);
    8167:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);

    8169:   if (!iscol || isrow == iscol) {
    8170:     PetscBool   stride;
    8171:     PetscMPIInt grabentirematrix = 0,grab;
    8172:     PetscObjectTypeCompare((PetscObject)isrow,ISSTRIDE,&stride);
    8173:     if (stride) {
    8174:       PetscInt first,step,n,rstart,rend;
    8175:       ISStrideGetInfo(isrow,&first,&step);
    8176:       if (step == 1) {
    8177:         MatGetOwnershipRange(mat,&rstart,&rend);
    8178:         if (rstart == first) {
    8179:           ISGetLocalSize(isrow,&n);
    8180:           if (n == rend-rstart) {
    8181:             grabentirematrix = 1;
    8182:           }
    8183:         }
    8184:       }
    8185:     }
    8186:     MPIU_Allreduce(&grabentirematrix,&grab,1,MPI_INT,MPI_MIN,PetscObjectComm((PetscObject)mat));
    8187:     if (grab) {
    8188:       PetscInfo(mat,"Getting entire matrix as submatrix\n");
    8189:       if (cll == MAT_INITIAL_MATRIX) {
    8190:         *newmat = mat;
    8191:         PetscObjectReference((PetscObject)mat);
    8192:       }
    8193:       return(0);
    8194:     }
    8195:   }

    8197:   if (!iscol) {
    8198:     ISCreateStride(PetscObjectComm((PetscObject)mat),mat->cmap->n,mat->cmap->rstart,1,&iscoltmp);
    8199:   } else {
    8200:     iscoltmp = iscol;
    8201:   }

    8203:   /* if original matrix is on just one processor then use submatrix generated */
    8204:   if (mat->ops->createsubmatrices && !mat->ops->createsubmatrix && size == 1 && cll == MAT_REUSE_MATRIX) {
    8205:     MatCreateSubMatrices(mat,1,&isrow,&iscoltmp,MAT_REUSE_MATRIX,&newmat);
    8206:     goto setproperties;
    8207:   } else if (mat->ops->createsubmatrices && !mat->ops->createsubmatrix && size == 1) {
    8208:     MatCreateSubMatrices(mat,1,&isrow,&iscoltmp,MAT_INITIAL_MATRIX,&local);
    8209:     *newmat = *local;
    8210:     PetscFree(local);
    8211:     goto setproperties;
    8212:   } else if (!mat->ops->createsubmatrix) {
    8213:     /* Create a new matrix type that implements the operation using the full matrix */
    8214:     PetscLogEventBegin(MAT_CreateSubMat,mat,0,0,0);
    8215:     switch (cll) {
    8216:     case MAT_INITIAL_MATRIX:
    8217:       MatCreateSubMatrixVirtual(mat,isrow,iscoltmp,newmat);
    8218:       break;
    8219:     case MAT_REUSE_MATRIX:
    8220:       MatSubMatrixVirtualUpdate(*newmat,mat,isrow,iscoltmp);
    8221:       break;
    8222:     default: SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"Invalid MatReuse, must be either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX");
    8223:     }
    8224:     PetscLogEventEnd(MAT_CreateSubMat,mat,0,0,0);
    8225:     goto setproperties;
    8226:   }

    8228:   if (!mat->ops->createsubmatrix) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    8229:   PetscLogEventBegin(MAT_CreateSubMat,mat,0,0,0);
    8230:   (*mat->ops->createsubmatrix)(mat,isrow,iscoltmp,cll,newmat);
    8231:   PetscLogEventEnd(MAT_CreateSubMat,mat,0,0,0);

    8233: setproperties:
    8234:   ISEqualUnsorted(isrow,iscoltmp,&flg);
    8235:   if (flg) {
    8236:     MatPropagateSymmetryOptions(mat,*newmat);
    8237:   }
    8238:   if (!iscol) {ISDestroy(&iscoltmp);}
    8239:   if (*newmat && cll == MAT_INITIAL_MATRIX) {PetscObjectStateIncrease((PetscObject)*newmat);}
    8240:   return(0);
    8241: }

    8243: /*@
    8244:    MatPropagateSymmetryOptions - Propagates symmetry options set on a matrix to another matrix

    8246:    Not Collective

    8248:    Input Parameters:
    8249: +  A - the matrix we wish to propagate options from
    8250: -  B - the matrix we wish to propagate options to

    8252:    Level: beginner

    8254:    Notes: Propagates the options associated to MAT_SYMMETRY_ETERNAL, MAT_STRUCTURALLY_SYMMETRIC, MAT_HERMITIAN, MAT_SPD and MAT_SYMMETRIC

    8256: .seealso: MatSetOption()
    8257: @*/
    8258: PetscErrorCode MatPropagateSymmetryOptions(Mat A, Mat B)
    8259: {

    8265:   if (A->symmetric_eternal) { /* symmetric_eternal does not have a corresponding *set flag */
    8266:     MatSetOption(B,MAT_SYMMETRY_ETERNAL,A->symmetric_eternal);
    8267:   }
    8268:   if (A->structurally_symmetric_set) {
    8269:     MatSetOption(B,MAT_STRUCTURALLY_SYMMETRIC,A->structurally_symmetric);
    8270:   }
    8271:   if (A->hermitian_set) {
    8272:     MatSetOption(B,MAT_HERMITIAN,A->hermitian);
    8273:   }
    8274:   if (A->spd_set) {
    8275:     MatSetOption(B,MAT_SPD,A->spd);
    8276:   }
    8277:   if (A->symmetric_set) {
    8278:     MatSetOption(B,MAT_SYMMETRIC,A->symmetric);
    8279:   }
    8280:   return(0);
    8281: }

    8283: /*@
    8284:    MatStashSetInitialSize - sets the sizes of the matrix stash, that is
    8285:    used during the assembly process to store values that belong to
    8286:    other processors.

    8288:    Not Collective

    8290:    Input Parameters:
    8291: +  mat   - the matrix
    8292: .  size  - the initial size of the stash.
    8293: -  bsize - the initial size of the block-stash(if used).

    8295:    Options Database Keys:
    8296: +   -matstash_initial_size <size> or <size0,size1,...sizep-1>
    8297: -   -matstash_block_initial_size <bsize>  or <bsize0,bsize1,...bsizep-1>

    8299:    Level: intermediate

    8301:    Notes:
    8302:      The block-stash is used for values set with MatSetValuesBlocked() while
    8303:      the stash is used for values set with MatSetValues()

    8305:      Run with the option -info and look for output of the form
    8306:      MatAssemblyBegin_MPIXXX:Stash has MM entries, uses nn mallocs.
    8307:      to determine the appropriate value, MM, to use for size and
    8308:      MatAssemblyBegin_MPIXXX:Block-Stash has BMM entries, uses nn mallocs.
    8309:      to determine the value, BMM to use for bsize

    8312: .seealso: MatAssemblyBegin(), MatAssemblyEnd(), Mat, MatStashGetInfo()

    8314: @*/
    8315: PetscErrorCode MatStashSetInitialSize(Mat mat,PetscInt size, PetscInt bsize)
    8316: {

    8322:   MatStashSetInitialSize_Private(&mat->stash,size);
    8323:   MatStashSetInitialSize_Private(&mat->bstash,bsize);
    8324:   return(0);
    8325: }

    8327: /*@
    8328:    MatInterpolateAdd - w = y + A*x or A'*x depending on the shape of
    8329:      the matrix

    8331:    Neighbor-wise Collective on Mat

    8333:    Input Parameters:
    8334: +  mat   - the matrix
    8335: .  x,y - the vectors
    8336: -  w - where the result is stored

    8338:    Level: intermediate

    8340:    Notes:
    8341:     w may be the same vector as y.

    8343:     This allows one to use either the restriction or interpolation (its transpose)
    8344:     matrix to do the interpolation

    8346: .seealso: MatMultAdd(), MatMultTransposeAdd(), MatRestrict()

    8348: @*/
    8349: PetscErrorCode MatInterpolateAdd(Mat A,Vec x,Vec y,Vec w)
    8350: {
    8352:   PetscInt       M,N,Ny;

    8359:   MatGetSize(A,&M,&N);
    8360:   VecGetSize(y,&Ny);
    8361:   if (M == Ny) {
    8362:     MatMultAdd(A,x,y,w);
    8363:   } else {
    8364:     MatMultTransposeAdd(A,x,y,w);
    8365:   }
    8366:   return(0);
    8367: }

    8369: /*@
    8370:    MatInterpolate - y = A*x or A'*x depending on the shape of
    8371:      the matrix

    8373:    Neighbor-wise Collective on Mat

    8375:    Input Parameters:
    8376: +  mat   - the matrix
    8377: -  x,y - the vectors

    8379:    Level: intermediate

    8381:    Notes:
    8382:     This allows one to use either the restriction or interpolation (its transpose)
    8383:     matrix to do the interpolation

    8385: .seealso: MatMultAdd(), MatMultTransposeAdd(), MatRestrict()

    8387: @*/
    8388: PetscErrorCode MatInterpolate(Mat A,Vec x,Vec y)
    8389: {
    8391:   PetscInt       M,N,Ny;

    8397:   MatGetSize(A,&M,&N);
    8398:   VecGetSize(y,&Ny);
    8399:   if (M == Ny) {
    8400:     MatMult(A,x,y);
    8401:   } else {
    8402:     MatMultTranspose(A,x,y);
    8403:   }
    8404:   return(0);
    8405: }

    8407: /*@
    8408:    MatRestrict - y = A*x or A'*x

    8410:    Neighbor-wise Collective on Mat

    8412:    Input Parameters:
    8413: +  mat   - the matrix
    8414: -  x,y - the vectors

    8416:    Level: intermediate

    8418:    Notes:
    8419:     This allows one to use either the restriction or interpolation (its transpose)
    8420:     matrix to do the restriction

    8422: .seealso: MatMultAdd(), MatMultTransposeAdd(), MatInterpolate()

    8424: @*/
    8425: PetscErrorCode MatRestrict(Mat A,Vec x,Vec y)
    8426: {
    8428:   PetscInt       M,N,Ny;

    8434:   MatGetSize(A,&M,&N);
    8435:   VecGetSize(y,&Ny);
    8436:   if (M == Ny) {
    8437:     MatMult(A,x,y);
    8438:   } else {
    8439:     MatMultTranspose(A,x,y);
    8440:   }
    8441:   return(0);
    8442: }

    8444: /*@
    8445:    MatMatInterpolateAdd - Y = W + A*X or W + A'*X

    8447:    Neighbor-wise Collective on Mat

    8449:    Input Parameters:
    8450: +  mat   - the matrix
    8451: -  w, x - the input dense matrices

    8453:    Output Parameters:
    8454: .  y - the output dense matrix

    8456:    Level: intermediate

    8458:    Notes:
    8459:     This allows one to use either the restriction or interpolation (its transpose)
    8460:     matrix to do the interpolation. y matrix can be reused if already created with the proper sizes,
    8461:     otherwise it will be recreated. y must be initialized to NULL if not supplied.

    8463: .seealso: MatInterpolateAdd(), MatMatInterpolate(), MatMatRestrict()

    8465: @*/
    8466: PetscErrorCode MatMatInterpolateAdd(Mat A,Mat x,Mat w,Mat *y)
    8467: {
    8469:   PetscInt       M,N,Mx,Nx,Mo,My = 0,Ny = 0;
    8470:   PetscBool      trans = PETSC_TRUE;
    8471:   MatReuse       reuse = MAT_INITIAL_MATRIX;

    8479:   MatGetSize(A,&M,&N);
    8480:   MatGetSize(x,&Mx,&Nx);
    8481:   if (N == Mx) trans = PETSC_FALSE;
    8482:   else if (M != Mx) SETERRQ4(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Size mismatch: A %Dx%D, X %Dx%D",M,N,Mx,Nx);
    8483:   Mo = trans ? N : M;
    8484:   if (*y) {
    8485:     MatGetSize(*y,&My,&Ny);
    8486:     if (Mo == My && Nx == Ny) { reuse = MAT_REUSE_MATRIX; }
    8487:     else {
    8488:       if (w && *y == w) SETERRQ6(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Cannot reuse y and w, size mismatch: A %Dx%D, X %Dx%D, Y %Dx%D",M,N,Mx,Nx,My,Ny);
    8489:       MatDestroy(y);
    8490:     }
    8491:   }

    8493:   if (w && *y == w) { /* this is to minimize changes in PCMG */
    8494:     PetscBool flg;

    8496:     PetscObjectQuery((PetscObject)*y,"__MatMatIntAdd_w",(PetscObject*)&w);
    8497:     if (w) {
    8498:       PetscInt My,Ny,Mw,Nw;

    8500:       PetscObjectTypeCompare((PetscObject)*y,((PetscObject)w)->type_name,&flg);
    8501:       MatGetSize(*y,&My,&Ny);
    8502:       MatGetSize(w,&Mw,&Nw);
    8503:       if (!flg || My != Mw || Ny != Nw) w = NULL;
    8504:     }
    8505:     if (!w) {
    8506:       MatDuplicate(*y,MAT_COPY_VALUES,&w);
    8507:       PetscObjectCompose((PetscObject)*y,"__MatMatIntAdd_w",(PetscObject)w);
    8508:       PetscLogObjectParent((PetscObject)*y,(PetscObject)w);
    8509:       PetscObjectDereference((PetscObject)w);
    8510:     } else {
    8511:       MatCopy(*y,w,UNKNOWN_NONZERO_PATTERN);
    8512:     }
    8513:   }
    8514:   if (!trans) {
    8515:     MatMatMult(A,x,reuse,PETSC_DEFAULT,y);
    8516:   } else {
    8517:     MatTransposeMatMult(A,x,reuse,PETSC_DEFAULT,y);
    8518:   }
    8519:   if (w) {
    8520:     MatAXPY(*y,1.0,w,UNKNOWN_NONZERO_PATTERN);
    8521:   }
    8522:   return(0);
    8523: }

    8525: /*@
    8526:    MatMatInterpolate - Y = A*X or A'*X

    8528:    Neighbor-wise Collective on Mat

    8530:    Input Parameters:
    8531: +  mat   - the matrix
    8532: -  x - the input dense matrix

    8534:    Output Parameters:
    8535: .  y - the output dense matrix

    8538:    Level: intermediate

    8540:    Notes:
    8541:     This allows one to use either the restriction or interpolation (its transpose)
    8542:     matrix to do the interpolation. y matrix can be reused if already created with the proper sizes,
    8543:     otherwise it will be recreated. y must be initialized to NULL if not supplied.

    8545: .seealso: MatInterpolate(), MatRestrict(), MatMatRestrict()

    8547: @*/
    8548: PetscErrorCode MatMatInterpolate(Mat A,Mat x,Mat *y)
    8549: {

    8553:   MatMatInterpolateAdd(A,x,NULL,y);
    8554:   return(0);
    8555: }

    8557: /*@
    8558:    MatMatRestrict - Y = A*X or A'*X

    8560:    Neighbor-wise Collective on Mat

    8562:    Input Parameters:
    8563: +  mat   - the matrix
    8564: -  x - the input dense matrix

    8566:    Output Parameters:
    8567: .  y - the output dense matrix

    8570:    Level: intermediate

    8572:    Notes:
    8573:     This allows one to use either the restriction or interpolation (its transpose)
    8574:     matrix to do the restriction. y matrix can be reused if already created with the proper sizes,
    8575:     otherwise it will be recreated. y must be initialized to NULL if not supplied.

    8577: .seealso: MatRestrict(), MatInterpolate(), MatMatInterpolate()
    8578: @*/
    8579: PetscErrorCode MatMatRestrict(Mat A,Mat x,Mat *y)
    8580: {

    8584:   MatMatInterpolateAdd(A,x,NULL,y);
    8585:   return(0);
    8586: }

    8588: /*@
    8589:    MatGetNullSpace - retrieves the null space of a matrix.

    8591:    Logically Collective on Mat

    8593:    Input Parameters:
    8594: +  mat - the matrix
    8595: -  nullsp - the null space object

    8597:    Level: developer

    8599: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatSetNullSpace()
    8600: @*/
    8601: PetscErrorCode MatGetNullSpace(Mat mat, MatNullSpace *nullsp)
    8602: {
    8606:   *nullsp = (mat->symmetric_set && mat->symmetric && !mat->nullsp) ? mat->transnullsp : mat->nullsp;
    8607:   return(0);
    8608: }

    8610: /*@
    8611:    MatSetNullSpace - attaches a null space to a matrix.

    8613:    Logically Collective on Mat

    8615:    Input Parameters:
    8616: +  mat - the matrix
    8617: -  nullsp - the null space object

    8619:    Level: advanced

    8621:    Notes:
    8622:       This null space is used by the linear solvers. Overwrites any previous null space that may have been attached

    8624:       For inconsistent singular systems (linear systems where the right hand side is not in the range of the operator) you also likely should
    8625:       call MatSetTransposeNullSpace(). This allows the linear system to be solved in a least squares sense.

    8627:       You can remove the null space by calling this routine with an nullsp of NULL

    8630:       The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
    8631:    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).
    8632:    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
    8633:    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
    8634:    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).

    8636:       Krylov solvers can produce the minimal norm solution to the least squares problem by utilizing MatNullSpaceRemove().

    8638:     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
    8639:     routine also automatically calls MatSetTransposeNullSpace().

    8641: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatGetNullSpace(), MatSetTransposeNullSpace(), MatGetTransposeNullSpace(), MatNullSpaceRemove()
    8642: @*/
    8643: PetscErrorCode MatSetNullSpace(Mat mat,MatNullSpace nullsp)
    8644: {

    8650:   if (nullsp) {PetscObjectReference((PetscObject)nullsp);}
    8651:   MatNullSpaceDestroy(&mat->nullsp);
    8652:   mat->nullsp = nullsp;
    8653:   if (mat->symmetric_set && mat->symmetric) {
    8654:     MatSetTransposeNullSpace(mat,nullsp);
    8655:   }
    8656:   return(0);
    8657: }

    8659: /*@
    8660:    MatGetTransposeNullSpace - retrieves the null space of the transpose of a matrix.

    8662:    Logically Collective on Mat

    8664:    Input Parameters:
    8665: +  mat - the matrix
    8666: -  nullsp - the null space object

    8668:    Level: developer

    8670: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatSetTransposeNullSpace(), MatSetNullSpace(), MatGetNullSpace()
    8671: @*/
    8672: PetscErrorCode MatGetTransposeNullSpace(Mat mat, MatNullSpace *nullsp)
    8673: {
    8678:   *nullsp = (mat->symmetric_set && mat->symmetric && !mat->transnullsp) ? mat->nullsp : mat->transnullsp;
    8679:   return(0);
    8680: }

    8682: /*@
    8683:    MatSetTransposeNullSpace - attaches a null space to a matrix.

    8685:    Logically Collective on Mat

    8687:    Input Parameters:
    8688: +  mat - the matrix
    8689: -  nullsp - the null space object

    8691:    Level: advanced

    8693:    Notes:
    8694:       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.
    8695:       You must also call MatSetNullSpace()

    8698:       The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
    8699:    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).
    8700:    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
    8701:    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
    8702:    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).

    8704:       Krylov solvers can produce the minimal norm solution to the least squares problem by utilizing MatNullSpaceRemove().

    8706: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNearNullSpace(), MatGetNullSpace(), MatSetNullSpace(), MatGetTransposeNullSpace(), MatNullSpaceRemove()
    8707: @*/
    8708: PetscErrorCode MatSetTransposeNullSpace(Mat mat,MatNullSpace nullsp)
    8709: {

    8715:   if (nullsp) {PetscObjectReference((PetscObject)nullsp);}
    8716:   MatNullSpaceDestroy(&mat->transnullsp);
    8717:   mat->transnullsp = nullsp;
    8718:   return(0);
    8719: }

    8721: /*@
    8722:    MatSetNearNullSpace - attaches a null space to a matrix, which is often the null space (rigid body modes) of the operator without boundary conditions
    8723:         This null space will be used to provide near null space vectors to a multigrid preconditioner built from this matrix.

    8725:    Logically Collective on Mat

    8727:    Input Parameters:
    8728: +  mat - the matrix
    8729: -  nullsp - the null space object

    8731:    Level: advanced

    8733:    Notes:
    8734:       Overwrites any previous near null space that may have been attached

    8736:       You can remove the null space by calling this routine with an nullsp of NULL

    8738: .seealso: MatCreate(), MatNullSpaceCreate(), MatSetNullSpace(), MatNullSpaceCreateRigidBody(), MatGetNearNullSpace()
    8739: @*/
    8740: PetscErrorCode MatSetNearNullSpace(Mat mat,MatNullSpace nullsp)
    8741: {

    8748:   MatCheckPreallocated(mat,1);
    8749:   if (nullsp) {PetscObjectReference((PetscObject)nullsp);}
    8750:   MatNullSpaceDestroy(&mat->nearnullsp);
    8751:   mat->nearnullsp = nullsp;
    8752:   return(0);
    8753: }

    8755: /*@
    8756:    MatGetNearNullSpace - Get null space attached with MatSetNearNullSpace()

    8758:    Not Collective

    8760:    Input Parameter:
    8761: .  mat - the matrix

    8763:    Output Parameter:
    8764: .  nullsp - the null space object, NULL if not set

    8766:    Level: developer

    8768: .seealso: MatSetNearNullSpace(), MatGetNullSpace(), MatNullSpaceCreate()
    8769: @*/
    8770: PetscErrorCode MatGetNearNullSpace(Mat mat,MatNullSpace *nullsp)
    8771: {
    8776:   MatCheckPreallocated(mat,1);
    8777:   *nullsp = mat->nearnullsp;
    8778:   return(0);
    8779: }

    8781: /*@C
    8782:    MatICCFactor - Performs in-place incomplete Cholesky factorization of matrix.

    8784:    Collective on Mat

    8786:    Input Parameters:
    8787: +  mat - the matrix
    8788: .  row - row/column permutation
    8789: .  fill - expected fill factor >= 1.0
    8790: -  level - level of fill, for ICC(k)

    8792:    Notes:
    8793:    Probably really in-place only when level of fill is zero, otherwise allocates
    8794:    new space to store factored matrix and deletes previous memory.

    8796:    Most users should employ the simplified KSP interface for linear solvers
    8797:    instead of working directly with matrix algebra routines such as this.
    8798:    See, e.g., KSPCreate().

    8800:    Level: developer

    8803: .seealso: MatICCFactorSymbolic(), MatLUFactorNumeric(), MatCholeskyFactor()

    8805:     Developer Note: fortran interface is not autogenerated as the f90
    8806:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    8808: @*/
    8809: PetscErrorCode MatICCFactor(Mat mat,IS row,const MatFactorInfo *info)
    8810: {

    8818:   if (mat->rmap->N != mat->cmap->N) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONG,"matrix must be square");
    8819:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    8820:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    8821:   if (!mat->ops->iccfactor) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    8822:   MatCheckPreallocated(mat,1);
    8823:   (*mat->ops->iccfactor)(mat,row,info);
    8824:   PetscObjectStateIncrease((PetscObject)mat);
    8825:   return(0);
    8826: }

    8828: /*@
    8829:    MatDiagonalScaleLocal - Scales columns of a matrix given the scaling values including the
    8830:          ghosted ones.

    8832:    Not Collective

    8834:    Input Parameters:
    8835: +  mat - the matrix
    8836: -  diag = the diagonal values, including ghost ones

    8838:    Level: developer

    8840:    Notes:
    8841:     Works only for MPIAIJ and MPIBAIJ matrices

    8843: .seealso: MatDiagonalScale()
    8844: @*/
    8845: PetscErrorCode MatDiagonalScaleLocal(Mat mat,Vec diag)
    8846: {
    8848:   PetscMPIInt    size;

    8855:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Matrix must be already assembled");
    8856:   PetscLogEventBegin(MAT_Scale,mat,0,0,0);
    8857:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    8858:   if (size == 1) {
    8859:     PetscInt n,m;
    8860:     VecGetSize(diag,&n);
    8861:     MatGetSize(mat,NULL,&m);
    8862:     if (m == n) {
    8863:       MatDiagonalScale(mat,NULL,diag);
    8864:     } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only supported for sequential matrices when no ghost points/periodic conditions");
    8865:   } else {
    8866:     PetscUseMethod(mat,"MatDiagonalScaleLocal_C",(Mat,Vec),(mat,diag));
    8867:   }
    8868:   PetscLogEventEnd(MAT_Scale,mat,0,0,0);
    8869:   PetscObjectStateIncrease((PetscObject)mat);
    8870:   return(0);
    8871: }

    8873: /*@
    8874:    MatGetInertia - Gets the inertia from a factored matrix

    8876:    Collective on Mat

    8878:    Input Parameter:
    8879: .  mat - the matrix

    8881:    Output Parameters:
    8882: +   nneg - number of negative eigenvalues
    8883: .   nzero - number of zero eigenvalues
    8884: -   npos - number of positive eigenvalues

    8886:    Level: advanced

    8888:    Notes:
    8889:     Matrix must have been factored by MatCholeskyFactor()

    8892: @*/
    8893: PetscErrorCode MatGetInertia(Mat mat,PetscInt *nneg,PetscInt *nzero,PetscInt *npos)
    8894: {

    8900:   if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    8901:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Numeric factor mat is not assembled");
    8902:   if (!mat->ops->getinertia) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    8903:   (*mat->ops->getinertia)(mat,nneg,nzero,npos);
    8904:   return(0);
    8905: }

    8907: /* ----------------------------------------------------------------*/
    8908: /*@C
    8909:    MatSolves - Solves A x = b, given a factored matrix, for a collection of vectors

    8911:    Neighbor-wise Collective on Mats

    8913:    Input Parameters:
    8914: +  mat - the factored matrix
    8915: -  b - the right-hand-side vectors

    8917:    Output Parameter:
    8918: .  x - the result vectors

    8920:    Notes:
    8921:    The vectors b and x cannot be the same.  I.e., one cannot
    8922:    call MatSolves(A,x,x).

    8924:    Notes:
    8925:    Most users should employ the simplified KSP interface for linear solvers
    8926:    instead of working directly with matrix algebra routines such as this.
    8927:    See, e.g., KSPCreate().

    8929:    Level: developer

    8931: .seealso: MatSolveAdd(), MatSolveTranspose(), MatSolveTransposeAdd(), MatSolve()
    8932: @*/
    8933: PetscErrorCode MatSolves(Mat mat,Vecs b,Vecs x)
    8934: {

    8940:   if (x == b) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_IDN,"x and b must be different vectors");
    8941:   if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Unfactored matrix");
    8942:   if (!mat->rmap->N && !mat->cmap->N) return(0);

    8944:   if (!mat->ops->solves) SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)mat)->type_name);
    8945:   MatCheckPreallocated(mat,1);
    8946:   PetscLogEventBegin(MAT_Solves,mat,0,0,0);
    8947:   (*mat->ops->solves)(mat,b,x);
    8948:   PetscLogEventEnd(MAT_Solves,mat,0,0,0);
    8949:   return(0);
    8950: }

    8952: /*@
    8953:    MatIsSymmetric - Test whether a matrix is symmetric

    8955:    Collective on Mat

    8957:    Input Parameter:
    8958: +  A - the matrix to test
    8959: -  tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact transpose)

    8961:    Output Parameters:
    8962: .  flg - the result

    8964:    Notes:
    8965:     For real numbers MatIsSymmetric() and MatIsHermitian() return identical results

    8967:    Level: intermediate

    8969: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetricKnown()
    8970: @*/
    8971: PetscErrorCode MatIsSymmetric(Mat A,PetscReal tol,PetscBool  *flg)
    8972: {

    8979:   if (!A->symmetric_set) {
    8980:     if (!A->ops->issymmetric) {
    8981:       MatType mattype;
    8982:       MatGetType(A,&mattype);
    8983:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for symmetric",mattype);
    8984:     }
    8985:     (*A->ops->issymmetric)(A,tol,flg);
    8986:     if (!tol) {
    8987:       MatSetOption(A,MAT_SYMMETRIC,*flg);
    8988:     }
    8989:   } else if (A->symmetric) {
    8990:     *flg = PETSC_TRUE;
    8991:   } else if (!tol) {
    8992:     *flg = PETSC_FALSE;
    8993:   } else {
    8994:     if (!A->ops->issymmetric) {
    8995:       MatType mattype;
    8996:       MatGetType(A,&mattype);
    8997:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for symmetric",mattype);
    8998:     }
    8999:     (*A->ops->issymmetric)(A,tol,flg);
    9000:   }
    9001:   return(0);
    9002: }

    9004: /*@
    9005:    MatIsHermitian - Test whether a matrix is Hermitian

    9007:    Collective on Mat

    9009:    Input Parameter:
    9010: +  A - the matrix to test
    9011: -  tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact Hermitian)

    9013:    Output Parameters:
    9014: .  flg - the result

    9016:    Level: intermediate

    9018: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(),
    9019:           MatIsSymmetricKnown(), MatIsSymmetric()
    9020: @*/
    9021: PetscErrorCode MatIsHermitian(Mat A,PetscReal tol,PetscBool  *flg)
    9022: {

    9029:   if (!A->hermitian_set) {
    9030:     if (!A->ops->ishermitian) {
    9031:       MatType mattype;
    9032:       MatGetType(A,&mattype);
    9033:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for hermitian",mattype);
    9034:     }
    9035:     (*A->ops->ishermitian)(A,tol,flg);
    9036:     if (!tol) {
    9037:       MatSetOption(A,MAT_HERMITIAN,*flg);
    9038:     }
    9039:   } else if (A->hermitian) {
    9040:     *flg = PETSC_TRUE;
    9041:   } else if (!tol) {
    9042:     *flg = PETSC_FALSE;
    9043:   } else {
    9044:     if (!A->ops->ishermitian) {
    9045:       MatType mattype;
    9046:       MatGetType(A,&mattype);
    9047:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix of type %s does not support checking for hermitian",mattype);
    9048:     }
    9049:     (*A->ops->ishermitian)(A,tol,flg);
    9050:   }
    9051:   return(0);
    9052: }

    9054: /*@
    9055:    MatIsSymmetricKnown - Checks the flag on the matrix to see if it is symmetric.

    9057:    Not Collective

    9059:    Input Parameter:
    9060: .  A - the matrix to check

    9062:    Output Parameters:
    9063: +  set - if the symmetric flag is set (this tells you if the next flag is valid)
    9064: -  flg - the result

    9066:    Level: advanced

    9068:    Note: Does not check the matrix values directly, so this may return unknown (set = PETSC_FALSE). Use MatIsSymmetric()
    9069:          if you want it explicitly checked

    9071: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetric()
    9072: @*/
    9073: PetscErrorCode MatIsSymmetricKnown(Mat A,PetscBool *set,PetscBool *flg)
    9074: {
    9079:   if (A->symmetric_set) {
    9080:     *set = PETSC_TRUE;
    9081:     *flg = A->symmetric;
    9082:   } else {
    9083:     *set = PETSC_FALSE;
    9084:   }
    9085:   return(0);
    9086: }

    9088: /*@
    9089:    MatIsHermitianKnown - Checks the flag on the matrix to see if it is hermitian.

    9091:    Not Collective

    9093:    Input Parameter:
    9094: .  A - the matrix to check

    9096:    Output Parameters:
    9097: +  set - if the hermitian flag is set (this tells you if the next flag is valid)
    9098: -  flg - the result

    9100:    Level: advanced

    9102:    Note: Does not check the matrix values directly, so this may return unknown (set = PETSC_FALSE). Use MatIsHermitian()
    9103:          if you want it explicitly checked

    9105: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsStructurallySymmetric(), MatSetOption(), MatIsSymmetric()
    9106: @*/
    9107: PetscErrorCode MatIsHermitianKnown(Mat A,PetscBool *set,PetscBool *flg)
    9108: {
    9113:   if (A->hermitian_set) {
    9114:     *set = PETSC_TRUE;
    9115:     *flg = A->hermitian;
    9116:   } else {
    9117:     *set = PETSC_FALSE;
    9118:   }
    9119:   return(0);
    9120: }

    9122: /*@
    9123:    MatIsStructurallySymmetric - Test whether a matrix is structurally symmetric

    9125:    Collective on Mat

    9127:    Input Parameter:
    9128: .  A - the matrix to test

    9130:    Output Parameters:
    9131: .  flg - the result

    9133:    Level: intermediate

    9135: .seealso: MatTranspose(), MatIsTranspose(), MatIsHermitian(), MatIsSymmetric(), MatSetOption()
    9136: @*/
    9137: PetscErrorCode MatIsStructurallySymmetric(Mat A,PetscBool *flg)
    9138: {

    9144:   if (!A->structurally_symmetric_set) {
    9145:     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);
    9146:     (*A->ops->isstructurallysymmetric)(A,flg);
    9147:     MatSetOption(A,MAT_STRUCTURALLY_SYMMETRIC,*flg);
    9148:   } else *flg = A->structurally_symmetric;
    9149:   return(0);
    9150: }

    9152: /*@
    9153:    MatStashGetInfo - Gets how many values are currently in the matrix stash, i.e. need
    9154:        to be communicated to other processors during the MatAssemblyBegin/End() process

    9156:     Not collective

    9158:    Input Parameter:
    9159: .   vec - the vector

    9161:    Output Parameters:
    9162: +   nstash   - the size of the stash
    9163: .   reallocs - the number of additional mallocs incurred.
    9164: .   bnstash   - the size of the block stash
    9165: -   breallocs - the number of additional mallocs incurred.in the block stash

    9167:    Level: advanced

    9169: .seealso: MatAssemblyBegin(), MatAssemblyEnd(), Mat, MatStashSetInitialSize()

    9171: @*/
    9172: PetscErrorCode MatStashGetInfo(Mat mat,PetscInt *nstash,PetscInt *reallocs,PetscInt *bnstash,PetscInt *breallocs)
    9173: {

    9177:   MatStashGetInfo_Private(&mat->stash,nstash,reallocs);
    9178:   MatStashGetInfo_Private(&mat->bstash,bnstash,breallocs);
    9179:   return(0);
    9180: }

    9182: /*@C
    9183:    MatCreateVecs - Get vector(s) compatible with the matrix, i.e. with the same
    9184:      parallel layout

    9186:    Collective on Mat

    9188:    Input Parameter:
    9189: .  mat - the matrix

    9191:    Output Parameter:
    9192: +   right - (optional) vector that the matrix can be multiplied against
    9193: -   left - (optional) vector that the matrix vector product can be stored in

    9195:    Notes:
    9196:     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().

    9198:   Notes:
    9199:     These are new vectors which are not owned by the Mat, they should be destroyed in VecDestroy() when no longer needed

    9201:   Level: advanced

    9203: .seealso: MatCreate(), VecDestroy()
    9204: @*/
    9205: PetscErrorCode MatCreateVecs(Mat mat,Vec *right,Vec *left)
    9206: {

    9212:   if (mat->ops->getvecs) {
    9213:     (*mat->ops->getvecs)(mat,right,left);
    9214:   } else {
    9215:     PetscInt rbs,cbs;
    9216:     MatGetBlockSizes(mat,&rbs,&cbs);
    9217:     if (right) {
    9218:       if (mat->cmap->n < 0) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"PetscLayout for columns not yet setup");
    9219:       VecCreate(PetscObjectComm((PetscObject)mat),right);
    9220:       VecSetSizes(*right,mat->cmap->n,PETSC_DETERMINE);
    9221:       VecSetBlockSize(*right,cbs);
    9222:       VecSetType(*right,mat->defaultvectype);
    9223:       PetscLayoutReference(mat->cmap,&(*right)->map);
    9224:     }
    9225:     if (left) {
    9226:       if (mat->rmap->n < 0) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"PetscLayout for rows not yet setup");
    9227:       VecCreate(PetscObjectComm((PetscObject)mat),left);
    9228:       VecSetSizes(*left,mat->rmap->n,PETSC_DETERMINE);
    9229:       VecSetBlockSize(*left,rbs);
    9230:       VecSetType(*left,mat->defaultvectype);
    9231:       PetscLayoutReference(mat->rmap,&(*left)->map);
    9232:     }
    9233:   }
    9234:   return(0);
    9235: }

    9237: /*@C
    9238:    MatFactorInfoInitialize - Initializes a MatFactorInfo data structure
    9239:      with default values.

    9241:    Not Collective

    9243:    Input Parameters:
    9244: .    info - the MatFactorInfo data structure

    9247:    Notes:
    9248:     The solvers are generally used through the KSP and PC objects, for example
    9249:           PCLU, PCILU, PCCHOLESKY, PCICC

    9251:    Level: developer

    9253: .seealso: MatFactorInfo

    9255:     Developer Note: fortran interface is not autogenerated as the f90
    9256:     interface defintion cannot be generated correctly [due to MatFactorInfo]

    9258: @*/

    9260: PetscErrorCode MatFactorInfoInitialize(MatFactorInfo *info)
    9261: {

    9265:   PetscMemzero(info,sizeof(MatFactorInfo));
    9266:   return(0);
    9267: }

    9269: /*@
    9270:    MatFactorSetSchurIS - Set indices corresponding to the Schur complement you wish to have computed

    9272:    Collective on Mat

    9274:    Input Parameters:
    9275: +  mat - the factored matrix
    9276: -  is - the index set defining the Schur indices (0-based)

    9278:    Notes:
    9279:     Call MatFactorSolveSchurComplement() or MatFactorSolveSchurComplementTranspose() after this call to solve a Schur complement system.

    9281:    You can call MatFactorGetSchurComplement() or MatFactorCreateSchurComplement() after this call.

    9283:    Level: developer

    9285: .seealso: MatGetFactor(), MatFactorGetSchurComplement(), MatFactorRestoreSchurComplement(), MatFactorCreateSchurComplement(), MatFactorSolveSchurComplement(),
    9286:           MatFactorSolveSchurComplementTranspose(), MatFactorSolveSchurComplement()

    9288: @*/
    9289: PetscErrorCode MatFactorSetSchurIS(Mat mat,IS is)
    9290: {
    9291:   PetscErrorCode ierr,(*f)(Mat,IS);

    9299:   if (!mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Only for factored matrix");
    9300:   PetscObjectQueryFunction((PetscObject)mat,"MatFactorSetSchurIS_C",&f);
    9301:   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");
    9302:   MatDestroy(&mat->schur);
    9303:   (*f)(mat,is);
    9304:   if (!mat->schur) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_PLIB,"Schur complement has not been created");
    9305:   return(0);
    9306: }

    9308: /*@
    9309:   MatFactorCreateSchurComplement - Create a Schur complement matrix object using Schur data computed during the factorization step

    9311:    Logically Collective on Mat

    9313:    Input Parameters:
    9314: +  F - the factored matrix obtained by calling MatGetFactor() from PETSc-MUMPS interface
    9315: .  S - location where to return the Schur complement, can be NULL
    9316: -  status - the status of the Schur complement matrix, can be NULL

    9318:    Notes:
    9319:    You must call MatFactorSetSchurIS() before calling this routine.

    9321:    The routine provides a copy of the Schur matrix stored within the solver data structures.
    9322:    The caller must destroy the object when it is no longer needed.
    9323:    If MatFactorInvertSchurComplement() has been called, the routine gets back the inverse.

    9325:    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)

    9327:    Developer Notes:
    9328:     The reason this routine exists is because the representation of the Schur complement within the factor matrix may be different than a standard PETSc
    9329:    matrix representation and we normally do not want to use the time or memory to make a copy as a regular PETSc matrix.

    9331:    See MatCreateSchurComplement() or MatGetSchurComplement() for ways to create virtual or approximate Schur complements.

    9333:    Level: advanced

    9335:    References:

    9337: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorGetSchurComplement(), MatFactorSchurStatus
    9338: @*/
    9339: PetscErrorCode MatFactorCreateSchurComplement(Mat F,Mat* S,MatFactorSchurStatus* status)
    9340: {

    9347:   if (S) {
    9348:     PetscErrorCode (*f)(Mat,Mat*);

    9350:     PetscObjectQueryFunction((PetscObject)F,"MatFactorCreateSchurComplement_C",&f);
    9351:     if (f) {
    9352:       (*f)(F,S);
    9353:     } else {
    9354:       MatDuplicate(F->schur,MAT_COPY_VALUES,S);
    9355:     }
    9356:   }
    9357:   if (status) *status = F->schur_status;
    9358:   return(0);
    9359: }

    9361: /*@
    9362:   MatFactorGetSchurComplement - Gets access to a Schur complement matrix using the current Schur data within a factored matrix

    9364:    Logically Collective on Mat

    9366:    Input Parameters:
    9367: +  F - the factored matrix obtained by calling MatGetFactor()
    9368: .  *S - location where to return the Schur complement, can be NULL
    9369: -  status - the status of the Schur complement matrix, can be NULL

    9371:    Notes:
    9372:    You must call MatFactorSetSchurIS() before calling this routine.

    9374:    Schur complement mode is currently implemented for sequential matrices.
    9375:    The routine returns a the Schur Complement stored within the data strutures of the solver.
    9376:    If MatFactorInvertSchurComplement() has previously been called, the returned matrix is actually the inverse of the Schur complement.
    9377:    The returned matrix should not be destroyed; the caller should call MatFactorRestoreSchurComplement() when the object is no longer needed.

    9379:    Use MatFactorCreateSchurComplement() to create a copy of the Schur complement matrix that is within a factored matrix

    9381:    See MatCreateSchurComplement() or MatGetSchurComplement() for ways to create virtual or approximate Schur complements.

    9383:    Level: advanced

    9385:    References:

    9387: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorRestoreSchurComplement(), MatFactorCreateSchurComplement(), MatFactorSchurStatus
    9388: @*/
    9389: PetscErrorCode MatFactorGetSchurComplement(Mat F,Mat* S,MatFactorSchurStatus* status)
    9390: {
    9395:   if (S) *S = F->schur;
    9396:   if (status) *status = F->schur_status;
    9397:   return(0);
    9398: }

    9400: /*@
    9401:   MatFactorRestoreSchurComplement - Restore the Schur complement matrix object obtained from a call to MatFactorGetSchurComplement

    9403:    Logically Collective on Mat

    9405:    Input Parameters:
    9406: +  F - the factored matrix obtained by calling MatGetFactor()
    9407: .  *S - location where the Schur complement is stored
    9408: -  status - the status of the Schur complement matrix (see MatFactorSchurStatus)

    9410:    Notes:

    9412:    Level: advanced

    9414:    References:

    9416: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorRestoreSchurComplement(), MatFactorCreateSchurComplement(), MatFactorSchurStatus
    9417: @*/
    9418: PetscErrorCode MatFactorRestoreSchurComplement(Mat F,Mat* S,MatFactorSchurStatus status)
    9419: {

    9424:   if (S) {
    9426:     *S = NULL;
    9427:   }
    9428:   F->schur_status = status;
    9429:   MatFactorUpdateSchurStatus_Private(F);
    9430:   return(0);
    9431: }

    9433: /*@
    9434:   MatFactorSolveSchurComplementTranspose - Solve the transpose of the Schur complement system computed during the factorization step

    9436:    Logically Collective on Mat

    9438:    Input Parameters:
    9439: +  F - the factored matrix obtained by calling MatGetFactor()
    9440: .  rhs - location where the right hand side of the Schur complement system is stored
    9441: -  sol - location where the solution of the Schur complement system has to be returned

    9443:    Notes:
    9444:    The sizes of the vectors should match the size of the Schur complement

    9446:    Must be called after MatFactorSetSchurIS()

    9448:    Level: advanced

    9450:    References:

    9452: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorSolveSchurComplement()
    9453: @*/
    9454: PetscErrorCode MatFactorSolveSchurComplementTranspose(Mat F, Vec rhs, Vec sol)
    9455: {

    9467:   MatFactorFactorizeSchurComplement(F);
    9468:   switch (F->schur_status) {
    9469:   case MAT_FACTOR_SCHUR_FACTORED:
    9470:     MatSolveTranspose(F->schur,rhs,sol);
    9471:     break;
    9472:   case MAT_FACTOR_SCHUR_INVERTED:
    9473:     MatMultTranspose(F->schur,rhs,sol);
    9474:     break;
    9475:   default:
    9476:     SETERRQ1(PetscObjectComm((PetscObject)F),PETSC_ERR_SUP,"Unhandled MatFactorSchurStatus %D",F->schur_status);
    9477:   }
    9478:   return(0);
    9479: }

    9481: /*@
    9482:   MatFactorSolveSchurComplement - Solve the Schur complement system computed during the factorization step

    9484:    Logically Collective on Mat

    9486:    Input Parameters:
    9487: +  F - the factored matrix obtained by calling MatGetFactor()
    9488: .  rhs - location where the right hand side of the Schur complement system is stored
    9489: -  sol - location where the solution of the Schur complement system has to be returned

    9491:    Notes:
    9492:    The sizes of the vectors should match the size of the Schur complement

    9494:    Must be called after MatFactorSetSchurIS()

    9496:    Level: advanced

    9498:    References:

    9500: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorSolveSchurComplementTranspose()
    9501: @*/
    9502: PetscErrorCode MatFactorSolveSchurComplement(Mat F, Vec rhs, Vec sol)
    9503: {

    9515:   MatFactorFactorizeSchurComplement(F);
    9516:   switch (F->schur_status) {
    9517:   case MAT_FACTOR_SCHUR_FACTORED:
    9518:     MatSolve(F->schur,rhs,sol);
    9519:     break;
    9520:   case MAT_FACTOR_SCHUR_INVERTED:
    9521:     MatMult(F->schur,rhs,sol);
    9522:     break;
    9523:   default:
    9524:     SETERRQ1(PetscObjectComm((PetscObject)F),PETSC_ERR_SUP,"Unhandled MatFactorSchurStatus %D",F->schur_status);
    9525:   }
    9526:   return(0);
    9527: }

    9529: /*@
    9530:   MatFactorInvertSchurComplement - Invert the Schur complement matrix computed during the factorization step

    9532:    Logically Collective on Mat

    9534:    Input Parameters:
    9535: .  F - the factored matrix obtained by calling MatGetFactor()

    9537:    Notes:
    9538:     Must be called after MatFactorSetSchurIS().

    9540:    Call MatFactorGetSchurComplement() or  MatFactorCreateSchurComplement() AFTER this call to actually compute the inverse and get access to it.

    9542:    Level: advanced

    9544:    References:

    9546: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorGetSchurComplement(), MatFactorCreateSchurComplement()
    9547: @*/
    9548: PetscErrorCode MatFactorInvertSchurComplement(Mat F)
    9549: {

    9555:   if (F->schur_status == MAT_FACTOR_SCHUR_INVERTED) return(0);
    9556:   MatFactorFactorizeSchurComplement(F);
    9557:   MatFactorInvertSchurComplement_Private(F);
    9558:   F->schur_status = MAT_FACTOR_SCHUR_INVERTED;
    9559:   return(0);
    9560: }

    9562: /*@
    9563:   MatFactorFactorizeSchurComplement - Factorize the Schur complement matrix computed during the factorization step

    9565:    Logically Collective on Mat

    9567:    Input Parameters:
    9568: .  F - the factored matrix obtained by calling MatGetFactor()

    9570:    Notes:
    9571:     Must be called after MatFactorSetSchurIS().

    9573:    Level: advanced

    9575:    References:

    9577: .seealso: MatGetFactor(), MatFactorSetSchurIS(), MatFactorInvertSchurComplement()
    9578: @*/
    9579: PetscErrorCode MatFactorFactorizeSchurComplement(Mat F)
    9580: {

    9586:   if (F->schur_status == MAT_FACTOR_SCHUR_INVERTED || F->schur_status == MAT_FACTOR_SCHUR_FACTORED) return(0);
    9587:   MatFactorFactorizeSchurComplement_Private(F);
    9588:   F->schur_status = MAT_FACTOR_SCHUR_FACTORED;
    9589:   return(0);
    9590: }

    9592: /*@
    9593:    MatPtAP - Creates the matrix product C = P^T * A * P

    9595:    Neighbor-wise Collective on Mat

    9597:    Input Parameters:
    9598: +  A - the matrix
    9599: .  P - the projection matrix
    9600: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9601: -  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(P)), use PETSC_DEFAULT if you do not have a good estimate
    9602:           if the result is a dense matrix this is irrelevent

    9604:    Output Parameters:
    9605: .  C - the product matrix

    9607:    Notes:
    9608:    C will be created and must be destroyed by the user with MatDestroy().

    9610:    For matrix types without special implementation the function fallbacks to MatMatMult() followed by MatTransposeMatMult().

    9612:    Level: intermediate

    9614: .seealso: MatMatMult(), MatRARt()
    9615: @*/
    9616: PetscErrorCode MatPtAP(Mat A,Mat P,MatReuse scall,PetscReal fill,Mat *C)
    9617: {

    9621:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*C,5);
    9622:   if (scall == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");

    9624:   if (scall == MAT_INITIAL_MATRIX) {
    9625:     MatProductCreate(A,P,NULL,C);
    9626:     MatProductSetType(*C,MATPRODUCT_PtAP);
    9627:     MatProductSetAlgorithm(*C,"default");
    9628:     MatProductSetFill(*C,fill);

    9630:     (*C)->product->api_user = PETSC_TRUE;
    9631:     MatProductSetFromOptions(*C);
    9632:     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);
    9633:     MatProductSymbolic(*C);
    9634:   } else { /* scall == MAT_REUSE_MATRIX */
    9635:     MatProductReplaceMats(A,P,NULL,*C);
    9636:   }

    9638:   MatProductNumeric(*C);
    9639:   if (A->symmetric_set && A->symmetric) {
    9640:     MatSetOption(*C,MAT_SYMMETRIC,PETSC_TRUE);
    9641:   }
    9642:   return(0);
    9643: }

    9645: /*@
    9646:    MatRARt - Creates the matrix product C = R * A * R^T

    9648:    Neighbor-wise Collective on Mat

    9650:    Input Parameters:
    9651: +  A - the matrix
    9652: .  R - the projection matrix
    9653: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9654: -  fill - expected fill as ratio of nnz(C)/nnz(A), use PETSC_DEFAULT if you do not have a good estimate
    9655:           if the result is a dense matrix this is irrelevent

    9657:    Output Parameters:
    9658: .  C - the product matrix

    9660:    Notes:
    9661:    C will be created and must be destroyed by the user with MatDestroy().

    9663:    This routine is currently only implemented for pairs of AIJ matrices and classes
    9664:    which inherit from AIJ. Due to PETSc sparse matrix block row distribution among processes,
    9665:    parallel MatRARt is implemented via explicit transpose of R, which could be very expensive.
    9666:    We recommend using MatPtAP().

    9668:    Level: intermediate

    9670: .seealso: MatMatMult(), MatPtAP()
    9671: @*/
    9672: PetscErrorCode MatRARt(Mat A,Mat R,MatReuse scall,PetscReal fill,Mat *C)
    9673: {

    9677:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*C,5);
    9678:   if (scall == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");

    9680:   if (scall == MAT_INITIAL_MATRIX) {
    9681:     MatProductCreate(A,R,NULL,C);
    9682:     MatProductSetType(*C,MATPRODUCT_RARt);
    9683:     MatProductSetAlgorithm(*C,"default");
    9684:     MatProductSetFill(*C,fill);

    9686:     (*C)->product->api_user = PETSC_TRUE;
    9687:     MatProductSetFromOptions(*C);
    9688:     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);
    9689:     MatProductSymbolic(*C);
    9690:   } else { /* scall == MAT_REUSE_MATRIX */
    9691:     MatProductReplaceMats(A,R,NULL,*C);
    9692:   }

    9694:   MatProductNumeric(*C);
    9695:   if (A->symmetric_set && A->symmetric) {
    9696:     MatSetOption(*C,MAT_SYMMETRIC,PETSC_TRUE);
    9697:   }
    9698:   return(0);
    9699: }

    9702: static PetscErrorCode MatProduct_Private(Mat A,Mat B,MatReuse scall,PetscReal fill,MatProductType ptype, Mat *C)
    9703: {

    9707:   if (scall == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");

    9709:   if (scall == MAT_INITIAL_MATRIX) {
    9710:     PetscInfo1(A,"Calling MatProduct API with MAT_INITIAL_MATRIX and product type %s\n",MatProductTypes[ptype]);
    9711:     MatProductCreate(A,B,NULL,C);
    9712:     MatProductSetType(*C,ptype);
    9713:     MatProductSetAlgorithm(*C,MATPRODUCTALGORITHM_DEFAULT);
    9714:     MatProductSetFill(*C,fill);

    9716:     (*C)->product->api_user = PETSC_TRUE;
    9717:     MatProductSetFromOptions(*C);
    9718:     MatProductSymbolic(*C);
    9719:   } else { /* scall == MAT_REUSE_MATRIX */
    9720:     Mat_Product *product = (*C)->product;

    9722:     PetscInfo2(A,"Calling MatProduct API with MAT_REUSE_MATRIX %s product present and product type %s\n",product ? "with" : "without",MatProductTypes[ptype]);
    9723:     if (!product) {
    9724:       /* user provide the dense matrix *C without calling MatProductCreate() */
    9725:       PetscBool isdense;

    9727:       PetscObjectBaseTypeCompareAny((PetscObject)(*C),&isdense,MATSEQDENSE,MATMPIDENSE,"");
    9728:       if (isdense) {
    9729:         /* user wants to reuse an assembled dense matrix */
    9730:         /* Create product -- see MatCreateProduct() */
    9731:         MatProductCreate_Private(A,B,NULL,*C);
    9732:         product = (*C)->product;
    9733:         product->fill     = fill;
    9734:         product->api_user = PETSC_TRUE;
    9735:         product->clear    = PETSC_TRUE;

    9737:         MatProductSetType(*C,ptype);
    9738:         MatProductSetFromOptions(*C);
    9739:         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);
    9740:         MatProductSymbolic(*C);
    9741:       } else SETERRQ(PetscObjectComm((PetscObject)(*C)),PETSC_ERR_SUP,"Call MatProductCreate() first");
    9742:     } else { /* user may change input matrices A or B when REUSE */
    9743:       MatProductReplaceMats(A,B,NULL,*C);
    9744:     }
    9745:   }
    9746:   MatProductNumeric(*C);
    9747:   return(0);
    9748: }

    9750: /*@
    9751:    MatMatMult - Performs Matrix-Matrix Multiplication C=A*B.

    9753:    Neighbor-wise Collective on Mat

    9755:    Input Parameters:
    9756: +  A - the left matrix
    9757: .  B - the right matrix
    9758: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9759: -  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if you do not have a good estimate
    9760:           if the result is a dense matrix this is irrelevent

    9762:    Output Parameters:
    9763: .  C - the product matrix

    9765:    Notes:
    9766:    Unless scall is MAT_REUSE_MATRIX C will be created.

    9768:    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
    9769:    call to this function with MAT_INITIAL_MATRIX.

    9771:    To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value actually needed.

    9773:    If you have many matrices with the same non-zero structure to multiply, you should use MatProductCreate()/MatProductSymbolic(C)/ReplaceMats(), and call MatProductNumeric() repeatedly.

    9775:    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.

    9777:    Level: intermediate

    9779: .seealso: MatTransposeMatMult(), MatMatTransposeMult(), MatPtAP()
    9780: @*/
    9781: PetscErrorCode MatMatMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    9782: {

    9786:   MatProduct_Private(A,B,scall,fill,MATPRODUCT_AB,C);
    9787:   return(0);
    9788: }

    9790: /*@
    9791:    MatMatTransposeMult - Performs Matrix-Matrix Multiplication C=A*B^T.

    9793:    Neighbor-wise Collective on Mat

    9795:    Input Parameters:
    9796: +  A - the left matrix
    9797: .  B - the right matrix
    9798: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9799: -  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if not known

    9801:    Output Parameters:
    9802: .  C - the product matrix

    9804:    Notes:
    9805:    C will be created if MAT_INITIAL_MATRIX and must be destroyed by the user with MatDestroy().

    9807:    MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call

    9809:   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    9810:    actually needed.

    9812:    This routine is currently only implemented for pairs of SeqAIJ matrices, for the SeqDense class,
    9813:    and for pairs of MPIDense matrices.

    9815:    Options Database Keys:
    9816: .  -matmattransmult_mpidense_mpidense_via {allgatherv,cyclic} - Choose between algorthims for MPIDense matrices: the
    9817:                                                                 first redundantly copies the transposed B matrix on each process and requiers O(log P) communication complexity;
    9818:                                                                 the second never stores more than one portion of the B matrix at a time by requires O(P) communication complexity.

    9820:    Level: intermediate

    9822: .seealso: MatMatMult(), MatTransposeMatMult() MatPtAP()
    9823: @*/
    9824: PetscErrorCode MatMatTransposeMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    9825: {

    9829:   MatProduct_Private(A,B,scall,fill,MATPRODUCT_ABt,C);
    9830:   return(0);
    9831: }

    9833: /*@
    9834:    MatTransposeMatMult - Performs Matrix-Matrix Multiplication C=A^T*B.

    9836:    Neighbor-wise Collective on Mat

    9838:    Input Parameters:
    9839: +  A - the left matrix
    9840: .  B - the right matrix
    9841: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9842: -  fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if not known

    9844:    Output Parameters:
    9845: .  C - the product matrix

    9847:    Notes:
    9848:    C will be created if MAT_INITIAL_MATRIX and must be destroyed by the user with MatDestroy().

    9850:    MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call.

    9852:   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    9853:    actually needed.

    9855:    This routine is currently implemented for pairs of AIJ matrices and pairs of SeqDense matrices and classes
    9856:    which inherit from SeqAIJ.  C will be of same type as the input matrices.

    9858:    Level: intermediate

    9860: .seealso: MatMatMult(), MatMatTransposeMult(), MatPtAP()
    9861: @*/
    9862: PetscErrorCode MatTransposeMatMult(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    9863: {

    9867:   MatProduct_Private(A,B,scall,fill,MATPRODUCT_AtB,C);
    9868:   return(0);
    9869: }

    9871: /*@
    9872:    MatMatMatMult - Performs Matrix-Matrix-Matrix Multiplication D=A*B*C.

    9874:    Neighbor-wise Collective on Mat

    9876:    Input Parameters:
    9877: +  A - the left matrix
    9878: .  B - the middle matrix
    9879: .  C - the right matrix
    9880: .  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    9881: -  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
    9882:           if the result is a dense matrix this is irrelevent

    9884:    Output Parameters:
    9885: .  D - the product matrix

    9887:    Notes:
    9888:    Unless scall is MAT_REUSE_MATRIX D will be created.

    9890:    MAT_REUSE_MATRIX can only be used if the matrices A, B and C have the same nonzero pattern as in the previous call

    9892:    To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    9893:    actually needed.

    9895:    If you have many matrices with the same non-zero structure to multiply, you
    9896:    should use MAT_REUSE_MATRIX in all calls but the first or

    9898:    Level: intermediate

    9900: .seealso: MatMatMult, MatPtAP()
    9901: @*/
    9902: PetscErrorCode MatMatMatMult(Mat A,Mat B,Mat C,MatReuse scall,PetscReal fill,Mat *D)
    9903: {

    9907:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*D,6);
    9908:   if (scall == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");

    9910:   if (scall == MAT_INITIAL_MATRIX) {
    9911:     MatProductCreate(A,B,C,D);
    9912:     MatProductSetType(*D,MATPRODUCT_ABC);
    9913:     MatProductSetAlgorithm(*D,"default");
    9914:     MatProductSetFill(*D,fill);

    9916:     (*D)->product->api_user = PETSC_TRUE;
    9917:     MatProductSetFromOptions(*D);
    9918:     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);
    9919:     MatProductSymbolic(*D);
    9920:   } else { /* user may change input matrices when REUSE */
    9921:     MatProductReplaceMats(A,B,C,*D);
    9922:   }
    9923:   MatProductNumeric(*D);
    9924:   return(0);
    9925: }

    9927: /*@
    9928:    MatCreateRedundantMatrix - Create redundant matrices and put them into processors of subcommunicators.

    9930:    Collective on Mat

    9932:    Input Parameters:
    9933: +  mat - the matrix
    9934: .  nsubcomm - the number of subcommunicators (= number of redundant parallel or sequential matrices)
    9935: .  subcomm - MPI communicator split from the communicator where mat resides in (or MPI_COMM_NULL if nsubcomm is used)
    9936: -  reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    9938:    Output Parameter:
    9939: .  matredundant - redundant matrix

    9941:    Notes:
    9942:    MAT_REUSE_MATRIX can only be used when the nonzero structure of the
    9943:    original matrix has not changed from that last call to MatCreateRedundantMatrix().

    9945:    This routine creates the duplicated matrices in subcommunicators; you should NOT create them before
    9946:    calling it.

    9948:    Level: advanced

    9951: .seealso: MatDestroy()
    9952: @*/
    9953: PetscErrorCode MatCreateRedundantMatrix(Mat mat,PetscInt nsubcomm,MPI_Comm subcomm,MatReuse reuse,Mat *matredundant)
    9954: {
    9956:   MPI_Comm       comm;
    9957:   PetscMPIInt    size;
    9958:   PetscInt       mloc_sub,nloc_sub,rstart,rend,M=mat->rmap->N,N=mat->cmap->N,bs=mat->rmap->bs;
    9959:   Mat_Redundant  *redund=NULL;
    9960:   PetscSubcomm   psubcomm=NULL;
    9961:   MPI_Comm       subcomm_in=subcomm;
    9962:   Mat            *matseq;
    9963:   IS             isrow,iscol;
    9964:   PetscBool      newsubcomm=PETSC_FALSE;

    9968:   if (nsubcomm && reuse == MAT_REUSE_MATRIX) {
    9971:   }

    9973:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    9974:   if (size == 1 || nsubcomm == 1) {
    9975:     if (reuse == MAT_INITIAL_MATRIX) {
    9976:       MatDuplicate(mat,MAT_COPY_VALUES,matredundant);
    9977:     } else {
    9978:       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");
    9979:       MatCopy(mat,*matredundant,SAME_NONZERO_PATTERN);
    9980:     }
    9981:     return(0);
    9982:   }

    9984:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    9985:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    9986:   MatCheckPreallocated(mat,1);

    9988:   PetscLogEventBegin(MAT_RedundantMat,mat,0,0,0);
    9989:   if (subcomm_in == MPI_COMM_NULL && reuse == MAT_INITIAL_MATRIX) { /* get subcomm if user does not provide subcomm */
    9990:     /* create psubcomm, then get subcomm */
    9991:     PetscObjectGetComm((PetscObject)mat,&comm);
    9992:     MPI_Comm_size(comm,&size);
    9993:     if (nsubcomm < 1 || nsubcomm > size) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"nsubcomm must between 1 and %D",size);

    9995:     PetscSubcommCreate(comm,&psubcomm);
    9996:     PetscSubcommSetNumber(psubcomm,nsubcomm);
    9997:     PetscSubcommSetType(psubcomm,PETSC_SUBCOMM_CONTIGUOUS);
    9998:     PetscSubcommSetFromOptions(psubcomm);
    9999:     PetscCommDuplicate(PetscSubcommChild(psubcomm),&subcomm,NULL);
    10000:     newsubcomm = PETSC_TRUE;
    10001:     PetscSubcommDestroy(&psubcomm);
    10002:   }

    10004:   /* get isrow, iscol and a local sequential matrix matseq[0] */
    10005:   if (reuse == MAT_INITIAL_MATRIX) {
    10006:     mloc_sub = PETSC_DECIDE;
    10007:     nloc_sub = PETSC_DECIDE;
    10008:     if (bs < 1) {
    10009:       PetscSplitOwnership(subcomm,&mloc_sub,&M);
    10010:       PetscSplitOwnership(subcomm,&nloc_sub,&N);
    10011:     } else {
    10012:       PetscSplitOwnershipBlock(subcomm,bs,&mloc_sub,&M);
    10013:       PetscSplitOwnershipBlock(subcomm,bs,&nloc_sub,&N);
    10014:     }
    10015:     MPI_Scan(&mloc_sub,&rend,1,MPIU_INT,MPI_SUM,subcomm);
    10016:     rstart = rend - mloc_sub;
    10017:     ISCreateStride(PETSC_COMM_SELF,mloc_sub,rstart,1,&isrow);
    10018:     ISCreateStride(PETSC_COMM_SELF,N,0,1,&iscol);
    10019:   } else { /* reuse == MAT_REUSE_MATRIX */
    10020:     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");
    10021:     /* retrieve subcomm */
    10022:     PetscObjectGetComm((PetscObject)(*matredundant),&subcomm);
    10023:     redund = (*matredundant)->redundant;
    10024:     isrow  = redund->isrow;
    10025:     iscol  = redund->iscol;
    10026:     matseq = redund->matseq;
    10027:   }
    10028:   MatCreateSubMatrices(mat,1,&isrow,&iscol,reuse,&matseq);

    10030:   /* get matredundant over subcomm */
    10031:   if (reuse == MAT_INITIAL_MATRIX) {
    10032:     MatCreateMPIMatConcatenateSeqMat(subcomm,matseq[0],nloc_sub,reuse,matredundant);

    10034:     /* create a supporting struct and attach it to C for reuse */
    10035:     PetscNewLog(*matredundant,&redund);
    10036:     (*matredundant)->redundant = redund;
    10037:     redund->isrow              = isrow;
    10038:     redund->iscol              = iscol;
    10039:     redund->matseq             = matseq;
    10040:     if (newsubcomm) {
    10041:       redund->subcomm          = subcomm;
    10042:     } else {
    10043:       redund->subcomm          = MPI_COMM_NULL;
    10044:     }
    10045:   } else {
    10046:     MatCreateMPIMatConcatenateSeqMat(subcomm,matseq[0],PETSC_DECIDE,reuse,matredundant);
    10047:   }
    10048:   PetscLogEventEnd(MAT_RedundantMat,mat,0,0,0);
    10049:   return(0);
    10050: }

    10052: /*@C
    10053:    MatGetMultiProcBlock - Create multiple [bjacobi] 'parallel submatrices' from
    10054:    a given 'mat' object. Each submatrix can span multiple procs.

    10056:    Collective on Mat

    10058:    Input Parameters:
    10059: +  mat - the matrix
    10060: .  subcomm - the subcommunicator obtained by com_split(comm)
    10061: -  scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    10063:    Output Parameter:
    10064: .  subMat - 'parallel submatrices each spans a given subcomm

    10066:   Notes:
    10067:   The submatrix partition across processors is dictated by 'subComm' a
    10068:   communicator obtained by com_split(comm). The comm_split
    10069:   is not restriced to be grouped with consecutive original ranks.

    10071:   Due the comm_split() usage, the parallel layout of the submatrices
    10072:   map directly to the layout of the original matrix [wrt the local
    10073:   row,col partitioning]. So the original 'DiagonalMat' naturally maps
    10074:   into the 'DiagonalMat' of the subMat, hence it is used directly from
    10075:   the subMat. However the offDiagMat looses some columns - and this is
    10076:   reconstructed with MatSetValues()

    10078:   Level: advanced

    10081: .seealso: MatCreateSubMatrices()
    10082: @*/
    10083: PetscErrorCode   MatGetMultiProcBlock(Mat mat, MPI_Comm subComm, MatReuse scall,Mat *subMat)
    10084: {
    10086:   PetscMPIInt    commsize,subCommSize;

    10089:   MPI_Comm_size(PetscObjectComm((PetscObject)mat),&commsize);
    10090:   MPI_Comm_size(subComm,&subCommSize);
    10091:   if (subCommSize > commsize) SETERRQ2(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_OUTOFRANGE,"CommSize %D < SubCommZize %D",commsize,subCommSize);

    10093:   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");
    10094:   PetscLogEventBegin(MAT_GetMultiProcBlock,mat,0,0,0);
    10095:   (*mat->ops->getmultiprocblock)(mat,subComm,scall,subMat);
    10096:   PetscLogEventEnd(MAT_GetMultiProcBlock,mat,0,0,0);
    10097:   return(0);
    10098: }

    10100: /*@
    10101:    MatGetLocalSubMatrix - Gets a reference to a submatrix specified in local numbering

    10103:    Not Collective

    10105:    Input Arguments:
    10106: +  mat - matrix to extract local submatrix from
    10107: .  isrow - local row indices for submatrix
    10108: -  iscol - local column indices for submatrix

    10110:    Output Arguments:
    10111: .  submat - the submatrix

    10113:    Level: intermediate

    10115:    Notes:
    10116:    The submat should be returned with MatRestoreLocalSubMatrix().

    10118:    Depending on the format of mat, the returned submat may not implement MatMult().  Its communicator may be
    10119:    the same as mat, it may be PETSC_COMM_SELF, or some other subcomm of mat's.

    10121:    The submat always implements MatSetValuesLocal().  If isrow and iscol have the same block size, then
    10122:    MatSetValuesBlockedLocal() will also be implemented.

    10124:    The mat must have had a ISLocalToGlobalMapping provided to it with MatSetLocalToGlobalMapping(). Note that
    10125:    matrices obtained with DMCreateMatrix() generally already have the local to global mapping provided.

    10127: .seealso: MatRestoreLocalSubMatrix(), MatCreateLocalRef(), MatSetLocalToGlobalMapping()
    10128: @*/
    10129: PetscErrorCode MatGetLocalSubMatrix(Mat mat,IS isrow,IS iscol,Mat *submat)
    10130: {

    10139:   if (!mat->rmap->mapping) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Matrix must have local to global mapping provided before this call");

    10141:   if (mat->ops->getlocalsubmatrix) {
    10142:     (*mat->ops->getlocalsubmatrix)(mat,isrow,iscol,submat);
    10143:   } else {
    10144:     MatCreateLocalRef(mat,isrow,iscol,submat);
    10145:   }
    10146:   return(0);
    10147: }

    10149: /*@
    10150:    MatRestoreLocalSubMatrix - Restores a reference to a submatrix specified in local numbering

    10152:    Not Collective

    10154:    Input Arguments:
    10155:    mat - matrix to extract local submatrix from
    10156:    isrow - local row indices for submatrix
    10157:    iscol - local column indices for submatrix
    10158:    submat - the submatrix

    10160:    Level: intermediate

    10162: .seealso: MatGetLocalSubMatrix()
    10163: @*/
    10164: PetscErrorCode MatRestoreLocalSubMatrix(Mat mat,IS isrow,IS iscol,Mat *submat)
    10165: {

    10174:   if (*submat) {
    10176:   }

    10178:   if (mat->ops->restorelocalsubmatrix) {
    10179:     (*mat->ops->restorelocalsubmatrix)(mat,isrow,iscol,submat);
    10180:   } else {
    10181:     MatDestroy(submat);
    10182:   }
    10183:   *submat = NULL;
    10184:   return(0);
    10185: }

    10187: /* --------------------------------------------------------*/
    10188: /*@
    10189:    MatFindZeroDiagonals - Finds all the rows of a matrix that have zero or no diagonal entry in the matrix

    10191:    Collective on Mat

    10193:    Input Parameter:
    10194: .  mat - the matrix

    10196:    Output Parameter:
    10197: .  is - if any rows have zero diagonals this contains the list of them

    10199:    Level: developer

    10201: .seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    10202: @*/
    10203: PetscErrorCode MatFindZeroDiagonals(Mat mat,IS *is)
    10204: {

    10210:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    10211:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

    10213:   if (!mat->ops->findzerodiagonals) {
    10214:     Vec                diag;
    10215:     const PetscScalar *a;
    10216:     PetscInt          *rows;
    10217:     PetscInt           rStart, rEnd, r, nrow = 0;

    10219:     MatCreateVecs(mat, &diag, NULL);
    10220:     MatGetDiagonal(mat, diag);
    10221:     MatGetOwnershipRange(mat, &rStart, &rEnd);
    10222:     VecGetArrayRead(diag, &a);
    10223:     for (r = 0; r < rEnd-rStart; ++r) if (a[r] == 0.0) ++nrow;
    10224:     PetscMalloc1(nrow, &rows);
    10225:     nrow = 0;
    10226:     for (r = 0; r < rEnd-rStart; ++r) if (a[r] == 0.0) rows[nrow++] = r+rStart;
    10227:     VecRestoreArrayRead(diag, &a);
    10228:     VecDestroy(&diag);
    10229:     ISCreateGeneral(PetscObjectComm((PetscObject) mat), nrow, rows, PETSC_OWN_POINTER, is);
    10230:   } else {
    10231:     (*mat->ops->findzerodiagonals)(mat, is);
    10232:   }
    10233:   return(0);
    10234: }

    10236: /*@
    10237:    MatFindOffBlockDiagonalEntries - Finds all the rows of a matrix that have entries outside of the main diagonal block (defined by the matrix block size)

    10239:    Collective on Mat

    10241:    Input Parameter:
    10242: .  mat - the matrix

    10244:    Output Parameter:
    10245: .  is - contains the list of rows with off block diagonal entries

    10247:    Level: developer

    10249: .seealso: MatMultTranspose(), MatMultAdd(), MatMultTransposeAdd()
    10250: @*/
    10251: PetscErrorCode MatFindOffBlockDiagonalEntries(Mat mat,IS *is)
    10252: {

    10258:   if (!mat->assembled) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    10259:   if (mat->factortype) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");

    10261:   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);
    10262:   (*mat->ops->findoffblockdiagonalentries)(mat,is);
    10263:   return(0);
    10264: }

    10266: /*@C
    10267:   MatInvertBlockDiagonal - Inverts the block diagonal entries.

    10269:   Collective on Mat

    10271:   Input Parameters:
    10272: . mat - the matrix

    10274:   Output Parameters:
    10275: . values - the block inverses in column major order (FORTRAN-like)

    10277:    Note:
    10278:    This routine is not available from Fortran.

    10280:   Level: advanced

    10282: .seealso: MatInvertBockDiagonalMat
    10283: @*/
    10284: PetscErrorCode MatInvertBlockDiagonal(Mat mat,const PetscScalar **values)
    10285: {

    10290:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    10291:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    10292:   if (!mat->ops->invertblockdiagonal) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for type %s",((PetscObject)mat)->type_name);
    10293:   (*mat->ops->invertblockdiagonal)(mat,values);
    10294:   return(0);
    10295: }

    10297: /*@C
    10298:   MatInvertVariableBlockDiagonal - Inverts the block diagonal entries.

    10300:   Collective on Mat

    10302:   Input Parameters:
    10303: + mat - the matrix
    10304: . nblocks - the number of blocks
    10305: - bsizes - the size of each block

    10307:   Output Parameters:
    10308: . values - the block inverses in column major order (FORTRAN-like)

    10310:    Note:
    10311:    This routine is not available from Fortran.

    10313:   Level: advanced

    10315: .seealso: MatInvertBockDiagonal()
    10316: @*/
    10317: PetscErrorCode MatInvertVariableBlockDiagonal(Mat mat,PetscInt nblocks,const PetscInt *bsizes,PetscScalar *values)
    10318: {

    10323:   if (!mat->assembled) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for unassembled matrix");
    10324:   if (mat->factortype) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Not for factored matrix");
    10325:   if (!mat->ops->invertvariableblockdiagonal) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for type",((PetscObject)mat)->type_name);
    10326:   (*mat->ops->invertvariableblockdiagonal)(mat,nblocks,bsizes,values);
    10327:   return(0);
    10328: }

    10330: /*@
    10331:   MatInvertBlockDiagonalMat - set matrix C to be the inverted block diagonal of matrix A

    10333:   Collective on Mat

    10335:   Input Parameters:
    10336: . A - the matrix

    10338:   Output Parameters:
    10339: . C - matrix with inverted block diagonal of A.  This matrix should be created and may have its type set.

    10341:   Notes: the blocksize of the matrix is used to determine the blocks on the diagonal of C

    10343:   Level: advanced

    10345: .seealso: MatInvertBockDiagonal()
    10346: @*/
    10347: PetscErrorCode MatInvertBlockDiagonalMat(Mat A,Mat C)
    10348: {
    10349:   PetscErrorCode     ierr;
    10350:   const PetscScalar *vals;
    10351:   PetscInt          *dnnz;
    10352:   PetscInt           M,N,m,n,rstart,rend,bs,i,j;

    10355:   MatInvertBlockDiagonal(A,&vals);
    10356:   MatGetBlockSize(A,&bs);
    10357:   MatGetSize(A,&M,&N);
    10358:   MatGetLocalSize(A,&m,&n);
    10359:   MatSetSizes(C,m,n,M,N);
    10360:   MatSetBlockSize(C,bs);
    10361:   PetscMalloc1(m/bs,&dnnz);
    10362:   for (j = 0; j < m/bs; j++) dnnz[j] = 1;
    10363:   MatXAIJSetPreallocation(C,bs,dnnz,NULL,NULL,NULL);
    10364:   PetscFree(dnnz);
    10365:   MatGetOwnershipRange(C,&rstart,&rend);
    10366:   MatSetOption(C,MAT_ROW_ORIENTED,PETSC_FALSE);
    10367:   for (i = rstart/bs; i < rend/bs; i++) {
    10368:     MatSetValuesBlocked(C,1,&i,1,&i,&vals[(i-rstart/bs)*bs*bs],INSERT_VALUES);
    10369:   }
    10370:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    10371:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    10372:   MatSetOption(C,MAT_ROW_ORIENTED,PETSC_TRUE);
    10373:   return(0);
    10374: }

    10376: /*@C
    10377:     MatTransposeColoringDestroy - Destroys a coloring context for matrix product C=A*B^T that was created
    10378:     via MatTransposeColoringCreate().

    10380:     Collective on MatTransposeColoring

    10382:     Input Parameter:
    10383: .   c - coloring context

    10385:     Level: intermediate

    10387: .seealso: MatTransposeColoringCreate()
    10388: @*/
    10389: PetscErrorCode MatTransposeColoringDestroy(MatTransposeColoring *c)
    10390: {
    10391:   PetscErrorCode       ierr;
    10392:   MatTransposeColoring matcolor=*c;

    10395:   if (!matcolor) return(0);
    10396:   if (--((PetscObject)matcolor)->refct > 0) {matcolor = NULL; return(0);}

    10398:   PetscFree3(matcolor->ncolumns,matcolor->nrows,matcolor->colorforrow);
    10399:   PetscFree(matcolor->rows);
    10400:   PetscFree(matcolor->den2sp);
    10401:   PetscFree(matcolor->colorforcol);
    10402:   PetscFree(matcolor->columns);
    10403:   if (matcolor->brows>0) {
    10404:     PetscFree(matcolor->lstart);
    10405:   }
    10406:   PetscHeaderDestroy(c);
    10407:   return(0);
    10408: }

    10410: /*@C
    10411:     MatTransColoringApplySpToDen - Given a symbolic matrix product C=A*B^T for which
    10412:     a MatTransposeColoring context has been created, computes a dense B^T by Apply
    10413:     MatTransposeColoring to sparse B.

    10415:     Collective on MatTransposeColoring

    10417:     Input Parameters:
    10418: +   B - sparse matrix B
    10419: .   Btdense - symbolic dense matrix B^T
    10420: -   coloring - coloring context created with MatTransposeColoringCreate()

    10422:     Output Parameter:
    10423: .   Btdense - dense matrix B^T

    10425:     Level: advanced

    10427:      Notes:
    10428:     These are used internally for some implementations of MatRARt()

    10430: .seealso: MatTransposeColoringCreate(), MatTransposeColoringDestroy(), MatTransColoringApplyDenToSp()

    10432: @*/
    10433: PetscErrorCode MatTransColoringApplySpToDen(MatTransposeColoring coloring,Mat B,Mat Btdense)
    10434: {

    10442:   if (!B->ops->transcoloringapplysptoden) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for this matrix type %s",((PetscObject)B)->type_name);
    10443:   (B->ops->transcoloringapplysptoden)(coloring,B,Btdense);
    10444:   return(0);
    10445: }

    10447: /*@C
    10448:     MatTransColoringApplyDenToSp - Given a symbolic matrix product Csp=A*B^T for which
    10449:     a MatTransposeColoring context has been created and a dense matrix Cden=A*Btdense
    10450:     in which Btdens is obtained from MatTransColoringApplySpToDen(), recover sparse matrix
    10451:     Csp from Cden.

    10453:     Collective on MatTransposeColoring

    10455:     Input Parameters:
    10456: +   coloring - coloring context created with MatTransposeColoringCreate()
    10457: -   Cden - matrix product of a sparse matrix and a dense matrix Btdense

    10459:     Output Parameter:
    10460: .   Csp - sparse matrix

    10462:     Level: advanced

    10464:      Notes:
    10465:     These are used internally for some implementations of MatRARt()

    10467: .seealso: MatTransposeColoringCreate(), MatTransposeColoringDestroy(), MatTransColoringApplySpToDen()

    10469: @*/
    10470: PetscErrorCode MatTransColoringApplyDenToSp(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
    10471: {

    10479:   if (!Csp->ops->transcoloringapplydentosp) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not supported for this matrix type %s",((PetscObject)Csp)->type_name);
    10480:   (Csp->ops->transcoloringapplydentosp)(matcoloring,Cden,Csp);
    10481:   MatAssemblyBegin(Csp,MAT_FINAL_ASSEMBLY);
    10482:   MatAssemblyEnd(Csp,MAT_FINAL_ASSEMBLY);
    10483:   return(0);
    10484: }

    10486: /*@C
    10487:    MatTransposeColoringCreate - Creates a matrix coloring context for matrix product C=A*B^T.

    10489:    Collective on Mat

    10491:    Input Parameters:
    10492: +  mat - the matrix product C
    10493: -  iscoloring - the coloring of the matrix; usually obtained with MatColoringCreate() or DMCreateColoring()

    10495:     Output Parameter:
    10496: .   color - the new coloring context

    10498:     Level: intermediate

    10500: .seealso: MatTransposeColoringDestroy(),  MatTransColoringApplySpToDen(),
    10501:            MatTransColoringApplyDenToSp()
    10502: @*/
    10503: PetscErrorCode MatTransposeColoringCreate(Mat mat,ISColoring iscoloring,MatTransposeColoring *color)
    10504: {
    10505:   MatTransposeColoring c;
    10506:   MPI_Comm             comm;
    10507:   PetscErrorCode       ierr;

    10510:   PetscLogEventBegin(MAT_TransposeColoringCreate,mat,0,0,0);
    10511:   PetscObjectGetComm((PetscObject)mat,&comm);
    10512:   PetscHeaderCreate(c,MAT_TRANSPOSECOLORING_CLASSID,"MatTransposeColoring","Matrix product C=A*B^T via coloring","Mat",comm,MatTransposeColoringDestroy,NULL);

    10514:   c->ctype = iscoloring->ctype;
    10515:   if (mat->ops->transposecoloringcreate) {
    10516:     (*mat->ops->transposecoloringcreate)(mat,iscoloring,c);
    10517:   } else SETERRQ1(PetscObjectComm((PetscObject)mat),PETSC_ERR_SUP,"Code not yet written for matrix type %s",((PetscObject)mat)->type_name);

    10519:   *color = c;
    10520:   PetscLogEventEnd(MAT_TransposeColoringCreate,mat,0,0,0);
    10521:   return(0);
    10522: }

    10524: /*@
    10525:       MatGetNonzeroState - Returns a 64 bit integer representing the current state of nonzeros in the matrix. If the
    10526:         matrix has had no new nonzero locations added to the matrix since the previous call then the value will be the
    10527:         same, otherwise it will be larger

    10529:      Not Collective

    10531:   Input Parameter:
    10532: .    A  - the matrix

    10534:   Output Parameter:
    10535: .    state - the current state

    10537:   Notes:
    10538:     You can only compare states from two different calls to the SAME matrix, you cannot compare calls between
    10539:          different matrices

    10541:   Level: intermediate

    10543: @*/
    10544: PetscErrorCode MatGetNonzeroState(Mat mat,PetscObjectState *state)
    10545: {
    10548:   *state = mat->nonzerostate;
    10549:   return(0);
    10550: }

    10552: /*@
    10553:       MatCreateMPIMatConcatenateSeqMat - Creates a single large PETSc matrix by concatenating sequential
    10554:                  matrices from each processor

    10556:     Collective

    10558:    Input Parameters:
    10559: +    comm - the communicators the parallel matrix will live on
    10560: .    seqmat - the input sequential matrices
    10561: .    n - number of local columns (or PETSC_DECIDE)
    10562: -    reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

    10564:    Output Parameter:
    10565: .    mpimat - the parallel matrix generated

    10567:     Level: advanced

    10569:    Notes:
    10570:     The number of columns of the matrix in EACH processor MUST be the same.

    10572: @*/
    10573: PetscErrorCode MatCreateMPIMatConcatenateSeqMat(MPI_Comm comm,Mat seqmat,PetscInt n,MatReuse reuse,Mat *mpimat)
    10574: {

    10578:   if (!seqmat->ops->creatempimatconcatenateseqmat) SETERRQ1(PetscObjectComm((PetscObject)seqmat),PETSC_ERR_SUP,"Mat type %s",((PetscObject)seqmat)->type_name);
    10579:   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");

    10581:   PetscLogEventBegin(MAT_Merge,seqmat,0,0,0);
    10582:   (*seqmat->ops->creatempimatconcatenateseqmat)(comm,seqmat,n,reuse,mpimat);
    10583:   PetscLogEventEnd(MAT_Merge,seqmat,0,0,0);
    10584:   return(0);
    10585: }

    10587: /*@
    10588:      MatSubdomainsCreateCoalesce - Creates index subdomains by coalescing adjacent
    10589:                  ranks' ownership ranges.

    10591:     Collective on A

    10593:    Input Parameters:
    10594: +    A   - the matrix to create subdomains from
    10595: -    N   - requested number of subdomains

    10598:    Output Parameters:
    10599: +    n   - number of subdomains resulting on this rank
    10600: -    iss - IS list with indices of subdomains on this rank

    10602:     Level: advanced

    10604:     Notes:
    10605:     number of subdomains must be smaller than the communicator size
    10606: @*/
    10607: PetscErrorCode MatSubdomainsCreateCoalesce(Mat A,PetscInt N,PetscInt *n,IS *iss[])
    10608: {
    10609:   MPI_Comm        comm,subcomm;
    10610:   PetscMPIInt     size,rank,color;
    10611:   PetscInt        rstart,rend,k;
    10612:   PetscErrorCode  ierr;

    10615:   PetscObjectGetComm((PetscObject)A,&comm);
    10616:   MPI_Comm_size(comm,&size);
    10617:   MPI_Comm_rank(comm,&rank);
    10618:   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);
    10619:   *n = 1;
    10620:   k = ((PetscInt)size)/N + ((PetscInt)size%N>0); /* There are up to k ranks to a color */
    10621:   color = rank/k;
    10622:   MPI_Comm_split(comm,color,rank,&subcomm);
    10623:   PetscMalloc1(1,iss);
    10624:   MatGetOwnershipRange(A,&rstart,&rend);
    10625:   ISCreateStride(subcomm,rend-rstart,rstart,1,iss[0]);
    10626:   MPI_Comm_free(&subcomm);
    10627:   return(0);
    10628: }

    10630: /*@
    10631:    MatGalerkin - Constructs the coarse grid problem via Galerkin projection.

    10633:    If the interpolation and restriction operators are the same, uses MatPtAP.
    10634:    If they are not the same, use MatMatMatMult.

    10636:    Once the coarse grid problem is constructed, correct for interpolation operators
    10637:    that are not of full rank, which can legitimately happen in the case of non-nested
    10638:    geometric multigrid.

    10640:    Input Parameters:
    10641: +  restrct - restriction operator
    10642: .  dA - fine grid matrix
    10643: .  interpolate - interpolation operator
    10644: .  reuse - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX
    10645: -  fill - expected fill, use PETSC_DEFAULT if you do not have a good estimate

    10647:    Output Parameters:
    10648: .  A - the Galerkin coarse matrix

    10650:    Options Database Key:
    10651: .  -pc_mg_galerkin <both,pmat,mat,none>

    10653:    Level: developer

    10655: .seealso: MatPtAP(), MatMatMatMult()
    10656: @*/
    10657: PetscErrorCode  MatGalerkin(Mat restrct, Mat dA, Mat interpolate, MatReuse reuse, PetscReal fill, Mat *A)
    10658: {
    10660:   IS             zerorows;
    10661:   Vec            diag;

    10664:   if (reuse == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Inplace product not supported");
    10665:   /* Construct the coarse grid matrix */
    10666:   if (interpolate == restrct) {
    10667:     MatPtAP(dA,interpolate,reuse,fill,A);
    10668:   } else {
    10669:     MatMatMatMult(restrct,dA,interpolate,reuse,fill,A);
    10670:   }

    10672:   /* If the interpolation matrix is not of full rank, A will have zero rows.
    10673:      This can legitimately happen in the case of non-nested geometric multigrid.
    10674:      In that event, we set the rows of the matrix to the rows of the identity,
    10675:      ignoring the equations (as the RHS will also be zero). */

    10677:   MatFindZeroRows(*A, &zerorows);

    10679:   if (zerorows != NULL) { /* if there are any zero rows */
    10680:     MatCreateVecs(*A, &diag, NULL);
    10681:     MatGetDiagonal(*A, diag);
    10682:     VecISSet(diag, zerorows, 1.0);
    10683:     MatDiagonalSet(*A, diag, INSERT_VALUES);
    10684:     VecDestroy(&diag);
    10685:     ISDestroy(&zerorows);
    10686:   }
    10687:   return(0);
    10688: }

    10690: /*@C
    10691:     MatSetOperation - Allows user to set a matrix operation for any matrix type

    10693:    Logically Collective on Mat

    10695:     Input Parameters:
    10696: +   mat - the matrix
    10697: .   op - the name of the operation
    10698: -   f - the function that provides the operation

    10700:    Level: developer

    10702:     Usage:
    10703: $      extern PetscErrorCode usermult(Mat,Vec,Vec);
    10704: $      MatCreateXXX(comm,...&A);
    10705: $      MatSetOperation(A,MATOP_MULT,(void(*)(void))usermult);

    10707:     Notes:
    10708:     See the file include/petscmat.h for a complete list of matrix
    10709:     operations, which all have the form MATOP_<OPERATION>, where
    10710:     <OPERATION> is the name (in all capital letters) of the
    10711:     user interface routine (e.g., MatMult() -> MATOP_MULT).

    10713:     All user-provided functions (except for MATOP_DESTROY) should have the same calling
    10714:     sequence as the usual matrix interface routines, since they
    10715:     are intended to be accessed via the usual matrix interface
    10716:     routines, e.g.,
    10717: $       MatMult(Mat,Vec,Vec) -> usermult(Mat,Vec,Vec)

    10719:     In particular each function MUST return an error code of 0 on success and
    10720:     nonzero on failure.

    10722:     This routine is distinct from MatShellSetOperation() in that it can be called on any matrix type.

    10724: .seealso: MatGetOperation(), MatCreateShell(), MatShellSetContext(), MatShellSetOperation()
    10725: @*/
    10726: PetscErrorCode MatSetOperation(Mat mat,MatOperation op,void (*f)(void))
    10727: {
    10730:   if (op == MATOP_VIEW && !mat->ops->viewnative && f != (void (*)(void))(mat->ops->view)) {
    10731:     mat->ops->viewnative = mat->ops->view;
    10732:   }
    10733:   (((void(**)(void))mat->ops)[op]) = f;
    10734:   return(0);
    10735: }

    10737: /*@C
    10738:     MatGetOperation - Gets a matrix operation for any matrix type.

    10740:     Not Collective

    10742:     Input Parameters:
    10743: +   mat - the matrix
    10744: -   op - the name of the operation

    10746:     Output Parameter:
    10747: .   f - the function that provides the operation

    10749:     Level: developer

    10751:     Usage:
    10752: $      PetscErrorCode (*usermult)(Mat,Vec,Vec);
    10753: $      MatGetOperation(A,MATOP_MULT,(void(**)(void))&usermult);

    10755:     Notes:
    10756:     See the file include/petscmat.h for a complete list of matrix
    10757:     operations, which all have the form MATOP_<OPERATION>, where
    10758:     <OPERATION> is the name (in all capital letters) of the
    10759:     user interface routine (e.g., MatMult() -> MATOP_MULT).

    10761:     This routine is distinct from MatShellGetOperation() in that it can be called on any matrix type.

    10763: .seealso: MatSetOperation(), MatCreateShell(), MatShellGetContext(), MatShellGetOperation()
    10764: @*/
    10765: PetscErrorCode MatGetOperation(Mat mat,MatOperation op,void(**f)(void))
    10766: {
    10769:   *f = (((void (**)(void))mat->ops)[op]);
    10770:   return(0);
    10771: }

    10773: /*@
    10774:     MatHasOperation - Determines whether the given matrix supports the particular
    10775:     operation.

    10777:    Not Collective

    10779:    Input Parameters:
    10780: +  mat - the matrix
    10781: -  op - the operation, for example, MATOP_GET_DIAGONAL

    10783:    Output Parameter:
    10784: .  has - either PETSC_TRUE or PETSC_FALSE

    10786:    Level: advanced

    10788:    Notes:
    10789:    See the file include/petscmat.h for a complete list of matrix
    10790:    operations, which all have the form MATOP_<OPERATION>, where
    10791:    <OPERATION> is the name (in all capital letters) of the
    10792:    user-level routine.  E.g., MatNorm() -> MATOP_NORM.

    10794: .seealso: MatCreateShell()
    10795: @*/
    10796: PetscErrorCode MatHasOperation(Mat mat,MatOperation op,PetscBool *has)
    10797: {

    10802:   /* symbolic product can be set before matrix type */
    10805:   if (mat->ops->hasoperation) {
    10806:     (*mat->ops->hasoperation)(mat,op,has);
    10807:   } else {
    10808:     if (((void**)mat->ops)[op]) *has =  PETSC_TRUE;
    10809:     else {
    10810:       *has = PETSC_FALSE;
    10811:       if (op == MATOP_CREATE_SUBMATRIX) {
    10812:         PetscMPIInt size;

    10814:         MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);
    10815:         if (size == 1) {
    10816:           MatHasOperation(mat,MATOP_CREATE_SUBMATRICES,has);
    10817:         }
    10818:       }
    10819:     }
    10820:   }
    10821:   return(0);
    10822: }

    10824: /*@
    10825:     MatHasCongruentLayouts - Determines whether the rows and columns layouts
    10826:     of the matrix are congruent

    10828:    Collective on mat

    10830:    Input Parameters:
    10831: .  mat - the matrix

    10833:    Output Parameter:
    10834: .  cong - either PETSC_TRUE or PETSC_FALSE

    10836:    Level: beginner

    10838:    Notes:

    10840: .seealso: MatCreate(), MatSetSizes()
    10841: @*/
    10842: PetscErrorCode MatHasCongruentLayouts(Mat mat,PetscBool *cong)
    10843: {

    10850:   if (!mat->rmap || !mat->cmap) {
    10851:     *cong = mat->rmap == mat->cmap ? PETSC_TRUE : PETSC_FALSE;
    10852:     return(0);
    10853:   }
    10854:   if (mat->congruentlayouts == PETSC_DECIDE) { /* first time we compare rows and cols layouts */
    10855:     PetscLayoutCompare(mat->rmap,mat->cmap,cong);
    10856:     if (*cong) mat->congruentlayouts = 1;
    10857:     else       mat->congruentlayouts = 0;
    10858:   } else *cong = mat->congruentlayouts ? PETSC_TRUE : PETSC_FALSE;
    10859:   return(0);
    10860: }

    10862: PetscErrorCode MatSetInf(Mat A)
    10863: {

    10867:   if (!A->ops->setinf) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"No support for this operation for this matrix type");
    10868:   (*A->ops->setinf)(A);
    10869:   return(0);
    10870: }