Actual source code: matrix.c

      1: /*
      2:    This is where the abstract matrix operations are defined
      3:    Portions of this code are under:
      4:    Copyright (c) 2022 Advanced Micro Devices, Inc. All rights reserved.
      5: */

      7: #include <petsc/private/matimpl.h>
      8: #include <petsc/private/isimpl.h>
      9: #include <petsc/private/vecimpl.h>

     11: /* Logging support */
     12: PetscClassId MAT_CLASSID;
     13: PetscClassId MAT_COLORING_CLASSID;
     14: PetscClassId MAT_FDCOLORING_CLASSID;
     15: PetscClassId MAT_TRANSPOSECOLORING_CLASSID;

     17: PetscLogEvent MAT_Mult, MAT_MultAdd, MAT_MultTranspose;
     18: PetscLogEvent MAT_ADot, MAT_ANorm;
     19: PetscLogEvent MAT_MultTransposeAdd, MAT_Solve, MAT_Solves, MAT_SolveAdd, MAT_SolveTranspose, MAT_MatSolve, MAT_MatTrSolve;
     20: PetscLogEvent MAT_SolveTransposeAdd, MAT_SOR, MAT_ForwardSolve, MAT_BackwardSolve, MAT_LUFactor, MAT_LUFactorSymbolic;
     21: PetscLogEvent MAT_LUFactorNumeric, MAT_CholeskyFactor, MAT_CholeskyFactorSymbolic, MAT_CholeskyFactorNumeric, MAT_ILUFactor;
     22: PetscLogEvent MAT_ILUFactorSymbolic, MAT_ICCFactorSymbolic, MAT_Copy, MAT_Convert, MAT_Scale, MAT_AssemblyBegin;
     23: PetscLogEvent MAT_QRFactorNumeric, MAT_QRFactorSymbolic, MAT_QRFactor;
     24: PetscLogEvent MAT_AssemblyEnd, MAT_SetValues, MAT_GetValues, MAT_GetRow, MAT_GetRowIJ, MAT_CreateSubMats, MAT_GetOrdering, MAT_RedundantMat, MAT_GetSeqNonzeroStructure;
     25: PetscLogEvent MAT_IncreaseOverlap, MAT_Partitioning, MAT_PartitioningND, MAT_Coarsen, MAT_ZeroEntries, MAT_Load, MAT_View, MAT_AXPY, MAT_FDColoringCreate;
     26: PetscLogEvent MAT_FDColoringSetUp, MAT_FDColoringApply, MAT_Transpose, MAT_FDColoringFunction, MAT_CreateSubMat;
     27: PetscLogEvent MAT_TransposeColoringCreate;
     28: PetscLogEvent MAT_MatMult, MAT_MatMultSymbolic, MAT_MatMultNumeric;
     29: PetscLogEvent MAT_PtAP, MAT_PtAPSymbolic, MAT_PtAPNumeric, MAT_RARt, MAT_RARtSymbolic, MAT_RARtNumeric;
     30: PetscLogEvent MAT_MatTransposeMult, MAT_MatTransposeMultSymbolic, MAT_MatTransposeMultNumeric;
     31: PetscLogEvent MAT_TransposeMatMult, MAT_TransposeMatMultSymbolic, MAT_TransposeMatMultNumeric;
     32: PetscLogEvent MAT_MatMatMult, MAT_MatMatMultSymbolic, MAT_MatMatMultNumeric;
     33: PetscLogEvent MAT_MultHermitianTranspose, MAT_MultHermitianTransposeAdd;
     34: PetscLogEvent MAT_Getsymtransreduced, MAT_GetBrowsOfAcols;
     35: PetscLogEvent MAT_GetBrowsOfAocols, MAT_Getlocalmat, MAT_Getlocalmatcondensed, MAT_Seqstompi, MAT_Seqstompinum, MAT_Seqstompisym;
     36: PetscLogEvent MAT_GetMultiProcBlock;
     37: PetscLogEvent MAT_CUSPARSECopyToGPU, MAT_CUSPARSECopyFromGPU, MAT_CUSPARSEGenerateTranspose, MAT_CUSPARSESolveAnalysis;
     38: PetscLogEvent MAT_HIPSPARSECopyToGPU, MAT_HIPSPARSECopyFromGPU, MAT_HIPSPARSEGenerateTranspose, MAT_HIPSPARSESolveAnalysis;
     39: PetscLogEvent MAT_PreallCOO, MAT_SetVCOO;
     40: PetscLogEvent MAT_CreateGraph;
     41: PetscLogEvent MAT_SetValuesBatch;
     42: PetscLogEvent MAT_ViennaCLCopyToGPU;
     43: PetscLogEvent MAT_CUDACopyToGPU, MAT_HIPCopyToGPU;
     44: PetscLogEvent MAT_DenseCopyToGPU, MAT_DenseCopyFromGPU;
     45: PetscLogEvent MAT_Merge, MAT_Residual, MAT_SetRandom;
     46: PetscLogEvent MAT_FactorFactS, MAT_FactorInvS;
     47: PetscLogEvent MATCOLORING_Apply, MATCOLORING_Comm, MATCOLORING_Local, MATCOLORING_ISCreate, MATCOLORING_SetUp, MATCOLORING_Weights;
     48: PetscLogEvent MAT_H2Opus_Build, MAT_H2Opus_Compress, MAT_H2Opus_Orthog, MAT_H2Opus_LR;

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

     52: /*@
     53:   MatSetRandom - Sets all components of a matrix to random numbers.

     55:   Logically Collective

     57:   Input Parameters:
     58: + x    - the matrix
     59: - rctx - the `PetscRandom` object, formed by `PetscRandomCreate()`, or `NULL` and
     60:           it will create one internally.

     62:   Example:
     63: .vb
     64:      PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
     65:      MatSetRandom(x,rctx);
     66:      PetscRandomDestroy(rctx);
     67: .ve

     69:   Level: intermediate

     71:   Notes:
     72:   For sparse matrices that have been preallocated but not been assembled, it randomly selects appropriate locations,

     74:   for sparse matrices that already have nonzero locations, it fills the locations with random numbers.

     76:   It generates an error if used on unassembled sparse matrices that have not been preallocated.

     78: .seealso: [](ch_matrices), `Mat`, `PetscRandom`, `PetscRandomCreate()`, `MatZeroEntries()`, `MatSetValues()`, `PetscRandomDestroy()`
     79: @*/
     80: PetscErrorCode MatSetRandom(Mat x, PetscRandom rctx)
     81: {
     82:   PetscRandom randObj = NULL;

     84:   PetscFunctionBegin;
     88:   MatCheckPreallocated(x, 1);

     90:   if (!rctx) {
     91:     MPI_Comm comm;
     92:     PetscCall(PetscObjectGetComm((PetscObject)x, &comm));
     93:     PetscCall(PetscRandomCreate(comm, &randObj));
     94:     PetscCall(PetscRandomSetType(randObj, x->defaultrandtype));
     95:     PetscCall(PetscRandomSetFromOptions(randObj));
     96:     rctx = randObj;
     97:   }
     98:   PetscCall(PetscLogEventBegin(MAT_SetRandom, x, rctx, 0, 0));
     99:   PetscUseTypeMethod(x, setrandom, rctx);
    100:   PetscCall(PetscLogEventEnd(MAT_SetRandom, x, rctx, 0, 0));

    102:   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
    103:   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
    104:   PetscCall(PetscRandomDestroy(&randObj));
    105:   PetscFunctionReturn(PETSC_SUCCESS);
    106: }

    108: /*@
    109:   MatCopyHashToXAIJ - copy hash table entries into an XAIJ matrix type

    111:   Logically Collective

    113:   Input Parameter:
    114: . A - A matrix in unassembled, hash table form

    116:   Output Parameter:
    117: . B - The XAIJ matrix. This can either be `A` or some matrix of equivalent size, e.g. obtained from `A` via `MatDuplicate()`

    119:   Example:
    120: .vb
    121:      PetscCall(MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &B));
    122:      PetscCall(MatCopyHashToXAIJ(A, B));
    123: .ve

    125:   Level: advanced

    127:   Notes:
    128:   If `B` is `A`, then the hash table data structure will be destroyed. `B` is assembled

    130: .seealso: [](ch_matrices), `Mat`, `MAT_USE_HASH_TABLE`
    131: @*/
    132: PetscErrorCode MatCopyHashToXAIJ(Mat A, Mat B)
    133: {
    134:   PetscFunctionBegin;
    136:   PetscUseTypeMethod(A, copyhashtoxaij, B);
    137:   PetscFunctionReturn(PETSC_SUCCESS);
    138: }

    140: /*@
    141:   MatFactorGetErrorZeroPivot - returns the pivot value that was determined to be zero and the row it occurred in

    143:   Logically Collective

    145:   Input Parameter:
    146: . mat - the factored matrix

    148:   Output Parameters:
    149: + pivot - the pivot value computed
    150: - row   - the row that the zero pivot occurred. This row value must be interpreted carefully due to row reorderings and which processes
    151:          the share the matrix

    153:   Level: advanced

    155:   Notes:
    156:   This routine does not work for factorizations done with external packages.

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

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

    162: .seealso: [](ch_matrices), `Mat`, `MatZeroEntries()`, `MatFactor()`, `MatGetFactor()`,
    163: `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`, `MatFactorClearError()`,
    164: `MAT_FACTOR_NUMERIC_ZEROPIVOT`
    165: @*/
    166: PetscErrorCode MatFactorGetErrorZeroPivot(Mat mat, PetscReal *pivot, PetscInt *row)
    167: {
    168:   PetscFunctionBegin;
    170:   PetscAssertPointer(pivot, 2);
    171:   PetscAssertPointer(row, 3);
    172:   *pivot = mat->factorerror_zeropivot_value;
    173:   *row   = mat->factorerror_zeropivot_row;
    174:   PetscFunctionReturn(PETSC_SUCCESS);
    175: }

    177: /*@
    178:   MatFactorGetError - gets the error code from a factorization

    180:   Logically Collective

    182:   Input Parameter:
    183: . mat - the factored matrix

    185:   Output Parameter:
    186: . err - the error code

    188:   Level: advanced

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

    193: .seealso: [](ch_matrices), `Mat`, `MatZeroEntries()`, `MatFactor()`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`,
    194:           `MatFactorClearError()`, `MatFactorGetErrorZeroPivot()`, `MatFactorError`
    195: @*/
    196: PetscErrorCode MatFactorGetError(Mat mat, MatFactorError *err)
    197: {
    198:   PetscFunctionBegin;
    200:   PetscAssertPointer(err, 2);
    201:   *err = mat->factorerrortype;
    202:   PetscFunctionReturn(PETSC_SUCCESS);
    203: }

    205: /*@
    206:   MatFactorClearError - clears the error code in a factorization

    208:   Logically Collective

    210:   Input Parameter:
    211: . mat - the factored matrix

    213:   Level: developer

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

    218: .seealso: [](ch_matrices), `Mat`, `MatZeroEntries()`, `MatFactor()`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`, `MatFactorGetError()`, `MatFactorGetErrorZeroPivot()`,
    219:           `MatGetErrorCode()`, `MatFactorError`
    220: @*/
    221: PetscErrorCode MatFactorClearError(Mat mat)
    222: {
    223:   PetscFunctionBegin;
    225:   mat->factorerrortype             = MAT_FACTOR_NOERROR;
    226:   mat->factorerror_zeropivot_value = 0.0;
    227:   mat->factorerror_zeropivot_row   = 0;
    228:   PetscFunctionReturn(PETSC_SUCCESS);
    229: }

    231: PetscErrorCode MatFindNonzeroRowsOrCols_Basic(Mat mat, PetscBool cols, PetscReal tol, IS *nonzero)
    232: {
    233:   Vec                r, l;
    234:   const PetscScalar *al;
    235:   PetscInt           i, nz, gnz, N, n, st;

    237:   PetscFunctionBegin;
    238:   PetscCall(MatCreateVecs(mat, &r, &l));
    239:   if (!cols) { /* nonzero rows */
    240:     PetscCall(MatGetOwnershipRange(mat, &st, NULL));
    241:     PetscCall(MatGetSize(mat, &N, NULL));
    242:     PetscCall(MatGetLocalSize(mat, &n, NULL));
    243:     PetscCall(VecSet(l, 0.0));
    244:     PetscCall(VecSetRandom(r, NULL));
    245:     PetscCall(MatMult(mat, r, l));
    246:     PetscCall(VecGetArrayRead(l, &al));
    247:   } else { /* nonzero columns */
    248:     PetscCall(MatGetOwnershipRangeColumn(mat, &st, NULL));
    249:     PetscCall(MatGetSize(mat, NULL, &N));
    250:     PetscCall(MatGetLocalSize(mat, NULL, &n));
    251:     PetscCall(VecSet(r, 0.0));
    252:     PetscCall(VecSetRandom(l, NULL));
    253:     PetscCall(MatMultTranspose(mat, l, r));
    254:     PetscCall(VecGetArrayRead(r, &al));
    255:   }
    256:   if (tol <= 0.0) {
    257:     for (i = 0, nz = 0; i < n; i++)
    258:       if (al[i] != 0.0) nz++;
    259:   } else {
    260:     for (i = 0, nz = 0; i < n; i++)
    261:       if (PetscAbsScalar(al[i]) > tol) nz++;
    262:   }
    263:   PetscCallMPI(MPIU_Allreduce(&nz, &gnz, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)mat)));
    264:   if (gnz != N) {
    265:     PetscInt *nzr;
    266:     PetscCall(PetscMalloc1(nz, &nzr));
    267:     if (nz) {
    268:       if (tol < 0) {
    269:         for (i = 0, nz = 0; i < n; i++)
    270:           if (al[i] != 0.0) nzr[nz++] = i + st;
    271:       } else {
    272:         for (i = 0, nz = 0; i < n; i++)
    273:           if (PetscAbsScalar(al[i]) > tol) nzr[nz++] = i + st;
    274:       }
    275:     }
    276:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)mat), nz, nzr, PETSC_OWN_POINTER, nonzero));
    277:   } else *nonzero = NULL;
    278:   if (!cols) { /* nonzero rows */
    279:     PetscCall(VecRestoreArrayRead(l, &al));
    280:   } else {
    281:     PetscCall(VecRestoreArrayRead(r, &al));
    282:   }
    283:   PetscCall(VecDestroy(&l));
    284:   PetscCall(VecDestroy(&r));
    285:   PetscFunctionReturn(PETSC_SUCCESS);
    286: }

    288: /*@
    289:   MatFindNonzeroRows - Locate all rows that are not completely zero in the matrix

    291:   Input Parameter:
    292: . mat - the matrix

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

    297:   Level: intermediate

    299:   Note:
    300:   `keptrows` is set to `NULL` if all rows are nonzero.

    302:   Developer Note:
    303:   If `keptrows` is not `NULL`, it must be sorted.

    305: .seealso: [](ch_matrices), `Mat`, `MatFindZeroRows()`
    306:  @*/
    307: PetscErrorCode MatFindNonzeroRows(Mat mat, IS *keptrows)
    308: {
    309:   PetscFunctionBegin;
    312:   PetscAssertPointer(keptrows, 2);
    313:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    314:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    315:   if (mat->ops->findnonzerorows) PetscUseTypeMethod(mat, findnonzerorows, keptrows);
    316:   else PetscCall(MatFindNonzeroRowsOrCols_Basic(mat, PETSC_FALSE, 0.0, keptrows));
    317:   if (keptrows && *keptrows) PetscCall(ISSetInfo(*keptrows, IS_SORTED, IS_GLOBAL, PETSC_FALSE, PETSC_TRUE));
    318:   PetscFunctionReturn(PETSC_SUCCESS);
    319: }

    321: /*@
    322:   MatFindZeroRows - Locate all rows that are completely zero in the matrix

    324:   Input Parameter:
    325: . mat - the matrix

    327:   Output Parameter:
    328: . zerorows - the rows that are completely zero

    330:   Level: intermediate

    332:   Note:
    333:   `zerorows` is set to `NULL` if no rows are zero.

    335: .seealso: [](ch_matrices), `Mat`, `MatFindNonzeroRows()`
    336:  @*/
    337: PetscErrorCode MatFindZeroRows(Mat mat, IS *zerorows)
    338: {
    339:   IS       keptrows;
    340:   PetscInt m, n;

    342:   PetscFunctionBegin;
    345:   PetscAssertPointer(zerorows, 2);
    346:   PetscCall(MatFindNonzeroRows(mat, &keptrows));
    347:   /* MatFindNonzeroRows sets keptrows to NULL if there are no zero rows.
    348:      In keeping with this convention, we set zerorows to NULL if there are no zero
    349:      rows. */
    350:   if (keptrows == NULL) {
    351:     *zerorows = NULL;
    352:   } else {
    353:     PetscCall(MatGetOwnershipRange(mat, &m, &n));
    354:     PetscCall(ISComplement(keptrows, m, n, zerorows));
    355:     PetscCall(ISDestroy(&keptrows));
    356:   }
    357:   PetscFunctionReturn(PETSC_SUCCESS);
    358: }

    360: /*@
    361:   MatGetDiagonalBlock - Returns the part of the matrix associated with the on-process coupling

    363:   Not Collective

    365:   Input Parameter:
    366: . A - the matrix

    368:   Output Parameter:
    369: . a - the diagonal part (which is a SEQUENTIAL matrix)

    371:   Level: advanced

    373:   Notes:
    374:   See `MatCreateAIJ()` for more information on the "diagonal part" of the matrix.

    376:   Use caution, as the reference count on the returned matrix is not incremented and it is used as part of `A`'s normal operation.

    378: .seealso: [](ch_matrices), `Mat`, `MatCreateAIJ()`, `MATAIJ`, `MATBAIJ`, `MATSBAIJ`
    379: @*/
    380: PetscErrorCode MatGetDiagonalBlock(Mat A, Mat *a)
    381: {
    382:   PetscFunctionBegin;
    385:   PetscAssertPointer(a, 2);
    386:   PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    387:   if (A->ops->getdiagonalblock) PetscUseTypeMethod(A, getdiagonalblock, a);
    388:   else {
    389:     PetscMPIInt size;

    391:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    392:     PetscCheck(size == 1, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for parallel matrix type %s", ((PetscObject)A)->type_name);
    393:     *a = A;
    394:   }
    395:   PetscFunctionReturn(PETSC_SUCCESS);
    396: }

    398: /*@
    399:   MatGetTrace - Gets the trace of a matrix. The sum of the diagonal entries.

    401:   Collective

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

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

    409:   Level: advanced

    411: .seealso: [](ch_matrices), `Mat`
    412: @*/
    413: PetscErrorCode MatGetTrace(Mat mat, PetscScalar *trace)
    414: {
    415:   Vec diag;

    417:   PetscFunctionBegin;
    419:   PetscAssertPointer(trace, 2);
    420:   PetscCall(MatCreateVecs(mat, &diag, NULL));
    421:   PetscCall(MatGetDiagonal(mat, diag));
    422:   PetscCall(VecSum(diag, trace));
    423:   PetscCall(VecDestroy(&diag));
    424:   PetscFunctionReturn(PETSC_SUCCESS);
    425: }

    427: /*@
    428:   MatRealPart - Zeros out the imaginary part of the matrix

    430:   Logically Collective

    432:   Input Parameter:
    433: . mat - the matrix

    435:   Level: advanced

    437: .seealso: [](ch_matrices), `Mat`, `MatImaginaryPart()`
    438: @*/
    439: PetscErrorCode MatRealPart(Mat mat)
    440: {
    441:   PetscFunctionBegin;
    444:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    445:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    446:   MatCheckPreallocated(mat, 1);
    447:   PetscUseTypeMethod(mat, realpart);
    448:   PetscFunctionReturn(PETSC_SUCCESS);
    449: }

    451: /*@C
    452:   MatGetGhosts - Get the global indices of all ghost nodes defined by the sparse matrix

    454:   Collective

    456:   Input Parameter:
    457: . mat - the matrix

    459:   Output Parameters:
    460: + nghosts - number of ghosts (for `MATBAIJ` and `MATSBAIJ` matrices there is one ghost for each matrix block)
    461: - ghosts  - the global indices of the ghost points

    463:   Level: advanced

    465:   Note:
    466:   `nghosts` and `ghosts` are suitable to pass into `VecCreateGhost()` or `VecCreateGhostBlock()`

    468: .seealso: [](ch_matrices), `Mat`, `VecCreateGhost()`, `VecCreateGhostBlock()`
    469: @*/
    470: PetscErrorCode MatGetGhosts(Mat mat, PetscInt *nghosts, const PetscInt *ghosts[])
    471: {
    472:   PetscFunctionBegin;
    475:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    476:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    477:   if (mat->ops->getghosts) PetscUseTypeMethod(mat, getghosts, nghosts, ghosts);
    478:   else {
    479:     if (nghosts) *nghosts = 0;
    480:     if (ghosts) *ghosts = NULL;
    481:   }
    482:   PetscFunctionReturn(PETSC_SUCCESS);
    483: }

    485: /*@
    486:   MatImaginaryPart - Moves the imaginary part of the matrix to the real part and zeros the imaginary part

    488:   Logically Collective

    490:   Input Parameter:
    491: . mat - the matrix

    493:   Level: advanced

    495: .seealso: [](ch_matrices), `Mat`, `MatRealPart()`
    496: @*/
    497: PetscErrorCode MatImaginaryPart(Mat mat)
    498: {
    499:   PetscFunctionBegin;
    502:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    503:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    504:   MatCheckPreallocated(mat, 1);
    505:   PetscUseTypeMethod(mat, imaginarypart);
    506:   PetscFunctionReturn(PETSC_SUCCESS);
    507: }

    509: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    510: /*@C
    511:   MatGetRow - Gets a row of a matrix.  You MUST call `MatRestoreRow()`
    512:   for each row that you get to ensure that your application does
    513:   not bleed memory.

    515:   Not Collective

    517:   Input Parameters:
    518: + mat - the matrix
    519: - row - the row to get

    521:   Output Parameters:
    522: + ncols - if not `NULL`, the number of nonzeros in `row`
    523: . cols  - if not `NULL`, the column numbers
    524: - vals  - if not `NULL`, the numerical values

    526:   Level: advanced

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

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

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

    539:   The user can only examine the values extracted with `MatGetRow()`;
    540:   the values CANNOT be altered.  To change the matrix entries, one
    541:   must use `MatSetValues()`.

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

    550:   Use `MatGetRowIJ()` and `MatRestoreRowIJ()` to access all the local indices of the sparse matrix.

    552:   Use `MatSeqAIJGetArray()` and similar functions to access the numerical values for certain matrix types directly.

    554:   Fortran Note:
    555: .vb
    556:   PetscInt, pointer :: cols(:)
    557:   PetscScalar, pointer :: vals(:)
    558: .ve

    560: .seealso: [](ch_matrices), `Mat`, `MatRestoreRow()`, `MatSetValues()`, `MatGetValues()`, `MatCreateSubMatrices()`, `MatGetDiagonal()`, `MatGetRowIJ()`, `MatRestoreRowIJ()`
    561: @*/
    562: PetscErrorCode MatGetRow(Mat mat, PetscInt row, PetscInt *ncols, const PetscInt *cols[], const PetscScalar *vals[])
    563: {
    564:   PetscInt incols;

    566:   PetscFunctionBegin;
    569:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    570:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    571:   MatCheckPreallocated(mat, 1);
    572:   PetscCheck(row >= mat->rmap->rstart && row < mat->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Only for local rows, %" PetscInt_FMT " not in [%" PetscInt_FMT ",%" PetscInt_FMT ")", row, mat->rmap->rstart, mat->rmap->rend);
    573:   PetscCall(PetscLogEventBegin(MAT_GetRow, mat, 0, 0, 0));
    574:   PetscUseTypeMethod(mat, getrow, row, &incols, (PetscInt **)cols, (PetscScalar **)vals);
    575:   if (ncols) *ncols = incols;
    576:   PetscCall(PetscLogEventEnd(MAT_GetRow, mat, 0, 0, 0));
    577:   PetscFunctionReturn(PETSC_SUCCESS);
    578: }

    580: /*@
    581:   MatConjugate - replaces the matrix values with their complex conjugates

    583:   Logically Collective

    585:   Input Parameter:
    586: . mat - the matrix

    588:   Level: advanced

    590: .seealso: [](ch_matrices), `Mat`, `MatRealPart()`, `MatImaginaryPart()`, `VecConjugate()`, `MatTranspose()`
    591: @*/
    592: PetscErrorCode MatConjugate(Mat mat)
    593: {
    594:   PetscFunctionBegin;
    596:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    597:   if (PetscDefined(USE_COMPLEX) && !(mat->symmetric == PETSC_BOOL3_TRUE && mat->hermitian == PETSC_BOOL3_TRUE)) {
    598:     PetscUseTypeMethod(mat, conjugate);
    599:     PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    600:   }
    601:   PetscFunctionReturn(PETSC_SUCCESS);
    602: }

    604: /*@C
    605:   MatRestoreRow - Frees any temporary space allocated by `MatGetRow()`.

    607:   Not Collective

    609:   Input Parameters:
    610: + mat   - the matrix
    611: . row   - the row to get
    612: . ncols - the number of nonzeros
    613: . cols  - the columns of the nonzeros
    614: - vals  - if nonzero the column values

    616:   Level: advanced

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

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

    625:   Fortran Note:
    626: .vb
    627:   PetscInt, pointer :: cols(:)
    628:   PetscScalar, pointer :: vals(:)
    629: .ve

    631: .seealso: [](ch_matrices), `Mat`, `MatGetRow()`
    632: @*/
    633: PetscErrorCode MatRestoreRow(Mat mat, PetscInt row, PetscInt *ncols, const PetscInt *cols[], const PetscScalar *vals[])
    634: {
    635:   PetscFunctionBegin;
    637:   if (ncols) PetscAssertPointer(ncols, 3);
    638:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    639:   PetscTryTypeMethod(mat, restorerow, row, ncols, (PetscInt **)cols, (PetscScalar **)vals);
    640:   if (ncols) *ncols = 0;
    641:   if (cols) *cols = NULL;
    642:   if (vals) *vals = NULL;
    643:   PetscFunctionReturn(PETSC_SUCCESS);
    644: }

    646: /*@
    647:   MatGetRowUpperTriangular - Sets a flag to enable calls to `MatGetRow()` for matrix in `MATSBAIJ` format.
    648:   You should call `MatRestoreRowUpperTriangular()` after calling` MatGetRow()` and `MatRestoreRow()` to disable the flag.

    650:   Not Collective

    652:   Input Parameter:
    653: . mat - the matrix

    655:   Level: advanced

    657:   Note:
    658:   The flag is to ensure that users are aware that `MatGetRow()` only provides the upper triangular part of the row for the matrices in `MATSBAIJ` format.

    660: .seealso: [](ch_matrices), `Mat`, `MATSBAIJ`, `MatRestoreRowUpperTriangular()`
    661: @*/
    662: PetscErrorCode MatGetRowUpperTriangular(Mat mat)
    663: {
    664:   PetscFunctionBegin;
    667:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    668:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    669:   MatCheckPreallocated(mat, 1);
    670:   PetscTryTypeMethod(mat, getrowuppertriangular);
    671:   PetscFunctionReturn(PETSC_SUCCESS);
    672: }

    674: /*@
    675:   MatRestoreRowUpperTriangular - Disable calls to `MatGetRow()` for matrix in `MATSBAIJ` format.

    677:   Not Collective

    679:   Input Parameter:
    680: . mat - the matrix

    682:   Level: advanced

    684:   Note:
    685:   This routine should be called after you have finished calls to `MatGetRow()` and `MatRestoreRow()`.

    687: .seealso: [](ch_matrices), `Mat`, `MATSBAIJ`, `MatGetRowUpperTriangular()`
    688: @*/
    689: PetscErrorCode MatRestoreRowUpperTriangular(Mat mat)
    690: {
    691:   PetscFunctionBegin;
    694:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    695:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    696:   MatCheckPreallocated(mat, 1);
    697:   PetscTryTypeMethod(mat, restorerowuppertriangular);
    698:   PetscFunctionReturn(PETSC_SUCCESS);
    699: }

    701: /*@
    702:   MatSetOptionsPrefix - Sets the prefix used for searching for all
    703:   `Mat` options in the database.

    705:   Logically Collective

    707:   Input Parameters:
    708: + A      - the matrix
    709: - prefix - the prefix to prepend to all option names

    711:   Level: advanced

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

    717:   This is NOT used for options for the factorization of the matrix. Normally the
    718:   prefix is automatically passed in from the PC calling the factorization. To set
    719:   it directly use  `MatSetOptionsPrefixFactor()`

    721: .seealso: [](ch_matrices), `Mat`, `MatSetFromOptions()`, `MatSetOptionsPrefixFactor()`
    722: @*/
    723: PetscErrorCode MatSetOptionsPrefix(Mat A, const char prefix[])
    724: {
    725:   PetscFunctionBegin;
    727:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)A, prefix));
    728:   PetscTryMethod(A, "MatSetOptionsPrefix_C", (Mat, const char[]), (A, prefix));
    729:   PetscFunctionReturn(PETSC_SUCCESS);
    730: }

    732: /*@
    733:   MatSetOptionsPrefixFactor - Sets the prefix used for searching for all matrix factor options in the database for
    734:   for matrices created with `MatGetFactor()`

    736:   Logically Collective

    738:   Input Parameters:
    739: + A      - the matrix
    740: - prefix - the prefix to prepend to all option names for the factored matrix

    742:   Level: developer

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

    748:   Normally the prefix is automatically passed in from the `PC` calling the factorization. To set
    749:   it directly when not using `KSP`/`PC` use  `MatSetOptionsPrefixFactor()`

    751: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatSetFromOptions()`, `MatSetOptionsPrefix()`, `MatAppendOptionsPrefixFactor()`
    752: @*/
    753: PetscErrorCode MatSetOptionsPrefixFactor(Mat A, const char prefix[])
    754: {
    755:   PetscFunctionBegin;
    757:   if (prefix) {
    758:     PetscAssertPointer(prefix, 2);
    759:     PetscCheck(prefix[0] != '-', PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Options prefix should not begin with a hyphen");
    760:     if (prefix != A->factorprefix) {
    761:       PetscCall(PetscFree(A->factorprefix));
    762:       PetscCall(PetscStrallocpy(prefix, &A->factorprefix));
    763:     }
    764:   } else PetscCall(PetscFree(A->factorprefix));
    765:   PetscFunctionReturn(PETSC_SUCCESS);
    766: }

    768: /*@
    769:   MatAppendOptionsPrefixFactor - Appends to the prefix used for searching for all matrix factor options in the database for
    770:   for matrices created with `MatGetFactor()`

    772:   Logically Collective

    774:   Input Parameters:
    775: + A      - the matrix
    776: - prefix - the prefix to prepend to all option names for the factored matrix

    778:   Level: developer

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

    784:   Normally the prefix is automatically passed in from the `PC` calling the factorization. To set
    785:   it directly when not using `KSP`/`PC` use  `MatAppendOptionsPrefixFactor()`

    787: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `PetscOptionsCreate()`, `PetscOptionsDestroy()`, `PetscObjectSetOptionsPrefix()`, `PetscObjectPrependOptionsPrefix()`,
    788:           `PetscObjectGetOptionsPrefix()`, `TSAppendOptionsPrefix()`, `SNESAppendOptionsPrefix()`, `KSPAppendOptionsPrefix()`, `MatSetOptionsPrefixFactor()`,
    789:           `MatSetOptionsPrefix()`
    790: @*/
    791: PetscErrorCode MatAppendOptionsPrefixFactor(Mat A, const char prefix[])
    792: {
    793:   size_t len1, len2, new_len;

    795:   PetscFunctionBegin;
    797:   if (!prefix) PetscFunctionReturn(PETSC_SUCCESS);
    798:   if (!A->factorprefix) {
    799:     PetscCall(MatSetOptionsPrefixFactor(A, prefix));
    800:     PetscFunctionReturn(PETSC_SUCCESS);
    801:   }
    802:   PetscCheck(prefix[0] != '-', PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Options prefix should not begin with a hyphen");

    804:   PetscCall(PetscStrlen(A->factorprefix, &len1));
    805:   PetscCall(PetscStrlen(prefix, &len2));
    806:   new_len = len1 + len2 + 1;
    807:   PetscCall(PetscRealloc(new_len * sizeof(*A->factorprefix), &A->factorprefix));
    808:   PetscCall(PetscStrncpy(A->factorprefix + len1, prefix, len2 + 1));
    809:   PetscFunctionReturn(PETSC_SUCCESS);
    810: }

    812: /*@
    813:   MatAppendOptionsPrefix - Appends to the prefix used for searching for all
    814:   matrix options in the database.

    816:   Logically Collective

    818:   Input Parameters:
    819: + A      - the matrix
    820: - prefix - the prefix to prepend to all option names

    822:   Level: advanced

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

    828: .seealso: [](ch_matrices), `Mat`, `MatGetOptionsPrefix()`, `MatAppendOptionsPrefixFactor()`, `MatSetOptionsPrefix()`
    829: @*/
    830: PetscErrorCode MatAppendOptionsPrefix(Mat A, const char prefix[])
    831: {
    832:   PetscFunctionBegin;
    834:   PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)A, prefix));
    835:   PetscTryMethod(A, "MatAppendOptionsPrefix_C", (Mat, const char[]), (A, prefix));
    836:   PetscFunctionReturn(PETSC_SUCCESS);
    837: }

    839: /*@
    840:   MatGetOptionsPrefix - Gets the prefix used for searching for all
    841:   matrix options in the database.

    843:   Not Collective

    845:   Input Parameter:
    846: . A - the matrix

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

    851:   Level: advanced

    853: .seealso: [](ch_matrices), `Mat`, `MatAppendOptionsPrefix()`, `MatSetOptionsPrefix()`, `MatAppendOptionsPrefixFactor()`, `MatSetOptionsPrefixFactor()`
    854: @*/
    855: PetscErrorCode MatGetOptionsPrefix(Mat A, const char *prefix[])
    856: {
    857:   PetscFunctionBegin;
    859:   PetscAssertPointer(prefix, 2);
    860:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)A, prefix));
    861:   PetscFunctionReturn(PETSC_SUCCESS);
    862: }

    864: /*@
    865:   MatGetState - Gets the state of a `Mat`. Same value as returned by `PetscObjectStateGet()`

    867:   Not Collective

    869:   Input Parameter:
    870: . A - the matrix

    872:   Output Parameter:
    873: . state - the object state

    875:   Level: advanced

    877:   Note:
    878:   Object state is an integer which gets increased every time
    879:   the object is changed. By saving and later querying the object state
    880:   one can determine whether information about the object is still current.

    882:   See `MatGetNonzeroState()` to determine if the nonzero structure of the matrix has changed.

    884: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `PetscObjectStateGet()`, `MatGetNonzeroState()`
    885: @*/
    886: PetscErrorCode MatGetState(Mat A, PetscObjectState *state)
    887: {
    888:   PetscFunctionBegin;
    890:   PetscAssertPointer(state, 2);
    891:   PetscCall(PetscObjectStateGet((PetscObject)A, state));
    892:   PetscFunctionReturn(PETSC_SUCCESS);
    893: }

    895: /*@
    896:   MatResetPreallocation - Reset matrix to use the original preallocation values provided by the user, for example with `MatXAIJSetPreallocation()`

    898:   Collective

    900:   Input Parameter:
    901: . A - the matrix

    903:   Level: beginner

    905:   Notes:
    906:   After calling `MatAssemblyBegin()` and `MatAssemblyEnd()` with `MAT_FINAL_ASSEMBLY` the matrix data structures represent the nonzeros assigned to the
    907:   matrix. If that space is less than the preallocated space that extra preallocated space is no longer available to take on new values. `MatResetPreallocation()`
    908:   makes all of the preallocation space available

    910:   Current values in the matrix are lost in this call

    912:   Currently only supported for  `MATAIJ` matrices.

    914: .seealso: [](ch_matrices), `Mat`, `MatSeqAIJSetPreallocation()`, `MatMPIAIJSetPreallocation()`, `MatXAIJSetPreallocation()`
    915: @*/
    916: PetscErrorCode MatResetPreallocation(Mat A)
    917: {
    918:   PetscFunctionBegin;
    921:   PetscUseMethod(A, "MatResetPreallocation_C", (Mat), (A));
    922:   PetscFunctionReturn(PETSC_SUCCESS);
    923: }

    925: /*@
    926:   MatResetHash - Reset the matrix so that it will use a hash table for the next round of `MatSetValues()` and `MatAssemblyBegin()`/`MatAssemblyEnd()`.

    928:   Collective

    930:   Input Parameter:
    931: . A - the matrix

    933:   Level: intermediate

    935:   Notes:
    936:   The matrix will again delete the hash table data structures after following calls to `MatAssemblyBegin()`/`MatAssemblyEnd()` with `MAT_FINAL_ASSEMBLY`.

    938:   Currently only supported for `MATAIJ` matrices.

    940: .seealso: [](ch_matrices), `Mat`, `MatResetPreallocation()`
    941: @*/
    942: PetscErrorCode MatResetHash(Mat A)
    943: {
    944:   PetscFunctionBegin;
    947:   PetscCheck(A->insertmode == NOT_SET_VALUES, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot reset to hash state after setting some values but not yet calling MatAssemblyBegin()/MatAssemblyEnd()");
    948:   if (A->num_ass == 0) PetscFunctionReturn(PETSC_SUCCESS);
    949:   PetscUseMethod(A, "MatResetHash_C", (Mat), (A));
    950:   /* These flags are used to determine whether certain setups occur */
    951:   A->was_assembled = PETSC_FALSE;
    952:   A->assembled     = PETSC_FALSE;
    953:   /* Log that the state of this object has changed; this will help guarantee that preconditioners get re-setup */
    954:   PetscCall(PetscObjectStateIncrease((PetscObject)A));
    955:   PetscFunctionReturn(PETSC_SUCCESS);
    956: }

    958: /*@
    959:   MatSetUp - Sets up the internal matrix data structures for later use by the matrix

    961:   Collective

    963:   Input Parameter:
    964: . A - the matrix

    966:   Level: advanced

    968:   Notes:
    969:   If the user has not set preallocation for this matrix then an efficient algorithm will be used for the first round of
    970:   setting values in the matrix.

    972:   This routine is called internally by other `Mat` functions when needed so rarely needs to be called by users

    974: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatCreate()`, `MatDestroy()`, `MatXAIJSetPreallocation()`
    975: @*/
    976: PetscErrorCode MatSetUp(Mat A)
    977: {
    978:   PetscFunctionBegin;
    980:   if (!((PetscObject)A)->type_name) {
    981:     PetscMPIInt size;

    983:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    984:     PetscCall(MatSetType(A, size == 1 ? MATSEQAIJ : MATMPIAIJ));
    985:   }
    986:   if (!A->preallocated) PetscTryTypeMethod(A, setup);
    987:   PetscCall(PetscLayoutSetUp(A->rmap));
    988:   PetscCall(PetscLayoutSetUp(A->cmap));
    989:   A->preallocated = PETSC_TRUE;
    990:   PetscFunctionReturn(PETSC_SUCCESS);
    991: }

    993: #if defined(PETSC_HAVE_SAWS)
    994: #include <petscviewersaws.h>
    995: #endif

    997: /*
    998:    If threadsafety is on extraneous matrices may be printed

    1000:    This flag cannot be stored in the matrix because the original matrix in MatView() may assemble a new matrix which is passed into MatViewFromOptions()
    1001: */
    1002: #if !defined(PETSC_HAVE_THREADSAFETY)
    1003: static PetscInt insidematview = 0;
    1004: #endif

    1006: /*@
    1007:   MatViewFromOptions - View properties of the matrix based on options set in the options database

    1009:   Collective

    1011:   Input Parameters:
    1012: + A    - the matrix
    1013: . obj  - optional additional object that provides the options prefix to use
    1014: - name - command line option

    1016:   Options Database Key:
    1017: . -name [viewertype][:...] - option name and values. See `PetscObjectViewFromOptions()` for the possible arguments

    1019:   Level: intermediate

    1021: .seealso: [](ch_matrices), `Mat`, `MatView()`, `PetscObjectViewFromOptions()`, `MatCreate()`
    1022: @*/
    1023: PetscErrorCode MatViewFromOptions(Mat A, PetscObject obj, const char name[])
    1024: {
    1025:   PetscFunctionBegin;
    1027: #if !defined(PETSC_HAVE_THREADSAFETY)
    1028:   if (insidematview) PetscFunctionReturn(PETSC_SUCCESS);
    1029: #endif
    1030:   PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
    1031:   PetscFunctionReturn(PETSC_SUCCESS);
    1032: }

    1034: /*@
    1035:   MatView - display information about a matrix in a variety ways

    1037:   Collective on viewer

    1039:   Input Parameters:
    1040: + mat    - the matrix
    1041: - viewer - visualization context

    1043:   Options Database Keys:
    1044: + -mat_view ::ascii_info         - Prints info on matrix at conclusion of `MatAssemblyEnd()`
    1045: . -mat_view ::ascii_info_detail  - Prints more detailed info
    1046: . -mat_view                      - Prints matrix in ASCII format
    1047: . -mat_view ::ascii_matlab       - Prints matrix in MATLAB format
    1048: . -mat_view draw                 - PetscDraws nonzero structure of matrix, using `MatView()` and `PetscDrawOpenX()`.
    1049: . -display name                  - Sets display name (default is host)
    1050: . -draw_pause sec                - Sets number of seconds to pause after display
    1051: . -mat_view socket               - Sends matrix to socket, can be accessed from MATLAB (see Users-Manual: ch_matlab for details)
    1052: . -viewer_socket_machine machine - -
    1053: . -viewer_socket_port port       - -
    1054: . -mat_view binary               - save matrix to file in binary format
    1055: - -viewer_binary_filename name   - -

    1057:   Level: beginner

    1059:   Notes:
    1060:   The available visualization contexts include
    1061: +    `PETSC_VIEWER_STDOUT_SELF`   - for sequential matrices
    1062: .    `PETSC_VIEWER_STDOUT_WORLD`  - for parallel matrices created on `PETSC_COMM_WORLD`
    1063: .    `PETSC_VIEWER_STDOUT_`(comm) - for matrices created on MPI communicator comm
    1064: -     `PETSC_VIEWER_DRAW_WORLD`   - graphical display of nonzero structure

    1066:   The user can open alternative visualization contexts with
    1067: +    `PetscViewerASCIIOpen()`  - Outputs matrix to a specified file
    1068: .    `PetscViewerBinaryOpen()` - Outputs matrix in binary to a  specified file; corresponding input uses `MatLoad()`
    1069: .    `PetscViewerDrawOpen()`   - Outputs nonzero matrix nonzero structure to an X window display
    1070: -    `PetscViewerSocketOpen()` - Outputs matrix to Socket viewer, `PETSCVIEWERSOCKET`. Only the `MATSEQDENSE` and `MATAIJ` types support this viewer.

    1072:   The user can call `PetscViewerPushFormat()` to specify the output
    1073:   format of ASCII printed objects (when using `PETSC_VIEWER_STDOUT_SELF`,
    1074:   `PETSC_VIEWER_STDOUT_WORLD` and `PetscViewerASCIIOpen()`).  Available formats include
    1075: +    `PETSC_VIEWER_DEFAULT`           - default, prints matrix contents
    1076: .    `PETSC_VIEWER_ASCII_MATLAB`      - prints matrix contents in MATLAB format
    1077: .    `PETSC_VIEWER_ASCII_DENSE`       - prints entire matrix including zeros
    1078: .    `PETSC_VIEWER_ASCII_COMMON`      - prints matrix contents, using a sparse  format common among all matrix types
    1079: .    `PETSC_VIEWER_ASCII_IMPL`        - prints matrix contents, using an implementation-specific format (which is in many cases the same as the default)
    1080: .    `PETSC_VIEWER_ASCII_INFO`        - prints basic information about the matrix size and structure (not the matrix entries)
    1081: -    `PETSC_VIEWER_ASCII_INFO_DETAIL` - prints more detailed information about the matrix nonzero structure (still not vector or matrix entries)

    1083:   The ASCII viewers are only recommended for small matrices on at most a moderate number of processes,
    1084:   the program will seemingly hang and take hours for larger matrices, for larger matrices one should use the binary format.

    1086:   In the debugger you can do "call MatView(mat,0)" to display the matrix. (The same holds for any PETSc object viewer).

    1088:   See the manual page for `MatLoad()` for the exact format of the binary file when the binary
    1089:   viewer is used.

    1091:   See share/petsc/matlab/PetscBinaryRead.m for a MATLAB code that can read in the binary file when the binary
    1092:   viewer is used and lib/petsc/bin/PetscBinaryIO.py for loading them into Python.

    1094:   One can use `-mat_view draw -draw_pause -1` to pause the graphical display of matrix nonzero structure,
    1095:   and then use the following mouse functions.
    1096: .vb
    1097:   left mouse: zoom in
    1098:   middle mouse: zoom out
    1099:   right mouse: continue with the simulation
    1100: .ve

    1102: .seealso: [](ch_matrices), `Mat`, `PetscViewerPushFormat()`, `PetscViewerASCIIOpen()`, `PetscViewerDrawOpen()`, `PetscViewer`,
    1103:           `PetscViewerSocketOpen()`, `PetscViewerBinaryOpen()`, `MatLoad()`, `MatViewFromOptions()`
    1104: @*/
    1105: PetscErrorCode MatView(Mat mat, PetscViewer viewer)
    1106: {
    1107:   PetscInt          rows, cols, rbs, cbs;
    1108:   PetscBool         isascii, isstring, issaws;
    1109:   PetscViewerFormat format;
    1110:   PetscMPIInt       size;

    1112:   PetscFunctionBegin;
    1115:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)mat), &viewer));

    1118:   PetscCall(PetscViewerGetFormat(viewer, &format));
    1119:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)viewer), &size));
    1120:   if (size == 1 && format == PETSC_VIEWER_LOAD_BALANCE) PetscFunctionReturn(PETSC_SUCCESS);

    1122: #if !defined(PETSC_HAVE_THREADSAFETY)
    1123:   insidematview++;
    1124: #endif
    1125:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));
    1126:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    1127:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSAWS, &issaws));
    1128:   PetscCheck((isascii && (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL)) || !mat->factortype, PetscObjectComm((PetscObject)viewer), PETSC_ERR_ARG_WRONGSTATE, "No viewers for factored matrix except ASCII, info, or info_detail");

    1130:   PetscCall(PetscLogEventBegin(MAT_View, mat, viewer, 0, 0));
    1131:   if (isascii) {
    1132:     if (!mat->preallocated) {
    1133:       PetscCall(PetscViewerASCIIPrintf(viewer, "Matrix has not been preallocated yet\n"));
    1134: #if !defined(PETSC_HAVE_THREADSAFETY)
    1135:       insidematview--;
    1136: #endif
    1137:       PetscCall(PetscLogEventEnd(MAT_View, mat, viewer, 0, 0));
    1138:       PetscFunctionReturn(PETSC_SUCCESS);
    1139:     }
    1140:     if (!mat->assembled) {
    1141:       PetscCall(PetscViewerASCIIPrintf(viewer, "Matrix has not been assembled yet\n"));
    1142: #if !defined(PETSC_HAVE_THREADSAFETY)
    1143:       insidematview--;
    1144: #endif
    1145:       PetscCall(PetscLogEventEnd(MAT_View, mat, viewer, 0, 0));
    1146:       PetscFunctionReturn(PETSC_SUCCESS);
    1147:     }
    1148:     PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)mat, viewer));
    1149:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1150:       MatNullSpace nullsp, transnullsp;

    1152:       PetscCall(PetscViewerASCIIPushTab(viewer));
    1153:       PetscCall(MatGetSize(mat, &rows, &cols));
    1154:       PetscCall(MatGetBlockSizes(mat, &rbs, &cbs));
    1155:       if (rbs != 1 || cbs != 1) {
    1156:         if (rbs != cbs) PetscCall(PetscViewerASCIIPrintf(viewer, "rows=%" PetscInt_FMT ", cols=%" PetscInt_FMT ", rbs=%" PetscInt_FMT ", cbs=%" PetscInt_FMT "%s\n", rows, cols, rbs, cbs, mat->bsizes ? " variable blocks set" : ""));
    1157:         else PetscCall(PetscViewerASCIIPrintf(viewer, "rows=%" PetscInt_FMT ", cols=%" PetscInt_FMT ", bs=%" PetscInt_FMT "%s\n", rows, cols, rbs, mat->bsizes ? " variable blocks set" : ""));
    1158:       } else PetscCall(PetscViewerASCIIPrintf(viewer, "rows=%" PetscInt_FMT ", cols=%" PetscInt_FMT "\n", rows, cols));
    1159:       if (mat->factortype) {
    1160:         MatSolverType solver;
    1161:         PetscCall(MatFactorGetSolverType(mat, &solver));
    1162:         PetscCall(PetscViewerASCIIPrintf(viewer, "package used to perform factorization: %s\n", solver));
    1163:       }
    1164:       if (mat->ops->getinfo) {
    1165:         PetscBool is_constant_or_diagonal;

    1167:         // Don't print nonzero information for constant or diagonal matrices, it just adds noise to the output
    1168:         PetscCall(PetscObjectTypeCompareAny((PetscObject)mat, &is_constant_or_diagonal, MATCONSTANTDIAGONAL, MATDIAGONAL, ""));
    1169:         if (!is_constant_or_diagonal) {
    1170:           MatInfo info;

    1172:           PetscCall(MatGetInfo(mat, MAT_GLOBAL_SUM, &info));
    1173:           PetscCall(PetscViewerASCIIPrintf(viewer, "total: nonzeros=%.f, allocated nonzeros=%.f\n", info.nz_used, info.nz_allocated));
    1174:           if (!mat->factortype) PetscCall(PetscViewerASCIIPrintf(viewer, "total number of mallocs used during MatSetValues calls=%" PetscInt_FMT "\n", (PetscInt)info.mallocs));
    1175:         }
    1176:       }
    1177:       PetscCall(MatGetNullSpace(mat, &nullsp));
    1178:       PetscCall(MatGetTransposeNullSpace(mat, &transnullsp));
    1179:       if (nullsp) PetscCall(PetscViewerASCIIPrintf(viewer, "  has attached null space\n"));
    1180:       if (transnullsp && transnullsp != nullsp) PetscCall(PetscViewerASCIIPrintf(viewer, "  has attached transposed null space\n"));
    1181:       PetscCall(MatGetNearNullSpace(mat, &nullsp));
    1182:       if (nullsp) PetscCall(PetscViewerASCIIPrintf(viewer, "  has attached near null space\n"));
    1183:       PetscCall(PetscViewerASCIIPushTab(viewer));
    1184:       PetscCall(MatProductView(mat, viewer));
    1185:       PetscCall(PetscViewerASCIIPopTab(viewer));
    1186:       if (mat->bsizes && format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1187:         IS tmp;

    1189:         PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)viewer), mat->nblocks, mat->bsizes, PETSC_USE_POINTER, &tmp));
    1190:         PetscCall(PetscObjectSetName((PetscObject)tmp, "Block Sizes"));
    1191:         PetscCall(PetscViewerASCIIPushTab(viewer));
    1192:         PetscCall(ISView(tmp, viewer));
    1193:         PetscCall(PetscViewerASCIIPopTab(viewer));
    1194:         PetscCall(ISDestroy(&tmp));
    1195:       }
    1196:     }
    1197:   } else if (issaws) {
    1198: #if defined(PETSC_HAVE_SAWS)
    1199:     PetscMPIInt rank;

    1201:     PetscCall(PetscObjectName((PetscObject)mat));
    1202:     PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
    1203:     if (!((PetscObject)mat)->amsmem && rank == 0) PetscCall(PetscObjectViewSAWs((PetscObject)mat, viewer));
    1204: #endif
    1205:   } else if (isstring) {
    1206:     const char *type;
    1207:     PetscCall(MatGetType(mat, &type));
    1208:     PetscCall(PetscViewerStringSPrintf(viewer, " MatType: %-7.7s", type));
    1209:     PetscTryTypeMethod(mat, view, viewer);
    1210:   }
    1211:   if ((format == PETSC_VIEWER_NATIVE || format == PETSC_VIEWER_LOAD_BALANCE) && mat->ops->viewnative) {
    1212:     PetscCall(PetscViewerASCIIPushTab(viewer));
    1213:     PetscUseTypeMethod(mat, viewnative, viewer);
    1214:     PetscCall(PetscViewerASCIIPopTab(viewer));
    1215:   } else if (mat->ops->view) {
    1216:     PetscCall(PetscViewerASCIIPushTab(viewer));
    1217:     PetscUseTypeMethod(mat, view, viewer);
    1218:     PetscCall(PetscViewerASCIIPopTab(viewer));
    1219:   }
    1220:   if (isascii) {
    1221:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1222:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscCall(PetscViewerASCIIPopTab(viewer));
    1223:   }
    1224:   PetscCall(PetscLogEventEnd(MAT_View, mat, viewer, 0, 0));
    1225: #if !defined(PETSC_HAVE_THREADSAFETY)
    1226:   insidematview--;
    1227: #endif
    1228:   PetscFunctionReturn(PETSC_SUCCESS);
    1229: }

    1231: #if defined(PETSC_USE_DEBUG)
    1232: #include <../src/sys/totalview/tv_data_display.h>
    1233: PETSC_UNUSED static int TV_display_type(const struct _p_Mat *mat)
    1234: {
    1235:   TV_add_row("Local rows", "int", &mat->rmap->n);
    1236:   TV_add_row("Local columns", "int", &mat->cmap->n);
    1237:   TV_add_row("Global rows", "int", &mat->rmap->N);
    1238:   TV_add_row("Global columns", "int", &mat->cmap->N);
    1239:   TV_add_row("Typename", TV_ascii_string_type, ((PetscObject)mat)->type_name);
    1240:   return TV_format_OK;
    1241: }
    1242: #endif

    1244: /*@
    1245:   MatLoad - Loads a matrix that has been stored in binary/HDF5 format
    1246:   with `MatView()`.  The matrix format is determined from the options database.
    1247:   Generates a parallel MPI matrix if the communicator has more than one
    1248:   processor.  The default matrix type is `MATAIJ`.

    1250:   Collective

    1252:   Input Parameters:
    1253: + mat    - the newly loaded matrix, this needs to have been created with `MatCreate()`
    1254:             or some related function before a call to `MatLoad()`
    1255: - viewer - `PETSCVIEWERBINARY`/`PETSCVIEWERHDF5` file viewer

    1257:   Options Database Key:
    1258: . -matload_block_size bs - set block size

    1260:   Level: beginner

    1262:   Notes:
    1263:   If the `Mat` type has not yet been given then `MATAIJ` is used, call `MatSetFromOptions()` on the
    1264:   `Mat` before calling this routine if you wish to set it from the options database.

    1266:   `MatLoad()` automatically loads into the options database any options
    1267:   given in the file filename.info where filename is the name of the file
    1268:   that was passed to the `PetscViewerBinaryOpen()`. The options in the info
    1269:   file will be ignored if you use the -viewer_binary_skip_info option.

    1271:   If the type or size of mat is not set before a call to `MatLoad()`, PETSc
    1272:   sets the default matrix type AIJ and sets the local and global sizes.
    1273:   If type and/or size is already set, then the same are used.

    1275:   In parallel, each processor can load a subset of rows (or the
    1276:   entire matrix).  This routine is especially useful when a large
    1277:   matrix is stored on disk and only part of it is desired on each
    1278:   processor.  For example, a parallel solver may access only some of
    1279:   the rows from each processor.  The algorithm used here reads
    1280:   relatively small blocks of data rather than reading the entire
    1281:   matrix and then subsetting it.

    1283:   Viewer's `PetscViewerType` must be either `PETSCVIEWERBINARY` or `PETSCVIEWERHDF5`.
    1284:   Such viewer can be created using `PetscViewerBinaryOpen()` or `PetscViewerHDF5Open()`,
    1285:   or the sequence like
    1286: .vb
    1287:     `PetscViewer` v;
    1288:     `PetscViewerCreate`(`PETSC_COMM_WORLD`,&v);
    1289:     `PetscViewerSetType`(v,`PETSCVIEWERBINARY`);
    1290:     `PetscViewerSetFromOptions`(v);
    1291:     `PetscViewerFileSetMode`(v,`FILE_MODE_READ`);
    1292:     `PetscViewerFileSetName`(v,"datafile");
    1293: .ve
    1294:   The optional `PetscViewerSetFromOptions()` call allows overriding `PetscViewerSetType()` using the option
    1295: .vb
    1296:   -viewer_type {binary, hdf5}
    1297: .ve

    1299:   See the example src/ksp/ksp/tutorials/ex27.c with the first approach,
    1300:   and src/mat/tutorials/ex10.c with the second approach.

    1302:   In case of `PETSCVIEWERBINARY`, a native PETSc binary format is used. Each of the blocks
    1303:   is read onto MPI rank 0 and then shipped to its destination MPI rank, one after another.
    1304:   Multiple objects, both matrices and vectors, can be stored within the same file.
    1305:   Their `PetscObject` name is ignored; they are loaded in the order of their storage.

    1307:   Most users should not need to know the details of the binary storage
    1308:   format, since `MatLoad()` and `MatView()` completely hide these details.
    1309:   But for anyone who is interested, the standard binary matrix storage
    1310:   format is

    1312: .vb
    1313:     PetscInt    MAT_FILE_CLASSID
    1314:     PetscInt    number of rows
    1315:     PetscInt    number of columns
    1316:     PetscInt    total number of nonzeros
    1317:     PetscInt    *number nonzeros in each row
    1318:     PetscInt    *column indices of all nonzeros (starting index is zero)
    1319:     PetscScalar *values of all nonzeros
    1320: .ve
    1321:   If PETSc was not configured with `--with-64-bit-indices` then only `MATMPIAIJ` matrices with more than `PETSC_INT_MAX` non-zeros can be
    1322:   stored or loaded (each MPI process part of the matrix must have less than `PETSC_INT_MAX` nonzeros). Since the total nonzero count in this
    1323:   case will not fit in a (32-bit) `PetscInt` the value `PETSC_INT_MAX` is used for the header entry `total number of nonzeros`.

    1325:   PETSc automatically does the byte swapping for
    1326:   machines that store the bytes reversed. Thus if you write your own binary
    1327:   read/write routines you have to swap the bytes; see `PetscBinaryRead()`
    1328:   and `PetscBinaryWrite()` to see how this may be done.

    1330:   In case of `PETSCVIEWERHDF5`, a parallel HDF5 reader is used.
    1331:   Each processor's chunk is loaded independently by its owning MPI process.
    1332:   Multiple objects, both matrices and vectors, can be stored within the same file.
    1333:   They are looked up by their PetscObject name.

    1335:   As the MATLAB MAT-File Version 7.3 format is also a HDF5 flavor, we decided to use
    1336:   by default the same structure and naming of the AIJ arrays and column count
    1337:   within the HDF5 file. This means that a MAT file saved with -v7.3 flag, e.g.
    1338: .vb
    1339:   save example.mat A b -v7.3
    1340: .ve
    1341:   can be directly read by this routine (see Reference 1 for details).

    1343:   Depending on your MATLAB version, this format might be a default,
    1344:   otherwise you can set it as default in Preferences.

    1346:   Unless -nocompression flag is used to save the file in MATLAB,
    1347:   PETSc must be configured with ZLIB package.

    1349:   See also examples src/mat/tutorials/ex10.c and src/ksp/ksp/tutorials/ex27.c

    1351:   This reader currently supports only real `MATSEQAIJ`, `MATMPIAIJ`, `MATSEQDENSE` and `MATMPIDENSE` matrices for `PETSCVIEWERHDF5`

    1353:   Corresponding `MatView()` is not yet implemented.

    1355:   The loaded matrix is actually a transpose of the original one in MATLAB,
    1356:   unless you push `PETSC_VIEWER_HDF5_MAT` format (see examples above).
    1357:   With this format, matrix is automatically transposed by PETSc,
    1358:   unless the matrix is marked as SPD or symmetric
    1359:   (see `MatSetOption()`, `MAT_SPD`, `MAT_SYMMETRIC`).

    1361:   See MATLAB Documentation on `save()`, <https://www.mathworks.com/help/matlab/ref/save.html#btox10b-1-version>

    1363: .seealso: [](ch_matrices), `Mat`, `PetscViewerBinaryOpen()`, `PetscViewerSetType()`, `MatView()`, `VecLoad()`
    1364:  @*/
    1365: PetscErrorCode MatLoad(Mat mat, PetscViewer viewer)
    1366: {
    1367:   PetscBool flg;

    1369:   PetscFunctionBegin;

    1373:   if (!((PetscObject)mat)->type_name) PetscCall(MatSetType(mat, MATAIJ));

    1375:   flg = PETSC_FALSE;
    1376:   PetscCall(PetscOptionsGetBool(((PetscObject)mat)->options, ((PetscObject)mat)->prefix, "-matload_symmetric", &flg, NULL));
    1377:   if (flg) {
    1378:     PetscCall(MatSetOption(mat, MAT_SYMMETRIC, PETSC_TRUE));
    1379:     PetscCall(MatSetOption(mat, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
    1380:   }
    1381:   flg = PETSC_FALSE;
    1382:   PetscCall(PetscOptionsGetBool(((PetscObject)mat)->options, ((PetscObject)mat)->prefix, "-matload_spd", &flg, NULL));
    1383:   if (flg) PetscCall(MatSetOption(mat, MAT_SPD, PETSC_TRUE));

    1385:   PetscCall(PetscLogEventBegin(MAT_Load, mat, viewer, 0, 0));
    1386:   PetscUseTypeMethod(mat, load, viewer);
    1387:   PetscCall(PetscLogEventEnd(MAT_Load, mat, viewer, 0, 0));
    1388:   PetscFunctionReturn(PETSC_SUCCESS);
    1389: }

    1391: static PetscErrorCode MatDestroy_Redundant(Mat_Redundant **redundant)
    1392: {
    1393:   Mat_Redundant *redund = *redundant;

    1395:   PetscFunctionBegin;
    1396:   if (redund) {
    1397:     if (redund->matseq) { /* via MatCreateSubMatrices()  */
    1398:       PetscCall(ISDestroy(&redund->isrow));
    1399:       PetscCall(ISDestroy(&redund->iscol));
    1400:       PetscCall(MatDestroySubMatrices(1, &redund->matseq));
    1401:     } else {
    1402:       PetscCall(PetscFree2(redund->send_rank, redund->recv_rank));
    1403:       PetscCall(PetscFree(redund->sbuf_j));
    1404:       PetscCall(PetscFree(redund->sbuf_a));
    1405:       for (PetscInt i = 0; i < redund->nrecvs; i++) {
    1406:         PetscCall(PetscFree(redund->rbuf_j[i]));
    1407:         PetscCall(PetscFree(redund->rbuf_a[i]));
    1408:       }
    1409:       PetscCall(PetscFree4(redund->sbuf_nz, redund->rbuf_nz, redund->rbuf_j, redund->rbuf_a));
    1410:     }

    1412:     PetscCall(PetscCommDestroy(&redund->subcomm));
    1413:     PetscCall(PetscFree(redund));
    1414:   }
    1415:   PetscFunctionReturn(PETSC_SUCCESS);
    1416: }

    1418: /*@
    1419:   MatDestroy - Frees space taken by a matrix.

    1421:   Collective

    1423:   Input Parameter:
    1424: . A - the matrix

    1426:   Level: beginner

    1428:   Developer Note:
    1429:   Some special arrays of matrices are not destroyed in this routine but instead by the routines called by
    1430:   `MatDestroySubMatrices()`. Thus one must be sure that any changes here must also be made in those routines.
    1431:   `MatHeaderMerge()` and `MatHeaderReplace()` also manipulate the data in the `Mat` object and likely need changes
    1432:   if changes are needed here.

    1434: .seealso: [](ch_matrices), `Mat`, `MatCreate()`
    1435: @*/
    1436: PetscErrorCode MatDestroy(Mat *A)
    1437: {
    1438:   PetscFunctionBegin;
    1439:   if (!*A) PetscFunctionReturn(PETSC_SUCCESS);
    1441:   if (--((PetscObject)*A)->refct > 0) {
    1442:     *A = NULL;
    1443:     PetscFunctionReturn(PETSC_SUCCESS);
    1444:   }

    1446:   /* if memory was published with SAWs then destroy it */
    1447:   PetscCall(PetscObjectSAWsViewOff((PetscObject)*A));
    1448:   PetscTryTypeMethod(*A, destroy);

    1450:   PetscCall(PetscFree((*A)->factorprefix));
    1451:   PetscCall(PetscFree((*A)->defaultvectype));
    1452:   PetscCall(PetscFree((*A)->defaultrandtype));
    1453:   PetscCall(PetscFree((*A)->bsizes));
    1454:   PetscCall(PetscFree((*A)->solvertype));
    1455:   for (PetscInt i = 0; i < MAT_FACTOR_NUM_TYPES; i++) PetscCall(PetscFree((*A)->preferredordering[i]));
    1456:   if ((*A)->redundant && (*A)->redundant->matseq[0] == *A) (*A)->redundant->matseq[0] = NULL;
    1457:   PetscCall(MatDestroy_Redundant(&(*A)->redundant));
    1458:   PetscCall(MatProductClear(*A));
    1459:   PetscCall(MatNullSpaceDestroy(&(*A)->nullsp));
    1460:   PetscCall(MatNullSpaceDestroy(&(*A)->transnullsp));
    1461:   PetscCall(MatNullSpaceDestroy(&(*A)->nearnullsp));
    1462:   PetscCall(MatDestroy(&(*A)->schur));
    1463:   PetscCall(VecDestroy(&(*A)->dot_vec));
    1464:   PetscCall(PetscLayoutDestroy(&(*A)->rmap));
    1465:   PetscCall(PetscLayoutDestroy(&(*A)->cmap));
    1466:   PetscCall(PetscHeaderDestroy(A));
    1467:   PetscFunctionReturn(PETSC_SUCCESS);
    1468: }

    1470: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    1471: /*@
    1472:   MatSetValues - Inserts or adds a block of values into a matrix.
    1473:   These values may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
    1474:   MUST be called after all calls to `MatSetValues()` have been completed.

    1476:   Not Collective

    1478:   Input Parameters:
    1479: + mat  - the matrix
    1480: . m    - the number of rows
    1481: . idxm - the global indices of the rows
    1482: . n    - the number of columns
    1483: . idxn - the global indices of the columns
    1484: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1485:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1486: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` to replace existing entries with new values

    1488:   Level: beginner

    1490:   Notes:
    1491:   Calls to `MatSetValues()` with the `INSERT_VALUES` and `ADD_VALUES`
    1492:   options cannot be mixed without intervening calls to the assembly
    1493:   routines.

    1495:   `MatSetValues()` uses 0-based row and column numbers in Fortran
    1496:   as well as in C.

    1498:   Negative indices may be passed in `idxm` and `idxn`, these rows and columns are
    1499:   simply ignored. This allows easily inserting element stiffness matrices
    1500:   with homogeneous Dirichlet boundary conditions that you don't want represented
    1501:   in the matrix.

    1503:   Efficiency Alert:
    1504:   The routine `MatSetValuesBlocked()` may offer much better efficiency
    1505:   for users of block sparse formats (`MATSEQBAIJ` and `MATMPIBAIJ`).

    1507:   Fortran Notes:
    1508:   If any of `idxm`, `idxn`, and `v` are scalars pass them using, for example,
    1509: .vb
    1510:   call MatSetValues(mat, one, [idxm], one, [idxn], [v], INSERT_VALUES, ierr)
    1511: .ve

    1513:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1515:   Developer Note:
    1516:   This is labeled with C so does not automatically generate Fortran stubs and interfaces
    1517:   because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    1519: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1520:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`
    1521: @*/
    1522: PetscErrorCode MatSetValues(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], const PetscScalar v[], InsertMode addv)
    1523: {
    1524:   PetscFunctionBeginHot;
    1527:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    1528:   PetscAssertPointer(idxm, 3);
    1529:   PetscAssertPointer(idxn, 5);
    1530:   MatCheckPreallocated(mat, 1);

    1532:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    1533:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");

    1535:   if (PetscDefined(USE_DEBUG)) {
    1536:     PetscInt i, j;

    1538:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    1539:     if (v) {
    1540:       for (i = 0; i < m; i++) {
    1541:         for (j = 0; j < n; j++) {
    1542:           if (mat->erroriffailure && PetscIsInfOrNanScalar(v[i * n + j]))
    1543: #if defined(PETSC_USE_COMPLEX)
    1544:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_FP, "Inserting %g+i%g at matrix entry (%" PetscInt_FMT ",%" PetscInt_FMT ")", (double)PetscRealPart(v[i * n + j]), (double)PetscImaginaryPart(v[i * n + j]), idxm[i], idxn[j]);
    1545: #else
    1546:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_FP, "Inserting %g at matrix entry (%" PetscInt_FMT ",%" PetscInt_FMT ")", (double)v[i * n + j], idxm[i], idxn[j]);
    1547: #endif
    1548:         }
    1549:       }
    1550:     }
    1551:     for (i = 0; i < m; i++) PetscCheck(idxm[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot insert in row %" PetscInt_FMT ", maximum is %" PetscInt_FMT, idxm[i], mat->rmap->N - 1);
    1552:     for (i = 0; i < n; i++) PetscCheck(idxn[i] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot insert in column %" PetscInt_FMT ", maximum is %" PetscInt_FMT, idxn[i], mat->cmap->N - 1);
    1553:   }

    1555:   if (mat->assembled) {
    1556:     mat->was_assembled = PETSC_TRUE;
    1557:     mat->assembled     = PETSC_FALSE;
    1558:   }
    1559:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    1560:   PetscUseTypeMethod(mat, setvalues, m, idxm, n, idxn, v, addv);
    1561:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    1562:   PetscFunctionReturn(PETSC_SUCCESS);
    1563: }

    1565: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    1566: /*@
    1567:   MatSetValuesIS - Inserts or adds a block of values into a matrix using an `IS` to indicate the rows and columns
    1568:   These values may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
    1569:   MUST be called after all calls to `MatSetValues()` have been completed.

    1571:   Not Collective

    1573:   Input Parameters:
    1574: + mat  - the matrix
    1575: . ism  - the rows to provide
    1576: . isn  - the columns to provide
    1577: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1578:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1579: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` to replace existing entries with new values

    1581:   Level: beginner

    1583:   Notes:
    1584:   By default, the values, `v`, are stored in row-major order. See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.

    1586:   Calls to `MatSetValues()` with the `INSERT_VALUES` and `ADD_VALUES`
    1587:   options cannot be mixed without intervening calls to the assembly
    1588:   routines.

    1590:   `MatSetValues()` uses 0-based row and column numbers in Fortran
    1591:   as well as in C.

    1593:   Negative indices may be passed in `ism` and `isn`, these rows and columns are
    1594:   simply ignored. This allows easily inserting element stiffness matrices
    1595:   with homogeneous Dirichlet boundary conditions that you don't want represented
    1596:   in the matrix.

    1598:   Fortran Note:
    1599:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1601:   Efficiency Alert:
    1602:   The routine `MatSetValuesBlocked()` may offer much better efficiency
    1603:   for users of block sparse formats (`MATSEQBAIJ` and `MATMPIBAIJ`).

    1605:   This is currently not optimized for any particular `ISType`

    1607: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatSetValues()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1608:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`
    1609: @*/
    1610: PetscErrorCode MatSetValuesIS(Mat mat, IS ism, IS isn, const PetscScalar v[], InsertMode addv)
    1611: {
    1612:   PetscInt        m, n;
    1613:   const PetscInt *rows, *cols;

    1615:   PetscFunctionBeginHot;
    1617:   PetscCall(ISGetIndices(ism, &rows));
    1618:   PetscCall(ISGetIndices(isn, &cols));
    1619:   PetscCall(ISGetLocalSize(ism, &m));
    1620:   PetscCall(ISGetLocalSize(isn, &n));
    1621:   PetscCall(MatSetValues(mat, m, rows, n, cols, v, addv));
    1622:   PetscCall(ISRestoreIndices(ism, &rows));
    1623:   PetscCall(ISRestoreIndices(isn, &cols));
    1624:   PetscFunctionReturn(PETSC_SUCCESS);
    1625: }

    1627: /*@
    1628:   MatSetValuesRowLocal - Inserts a row (block row for `MATBAIJ` matrices) of nonzero
    1629:   values into a matrix

    1631:   Not Collective

    1633:   Input Parameters:
    1634: + mat - the matrix
    1635: . row - the (block) row to set
    1636: - v   - a one-dimensional array that contains the values. For `MATBAIJ` they are implicitly stored as a two-dimensional array, by default in row-major order.
    1637:         See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.

    1639:   Level: intermediate

    1641:   Notes:
    1642:   The values, `v`, are column-oriented (for the block version) and sorted

    1644:   All the nonzero values in `row` must be provided

    1646:   The matrix must have previously had its column indices set, likely by having been assembled.

    1648:   `row` must belong to this MPI process

    1650:   Fortran Note:
    1651:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1653: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1654:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`, `MatSetValues()`, `MatSetValuesRow()`, `MatSetLocalToGlobalMapping()`
    1655: @*/
    1656: PetscErrorCode MatSetValuesRowLocal(Mat mat, PetscInt row, const PetscScalar v[])
    1657: {
    1658:   PetscInt globalrow;

    1660:   PetscFunctionBegin;
    1663:   PetscAssertPointer(v, 3);
    1664:   PetscCall(ISLocalToGlobalMappingApply(mat->rmap->mapping, 1, &row, &globalrow));
    1665:   PetscCall(MatSetValuesRow(mat, globalrow, v));
    1666:   PetscFunctionReturn(PETSC_SUCCESS);
    1667: }

    1669: /*@
    1670:   MatSetValuesRow - Inserts a row (block row for `MATBAIJ` matrices) of nonzero
    1671:   values into a matrix

    1673:   Not Collective

    1675:   Input Parameters:
    1676: + mat - the matrix
    1677: . row - the (block) row to set
    1678: - 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

    1680:   Level: advanced

    1682:   Notes:
    1683:   The values, `v`, are column-oriented for the block version.

    1685:   All the nonzeros in `row` must be provided

    1687:   THE MATRIX MUST HAVE PREVIOUSLY HAD ITS COLUMN INDICES SET. IT IS RARE THAT THIS ROUTINE IS USED, usually `MatSetValues()` is used.

    1689:   `row` must belong to this process

    1691: .seealso: [](ch_matrices), `Mat`, `MatSetValues()`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1692:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`
    1693: @*/
    1694: PetscErrorCode MatSetValuesRow(Mat mat, PetscInt row, const PetscScalar v[])
    1695: {
    1696:   PetscFunctionBeginHot;
    1699:   MatCheckPreallocated(mat, 1);
    1700:   PetscAssertPointer(v, 3);
    1701:   PetscCheck(mat->insertmode != ADD_VALUES, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add and insert values");
    1702:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    1703:   mat->insertmode = INSERT_VALUES;

    1705:   if (mat->assembled) {
    1706:     mat->was_assembled = PETSC_TRUE;
    1707:     mat->assembled     = PETSC_FALSE;
    1708:   }
    1709:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    1710:   PetscUseTypeMethod(mat, setvaluesrow, row, v);
    1711:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    1712:   PetscFunctionReturn(PETSC_SUCCESS);
    1713: }

    1715: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    1716: /*@
    1717:   MatSetValuesStencil - Inserts or adds a block of values into a matrix.
    1718:   Using structured grid indexing

    1720:   Not Collective

    1722:   Input Parameters:
    1723: + mat  - the matrix
    1724: . m    - number of rows being entered
    1725: . idxm - grid coordinates (and component number when dof > 1) for matrix rows being entered
    1726: . n    - number of columns being entered
    1727: . idxn - grid coordinates (and component number when dof > 1) for matrix columns being entered
    1728: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1729:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1730: - addv - either `ADD_VALUES` to add to existing entries at that location or `INSERT_VALUES` to replace existing entries with new values

    1732:   Level: beginner

    1734:   Notes:
    1735:   By default the values, `v`, are row-oriented.  See `MatSetOption()` for other options.

    1737:   Calls to `MatSetValuesStencil()` with the `INSERT_VALUES` and `ADD_VALUES`
    1738:   options cannot be mixed without intervening calls to the assembly
    1739:   routines.

    1741:   The grid coordinates are across the entire grid, not just the local portion

    1743:   `MatSetValuesStencil()` uses 0-based row and column numbers in Fortran
    1744:   as well as in C.

    1746:   For setting/accessing vector values via array coordinates you can use the `DMDAVecGetArray()` routine

    1748:   In order to use this routine you must either obtain the matrix with `DMCreateMatrix()`
    1749:   or call `MatSetLocalToGlobalMapping()` and `MatSetStencil()` first.

    1751:   The columns and rows in the stencil passed in MUST be contained within the
    1752:   ghost region of the given process as set with DMDACreateXXX() or `MatSetStencil()`. For example,
    1753:   if you create a `DMDA` with an overlap of one grid level and on a particular process its first
    1754:   local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
    1755:   first i index you can use in your column and row indices in `MatSetStencil()` is 5.

    1757:   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    1758:   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    1759:   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    1760:   `DM_BOUNDARY_PERIODIC` boundary type.

    1762:   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
    1763:   a single value per point) you can skip filling those indices.

    1765:   Inspired by the structured grid interface to the HYPRE package
    1766:   (https://computation.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)

    1768:   Fortran Note:
    1769:   If `y` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1771:   Efficiency Alert:
    1772:   The routine `MatSetValuesBlockedStencil()` may offer much better efficiency
    1773:   for users of block sparse formats (`MATSEQBAIJ` and `MATMPIBAIJ`).

    1775: .seealso: [](ch_matrices), `Mat`, `DMDA`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1776:           `MatSetValues()`, `MatSetValuesBlockedStencil()`, `MatSetStencil()`, `DMCreateMatrix()`, `DMDAVecGetArray()`, `MatStencil`
    1777: @*/
    1778: PetscErrorCode MatSetValuesStencil(Mat mat, PetscInt m, const MatStencil idxm[], PetscInt n, const MatStencil idxn[], const PetscScalar v[], InsertMode addv)
    1779: {
    1780:   PetscInt  buf[8192], *bufm = NULL, *bufn = NULL, *jdxm, *jdxn;
    1781:   PetscInt  j, i, dim = mat->stencil.dim, *dims = mat->stencil.dims + 1, tmp;
    1782:   PetscInt *starts = mat->stencil.starts, *dxm = (PetscInt *)idxm, *dxn = (PetscInt *)idxn, sdim = dim - (1 - (PetscInt)mat->stencil.noc);

    1784:   PetscFunctionBegin;
    1785:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    1788:   PetscAssertPointer(idxm, 3);
    1789:   PetscAssertPointer(idxn, 5);

    1791:   if ((m + n) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    1792:     jdxm = buf;
    1793:     jdxn = buf + m;
    1794:   } else {
    1795:     PetscCall(PetscMalloc2(m, &bufm, n, &bufn));
    1796:     jdxm = bufm;
    1797:     jdxn = bufn;
    1798:   }
    1799:   for (i = 0; i < m; i++) {
    1800:     for (j = 0; j < 3 - sdim; j++) dxm++;
    1801:     tmp = *dxm++ - starts[0];
    1802:     for (j = 0; j < dim - 1; j++) {
    1803:       if ((*dxm++ - starts[j + 1]) < 0 || tmp < 0) tmp = -1;
    1804:       else tmp = tmp * dims[j] + *(dxm - 1) - starts[j + 1];
    1805:     }
    1806:     if (mat->stencil.noc) dxm++;
    1807:     jdxm[i] = tmp;
    1808:   }
    1809:   for (i = 0; i < n; i++) {
    1810:     for (j = 0; j < 3 - sdim; j++) dxn++;
    1811:     tmp = *dxn++ - starts[0];
    1812:     for (j = 0; j < dim - 1; j++) {
    1813:       if ((*dxn++ - starts[j + 1]) < 0 || tmp < 0) tmp = -1;
    1814:       else tmp = tmp * dims[j] + *(dxn - 1) - starts[j + 1];
    1815:     }
    1816:     if (mat->stencil.noc) dxn++;
    1817:     jdxn[i] = tmp;
    1818:   }
    1819:   PetscCall(MatSetValuesLocal(mat, m, jdxm, n, jdxn, v, addv));
    1820:   PetscCall(PetscFree2(bufm, bufn));
    1821:   PetscFunctionReturn(PETSC_SUCCESS);
    1822: }

    1824: /*@
    1825:   MatSetValuesBlockedStencil - Inserts or adds a block of values into a matrix.
    1826:   Using structured grid indexing

    1828:   Not Collective

    1830:   Input Parameters:
    1831: + mat  - the matrix
    1832: . m    - number of rows being entered
    1833: . idxm - grid coordinates for matrix rows being entered
    1834: . n    - number of columns being entered
    1835: . idxn - grid coordinates for matrix columns being entered
    1836: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1837:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1838: - addv - either `ADD_VALUES` to add to existing entries or `INSERT_VALUES` to replace existing entries with new values

    1840:   Level: beginner

    1842:   Notes:
    1843:   By default the values, `v`, are row-oriented and unsorted.
    1844:   See `MatSetOption()` for other options.

    1846:   Calls to `MatSetValuesBlockedStencil()` with the `INSERT_VALUES` and `ADD_VALUES`
    1847:   options cannot be mixed without intervening calls to the assembly
    1848:   routines.

    1850:   The grid coordinates are across the entire grid, not just the local portion

    1852:   `MatSetValuesBlockedStencil()` uses 0-based row and column numbers in Fortran
    1853:   as well as in C.

    1855:   For setting/accessing vector values via array coordinates you can use the `DMDAVecGetArray()` routine

    1857:   In order to use this routine you must either obtain the matrix with `DMCreateMatrix()`
    1858:   or call `MatSetBlockSize()`, `MatSetLocalToGlobalMapping()` and `MatSetStencil()` first.

    1860:   The columns and rows in the stencil passed in MUST be contained within the
    1861:   ghost region of the given process as set with DMDACreateXXX() or `MatSetStencil()`. For example,
    1862:   if you create a `DMDA` with an overlap of one grid level and on a particular process its first
    1863:   local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
    1864:   first i index you can use in your column and row indices in `MatSetStencil()` is 5.

    1866:   Negative indices may be passed in `idxm` and `idxn`, these rows and columns are
    1867:   simply ignored. This allows easily inserting element stiffness matrices
    1868:   with homogeneous Dirichlet boundary conditions that you don't want represented
    1869:   in the matrix.

    1871:   Inspired by the structured grid interface to the HYPRE package
    1872:   (https://computation.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)

    1874:   Fortran Notes:
    1875:   `idxm` and `idxn` should be declared as
    1876: .vb
    1877:     MatStencil idxm(4,m),idxn(4,n)
    1878: .ve
    1879:   and the values inserted using
    1880: .vb
    1881:     idxm(MatStencil_i,1) = i
    1882:     idxm(MatStencil_j,1) = j
    1883:     idxm(MatStencil_k,1) = k
    1884:    etc
    1885: .ve

    1887:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1889: .seealso: [](ch_matrices), `Mat`, `DMDA`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1890:           `MatSetValues()`, `MatSetValuesStencil()`, `MatSetStencil()`, `DMCreateMatrix()`, `DMDAVecGetArray()`, `MatStencil`,
    1891:           `MatSetBlockSize()`, `MatSetLocalToGlobalMapping()`
    1892: @*/
    1893: PetscErrorCode MatSetValuesBlockedStencil(Mat mat, PetscInt m, const MatStencil idxm[], PetscInt n, const MatStencil idxn[], const PetscScalar v[], InsertMode addv)
    1894: {
    1895:   PetscInt  buf[8192], *bufm = NULL, *bufn = NULL, *jdxm, *jdxn;
    1896:   PetscInt  j, i, dim = mat->stencil.dim, *dims = mat->stencil.dims + 1, tmp;
    1897:   PetscInt *starts = mat->stencil.starts, *dxm = (PetscInt *)idxm, *dxn = (PetscInt *)idxn, sdim = dim - (1 - (PetscInt)mat->stencil.noc);

    1899:   PetscFunctionBegin;
    1900:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    1903:   PetscAssertPointer(idxm, 3);
    1904:   PetscAssertPointer(idxn, 5);
    1905:   PetscAssertPointer(v, 6);

    1907:   if ((m + n) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    1908:     jdxm = buf;
    1909:     jdxn = buf + m;
    1910:   } else {
    1911:     PetscCall(PetscMalloc2(m, &bufm, n, &bufn));
    1912:     jdxm = bufm;
    1913:     jdxn = bufn;
    1914:   }
    1915:   for (i = 0; i < m; i++) {
    1916:     for (j = 0; j < 3 - sdim; j++) dxm++;
    1917:     tmp = *dxm++ - starts[0];
    1918:     for (j = 0; j < sdim - 1; j++) {
    1919:       if ((*dxm++ - starts[j + 1]) < 0 || tmp < 0) tmp = -1;
    1920:       else tmp = tmp * dims[j] + *(dxm - 1) - starts[j + 1];
    1921:     }
    1922:     dxm++;
    1923:     jdxm[i] = tmp;
    1924:   }
    1925:   for (i = 0; i < n; i++) {
    1926:     for (j = 0; j < 3 - sdim; j++) dxn++;
    1927:     tmp = *dxn++ - starts[0];
    1928:     for (j = 0; j < sdim - 1; j++) {
    1929:       if ((*dxn++ - starts[j + 1]) < 0 || tmp < 0) tmp = -1;
    1930:       else tmp = tmp * dims[j] + *(dxn - 1) - starts[j + 1];
    1931:     }
    1932:     dxn++;
    1933:     jdxn[i] = tmp;
    1934:   }
    1935:   PetscCall(MatSetValuesBlockedLocal(mat, m, jdxm, n, jdxn, v, addv));
    1936:   PetscCall(PetscFree2(bufm, bufn));
    1937:   PetscFunctionReturn(PETSC_SUCCESS);
    1938: }

    1940: /*@
    1941:   MatSetStencil - Sets the grid information for setting values into a matrix via
    1942:   `MatSetValuesStencil()`

    1944:   Not Collective

    1946:   Input Parameters:
    1947: + mat    - the matrix
    1948: . dim    - dimension of the grid 1, 2, or 3
    1949: . dims   - number of grid points in x, y, and z direction, including ghost points on your processor
    1950: . starts - starting point of ghost nodes on your processor in x, y, and z direction
    1951: - dof    - number of degrees of freedom per node

    1953:   Level: beginner

    1955:   Notes:
    1956:   Inspired by the structured grid interface to the HYPRE package
    1957:   (www.llnl.gov/CASC/hyper)

    1959:   For matrices generated with `DMCreateMatrix()` this routine is automatically called and so not needed by the
    1960:   user.

    1962: .seealso: [](ch_matrices), `Mat`, `MatStencil`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1963:           `MatSetValues()`, `MatSetValuesBlockedStencil()`, `MatSetValuesStencil()`
    1964: @*/
    1965: PetscErrorCode MatSetStencil(Mat mat, PetscInt dim, const PetscInt dims[], const PetscInt starts[], PetscInt dof)
    1966: {
    1967:   PetscFunctionBegin;
    1969:   PetscAssertPointer(dims, 3);
    1970:   PetscAssertPointer(starts, 4);

    1972:   mat->stencil.dim = dim + (dof > 1);
    1973:   for (PetscInt i = 0; i < dim; i++) {
    1974:     mat->stencil.dims[i]   = dims[dim - i - 1]; /* copy the values in backwards */
    1975:     mat->stencil.starts[i] = starts[dim - i - 1];
    1976:   }
    1977:   mat->stencil.dims[dim]   = dof;
    1978:   mat->stencil.starts[dim] = 0;
    1979:   mat->stencil.noc         = (PetscBool)(dof == 1);
    1980:   PetscFunctionReturn(PETSC_SUCCESS);
    1981: }

    1983: /*@
    1984:   MatSetValuesBlocked - Inserts or adds a block of values into a matrix.

    1986:   Not Collective

    1988:   Input Parameters:
    1989: + mat  - the matrix
    1990: . m    - the number of block rows
    1991: . idxm - the global block indices
    1992: . n    - the number of block columns
    1993: . idxn - the global block indices
    1994: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1995:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1996: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` replaces existing entries with new values

    1998:   Level: intermediate

    2000:   Notes:
    2001:   If you create the matrix yourself (that is not with a call to `DMCreateMatrix()`) then you MUST call
    2002:   MatXXXXSetPreallocation() or `MatSetUp()` before using this routine.

    2004:   The `m` and `n` count the NUMBER of blocks in the row direction and column direction,
    2005:   NOT the total number of rows/columns; for example, if the block size is 2 and
    2006:   you are passing in values for rows 2,3,4,5  then `m` would be 2 (not 4).
    2007:   The values in `idxm` would be 1 2; that is the first index for each block divided by
    2008:   the block size.

    2010:   You must call `MatSetBlockSize()` when constructing this matrix (before
    2011:   preallocating it).

    2013:   By default, the values, `v`, are stored in row-major order. See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.

    2015:   Calls to `MatSetValuesBlocked()` with the `INSERT_VALUES` and `ADD_VALUES`
    2016:   options cannot be mixed without intervening calls to the assembly
    2017:   routines.

    2019:   `MatSetValuesBlocked()` uses 0-based row and column numbers in Fortran
    2020:   as well as in C.

    2022:   Negative indices may be passed in `idxm` and `idxn`, these rows and columns are
    2023:   simply ignored. This allows easily inserting element stiffness matrices
    2024:   with homogeneous Dirichlet boundary conditions that you don't want represented
    2025:   in the matrix.

    2027:   Each time an entry is set within a sparse matrix via `MatSetValues()`,
    2028:   internal searching must be done to determine where to place the
    2029:   data in the matrix storage space.  By instead inserting blocks of
    2030:   entries via `MatSetValuesBlocked()`, the overhead of matrix assembly is
    2031:   reduced.

    2033:   Example:
    2034: .vb
    2035:    Suppose m=n=2 and block size(bs) = 2 The array is

    2037:    1  2  | 3  4
    2038:    5  6  | 7  8
    2039:    - - - | - - -
    2040:    9  10 | 11 12
    2041:    13 14 | 15 16

    2043:    v[] should be passed in like
    2044:    v[] = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]

    2046:   If you are not using row-oriented storage of v (that is you called MatSetOption(mat,MAT_ROW_ORIENTED,PETSC_FALSE)) then
    2047:    v[] = [1,5,9,13,2,6,10,14,3,7,11,15,4,8,12,16]
    2048: .ve

    2050:   Fortran Notes:
    2051:   If any of `idmx`, `idxn`, and `v` are scalars pass them using, for example,
    2052: .vb
    2053:   call MatSetValuesBlocked(mat, one, [idxm], one, [idxn], [v], INSERT_VALUES, ierr)
    2054: .ve

    2056:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    2058: .seealso: [](ch_matrices), `Mat`, `MatSetBlockSize()`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValues()`, `MatSetValuesBlockedLocal()`
    2059: @*/
    2060: PetscErrorCode MatSetValuesBlocked(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], const PetscScalar v[], InsertMode addv)
    2061: {
    2062:   PetscFunctionBeginHot;
    2065:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    2066:   PetscAssertPointer(idxm, 3);
    2067:   PetscAssertPointer(idxn, 5);
    2068:   MatCheckPreallocated(mat, 1);
    2069:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    2070:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    2071:   if (PetscDefined(USE_DEBUG)) {
    2072:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2073:     PetscCheck(mat->ops->setvaluesblocked || mat->ops->setvalues, PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2074:   }
    2075:   if (PetscDefined(USE_DEBUG)) {
    2076:     PetscInt rbs, cbs, M, N, i;
    2077:     PetscCall(MatGetBlockSizes(mat, &rbs, &cbs));
    2078:     PetscCall(MatGetSize(mat, &M, &N));
    2079:     for (i = 0; i < m; i++) PetscCheck(idxm[i] * rbs < M, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row block %" PetscInt_FMT " contains an index %" PetscInt_FMT "*%" PetscInt_FMT " greater than row length %" PetscInt_FMT, i, idxm[i], rbs, M);
    2080:     for (i = 0; i < n; i++)
    2081:       PetscCheck(idxn[i] * cbs < N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column block %" PetscInt_FMT " contains an index %" PetscInt_FMT "*%" PetscInt_FMT " greater than column length %" PetscInt_FMT, i, idxn[i], cbs, N);
    2082:   }
    2083:   if (mat->assembled) {
    2084:     mat->was_assembled = PETSC_TRUE;
    2085:     mat->assembled     = PETSC_FALSE;
    2086:   }
    2087:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    2088:   if (mat->ops->setvaluesblocked) PetscUseTypeMethod(mat, setvaluesblocked, m, idxm, n, idxn, v, addv);
    2089:   else {
    2090:     PetscInt buf[8192], *bufr = NULL, *bufc = NULL, *iidxm, *iidxn;
    2091:     PetscInt i, j, bs, cbs;

    2093:     PetscCall(MatGetBlockSizes(mat, &bs, &cbs));
    2094:     if ((m * bs + n * cbs) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    2095:       iidxm = buf;
    2096:       iidxn = buf + m * bs;
    2097:     } else {
    2098:       PetscCall(PetscMalloc2(m * bs, &bufr, n * cbs, &bufc));
    2099:       iidxm = bufr;
    2100:       iidxn = bufc;
    2101:     }
    2102:     for (i = 0; i < m; i++) {
    2103:       for (j = 0; j < bs; j++) iidxm[i * bs + j] = bs * idxm[i] + j;
    2104:     }
    2105:     if (m != n || bs != cbs || idxm != idxn) {
    2106:       for (i = 0; i < n; i++) {
    2107:         for (j = 0; j < cbs; j++) iidxn[i * cbs + j] = cbs * idxn[i] + j;
    2108:       }
    2109:     } else iidxn = iidxm;
    2110:     PetscCall(MatSetValues(mat, m * bs, iidxm, n * cbs, iidxn, v, addv));
    2111:     PetscCall(PetscFree2(bufr, bufc));
    2112:   }
    2113:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    2114:   PetscFunctionReturn(PETSC_SUCCESS);
    2115: }

    2117: /*@
    2118:   MatGetValues - Gets a block of local values from a matrix.

    2120:   Not Collective; can only return values that are owned by the give process

    2122:   Input Parameters:
    2123: + mat  - the matrix
    2124: . v    - a logically two-dimensional array for storing the values
    2125: . m    - the number of rows
    2126: . idxm - the  global indices of the rows
    2127: . n    - the number of columns
    2128: - idxn - the global indices of the columns

    2130:   Level: advanced

    2132:   Notes:
    2133:   The user must allocate space (m*n `PetscScalar`s) for the values, `v`.
    2134:   The values, `v`, are then returned in a row-oriented format,
    2135:   analogous to that used by default in `MatSetValues()`.

    2137:   `MatGetValues()` uses 0-based row and column numbers in
    2138:   Fortran as well as in C.

    2140:   `MatGetValues()` requires that the matrix has been assembled
    2141:   with `MatAssemblyBegin()`/`MatAssemblyEnd()`.  Thus, calls to
    2142:   `MatSetValues()` and `MatGetValues()` CANNOT be made in succession
    2143:   without intermediate matrix assembly.

    2145:   Negative row or column indices will be ignored and those locations in `v` will be
    2146:   left unchanged.

    2148:   For the standard row-based matrix formats, `idxm` can only contain rows owned by the requesting MPI process.
    2149:   That is, rows with global index greater than or equal to rstart and less than rend where rstart and rend are obtainable
    2150:   from `MatGetOwnershipRange`(mat,&rstart,&rend).

    2152: .seealso: [](ch_matrices), `Mat`, `MatGetRow()`, `MatCreateSubMatrices()`, `MatSetValues()`, `MatGetOwnershipRange()`, `MatGetValuesLocal()`, `MatGetValue()`
    2153: @*/
    2154: PetscErrorCode MatGetValues(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], PetscScalar v[])
    2155: {
    2156:   PetscFunctionBegin;
    2159:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS);
    2160:   PetscAssertPointer(idxm, 3);
    2161:   PetscAssertPointer(idxn, 5);
    2162:   PetscAssertPointer(v, 6);
    2163:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2164:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2165:   MatCheckPreallocated(mat, 1);

    2167:   PetscCall(PetscLogEventBegin(MAT_GetValues, mat, 0, 0, 0));
    2168:   PetscUseTypeMethod(mat, getvalues, m, idxm, n, idxn, v);
    2169:   PetscCall(PetscLogEventEnd(MAT_GetValues, mat, 0, 0, 0));
    2170:   PetscFunctionReturn(PETSC_SUCCESS);
    2171: }

    2173: /*@
    2174:   MatGetValuesLocal - retrieves values from certain locations in a matrix using the local numbering of the indices
    2175:   defined previously by `MatSetLocalToGlobalMapping()`

    2177:   Not Collective

    2179:   Input Parameters:
    2180: + mat  - the matrix
    2181: . nrow - number of rows
    2182: . irow - the row local indices
    2183: . ncol - number of columns
    2184: - icol - the column local indices

    2186:   Output Parameter:
    2187: . y - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    2188:       See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.

    2190:   Level: advanced

    2192:   Notes:
    2193:   If you create the matrix yourself (that is not with a call to `DMCreateMatrix()`) then you MUST call `MatSetLocalToGlobalMapping()` before using this routine.

    2195:   This routine can only return values that are owned by the requesting MPI process. That is, for standard matrix formats, rows that, in the global numbering,
    2196:   are greater than or equal to rstart and less than rend where rstart and rend are obtainable from `MatGetOwnershipRange`(mat,&rstart,&rend). One can
    2197:   determine if the resulting global row associated with the local row r is owned by the requesting MPI process by applying the `ISLocalToGlobalMapping` set
    2198:   with `MatSetLocalToGlobalMapping()`.

    2200: .seealso: [](ch_matrices), `Mat`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValues()`, `MatSetLocalToGlobalMapping()`,
    2201:           `MatSetValuesLocal()`, `MatGetValues()`
    2202: @*/
    2203: PetscErrorCode MatGetValuesLocal(Mat mat, PetscInt nrow, const PetscInt irow[], PetscInt ncol, const PetscInt icol[], PetscScalar y[])
    2204: {
    2205:   PetscFunctionBeginHot;
    2208:   MatCheckPreallocated(mat, 1);
    2209:   if (!nrow || !ncol) PetscFunctionReturn(PETSC_SUCCESS); /* no values to retrieve */
    2210:   PetscAssertPointer(irow, 3);
    2211:   PetscAssertPointer(icol, 5);
    2212:   if (PetscDefined(USE_DEBUG)) {
    2213:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2214:     PetscCheck(mat->ops->getvalueslocal || mat->ops->getvalues, PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2215:   }
    2216:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2217:   PetscCall(PetscLogEventBegin(MAT_GetValues, mat, 0, 0, 0));
    2218:   if (mat->ops->getvalueslocal) PetscUseTypeMethod(mat, getvalueslocal, nrow, irow, ncol, icol, y);
    2219:   else {
    2220:     PetscInt buf[8192], *bufr = NULL, *bufc = NULL, *irowm, *icolm;
    2221:     if ((nrow + ncol) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    2222:       irowm = buf;
    2223:       icolm = buf + nrow;
    2224:     } else {
    2225:       PetscCall(PetscMalloc2(nrow, &bufr, ncol, &bufc));
    2226:       irowm = bufr;
    2227:       icolm = bufc;
    2228:     }
    2229:     PetscCheck(mat->rmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MatGetValuesLocal() cannot proceed without local-to-global row mapping (See MatSetLocalToGlobalMapping()).");
    2230:     PetscCheck(mat->cmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MatGetValuesLocal() cannot proceed without local-to-global column mapping (See MatSetLocalToGlobalMapping()).");
    2231:     PetscCall(ISLocalToGlobalMappingApply(mat->rmap->mapping, nrow, irow, irowm));
    2232:     PetscCall(ISLocalToGlobalMappingApply(mat->cmap->mapping, ncol, icol, icolm));
    2233:     PetscCall(MatGetValues(mat, nrow, irowm, ncol, icolm, y));
    2234:     PetscCall(PetscFree2(bufr, bufc));
    2235:   }
    2236:   PetscCall(PetscLogEventEnd(MAT_GetValues, mat, 0, 0, 0));
    2237:   PetscFunctionReturn(PETSC_SUCCESS);
    2238: }

    2240: /*@
    2241:   MatSetValuesBatch - Adds (`ADD_VALUES`) many blocks of values into a matrix at once. The blocks must all be square and
    2242:   the same size. Currently, this can only be called once and creates the given matrix.

    2244:   Not Collective

    2246:   Input Parameters:
    2247: + mat  - the matrix
    2248: . nb   - the number of blocks
    2249: . bs   - the number of rows (and columns) in each block
    2250: . rows - a concatenation of the rows for each block
    2251: - v    - a concatenation of logically two-dimensional arrays of values

    2253:   Level: advanced

    2255:   Notes:
    2256:   `MatSetPreallocationCOO()` and `MatSetValuesCOO()` may be a better way to provide the values

    2258:   In the future, we will extend this routine to handle rectangular blocks, and to allow multiple calls for a given matrix.

    2260: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    2261:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`, `MatSetValues()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    2262: @*/
    2263: PetscErrorCode MatSetValuesBatch(Mat mat, PetscInt nb, PetscInt bs, PetscInt rows[], const PetscScalar v[])
    2264: {
    2265:   PetscFunctionBegin;
    2268:   PetscAssertPointer(rows, 4);
    2269:   PetscAssertPointer(v, 5);
    2270:   PetscAssert(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");

    2272:   PetscCall(PetscLogEventBegin(MAT_SetValuesBatch, mat, 0, 0, 0));
    2273:   if (mat->ops->setvaluesbatch) PetscUseTypeMethod(mat, setvaluesbatch, nb, bs, rows, v);
    2274:   else {
    2275:     for (PetscInt b = 0; b < nb; ++b) PetscCall(MatSetValues(mat, bs, &rows[b * bs], bs, &rows[b * bs], &v[b * bs * bs], ADD_VALUES));
    2276:   }
    2277:   PetscCall(PetscLogEventEnd(MAT_SetValuesBatch, mat, 0, 0, 0));
    2278:   PetscFunctionReturn(PETSC_SUCCESS);
    2279: }

    2281: /*@
    2282:   MatSetLocalToGlobalMapping - Sets a local-to-global numbering for use by
    2283:   the routine `MatSetValuesLocal()` to allow users to insert matrix entries
    2284:   using a local (per-processor) numbering.

    2286:   Not Collective

    2288:   Input Parameters:
    2289: + x        - the matrix
    2290: . rmapping - row mapping created with `ISLocalToGlobalMappingCreate()` or `ISLocalToGlobalMappingCreateIS()`
    2291: - cmapping - column mapping

    2293:   Level: intermediate

    2295:   Note:
    2296:   If the matrix is obtained with `DMCreateMatrix()` then this may already have been called on the matrix

    2298: .seealso: [](ch_matrices), `Mat`, `DM`, `DMCreateMatrix()`, `MatGetLocalToGlobalMapping()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValues()`, `MatSetValuesLocal()`, `MatGetValuesLocal()`
    2299: @*/
    2300: PetscErrorCode MatSetLocalToGlobalMapping(Mat x, ISLocalToGlobalMapping rmapping, ISLocalToGlobalMapping cmapping)
    2301: {
    2302:   PetscFunctionBegin;
    2307:   if (x->ops->setlocaltoglobalmapping) PetscUseTypeMethod(x, setlocaltoglobalmapping, rmapping, cmapping);
    2308:   else {
    2309:     PetscCall(PetscLayoutSetISLocalToGlobalMapping(x->rmap, rmapping));
    2310:     PetscCall(PetscLayoutSetISLocalToGlobalMapping(x->cmap, cmapping));
    2311:   }
    2312:   PetscFunctionReturn(PETSC_SUCCESS);
    2313: }

    2315: /*@
    2316:   MatGetLocalToGlobalMapping - Gets the local-to-global numbering set by `MatSetLocalToGlobalMapping()`

    2318:   Not Collective

    2320:   Input Parameter:
    2321: . A - the matrix

    2323:   Output Parameters:
    2324: + rmapping - row mapping
    2325: - cmapping - column mapping

    2327:   Level: advanced

    2329: .seealso: [](ch_matrices), `Mat`, `MatSetLocalToGlobalMapping()`, `MatSetValuesLocal()`
    2330: @*/
    2331: PetscErrorCode MatGetLocalToGlobalMapping(Mat A, ISLocalToGlobalMapping *rmapping, ISLocalToGlobalMapping *cmapping)
    2332: {
    2333:   PetscFunctionBegin;
    2336:   if (rmapping) {
    2337:     PetscAssertPointer(rmapping, 2);
    2338:     *rmapping = A->rmap->mapping;
    2339:   }
    2340:   if (cmapping) {
    2341:     PetscAssertPointer(cmapping, 3);
    2342:     *cmapping = A->cmap->mapping;
    2343:   }
    2344:   PetscFunctionReturn(PETSC_SUCCESS);
    2345: }

    2347: /*@
    2348:   MatSetLayouts - Sets the `PetscLayout` objects for rows and columns of a matrix

    2350:   Logically Collective

    2352:   Input Parameters:
    2353: + A    - the matrix
    2354: . rmap - row layout
    2355: - cmap - column layout

    2357:   Level: advanced

    2359:   Note:
    2360:   The `PetscLayout` objects are usually created automatically for the matrix so this routine rarely needs to be called.

    2362: .seealso: [](ch_matrices), `Mat`, `PetscLayout`, `MatCreateVecs()`, `MatGetLocalToGlobalMapping()`, `MatGetLayouts()`
    2363: @*/
    2364: PetscErrorCode MatSetLayouts(Mat A, PetscLayout rmap, PetscLayout cmap)
    2365: {
    2366:   PetscFunctionBegin;
    2368:   PetscCall(PetscLayoutReference(rmap, &A->rmap));
    2369:   PetscCall(PetscLayoutReference(cmap, &A->cmap));
    2370:   PetscFunctionReturn(PETSC_SUCCESS);
    2371: }

    2373: /*@
    2374:   MatGetLayouts - Gets the `PetscLayout` objects for rows and columns

    2376:   Not Collective

    2378:   Input Parameter:
    2379: . A - the matrix

    2381:   Output Parameters:
    2382: + rmap - row layout
    2383: - cmap - column layout

    2385:   Level: advanced

    2387: .seealso: [](ch_matrices), `Mat`, [Matrix Layouts](sec_matlayout), `PetscLayout`, `MatCreateVecs()`, `MatGetLocalToGlobalMapping()`, `MatSetLayouts()`
    2388: @*/
    2389: PetscErrorCode MatGetLayouts(Mat A, PetscLayout *rmap, PetscLayout *cmap)
    2390: {
    2391:   PetscFunctionBegin;
    2394:   if (rmap) {
    2395:     PetscAssertPointer(rmap, 2);
    2396:     *rmap = A->rmap;
    2397:   }
    2398:   if (cmap) {
    2399:     PetscAssertPointer(cmap, 3);
    2400:     *cmap = A->cmap;
    2401:   }
    2402:   PetscFunctionReturn(PETSC_SUCCESS);
    2403: }

    2405: /*@
    2406:   MatSetValuesLocal - Inserts or adds values into certain locations of a matrix,
    2407:   using a local numbering of the rows and columns.

    2409:   Not Collective

    2411:   Input Parameters:
    2412: + mat  - the matrix
    2413: . nrow - number of rows
    2414: . irow - the row local indices
    2415: . ncol - number of columns
    2416: . icol - the column local indices
    2417: . y    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    2418:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    2419: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` to replace existing entries with new values

    2421:   Level: intermediate

    2423:   Notes:
    2424:   If you create the matrix yourself (that is not with a call to `DMCreateMatrix()`) then you MUST call `MatSetLocalToGlobalMapping()` before using this routine

    2426:   Calls to `MatSetValuesLocal()` with the `INSERT_VALUES` and `ADD_VALUES`
    2427:   options cannot be mixed without intervening calls to the assembly
    2428:   routines.

    2430:   These values may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
    2431:   MUST be called after all calls to `MatSetValuesLocal()` have been completed.

    2433:   Fortran Notes:
    2434:   If any of `irow`, `icol`, and `y` are scalars pass them using, for example,
    2435: .vb
    2436:   call MatSetValuesLocal(mat, one, [irow], one, [icol], [y], INSERT_VALUES, ierr)
    2437: .ve

    2439:   If `y` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    2441: .seealso: [](ch_matrices), `Mat`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValues()`, `MatSetLocalToGlobalMapping()`,
    2442:           `MatGetValuesLocal()`
    2443: @*/
    2444: PetscErrorCode MatSetValuesLocal(Mat mat, PetscInt nrow, const PetscInt irow[], PetscInt ncol, const PetscInt icol[], const PetscScalar y[], InsertMode addv)
    2445: {
    2446:   PetscFunctionBeginHot;
    2449:   MatCheckPreallocated(mat, 1);
    2450:   if (!nrow || !ncol) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    2451:   PetscAssertPointer(irow, 3);
    2452:   PetscAssertPointer(icol, 5);
    2453:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    2454:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    2455:   if (PetscDefined(USE_DEBUG)) {
    2456:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2457:     PetscCheck(mat->ops->setvalueslocal || mat->ops->setvalues, PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2458:   }

    2460:   if (mat->assembled) {
    2461:     mat->was_assembled = PETSC_TRUE;
    2462:     mat->assembled     = PETSC_FALSE;
    2463:   }
    2464:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    2465:   if (mat->ops->setvalueslocal) PetscUseTypeMethod(mat, setvalueslocal, nrow, irow, ncol, icol, y, addv);
    2466:   else {
    2467:     PetscInt        buf[8192], *bufr = NULL, *bufc = NULL;
    2468:     const PetscInt *irowm, *icolm;

    2470:     if ((!mat->rmap->mapping && !mat->cmap->mapping) || (nrow + ncol) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    2471:       bufr  = buf;
    2472:       bufc  = buf + nrow;
    2473:       irowm = bufr;
    2474:       icolm = bufc;
    2475:     } else {
    2476:       PetscCall(PetscMalloc2(nrow, &bufr, ncol, &bufc));
    2477:       irowm = bufr;
    2478:       icolm = bufc;
    2479:     }
    2480:     if (mat->rmap->mapping) PetscCall(ISLocalToGlobalMappingApply(mat->rmap->mapping, nrow, irow, bufr));
    2481:     else irowm = irow;
    2482:     if (mat->cmap->mapping) {
    2483:       if (mat->cmap->mapping != mat->rmap->mapping || ncol != nrow || icol != irow) PetscCall(ISLocalToGlobalMappingApply(mat->cmap->mapping, ncol, icol, bufc));
    2484:       else icolm = irowm;
    2485:     } else icolm = icol;
    2486:     PetscCall(MatSetValues(mat, nrow, irowm, ncol, icolm, y, addv));
    2487:     if (bufr != buf) PetscCall(PetscFree2(bufr, bufc));
    2488:   }
    2489:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    2490:   PetscFunctionReturn(PETSC_SUCCESS);
    2491: }

    2493: /*@
    2494:   MatSetValuesBlockedLocal - Inserts or adds values into certain locations of a matrix,
    2495:   using a local ordering of the nodes a block at a time.

    2497:   Not Collective

    2499:   Input Parameters:
    2500: + mat  - the matrix
    2501: . nrow - number of rows
    2502: . irow - the row local indices
    2503: . ncol - number of columns
    2504: . icol - the column local indices
    2505: . y    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    2506:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    2507: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` to replace existing entries with new values

    2509:   Level: intermediate

    2511:   Notes:
    2512:   If you create the matrix yourself (that is not with a call to `DMCreateMatrix()`) then you MUST call `MatSetBlockSize()` and `MatSetLocalToGlobalMapping()`
    2513:   before using this routineBefore calling `MatSetValuesLocal()`, the user must first set the

    2515:   Calls to `MatSetValuesBlockedLocal()` with the `INSERT_VALUES` and `ADD_VALUES`
    2516:   options cannot be mixed without intervening calls to the assembly
    2517:   routines.

    2519:   These values may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
    2520:   MUST be called after all calls to `MatSetValuesBlockedLocal()` have been completed.

    2522:   Fortran Notes:
    2523:   If any of `irow`, `icol`, and `y` are scalars pass them using, for example,
    2524: .vb
    2525:   call MatSetValuesBlockedLocal(mat, one, [irow], one, [icol], [y], INSERT_VALUES, ierr)
    2526: .ve

    2528:   If `y` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    2530: .seealso: [](ch_matrices), `Mat`, `MatSetBlockSize()`, `MatSetLocalToGlobalMapping()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`,
    2531:           `MatSetValuesLocal()`, `MatSetValuesBlocked()`
    2532: @*/
    2533: PetscErrorCode MatSetValuesBlockedLocal(Mat mat, PetscInt nrow, const PetscInt irow[], PetscInt ncol, const PetscInt icol[], const PetscScalar y[], InsertMode addv)
    2534: {
    2535:   PetscFunctionBeginHot;
    2538:   MatCheckPreallocated(mat, 1);
    2539:   if (!nrow || !ncol) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    2540:   PetscAssertPointer(irow, 3);
    2541:   PetscAssertPointer(icol, 5);
    2542:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    2543:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    2544:   if (PetscDefined(USE_DEBUG)) {
    2545:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2546:     PetscCheck(mat->ops->setvaluesblockedlocal || mat->ops->setvaluesblocked || mat->ops->setvalueslocal || mat->ops->setvalues, PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2547:   }

    2549:   if (mat->assembled) {
    2550:     mat->was_assembled = PETSC_TRUE;
    2551:     mat->assembled     = PETSC_FALSE;
    2552:   }
    2553:   if (PetscUnlikelyDebug(mat->rmap->mapping)) { /* Condition on the mapping existing, because MatSetValuesBlockedLocal_IS does not require it to be set. */
    2554:     PetscInt irbs, rbs;
    2555:     PetscCall(MatGetBlockSizes(mat, &rbs, NULL));
    2556:     PetscCall(ISLocalToGlobalMappingGetBlockSize(mat->rmap->mapping, &irbs));
    2557:     PetscCheck(rbs == irbs, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Different row block sizes! mat %" PetscInt_FMT ", row l2g map %" PetscInt_FMT, rbs, irbs);
    2558:   }
    2559:   if (PetscUnlikelyDebug(mat->cmap->mapping)) {
    2560:     PetscInt icbs, cbs;
    2561:     PetscCall(MatGetBlockSizes(mat, NULL, &cbs));
    2562:     PetscCall(ISLocalToGlobalMappingGetBlockSize(mat->cmap->mapping, &icbs));
    2563:     PetscCheck(cbs == icbs, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Different col block sizes! mat %" PetscInt_FMT ", col l2g map %" PetscInt_FMT, cbs, icbs);
    2564:   }
    2565:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    2566:   if (mat->ops->setvaluesblockedlocal) PetscUseTypeMethod(mat, setvaluesblockedlocal, nrow, irow, ncol, icol, y, addv);
    2567:   else {
    2568:     PetscInt        buf[8192], *bufr = NULL, *bufc = NULL;
    2569:     const PetscInt *irowm, *icolm;

    2571:     if ((!mat->rmap->mapping && !mat->cmap->mapping) || (nrow + ncol) <= ((PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf))) {
    2572:       bufr  = buf;
    2573:       bufc  = buf + nrow;
    2574:       irowm = bufr;
    2575:       icolm = bufc;
    2576:     } else {
    2577:       PetscCall(PetscMalloc2(nrow, &bufr, ncol, &bufc));
    2578:       irowm = bufr;
    2579:       icolm = bufc;
    2580:     }
    2581:     if (mat->rmap->mapping) PetscCall(ISLocalToGlobalMappingApplyBlock(mat->rmap->mapping, nrow, irow, bufr));
    2582:     else irowm = irow;
    2583:     if (mat->cmap->mapping) {
    2584:       if (mat->cmap->mapping != mat->rmap->mapping || ncol != nrow || icol != irow) PetscCall(ISLocalToGlobalMappingApplyBlock(mat->cmap->mapping, ncol, icol, bufc));
    2585:       else icolm = irowm;
    2586:     } else icolm = icol;
    2587:     PetscCall(MatSetValuesBlocked(mat, nrow, irowm, ncol, icolm, y, addv));
    2588:     if (bufr != buf) PetscCall(PetscFree2(bufr, bufc));
    2589:   }
    2590:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    2591:   PetscFunctionReturn(PETSC_SUCCESS);
    2592: }

    2594: /*@
    2595:   MatMultDiagonalBlock - Computes the matrix-vector product, $y = Dx$. Where `D` is defined by the inode or block structure of the diagonal

    2597:   Collective

    2599:   Input Parameters:
    2600: + mat - the matrix
    2601: - x   - the vector to be multiplied

    2603:   Output Parameter:
    2604: . y - the result

    2606:   Level: developer

    2608:   Note:
    2609:   The vectors `x` and `y` cannot be the same.  I.e., one cannot
    2610:   call `MatMultDiagonalBlock`(A,y,y).

    2612: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatMultTranspose()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    2613: @*/
    2614: PetscErrorCode MatMultDiagonalBlock(Mat mat, Vec x, Vec y)
    2615: {
    2616:   PetscFunctionBegin;

    2622:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2623:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2624:   PetscCheck(x != y, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "x and y must be different vectors");
    2625:   MatCheckPreallocated(mat, 1);

    2627:   PetscUseTypeMethod(mat, multdiagonalblock, x, y);
    2628:   PetscCall(PetscObjectStateIncrease((PetscObject)y));
    2629:   PetscFunctionReturn(PETSC_SUCCESS);
    2630: }

    2632: /*@
    2633:   MatMult - Computes the matrix-vector product, $y = Ax$.

    2635:   Neighbor-wise Collective

    2637:   Input Parameters:
    2638: + mat - the matrix
    2639: - x   - the vector to be multiplied

    2641:   Output Parameter:
    2642: . y - the result

    2644:   Level: beginner

    2646:   Note:
    2647:   The vectors `x` and `y` cannot be the same.  I.e., one cannot
    2648:   call `MatMult`(A,y,y).

    2650: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    2651: @*/
    2652: PetscErrorCode MatMult(Mat mat, Vec x, Vec y)
    2653: {
    2654:   PetscFunctionBegin;
    2658:   VecCheckAssembled(x);
    2660:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2661:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2662:   PetscCheck(x != y, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "x and y must be different vectors");
    2663:   PetscCheck(mat->cmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, x->map->N);
    2664:   PetscCheck(mat->rmap->N == y->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, y->map->N);
    2665:   PetscCheck(mat->cmap->n == x->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->n, x->map->n);
    2666:   PetscCheck(mat->rmap->n == y->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, y->map->n);
    2667:   PetscCall(VecSetErrorIfLocked(y, 3));
    2668:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
    2669:   MatCheckPreallocated(mat, 1);

    2671:   PetscCall(VecLockReadPush(x));
    2672:   PetscCall(PetscLogEventBegin(MAT_Mult, mat, x, y, 0));
    2673:   PetscUseTypeMethod(mat, mult, x, y);
    2674:   PetscCall(PetscLogEventEnd(MAT_Mult, mat, x, y, 0));
    2675:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_FALSE));
    2676:   PetscCall(VecLockReadPop(x));
    2677:   PetscFunctionReturn(PETSC_SUCCESS);
    2678: }

    2680: /*@
    2681:   MatMultTranspose - Computes matrix transpose times a vector $y = A^T * x$.

    2683:   Neighbor-wise Collective

    2685:   Input Parameters:
    2686: + mat - the matrix
    2687: - x   - the vector to be multiplied

    2689:   Output Parameter:
    2690: . y - the result

    2692:   Level: beginner

    2694:   Notes:
    2695:   The vectors `x` and `y` cannot be the same.  I.e., one cannot
    2696:   call `MatMultTranspose`(A,y,y).

    2698:   For complex numbers this does NOT compute the Hermitian (complex conjugate) transpose multiple,
    2699:   use `MatMultHermitianTranspose()`

    2701: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatMultAdd()`, `MatMultTransposeAdd()`, `MatMultHermitianTranspose()`, `MatTranspose()`
    2702: @*/
    2703: PetscErrorCode MatMultTranspose(Mat mat, Vec x, Vec y)
    2704: {
    2705:   PetscErrorCode (*op)(Mat, Vec, Vec) = NULL;

    2707:   PetscFunctionBegin;
    2711:   VecCheckAssembled(x);

    2714:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2715:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2716:   PetscCheck(x != y, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "x and y must be different vectors");
    2717:   PetscCheck(mat->cmap->N == y->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, y->map->N);
    2718:   PetscCheck(mat->rmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, x->map->N);
    2719:   PetscCheck(mat->cmap->n == y->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->n, y->map->n);
    2720:   PetscCheck(mat->rmap->n == x->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, x->map->n);
    2721:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
    2722:   MatCheckPreallocated(mat, 1);

    2724:   if (!mat->ops->multtranspose) {
    2725:     if (mat->symmetric == PETSC_BOOL3_TRUE && mat->ops->mult) op = mat->ops->mult;
    2726:     PetscCheck(op, 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);
    2727:   } else op = mat->ops->multtranspose;
    2728:   PetscCall(PetscLogEventBegin(MAT_MultTranspose, mat, x, y, 0));
    2729:   PetscCall(VecLockReadPush(x));
    2730:   PetscCall((*op)(mat, x, y));
    2731:   PetscCall(VecLockReadPop(x));
    2732:   PetscCall(PetscLogEventEnd(MAT_MultTranspose, mat, x, y, 0));
    2733:   PetscCall(PetscObjectStateIncrease((PetscObject)y));
    2734:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_FALSE));
    2735:   PetscFunctionReturn(PETSC_SUCCESS);
    2736: }

    2738: /*@
    2739:   MatMultHermitianTranspose - Computes matrix Hermitian-transpose times a vector $y = A^H * x$.

    2741:   Neighbor-wise Collective

    2743:   Input Parameters:
    2744: + mat - the matrix
    2745: - x   - the vector to be multiplied

    2747:   Output Parameter:
    2748: . y - the result

    2750:   Level: beginner

    2752:   Notes:
    2753:   The vectors `x` and `y` cannot be the same.  I.e., one cannot
    2754:   call `MatMultHermitianTranspose`(A,y,y).

    2756:   Also called the conjugate transpose, complex conjugate transpose, or adjoint.

    2758:   For real numbers `MatMultTranspose()` and `MatMultHermitianTranspose()` are identical.

    2760: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatMultAdd()`, `MatMultHermitianTransposeAdd()`, `MatMultTranspose()`
    2761: @*/
    2762: PetscErrorCode MatMultHermitianTranspose(Mat mat, Vec x, Vec y)
    2763: {
    2764:   PetscFunctionBegin;

    2770:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2771:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2772:   PetscCheck(x != y, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "x and y must be different vectors");
    2773:   PetscCheck(mat->cmap->N == y->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, y->map->N);
    2774:   PetscCheck(mat->rmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, x->map->N);
    2775:   PetscCheck(mat->cmap->n == y->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->n, y->map->n);
    2776:   PetscCheck(mat->rmap->n == x->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, x->map->n);
    2777:   MatCheckPreallocated(mat, 1);

    2779:   PetscCall(PetscLogEventBegin(MAT_MultHermitianTranspose, mat, x, y, 0));
    2780: #if defined(PETSC_USE_COMPLEX)
    2781:   if (mat->ops->multhermitiantranspose || (mat->hermitian == PETSC_BOOL3_TRUE && mat->ops->mult)) {
    2782:     PetscCall(VecLockReadPush(x));
    2783:     if (mat->ops->multhermitiantranspose) PetscUseTypeMethod(mat, multhermitiantranspose, x, y);
    2784:     else PetscUseTypeMethod(mat, mult, x, y);
    2785:     PetscCall(VecLockReadPop(x));
    2786:   } else {
    2787:     Vec w;
    2788:     PetscCall(VecDuplicate(x, &w));
    2789:     PetscCall(VecCopy(x, w));
    2790:     PetscCall(VecConjugate(w));
    2791:     PetscCall(MatMultTranspose(mat, w, y));
    2792:     PetscCall(VecDestroy(&w));
    2793:     PetscCall(VecConjugate(y));
    2794:   }
    2795:   PetscCall(PetscObjectStateIncrease((PetscObject)y));
    2796: #else
    2797:   PetscCall(MatMultTranspose(mat, x, y));
    2798: #endif
    2799:   PetscCall(PetscLogEventEnd(MAT_MultHermitianTranspose, mat, x, y, 0));
    2800:   PetscFunctionReturn(PETSC_SUCCESS);
    2801: }

    2803: /*@
    2804:   MatMultAdd -  Computes $v3 = v2 + A * v1$.

    2806:   Neighbor-wise Collective

    2808:   Input Parameters:
    2809: + mat - the matrix
    2810: . v1  - the vector to be multiplied by `mat`
    2811: - v2  - the vector to be added to the result

    2813:   Output Parameter:
    2814: . v3 - the result

    2816:   Level: beginner

    2818:   Note:
    2819:   The vectors `v1` and `v3` cannot be the same.  I.e., one cannot
    2820:   call `MatMultAdd`(A,v1,v2,v1).

    2822: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMult()`, `MatMultTransposeAdd()`
    2823: @*/
    2824: PetscErrorCode MatMultAdd(Mat mat, Vec v1, Vec v2, Vec v3)
    2825: {
    2826:   PetscFunctionBegin;

    2833:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2834:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2835:   PetscCheck(mat->cmap->N == v1->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec v1: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, v1->map->N);
    2836:   /* PetscCheck(mat->rmap->N == v2->map->N,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec v2: global dim %" PetscInt_FMT " %" PetscInt_FMT,mat->rmap->N,v2->map->N);
    2837:      PetscCheck(mat->rmap->N == v3->map->N,PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Mat mat,Vec v3: global dim %" PetscInt_FMT " %" PetscInt_FMT,mat->rmap->N,v3->map->N); */
    2838:   PetscCheck(mat->rmap->n == v3->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec v3: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, v3->map->n);
    2839:   PetscCheck(mat->rmap->n == v2->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec v2: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, v2->map->n);
    2840:   PetscCheck(v1 != v3, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "v1 and v3 must be different vectors");
    2841:   MatCheckPreallocated(mat, 1);

    2843:   PetscCall(PetscLogEventBegin(MAT_MultAdd, mat, v1, v2, v3));
    2844:   PetscCall(VecLockReadPush(v1));
    2845:   PetscUseTypeMethod(mat, multadd, v1, v2, v3);
    2846:   PetscCall(VecLockReadPop(v1));
    2847:   PetscCall(PetscLogEventEnd(MAT_MultAdd, mat, v1, v2, v3));
    2848:   PetscCall(PetscObjectStateIncrease((PetscObject)v3));
    2849:   PetscFunctionReturn(PETSC_SUCCESS);
    2850: }

    2852: /*@
    2853:   MatMultTransposeAdd - Computes $v3 = v2 + A^T * v1$.

    2855:   Neighbor-wise Collective

    2857:   Input Parameters:
    2858: + mat - the matrix
    2859: . v1  - the vector to be multiplied by the transpose of the matrix
    2860: - v2  - the vector to be added to the result

    2862:   Output Parameter:
    2863: . v3 - the result

    2865:   Level: beginner

    2867:   Note:
    2868:   The vectors `v1` and `v3` cannot be the same.  I.e., one cannot
    2869:   call `MatMultTransposeAdd`(A,v1,v2,v1).

    2871: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMultAdd()`, `MatMult()`
    2872: @*/
    2873: PetscErrorCode MatMultTransposeAdd(Mat mat, Vec v1, Vec v2, Vec v3)
    2874: {
    2875:   PetscErrorCode (*op)(Mat, Vec, Vec, Vec) = (!mat->ops->multtransposeadd && mat->symmetric) ? mat->ops->multadd : mat->ops->multtransposeadd;

    2877:   PetscFunctionBegin;

    2884:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2885:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2886:   PetscCheck(mat->rmap->N == v1->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec v1: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, v1->map->N);
    2887:   PetscCheck(mat->cmap->N == v2->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec v2: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, v2->map->N);
    2888:   PetscCheck(mat->cmap->N == v3->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec v3: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, v3->map->N);
    2889:   PetscCheck(v1 != v3, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "v1 and v3 must be different vectors");
    2890:   PetscCheck(op, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2891:   MatCheckPreallocated(mat, 1);

    2893:   PetscCall(PetscLogEventBegin(MAT_MultTransposeAdd, mat, v1, v2, v3));
    2894:   PetscCall(VecLockReadPush(v1));
    2895:   PetscCall((*op)(mat, v1, v2, v3));
    2896:   PetscCall(VecLockReadPop(v1));
    2897:   PetscCall(PetscLogEventEnd(MAT_MultTransposeAdd, mat, v1, v2, v3));
    2898:   PetscCall(PetscObjectStateIncrease((PetscObject)v3));
    2899:   PetscFunctionReturn(PETSC_SUCCESS);
    2900: }

    2902: /*@
    2903:   MatMultHermitianTransposeAdd - Computes $v3 = v2 + A^H * v1$.

    2905:   Neighbor-wise Collective

    2907:   Input Parameters:
    2908: + mat - the matrix
    2909: . v1  - the vector to be multiplied by the Hermitian transpose
    2910: - v2  - the vector to be added to the result

    2912:   Output Parameter:
    2913: . v3 - the result

    2915:   Level: beginner

    2917:   Note:
    2918:   The vectors `v1` and `v3` cannot be the same.  I.e., one cannot
    2919:   call `MatMultHermitianTransposeAdd`(A,v1,v2,v1).

    2921: .seealso: [](ch_matrices), `Mat`, `MatMultHermitianTranspose()`, `MatMultTranspose()`, `MatMultAdd()`, `MatMult()`
    2922: @*/
    2923: PetscErrorCode MatMultHermitianTransposeAdd(Mat mat, Vec v1, Vec v2, Vec v3)
    2924: {
    2925:   PetscFunctionBegin;

    2932:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2933:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2934:   PetscCheck(v1 != v3, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "v1 and v3 must be different vectors");
    2935:   PetscCheck(mat->rmap->N == v1->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec v1: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, v1->map->N);
    2936:   PetscCheck(mat->cmap->N == v2->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec v2: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, v2->map->N);
    2937:   PetscCheck(mat->cmap->N == v3->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec v3: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, v3->map->N);
    2938:   MatCheckPreallocated(mat, 1);

    2940:   PetscCall(PetscLogEventBegin(MAT_MultHermitianTransposeAdd, mat, v1, v2, v3));
    2941:   PetscCall(VecLockReadPush(v1));
    2942:   if (mat->ops->multhermitiantransposeadd) PetscUseTypeMethod(mat, multhermitiantransposeadd, v1, v2, v3);
    2943:   else {
    2944:     Vec w, z;
    2945:     PetscCall(VecDuplicate(v1, &w));
    2946:     PetscCall(VecCopy(v1, w));
    2947:     PetscCall(VecConjugate(w));
    2948:     PetscCall(VecDuplicate(v3, &z));
    2949:     PetscCall(MatMultTranspose(mat, w, z));
    2950:     PetscCall(VecDestroy(&w));
    2951:     PetscCall(VecConjugate(z));
    2952:     if (v2 != v3) PetscCall(VecWAXPY(v3, 1.0, v2, z));
    2953:     else PetscCall(VecAXPY(v3, 1.0, z));
    2954:     PetscCall(VecDestroy(&z));
    2955:   }
    2956:   PetscCall(VecLockReadPop(v1));
    2957:   PetscCall(PetscLogEventEnd(MAT_MultHermitianTransposeAdd, mat, v1, v2, v3));
    2958:   PetscCall(PetscObjectStateIncrease((PetscObject)v3));
    2959:   PetscFunctionReturn(PETSC_SUCCESS);
    2960: }

    2962: PetscErrorCode MatADot_Default(Mat mat, Vec x, Vec y, PetscScalar *val)
    2963: {
    2964:   PetscFunctionBegin;
    2965:   if (!mat->dot_vec) PetscCall(MatCreateVecs(mat, &mat->dot_vec, NULL));
    2966:   PetscCall(MatMult(mat, x, mat->dot_vec));
    2967:   PetscCall(VecDot(mat->dot_vec, y, val));
    2968:   PetscFunctionReturn(PETSC_SUCCESS);
    2969: }

    2971: PetscErrorCode MatANorm_Default(Mat mat, Vec x, PetscReal *val)
    2972: {
    2973:   PetscScalar sval;

    2975:   PetscFunctionBegin;
    2976:   PetscCall(MatADot_Default(mat, x, x, &sval));
    2977:   PetscCheck(PetscRealPart(sval) >= 0.0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "Matrix argument is not positive definite");
    2978:   PetscCheck(PetscAbsReal(PetscImaginaryPart(sval)) < 100 * PETSC_MACHINE_EPSILON, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "Matrix argument is not Hermitian");
    2979:   *val = PetscSqrtReal(PetscRealPart(sval));
    2980:   PetscFunctionReturn(PETSC_SUCCESS);
    2981: }

    2983: /*@
    2984:   MatADot - Computes the inner product with respect to a matrix, i.e., $(x, y)_A = y^H A x$ where $A$ is symmetric (Hermitian when using complex)
    2985:   positive definite.

    2987:   Collective

    2989:   Input Parameters:
    2990: + mat - matrix used to define the inner product
    2991: . x   - first vector
    2992: - y   - second vector

    2994:   Output Parameter:
    2995: . val - the dot product with respect to `A`

    2997:   Level: intermediate

    2999:   Note:
    3000:   For complex vectors, `MatADot()` computes
    3001: $$
    3002:   val = (x,y)_A = y^H A x,
    3003: $$
    3004:   where $y^H$ denotes the conjugate transpose of `y`. Note that this corresponds to the "mathematicians" complex
    3005:   inner product where the SECOND argument gets the complex conjugate.

    3007: .seealso: [](ch_matrices), `Mat`, `MatANorm()`, `VecDot()`, `VecNorm()`, `MatMult()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    3008: @*/
    3009: PetscErrorCode MatADot(Mat mat, Vec x, Vec y, PetscScalar *val)
    3010: {
    3011:   PetscFunctionBegin;
    3015:   VecCheckAssembled(x);
    3017:   VecCheckAssembled(y);
    3020:   PetscAssertPointer(val, 4);
    3021:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3022:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3023:   PetscCheck(mat->cmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, x->map->N);
    3024:   PetscCheck(mat->rmap->N == y->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, y->map->N);
    3025:   PetscCheck(mat->cmap->n == x->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->n, x->map->n);
    3026:   PetscCheck(mat->rmap->n == y->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, y->map->n);
    3027:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
    3028:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_TRUE));
    3029:   MatCheckPreallocated(mat, 1);

    3031:   PetscCall(VecLockReadPush(x));
    3032:   PetscCall(VecLockReadPush(y));
    3033:   PetscCall(PetscLogEventBegin(MAT_ADot, mat, x, y, 0));
    3034:   PetscUseTypeMethod(mat, adot, x, y, val);
    3035:   PetscCall(PetscLogEventEnd(MAT_ADot, mat, x, y, 0));
    3036:   PetscCall(VecLockReadPop(y));
    3037:   PetscCall(VecLockReadPop(x));
    3038:   PetscFunctionReturn(PETSC_SUCCESS);
    3039: }

    3041: /*@
    3042:   MatANorm - Computes the norm with respect to a matrix, i.e., $(x, x)_A^{1/2} = (x^H A x)^{1/2}$ where $A$ is symmetric (Hermitian when using complex)
    3043:   positive definite.

    3045:   Collective

    3047:   Input Parameters:
    3048: + mat - matrix used to define norm
    3049: - x   - the vector to compute the norm of

    3051:   Output Parameter:
    3052: . val - the norm with respect to `A`

    3054:   Level: intermediate

    3056:   Note:
    3057:   For complex vectors, `MatANorm()` computes
    3058: $$
    3059:   val = (x,x)_A^{1/2} = (x^H A x)^{1/2},
    3060: $$
    3061:   where $x^H$ denotes the conjugate transpose of `x`.

    3063: .seealso: [](ch_matrices), `Mat`, `MatADot()`, `VecDot()`, `VecNorm()`, `MatMult()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    3064: @*/
    3065: PetscErrorCode MatANorm(Mat mat, Vec x, PetscReal *val)
    3066: {
    3067:   PetscFunctionBegin;
    3071:   VecCheckAssembled(x);
    3073:   PetscAssertPointer(val, 3);
    3074:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3075:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3076:   PetscCheck(mat->cmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, x->map->N);
    3077:   PetscCheck(mat->rmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, x->map->N);
    3078:   PetscCheck(mat->cmap->n == x->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->n, x->map->n);
    3079:   PetscCheck(mat->rmap->n == x->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, x->map->n);
    3080:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
    3081:   MatCheckPreallocated(mat, 1);

    3083:   PetscCall(VecLockReadPush(x));
    3084:   PetscCall(PetscLogEventBegin(MAT_ANorm, mat, x, 0, 0));
    3085:   PetscUseTypeMethod(mat, anorm, x, val);
    3086:   PetscCall(PetscLogEventEnd(MAT_ANorm, mat, x, 0, 0));
    3087:   PetscCall(VecLockReadPop(x));
    3088:   PetscFunctionReturn(PETSC_SUCCESS);
    3089: }

    3091: /*@
    3092:   MatGetFactorType - gets the type of factorization a matrix is

    3094:   Not Collective

    3096:   Input Parameter:
    3097: . mat - the matrix

    3099:   Output Parameter:
    3100: . t - the type, one of `MAT_FACTOR_NONE`, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ILU`, `MAT_FACTOR_ICC,MAT_FACTOR_ILUDT`, `MAT_FACTOR_QR`

    3102:   Level: intermediate

    3104: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorType`, `MatGetFactor()`, `MatSetFactorType()`, `MAT_FACTOR_NONE`, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ILU`,
    3105:           `MAT_FACTOR_ICC`, `MAT_FACTOR_ILUDT`, `MAT_FACTOR_QR`
    3106: @*/
    3107: PetscErrorCode MatGetFactorType(Mat mat, MatFactorType *t)
    3108: {
    3109:   PetscFunctionBegin;
    3112:   PetscAssertPointer(t, 2);
    3113:   *t = mat->factortype;
    3114:   PetscFunctionReturn(PETSC_SUCCESS);
    3115: }

    3117: /*@
    3118:   MatSetFactorType - sets the type of factorization a matrix is

    3120:   Logically Collective

    3122:   Input Parameters:
    3123: + mat - the matrix
    3124: - t   - the type, one of `MAT_FACTOR_NONE`, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ILU`, `MAT_FACTOR_ICC,MAT_FACTOR_ILUDT`, `MAT_FACTOR_QR`

    3126:   Level: intermediate

    3128: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorType`, `MatGetFactor()`, `MatGetFactorType()`, `MAT_FACTOR_NONE`, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ILU`,
    3129:           `MAT_FACTOR_ICC`, `MAT_FACTOR_ILUDT`, `MAT_FACTOR_QR`
    3130: @*/
    3131: PetscErrorCode MatSetFactorType(Mat mat, MatFactorType t)
    3132: {
    3133:   PetscFunctionBegin;
    3136:   mat->factortype = t;
    3137:   PetscFunctionReturn(PETSC_SUCCESS);
    3138: }

    3140: /*@
    3141:   MatGetInfo - Returns information about matrix storage (number of
    3142:   nonzeros, memory, etc.).

    3144:   Collective if `MAT_GLOBAL_MAX` or `MAT_GLOBAL_SUM` is used as the flag

    3146:   Input Parameters:
    3147: + mat  - the matrix
    3148: - flag - flag indicating the type of parameters to be returned (`MAT_LOCAL` - local matrix, `MAT_GLOBAL_MAX` - maximum over all processors, `MAT_GLOBAL_SUM` - sum over all processors)

    3150:   Output Parameter:
    3151: . info - matrix information context

    3153:   Options Database Key:
    3154: . -mat_view ::ascii_info - print matrix info to `PETSC_STDOUT`

    3156:   Level: intermediate

    3158:   Notes:
    3159:   The `MatInfo` context contains a variety of matrix data, including
    3160:   number of nonzeros allocated and used, number of mallocs during
    3161:   matrix assembly, etc.  Additional information for factored matrices
    3162:   is provided (such as the fill ratio, number of mallocs during
    3163:   factorization, etc.).

    3165:   Example:
    3166:   See the file ${PETSC_DIR}/include/petscmat.h for a complete list of
    3167:   data within the `MatInfo` context.  For example,
    3168: .vb
    3169:       MatInfo info;
    3170:       Mat     A;
    3171:       double  mal, nz_a, nz_u;

    3173:       MatGetInfo(A, MAT_LOCAL, &info);
    3174:       mal  = info.mallocs;
    3175:       nz_a = info.nz_allocated;
    3176: .ve

    3178: .seealso: [](ch_matrices), `Mat`, `MatInfo`, `MatStashGetInfo()`
    3179: @*/
    3180: PetscErrorCode MatGetInfo(Mat mat, MatInfoType flag, MatInfo *info)
    3181: {
    3182:   PetscFunctionBegin;
    3185:   PetscAssertPointer(info, 3);
    3186:   MatCheckPreallocated(mat, 1);
    3187:   PetscUseTypeMethod(mat, getinfo, flag, info);
    3188:   PetscFunctionReturn(PETSC_SUCCESS);
    3189: }

    3191: /*
    3192:    This is used by external packages where it is not easy to get the info from the actual
    3193:    matrix factorization.
    3194: */
    3195: PetscErrorCode MatGetInfo_External(Mat A, MatInfoType flag, MatInfo *info)
    3196: {
    3197:   PetscFunctionBegin;
    3198:   PetscCall(PetscMemzero(info, sizeof(MatInfo)));
    3199:   PetscFunctionReturn(PETSC_SUCCESS);
    3200: }

    3202: /*@
    3203:   MatLUFactor - Performs in-place LU factorization of matrix.

    3205:   Collective

    3207:   Input Parameters:
    3208: + mat  - the matrix
    3209: . row  - row permutation
    3210: . col  - column permutation
    3211: - info - options for factorization, includes
    3212: .vb
    3213:           fill - expected fill as ratio of original fill.
    3214:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3215:                    Run with the option -info to determine an optimal value to use
    3216: .ve

    3218:   Level: developer

    3220:   Notes:
    3221:   Most users should employ the `KSP` interface for linear solvers
    3222:   instead of working directly with matrix algebra routines such as this.
    3223:   See, e.g., `KSPCreate()`.

    3225:   This changes the state of the matrix to a factored matrix; it cannot be used
    3226:   for example with `MatSetValues()` unless one first calls `MatSetUnfactored()`.

    3228:   This is really in-place only for dense matrices, the preferred approach is to use `MatGetFactor()`, `MatLUFactorSymbolic()`, and `MatLUFactorNumeric()`
    3229:   when not using `KSP`.

    3231:   Fortran Note:
    3232:   A valid (non-null) `info` argument must be provided

    3234: .seealso: [](ch_matrices), [Matrix Factorization](sec_matfactor), `Mat`, `MatFactorType`, `MatLUFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`,
    3235:           `MatGetOrdering()`, `MatSetUnfactored()`, `MatFactorInfo`, `MatGetFactor()`
    3236: @*/
    3237: PetscErrorCode MatLUFactor(Mat mat, IS row, IS col, const MatFactorInfo *info)
    3238: {
    3239:   MatFactorInfo tinfo;

    3241:   PetscFunctionBegin;
    3245:   if (info) PetscAssertPointer(info, 4);
    3247:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3248:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3249:   MatCheckPreallocated(mat, 1);
    3250:   if (!info) {
    3251:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3252:     info = &tinfo;
    3253:   }

    3255:   PetscCall(PetscLogEventBegin(MAT_LUFactor, mat, row, col, 0));
    3256:   PetscUseTypeMethod(mat, lufactor, row, col, info);
    3257:   PetscCall(PetscLogEventEnd(MAT_LUFactor, mat, row, col, 0));
    3258:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    3259:   PetscFunctionReturn(PETSC_SUCCESS);
    3260: }

    3262: /*@
    3263:   MatILUFactor - Performs in-place ILU factorization of matrix.

    3265:   Collective

    3267:   Input Parameters:
    3268: + mat  - the matrix
    3269: . row  - row permutation
    3270: . col  - column permutation
    3271: - info - structure containing
    3272: .vb
    3273:       levels - number of levels of fill.
    3274:       expected fill - as ratio of original fill.
    3275:       1 or 0 - indicating force fill on diagonal (improves robustness for matrices
    3276:                 missing diagonal entries)
    3277: .ve

    3279:   Level: developer

    3281:   Notes:
    3282:   Most users should employ the `KSP` interface for linear solvers
    3283:   instead of working directly with matrix algebra routines such as this.
    3284:   See, e.g., `KSPCreate()`.

    3286:   Probably really in-place only when level of fill is zero, otherwise allocates
    3287:   new space to store factored matrix and deletes previous memory. The preferred approach is to use `MatGetFactor()`, `MatILUFactorSymbolic()`, and `MatILUFactorNumeric()`
    3288:   when not using `KSP`.

    3290:   Fortran Note:
    3291:   A valid (non-null) `info` argument must be provided

    3293: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatILUFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`, `MatFactorInfo`
    3294: @*/
    3295: PetscErrorCode MatILUFactor(Mat mat, IS row, IS col, const MatFactorInfo *info)
    3296: {
    3297:   PetscFunctionBegin;
    3301:   PetscAssertPointer(info, 4);
    3303:   PetscCheck(mat->rmap->N == mat->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "matrix must be square");
    3304:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3305:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3306:   MatCheckPreallocated(mat, 1);

    3308:   PetscCall(PetscLogEventBegin(MAT_ILUFactor, mat, row, col, 0));
    3309:   PetscUseTypeMethod(mat, ilufactor, row, col, info);
    3310:   PetscCall(PetscLogEventEnd(MAT_ILUFactor, mat, row, col, 0));
    3311:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    3312:   PetscFunctionReturn(PETSC_SUCCESS);
    3313: }

    3315: /*@
    3316:   MatLUFactorSymbolic - Performs symbolic LU factorization of matrix.
    3317:   Call this routine before calling `MatLUFactorNumeric()` and after `MatGetFactor()`.

    3319:   Collective

    3321:   Input Parameters:
    3322: + fact - the factor matrix obtained with `MatGetFactor()`
    3323: . mat  - the matrix
    3324: . row  - the row permutation
    3325: . col  - the column permutation
    3326: - info - options for factorization, includes
    3327: .vb
    3328:           fill - expected fill as ratio of original fill. Run with the option -info to determine an optimal value to use
    3329:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3330: .ve

    3332:   Level: developer

    3334:   Notes:
    3335:   See [Matrix Factorization](sec_matfactor) for additional information about factorizations

    3337:   Most users should employ the simplified `KSP` interface for linear solvers
    3338:   instead of working directly with matrix algebra routines such as this.
    3339:   See, e.g., `KSPCreate()`.

    3341:   Fortran Note:
    3342:   A valid (non-null) `info` argument must be provided

    3344: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatLUFactor()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`, `MatFactorInfo`, `MatFactorInfoInitialize()`
    3345: @*/
    3346: PetscErrorCode MatLUFactorSymbolic(Mat fact, Mat mat, IS row, IS col, const MatFactorInfo *info)
    3347: {
    3348:   MatFactorInfo tinfo;

    3350:   PetscFunctionBegin;
    3355:   if (info) PetscAssertPointer(info, 5);
    3358:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3359:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3360:   MatCheckPreallocated(mat, 2);
    3361:   if (!info) {
    3362:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3363:     info = &tinfo;
    3364:   }

    3366:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_LUFactorSymbolic, mat, row, col, 0));
    3367:   PetscUseTypeMethod(fact, lufactorsymbolic, mat, row, col, info);
    3368:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_LUFactorSymbolic, mat, row, col, 0));
    3369:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3370:   PetscFunctionReturn(PETSC_SUCCESS);
    3371: }

    3373: /*@
    3374:   MatLUFactorNumeric - Performs numeric LU factorization of a matrix.
    3375:   Call this routine after first calling `MatLUFactorSymbolic()` and `MatGetFactor()`.

    3377:   Collective

    3379:   Input Parameters:
    3380: + fact - the factor matrix obtained with `MatGetFactor()`
    3381: . mat  - the matrix
    3382: - info - options for factorization

    3384:   Level: developer

    3386:   Notes:
    3387:   See `MatLUFactor()` for in-place factorization.  See
    3388:   `MatCholeskyFactorNumeric()` for the symmetric, positive definite case.

    3390:   Most users should employ the `KSP` interface for linear solvers
    3391:   instead of working directly with matrix algebra routines such as this.
    3392:   See, e.g., `KSPCreate()`.

    3394:   Fortran Note:
    3395:   A valid (non-null) `info` argument must be provided

    3397: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatFactorInfo`, `MatLUFactorSymbolic()`, `MatLUFactor()`, `MatCholeskyFactor()`
    3398: @*/
    3399: PetscErrorCode MatLUFactorNumeric(Mat fact, Mat mat, const MatFactorInfo *info)
    3400: {
    3401:   MatFactorInfo tinfo;

    3403:   PetscFunctionBegin;
    3408:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3409:   PetscCheck(mat->rmap->N == (fact)->rmap->N && mat->cmap->N == (fact)->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Mat fact: global dimensions are different %" PetscInt_FMT " should = %" PetscInt_FMT " %" PetscInt_FMT " should = %" PetscInt_FMT,
    3410:              mat->rmap->N, (fact)->rmap->N, mat->cmap->N, (fact)->cmap->N);

    3412:   MatCheckPreallocated(mat, 2);
    3413:   if (!info) {
    3414:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3415:     info = &tinfo;
    3416:   }

    3418:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_LUFactorNumeric, mat, fact, 0, 0));
    3419:   else PetscCall(PetscLogEventBegin(MAT_LUFactor, mat, fact, 0, 0));
    3420:   PetscUseTypeMethod(fact, lufactornumeric, mat, info);
    3421:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_LUFactorNumeric, mat, fact, 0, 0));
    3422:   else PetscCall(PetscLogEventEnd(MAT_LUFactor, mat, fact, 0, 0));
    3423:   PetscCall(MatViewFromOptions(fact, NULL, "-mat_factor_view"));
    3424:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3425:   PetscFunctionReturn(PETSC_SUCCESS);
    3426: }

    3428: /*@
    3429:   MatCholeskyFactor - Performs in-place Cholesky factorization of a
    3430:   symmetric matrix.

    3432:   Collective

    3434:   Input Parameters:
    3435: + mat  - the matrix
    3436: . perm - row and column permutations
    3437: - info - expected fill as ratio of original fill

    3439:   Level: developer

    3441:   Notes:
    3442:   See `MatLUFactor()` for the nonsymmetric case.  See also `MatGetFactor()`,
    3443:   `MatCholeskyFactorSymbolic()`, and `MatCholeskyFactorNumeric()`.

    3445:   Most users should employ the `KSP` interface for linear solvers
    3446:   instead of working directly with matrix algebra routines such as this.
    3447:   See, e.g., `KSPCreate()`.

    3449:   Fortran Note:
    3450:   A valid (non-null) `info` argument must be provided

    3452: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatFactorInfo`, `MatLUFactor()`, `MatCholeskyFactorSymbolic()`, `MatCholeskyFactorNumeric()`,
    3453:           `MatGetOrdering()`
    3454: @*/
    3455: PetscErrorCode MatCholeskyFactor(Mat mat, IS perm, const MatFactorInfo *info)
    3456: {
    3457:   MatFactorInfo tinfo;

    3459:   PetscFunctionBegin;
    3462:   if (info) PetscAssertPointer(info, 3);
    3464:   PetscCheck(mat->rmap->N == mat->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "Matrix must be square");
    3465:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3466:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3467:   MatCheckPreallocated(mat, 1);
    3468:   if (!info) {
    3469:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3470:     info = &tinfo;
    3471:   }

    3473:   PetscCall(PetscLogEventBegin(MAT_CholeskyFactor, mat, perm, 0, 0));
    3474:   PetscUseTypeMethod(mat, choleskyfactor, perm, info);
    3475:   PetscCall(PetscLogEventEnd(MAT_CholeskyFactor, mat, perm, 0, 0));
    3476:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    3477:   PetscFunctionReturn(PETSC_SUCCESS);
    3478: }

    3480: /*@
    3481:   MatCholeskyFactorSymbolic - Performs symbolic Cholesky factorization
    3482:   of a symmetric matrix.

    3484:   Collective

    3486:   Input Parameters:
    3487: + fact - the factor matrix obtained with `MatGetFactor()`
    3488: . mat  - the matrix
    3489: . perm - row and column permutations
    3490: - info - options for factorization, includes
    3491: .vb
    3492:           fill - expected fill as ratio of original fill.
    3493:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3494:                    Run with the option -info to determine an optimal value to use
    3495: .ve

    3497:   Level: developer

    3499:   Notes:
    3500:   See `MatLUFactorSymbolic()` for the nonsymmetric case.  See also
    3501:   `MatCholeskyFactor()` and `MatCholeskyFactorNumeric()`.

    3503:   Most users should employ the `KSP` interface for linear solvers
    3504:   instead of working directly with matrix algebra routines such as this.
    3505:   See, e.g., `KSPCreate()`.

    3507:   Fortran Note:
    3508:   A valid (non-null) `info` argument must be provided

    3510: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorInfo`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatCholeskyFactor()`, `MatCholeskyFactorNumeric()`,
    3511:           `MatGetOrdering()`
    3512: @*/
    3513: PetscErrorCode MatCholeskyFactorSymbolic(Mat fact, Mat mat, IS perm, const MatFactorInfo *info)
    3514: {
    3515:   MatFactorInfo tinfo;

    3517:   PetscFunctionBegin;
    3521:   if (info) PetscAssertPointer(info, 4);
    3524:   PetscCheck(mat->rmap->N == mat->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "Matrix must be square");
    3525:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3526:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3527:   MatCheckPreallocated(mat, 2);
    3528:   if (!info) {
    3529:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3530:     info = &tinfo;
    3531:   }

    3533:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_CholeskyFactorSymbolic, mat, perm, 0, 0));
    3534:   PetscUseTypeMethod(fact, choleskyfactorsymbolic, mat, perm, info);
    3535:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_CholeskyFactorSymbolic, mat, perm, 0, 0));
    3536:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3537:   PetscFunctionReturn(PETSC_SUCCESS);
    3538: }

    3540: /*@
    3541:   MatCholeskyFactorNumeric - Performs numeric Cholesky factorization
    3542:   of a symmetric matrix. Call this routine after first calling `MatGetFactor()` and
    3543:   `MatCholeskyFactorSymbolic()`.

    3545:   Collective

    3547:   Input Parameters:
    3548: + fact - the factor matrix obtained with `MatGetFactor()`, where the factored values are stored
    3549: . mat  - the initial matrix that is to be factored
    3550: - info - options for factorization

    3552:   Level: developer

    3554:   Note:
    3555:   Most users should employ the `KSP` interface for linear solvers
    3556:   instead of working directly with matrix algebra routines such as this.
    3557:   See, e.g., `KSPCreate()`.

    3559:   Fortran Note:
    3560:   A valid (non-null) `info` argument must be provided

    3562: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorInfo`, `MatGetFactor()`, `MatCholeskyFactorSymbolic()`, `MatCholeskyFactor()`, `MatLUFactorNumeric()`
    3563: @*/
    3564: PetscErrorCode MatCholeskyFactorNumeric(Mat fact, Mat mat, const MatFactorInfo *info)
    3565: {
    3566:   MatFactorInfo tinfo;

    3568:   PetscFunctionBegin;
    3573:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3574:   PetscCheck(mat->rmap->N == (fact)->rmap->N && mat->cmap->N == (fact)->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Mat fact: global dim %" PetscInt_FMT " should = %" PetscInt_FMT " %" PetscInt_FMT " should = %" PetscInt_FMT,
    3575:              mat->rmap->N, (fact)->rmap->N, mat->cmap->N, (fact)->cmap->N);
    3576:   MatCheckPreallocated(mat, 2);
    3577:   if (!info) {
    3578:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3579:     info = &tinfo;
    3580:   }

    3582:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_CholeskyFactorNumeric, mat, fact, 0, 0));
    3583:   else PetscCall(PetscLogEventBegin(MAT_CholeskyFactor, mat, fact, 0, 0));
    3584:   PetscUseTypeMethod(fact, choleskyfactornumeric, mat, info);
    3585:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_CholeskyFactorNumeric, mat, fact, 0, 0));
    3586:   else PetscCall(PetscLogEventEnd(MAT_CholeskyFactor, mat, fact, 0, 0));
    3587:   PetscCall(MatViewFromOptions(fact, NULL, "-mat_factor_view"));
    3588:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3589:   PetscFunctionReturn(PETSC_SUCCESS);
    3590: }

    3592: /*@
    3593:   MatQRFactor - Performs in-place QR factorization of matrix.

    3595:   Collective

    3597:   Input Parameters:
    3598: + mat  - the matrix
    3599: . col  - column permutation
    3600: - info - options for factorization, includes
    3601: .vb
    3602:           fill - expected fill as ratio of original fill.
    3603:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3604:                    Run with the option -info to determine an optimal value to use
    3605: .ve

    3607:   Level: developer

    3609:   Notes:
    3610:   Most users should employ the `KSP` interface for linear solvers
    3611:   instead of working directly with matrix algebra routines such as this.
    3612:   See, e.g., `KSPCreate()`.

    3614:   This changes the state of the matrix to a factored matrix; it cannot be used
    3615:   for example with `MatSetValues()` unless one first calls `MatSetUnfactored()`.

    3617:   Fortran Note:
    3618:   A valid (non-null) `info` argument must be provided

    3620: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorInfo`, `MatGetFactor()`, `MatQRFactorSymbolic()`, `MatQRFactorNumeric()`, `MatLUFactor()`,
    3621:           `MatSetUnfactored()`
    3622: @*/
    3623: PetscErrorCode MatQRFactor(Mat mat, IS col, const MatFactorInfo *info)
    3624: {
    3625:   PetscFunctionBegin;
    3628:   if (info) PetscAssertPointer(info, 3);
    3630:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3631:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3632:   MatCheckPreallocated(mat, 1);
    3633:   PetscCall(PetscLogEventBegin(MAT_QRFactor, mat, col, 0, 0));
    3634:   PetscUseMethod(mat, "MatQRFactor_C", (Mat, IS, const MatFactorInfo *), (mat, col, info));
    3635:   PetscCall(PetscLogEventEnd(MAT_QRFactor, mat, col, 0, 0));
    3636:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    3637:   PetscFunctionReturn(PETSC_SUCCESS);
    3638: }

    3640: /*@
    3641:   MatQRFactorSymbolic - Performs symbolic QR factorization of matrix.
    3642:   Call this routine after `MatGetFactor()` but before calling `MatQRFactorNumeric()`.

    3644:   Collective

    3646:   Input Parameters:
    3647: + fact - the factor matrix obtained with `MatGetFactor()`
    3648: . mat  - the matrix
    3649: . col  - column permutation
    3650: - info - options for factorization, includes
    3651: .vb
    3652:           fill - expected fill as ratio of original fill.
    3653:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3654:                    Run with the option -info to determine an optimal value to use
    3655: .ve

    3657:   Level: developer

    3659:   Note:
    3660:   Most users should employ the `KSP` interface for linear solvers
    3661:   instead of working directly with matrix algebra routines such as this.
    3662:   See, e.g., `KSPCreate()`.

    3664:   Fortran Note:
    3665:   A valid (non-null) `info` argument must be provided

    3667: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatFactorInfo`, `MatQRFactor()`, `MatQRFactorNumeric()`, `MatLUFactor()`, `MatFactorInfoInitialize()`
    3668: @*/
    3669: PetscErrorCode MatQRFactorSymbolic(Mat fact, Mat mat, IS col, const MatFactorInfo *info)
    3670: {
    3671:   MatFactorInfo tinfo;

    3673:   PetscFunctionBegin;
    3677:   if (info) PetscAssertPointer(info, 4);
    3680:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3681:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3682:   MatCheckPreallocated(mat, 2);
    3683:   if (!info) {
    3684:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3685:     info = &tinfo;
    3686:   }

    3688:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_QRFactorSymbolic, fact, mat, col, 0));
    3689:   PetscUseMethod(fact, "MatQRFactorSymbolic_C", (Mat, Mat, IS, const MatFactorInfo *), (fact, mat, col, info));
    3690:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_QRFactorSymbolic, fact, mat, col, 0));
    3691:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3692:   PetscFunctionReturn(PETSC_SUCCESS);
    3693: }

    3695: /*@
    3696:   MatQRFactorNumeric - Performs numeric QR factorization of a matrix.
    3697:   Call this routine after first calling `MatGetFactor()`, and `MatQRFactorSymbolic()`.

    3699:   Collective

    3701:   Input Parameters:
    3702: + fact - the factor matrix obtained with `MatGetFactor()`
    3703: . mat  - the matrix
    3704: - info - options for factorization

    3706:   Level: developer

    3708:   Notes:
    3709:   See `MatQRFactor()` for in-place factorization.

    3711:   Most users should employ the `KSP` interface for linear solvers
    3712:   instead of working directly with matrix algebra routines such as this.
    3713:   See, e.g., `KSPCreate()`.

    3715:   Fortran Note:
    3716:   A valid (non-null) `info` argument must be provided

    3718: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorInfo`, `MatGetFactor()`, `MatQRFactor()`, `MatQRFactorSymbolic()`, `MatLUFactor()`
    3719: @*/
    3720: PetscErrorCode MatQRFactorNumeric(Mat fact, Mat mat, const MatFactorInfo *info)
    3721: {
    3722:   MatFactorInfo tinfo;

    3724:   PetscFunctionBegin;
    3729:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3730:   PetscCheck(mat->rmap->N == fact->rmap->N && mat->cmap->N == fact->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Mat fact: global dimensions are different %" PetscInt_FMT " should = %" PetscInt_FMT " %" PetscInt_FMT " should = %" PetscInt_FMT,
    3731:              mat->rmap->N, (fact)->rmap->N, mat->cmap->N, (fact)->cmap->N);

    3733:   MatCheckPreallocated(mat, 2);
    3734:   if (!info) {
    3735:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3736:     info = &tinfo;
    3737:   }

    3739:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_QRFactorNumeric, mat, fact, 0, 0));
    3740:   else PetscCall(PetscLogEventBegin(MAT_QRFactor, mat, fact, 0, 0));
    3741:   PetscUseMethod(fact, "MatQRFactorNumeric_C", (Mat, Mat, const MatFactorInfo *), (fact, mat, info));
    3742:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_QRFactorNumeric, mat, fact, 0, 0));
    3743:   else PetscCall(PetscLogEventEnd(MAT_QRFactor, mat, fact, 0, 0));
    3744:   PetscCall(MatViewFromOptions(fact, NULL, "-mat_factor_view"));
    3745:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3746:   PetscFunctionReturn(PETSC_SUCCESS);
    3747: }

    3749: /*@
    3750:   MatSolve - Solves $A x = b$, given a factored matrix.

    3752:   Neighbor-wise Collective

    3754:   Input Parameters:
    3755: + mat - the factored matrix
    3756: - b   - the right-hand-side vector

    3758:   Output Parameter:
    3759: . x - the result vector

    3761:   Level: developer

    3763:   Notes:
    3764:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    3765:   call `MatSolve`(A,x,x).

    3767:   Most users should employ the `KSP` interface for linear solvers
    3768:   instead of working directly with matrix algebra routines such as this.
    3769:   See, e.g., `KSPCreate()`.

    3771: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatLUFactor()`, `MatSolveAdd()`, `MatSolveTranspose()`, `MatSolveTransposeAdd()`
    3772: @*/
    3773: PetscErrorCode MatSolve(Mat mat, Vec b, Vec x)
    3774: {
    3775:   PetscFunctionBegin;
    3780:   PetscCheckSameComm(mat, 1, b, 2);
    3781:   PetscCheckSameComm(mat, 1, x, 3);
    3782:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    3783:   PetscCheck(mat->cmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, x->map->N);
    3784:   PetscCheck(mat->rmap->N == b->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, b->map->N);
    3785:   PetscCheck(mat->rmap->n == b->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, b->map->n);
    3786:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3787:   MatCheckPreallocated(mat, 1);

    3789:   PetscCall(PetscLogEventBegin(MAT_Solve, mat, b, x, 0));
    3790:   PetscCall(VecFlag(x, mat->factorerrortype));
    3791:   if (mat->factorerrortype) PetscCall(PetscInfo(mat, "MatFactorError %d\n", mat->factorerrortype));
    3792:   else PetscUseTypeMethod(mat, solve, b, x);
    3793:   PetscCall(PetscLogEventEnd(MAT_Solve, mat, b, x, 0));
    3794:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    3795:   PetscFunctionReturn(PETSC_SUCCESS);
    3796: }

    3798: static PetscErrorCode MatMatSolve_Basic(Mat A, Mat B, Mat X, PetscBool trans)
    3799: {
    3800:   Vec      b, x;
    3801:   PetscInt N, i;
    3802:   PetscErrorCode (*f)(Mat, Vec, Vec);
    3803:   PetscBool Abound, Bneedconv = PETSC_FALSE, Xneedconv = PETSC_FALSE;

    3805:   PetscFunctionBegin;
    3806:   if (A->factorerrortype) {
    3807:     PetscCall(PetscInfo(A, "MatFactorError %d\n", A->factorerrortype));
    3808:     PetscCall(MatSetInf(X));
    3809:     PetscFunctionReturn(PETSC_SUCCESS);
    3810:   }
    3811:   f = (!trans || (!A->ops->solvetranspose && A->symmetric)) ? A->ops->solve : A->ops->solvetranspose;
    3812:   PetscCheck(f, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Mat type %s", ((PetscObject)A)->type_name);
    3813:   PetscCall(MatBoundToCPU(A, &Abound));
    3814:   if (!Abound) {
    3815:     PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &Bneedconv, MATSEQDENSE, MATMPIDENSE, ""));
    3816:     PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &Xneedconv, MATSEQDENSE, MATMPIDENSE, ""));
    3817:   }
    3818: #if PetscDefined(HAVE_CUDA)
    3819:   if (Bneedconv) PetscCall(MatConvert(B, MATDENSECUDA, MAT_INPLACE_MATRIX, &B));
    3820:   if (Xneedconv) PetscCall(MatConvert(X, MATDENSECUDA, MAT_INPLACE_MATRIX, &X));
    3821: #elif PetscDefined(HAVE_HIP)
    3822:   if (Bneedconv) PetscCall(MatConvert(B, MATDENSEHIP, MAT_INPLACE_MATRIX, &B));
    3823:   if (Xneedconv) PetscCall(MatConvert(X, MATDENSEHIP, MAT_INPLACE_MATRIX, &X));
    3824: #endif
    3825:   PetscCall(MatGetSize(B, NULL, &N));
    3826:   for (i = 0; i < N; i++) {
    3827:     PetscCall(MatDenseGetColumnVecRead(B, i, &b));
    3828:     PetscCall(MatDenseGetColumnVecWrite(X, i, &x));
    3829:     PetscCall((*f)(A, b, x));
    3830:     PetscCall(MatDenseRestoreColumnVecWrite(X, i, &x));
    3831:     PetscCall(MatDenseRestoreColumnVecRead(B, i, &b));
    3832:   }
    3833:   if (Bneedconv) PetscCall(MatConvert(B, MATDENSE, MAT_INPLACE_MATRIX, &B));
    3834:   if (Xneedconv) PetscCall(MatConvert(X, MATDENSE, MAT_INPLACE_MATRIX, &X));
    3835:   PetscFunctionReturn(PETSC_SUCCESS);
    3836: }

    3838: /*@
    3839:   MatMatSolve - Solves $A X = B$, given a factored matrix.

    3841:   Neighbor-wise Collective

    3843:   Input Parameters:
    3844: + A - the factored matrix
    3845: - B - the right-hand-side matrix `MATDENSE` (or sparse `MATAIJ`-- when using MUMPS)

    3847:   Output Parameter:
    3848: . X - the result matrix (dense matrix)

    3850:   Level: developer

    3852:   Note:
    3853:   If `B` is a `MATDENSE` matrix then one can call `MatMatSolve`(A,B,B) except with `MATSOLVERMKL_CPARDISO`;
    3854:   otherwise, `B` and `X` cannot be the same.

    3856: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatSolve()`, `MatMatSolveTranspose()`, `MatLUFactor()`, `MatCholeskyFactor()`
    3857: @*/
    3858: PetscErrorCode MatMatSolve(Mat A, Mat B, Mat X)
    3859: {
    3860:   PetscFunctionBegin;
    3865:   PetscCheckSameComm(A, 1, B, 2);
    3866:   PetscCheckSameComm(A, 1, X, 3);
    3867:   PetscCheck(A->cmap->N == X->rmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Mat A,Mat X: global dim %" PetscInt_FMT " %" PetscInt_FMT, A->cmap->N, X->rmap->N);
    3868:   PetscCheck(A->rmap->N == B->rmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Mat A,Mat B: global dim %" PetscInt_FMT " %" PetscInt_FMT, A->rmap->N, B->rmap->N);
    3869:   PetscCheck(X->cmap->N == B->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Solution matrix must have same number of columns as rhs matrix");
    3870:   if (!A->rmap->N && !A->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3871:   MatCheckPreallocated(A, 1);

    3873:   PetscCall(PetscLogEventBegin(MAT_MatSolve, A, B, X, 0));
    3874:   if (!A->ops->matsolve) {
    3875:     PetscCall(PetscInfo(A, "Mat type %s using basic MatMatSolve\n", ((PetscObject)A)->type_name));
    3876:     PetscCall(MatMatSolve_Basic(A, B, X, PETSC_FALSE));
    3877:   } else PetscUseTypeMethod(A, matsolve, B, X);
    3878:   PetscCall(PetscLogEventEnd(MAT_MatSolve, A, B, X, 0));
    3879:   PetscCall(PetscObjectStateIncrease((PetscObject)X));
    3880:   PetscFunctionReturn(PETSC_SUCCESS);
    3881: }

    3883: /*@
    3884:   MatMatSolveTranspose - Solves $A^T X = B $, given a factored matrix.

    3886:   Neighbor-wise Collective

    3888:   Input Parameters:
    3889: + A - the factored matrix
    3890: - B - the right-hand-side matrix  (`MATDENSE` matrix)

    3892:   Output Parameter:
    3893: . X - the result matrix (dense matrix)

    3895:   Level: developer

    3897:   Note:
    3898:   The matrices `B` and `X` cannot be the same.  I.e., one cannot
    3899:   call `MatMatSolveTranspose`(A,X,X).

    3901: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatSolveTranspose()`, `MatMatSolve()`, `MatLUFactor()`, `MatCholeskyFactor()`
    3902: @*/
    3903: PetscErrorCode MatMatSolveTranspose(Mat A, Mat B, Mat X)
    3904: {
    3905:   PetscFunctionBegin;
    3910:   PetscCheckSameComm(A, 1, B, 2);
    3911:   PetscCheckSameComm(A, 1, X, 3);
    3912:   PetscCheck(X != B, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_IDN, "X and B must be different matrices");
    3913:   PetscCheck(A->cmap->N == X->rmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Mat A,Mat X: global dim %" PetscInt_FMT " %" PetscInt_FMT, A->cmap->N, X->rmap->N);
    3914:   PetscCheck(A->rmap->N == B->rmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Mat A,Mat B: global dim %" PetscInt_FMT " %" PetscInt_FMT, A->rmap->N, B->rmap->N);
    3915:   PetscCheck(A->rmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat A,Mat B: local dim %" PetscInt_FMT " %" PetscInt_FMT, A->rmap->n, B->rmap->n);
    3916:   PetscCheck(X->cmap->N >= B->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Solution matrix must have same number of columns as rhs matrix");
    3917:   if (!A->rmap->N && !A->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3918:   MatCheckPreallocated(A, 1);

    3920:   PetscCall(PetscLogEventBegin(MAT_MatSolve, A, B, X, 0));
    3921:   if (!A->ops->matsolvetranspose) {
    3922:     PetscCall(PetscInfo(A, "Mat type %s using basic MatMatSolveTranspose\n", ((PetscObject)A)->type_name));
    3923:     PetscCall(MatMatSolve_Basic(A, B, X, PETSC_TRUE));
    3924:   } else PetscUseTypeMethod(A, matsolvetranspose, B, X);
    3925:   PetscCall(PetscLogEventEnd(MAT_MatSolve, A, B, X, 0));
    3926:   PetscCall(PetscObjectStateIncrease((PetscObject)X));
    3927:   PetscFunctionReturn(PETSC_SUCCESS);
    3928: }

    3930: /*@
    3931:   MatMatTransposeSolve - Solves $A X = B^T$, given a factored matrix.

    3933:   Neighbor-wise Collective

    3935:   Input Parameters:
    3936: + A  - the factored matrix
    3937: - Bt - the transpose of right-hand-side matrix as a `MATDENSE`

    3939:   Output Parameter:
    3940: . X - the result matrix (dense matrix)

    3942:   Level: developer

    3944:   Note:
    3945:   For MUMPS, it only supports centralized sparse compressed column format on the host processor for right-hand side matrix. User must create `Bt` in sparse compressed row
    3946:   format on the host processor and call `MatMatTransposeSolve()` to implement MUMPS' `MatMatSolve()`.

    3948: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatMatSolve()`, `MatMatSolveTranspose()`, `MatLUFactor()`, `MatCholeskyFactor()`
    3949: @*/
    3950: PetscErrorCode MatMatTransposeSolve(Mat A, Mat Bt, Mat X)
    3951: {
    3952:   PetscFunctionBegin;
    3957:   PetscCheckSameComm(A, 1, Bt, 2);
    3958:   PetscCheckSameComm(A, 1, X, 3);

    3960:   PetscCheck(X != Bt, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_IDN, "X and B must be different matrices");
    3961:   PetscCheck(A->cmap->N == X->rmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Mat A,Mat X: global dim %" PetscInt_FMT " %" PetscInt_FMT, A->cmap->N, X->rmap->N);
    3962:   PetscCheck(A->rmap->N == Bt->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Mat A,Mat Bt: global dim %" PetscInt_FMT " %" PetscInt_FMT, A->rmap->N, Bt->cmap->N);
    3963:   PetscCheck(X->cmap->N >= Bt->rmap->N, PetscObjectComm((PetscObject)X), PETSC_ERR_ARG_SIZ, "Solution matrix must have same number of columns as row number of the rhs matrix");
    3964:   if (!A->rmap->N && !A->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3965:   PetscCheck(A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Unfactored matrix");
    3966:   MatCheckPreallocated(A, 1);

    3968:   PetscCall(PetscLogEventBegin(MAT_MatTrSolve, A, Bt, X, 0));
    3969:   PetscUseTypeMethod(A, mattransposesolve, Bt, X);
    3970:   PetscCall(PetscLogEventEnd(MAT_MatTrSolve, A, Bt, X, 0));
    3971:   PetscCall(PetscObjectStateIncrease((PetscObject)X));
    3972:   PetscFunctionReturn(PETSC_SUCCESS);
    3973: }

    3975: /*@
    3976:   MatForwardSolve - Solves $ L x = b $, given a factored matrix, $A = LU $, or
    3977:   $U^T*D^(1/2) x = b$, given a factored symmetric matrix, $A = U^T*D*U$,

    3979:   Neighbor-wise Collective

    3981:   Input Parameters:
    3982: + mat - the factored matrix
    3983: - b   - the right-hand-side vector

    3985:   Output Parameter:
    3986: . x - the result vector

    3988:   Level: developer

    3990:   Notes:
    3991:   `MatSolve()` should be used for most applications, as it performs
    3992:   a forward solve followed by a backward solve.

    3994:   The vectors `b` and `x` cannot be the same,  i.e., one cannot
    3995:   call `MatForwardSolve`(A,x,x).

    3997:   For matrix in `MATSEQBAIJ` format with block size larger than 1,
    3998:   the diagonal blocks are not implemented as $D = D^(1/2) * D^(1/2)$ yet.
    3999:   `MatForwardSolve()` solves $U^T*D y = b$, and
    4000:   `MatBackwardSolve()` solves $U x = y$.
    4001:   Thus they do not provide a symmetric preconditioner.

    4003: .seealso: [](ch_matrices), `Mat`, `MatBackwardSolve()`, `MatGetFactor()`, `MatSolve()`
    4004: @*/
    4005: PetscErrorCode MatForwardSolve(Mat mat, Vec b, Vec x)
    4006: {
    4007:   PetscFunctionBegin;
    4012:   PetscCheckSameComm(mat, 1, b, 2);
    4013:   PetscCheckSameComm(mat, 1, x, 3);
    4014:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    4015:   PetscCheck(mat->cmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, x->map->N);
    4016:   PetscCheck(mat->rmap->N == b->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, b->map->N);
    4017:   PetscCheck(mat->rmap->n == b->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, b->map->n);
    4018:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    4019:   MatCheckPreallocated(mat, 1);

    4021:   PetscCall(PetscLogEventBegin(MAT_ForwardSolve, mat, b, x, 0));
    4022:   PetscUseTypeMethod(mat, forwardsolve, b, x);
    4023:   PetscCall(PetscLogEventEnd(MAT_ForwardSolve, mat, b, x, 0));
    4024:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4025:   PetscFunctionReturn(PETSC_SUCCESS);
    4026: }

    4028: /*@
    4029:   MatBackwardSolve - Solves $U x = b$, given a factored matrix, $A = LU$.
    4030:   $D^(1/2) U x = b$, given a factored symmetric matrix, $A = U^T*D*U$,

    4032:   Neighbor-wise Collective

    4034:   Input Parameters:
    4035: + mat - the factored matrix
    4036: - b   - the right-hand-side vector

    4038:   Output Parameter:
    4039: . x - the result vector

    4041:   Level: developer

    4043:   Notes:
    4044:   `MatSolve()` should be used for most applications, as it performs
    4045:   a forward solve followed by a backward solve.

    4047:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    4048:   call `MatBackwardSolve`(A,x,x).

    4050:   For matrix in `MATSEQBAIJ` format with block size larger than 1,
    4051:   the diagonal blocks are not implemented as $D = D^(1/2) * D^(1/2)$ yet.
    4052:   `MatForwardSolve()` solves $U^T*D y = b$, and
    4053:   `MatBackwardSolve()` solves $U x = y$.
    4054:   Thus they do not provide a symmetric preconditioner.

    4056: .seealso: [](ch_matrices), `Mat`, `MatForwardSolve()`, `MatGetFactor()`, `MatSolve()`
    4057: @*/
    4058: PetscErrorCode MatBackwardSolve(Mat mat, Vec b, Vec x)
    4059: {
    4060:   PetscFunctionBegin;
    4065:   PetscCheckSameComm(mat, 1, b, 2);
    4066:   PetscCheckSameComm(mat, 1, x, 3);
    4067:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    4068:   PetscCheck(mat->cmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, x->map->N);
    4069:   PetscCheck(mat->rmap->N == b->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, b->map->N);
    4070:   PetscCheck(mat->rmap->n == b->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, b->map->n);
    4071:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    4072:   MatCheckPreallocated(mat, 1);

    4074:   PetscCall(PetscLogEventBegin(MAT_BackwardSolve, mat, b, x, 0));
    4075:   PetscUseTypeMethod(mat, backwardsolve, b, x);
    4076:   PetscCall(PetscLogEventEnd(MAT_BackwardSolve, mat, b, x, 0));
    4077:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4078:   PetscFunctionReturn(PETSC_SUCCESS);
    4079: }

    4081: /*@
    4082:   MatSolveAdd - Computes $x = y + A^{-1}*b$, given a factored matrix.

    4084:   Neighbor-wise Collective

    4086:   Input Parameters:
    4087: + mat - the factored matrix
    4088: . b   - the right-hand-side vector
    4089: - y   - the vector to be added to

    4091:   Output Parameter:
    4092: . x - the result vector

    4094:   Level: developer

    4096:   Note:
    4097:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    4098:   call `MatSolveAdd`(A,x,y,x).

    4100: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatSolve()`, `MatGetFactor()`, `MatSolveTranspose()`, `MatSolveTransposeAdd()`
    4101: @*/
    4102: PetscErrorCode MatSolveAdd(Mat mat, Vec b, Vec y, Vec x)
    4103: {
    4104:   PetscScalar one = 1.0;
    4105:   Vec         tmp;

    4107:   PetscFunctionBegin;
    4113:   PetscCheckSameComm(mat, 1, b, 2);
    4114:   PetscCheckSameComm(mat, 1, y, 3);
    4115:   PetscCheckSameComm(mat, 1, x, 4);
    4116:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    4117:   PetscCheck(mat->cmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, x->map->N);
    4118:   PetscCheck(mat->rmap->N == b->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, b->map->N);
    4119:   PetscCheck(mat->rmap->N == y->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, y->map->N);
    4120:   PetscCheck(mat->rmap->n == b->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, b->map->n);
    4121:   PetscCheck(x->map->n == y->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Vec x,Vec y: local dim %" PetscInt_FMT " %" PetscInt_FMT, x->map->n, y->map->n);
    4122:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    4123:   MatCheckPreallocated(mat, 1);

    4125:   PetscCall(PetscLogEventBegin(MAT_SolveAdd, mat, b, x, y));
    4126:   PetscCall(VecFlag(x, mat->factorerrortype));
    4127:   if (mat->factorerrortype) {
    4128:     PetscCall(PetscInfo(mat, "MatFactorError %d\n", mat->factorerrortype));
    4129:   } else if (mat->ops->solveadd) {
    4130:     PetscUseTypeMethod(mat, solveadd, b, y, x);
    4131:   } else {
    4132:     /* do the solve then the add manually */
    4133:     if (x != y) {
    4134:       PetscCall(MatSolve(mat, b, x));
    4135:       PetscCall(VecAXPY(x, one, y));
    4136:     } else {
    4137:       PetscCall(VecDuplicate(x, &tmp));
    4138:       PetscCall(VecCopy(x, tmp));
    4139:       PetscCall(MatSolve(mat, b, x));
    4140:       PetscCall(VecAXPY(x, one, tmp));
    4141:       PetscCall(VecDestroy(&tmp));
    4142:     }
    4143:   }
    4144:   PetscCall(PetscLogEventEnd(MAT_SolveAdd, mat, b, x, y));
    4145:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4146:   PetscFunctionReturn(PETSC_SUCCESS);
    4147: }

    4149: /*@
    4150:   MatSolveTranspose - Solves $A^T x = b$, given a factored matrix.

    4152:   Neighbor-wise Collective

    4154:   Input Parameters:
    4155: + mat - the factored matrix
    4156: - b   - the right-hand-side vector

    4158:   Output Parameter:
    4159: . x - the result vector

    4161:   Level: developer

    4163:   Notes:
    4164:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    4165:   call `MatSolveTranspose`(A,x,x).

    4167:   Most users should employ the `KSP` interface for linear solvers
    4168:   instead of working directly with matrix algebra routines such as this.
    4169:   See, e.g., `KSPCreate()`.

    4171: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `KSP`, `MatSolve()`, `MatSolveAdd()`, `MatSolveTransposeAdd()`
    4172: @*/
    4173: PetscErrorCode MatSolveTranspose(Mat mat, Vec b, Vec x)
    4174: {
    4175:   PetscErrorCode (*f)(Mat, Vec, Vec) = (!mat->ops->solvetranspose && mat->symmetric) ? mat->ops->solve : mat->ops->solvetranspose;

    4177:   PetscFunctionBegin;
    4182:   PetscCheckSameComm(mat, 1, b, 2);
    4183:   PetscCheckSameComm(mat, 1, x, 3);
    4184:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    4185:   PetscCheck(mat->rmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, x->map->N);
    4186:   PetscCheck(mat->cmap->N == b->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, b->map->N);
    4187:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    4188:   MatCheckPreallocated(mat, 1);
    4189:   PetscCall(PetscLogEventBegin(MAT_SolveTranspose, mat, b, x, 0));
    4190:   PetscCall(VecFlag(x, mat->factorerrortype));
    4191:   if (mat->factorerrortype) {
    4192:     PetscCall(PetscInfo(mat, "MatFactorError %d\n", mat->factorerrortype));
    4193:   } else {
    4194:     PetscCheck(f, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Matrix type %s", ((PetscObject)mat)->type_name);
    4195:     PetscCall((*f)(mat, b, x));
    4196:   }
    4197:   PetscCall(PetscLogEventEnd(MAT_SolveTranspose, mat, b, x, 0));
    4198:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4199:   PetscFunctionReturn(PETSC_SUCCESS);
    4200: }

    4202: /*@
    4203:   MatSolveTransposeAdd - Computes $x = y + A^{-T} b$
    4204:   factored matrix.

    4206:   Neighbor-wise Collective

    4208:   Input Parameters:
    4209: + mat - the factored matrix
    4210: . b   - the right-hand-side vector
    4211: - y   - the vector to be added to

    4213:   Output Parameter:
    4214: . x - the result vector

    4216:   Level: developer

    4218:   Note:
    4219:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    4220:   call `MatSolveTransposeAdd`(A,x,y,x).

    4222: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatSolve()`, `MatSolveAdd()`, `MatSolveTranspose()`
    4223: @*/
    4224: PetscErrorCode MatSolveTransposeAdd(Mat mat, Vec b, Vec y, Vec x)
    4225: {
    4226:   PetscScalar one = 1.0;
    4227:   Vec         tmp;
    4228:   PetscErrorCode (*f)(Mat, Vec, Vec, Vec) = (!mat->ops->solvetransposeadd && mat->symmetric) ? mat->ops->solveadd : mat->ops->solvetransposeadd;

    4230:   PetscFunctionBegin;
    4236:   PetscCheckSameComm(mat, 1, b, 2);
    4237:   PetscCheckSameComm(mat, 1, y, 3);
    4238:   PetscCheckSameComm(mat, 1, x, 4);
    4239:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    4240:   PetscCheck(mat->rmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, x->map->N);
    4241:   PetscCheck(mat->cmap->N == b->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, b->map->N);
    4242:   PetscCheck(mat->cmap->N == y->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec y: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, y->map->N);
    4243:   PetscCheck(x->map->n == y->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Vec x,Vec y: local dim %" PetscInt_FMT " %" PetscInt_FMT, x->map->n, y->map->n);
    4244:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    4245:   MatCheckPreallocated(mat, 1);

    4247:   PetscCall(PetscLogEventBegin(MAT_SolveTransposeAdd, mat, b, x, y));
    4248:   PetscCall(VecFlag(x, mat->factorerrortype));
    4249:   if (mat->factorerrortype) {
    4250:     PetscCall(PetscInfo(mat, "MatFactorError %d\n", mat->factorerrortype));
    4251:   } else if (f) {
    4252:     PetscCall((*f)(mat, b, y, x));
    4253:   } else {
    4254:     /* do the solve then the add manually */
    4255:     if (x != y) {
    4256:       PetscCall(MatSolveTranspose(mat, b, x));
    4257:       PetscCall(VecAXPY(x, one, y));
    4258:     } else {
    4259:       PetscCall(VecDuplicate(x, &tmp));
    4260:       PetscCall(VecCopy(x, tmp));
    4261:       PetscCall(MatSolveTranspose(mat, b, x));
    4262:       PetscCall(VecAXPY(x, one, tmp));
    4263:       PetscCall(VecDestroy(&tmp));
    4264:     }
    4265:   }
    4266:   PetscCall(PetscLogEventEnd(MAT_SolveTransposeAdd, mat, b, x, y));
    4267:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4268:   PetscFunctionReturn(PETSC_SUCCESS);
    4269: }

    4271: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    4272: /*@
    4273:   MatSOR - Computes relaxation (SOR, Gauss-Seidel) sweeps.

    4275:   Neighbor-wise Collective

    4277:   Input Parameters:
    4278: + mat   - the matrix
    4279: . b     - the right-hand side
    4280: . omega - the relaxation factor
    4281: . flag  - flag indicating the type of SOR (see below)
    4282: . shift - diagonal shift
    4283: . its   - the number of iterations
    4284: - lits  - the number of local iterations

    4286:   Output Parameter:
    4287: . x - the solution (can contain an initial guess, use option `SOR_ZERO_INITIAL_GUESS` to indicate no guess)

    4289:   SOR Flags:
    4290: +     `SOR_FORWARD_SWEEP` - forward SOR
    4291: .     `SOR_BACKWARD_SWEEP` - backward SOR
    4292: .     `SOR_SYMMETRIC_SWEEP` - SSOR (symmetric SOR)
    4293: .     `SOR_LOCAL_FORWARD_SWEEP` - local forward SOR
    4294: .     `SOR_LOCAL_BACKWARD_SWEEP` - local forward SOR
    4295: .     `SOR_LOCAL_SYMMETRIC_SWEEP` - local SSOR
    4296: .     `SOR_EISENSTAT` - SOR with Eisenstat trick
    4297: .     `SOR_APPLY_UPPER`, `SOR_APPLY_LOWER` - applies upper/lower triangular part of matrix to vector (with `omega`)
    4298: -     `SOR_ZERO_INITIAL_GUESS` - zero initial guess

    4300:   Level: developer

    4302:   Notes:
    4303:   `SOR_LOCAL_FORWARD_SWEEP`, `SOR_LOCAL_BACKWARD_SWEEP`, and
    4304:   `SOR_LOCAL_SYMMETRIC_SWEEP` perform separate independent smoothings
    4305:   on each processor.

    4307:   Application programmers will not generally use `MatSOR()` directly,
    4308:   but instead will employ `PCSOR` or `PCEISENSTAT`

    4310:   For `MATBAIJ`, `MATSBAIJ`, and `MATAIJ` matrices with inodes, this does a block SOR smoothing, otherwise it does a pointwise smoothing.
    4311:   For `MATAIJ` matrices with inodes, the block sizes are determined by the inode sizes, not the block size set with `MatSetBlockSize()`

    4313:   Vectors `x` and `b` CANNOT be the same

    4315:   The flags are implemented as bitwise inclusive or operations.
    4316:   For example, use (`SOR_ZERO_INITIAL_GUESS` | `SOR_SYMMETRIC_SWEEP`)
    4317:   to specify a zero initial guess for SSOR.

    4319:   Developer Note:
    4320:   We should add block SOR support for `MATAIJ` matrices with block size set to greater than one and no inodes

    4322: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `KSP`, `PC`, `MatGetFactor()`
    4323: @*/
    4324: PetscErrorCode MatSOR(Mat mat, Vec b, PetscReal omega, MatSORType flag, PetscReal shift, PetscInt its, PetscInt lits, Vec x)
    4325: {
    4326:   PetscFunctionBegin;
    4331:   PetscCheckSameComm(mat, 1, b, 2);
    4332:   PetscCheckSameComm(mat, 1, x, 8);
    4333:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    4334:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4335:   PetscCheck(mat->cmap->N == x->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec x: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->cmap->N, x->map->N);
    4336:   PetscCheck(mat->rmap->N == b->map->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: global dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->N, b->map->N);
    4337:   PetscCheck(mat->rmap->n == b->map->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Mat mat,Vec b: local dim %" PetscInt_FMT " %" PetscInt_FMT, mat->rmap->n, b->map->n);
    4338:   PetscCheck(its > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Relaxation requires global its %" PetscInt_FMT " positive", its);
    4339:   PetscCheck(lits > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Relaxation requires local its %" PetscInt_FMT " positive", lits);
    4340:   PetscCheck(b != x, PETSC_COMM_SELF, PETSC_ERR_ARG_IDN, "b and x vector cannot be the same");

    4342:   MatCheckPreallocated(mat, 1);
    4343:   PetscCall(PetscLogEventBegin(MAT_SOR, mat, b, x, 0));
    4344:   PetscUseTypeMethod(mat, sor, b, omega, flag, shift, its, lits, x);
    4345:   PetscCall(PetscLogEventEnd(MAT_SOR, mat, b, x, 0));
    4346:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4347:   PetscFunctionReturn(PETSC_SUCCESS);
    4348: }

    4350: /*
    4351:       Default matrix copy routine.
    4352: */
    4353: PetscErrorCode MatCopy_Basic(Mat A, Mat B, MatStructure str)
    4354: {
    4355:   PetscInt           i, rstart = 0, rend = 0, nz;
    4356:   const PetscInt    *cwork;
    4357:   const PetscScalar *vwork;

    4359:   PetscFunctionBegin;
    4360:   if (B->assembled) PetscCall(MatZeroEntries(B));
    4361:   if (str == SAME_NONZERO_PATTERN) {
    4362:     PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
    4363:     for (i = rstart; i < rend; i++) {
    4364:       PetscCall(MatGetRow(A, i, &nz, &cwork, &vwork));
    4365:       PetscCall(MatSetValues(B, 1, &i, nz, cwork, vwork, INSERT_VALUES));
    4366:       PetscCall(MatRestoreRow(A, i, &nz, &cwork, &vwork));
    4367:     }
    4368:   } else {
    4369:     PetscCall(MatAYPX(B, 0.0, A, str));
    4370:   }
    4371:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    4372:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    4373:   PetscFunctionReturn(PETSC_SUCCESS);
    4374: }

    4376: /*@
    4377:   MatCopy - Copies a matrix to another matrix.

    4379:   Collective

    4381:   Input Parameters:
    4382: + A   - the matrix
    4383: - str - `SAME_NONZERO_PATTERN` or `DIFFERENT_NONZERO_PATTERN`

    4385:   Output Parameter:
    4386: . B - where the copy is put

    4388:   Level: intermediate

    4390:   Notes:
    4391:   If you use `SAME_NONZERO_PATTERN`, then the two matrices must have the same nonzero pattern or the routine will crash.

    4393:   `MatCopy()` copies the matrix entries of a matrix to another existing
    4394:   matrix (after first zeroing the second matrix).  A related routine is
    4395:   `MatConvert()`, which first creates a new matrix and then copies the data.

    4397: .seealso: [](ch_matrices), `Mat`, `MatConvert()`, `MatDuplicate()`
    4398: @*/
    4399: PetscErrorCode MatCopy(Mat A, Mat B, MatStructure str)
    4400: {
    4401:   PetscInt i;

    4403:   PetscFunctionBegin;
    4408:   PetscCheckSameComm(A, 1, B, 2);
    4409:   MatCheckPreallocated(B, 2);
    4410:   PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    4411:   PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4412:   PetscCheck(A->rmap->N == B->rmap->N && A->cmap->N == B->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Mat A,Mat B: global dim (%" PetscInt_FMT ",%" PetscInt_FMT ") (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->N, B->rmap->N,
    4413:              A->cmap->N, B->cmap->N);
    4414:   MatCheckPreallocated(A, 1);
    4415:   if (A == B) PetscFunctionReturn(PETSC_SUCCESS);

    4417:   PetscCall(PetscLogEventBegin(MAT_Copy, A, B, 0, 0));
    4418:   if (A->ops->copy) PetscUseTypeMethod(A, copy, B, str);
    4419:   else PetscCall(MatCopy_Basic(A, B, str));

    4421:   B->stencil.dim = A->stencil.dim;
    4422:   B->stencil.noc = A->stencil.noc;
    4423:   for (i = 0; i <= A->stencil.dim + (A->stencil.noc ? 0 : -1); i++) {
    4424:     B->stencil.dims[i]   = A->stencil.dims[i];
    4425:     B->stencil.starts[i] = A->stencil.starts[i];
    4426:   }

    4428:   PetscCall(PetscLogEventEnd(MAT_Copy, A, B, 0, 0));
    4429:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    4430:   PetscFunctionReturn(PETSC_SUCCESS);
    4431: }

    4433: /*@
    4434:   MatConvert - Converts a matrix to another matrix, either of the same
    4435:   or different type.

    4437:   Collective

    4439:   Input Parameters:
    4440: + mat     - the matrix
    4441: . newtype - new matrix type.  Use `MATSAME` to create a new matrix of the
    4442:             same type as the original matrix.
    4443: - reuse   - denotes if the destination matrix is to be created or reused.
    4444:             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
    4445:             `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).

    4447:   Output Parameter:
    4448: . M - pointer to place new matrix

    4450:   Level: intermediate

    4452:   Notes:
    4453:   `MatConvert()` first creates a new matrix and then copies the data from
    4454:   the first matrix.  A related routine is `MatCopy()`, which copies the matrix
    4455:   entries of one matrix to another already existing matrix context.

    4457:   Cannot be used to convert a sequential matrix to parallel or parallel to sequential,
    4458:   the MPI communicator of the generated matrix is always the same as the communicator
    4459:   of the input matrix.

    4461: .seealso: [](ch_matrices), `Mat`, `MatCopy()`, `MatDuplicate()`, `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, `MAT_INPLACE_MATRIX`
    4462: @*/
    4463: PetscErrorCode MatConvert(Mat mat, MatType newtype, MatReuse reuse, Mat *M)
    4464: {
    4465:   PetscBool  sametype, issame, flg;
    4466:   PetscBool3 issymmetric, ishermitian, isspd;
    4467:   char       convname[256], mtype[256];
    4468:   Mat        B;

    4470:   PetscFunctionBegin;
    4473:   PetscAssertPointer(M, 4);
    4474:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    4475:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4476:   MatCheckPreallocated(mat, 1);

    4478:   PetscCall(PetscOptionsGetString(((PetscObject)mat)->options, ((PetscObject)mat)->prefix, "-matconvert_type", mtype, sizeof(mtype), &flg));
    4479:   if (flg) newtype = mtype;

    4481:   PetscCall(PetscObjectTypeCompare((PetscObject)mat, newtype, &sametype));
    4482:   PetscCall(PetscStrcmp(newtype, "same", &issame));
    4483:   PetscCheck(!(reuse == MAT_INPLACE_MATRIX) || !(mat != *M), PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "MAT_INPLACE_MATRIX requires same input and output matrix");
    4484:   if (reuse == MAT_REUSE_MATRIX) {
    4486:     PetscCheck(mat != *M, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "MAT_REUSE_MATRIX means reuse matrix in final argument, perhaps you mean MAT_INPLACE_MATRIX");
    4487:   }

    4489:   if ((reuse == MAT_INPLACE_MATRIX) && (issame || sametype)) {
    4490:     PetscCall(PetscInfo(mat, "Early return for inplace %s %d %d\n", ((PetscObject)mat)->type_name, sametype, issame));
    4491:     PetscFunctionReturn(PETSC_SUCCESS);
    4492:   }

    4494:   /* Cache Mat options because some converters use MatHeaderReplace() */
    4495:   issymmetric = mat->symmetric;
    4496:   ishermitian = mat->hermitian;
    4497:   isspd       = mat->spd;

    4499:   if ((sametype || issame) && (reuse == MAT_INITIAL_MATRIX) && mat->ops->duplicate) {
    4500:     PetscCall(PetscInfo(mat, "Calling duplicate for initial matrix %s %d %d\n", ((PetscObject)mat)->type_name, sametype, issame));
    4501:     PetscUseTypeMethod(mat, duplicate, MAT_COPY_VALUES, M);
    4502:   } else {
    4503:     PetscErrorCode (*conv)(Mat, MatType, MatReuse, Mat *) = NULL;
    4504:     const char *prefix[3]                                 = {"seq", "mpi", ""};
    4505:     PetscInt    i;
    4506:     /*
    4507:        Order of precedence:
    4508:        0) See if newtype is a superclass of the current matrix.
    4509:        1) See if a specialized converter is known to the current matrix.
    4510:        2) See if a specialized converter is known to the desired matrix class.
    4511:        3) See if a good general converter is registered for the desired class
    4512:           (as of 6/27/03 only MATMPIADJ falls into this category).
    4513:        4) See if a good general converter is known for the current matrix.
    4514:        5) Use a really basic converter.
    4515:     */

    4517:     /* 0) See if newtype is a superclass of the current matrix.
    4518:           i.e mat is mpiaij and newtype is aij */
    4519:     for (i = 0; i < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(prefix); i++) {
    4520:       PetscCall(PetscStrncpy(convname, prefix[i], sizeof(convname)));
    4521:       PetscCall(PetscStrlcat(convname, newtype, sizeof(convname)));
    4522:       PetscCall(PetscStrcmp(convname, ((PetscObject)mat)->type_name, &flg));
    4523:       PetscCall(PetscInfo(mat, "Check superclass %s %s -> %d\n", convname, ((PetscObject)mat)->type_name, flg));
    4524:       if (flg) {
    4525:         if (reuse == MAT_INPLACE_MATRIX) {
    4526:           PetscCall(PetscInfo(mat, "Early return\n"));
    4527:           PetscFunctionReturn(PETSC_SUCCESS);
    4528:         } else if (reuse == MAT_INITIAL_MATRIX && mat->ops->duplicate) {
    4529:           PetscCall(PetscInfo(mat, "Calling MatDuplicate\n"));
    4530:           PetscUseTypeMethod(mat, duplicate, MAT_COPY_VALUES, M);
    4531:           PetscFunctionReturn(PETSC_SUCCESS);
    4532:         } else if (reuse == MAT_REUSE_MATRIX && mat->ops->copy) {
    4533:           PetscCall(PetscInfo(mat, "Calling MatCopy\n"));
    4534:           PetscCall(MatCopy(mat, *M, SAME_NONZERO_PATTERN));
    4535:           PetscFunctionReturn(PETSC_SUCCESS);
    4536:         }
    4537:       }
    4538:     }
    4539:     /* 1) See if a specialized converter is known to the current matrix and the desired class */
    4540:     for (i = 0; i < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(prefix); i++) {
    4541:       PetscCall(PetscStrncpy(convname, "MatConvert_", sizeof(convname)));
    4542:       PetscCall(PetscStrlcat(convname, ((PetscObject)mat)->type_name, sizeof(convname)));
    4543:       PetscCall(PetscStrlcat(convname, "_", sizeof(convname)));
    4544:       PetscCall(PetscStrlcat(convname, prefix[i], sizeof(convname)));
    4545:       PetscCall(PetscStrlcat(convname, issame ? ((PetscObject)mat)->type_name : newtype, sizeof(convname)));
    4546:       PetscCall(PetscStrlcat(convname, "_C", sizeof(convname)));
    4547:       PetscCall(PetscObjectQueryFunction((PetscObject)mat, convname, &conv));
    4548:       PetscCall(PetscInfo(mat, "Check specialized (1) %s (%s) -> %d\n", convname, ((PetscObject)mat)->type_name, !!conv));
    4549:       if (conv) goto foundconv;
    4550:     }

    4552:     /* 2)  See if a specialized converter is known to the desired matrix class. */
    4553:     PetscCall(MatCreate(PetscObjectComm((PetscObject)mat), &B));
    4554:     PetscCall(MatSetSizes(B, mat->rmap->n, mat->cmap->n, mat->rmap->N, mat->cmap->N));
    4555:     PetscCall(MatSetType(B, newtype));
    4556:     for (i = 0; i < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(prefix); i++) {
    4557:       PetscCall(PetscStrncpy(convname, "MatConvert_", sizeof(convname)));
    4558:       PetscCall(PetscStrlcat(convname, ((PetscObject)mat)->type_name, sizeof(convname)));
    4559:       PetscCall(PetscStrlcat(convname, "_", sizeof(convname)));
    4560:       PetscCall(PetscStrlcat(convname, prefix[i], sizeof(convname)));
    4561:       PetscCall(PetscStrlcat(convname, newtype, sizeof(convname)));
    4562:       PetscCall(PetscStrlcat(convname, "_C", sizeof(convname)));
    4563:       PetscCall(PetscObjectQueryFunction((PetscObject)B, convname, &conv));
    4564:       PetscCall(PetscInfo(mat, "Check specialized (2) %s (%s) -> %d\n", convname, ((PetscObject)B)->type_name, !!conv));
    4565:       if (conv) {
    4566:         PetscCall(MatDestroy(&B));
    4567:         goto foundconv;
    4568:       }
    4569:     }

    4571:     /* 3) See if a good general converter is registered for the desired class */
    4572:     conv = B->ops->convertfrom;
    4573:     PetscCall(PetscInfo(mat, "Check convertfrom (%s) -> %d\n", ((PetscObject)B)->type_name, !!conv));
    4574:     PetscCall(MatDestroy(&B));
    4575:     if (conv) goto foundconv;

    4577:     /* 4) See if a good general converter is known for the current matrix */
    4578:     if (mat->ops->convert) conv = mat->ops->convert;
    4579:     PetscCall(PetscInfo(mat, "Check general convert (%s) -> %d\n", ((PetscObject)mat)->type_name, !!conv));
    4580:     if (conv) goto foundconv;

    4582:     /* 5) Use a really basic converter. */
    4583:     PetscCall(PetscInfo(mat, "Using MatConvert_Basic\n"));
    4584:     conv = MatConvert_Basic;

    4586:   foundconv:
    4587:     PetscCall(PetscLogEventBegin(MAT_Convert, mat, 0, 0, 0));
    4588:     PetscCall((*conv)(mat, newtype, reuse, M));
    4589:     if (mat->rmap->mapping && mat->cmap->mapping && !(*M)->rmap->mapping && !(*M)->cmap->mapping) {
    4590:       /* the block sizes must be same if the mappings are copied over */
    4591:       (*M)->rmap->bs = mat->rmap->bs;
    4592:       (*M)->cmap->bs = mat->cmap->bs;
    4593:       PetscCall(PetscObjectReference((PetscObject)mat->rmap->mapping));
    4594:       PetscCall(PetscObjectReference((PetscObject)mat->cmap->mapping));
    4595:       (*M)->rmap->mapping = mat->rmap->mapping;
    4596:       (*M)->cmap->mapping = mat->cmap->mapping;
    4597:     }
    4598:     (*M)->stencil.dim = mat->stencil.dim;
    4599:     (*M)->stencil.noc = mat->stencil.noc;
    4600:     for (i = 0; i <= mat->stencil.dim + (mat->stencil.noc ? 0 : -1); i++) {
    4601:       (*M)->stencil.dims[i]   = mat->stencil.dims[i];
    4602:       (*M)->stencil.starts[i] = mat->stencil.starts[i];
    4603:     }
    4604:     PetscCall(PetscLogEventEnd(MAT_Convert, mat, 0, 0, 0));
    4605:   }
    4606:   PetscCall(PetscObjectStateIncrease((PetscObject)*M));

    4608:   /* Reset Mat options */
    4609:   if (issymmetric != PETSC_BOOL3_UNKNOWN) PetscCall(MatSetOption(*M, MAT_SYMMETRIC, PetscBool3ToBool(issymmetric)));
    4610:   if (ishermitian != PETSC_BOOL3_UNKNOWN) PetscCall(MatSetOption(*M, MAT_HERMITIAN, PetscBool3ToBool(ishermitian)));
    4611:   if (isspd != PETSC_BOOL3_UNKNOWN) PetscCall(MatSetOption(*M, MAT_SPD, PetscBool3ToBool(isspd)));
    4612:   PetscFunctionReturn(PETSC_SUCCESS);
    4613: }

    4615: /*@
    4616:   MatFactorGetSolverType - Returns name of the package providing the factorization routines

    4618:   Not Collective

    4620:   Input Parameter:
    4621: . mat - the matrix, must be a factored matrix

    4623:   Output Parameter:
    4624: . type - the string name of the package (do not free this string)

    4626:   Level: intermediate

    4628: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatSolverType`, `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`
    4629: @*/
    4630: PetscErrorCode MatFactorGetSolverType(Mat mat, MatSolverType *type)
    4631: {
    4632:   PetscErrorCode (*conv)(Mat, MatSolverType *);

    4634:   PetscFunctionBegin;
    4637:   PetscAssertPointer(type, 2);
    4638:   PetscCheck(mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    4639:   PetscCall(PetscObjectQueryFunction((PetscObject)mat, "MatFactorGetSolverType_C", &conv));
    4640:   if (conv) PetscCall((*conv)(mat, type));
    4641:   else *type = MATSOLVERPETSC;
    4642:   PetscFunctionReturn(PETSC_SUCCESS);
    4643: }

    4645: typedef struct _MatSolverTypeForSpecifcType *MatSolverTypeForSpecifcType;
    4646: struct _MatSolverTypeForSpecifcType {
    4647:   MatType mtype;
    4648:   /* no entry for MAT_FACTOR_NONE */
    4649:   PetscErrorCode (*createfactor[MAT_FACTOR_NUM_TYPES - 1])(Mat, MatFactorType, Mat *);
    4650:   MatSolverTypeForSpecifcType next;
    4651: };

    4653: typedef struct _MatSolverTypeHolder *MatSolverTypeHolder;
    4654: struct _MatSolverTypeHolder {
    4655:   char                       *name;
    4656:   MatSolverTypeForSpecifcType handlers;
    4657:   MatSolverTypeHolder         next;
    4658: };

    4660: static MatSolverTypeHolder MatSolverTypeHolders = NULL;

    4662: /*@C
    4663:   MatSolverTypeRegister - Registers a `MatSolverType` that works for a particular matrix type

    4665:   Logically Collective, No Fortran Support

    4667:   Input Parameters:
    4668: + package      - name of the package, for example `petsc` or `superlu`
    4669: . mtype        - the matrix type that works with this package
    4670: . ftype        - the type of factorization supported by the package
    4671: - createfactor - routine that will create the factored matrix ready to be used

    4673:   Level: developer

    4675: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorGetSolverType()`, `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`,
    4676:   `MatGetFactor()`
    4677: @*/
    4678: PetscErrorCode MatSolverTypeRegister(MatSolverType package, MatType mtype, MatFactorType ftype, PetscErrorCode (*createfactor)(Mat, MatFactorType, Mat *))
    4679: {
    4680:   MatSolverTypeHolder         next = MatSolverTypeHolders, prev = NULL;
    4681:   PetscBool                   flg;
    4682:   MatSolverTypeForSpecifcType inext, iprev = NULL;

    4684:   PetscFunctionBegin;
    4685:   PetscCall(MatInitializePackage());
    4686:   if (!next) {
    4687:     PetscCall(PetscNew(&MatSolverTypeHolders));
    4688:     PetscCall(PetscStrallocpy(package, &MatSolverTypeHolders->name));
    4689:     PetscCall(PetscNew(&MatSolverTypeHolders->handlers));
    4690:     PetscCall(PetscStrallocpy(mtype, (char **)&MatSolverTypeHolders->handlers->mtype));
    4691:     MatSolverTypeHolders->handlers->createfactor[(int)ftype - 1] = createfactor;
    4692:     PetscFunctionReturn(PETSC_SUCCESS);
    4693:   }
    4694:   while (next) {
    4695:     PetscCall(PetscStrcasecmp(package, next->name, &flg));
    4696:     if (flg) {
    4697:       PetscCheck(next->handlers, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MatSolverTypeHolder is missing handlers");
    4698:       inext = next->handlers;
    4699:       while (inext) {
    4700:         PetscCall(PetscStrcasecmp(mtype, inext->mtype, &flg));
    4701:         if (flg) {
    4702:           inext->createfactor[(int)ftype - 1] = createfactor;
    4703:           PetscFunctionReturn(PETSC_SUCCESS);
    4704:         }
    4705:         iprev = inext;
    4706:         inext = inext->next;
    4707:       }
    4708:       PetscCall(PetscNew(&iprev->next));
    4709:       PetscCall(PetscStrallocpy(mtype, (char **)&iprev->next->mtype));
    4710:       iprev->next->createfactor[(int)ftype - 1] = createfactor;
    4711:       PetscFunctionReturn(PETSC_SUCCESS);
    4712:     }
    4713:     prev = next;
    4714:     next = next->next;
    4715:   }
    4716:   PetscCall(PetscNew(&prev->next));
    4717:   PetscCall(PetscStrallocpy(package, &prev->next->name));
    4718:   PetscCall(PetscNew(&prev->next->handlers));
    4719:   PetscCall(PetscStrallocpy(mtype, (char **)&prev->next->handlers->mtype));
    4720:   prev->next->handlers->createfactor[(int)ftype - 1] = createfactor;
    4721:   PetscFunctionReturn(PETSC_SUCCESS);
    4722: }

    4724: /*@C
    4725:   MatSolverTypeGet - Gets the function that creates the factor matrix if it exist

    4727:   Input Parameters:
    4728: + type  - name of the package, for example `petsc` or `superlu`, if this is `NULL`, then the first result that satisfies the other criteria is returned
    4729: . ftype - the type of factorization supported by the type
    4730: - mtype - the matrix type that works with this type

    4732:   Output Parameters:
    4733: + foundtype    - `PETSC_TRUE` if the type was registered
    4734: . foundmtype   - `PETSC_TRUE` if the type supports the requested mtype
    4735: - createfactor - routine that will create the factored matrix ready to be used or `NULL` if not found

    4737:   Calling sequence of `createfactor`:
    4738: + A     - the matrix providing the factor matrix
    4739: . ftype - the `MatFactorType` of the factor requested
    4740: - B     - the new factor matrix that responds to MatXXFactorSymbolic,Numeric() functions, such as `MatLUFactorSymbolic()`

    4742:   Level: developer

    4744:   Note:
    4745:   When `type` is `NULL` the available functions are searched for based on the order of the calls to `MatSolverTypeRegister()` in `MatInitializePackage()`.
    4746:   Since different PETSc configurations may have different external solvers, seemingly identical runs with different PETSc configurations may use a different solver.
    4747:   For example if one configuration had `--download-mumps` while a different one had `--download-superlu_dist`.

    4749: .seealso: [](ch_matrices), `Mat`, `MatFactorType`, `MatType`, `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`, `MatSolverTypeRegister()`, `MatGetFactor()`,
    4750:           `MatInitializePackage()`
    4751: @*/
    4752: PetscErrorCode MatSolverTypeGet(MatSolverType type, MatType mtype, MatFactorType ftype, PetscBool *foundtype, PetscBool *foundmtype, PetscErrorCode (**createfactor)(Mat A, MatFactorType ftype, Mat *B))
    4753: {
    4754:   MatSolverTypeHolder         next = MatSolverTypeHolders;
    4755:   PetscBool                   flg;
    4756:   MatSolverTypeForSpecifcType inext;

    4758:   PetscFunctionBegin;
    4759:   if (foundtype) *foundtype = PETSC_FALSE;
    4760:   if (foundmtype) *foundmtype = PETSC_FALSE;
    4761:   if (createfactor) *createfactor = NULL;

    4763:   if (type) {
    4764:     while (next) {
    4765:       PetscCall(PetscStrcasecmp(type, next->name, &flg));
    4766:       if (flg) {
    4767:         if (foundtype) *foundtype = PETSC_TRUE;
    4768:         inext = next->handlers;
    4769:         while (inext) {
    4770:           PetscCall(PetscStrbeginswith(mtype, inext->mtype, &flg));
    4771:           if (flg) {
    4772:             if (foundmtype) *foundmtype = PETSC_TRUE;
    4773:             if (createfactor) *createfactor = inext->createfactor[(int)ftype - 1];
    4774:             PetscFunctionReturn(PETSC_SUCCESS);
    4775:           }
    4776:           inext = inext->next;
    4777:         }
    4778:       }
    4779:       next = next->next;
    4780:     }
    4781:   } else {
    4782:     while (next) {
    4783:       inext = next->handlers;
    4784:       while (inext) {
    4785:         PetscCall(PetscStrcmp(mtype, inext->mtype, &flg));
    4786:         if (flg && inext->createfactor[(int)ftype - 1]) {
    4787:           if (foundtype) *foundtype = PETSC_TRUE;
    4788:           if (foundmtype) *foundmtype = PETSC_TRUE;
    4789:           if (createfactor) *createfactor = inext->createfactor[(int)ftype - 1];
    4790:           PetscFunctionReturn(PETSC_SUCCESS);
    4791:         }
    4792:         inext = inext->next;
    4793:       }
    4794:       next = next->next;
    4795:     }
    4796:     /* try with base classes inext->mtype */
    4797:     next = MatSolverTypeHolders;
    4798:     while (next) {
    4799:       inext = next->handlers;
    4800:       while (inext) {
    4801:         PetscCall(PetscStrbeginswith(mtype, inext->mtype, &flg));
    4802:         if (flg && inext->createfactor[(int)ftype - 1]) {
    4803:           if (foundtype) *foundtype = PETSC_TRUE;
    4804:           if (foundmtype) *foundmtype = PETSC_TRUE;
    4805:           if (createfactor) *createfactor = inext->createfactor[(int)ftype - 1];
    4806:           PetscFunctionReturn(PETSC_SUCCESS);
    4807:         }
    4808:         inext = inext->next;
    4809:       }
    4810:       next = next->next;
    4811:     }
    4812:   }
    4813:   PetscFunctionReturn(PETSC_SUCCESS);
    4814: }

    4816: PetscErrorCode MatSolverTypeDestroy(void)
    4817: {
    4818:   MatSolverTypeHolder         next = MatSolverTypeHolders, prev;
    4819:   MatSolverTypeForSpecifcType inext, iprev;

    4821:   PetscFunctionBegin;
    4822:   while (next) {
    4823:     PetscCall(PetscFree(next->name));
    4824:     inext = next->handlers;
    4825:     while (inext) {
    4826:       PetscCall(PetscFree(inext->mtype));
    4827:       iprev = inext;
    4828:       inext = inext->next;
    4829:       PetscCall(PetscFree(iprev));
    4830:     }
    4831:     prev = next;
    4832:     next = next->next;
    4833:     PetscCall(PetscFree(prev));
    4834:   }
    4835:   MatSolverTypeHolders = NULL;
    4836:   PetscFunctionReturn(PETSC_SUCCESS);
    4837: }

    4839: /*@
    4840:   MatFactorGetCanUseOrdering - Indicates if the factorization can use the ordering provided in `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`

    4842:   Logically Collective

    4844:   Input Parameter:
    4845: . mat - the matrix

    4847:   Output Parameter:
    4848: . flg - `PETSC_TRUE` if uses the ordering

    4850:   Level: developer

    4852:   Note:
    4853:   Most internal PETSc factorizations use the ordering passed to the factorization routine but external
    4854:   packages do not, thus we want to skip generating the ordering when it is not needed or used.

    4856: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`
    4857: @*/
    4858: PetscErrorCode MatFactorGetCanUseOrdering(Mat mat, PetscBool *flg)
    4859: {
    4860:   PetscFunctionBegin;
    4861:   *flg = mat->canuseordering;
    4862:   PetscFunctionReturn(PETSC_SUCCESS);
    4863: }

    4865: /*@
    4866:   MatFactorGetPreferredOrdering - The preferred ordering for a particular matrix factor object

    4868:   Logically Collective

    4870:   Input Parameters:
    4871: + mat   - the matrix obtained with `MatGetFactor()`
    4872: - ftype - the factorization type to be used

    4874:   Output Parameter:
    4875: . otype - the preferred ordering type

    4877:   Level: developer

    4879: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorType`, `MatOrderingType`, `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`
    4880: @*/
    4881: PetscErrorCode MatFactorGetPreferredOrdering(Mat mat, MatFactorType ftype, MatOrderingType *otype)
    4882: {
    4883:   PetscFunctionBegin;
    4884:   *otype = mat->preferredordering[ftype];
    4885:   PetscCheck(*otype, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MatFactor did not have a preferred ordering");
    4886:   PetscFunctionReturn(PETSC_SUCCESS);
    4887: }

    4889: /*@
    4890:   MatGetFactor - Returns a matrix suitable to calls to routines such as `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`, `MatILUFactorSymbolic()`,
    4891:   `MatICCFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactorNumeric()`, `MatILUFactorNumeric()`, and
    4892:   `MatICCFactorNumeric()`

    4894:   Collective

    4896:   Input Parameters:
    4897: + mat   - the matrix
    4898: . type  - name of solver type, for example, `superlu_dist`, `petsc` (to use PETSc's solver if it is available), if this is `NULL`, then the first result that satisfies
    4899:           the other criteria is returned
    4900: - ftype - factor type, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ICC`, `MAT_FACTOR_ILU`, `MAT_FACTOR_QR`

    4902:   Output Parameter:
    4903: . f - the factor matrix used with MatXXFactorSymbolic,Numeric() calls. Can be `NULL` in some cases, see notes below.

    4905:   Options Database Keys:
    4906: + -pc_factor_mat_solver_type type            - choose the type at run time. When using `KSP` solvers
    4907: . -pc_factor_mat_factor_on_host (true|false) - do matrix factorization on host (with device matrices). Default is doing it on device
    4908: - -pc_factor_mat_solve_on_host (true|false)  - do matrix solve on host (with device matrices). Default is doing it on device

    4910:   Level: intermediate

    4912:   Notes:
    4913:   Some of the packages, such as MUMPS, have options for controlling the factorization, these are in the form `-prefix_mat_packagename_packageoption`
    4914:   (for example, `-mat_mumps_icntl_6 1`)  where `prefix` is normally set automatically from the calling `KSP`/`PC`. If `MatGetFactor()` is called directly,
    4915:   without using a `PC`, one can set the prefix by
    4916:   calling `MatSetOptionsPrefixFactor()` on the originating matrix or  `MatSetOptionsPrefix()` on the resulting factor matrix.

    4918:   Some PETSc matrix formats have alternative solvers available that are provided by alternative packages
    4919:   such as PaStiX, SuperLU_DIST, MUMPS etc. PETSc must have been configured to use the external solver,
    4920:   using the corresponding `./configure` option such as `--download-package` or `--with-package-dir`.

    4922:   When `type` is `NULL` the available results are searched for based on the order of the calls to `MatSolverTypeRegister()` in `MatInitializePackage()`.
    4923:   Since different PETSc configurations may have different external solvers, seemingly identical runs with different PETSc configurations may use a different solver.
    4924:   For example if one configuration had `--download-mumps` while a different one had `--download-superlu_dist`.

    4926:   The return matrix can be `NULL` if the requested factorization is not available, since some combinations of matrix types and factorization
    4927:   types registered with `MatSolverTypeRegister()` cannot be fully tested if not at runtime.

    4929:   Developer Note:
    4930:   This should actually be called `MatCreateFactor()` since it creates a new factor object

    4932:   The `MatGetFactor()` implementations should not be accessing the PETSc options database or making other decisions about solver options,
    4933:   that should be delayed until the later operations. This is to ensure the correct options prefix has been set in the factor matrix.

    4935: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `KSP`, `MatSolverType`, `MatFactorType`, `MatCopy()`, `MatDuplicate()`,
    4936:           `MatGetFactorAvailable()`, `MatFactorGetCanUseOrdering()`, `MatSolverTypeRegister()`, `MatSolverTypeGet()`,
    4937:           `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ICC`, `MAT_FACTOR_ILU`, `MAT_FACTOR_QR`, `MatInitializePackage()`,
    4938:           `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`, `MatILUFactorSymbolic()`,
    4939:           `MatICCFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactorNumeric()`, `MatILUFactorNumeric()`,
    4940:           `MatICCFactorNumeric()`
    4941: @*/
    4942: PetscErrorCode MatGetFactor(Mat mat, MatSolverType type, MatFactorType ftype, Mat *f)
    4943: {
    4944:   PetscBool foundtype, foundmtype, shell, hasop = PETSC_FALSE;
    4945:   PetscErrorCode (*conv)(Mat, MatFactorType, Mat *);

    4947:   PetscFunctionBegin;

    4951:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4952:   MatCheckPreallocated(mat, 1);

    4954:   PetscCall(MatIsShell(mat, &shell));
    4955:   if (shell) PetscCall(MatHasOperation(mat, MATOP_GET_FACTOR, &hasop));
    4956:   if (hasop) {
    4957:     PetscUseTypeMethod(mat, getfactor, type, ftype, f);
    4958:     PetscFunctionReturn(PETSC_SUCCESS);
    4959:   }

    4961:   PetscCall(MatSolverTypeGet(type, ((PetscObject)mat)->type_name, ftype, &foundtype, &foundmtype, &conv));
    4962:   if (!foundtype) {
    4963:     if (type) {
    4964:       SETERRQ(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],
    4965:               ((PetscObject)mat)->type_name, type);
    4966:     } else {
    4967:       SETERRQ(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);
    4968:     }
    4969:   }
    4970:   PetscCheck(foundmtype, PetscObjectComm((PetscObject)mat), PETSC_ERR_MISSING_FACTOR, "MatSolverType %s does not support matrix type %s", type, ((PetscObject)mat)->type_name);
    4971:   PetscCheck(conv, 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);

    4973:   PetscCall((*conv)(mat, ftype, f));
    4974:   if (mat->factorprefix) PetscCall(MatSetOptionsPrefix(*f, mat->factorprefix));
    4975:   PetscFunctionReturn(PETSC_SUCCESS);
    4976: }

    4978: /*@
    4979:   MatGetFactorAvailable - Returns a flag if matrix supports particular type and factor type

    4981:   Not Collective

    4983:   Input Parameters:
    4984: + mat   - the matrix
    4985: . type  - name of solver type, for example, `superlu`, `petsc` (to use PETSc's default)
    4986: - ftype - factor type, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ICC`, `MAT_FACTOR_ILU`, `MAT_FACTOR_QR`

    4988:   Output Parameter:
    4989: . flg - PETSC_TRUE if the factorization is available

    4991:   Level: intermediate

    4993:   Notes:
    4994:   Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
    4995:   such as pastix, superlu, mumps etc.

    4997:   PETSc must have been ./configure to use the external solver, using the option --download-package

    4999:   Developer Note:
    5000:   This should actually be called `MatCreateFactorAvailable()` since `MatGetFactor()` creates a new factor object

    5002: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatSolverType`, `MatFactorType`, `MatGetFactor()`, `MatCopy()`, `MatDuplicate()`, `MatSolverTypeRegister()`,
    5003:           `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ICC`, `MAT_FACTOR_ILU`, `MAT_FACTOR_QR`, `MatSolverTypeGet()`
    5004: @*/
    5005: PetscErrorCode MatGetFactorAvailable(Mat mat, MatSolverType type, MatFactorType ftype, PetscBool *flg)
    5006: {
    5007:   PetscErrorCode (*gconv)(Mat, MatFactorType, Mat *);

    5009:   PetscFunctionBegin;
    5011:   PetscAssertPointer(flg, 4);

    5013:   *flg = PETSC_FALSE;
    5014:   if (!((PetscObject)mat)->type_name) PetscFunctionReturn(PETSC_SUCCESS);

    5016:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5017:   MatCheckPreallocated(mat, 1);

    5019:   PetscCall(MatSolverTypeGet(type, ((PetscObject)mat)->type_name, ftype, NULL, NULL, &gconv));
    5020:   *flg = gconv ? PETSC_TRUE : PETSC_FALSE;
    5021:   PetscFunctionReturn(PETSC_SUCCESS);
    5022: }

    5024: /*@
    5025:   MatDuplicate - Duplicates a matrix including the non-zero structure.

    5027:   Collective

    5029:   Input Parameters:
    5030: + mat - the matrix
    5031: - op  - One of `MAT_DO_NOT_COPY_VALUES`, `MAT_COPY_VALUES`, or `MAT_SHARE_NONZERO_PATTERN`.
    5032:         See the manual page for `MatDuplicateOption()` for an explanation of these options.

    5034:   Output Parameter:
    5035: . M - pointer to place new matrix

    5037:   Level: intermediate

    5039:   Notes:
    5040:   You cannot change the nonzero pattern for the parent or child matrix later if you use `MAT_SHARE_NONZERO_PATTERN`.

    5042:   If `op` is not `MAT_COPY_VALUES` the numerical values in the new matrix are zeroed.

    5044:   May be called with an unassembled input `Mat` if `MAT_DO_NOT_COPY_VALUES` is used, in which case the output `Mat` is unassembled as well.

    5046:   When original mat is a product of matrix operation, e.g., an output of `MatMatMult()` or `MatCreateSubMatrix()`, only the matrix data structure of `mat`
    5047:   is duplicated and the internal data structures created for the reuse of previous matrix operations are not duplicated.
    5048:   User should not use `MatDuplicate()` to create new matrix `M` if `M` is intended to be reused as the product of matrix operation.

    5050: .seealso: [](ch_matrices), `Mat`, `MatCopy()`, `MatConvert()`, `MatDuplicateOption`
    5051: @*/
    5052: PetscErrorCode MatDuplicate(Mat mat, MatDuplicateOption op, Mat *M)
    5053: {
    5054:   Mat               B;
    5055:   VecType           vtype;
    5056:   PetscInt          i;
    5057:   PetscObject       dm, container_h, container_d;
    5058:   PetscErrorCodeFn *viewf;

    5060:   PetscFunctionBegin;
    5063:   PetscAssertPointer(M, 3);
    5064:   PetscCheck(op != MAT_COPY_VALUES || mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MAT_COPY_VALUES not allowed for unassembled matrix");
    5065:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5066:   MatCheckPreallocated(mat, 1);

    5068:   PetscCall(PetscLogEventBegin(MAT_Convert, mat, 0, 0, 0));
    5069:   PetscUseTypeMethod(mat, duplicate, op, M);
    5070:   PetscCall(PetscLogEventEnd(MAT_Convert, mat, 0, 0, 0));
    5071:   B = *M;

    5073:   PetscCall(MatGetOperation(mat, MATOP_VIEW, &viewf));
    5074:   if (viewf) PetscCall(MatSetOperation(B, MATOP_VIEW, viewf));
    5075:   PetscCall(MatGetVecType(mat, &vtype));
    5076:   PetscCall(MatSetVecType(B, vtype));

    5078:   B->stencil.dim = mat->stencil.dim;
    5079:   B->stencil.noc = mat->stencil.noc;
    5080:   for (i = 0; i <= mat->stencil.dim + (mat->stencil.noc ? 0 : -1); i++) {
    5081:     B->stencil.dims[i]   = mat->stencil.dims[i];
    5082:     B->stencil.starts[i] = mat->stencil.starts[i];
    5083:   }

    5085:   B->nooffproczerorows = mat->nooffproczerorows;
    5086:   B->nooffprocentries  = mat->nooffprocentries;

    5088:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_dm", &dm));
    5089:   if (dm) PetscCall(PetscObjectCompose((PetscObject)B, "__PETSc_dm", dm));
    5090:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", &container_h));
    5091:   if (container_h) PetscCall(PetscObjectCompose((PetscObject)B, "__PETSc_MatCOOStruct_Host", container_h));
    5092:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Device", &container_d));
    5093:   if (container_d) PetscCall(PetscObjectCompose((PetscObject)B, "__PETSc_MatCOOStruct_Device", container_d));
    5094:   if (op == MAT_COPY_VALUES) PetscCall(MatPropagateSymmetryOptions(mat, B));
    5095:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    5096:   PetscFunctionReturn(PETSC_SUCCESS);
    5097: }

    5099: /*@
    5100:   MatGetDiagonal - Gets the diagonal of a matrix as a `Vec`

    5102:   Logically Collective

    5104:   Input Parameter:
    5105: . mat - the matrix

    5107:   Output Parameter:
    5108: . v - the diagonal of the matrix

    5110:   Level: intermediate

    5112:   Note:
    5113:   If `mat` has local sizes `n` x `m`, this routine fills the first `ndiag = min(n, m)` entries
    5114:   of `v` with the diagonal values. Thus `v` must have local size of at least `ndiag`. If `v`
    5115:   is larger than `ndiag`, the values of the remaining entries are unspecified.

    5117:   Currently only correct in parallel for square matrices.

    5119: .seealso: [](ch_matrices), `Mat`, `Vec`, `MatGetRow()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMaxAbs()`
    5120: @*/
    5121: PetscErrorCode MatGetDiagonal(Mat mat, Vec v)
    5122: {
    5123:   PetscFunctionBegin;
    5127:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5128:   MatCheckPreallocated(mat, 1);
    5129:   if (PetscDefined(USE_DEBUG)) {
    5130:     PetscInt nv, row, col, ndiag;

    5132:     PetscCall(VecGetLocalSize(v, &nv));
    5133:     PetscCall(MatGetLocalSize(mat, &row, &col));
    5134:     ndiag = PetscMin(row, col);
    5135:     PetscCheck(nv >= ndiag, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming Mat and Vec. Vec local size %" PetscInt_FMT " < Mat local diagonal length %" PetscInt_FMT, nv, ndiag);
    5136:   }

    5138:   PetscUseTypeMethod(mat, getdiagonal, v);
    5139:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5140:   PetscFunctionReturn(PETSC_SUCCESS);
    5141: }

    5143: /*@
    5144:   MatGetRowMin - Gets the minimum value (of the real part) of each
    5145:   row of the matrix

    5147:   Logically Collective

    5149:   Input Parameter:
    5150: . mat - the matrix

    5152:   Output Parameters:
    5153: + v   - the vector for storing the maximums
    5154: - idx - the indices of the column found for each row (optional, pass `NULL` if not needed)

    5156:   Level: intermediate

    5158:   Note:
    5159:   The result of this call are the same as if one converted the matrix to dense format
    5160:   and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    5162:   This code is only implemented for a couple of matrix formats.

    5164: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMaxAbs()`, `MatGetRowMinAbs()`,
    5165:           `MatGetRowMax()`
    5166: @*/
    5167: PetscErrorCode MatGetRowMin(Mat mat, Vec v, PetscInt idx[])
    5168: {
    5169:   PetscFunctionBegin;
    5173:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");

    5175:   if (!mat->cmap->N) {
    5176:     PetscCall(VecSet(v, PETSC_MAX_REAL));
    5177:     if (idx) {
    5178:       PetscInt i, m = mat->rmap->n;
    5179:       for (i = 0; i < m; i++) idx[i] = -1;
    5180:     }
    5181:   } else {
    5182:     MatCheckPreallocated(mat, 1);
    5183:   }
    5184:   PetscUseTypeMethod(mat, getrowmin, v, idx);
    5185:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5186:   PetscFunctionReturn(PETSC_SUCCESS);
    5187: }

    5189: /*@
    5190:   MatGetRowMinAbs - Gets the minimum value (in absolute value) of each
    5191:   row of the matrix

    5193:   Logically Collective

    5195:   Input Parameter:
    5196: . mat - the matrix

    5198:   Output Parameters:
    5199: + v   - the vector for storing the minimums
    5200: - idx - the indices of the column found for each row (or `NULL` if not needed)

    5202:   Level: intermediate

    5204:   Notes:
    5205:   if a row is completely empty or has only 0.0 values, then the `idx` value for that
    5206:   row is 0 (the first column).

    5208:   This code is only implemented for a couple of matrix formats.

    5210: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMax()`, `MatGetRowMaxAbs()`, `MatGetRowMin()`
    5211: @*/
    5212: PetscErrorCode MatGetRowMinAbs(Mat mat, Vec v, PetscInt idx[])
    5213: {
    5214:   PetscFunctionBegin;
    5218:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5219:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");

    5221:   if (!mat->cmap->N) {
    5222:     PetscCall(VecSet(v, 0.0));
    5223:     if (idx) {
    5224:       PetscInt i, m = mat->rmap->n;
    5225:       for (i = 0; i < m; i++) idx[i] = -1;
    5226:     }
    5227:   } else {
    5228:     MatCheckPreallocated(mat, 1);
    5229:     if (idx) PetscCall(PetscArrayzero(idx, mat->rmap->n));
    5230:     PetscUseTypeMethod(mat, getrowminabs, v, idx);
    5231:   }
    5232:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5233:   PetscFunctionReturn(PETSC_SUCCESS);
    5234: }

    5236: /*@
    5237:   MatGetRowMax - Gets the maximum value (of the real part) of each
    5238:   row of the matrix

    5240:   Logically Collective

    5242:   Input Parameter:
    5243: . mat - the matrix

    5245:   Output Parameters:
    5246: + v   - the vector for storing the maximums
    5247: - idx - the indices of the column found for each row (optional, otherwise pass `NULL`)

    5249:   Level: intermediate

    5251:   Notes:
    5252:   The result of this call are the same as if one converted the matrix to dense format
    5253:   and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    5255:   This code is only implemented for a couple of matrix formats.

    5257: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMaxAbs()`, `MatGetRowMin()`, `MatGetRowMinAbs()`
    5258: @*/
    5259: PetscErrorCode MatGetRowMax(Mat mat, Vec v, PetscInt idx[])
    5260: {
    5261:   PetscFunctionBegin;
    5265:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");

    5267:   if (!mat->cmap->N) {
    5268:     PetscCall(VecSet(v, PETSC_MIN_REAL));
    5269:     if (idx) {
    5270:       PetscInt i, m = mat->rmap->n;
    5271:       for (i = 0; i < m; i++) idx[i] = -1;
    5272:     }
    5273:   } else {
    5274:     MatCheckPreallocated(mat, 1);
    5275:     PetscUseTypeMethod(mat, getrowmax, v, idx);
    5276:   }
    5277:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5278:   PetscFunctionReturn(PETSC_SUCCESS);
    5279: }

    5281: /*@
    5282:   MatGetRowMaxAbs - Gets the maximum value (in absolute value) of each
    5283:   row of the matrix

    5285:   Logically Collective

    5287:   Input Parameter:
    5288: . mat - the matrix

    5290:   Output Parameters:
    5291: + v   - the vector for storing the maximums
    5292: - idx - the indices of the column found for each row (or `NULL` if not needed)

    5294:   Level: intermediate

    5296:   Notes:
    5297:   if a row is completely empty or has only 0.0 values, then the `idx` value for that
    5298:   row is 0 (the first column).

    5300:   This code is only implemented for a couple of matrix formats.

    5302: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowSum()`, `MatGetRowMin()`, `MatGetRowMinAbs()`
    5303: @*/
    5304: PetscErrorCode MatGetRowMaxAbs(Mat mat, Vec v, PetscInt idx[])
    5305: {
    5306:   PetscFunctionBegin;
    5310:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");

    5312:   if (!mat->cmap->N) {
    5313:     PetscCall(VecSet(v, 0.0));
    5314:     if (idx) {
    5315:       PetscInt i, m = mat->rmap->n;
    5316:       for (i = 0; i < m; i++) idx[i] = -1;
    5317:     }
    5318:   } else {
    5319:     MatCheckPreallocated(mat, 1);
    5320:     if (idx) PetscCall(PetscArrayzero(idx, mat->rmap->n));
    5321:     PetscUseTypeMethod(mat, getrowmaxabs, v, idx);
    5322:   }
    5323:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5324:   PetscFunctionReturn(PETSC_SUCCESS);
    5325: }

    5327: /*@
    5328:   MatGetRowSumAbs - Gets the sum value (in absolute value) of each row of the matrix

    5330:   Logically Collective

    5332:   Input Parameter:
    5333: . mat - the matrix

    5335:   Output Parameter:
    5336: . v - the vector for storing the sum

    5338:   Level: intermediate

    5340:   This code is only implemented for a couple of matrix formats.

    5342: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMax()`, `MatGetRowMin()`, `MatGetRowMinAbs()`
    5343: @*/
    5344: PetscErrorCode MatGetRowSumAbs(Mat mat, Vec v)
    5345: {
    5346:   PetscFunctionBegin;
    5350:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");

    5352:   if (!mat->cmap->N) PetscCall(VecSet(v, 0.0));
    5353:   else {
    5354:     MatCheckPreallocated(mat, 1);
    5355:     PetscUseTypeMethod(mat, getrowsumabs, v);
    5356:   }
    5357:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5358:   PetscFunctionReturn(PETSC_SUCCESS);
    5359: }

    5361: /*@
    5362:   MatGetRowSum - Gets the sum of each row of the matrix

    5364:   Logically or Neighborhood Collective

    5366:   Input Parameter:
    5367: . mat - the matrix

    5369:   Output Parameter:
    5370: . v - the vector for storing the sum of rows

    5372:   Level: intermediate

    5374:   Note:
    5375:   This code is slow since it is not currently specialized for different formats

    5377: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMax()`, `MatGetRowMin()`, `MatGetRowMaxAbs()`, `MatGetRowMinAbs()`, `MatGetRowSumAbs()`
    5378: @*/
    5379: PetscErrorCode MatGetRowSum(Mat mat, Vec v)
    5380: {
    5381:   Vec ones;

    5383:   PetscFunctionBegin;
    5387:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5388:   MatCheckPreallocated(mat, 1);
    5389:   PetscCall(MatCreateVecs(mat, &ones, NULL));
    5390:   PetscCall(VecSet(ones, 1.));
    5391:   PetscCall(MatMult(mat, ones, v));
    5392:   PetscCall(VecDestroy(&ones));
    5393:   PetscFunctionReturn(PETSC_SUCCESS);
    5394: }

    5396: /*@
    5397:   MatTransposeSetPrecursor - Set the matrix from which the second matrix will receive numerical transpose data with a call to `MatTranspose`(A,`MAT_REUSE_MATRIX`,&B)
    5398:   when B was not obtained with `MatTranspose`(A,`MAT_INITIAL_MATRIX`,&B)

    5400:   Collective

    5402:   Input Parameter:
    5403: . mat - the matrix to provide the transpose

    5405:   Output Parameter:
    5406: . B - the matrix to contain the transpose; it MUST have the nonzero structure of the transpose of A or the code will crash or generate incorrect results

    5408:   Level: advanced

    5410:   Note:
    5411:   Normally the use of `MatTranspose`(A, `MAT_REUSE_MATRIX`, &B) requires that `B` was obtained with a call to `MatTranspose`(A, `MAT_INITIAL_MATRIX`, &B). This
    5412:   routine allows bypassing that call.

    5414: .seealso: [](ch_matrices), `Mat`, `MatTransposeSymbolic()`, `MatTranspose()`, `MatMultTranspose()`, `MatMultTransposeAdd()`, `MatIsTranspose()`, `MatReuse`, `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, `MAT_INPLACE_MATRIX`
    5415: @*/
    5416: PetscErrorCode MatTransposeSetPrecursor(Mat mat, Mat B)
    5417: {
    5418:   MatParentState *rb = NULL;

    5420:   PetscFunctionBegin;
    5421:   PetscCall(PetscNew(&rb));
    5422:   rb->id    = ((PetscObject)mat)->id;
    5423:   rb->state = 0;
    5424:   PetscCall(MatGetNonzeroState(mat, &rb->nonzerostate));
    5425:   PetscCall(PetscObjectContainerCompose((PetscObject)B, "MatTransposeParent", rb, PetscCtxDestroyDefault));
    5426:   PetscFunctionReturn(PETSC_SUCCESS);
    5427: }

    5429: static PetscErrorCode MatTranspose_Private(Mat mat, MatReuse reuse, Mat *B, PetscBool conjugate)
    5430: {
    5431:   PetscContainer  rB                        = NULL;
    5432:   MatParentState *rb                        = NULL;
    5433:   PetscErrorCode (*f)(Mat, MatReuse, Mat *) = NULL;

    5435:   PetscFunctionBegin;
    5438:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5439:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5440:   PetscCheck(reuse != MAT_INPLACE_MATRIX || mat == *B, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "MAT_INPLACE_MATRIX requires last matrix to match first");
    5441:   PetscCheck(reuse != MAT_REUSE_MATRIX || mat != *B, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Perhaps you mean MAT_INPLACE_MATRIX");
    5442:   MatCheckPreallocated(mat, 1);
    5443:   if (reuse == MAT_REUSE_MATRIX) {
    5444:     PetscCall(PetscObjectQuery((PetscObject)*B, "MatTransposeParent", (PetscObject *)&rB));
    5445:     PetscCheck(rB, PetscObjectComm((PetscObject)*B), PETSC_ERR_ARG_WRONG, "Reuse matrix used was not generated from call to MatTranspose(). Suggest MatTransposeSetPrecursor().");
    5446:     PetscCall(PetscContainerGetPointer(rB, &rb));
    5447:     PetscCheck(rb->id == ((PetscObject)mat)->id, PetscObjectComm((PetscObject)*B), PETSC_ERR_ARG_WRONG, "Reuse matrix used was not generated from input matrix");
    5448:     if (rb->state == ((PetscObject)mat)->state) PetscFunctionReturn(PETSC_SUCCESS);
    5449:   }

    5451:   if (conjugate) {
    5452:     f = mat->ops->hermitiantranspose;
    5453:     if (f) PetscCall((*f)(mat, reuse, B));
    5454:   }
    5455:   if (!f && !(reuse == MAT_INPLACE_MATRIX && mat->hermitian == PETSC_BOOL3_TRUE && conjugate)) {
    5456:     PetscCall(PetscLogEventBegin(MAT_Transpose, mat, 0, 0, 0));
    5457:     if (reuse != MAT_INPLACE_MATRIX || mat->symmetric != PETSC_BOOL3_TRUE) {
    5458:       PetscUseTypeMethod(mat, transpose, reuse, B);
    5459:       PetscCall(PetscObjectStateIncrease((PetscObject)*B));
    5460:     }
    5461:     PetscCall(PetscLogEventEnd(MAT_Transpose, mat, 0, 0, 0));
    5462:     if (conjugate) PetscCall(MatConjugate(*B));
    5463:   }

    5465:   if (reuse == MAT_INITIAL_MATRIX) PetscCall(MatTransposeSetPrecursor(mat, *B));
    5466:   if (reuse != MAT_INPLACE_MATRIX) {
    5467:     PetscCall(PetscObjectQuery((PetscObject)*B, "MatTransposeParent", (PetscObject *)&rB));
    5468:     PetscCall(PetscContainerGetPointer(rB, &rb));
    5469:     rb->state        = ((PetscObject)mat)->state;
    5470:     rb->nonzerostate = mat->nonzerostate;
    5471:   }
    5472:   PetscFunctionReturn(PETSC_SUCCESS);
    5473: }

    5475: /*@
    5476:   MatTranspose - Computes the transpose of a matrix, either in-place or out-of-place.

    5478:   Collective

    5480:   Input Parameters:
    5481: + mat   - the matrix to transpose
    5482: - reuse - either `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, or `MAT_INPLACE_MATRIX`

    5484:   Output Parameter:
    5485: . B - the transpose of the matrix

    5487:   Level: intermediate

    5489:   Notes:
    5490:   If you use `MAT_INPLACE_MATRIX` then you must pass in `&mat` for `B`

    5492:   `MAT_REUSE_MATRIX` uses the `B` matrix obtained from a previous call to this function with `MAT_INITIAL_MATRIX` to store the transpose. If you already have a matrix to contain the
    5493:   transpose, call `MatTransposeSetPrecursor(mat, B)` before calling this routine.

    5495:   If the nonzero structure of `mat` changed from the previous call to this function with the same matrices an error will be generated for some matrix types.

    5497:   Consider using `MatCreateTranspose()` instead if you only need a matrix that behaves like the transpose but don't need the storage to be changed.
    5498:   For example, the result of `MatCreateTranspose()` will compute the transpose of the given matrix times a vector for matrix-vector products computed with `MatMult()`.

    5500:   If `mat` is unchanged from the last call this function returns immediately without recomputing the result

    5502:   If you only need the symbolic transpose of a matrix, and not the numerical values, use `MatTransposeSymbolic()`

    5504: .seealso: [](ch_matrices), `Mat`, `MatTransposeSetPrecursor()`, `MatMultTranspose()`, `MatMultTransposeAdd()`, `MatIsTranspose()`, `MatReuse`, `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, `MAT_INPLACE_MATRIX`,
    5505:           `MatTransposeSymbolic()`, `MatCreateTranspose()`
    5506: @*/
    5507: PetscErrorCode MatTranspose(Mat mat, MatReuse reuse, Mat *B)
    5508: {
    5509:   PetscFunctionBegin;
    5510:   PetscCall(MatTranspose_Private(mat, reuse, B, PETSC_FALSE));
    5511:   PetscFunctionReturn(PETSC_SUCCESS);
    5512: }

    5514: /*@
    5515:   MatTransposeSymbolic - Computes the symbolic part of the transpose of a matrix.

    5517:   Collective

    5519:   Input Parameter:
    5520: . A - the matrix to transpose

    5522:   Output Parameter:
    5523: . B - the transpose. This is a complete matrix but the numerical portion is invalid. One can call `MatTranspose`(A,`MAT_REUSE_MATRIX`,&B) to compute the
    5524:       numerical portion.

    5526:   Level: intermediate

    5528:   Note:
    5529:   This is not supported for many matrix types, use `MatTranspose()` in those cases

    5531: .seealso: [](ch_matrices), `Mat`, `MatTransposeSetPrecursor()`, `MatTranspose()`, `MatMultTranspose()`, `MatMultTransposeAdd()`, `MatIsTranspose()`, `MatReuse`, `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, `MAT_INPLACE_MATRIX`
    5532: @*/
    5533: PetscErrorCode MatTransposeSymbolic(Mat A, Mat *B)
    5534: {
    5535:   PetscFunctionBegin;
    5538:   PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5539:   PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5540:   PetscCall(PetscLogEventBegin(MAT_Transpose, A, 0, 0, 0));
    5541:   PetscUseTypeMethod(A, transposesymbolic, B);
    5542:   PetscCall(PetscLogEventEnd(MAT_Transpose, A, 0, 0, 0));

    5544:   PetscCall(MatTransposeSetPrecursor(A, *B));
    5545:   PetscFunctionReturn(PETSC_SUCCESS);
    5546: }

    5548: PetscErrorCode MatTransposeCheckNonzeroState_Private(Mat A, Mat B)
    5549: {
    5550:   PetscContainer  rB;
    5551:   MatParentState *rb;

    5553:   PetscFunctionBegin;
    5556:   PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5557:   PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5558:   PetscCall(PetscObjectQuery((PetscObject)B, "MatTransposeParent", (PetscObject *)&rB));
    5559:   PetscCheck(rB, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONG, "Reuse matrix used was not generated from call to MatTranspose()");
    5560:   PetscCall(PetscContainerGetPointer(rB, &rb));
    5561:   PetscCheck(rb->id == ((PetscObject)A)->id, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONG, "Reuse matrix used was not generated from input matrix");
    5562:   PetscCheck(rb->nonzerostate == A->nonzerostate, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONGSTATE, "Reuse matrix has changed nonzero structure");
    5563:   PetscFunctionReturn(PETSC_SUCCESS);
    5564: }

    5566: /*@
    5567:   MatIsTranspose - Test whether a matrix is another one's transpose,
    5568:   or its own, in which case it tests symmetry.

    5570:   Collective

    5572:   Input Parameters:
    5573: + A   - the matrix to test
    5574: . B   - the matrix to test against, this can equal the first parameter
    5575: - tol - tolerance, differences between entries smaller than this are counted as zero

    5577:   Output Parameter:
    5578: . flg - the result

    5580:   Level: intermediate

    5582:   Notes:
    5583:   The sequential algorithm has a running time of the order of the number of nonzeros; the parallel
    5584:   test involves parallel copies of the block off-diagonal parts of the matrix.

    5586: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatIsSymmetric()`, `MatIsHermitian()`
    5587: @*/
    5588: PetscErrorCode MatIsTranspose(Mat A, Mat B, PetscReal tol, PetscBool *flg)
    5589: {
    5590:   PetscErrorCode (*f)(Mat, Mat, PetscReal, PetscBool *), (*g)(Mat, Mat, PetscReal, PetscBool *);

    5592:   PetscFunctionBegin;
    5595:   PetscAssertPointer(flg, 4);
    5596:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatIsTranspose_C", &f));
    5597:   PetscCall(PetscObjectQueryFunction((PetscObject)B, "MatIsTranspose_C", &g));
    5598:   *flg = PETSC_FALSE;
    5599:   if (f && g) {
    5600:     PetscCheck(f == g, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_NOTSAMETYPE, "Matrices do not have the same comparator for symmetry test");
    5601:     PetscCall((*f)(A, B, tol, flg));
    5602:   } else {
    5603:     MatType mattype;

    5605:     PetscCall(MatGetType(f ? B : A, &mattype));
    5606:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Matrix of type %s does not support checking for transpose", mattype);
    5607:   }
    5608:   PetscFunctionReturn(PETSC_SUCCESS);
    5609: }

    5611: /*@
    5612:   MatHermitianTranspose - Computes an in-place or out-of-place Hermitian transpose of a matrix in complex conjugate.

    5614:   Collective

    5616:   Input Parameters:
    5617: + mat   - the matrix to transpose and complex conjugate
    5618: - reuse - either `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, or `MAT_INPLACE_MATRIX`

    5620:   Output Parameter:
    5621: . B - the Hermitian transpose

    5623:   Level: intermediate

    5625: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatMultTranspose()`, `MatMultTransposeAdd()`, `MatIsTranspose()`, `MatReuse`
    5626: @*/
    5627: PetscErrorCode MatHermitianTranspose(Mat mat, MatReuse reuse, Mat *B)
    5628: {
    5629:   PetscFunctionBegin;
    5630:   PetscCall(MatTranspose_Private(mat, reuse, B, PETSC_TRUE));
    5631:   PetscFunctionReturn(PETSC_SUCCESS);
    5632: }

    5634: /*@
    5635:   MatIsHermitianTranspose - Test whether a matrix is another one's Hermitian transpose,

    5637:   Collective

    5639:   Input Parameters:
    5640: + A   - the matrix to test
    5641: . B   - the matrix to test against, this can equal the first parameter
    5642: - tol - tolerance, differences between entries smaller than this are counted as zero

    5644:   Output Parameter:
    5645: . flg - the result

    5647:   Level: intermediate

    5649:   Notes:
    5650:   Only available for `MATAIJ` matrices.

    5652:   The sequential algorithm
    5653:   has a running time of the order of the number of nonzeros; the parallel
    5654:   test involves parallel copies of the block off-diagonal parts of the matrix.

    5656: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatIsSymmetric()`, `MatIsHermitian()`, `MatIsTranspose()`
    5657: @*/
    5658: PetscErrorCode MatIsHermitianTranspose(Mat A, Mat B, PetscReal tol, PetscBool *flg)
    5659: {
    5660:   PetscErrorCode (*f)(Mat, Mat, PetscReal, PetscBool *), (*g)(Mat, Mat, PetscReal, PetscBool *);

    5662:   PetscFunctionBegin;
    5665:   PetscAssertPointer(flg, 4);
    5666:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatIsHermitianTranspose_C", &f));
    5667:   PetscCall(PetscObjectQueryFunction((PetscObject)B, "MatIsHermitianTranspose_C", &g));
    5668:   if (f && g) {
    5669:     PetscCheck(f == g, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_NOTSAMETYPE, "Matrices do not have the same comparator for Hermitian test");
    5670:     PetscCall((*f)(A, B, tol, flg));
    5671:   } else {
    5672:     MatType mattype;

    5674:     PetscCall(MatGetType(f ? B : A, &mattype));
    5675:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Matrix of type %s does not support checking for Hermitian transpose", mattype);
    5676:   }
    5677:   PetscFunctionReturn(PETSC_SUCCESS);
    5678: }

    5680: /*@
    5681:   MatPermute - Creates a new matrix with rows and columns permuted from the
    5682:   original.

    5684:   Collective

    5686:   Input Parameters:
    5687: + mat - the matrix to permute
    5688: . row - row permutation, each processor supplies only the permutation for its rows
    5689: - col - column permutation, each processor supplies only the permutation for its columns

    5691:   Output Parameter:
    5692: . B - the permuted matrix

    5694:   Level: advanced

    5696:   Note:
    5697:   The index sets map from row/col of permuted matrix to row/col of original matrix.
    5698:   The index sets should be on the same communicator as mat and have the same local sizes.

    5700:   Developer Note:
    5701:   If you want to implement `MatPermute()` for a matrix type, and your approach doesn't
    5702:   exploit the fact that row and col are permutations, consider implementing the
    5703:   more general `MatCreateSubMatrix()` instead.

    5705: .seealso: [](ch_matrices), `Mat`, `MatGetOrdering()`, `ISAllGather()`, `MatCreateSubMatrix()`
    5706: @*/
    5707: PetscErrorCode MatPermute(Mat mat, IS row, IS col, Mat *B)
    5708: {
    5709:   PetscFunctionBegin;
    5714:   PetscAssertPointer(B, 4);
    5715:   PetscCheckSameComm(mat, 1, row, 2);
    5716:   if (row != col) PetscCheckSameComm(row, 2, col, 3);
    5717:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5718:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5719:   PetscCheck(mat->ops->permute || mat->ops->createsubmatrix, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatPermute not available for Mat type %s", ((PetscObject)mat)->type_name);
    5720:   MatCheckPreallocated(mat, 1);

    5722:   if (mat->ops->permute) {
    5723:     PetscUseTypeMethod(mat, permute, row, col, B);
    5724:     PetscCall(PetscObjectStateIncrease((PetscObject)*B));
    5725:   } else {
    5726:     PetscCall(MatCreateSubMatrix(mat, row, col, MAT_INITIAL_MATRIX, B));
    5727:   }
    5728:   PetscFunctionReturn(PETSC_SUCCESS);
    5729: }

    5731: /*@
    5732:   MatEqual - Compares two matrices.

    5734:   Collective

    5736:   Input Parameters:
    5737: + A - the first matrix
    5738: - B - the second matrix

    5740:   Output Parameter:
    5741: . flg - `PETSC_TRUE` if the matrices are equal; `PETSC_FALSE` otherwise.

    5743:   Level: intermediate

    5745:   Note:
    5746:   If either of the matrix is "matrix-free", meaning the matrix entries are not stored explicitly then equality is determined by comparing
    5747:   the results of several matrix-vector product using randomly created vectors, see `MatMultEqual()`.

    5749: .seealso: [](ch_matrices), `Mat`, `MatMultEqual()`
    5750: @*/
    5751: PetscErrorCode MatEqual(Mat A, Mat B, PetscBool *flg)
    5752: {
    5753:   PetscFunctionBegin;
    5758:   PetscAssertPointer(flg, 3);
    5759:   PetscCheckSameComm(A, 1, B, 2);
    5760:   MatCheckPreallocated(A, 1);
    5761:   MatCheckPreallocated(B, 2);
    5762:   PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5763:   PetscCheck(B->assembled, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5764:   PetscCheck(A->rmap->N == B->rmap->N && A->cmap->N == B->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Mat A,Mat B: global dim %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT, A->rmap->N, B->rmap->N, A->cmap->N,
    5765:              B->cmap->N);
    5766:   if (A->ops->equal && A->ops->equal == B->ops->equal) PetscUseTypeMethod(A, equal, B, flg);
    5767:   else PetscCall(MatMultEqual(A, B, 10, flg));
    5768:   PetscFunctionReturn(PETSC_SUCCESS);
    5769: }

    5771: /*@
    5772:   MatDiagonalScale - Scales a matrix on the left and right by diagonal
    5773:   matrices that are stored as vectors.  Either of the two scaling
    5774:   matrices can be `NULL`.

    5776:   Collective

    5778:   Input Parameters:
    5779: + mat - the matrix to be scaled
    5780: . l   - the left scaling vector (or `NULL`)
    5781: - r   - the right scaling vector (or `NULL`)

    5783:   Level: intermediate

    5785:   Note:
    5786:   `MatDiagonalScale()` computes $A = LAR$, where
    5787:   L = a diagonal matrix (stored as a vector), R = a diagonal matrix (stored as a vector)
    5788:   The L scales the rows of the matrix, the R scales the columns of the matrix.

    5790: .seealso: [](ch_matrices), `Mat`, `MatScale()`, `MatShift()`, `MatDiagonalSet()`
    5791: @*/
    5792: PetscErrorCode MatDiagonalScale(Mat mat, Vec l, Vec r)
    5793: {
    5794:   PetscBool flg = PETSC_FALSE;

    5796:   PetscFunctionBegin;
    5799:   if (l) {
    5801:     PetscCheckSameComm(mat, 1, l, 2);
    5802:   }
    5803:   if (r) {
    5805:     PetscCheckSameComm(mat, 1, r, 3);
    5806:   }
    5807:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5808:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5809:   MatCheckPreallocated(mat, 1);
    5810:   if (!l && !r) PetscFunctionReturn(PETSC_SUCCESS);

    5812:   PetscCall(PetscLogEventBegin(MAT_Scale, mat, 0, 0, 0));
    5813:   PetscUseTypeMethod(mat, diagonalscale, l, r);
    5814:   PetscCall(PetscLogEventEnd(MAT_Scale, mat, 0, 0, 0));
    5815:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    5816:   if (l != r && (PetscBool3ToBool(mat->symmetric) || PetscBool3ToBool(mat->hermitian))) {
    5817:     if (!PetscDefined(USE_COMPLEX) || PetscBool3ToBool(mat->symmetric)) {
    5818:       if (l && r) PetscCall(VecEqual(l, r, &flg));
    5819:       if (!flg) {
    5820:         PetscCall(PetscObjectTypeCompareAny((PetscObject)mat, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));
    5821:         PetscCheck(!flg, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "For symmetric format, left and right scaling vectors must be the same");
    5822:         mat->symmetric = mat->spd = PETSC_BOOL3_FALSE;
    5823:         if (!PetscDefined(USE_COMPLEX)) mat->hermitian = PETSC_BOOL3_FALSE;
    5824:         else mat->hermitian = PETSC_BOOL3_UNKNOWN;
    5825:       }
    5826:     }
    5827:     if (PetscDefined(USE_COMPLEX) && PetscBool3ToBool(mat->hermitian)) {
    5828:       flg = PETSC_FALSE;
    5829:       if (l && r) {
    5830:         Vec conjugate;

    5832:         PetscCall(VecDuplicate(l, &conjugate));
    5833:         PetscCall(VecCopy(l, conjugate));
    5834:         PetscCall(VecConjugate(conjugate));
    5835:         PetscCall(VecEqual(conjugate, r, &flg));
    5836:         PetscCall(VecDestroy(&conjugate));
    5837:       }
    5838:       if (!flg) {
    5839:         PetscCall(PetscObjectTypeCompareAny((PetscObject)mat, &flg, MATSEQSBAIJ, MATMPISBAIJ, ""));
    5840:         PetscCheck(!flg, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "For symmetric format and Hermitian matrix, left and right scaling vectors must be conjugate one of the other");
    5841:         mat->hermitian = PETSC_BOOL3_FALSE;
    5842:         mat->symmetric = mat->spd = PETSC_BOOL3_UNKNOWN;
    5843:       }
    5844:     }
    5845:   }
    5846:   PetscFunctionReturn(PETSC_SUCCESS);
    5847: }

    5849: /*@
    5850:   MatScale - Scales all elements of a matrix by a given number.

    5852:   Logically Collective

    5854:   Input Parameters:
    5855: + mat - the matrix to be scaled
    5856: - a   - the scaling value

    5858:   Level: intermediate

    5860: .seealso: [](ch_matrices), `Mat`, `MatDiagonalScale()`
    5861: @*/
    5862: PetscErrorCode MatScale(Mat mat, PetscScalar a)
    5863: {
    5864:   PetscFunctionBegin;
    5867:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5868:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5870:   MatCheckPreallocated(mat, 1);

    5872:   PetscCall(PetscLogEventBegin(MAT_Scale, mat, 0, 0, 0));
    5873:   if (a != (PetscScalar)1.0) {
    5874:     PetscUseTypeMethod(mat, scale, a);
    5875:     PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    5876:   }
    5877:   PetscCall(PetscLogEventEnd(MAT_Scale, mat, 0, 0, 0));
    5878:   PetscFunctionReturn(PETSC_SUCCESS);
    5879: }

    5881: /*@
    5882:   MatNorm - Calculates various norms of a matrix.

    5884:   Collective

    5886:   Input Parameters:
    5887: + mat  - the matrix
    5888: - type - the type of norm, `NORM_1`, `NORM_FROBENIUS`, `NORM_INFINITY`

    5890:   Output Parameter:
    5891: . nrm - the resulting norm

    5893:   Level: intermediate

    5895: .seealso: [](ch_matrices), `Mat`
    5896: @*/
    5897: PetscErrorCode MatNorm(Mat mat, NormType type, PetscReal *nrm)
    5898: {
    5899:   PetscFunctionBegin;
    5902:   PetscAssertPointer(nrm, 3);

    5904:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5905:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5906:   MatCheckPreallocated(mat, 1);

    5908:   PetscUseTypeMethod(mat, norm, type, nrm);
    5909:   PetscFunctionReturn(PETSC_SUCCESS);
    5910: }

    5912: /*
    5913:      This variable is used to prevent counting of MatAssemblyBegin() that
    5914:    are called from within a MatAssemblyEnd().
    5915: */
    5916: static PetscInt MatAssemblyEnd_InUse = 0;
    5917: /*@
    5918:   MatAssemblyBegin - Begins assembling the matrix.  This routine should
    5919:   be called after completing all calls to `MatSetValues()`.

    5921:   Collective

    5923:   Input Parameters:
    5924: + mat  - the matrix
    5925: - type - type of assembly, either `MAT_FLUSH_ASSEMBLY` or `MAT_FINAL_ASSEMBLY`

    5927:   Level: beginner

    5929:   Notes:
    5930:   `MatSetValues()` generally caches the values that belong to other MPI processes.  The matrix is ready to
    5931:   use only after `MatAssemblyBegin()` and `MatAssemblyEnd()` have been called.

    5933:   Use `MAT_FLUSH_ASSEMBLY` when switching between `ADD_VALUES` and `INSERT_VALUES`
    5934:   in `MatSetValues()`; use `MAT_FINAL_ASSEMBLY` for the final assembly before
    5935:   using the matrix.

    5937:   ALL processes that share a matrix MUST call `MatAssemblyBegin()` and `MatAssemblyEnd()` the SAME NUMBER of times, and each time with the
    5938:   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
    5939:   a global collective operation requiring all processes that share the matrix.

    5941:   Space for preallocated nonzeros that is not filled by a call to `MatSetValues()` or a related routine are compressed
    5942:   out by assembly. If you intend to use that extra space on a subsequent assembly, be sure to insert explicit zeros
    5943:   before `MAT_FINAL_ASSEMBLY` so the space is not compressed out.

    5945: .seealso: [](ch_matrices), `Mat`, `MatAssemblyEnd()`, `MatSetValues()`, `MatAssembled()`
    5946: @*/
    5947: PetscErrorCode MatAssemblyBegin(Mat mat, MatAssemblyType type)
    5948: {
    5949:   PetscFunctionBegin;
    5952:   MatCheckPreallocated(mat, 1);
    5953:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix. Did you forget to call MatSetUnfactored()?");
    5954:   if (mat->assembled) {
    5955:     mat->was_assembled = PETSC_TRUE;
    5956:     mat->assembled     = PETSC_FALSE;
    5957:   }

    5959:   if (!MatAssemblyEnd_InUse) {
    5960:     PetscCall(PetscLogEventBegin(MAT_AssemblyBegin, mat, 0, 0, 0));
    5961:     PetscTryTypeMethod(mat, assemblybegin, type);
    5962:     PetscCall(PetscLogEventEnd(MAT_AssemblyBegin, mat, 0, 0, 0));
    5963:   } else PetscTryTypeMethod(mat, assemblybegin, type);
    5964:   PetscFunctionReturn(PETSC_SUCCESS);
    5965: }

    5967: /*@
    5968:   MatAssembled - Indicates if a matrix has been assembled and is ready for
    5969:   use; for example, in matrix-vector product.

    5971:   Not Collective

    5973:   Input Parameter:
    5974: . mat - the matrix

    5976:   Output Parameter:
    5977: . assembled - `PETSC_TRUE` or `PETSC_FALSE`

    5979:   Level: advanced

    5981: .seealso: [](ch_matrices), `Mat`, `MatAssemblyEnd()`, `MatSetValues()`, `MatAssemblyBegin()`
    5982: @*/
    5983: PetscErrorCode MatAssembled(Mat mat, PetscBool *assembled)
    5984: {
    5985:   PetscFunctionBegin;
    5987:   PetscAssertPointer(assembled, 2);
    5988:   *assembled = mat->assembled;
    5989:   PetscFunctionReturn(PETSC_SUCCESS);
    5990: }

    5992: /*@
    5993:   MatAssemblyEnd - Completes assembling the matrix.  This routine should
    5994:   be called after `MatAssemblyBegin()`.

    5996:   Collective

    5998:   Input Parameters:
    5999: + mat  - the matrix
    6000: - type - type of assembly, either `MAT_FLUSH_ASSEMBLY` or `MAT_FINAL_ASSEMBLY`

    6002:   Options Database Key:
    6003: . -mat_view [viewertype][:...] - option name and values. See `MatViewFromOptions()`/`PetscObjectViewFromOptions()` for the possible arguments

    6005:   Level: beginner

    6007: .seealso: [](ch_matrices), `Mat`, `MatAssemblyBegin()`, `MatSetValues()`, `PetscDrawOpenX()`, `PetscDrawCreate()`, `MatView()`, `MatAssembled()`, `PetscViewerSocketOpen()`,
    6008:           `MatViewFromOptions()`, `PetscObjectViewFromOptions()`
    6009: @*/
    6010: PetscErrorCode MatAssemblyEnd(Mat mat, MatAssemblyType type)
    6011: {
    6012:   static PetscInt inassm = 0;
    6013:   PetscBool       flg    = PETSC_FALSE;

    6015:   PetscFunctionBegin;

    6019:   inassm++;
    6020:   MatAssemblyEnd_InUse++;
    6021:   if (MatAssemblyEnd_InUse == 1) { /* Do the logging only the first time through */
    6022:     PetscCall(PetscLogEventBegin(MAT_AssemblyEnd, mat, 0, 0, 0));
    6023:     PetscTryTypeMethod(mat, assemblyend, type);
    6024:     PetscCall(PetscLogEventEnd(MAT_AssemblyEnd, mat, 0, 0, 0));
    6025:   } else PetscTryTypeMethod(mat, assemblyend, type);

    6027:   /* Flush assembly is not a true assembly */
    6028:   if (type != MAT_FLUSH_ASSEMBLY) {
    6029:     if (mat->num_ass) {
    6030:       if (!mat->symmetry_eternal) {
    6031:         mat->symmetric = PETSC_BOOL3_UNKNOWN;
    6032:         mat->hermitian = PETSC_BOOL3_UNKNOWN;
    6033:       }
    6034:       if (!mat->structural_symmetry_eternal && mat->ass_nonzerostate != mat->nonzerostate) mat->structurally_symmetric = PETSC_BOOL3_UNKNOWN;
    6035:       if (!mat->spd_eternal) mat->spd = PETSC_BOOL3_UNKNOWN;
    6036:     }
    6037:     mat->num_ass++;
    6038:     mat->assembled        = PETSC_TRUE;
    6039:     mat->ass_nonzerostate = mat->nonzerostate;
    6040:   }

    6042:   mat->insertmode = NOT_SET_VALUES;
    6043:   MatAssemblyEnd_InUse--;
    6044:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6045:   if (inassm == 1 && type != MAT_FLUSH_ASSEMBLY) {
    6046:     PetscCall(MatViewFromOptions(mat, NULL, "-mat_view"));

    6048:     if (mat->checksymmetryonassembly) {
    6049:       PetscCall(MatIsSymmetric(mat, mat->checksymmetrytol, &flg));
    6050:       if (flg) {
    6051:         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "Matrix is symmetric (tolerance %g)\n", (double)mat->checksymmetrytol));
    6052:       } else {
    6053:         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "Matrix is not symmetric (tolerance %g)\n", (double)mat->checksymmetrytol));
    6054:       }
    6055:     }
    6056:     if (mat->nullsp && mat->checknullspaceonassembly) PetscCall(MatNullSpaceTest(mat->nullsp, mat, NULL));
    6057:   }
    6058:   inassm--;
    6059:   PetscFunctionReturn(PETSC_SUCCESS);
    6060: }

    6062: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    6063: /*@
    6064:   MatSetOption - Sets a parameter option for a matrix. Some options
    6065:   may be specific to certain storage formats.  Some options
    6066:   determine how values will be inserted (or added). Sorted,
    6067:   row-oriented input will generally assemble the fastest. The default
    6068:   is row-oriented.

    6070:   Logically Collective for certain operations, such as `MAT_SPD`, not collective for `MAT_ROW_ORIENTED`, see `MatOption`

    6072:   Input Parameters:
    6073: + mat - the matrix
    6074: . op  - the option, one of those listed below (and possibly others),
    6075: - flg - turn the option on (`PETSC_TRUE`) or off (`PETSC_FALSE`)

    6077:   Options Describing Matrix Structure:
    6078: + `MAT_SPD`                         - symmetric positive definite
    6079: . `MAT_SYMMETRIC`                   - symmetric in terms of both structure and value
    6080: . `MAT_HERMITIAN`                   - transpose is the complex conjugation
    6081: . `MAT_STRUCTURALLY_SYMMETRIC`      - symmetric nonzero structure
    6082: . `MAT_SYMMETRY_ETERNAL`            - indicates the symmetry (or Hermitian structure) or its absence will persist through any changes to the matrix
    6083: . `MAT_STRUCTURAL_SYMMETRY_ETERNAL` - indicates the structural symmetry or its absence will persist through any changes to the matrix
    6084: . `MAT_SPD_ETERNAL`                 - indicates the value of `MAT_SPD` (true or false) will persist through any changes to the matrix

    6086:    These are not really options of the matrix, they are knowledge about the structure of the matrix that users may provide so that they
    6087:    do not need to be computed (usually at a high cost)

    6089:    Options For Use with `MatSetValues()`:
    6090:    Insert a logically dense subblock, which can be
    6091: . `MAT_ROW_ORIENTED`                - row-oriented (default)

    6093:    These options reflect the data you pass in with `MatSetValues()`; it has
    6094:    nothing to do with how the data is stored internally in the matrix
    6095:    data structure.

    6097:    When (re)assembling a matrix, we can restrict the input for
    6098:    efficiency/debugging purposes.  These options include
    6099: . `MAT_NEW_NONZERO_LOCATIONS`       - additional insertions will be allowed if they generate a new nonzero (slow)
    6100: . `MAT_FORCE_DIAGONAL_ENTRIES`      - forces diagonal entries to be allocated
    6101: . `MAT_IGNORE_OFF_PROC_ENTRIES`     - drops off-processor entries
    6102: . `MAT_NEW_NONZERO_LOCATION_ERR`    - generates an error for new matrix entry
    6103: . `MAT_USE_HASH_TABLE`              - uses a hash table to speed up matrix assembly
    6104: . `MAT_NO_OFF_PROC_ENTRIES`         - you know each process will only set values for its own rows, will generate an error if
    6105:         any process sets values for another process. This avoids all reductions in the MatAssembly routines and thus improves
    6106:         performance for very large process counts.
    6107: - `MAT_SUBSET_OFF_PROC_ENTRIES`     - you know that the first assembly after setting this flag will set a superset
    6108:         of the off-process entries required for all subsequent assemblies. This avoids a rendezvous step in the MatAssembly
    6109:         functions, instead sending only neighbor messages.

    6111:   Level: intermediate

    6113:   Notes:
    6114:   Except for `MAT_UNUSED_NONZERO_LOCATION_ERR` and  `MAT_ROW_ORIENTED` all processes that share the matrix must pass the same value in flg!

    6116:   Some options are relevant only for particular matrix types and
    6117:   are thus ignored by others.  Other options are not supported by
    6118:   certain matrix types and will generate an error message if set.

    6120:   If using Fortran to compute a matrix, one may need to
    6121:   use the column-oriented option (or convert to the row-oriented
    6122:   format).

    6124:   `MAT_NEW_NONZERO_LOCATIONS` set to `PETSC_FALSE` indicates that any add or insertion
    6125:   that would generate a new entry in the nonzero structure is instead
    6126:   ignored.  Thus, if memory has not already been allocated for this particular
    6127:   data, then the insertion is ignored. For dense matrices, in which
    6128:   the entire array is allocated, no entries are ever ignored.
    6129:   Set after the first `MatAssemblyEnd()`. If this option is set, then the `MatAssemblyBegin()`/`MatAssemblyEnd()` processes has one less global reduction

    6131:   `MAT_NEW_NONZERO_LOCATION_ERR` set to PETSC_TRUE indicates that any add or insertion
    6132:   that would generate a new entry in the nonzero structure instead produces
    6133:   an error. (Currently supported for `MATAIJ` and `MATBAIJ` formats only.) If this option is set, then the `MatAssemblyBegin()`/`MatAssemblyEnd()` processes has one less global reduction

    6135:   `MAT_NEW_NONZERO_ALLOCATION_ERR` set to `PETSC_TRUE` indicates that any add or insertion
    6136:   that would generate a new entry that has not been preallocated will
    6137:   instead produce an error. (Currently supported for `MATAIJ` and `MATBAIJ` formats
    6138:   only.) This is a useful flag when debugging matrix memory preallocation.
    6139:   If this option is set, then the `MatAssemblyBegin()`/`MatAssemblyEnd()` processes has one less global reduction

    6141:   `MAT_IGNORE_OFF_PROC_ENTRIES` set to `PETSC_TRUE` indicates entries destined for
    6142:   other processors should be dropped, rather than stashed.
    6143:   This is useful if you know that the "owning" processor is also
    6144:   always generating the correct matrix entries, so that PETSc need
    6145:   not transfer duplicate entries generated on another processor.

    6147:   `MAT_USE_HASH_TABLE` indicates that a hash table be used to improve the
    6148:   searches during matrix assembly. When this flag is set, the hash table
    6149:   is created during the first matrix assembly. This hash table is
    6150:   used the next time through, during `MatSetValues()`/`MatSetValuesBlocked()`
    6151:   to improve the searching of indices. `MAT_NEW_NONZERO_LOCATIONS` flag
    6152:   should be used with `MAT_USE_HASH_TABLE` flag. This option is currently
    6153:   supported by `MATMPIBAIJ` format only.

    6155:   `MAT_KEEP_NONZERO_PATTERN` indicates when `MatZeroRows()` is called the zeroed entries
    6156:   are kept in the nonzero structure. This flag is not used for `MatZeroRowsColumns()`

    6158:   `MAT_IGNORE_ZERO_ENTRIES` - for `MATAIJ` and `MATIS` matrices this will stop zero values from creating
    6159:   a zero location in the matrix

    6161:   `MAT_USE_INODES` - indicates using inode version of the code - works with `MATAIJ` matrix types

    6163:   `MAT_NO_OFF_PROC_ZERO_ROWS` - you know each process will only zero its own rows. This avoids all reductions in the
    6164:   zero row routines and thus improves performance for very large process counts.

    6166:   `MAT_IGNORE_LOWER_TRIANGULAR` - For `MATSBAIJ` matrices will ignore any insertions you make in the lower triangular
    6167:   part of the matrix (since they should match the upper triangular part).

    6169:   `MAT_SORTED_FULL` - each process provides exactly its local rows; all column indices for a given row are passed in a
    6170:   single call to `MatSetValues()`, preallocation is perfect, row-oriented, `INSERT_VALUES` is used. Common
    6171:   with finite difference schemes with non-periodic boundary conditions.

    6173:   Developer Note:
    6174:   `MAT_SYMMETRY_ETERNAL`, `MAT_STRUCTURAL_SYMMETRY_ETERNAL`, and `MAT_SPD_ETERNAL` are used by `MatAssemblyEnd()` and in other
    6175:   places where otherwise the value of `MAT_SYMMETRIC`, `MAT_STRUCTURALLY_SYMMETRIC` or `MAT_SPD` would need to be changed back
    6176:   to `PETSC_BOOL3_UNKNOWN` because the matrix values had changed so the code cannot be certain that the related property had
    6177:   not changed.

    6179: .seealso: [](ch_matrices), `MatOption`, `Mat`, `MatGetOption()`
    6180: @*/
    6181: PetscErrorCode MatSetOption(Mat mat, MatOption op, PetscBool flg)
    6182: {
    6183:   PetscFunctionBegin;
    6185:   if (op > 0) {
    6188:   }

    6190:   PetscCheck(((int)op) > MAT_OPTION_MIN && ((int)op) < MAT_OPTION_MAX, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Options %d is out of range", (int)op);

    6192:   switch (op) {
    6193:   case MAT_FORCE_DIAGONAL_ENTRIES:
    6194:     mat->force_diagonals = flg;
    6195:     PetscFunctionReturn(PETSC_SUCCESS);
    6196:   case MAT_NO_OFF_PROC_ENTRIES:
    6197:     mat->nooffprocentries = flg;
    6198:     PetscFunctionReturn(PETSC_SUCCESS);
    6199:   case MAT_SUBSET_OFF_PROC_ENTRIES:
    6200:     mat->assembly_subset = flg;
    6201:     if (!mat->assembly_subset) { /* See the same logic in VecAssembly wrt VEC_SUBSET_OFF_PROC_ENTRIES */
    6202: #if !defined(PETSC_HAVE_MPIUNI)
    6203:       PetscCall(MatStashScatterDestroy_BTS(&mat->stash));
    6204: #endif
    6205:       mat->stash.first_assembly_done = PETSC_FALSE;
    6206:     }
    6207:     PetscFunctionReturn(PETSC_SUCCESS);
    6208:   case MAT_NO_OFF_PROC_ZERO_ROWS:
    6209:     mat->nooffproczerorows = flg;
    6210:     PetscFunctionReturn(PETSC_SUCCESS);
    6211:   case MAT_SPD:
    6212:     if (flg) {
    6213:       mat->spd                    = PETSC_BOOL3_TRUE;
    6214:       mat->symmetric              = PETSC_BOOL3_TRUE;
    6215:       mat->structurally_symmetric = PETSC_BOOL3_TRUE;
    6216: #if !defined(PETSC_USE_COMPLEX)
    6217:       mat->hermitian = PETSC_BOOL3_TRUE;
    6218: #endif
    6219:     } else {
    6220:       mat->spd = PETSC_BOOL3_FALSE;
    6221:     }
    6222:     break;
    6223:   case MAT_SYMMETRIC:
    6224:     mat->symmetric = PetscBoolToBool3(flg);
    6225:     if (flg) mat->structurally_symmetric = PETSC_BOOL3_TRUE;
    6226: #if !defined(PETSC_USE_COMPLEX)
    6227:     mat->hermitian = PetscBoolToBool3(flg);
    6228: #endif
    6229:     break;
    6230:   case MAT_HERMITIAN:
    6231:     mat->hermitian = PetscBoolToBool3(flg);
    6232:     if (flg) mat->structurally_symmetric = PETSC_BOOL3_TRUE;
    6233: #if !defined(PETSC_USE_COMPLEX)
    6234:     mat->symmetric = PetscBoolToBool3(flg);
    6235: #endif
    6236:     break;
    6237:   case MAT_STRUCTURALLY_SYMMETRIC:
    6238:     mat->structurally_symmetric = PetscBoolToBool3(flg);
    6239:     break;
    6240:   case MAT_SYMMETRY_ETERNAL:
    6241:     PetscCheck(mat->symmetric != PETSC_BOOL3_UNKNOWN, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot set MAT_SYMMETRY_ETERNAL without first setting MAT_SYMMETRIC to true or false");
    6242:     mat->symmetry_eternal = flg;
    6243:     if (flg) mat->structural_symmetry_eternal = PETSC_TRUE;
    6244:     break;
    6245:   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
    6246:     PetscCheck(mat->structurally_symmetric != PETSC_BOOL3_UNKNOWN, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot set MAT_STRUCTURAL_SYMMETRY_ETERNAL without first setting MAT_STRUCTURALLY_SYMMETRIC to true or false");
    6247:     mat->structural_symmetry_eternal = flg;
    6248:     break;
    6249:   case MAT_SPD_ETERNAL:
    6250:     PetscCheck(mat->spd != PETSC_BOOL3_UNKNOWN, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot set MAT_SPD_ETERNAL without first setting MAT_SPD to true or false");
    6251:     mat->spd_eternal = flg;
    6252:     if (flg) {
    6253:       mat->structural_symmetry_eternal = PETSC_TRUE;
    6254:       mat->symmetry_eternal            = PETSC_TRUE;
    6255:     }
    6256:     break;
    6257:   case MAT_STRUCTURE_ONLY:
    6258:     mat->structure_only = flg;
    6259:     break;
    6260:   case MAT_SORTED_FULL:
    6261:     mat->sortedfull = flg;
    6262:     break;
    6263:   default:
    6264:     break;
    6265:   }
    6266:   PetscTryTypeMethod(mat, setoption, op, flg);
    6267:   PetscFunctionReturn(PETSC_SUCCESS);
    6268: }

    6270: /*@
    6271:   MatGetOption - Gets a parameter option that has been set for a matrix.

    6273:   Logically Collective

    6275:   Input Parameters:
    6276: + mat - the matrix
    6277: - op  - the option, this only responds to certain options, check the code for which ones

    6279:   Output Parameter:
    6280: . flg - turn the option on (`PETSC_TRUE`) or off (`PETSC_FALSE`)

    6282:   Level: intermediate

    6284:   Notes:
    6285:   Can only be called after `MatSetSizes()` and `MatSetType()` have been set.

    6287:   Certain option values may be unknown, for those use the routines `MatIsSymmetric()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, or
    6288:   `MatIsSymmetricKnown()`, `MatIsHermitianKnown()`, `MatIsStructurallySymmetricKnown()`

    6290: .seealso: [](ch_matrices), `Mat`, `MatOption`, `MatSetOption()`, `MatIsSymmetric()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`,
    6291:     `MatIsSymmetricKnown()`, `MatIsHermitianKnown()`, `MatIsStructurallySymmetricKnown()`
    6292: @*/
    6293: PetscErrorCode MatGetOption(Mat mat, MatOption op, PetscBool *flg)
    6294: {
    6295:   PetscFunctionBegin;

    6299:   PetscCheck(((int)op) > MAT_OPTION_MIN && ((int)op) < MAT_OPTION_MAX, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Options %d is out of range", (int)op);
    6300:   PetscCheck(((PetscObject)mat)->type_name, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_TYPENOTSET, "Cannot get options until type and size have been set, see MatSetType() and MatSetSizes()");

    6302:   switch (op) {
    6303:   case MAT_NO_OFF_PROC_ENTRIES:
    6304:     *flg = mat->nooffprocentries;
    6305:     break;
    6306:   case MAT_NO_OFF_PROC_ZERO_ROWS:
    6307:     *flg = mat->nooffproczerorows;
    6308:     break;
    6309:   case MAT_SYMMETRIC:
    6310:     SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Use MatIsSymmetric() or MatIsSymmetricKnown()");
    6311:     break;
    6312:   case MAT_HERMITIAN:
    6313:     SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Use MatIsHermitian() or MatIsHermitianKnown()");
    6314:     break;
    6315:   case MAT_STRUCTURALLY_SYMMETRIC:
    6316:     SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Use MatIsStructurallySymmetric() or MatIsStructurallySymmetricKnown()");
    6317:     break;
    6318:   case MAT_SPD:
    6319:     SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Use MatIsSPDKnown()");
    6320:     break;
    6321:   case MAT_SYMMETRY_ETERNAL:
    6322:     *flg = mat->symmetry_eternal;
    6323:     break;
    6324:   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
    6325:     *flg = mat->symmetry_eternal;
    6326:     break;
    6327:   default:
    6328:     break;
    6329:   }
    6330:   PetscFunctionReturn(PETSC_SUCCESS);
    6331: }

    6333: /*@
    6334:   MatZeroEntries - Zeros all entries of a matrix.  For sparse matrices
    6335:   this routine retains the old nonzero structure.

    6337:   Logically Collective

    6339:   Input Parameter:
    6340: . mat - the matrix

    6342:   Level: intermediate

    6344:   Note:
    6345:   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.
    6346:   See the Performance chapter of the users manual for information on preallocating matrices.

    6348: .seealso: [](ch_matrices), `Mat`, `MatZeroRows()`, `MatZeroRowsColumns()`
    6349: @*/
    6350: PetscErrorCode MatZeroEntries(Mat mat)
    6351: {
    6352:   PetscFunctionBegin;
    6355:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6356:   PetscCheck(mat->insertmode == NOT_SET_VALUES, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for matrices where you have set values but not yet assembled");
    6357:   MatCheckPreallocated(mat, 1);

    6359:   PetscCall(PetscLogEventBegin(MAT_ZeroEntries, mat, 0, 0, 0));
    6360:   PetscUseTypeMethod(mat, zeroentries);
    6361:   PetscCall(PetscLogEventEnd(MAT_ZeroEntries, mat, 0, 0, 0));
    6362:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6363:   PetscFunctionReturn(PETSC_SUCCESS);
    6364: }

    6366: /*@
    6367:   MatZeroRowsColumns - Zeros all entries (except possibly the main diagonal)
    6368:   of a set of rows and columns of a matrix.

    6370:   Collective

    6372:   Input Parameters:
    6373: + mat     - the matrix
    6374: . numRows - the number of rows/columns to zero
    6375: . rows    - the global row indices
    6376: . diag    - value put in the diagonal of the eliminated rows
    6377: . x       - optional vector of the solution for zeroed rows (other entries in vector are not used), these must be set before this call
    6378: - b       - optional vector of the right-hand side, that will be adjusted by provided solution entries

    6380:   Level: intermediate

    6382:   Notes:
    6383:   This routine, along with `MatZeroRows()`, is typically used to eliminate known Dirichlet boundary conditions from a linear system.

    6385:   For each zeroed row, the value of the corresponding `b` is set to diag times the value of the corresponding `x`.
    6386:   The other entries of `b` will be adjusted by the known values of `x` times the corresponding matrix entries in the columns that are being eliminated

    6388:   If the resulting linear system is to be solved with `KSP` then one can (but does not have to) call `KSPSetInitialGuessNonzero()` to allow the
    6389:   Krylov method to take advantage of the known solution on the zeroed rows.

    6391:   For the parallel case, all processes that share the matrix (i.e.,
    6392:   those in the communicator used for matrix creation) MUST call this
    6393:   routine, regardless of whether any rows being zeroed are owned by
    6394:   them.

    6396:   Unlike `MatZeroRows()`, this ignores the `MAT_KEEP_NONZERO_PATTERN` option value set with `MatSetOption()`, it merely zeros those entries in the matrix, but never
    6397:   removes them from the nonzero pattern. The nonzero pattern of the matrix can still change if a nonzero needs to be inserted on a diagonal entry that was previously
    6398:   missing.

    6400:   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6401:   list only rows local to itself).

    6403:   The option `MAT_NO_OFF_PROC_ZERO_ROWS` does not apply to this routine.

    6405: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRows()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6406:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6407: @*/
    6408: PetscErrorCode MatZeroRowsColumns(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    6409: {
    6410:   PetscFunctionBegin;
    6413:   if (numRows) PetscAssertPointer(rows, 3);
    6414:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6415:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6416:   MatCheckPreallocated(mat, 1);

    6418:   PetscUseTypeMethod(mat, zerorowscolumns, numRows, rows, diag, x, b);
    6419:   PetscCall(MatViewFromOptions(mat, NULL, "-mat_view"));
    6420:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6421:   PetscFunctionReturn(PETSC_SUCCESS);
    6422: }

    6424: /*@
    6425:   MatZeroRowsColumnsIS - Zeros all entries (except possibly the main diagonal)
    6426:   of a set of rows and columns of a matrix.

    6428:   Collective

    6430:   Input Parameters:
    6431: + mat  - the matrix
    6432: . is   - the rows to zero
    6433: . diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6434: . x    - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6435: - b    - optional vector of right-hand side, that will be adjusted by provided solution

    6437:   Level: intermediate

    6439:   Note:
    6440:   See `MatZeroRowsColumns()` for details on how this routine operates.

    6442: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6443:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRows()`, `MatZeroRowsColumnsStencil()`
    6444: @*/
    6445: PetscErrorCode MatZeroRowsColumnsIS(Mat mat, IS is, PetscScalar diag, Vec x, Vec b)
    6446: {
    6447:   PetscInt        numRows;
    6448:   const PetscInt *rows;

    6450:   PetscFunctionBegin;
    6455:   PetscCall(ISGetLocalSize(is, &numRows));
    6456:   PetscCall(ISGetIndices(is, &rows));
    6457:   PetscCall(MatZeroRowsColumns(mat, numRows, rows, diag, x, b));
    6458:   PetscCall(ISRestoreIndices(is, &rows));
    6459:   PetscFunctionReturn(PETSC_SUCCESS);
    6460: }

    6462: /*@
    6463:   MatZeroRows - Zeros all entries (except possibly the main diagonal)
    6464:   of a set of rows of a matrix.

    6466:   Collective

    6468:   Input Parameters:
    6469: + mat     - the matrix
    6470: . numRows - the number of rows to zero
    6471: . rows    - the global row indices
    6472: . diag    - value put in the diagonal of the zeroed rows
    6473: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used), these must be set before this call
    6474: - b       - optional vector of right-hand side, that will be adjusted by provided solution entries

    6476:   Level: intermediate

    6478:   Notes:
    6479:   This routine, along with `MatZeroRowsColumns()`, is typically used to eliminate known Dirichlet boundary conditions from a linear system.

    6481:   For each zeroed row, the value of the corresponding `b` is set to `diag` times the value of the corresponding `x`.

    6483:   If the resulting linear system is to be solved with `KSP` then one can (but does not have to) call `KSPSetInitialGuessNonzero()` to allow the
    6484:   Krylov method to take advantage of the known solution on the zeroed rows.

    6486:   May be followed by using a `PC` of type `PCREDISTRIBUTE` to solve the reduced problem (`PCDISTRIBUTE` completely eliminates the zeroed rows and their corresponding columns)
    6487:   from the matrix.

    6489:   Unlike `MatZeroRowsColumns()` for the `MATAIJ` and `MATBAIJ` matrix formats this removes the old nonzero structure, from the eliminated rows of the matrix
    6490:   but does not release memory.  Because of this removal matrix-vector products with the adjusted matrix will be a bit faster. For the dense
    6491:   formats this does not alter the nonzero structure.

    6493:   If the option `MatSetOption`(mat,`MAT_KEEP_NONZERO_PATTERN`,`PETSC_TRUE`) the nonzero structure
    6494:   of the matrix is not changed the values are
    6495:   merely zeroed.

    6497:   The user can set a value in the diagonal entry (or for the `MATAIJ` format
    6498:   formats can optionally remove the main diagonal entry from the
    6499:   nonzero structure as well, by passing 0.0 as the final argument).

    6501:   For the parallel case, all processes that share the matrix (i.e.,
    6502:   those in the communicator used for matrix creation) MUST call this
    6503:   routine, regardless of whether any rows being zeroed are owned by
    6504:   them.

    6506:   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6507:   list only rows local to itself).

    6509:   You can call `MatSetOption`(mat,`MAT_NO_OFF_PROC_ZERO_ROWS`,`PETSC_TRUE`) if each process indicates only rows it
    6510:   owns that are to be zeroed. This saves a global synchronization in the implementation.

    6512: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6513:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`, `PCREDISTRIBUTE`, `MAT_KEEP_NONZERO_PATTERN`
    6514: @*/
    6515: PetscErrorCode MatZeroRows(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    6516: {
    6517:   PetscFunctionBegin;
    6520:   if (numRows) PetscAssertPointer(rows, 3);
    6521:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6522:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6523:   MatCheckPreallocated(mat, 1);

    6525:   PetscUseTypeMethod(mat, zerorows, numRows, rows, diag, x, b);
    6526:   PetscCall(MatViewFromOptions(mat, NULL, "-mat_view"));
    6527:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6528:   PetscFunctionReturn(PETSC_SUCCESS);
    6529: }

    6531: /*@
    6532:   MatZeroRowsIS - Zeros all entries (except possibly the main diagonal)
    6533:   of a set of rows of a matrix indicated by an `IS`

    6535:   Collective

    6537:   Input Parameters:
    6538: + mat  - the matrix
    6539: . is   - index set, `IS`, of rows to remove (if `NULL` then no row is removed)
    6540: . diag - value put in all diagonals of eliminated rows
    6541: . x    - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6542: - b    - optional vector of right-hand side, that will be adjusted by provided solution

    6544:   Level: intermediate

    6546:   Note:
    6547:   See `MatZeroRows()` for details on how this routine operates.

    6549: .seealso: [](ch_matrices), `Mat`, `MatZeroRows()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6550:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`, `IS`
    6551: @*/
    6552: PetscErrorCode MatZeroRowsIS(Mat mat, IS is, PetscScalar diag, Vec x, Vec b)
    6553: {
    6554:   PetscInt        numRows = 0;
    6555:   const PetscInt *rows    = NULL;

    6557:   PetscFunctionBegin;
    6560:   if (is) {
    6562:     PetscCall(ISGetLocalSize(is, &numRows));
    6563:     PetscCall(ISGetIndices(is, &rows));
    6564:   }
    6565:   PetscCall(MatZeroRows(mat, numRows, rows, diag, x, b));
    6566:   if (is) PetscCall(ISRestoreIndices(is, &rows));
    6567:   PetscFunctionReturn(PETSC_SUCCESS);
    6568: }

    6570: /*@
    6571:   MatZeroRowsStencil - Zeros all entries (except possibly the main diagonal)
    6572:   of a set of rows of a matrix indicated by a `MatStencil`. These rows must be local to the process.

    6574:   Collective

    6576:   Input Parameters:
    6577: + mat     - the matrix
    6578: . numRows - the number of rows to remove
    6579: . rows    - the grid coordinates (and component number when dof > 1) for matrix rows indicated by an array of `MatStencil`
    6580: . diag    - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6581: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6582: - b       - optional vector of right-hand side, that will be adjusted by provided solution

    6584:   Level: intermediate

    6586:   Notes:
    6587:   See `MatZeroRows()` for details on how this routine operates.

    6589:   The grid coordinates are across the entire grid, not just the local portion

    6591:   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    6592:   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    6593:   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    6594:   `DM_BOUNDARY_PERIODIC` boundary type.

    6596:   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
    6597:   a single value per point) you can skip filling those indices.

    6599:   Fortran Note:
    6600:   `idxm` and `idxn` should be declared as
    6601: .vb
    6602:     MatStencil idxm(4, m)
    6603: .ve
    6604:   and the values inserted using
    6605: .vb
    6606:     idxm(MatStencil_i, 1) = i
    6607:     idxm(MatStencil_j, 1) = j
    6608:     idxm(MatStencil_k, 1) = k
    6609:     idxm(MatStencil_c, 1) = c
    6610:    etc
    6611: .ve

    6613: .seealso: [](ch_matrices), `Mat`, `MatStencil`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRows()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6614:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6615: @*/
    6616: PetscErrorCode MatZeroRowsStencil(Mat mat, PetscInt numRows, const MatStencil rows[], PetscScalar diag, Vec x, Vec b)
    6617: {
    6618:   PetscInt  dim    = mat->stencil.dim;
    6619:   PetscInt  sdim   = dim - (1 - (PetscInt)mat->stencil.noc);
    6620:   PetscInt *dims   = mat->stencil.dims + 1;
    6621:   PetscInt *starts = mat->stencil.starts;
    6622:   PetscInt *dxm    = (PetscInt *)rows;
    6623:   PetscInt *jdxm, i, j, tmp, numNewRows = 0;

    6625:   PetscFunctionBegin;
    6628:   if (numRows) PetscAssertPointer(rows, 3);

    6630:   PetscCall(PetscMalloc1(numRows, &jdxm));
    6631:   for (i = 0; i < numRows; ++i) {
    6632:     /* Skip unused dimensions (they are ordered k, j, i, c) */
    6633:     for (j = 0; j < 3 - sdim; ++j) dxm++;
    6634:     /* Local index in X dir */
    6635:     tmp = *dxm++ - starts[0];
    6636:     /* Loop over remaining dimensions */
    6637:     for (j = 0; j < dim - 1; ++j) {
    6638:       /* If nonlocal, set index to be negative */
    6639:       if ((*dxm++ - starts[j + 1]) < 0 || tmp < 0) tmp = PETSC_INT_MIN;
    6640:       /* Update local index */
    6641:       else tmp = tmp * dims[j] + *(dxm - 1) - starts[j + 1];
    6642:     }
    6643:     /* Skip component slot if necessary */
    6644:     if (mat->stencil.noc) dxm++;
    6645:     /* Local row number */
    6646:     if (tmp >= 0) jdxm[numNewRows++] = tmp;
    6647:   }
    6648:   PetscCall(MatZeroRowsLocal(mat, numNewRows, jdxm, diag, x, b));
    6649:   PetscCall(PetscFree(jdxm));
    6650:   PetscFunctionReturn(PETSC_SUCCESS);
    6651: }

    6653: /*@
    6654:   MatZeroRowsColumnsStencil - Zeros all row and column entries (except possibly the main diagonal)
    6655:   of a set of rows and columns of a matrix.

    6657:   Collective

    6659:   Input Parameters:
    6660: + mat     - the matrix
    6661: . numRows - the number of rows/columns to remove
    6662: . rows    - the grid coordinates (and component number when dof > 1) for matrix rows
    6663: . diag    - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6664: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6665: - b       - optional vector of right-hand side, that will be adjusted by provided solution

    6667:   Level: intermediate

    6669:   Notes:
    6670:   See `MatZeroRowsColumns()` for details on how this routine operates.

    6672:   The grid coordinates are across the entire grid, not just the local portion

    6674:   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    6675:   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    6676:   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    6677:   `DM_BOUNDARY_PERIODIC` boundary type.

    6679:   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
    6680:   a single value per point) you can skip filling those indices.

    6682:   Fortran Note:
    6683:   `idxm` and `idxn` should be declared as
    6684: .vb
    6685:     MatStencil idxm(4, m)
    6686: .ve
    6687:   and the values inserted using
    6688: .vb
    6689:     idxm(MatStencil_i, 1) = i
    6690:     idxm(MatStencil_j, 1) = j
    6691:     idxm(MatStencil_k, 1) = k
    6692:     idxm(MatStencil_c, 1) = c
    6693:     etc
    6694: .ve

    6696: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6697:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRows()`
    6698: @*/
    6699: PetscErrorCode MatZeroRowsColumnsStencil(Mat mat, PetscInt numRows, const MatStencil rows[], PetscScalar diag, Vec x, Vec b)
    6700: {
    6701:   PetscInt  dim    = mat->stencil.dim;
    6702:   PetscInt  sdim   = dim - (1 - (PetscInt)mat->stencil.noc);
    6703:   PetscInt *dims   = mat->stencil.dims + 1;
    6704:   PetscInt *starts = mat->stencil.starts;
    6705:   PetscInt *dxm    = (PetscInt *)rows;
    6706:   PetscInt *jdxm, i, j, tmp, numNewRows = 0;

    6708:   PetscFunctionBegin;
    6711:   if (numRows) PetscAssertPointer(rows, 3);

    6713:   PetscCall(PetscMalloc1(numRows, &jdxm));
    6714:   for (i = 0; i < numRows; ++i) {
    6715:     /* Skip unused dimensions (they are ordered k, j, i, c) */
    6716:     for (j = 0; j < 3 - sdim; ++j) dxm++;
    6717:     /* Local index in X dir */
    6718:     tmp = *dxm++ - starts[0];
    6719:     /* Loop over remaining dimensions */
    6720:     for (j = 0; j < dim - 1; ++j) {
    6721:       /* If nonlocal, set index to be negative */
    6722:       if ((*dxm++ - starts[j + 1]) < 0 || tmp < 0) tmp = PETSC_INT_MIN;
    6723:       /* Update local index */
    6724:       else tmp = tmp * dims[j] + *(dxm - 1) - starts[j + 1];
    6725:     }
    6726:     /* Skip component slot if necessary */
    6727:     if (mat->stencil.noc) dxm++;
    6728:     /* Local row number */
    6729:     if (tmp >= 0) jdxm[numNewRows++] = tmp;
    6730:   }
    6731:   PetscCall(MatZeroRowsColumnsLocal(mat, numNewRows, jdxm, diag, x, b));
    6732:   PetscCall(PetscFree(jdxm));
    6733:   PetscFunctionReturn(PETSC_SUCCESS);
    6734: }

    6736: /*@
    6737:   MatZeroRowsLocal - Zeros all entries (except possibly the main diagonal)
    6738:   of a set of rows of a matrix; using local numbering of rows.

    6740:   Collective

    6742:   Input Parameters:
    6743: + mat     - the matrix
    6744: . numRows - the number of rows to remove
    6745: . rows    - the local row indices
    6746: . diag    - value put in all diagonals of eliminated rows
    6747: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6748: - b       - optional vector of right-hand side, that will be adjusted by provided solution

    6750:   Level: intermediate

    6752:   Notes:
    6753:   Before calling `MatZeroRowsLocal()`, the user must first set the
    6754:   local-to-global mapping by calling MatSetLocalToGlobalMapping(), this is often already set for matrices obtained with `DMCreateMatrix()`.

    6756:   See `MatZeroRows()` for details on how this routine operates.

    6758: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRows()`, `MatSetOption()`,
    6759:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6760: @*/
    6761: PetscErrorCode MatZeroRowsLocal(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    6762: {
    6763:   PetscFunctionBegin;
    6766:   if (numRows) PetscAssertPointer(rows, 3);
    6767:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6768:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6769:   MatCheckPreallocated(mat, 1);

    6771:   if (mat->ops->zerorowslocal) {
    6772:     PetscUseTypeMethod(mat, zerorowslocal, numRows, rows, diag, x, b);
    6773:   } else {
    6774:     IS        is, newis;
    6775:     PetscInt *newRows, nl = 0;

    6777:     PetscCheck(mat->rmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Need to provide local to global mapping to matrix first");
    6778:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, numRows, rows, PETSC_USE_POINTER, &is));
    6779:     PetscCall(ISLocalToGlobalMappingApplyIS(mat->rmap->mapping, is, &newis));
    6780:     PetscCall(ISGetIndices(newis, (const PetscInt **)&newRows));
    6781:     for (PetscInt i = 0; i < numRows; i++)
    6782:       if (newRows[i] > -1) newRows[nl++] = newRows[i];
    6783:     PetscUseTypeMethod(mat, zerorows, nl, newRows, diag, x, b);
    6784:     PetscCall(ISRestoreIndices(newis, (const PetscInt **)&newRows));
    6785:     PetscCall(ISDestroy(&newis));
    6786:     PetscCall(ISDestroy(&is));
    6787:   }
    6788:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6789:   PetscFunctionReturn(PETSC_SUCCESS);
    6790: }

    6792: /*@
    6793:   MatZeroRowsLocalIS - Zeros all entries (except possibly the main diagonal)
    6794:   of a set of rows of a matrix; using local numbering of rows.

    6796:   Collective

    6798:   Input Parameters:
    6799: + mat  - the matrix
    6800: . is   - index set of rows to remove
    6801: . diag - value put in all diagonals of eliminated rows
    6802: . x    - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6803: - b    - optional vector of right-hand side, that will be adjusted by provided solution

    6805:   Level: intermediate

    6807:   Notes:
    6808:   Before calling `MatZeroRowsLocalIS()`, the user must first set the
    6809:   local-to-global mapping by calling `MatSetLocalToGlobalMapping()`, this is often already set for matrices obtained with `DMCreateMatrix()`.

    6811:   See `MatZeroRows()` for details on how this routine operates.

    6813: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRows()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6814:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6815: @*/
    6816: PetscErrorCode MatZeroRowsLocalIS(Mat mat, IS is, PetscScalar diag, Vec x, Vec b)
    6817: {
    6818:   PetscInt        numRows;
    6819:   const PetscInt *rows;

    6821:   PetscFunctionBegin;
    6825:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6826:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6827:   MatCheckPreallocated(mat, 1);

    6829:   PetscCall(ISGetLocalSize(is, &numRows));
    6830:   PetscCall(ISGetIndices(is, &rows));
    6831:   PetscCall(MatZeroRowsLocal(mat, numRows, rows, diag, x, b));
    6832:   PetscCall(ISRestoreIndices(is, &rows));
    6833:   PetscFunctionReturn(PETSC_SUCCESS);
    6834: }

    6836: /*@
    6837:   MatZeroRowsColumnsLocal - Zeros all entries (except possibly the main diagonal)
    6838:   of a set of rows and columns of a matrix; using local numbering of rows.

    6840:   Collective

    6842:   Input Parameters:
    6843: + mat     - the matrix
    6844: . numRows - the number of rows to remove
    6845: . rows    - the global row indices
    6846: . diag    - value put in all diagonals of eliminated rows
    6847: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6848: - b       - optional vector of right-hand side, that will be adjusted by provided solution

    6850:   Level: intermediate

    6852:   Notes:
    6853:   Before calling `MatZeroRowsColumnsLocal()`, the user must first set the
    6854:   local-to-global mapping by calling `MatSetLocalToGlobalMapping()`, this is often already set for matrices obtained with `DMCreateMatrix()`.

    6856:   See `MatZeroRowsColumns()` for details on how this routine operates.

    6858: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6859:           `MatZeroRows()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6860: @*/
    6861: PetscErrorCode MatZeroRowsColumnsLocal(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    6862: {
    6863:   PetscFunctionBegin;
    6866:   if (numRows) PetscAssertPointer(rows, 3);
    6867:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6868:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6869:   MatCheckPreallocated(mat, 1);

    6871:   if (mat->ops->zerorowscolumnslocal) {
    6872:     PetscUseTypeMethod(mat, zerorowscolumnslocal, numRows, rows, diag, x, b);
    6873:   } else {
    6874:     IS        is, newis;
    6875:     PetscInt *newRows, nl = 0;

    6877:     PetscCheck(mat->rmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Need to provide local to global mapping to matrix first");
    6878:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, numRows, rows, PETSC_USE_POINTER, &is));
    6879:     PetscCall(ISLocalToGlobalMappingApplyIS(mat->rmap->mapping, is, &newis));
    6880:     PetscCall(ISGetIndices(newis, (const PetscInt **)&newRows));
    6881:     for (PetscInt i = 0; i < numRows; i++)
    6882:       if (newRows[i] > -1) newRows[nl++] = newRows[i];
    6883:     PetscUseTypeMethod(mat, zerorowscolumns, nl, newRows, diag, x, b);
    6884:     PetscCall(ISRestoreIndices(newis, (const PetscInt **)&newRows));
    6885:     PetscCall(ISDestroy(&newis));
    6886:     PetscCall(ISDestroy(&is));
    6887:   }
    6888:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6889:   PetscFunctionReturn(PETSC_SUCCESS);
    6890: }

    6892: /*@
    6893:   MatZeroRowsColumnsLocalIS - Zeros all entries (except possibly the main diagonal)
    6894:   of a set of rows and columns of a matrix; using local numbering of rows.

    6896:   Collective

    6898:   Input Parameters:
    6899: + mat  - the matrix
    6900: . is   - index set of rows to remove
    6901: . diag - value put in all diagonals of eliminated rows
    6902: . x    - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6903: - b    - optional vector of right-hand side, that will be adjusted by provided solution

    6905:   Level: intermediate

    6907:   Notes:
    6908:   Before calling `MatZeroRowsColumnsLocalIS()`, the user must first set the
    6909:   local-to-global mapping by calling `MatSetLocalToGlobalMapping()`, this is often already set for matrices obtained with `DMCreateMatrix()`.

    6911:   See `MatZeroRowsColumns()` for details on how this routine operates.

    6913: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6914:           `MatZeroRowsColumnsLocal()`, `MatZeroRows()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6915: @*/
    6916: PetscErrorCode MatZeroRowsColumnsLocalIS(Mat mat, IS is, PetscScalar diag, Vec x, Vec b)
    6917: {
    6918:   PetscInt        numRows;
    6919:   const PetscInt *rows;

    6921:   PetscFunctionBegin;
    6925:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6926:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6927:   MatCheckPreallocated(mat, 1);

    6929:   PetscCall(ISGetLocalSize(is, &numRows));
    6930:   PetscCall(ISGetIndices(is, &rows));
    6931:   PetscCall(MatZeroRowsColumnsLocal(mat, numRows, rows, diag, x, b));
    6932:   PetscCall(ISRestoreIndices(is, &rows));
    6933:   PetscFunctionReturn(PETSC_SUCCESS);
    6934: }

    6936: /*@
    6937:   MatGetSize - Returns the numbers of rows and columns in a matrix.

    6939:   Not Collective

    6941:   Input Parameter:
    6942: . mat - the matrix

    6944:   Output Parameters:
    6945: + m - the number of global rows
    6946: - n - the number of global columns

    6948:   Level: beginner

    6950:   Note:
    6951:   Both output parameters can be `NULL` on input.

    6953: .seealso: [](ch_matrices), `Mat`, `MatSetSizes()`, `MatGetLocalSize()`
    6954: @*/
    6955: PetscErrorCode MatGetSize(Mat mat, PetscInt *m, PetscInt *n)
    6956: {
    6957:   PetscFunctionBegin;
    6959:   if (m) *m = mat->rmap->N;
    6960:   if (n) *n = mat->cmap->N;
    6961:   PetscFunctionReturn(PETSC_SUCCESS);
    6962: }

    6964: /*@
    6965:   MatGetLocalSize - For most matrix formats, excluding `MATELEMENTAL` and `MATSCALAPACK`, Returns the number of local rows and local columns
    6966:   of a matrix. For all matrices this is the local size of the left and right vectors as returned by `MatCreateVecs()`.

    6968:   Not Collective

    6970:   Input Parameter:
    6971: . mat - the matrix

    6973:   Output Parameters:
    6974: + m - the number of local rows, use `NULL` to not obtain this value
    6975: - n - the number of local columns, use `NULL` to not obtain this value

    6977:   Level: beginner

    6979: .seealso: [](ch_matrices), `Mat`, `MatSetSizes()`, `MatGetSize()`
    6980: @*/
    6981: PetscErrorCode MatGetLocalSize(Mat mat, PetscInt *m, PetscInt *n)
    6982: {
    6983:   PetscFunctionBegin;
    6985:   if (m) PetscAssertPointer(m, 2);
    6986:   if (n) PetscAssertPointer(n, 3);
    6987:   if (m) *m = mat->rmap->n;
    6988:   if (n) *n = mat->cmap->n;
    6989:   PetscFunctionReturn(PETSC_SUCCESS);
    6990: }

    6992: /*@
    6993:   MatGetOwnershipRangeColumn - Returns the range of matrix columns associated with rows of a
    6994:   vector one multiplies this matrix by that are owned by this processor.

    6996:   Not Collective, unless matrix has not been allocated, then collective

    6998:   Input Parameter:
    6999: . mat - the matrix

    7001:   Output Parameters:
    7002: + m - the global index of the first local column, use `NULL` to not obtain this value
    7003: - n - one more than the global index of the last local column, use `NULL` to not obtain this value

    7005:   Level: developer

    7007:   Notes:
    7008:   If the `Mat` was obtained from a `DM` with `DMCreateMatrix()`, then the range values are determined by the specific `DM`.

    7010:   If the `Mat` was created directly the range values are determined by the local size passed to `MatSetSizes()` or `MatCreateAIJ()`.
    7011:   If `PETSC_DECIDE` was passed as the local size, then the vector uses default values for the range using `PetscSplitOwnership()`.

    7013:   For certain `DM`, such as `DMDA`, it is better to use `DM` specific routines, such as `DMDAGetGhostCorners()`, to determine
    7014:   the local values in the matrix.

    7016:   Returns the columns of the "diagonal block" for most sparse matrix formats. See [Matrix
    7017:   Layouts](sec_matlayout) for details on matrix layouts.

    7019: .seealso: [](ch_matrices), `Mat`, `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangesColumn()`, `PetscLayout`,
    7020:           `MatSetSizes()`, `MatCreateAIJ()`, `DMDAGetGhostCorners()`, `DM`
    7021: @*/
    7022: PetscErrorCode MatGetOwnershipRangeColumn(Mat mat, PetscInt *m, PetscInt *n)
    7023: {
    7024:   PetscFunctionBegin;
    7027:   if (m) PetscAssertPointer(m, 2);
    7028:   if (n) PetscAssertPointer(n, 3);
    7029:   MatCheckPreallocated(mat, 1);
    7030:   if (m) *m = mat->cmap->rstart;
    7031:   if (n) *n = mat->cmap->rend;
    7032:   PetscFunctionReturn(PETSC_SUCCESS);
    7033: }

    7035: /*@
    7036:   MatGetOwnershipRange - For matrices that own values by row, excludes `MATELEMENTAL` and `MATSCALAPACK`, returns the range of matrix rows owned by
    7037:   this MPI process.

    7039:   Not Collective

    7041:   Input Parameter:
    7042: . mat - the matrix

    7044:   Output Parameters:
    7045: + m - the global index of the first local row, use `NULL` to not obtain this value
    7046: - n - one more than the global index of the last local row, use `NULL` to not obtain this value

    7048:   Level: beginner

    7050:   Notes:
    7051:   If the `Mat` was obtained from a `DM` with `DMCreateMatrix()`, then the range values are determined by the specific `DM`.

    7053:   If the `Mat` was created directly the range values are determined by the local size passed to `MatSetSizes()` or `MatCreateAIJ()`.
    7054:   If `PETSC_DECIDE` was passed as the local size, then the vector uses default values for the range using `PetscSplitOwnership()`.

    7056:   For certain `DM`, such as `DMDA`, it is better to use `DM` specific routines, such as `DMDAGetGhostCorners()`, to determine
    7057:   the local values in the matrix.

    7059:   The high argument is one more than the last element stored locally.

    7061:   For all matrices  it returns the range of matrix rows associated with rows of a vector that
    7062:   would contain the result of a matrix vector product with this matrix. See [Matrix
    7063:   Layouts](sec_matlayout) for details on matrix layouts.

    7065: .seealso: [](ch_matrices), `Mat`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`, `MatGetOwnershipRangesColumn()`, `PetscSplitOwnership()`,
    7066:           `PetscSplitOwnershipBlock()`, `PetscLayout`, `MatSetSizes()`, `MatCreateAIJ()`, `DMDAGetGhostCorners()`, `DM`
    7067: @*/
    7068: PetscErrorCode MatGetOwnershipRange(Mat mat, PetscInt *m, PetscInt *n)
    7069: {
    7070:   PetscFunctionBegin;
    7073:   if (m) PetscAssertPointer(m, 2);
    7074:   if (n) PetscAssertPointer(n, 3);
    7075:   MatCheckPreallocated(mat, 1);
    7076:   if (m) *m = mat->rmap->rstart;
    7077:   if (n) *n = mat->rmap->rend;
    7078:   PetscFunctionReturn(PETSC_SUCCESS);
    7079: }

    7081: /*@C
    7082:   MatGetOwnershipRanges - For matrices that own values by row, excludes `MATELEMENTAL` and
    7083:   `MATSCALAPACK`, returns the range of matrix rows owned by each process.

    7085:   Not Collective, unless matrix has not been allocated

    7087:   Input Parameter:
    7088: . mat - the matrix

    7090:   Output Parameter:
    7091: . ranges - start of each processors portion plus one more than the total length at the end, of length `size` + 1
    7092:            where `size` is the number of MPI processes used by `mat`

    7094:   Level: beginner

    7096:   Notes:
    7097:   If the `Mat` was obtained from a `DM` with `DMCreateMatrix()`, then the range values are determined by the specific `DM`.

    7099:   If the `Mat` was created directly the range values are determined by the local size passed to `MatSetSizes()` or `MatCreateAIJ()`.
    7100:   If `PETSC_DECIDE` was passed as the local size, then the vector uses default values for the range using `PetscSplitOwnership()`.

    7102:   For certain `DM`, such as `DMDA`, it is better to use `DM` specific routines, such as `DMDAGetGhostCorners()`, to determine
    7103:   the local values in the matrix.

    7105:   For all matrices  it returns the ranges of matrix rows associated with rows of a vector that
    7106:   would contain the result of a matrix vector product with this matrix. See [Matrix
    7107:   Layouts](sec_matlayout) for details on matrix layouts.

    7109: .seealso: [](ch_matrices), `Mat`, `MatGetOwnershipRange()`, `MatGetOwnershipRangeColumn()`, `MatGetOwnershipRangesColumn()`, `PetscLayout`,
    7110:           `PetscSplitOwnership()`, `PetscSplitOwnershipBlock()`, `MatSetSizes()`, `MatCreateAIJ()`,
    7111:           `DMDAGetGhostCorners()`, `DM`
    7112: @*/
    7113: PetscErrorCode MatGetOwnershipRanges(Mat mat, const PetscInt *ranges[])
    7114: {
    7115:   PetscFunctionBegin;
    7118:   MatCheckPreallocated(mat, 1);
    7119:   PetscCall(PetscLayoutGetRanges(mat->rmap, ranges));
    7120:   PetscFunctionReturn(PETSC_SUCCESS);
    7121: }

    7123: /*@C
    7124:   MatGetOwnershipRangesColumn - Returns the ranges of matrix columns associated with rows of a
    7125:   vector one multiplies this vector by that are owned by each processor.

    7127:   Not Collective, unless matrix has not been allocated

    7129:   Input Parameter:
    7130: . mat - the matrix

    7132:   Output Parameter:
    7133: . ranges - start of each processors portion plus one more than the total length at the end

    7135:   Level: beginner

    7137:   Notes:
    7138:   If the `Mat` was obtained from a `DM` with `DMCreateMatrix()`, then the range values are determined by the specific `DM`.

    7140:   If the `Mat` was created directly the range values are determined by the local size passed to `MatSetSizes()` or `MatCreateAIJ()`.
    7141:   If `PETSC_DECIDE` was passed as the local size, then the vector uses default values for the range using `PetscSplitOwnership()`.

    7143:   For certain `DM`, such as `DMDA`, it is better to use `DM` specific routines, such as `DMDAGetGhostCorners()`, to determine
    7144:   the local values in the matrix.

    7146:   Returns the columns of the "diagonal blocks", for most sparse matrix formats. See [Matrix
    7147:   Layouts](sec_matlayout) for details on matrix layouts.

    7149: .seealso: [](ch_matrices), `Mat`, `MatGetOwnershipRange()`, `MatGetOwnershipRangeColumn()`, `MatGetOwnershipRanges()`,
    7150:           `PetscSplitOwnership()`, `PetscSplitOwnershipBlock()`, `PetscLayout`, `MatSetSizes()`, `MatCreateAIJ()`,
    7151:           `DMDAGetGhostCorners()`, `DM`
    7152: @*/
    7153: PetscErrorCode MatGetOwnershipRangesColumn(Mat mat, const PetscInt *ranges[])
    7154: {
    7155:   PetscFunctionBegin;
    7158:   MatCheckPreallocated(mat, 1);
    7159:   PetscCall(PetscLayoutGetRanges(mat->cmap, ranges));
    7160:   PetscFunctionReturn(PETSC_SUCCESS);
    7161: }

    7163: /*@
    7164:   MatGetOwnershipIS - Get row and column ownership of a matrices' values as index sets.

    7166:   Not Collective

    7168:   Input Parameter:
    7169: . A - matrix

    7171:   Output Parameters:
    7172: + rows - rows in which this process owns elements, , use `NULL` to not obtain this value
    7173: - cols - columns in which this process owns elements, use `NULL` to not obtain this value

    7175:   Level: intermediate

    7177:   Note:
    7178:   You should call `ISDestroy()` on the returned `IS`

    7180:   For most matrices, excluding `MATELEMENTAL` and `MATSCALAPACK`, this corresponds to values
    7181:   returned by `MatGetOwnershipRange()`, `MatGetOwnershipRangeColumn()`. For `MATELEMENTAL` and
    7182:   `MATSCALAPACK` the ownership is more complicated. See [Matrix Layouts](sec_matlayout) for
    7183:   details on matrix layouts.

    7185: .seealso: [](ch_matrices), `IS`, `Mat`, `MatGetOwnershipRanges()`, `MatSetValues()`, `MATELEMENTAL`, `MATSCALAPACK`
    7186: @*/
    7187: PetscErrorCode MatGetOwnershipIS(Mat A, IS *rows, IS *cols)
    7188: {
    7189:   PetscErrorCode (*f)(Mat, IS *, IS *);

    7191:   PetscFunctionBegin;
    7194:   MatCheckPreallocated(A, 1);
    7195:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatGetOwnershipIS_C", &f));
    7196:   if (f) {
    7197:     PetscCall((*f)(A, rows, cols));
    7198:   } else { /* Create a standard row-based partition, each process is responsible for ALL columns in their row block */
    7199:     if (rows) PetscCall(ISCreateStride(PETSC_COMM_SELF, A->rmap->n, A->rmap->rstart, 1, rows));
    7200:     if (cols) PetscCall(ISCreateStride(PETSC_COMM_SELF, A->cmap->N, 0, 1, cols));
    7201:   }
    7202:   PetscFunctionReturn(PETSC_SUCCESS);
    7203: }

    7205: /*@
    7206:   MatILUFactorSymbolic - Performs symbolic ILU factorization of a matrix obtained with `MatGetFactor()`
    7207:   Uses levels of fill only, not drop tolerance. Use `MatLUFactorNumeric()`
    7208:   to complete the factorization.

    7210:   Collective

    7212:   Input Parameters:
    7213: + fact - the factorized matrix obtained with `MatGetFactor()`
    7214: . mat  - the matrix
    7215: . row  - row permutation
    7216: . col  - column permutation
    7217: - info - structure containing
    7218: .vb
    7219:       levels - number of levels of fill.
    7220:       expected fill - as ratio of original fill.
    7221:       1 or 0 - indicating force fill on diagonal (improves robustness for matrices
    7222:                 missing diagonal entries)
    7223: .ve

    7225:   Level: developer

    7227:   Notes:
    7228:   See [Matrix Factorization](sec_matfactor) for additional information.

    7230:   Most users should employ the `KSP` interface for linear solvers
    7231:   instead of working directly with matrix algebra routines such as this.
    7232:   See, e.g., `KSPCreate()`.

    7234:   Uses the definition of level of fill as in Y. Saad, {cite}`saad2003`

    7236:   Fortran Note:
    7237:   A valid (non-null) `info` argument must be provided

    7239: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`,
    7240:           `MatGetOrdering()`, `MatFactorInfo`
    7241: @*/
    7242: PetscErrorCode MatILUFactorSymbolic(Mat fact, Mat mat, IS row, IS col, const MatFactorInfo *info)
    7243: {
    7244:   PetscFunctionBegin;
    7249:   PetscAssertPointer(info, 5);
    7250:   PetscAssertPointer(fact, 1);
    7251:   PetscCheck(info->levels >= 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Levels of fill negative %" PetscInt_FMT, (PetscInt)info->levels);
    7252:   PetscCheck(info->fill >= 1.0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Expected fill less than 1.0 %g", (double)info->fill);
    7253:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7254:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7255:   MatCheckPreallocated(mat, 2);

    7257:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_ILUFactorSymbolic, mat, row, col, 0));
    7258:   PetscUseTypeMethod(fact, ilufactorsymbolic, mat, row, col, info);
    7259:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_ILUFactorSymbolic, mat, row, col, 0));
    7260:   PetscFunctionReturn(PETSC_SUCCESS);
    7261: }

    7263: /*@
    7264:   MatICCFactorSymbolic - Performs symbolic incomplete
    7265:   Cholesky factorization for a symmetric matrix.  Use
    7266:   `MatCholeskyFactorNumeric()` to complete the factorization.

    7268:   Collective

    7270:   Input Parameters:
    7271: + fact - the factorized matrix obtained with `MatGetFactor()`
    7272: . mat  - the matrix to be factored
    7273: . perm - row and column permutation
    7274: - info - structure containing
    7275: .vb
    7276:       levels - number of levels of fill.
    7277:       expected fill - as ratio of original fill.
    7278: .ve

    7280:   Level: developer

    7282:   Notes:
    7283:   Most users should employ the `KSP` interface for linear solvers
    7284:   instead of working directly with matrix algebra routines such as this.
    7285:   See, e.g., `KSPCreate()`.

    7287:   This uses the definition of level of fill as in Y. Saad {cite}`saad2003`

    7289:   Fortran Note:
    7290:   A valid (non-null) `info` argument must be provided

    7292: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCholeskyFactorNumeric()`, `MatCholeskyFactor()`, `MatFactorInfo`
    7293: @*/
    7294: PetscErrorCode MatICCFactorSymbolic(Mat fact, Mat mat, IS perm, const MatFactorInfo *info)
    7295: {
    7296:   PetscFunctionBegin;
    7300:   PetscAssertPointer(info, 4);
    7301:   PetscAssertPointer(fact, 1);
    7302:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7303:   PetscCheck(info->levels >= 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Levels negative %" PetscInt_FMT, (PetscInt)info->levels);
    7304:   PetscCheck(info->fill >= 1.0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Expected fill less than 1.0 %g", (double)info->fill);
    7305:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7306:   MatCheckPreallocated(mat, 2);

    7308:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_ICCFactorSymbolic, mat, perm, 0, 0));
    7309:   PetscUseTypeMethod(fact, iccfactorsymbolic, mat, perm, info);
    7310:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_ICCFactorSymbolic, mat, perm, 0, 0));
    7311:   PetscFunctionReturn(PETSC_SUCCESS);
    7312: }

    7314: /*@C
    7315:   MatCreateSubMatrices - Extracts several submatrices from a matrix. If submat
    7316:   points to an array of valid matrices, they may be reused to store the new
    7317:   submatrices.

    7319:   Collective

    7321:   Input Parameters:
    7322: + mat   - the matrix
    7323: . n     - the number of submatrixes to be extracted (on this processor, may be zero)
    7324: . irow  - index set of rows to extract
    7325: . icol  - index set of columns to extract
    7326: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    7328:   Output Parameter:
    7329: . submat - the array of submatrices

    7331:   Level: advanced

    7333:   Notes:
    7334:   `MatCreateSubMatrices()` can extract ONLY sequential submatrices
    7335:   (from both sequential and parallel matrices). Use `MatCreateSubMatrix()`
    7336:   to extract a parallel submatrix.

    7338:   Some matrix types place restrictions on the row and column
    7339:   indices, such as that they be sorted or that they be equal to each other.

    7341:   The index sets may not have duplicate entries.

    7343:   When extracting submatrices from a parallel matrix, each processor can
    7344:   form a different submatrix by setting the rows and columns of its
    7345:   individual index sets according to the local submatrix desired.

    7347:   When finished using the submatrices, the user should destroy
    7348:   them with `MatDestroySubMatrices()`.

    7350:   `MAT_REUSE_MATRIX` can only be used when the nonzero structure of the
    7351:   original matrix has not changed from that last call to `MatCreateSubMatrices()`.

    7353:   This routine creates the matrices in submat; you should NOT create them before
    7354:   calling it. It also allocates the array of matrix pointers submat.

    7356:   For `MATBAIJ` matrices the index sets must respect the block structure, that is if they
    7357:   request one row/column in a block, they must request all rows/columns that are in
    7358:   that block. For example, if the block size is 2 you cannot request just row 0 and
    7359:   column 0.

    7361:   Fortran Note:
    7362: .vb
    7363:   Mat, pointer :: submat(:)
    7364: .ve

    7366: .seealso: [](ch_matrices), `Mat`, `MatDestroySubMatrices()`, `MatCreateSubMatrix()`, `MatGetRow()`, `MatGetDiagonal()`, `MatReuse`
    7367: @*/
    7368: PetscErrorCode MatCreateSubMatrices(Mat mat, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
    7369: {
    7370:   PetscInt  i;
    7371:   PetscBool eq;

    7373:   PetscFunctionBegin;
    7376:   if (n) {
    7377:     PetscAssertPointer(irow, 3);
    7379:     PetscAssertPointer(icol, 4);
    7381:   }
    7382:   PetscAssertPointer(submat, 6);
    7383:   if (n && scall == MAT_REUSE_MATRIX) {
    7384:     PetscAssertPointer(*submat, 6);
    7386:   }
    7387:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7388:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7389:   MatCheckPreallocated(mat, 1);
    7390:   PetscCall(PetscLogEventBegin(MAT_CreateSubMats, mat, 0, 0, 0));
    7391:   PetscUseTypeMethod(mat, createsubmatrices, n, irow, icol, scall, submat);
    7392:   PetscCall(PetscLogEventEnd(MAT_CreateSubMats, mat, 0, 0, 0));
    7393:   for (i = 0; i < n; i++) {
    7394:     (*submat)[i]->factortype = MAT_FACTOR_NONE; /* in case in place factorization was previously done on submatrix */
    7395:     PetscCall(ISEqualUnsorted(irow[i], icol[i], &eq));
    7396:     if (eq) PetscCall(MatPropagateSymmetryOptions(mat, (*submat)[i]));
    7397: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
    7398:     if (mat->boundtocpu && mat->bindingpropagates) {
    7399:       PetscCall(MatBindToCPU((*submat)[i], PETSC_TRUE));
    7400:       PetscCall(MatSetBindingPropagates((*submat)[i], PETSC_TRUE));
    7401:     }
    7402: #endif
    7403:   }
    7404:   PetscFunctionReturn(PETSC_SUCCESS);
    7405: }

    7407: /*@C
    7408:   MatCreateSubMatricesMPI - Extracts MPI submatrices across a sub communicator of `mat` (by pairs of `IS` that may live on subcomms).

    7410:   Collective

    7412:   Input Parameters:
    7413: + mat   - the matrix
    7414: . n     - the number of submatrixes to be extracted
    7415: . irow  - index set of rows to extract
    7416: . icol  - index set of columns to extract
    7417: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    7419:   Output Parameter:
    7420: . submat - the array of submatrices

    7422:   Level: advanced

    7424:   Note:
    7425:   This is used by `PCGASM`

    7427: .seealso: [](ch_matrices), `Mat`, `PCGASM`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRow()`, `MatGetDiagonal()`, `MatReuse`
    7428: @*/
    7429: PetscErrorCode MatCreateSubMatricesMPI(Mat mat, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
    7430: {
    7431:   PetscInt  i;
    7432:   PetscBool eq;

    7434:   PetscFunctionBegin;
    7437:   if (n) {
    7438:     PetscAssertPointer(irow, 3);
    7440:     PetscAssertPointer(icol, 4);
    7442:   }
    7443:   PetscAssertPointer(submat, 6);
    7444:   if (n && scall == MAT_REUSE_MATRIX) {
    7445:     PetscAssertPointer(*submat, 6);
    7447:   }
    7448:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7449:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7450:   MatCheckPreallocated(mat, 1);

    7452:   PetscCall(PetscLogEventBegin(MAT_CreateSubMats, mat, 0, 0, 0));
    7453:   PetscUseTypeMethod(mat, createsubmatricesmpi, n, irow, icol, scall, submat);
    7454:   PetscCall(PetscLogEventEnd(MAT_CreateSubMats, mat, 0, 0, 0));
    7455:   for (i = 0; i < n; i++) {
    7456:     PetscCall(ISEqualUnsorted(irow[i], icol[i], &eq));
    7457:     if (eq) PetscCall(MatPropagateSymmetryOptions(mat, (*submat)[i]));
    7458:   }
    7459:   PetscFunctionReturn(PETSC_SUCCESS);
    7460: }

    7462: /*@C
    7463:   MatDestroyMatrices - Destroys an array of matrices

    7465:   Collective

    7467:   Input Parameters:
    7468: + n   - the number of local matrices
    7469: - mat - the matrices (this is a pointer to the array of matrices)

    7471:   Level: advanced

    7473:   Notes:
    7474:   Frees not only the matrices, but also the array that contains the matrices

    7476:   For matrices obtained with  `MatCreateSubMatrices()` use `MatDestroySubMatrices()`

    7478: .seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatDestroySubMatrices()`
    7479: @*/
    7480: PetscErrorCode MatDestroyMatrices(PetscInt n, Mat *mat[])
    7481: {
    7482:   PetscInt i;

    7484:   PetscFunctionBegin;
    7485:   if (!*mat) PetscFunctionReturn(PETSC_SUCCESS);
    7486:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Trying to destroy negative number of matrices %" PetscInt_FMT, n);
    7487:   PetscAssertPointer(mat, 2);

    7489:   for (i = 0; i < n; i++) PetscCall(MatDestroy(&(*mat)[i]));

    7491:   /* memory is allocated even if n = 0 */
    7492:   PetscCall(PetscFree(*mat));
    7493:   PetscFunctionReturn(PETSC_SUCCESS);
    7494: }

    7496: /*@C
    7497:   MatDestroySubMatrices - Destroys a set of matrices obtained with `MatCreateSubMatrices()`.

    7499:   Collective

    7501:   Input Parameters:
    7502: + n   - the number of local matrices
    7503: - mat - the matrices (this is a pointer to the array of matrices, to match the calling sequence of `MatCreateSubMatrices()`)

    7505:   Level: advanced

    7507:   Note:
    7508:   Frees not only the matrices, but also the array that contains the matrices

    7510: .seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatDestroyMatrices()`
    7511: @*/
    7512: PetscErrorCode MatDestroySubMatrices(PetscInt n, Mat *mat[])
    7513: {
    7514:   Mat mat0;

    7516:   PetscFunctionBegin;
    7517:   if (!*mat) PetscFunctionReturn(PETSC_SUCCESS);
    7518:   /* mat[] is an array of length n+1, see MatCreateSubMatrices_xxx() */
    7519:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Trying to destroy negative number of matrices %" PetscInt_FMT, n);
    7520:   PetscAssertPointer(mat, 2);

    7522:   mat0 = (*mat)[0];
    7523:   if (mat0 && mat0->ops->destroysubmatrices) {
    7524:     PetscCall((*mat0->ops->destroysubmatrices)(n, mat));
    7525:   } else {
    7526:     PetscCall(MatDestroyMatrices(n, mat));
    7527:   }
    7528:   PetscFunctionReturn(PETSC_SUCCESS);
    7529: }

    7531: /*@
    7532:   MatGetSeqNonzeroStructure - Extracts the nonzero structure from a matrix and stores it, in its entirety, on each process

    7534:   Collective

    7536:   Input Parameter:
    7537: . mat - the matrix

    7539:   Output Parameter:
    7540: . matstruct - the sequential matrix with the nonzero structure of `mat`

    7542:   Level: developer

    7544: .seealso: [](ch_matrices), `Mat`, `MatDestroySeqNonzeroStructure()`, `MatCreateSubMatrices()`, `MatDestroyMatrices()`
    7545: @*/
    7546: PetscErrorCode MatGetSeqNonzeroStructure(Mat mat, Mat *matstruct)
    7547: {
    7548:   PetscFunctionBegin;
    7550:   PetscAssertPointer(matstruct, 2);

    7553:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7554:   MatCheckPreallocated(mat, 1);

    7556:   PetscCall(PetscLogEventBegin(MAT_GetSeqNonzeroStructure, mat, 0, 0, 0));
    7557:   PetscUseTypeMethod(mat, getseqnonzerostructure, matstruct);
    7558:   PetscCall(PetscLogEventEnd(MAT_GetSeqNonzeroStructure, mat, 0, 0, 0));
    7559:   PetscFunctionReturn(PETSC_SUCCESS);
    7560: }

    7562: /*@C
    7563:   MatDestroySeqNonzeroStructure - Destroys matrix obtained with `MatGetSeqNonzeroStructure()`.

    7565:   Collective

    7567:   Input Parameter:
    7568: . mat - the matrix

    7570:   Level: advanced

    7572:   Note:
    7573:   This is not needed, one can just call `MatDestroy()`

    7575: .seealso: [](ch_matrices), `Mat`, `MatGetSeqNonzeroStructure()`
    7576: @*/
    7577: PetscErrorCode MatDestroySeqNonzeroStructure(Mat *mat)
    7578: {
    7579:   PetscFunctionBegin;
    7580:   PetscAssertPointer(mat, 1);
    7581:   PetscCall(MatDestroy(mat));
    7582:   PetscFunctionReturn(PETSC_SUCCESS);
    7583: }

    7585: /*@
    7586:   MatIncreaseOverlap - Given a set of submatrices indicated by index sets,
    7587:   replaces the index sets by larger ones that represent submatrices with
    7588:   additional overlap.

    7590:   Collective

    7592:   Input Parameters:
    7593: + mat - the matrix
    7594: . n   - the number of index sets
    7595: . is  - the array of index sets (these index sets will changed during the call)
    7596: - ov  - the additional overlap requested

    7598:   Options Database Key:
    7599: . -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

    7601:   Level: developer

    7603:   Note:
    7604:   The computed overlap preserves the matrix block sizes when the blocks are square.
    7605:   That is: if a matrix nonzero for a given block would increase the overlap all columns associated with
    7606:   that block are included in the overlap regardless of whether each specific column would increase the overlap.

    7608: .seealso: [](ch_matrices), `Mat`, `PCASM`, `MatSetBlockSize()`, `MatIncreaseOverlapSplit()`, `MatCreateSubMatrices()`
    7609: @*/
    7610: PetscErrorCode MatIncreaseOverlap(Mat mat, PetscInt n, IS is[], PetscInt ov)
    7611: {
    7612:   PetscInt i, bs, cbs;

    7614:   PetscFunctionBegin;
    7618:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have one or more domains, you have %" PetscInt_FMT, n);
    7619:   if (n) {
    7620:     PetscAssertPointer(is, 3);
    7622:   }
    7623:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7624:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7625:   MatCheckPreallocated(mat, 1);

    7627:   if (!ov || !n) PetscFunctionReturn(PETSC_SUCCESS);
    7628:   PetscCall(PetscLogEventBegin(MAT_IncreaseOverlap, mat, 0, 0, 0));
    7629:   PetscUseTypeMethod(mat, increaseoverlap, n, is, ov);
    7630:   PetscCall(PetscLogEventEnd(MAT_IncreaseOverlap, mat, 0, 0, 0));
    7631:   PetscCall(MatGetBlockSizes(mat, &bs, &cbs));
    7632:   if (bs == cbs) {
    7633:     for (i = 0; i < n; i++) PetscCall(ISSetBlockSize(is[i], bs));
    7634:   }
    7635:   PetscFunctionReturn(PETSC_SUCCESS);
    7636: }

    7638: PetscErrorCode MatIncreaseOverlapSplit_Single(Mat, IS *, PetscInt);

    7640: /*@
    7641:   MatIncreaseOverlapSplit - Given a set of submatrices indicated by index sets across
    7642:   a sub communicator, replaces the index sets by larger ones that represent submatrices with
    7643:   additional overlap.

    7645:   Collective

    7647:   Input Parameters:
    7648: + mat - the matrix
    7649: . n   - the number of index sets
    7650: . is  - the array of index sets (these index sets will changed during the call)
    7651: - ov  - the additional overlap requested

    7653:   `   Options Database Key:
    7654: . -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

    7656:   Level: developer

    7658: .seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatIncreaseOverlap()`
    7659: @*/
    7660: PetscErrorCode MatIncreaseOverlapSplit(Mat mat, PetscInt n, IS is[], PetscInt ov)
    7661: {
    7662:   PetscInt i;

    7664:   PetscFunctionBegin;
    7667:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have one or more domains, you have %" PetscInt_FMT, n);
    7668:   if (n) {
    7669:     PetscAssertPointer(is, 3);
    7671:   }
    7672:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7673:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7674:   MatCheckPreallocated(mat, 1);
    7675:   if (!ov) PetscFunctionReturn(PETSC_SUCCESS);
    7676:   PetscCall(PetscLogEventBegin(MAT_IncreaseOverlap, mat, 0, 0, 0));
    7677:   for (i = 0; i < n; i++) PetscCall(MatIncreaseOverlapSplit_Single(mat, &is[i], ov));
    7678:   PetscCall(PetscLogEventEnd(MAT_IncreaseOverlap, mat, 0, 0, 0));
    7679:   PetscFunctionReturn(PETSC_SUCCESS);
    7680: }

    7682: /*@
    7683:   MatGetBlockSize - Returns the matrix block size.

    7685:   Not Collective

    7687:   Input Parameter:
    7688: . mat - the matrix

    7690:   Output Parameter:
    7691: . bs - block size

    7693:   Level: intermediate

    7695:   Notes:
    7696:   Block row formats are `MATBAIJ` and `MATSBAIJ` ALWAYS have square block storage in the matrix.

    7698:   If the block size has not been set yet this routine returns 1.

    7700: .seealso: [](ch_matrices), `Mat`, `MATBAIJ`, `MATSBAIJ`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSizes()`
    7701: @*/
    7702: PetscErrorCode MatGetBlockSize(Mat mat, PetscInt *bs)
    7703: {
    7704:   PetscFunctionBegin;
    7706:   PetscAssertPointer(bs, 2);
    7707:   *bs = mat->rmap->bs;
    7708:   PetscFunctionReturn(PETSC_SUCCESS);
    7709: }

    7711: /*@
    7712:   MatGetBlockSizes - Returns the matrix block row and column sizes.

    7714:   Not Collective

    7716:   Input Parameter:
    7717: . mat - the matrix

    7719:   Output Parameters:
    7720: + rbs - row block size
    7721: - cbs - column block size

    7723:   Level: intermediate

    7725:   Notes:
    7726:   Block row formats are `MATBAIJ` and `MATSBAIJ` ALWAYS have square block storage in the matrix.
    7727:   If you pass a different block size for the columns than the rows, the row block size determines the square block storage.

    7729:   If a block size has not been set yet this routine returns 1.

    7731: .seealso: [](ch_matrices), `Mat`, `MATBAIJ`, `MATSBAIJ`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSize()`, `MatSetBlockSizes()`
    7732: @*/
    7733: PetscErrorCode MatGetBlockSizes(Mat mat, PetscInt *rbs, PetscInt *cbs)
    7734: {
    7735:   PetscFunctionBegin;
    7737:   if (rbs) PetscAssertPointer(rbs, 2);
    7738:   if (cbs) PetscAssertPointer(cbs, 3);
    7739:   if (rbs) *rbs = mat->rmap->bs;
    7740:   if (cbs) *cbs = mat->cmap->bs;
    7741:   PetscFunctionReturn(PETSC_SUCCESS);
    7742: }

    7744: /*@
    7745:   MatSetBlockSize - Sets the matrix block size.

    7747:   Logically Collective

    7749:   Input Parameters:
    7750: + mat - the matrix
    7751: - bs  - block size

    7753:   Level: intermediate

    7755:   Notes:
    7756:   Block row formats are `MATBAIJ` and `MATSBAIJ` formats ALWAYS have square block storage in the matrix.
    7757:   This must be called before `MatSetUp()` or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later.

    7759:   For `MATAIJ` matrix format, this function can be called at a later stage, provided that the specified block size
    7760:   is compatible with the matrix local sizes.

    7762: .seealso: [](ch_matrices), `Mat`, `MATBAIJ`, `MATSBAIJ`, `MATAIJ`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSizes()`, `MatGetBlockSizes()`
    7763: @*/
    7764: PetscErrorCode MatSetBlockSize(Mat mat, PetscInt bs)
    7765: {
    7766:   PetscFunctionBegin;
    7769:   PetscCall(MatSetBlockSizes(mat, bs, bs));
    7770:   PetscFunctionReturn(PETSC_SUCCESS);
    7771: }

    7773: typedef struct {
    7774:   PetscInt         n;
    7775:   IS              *is;
    7776:   Mat             *mat;
    7777:   PetscObjectState nonzerostate;
    7778:   Mat              C;
    7779: } EnvelopeData;

    7781: static PetscErrorCode EnvelopeDataDestroy(PetscCtxRt ptr)
    7782: {
    7783:   EnvelopeData *edata = *(EnvelopeData **)ptr;

    7785:   PetscFunctionBegin;
    7786:   for (PetscInt i = 0; i < edata->n; i++) PetscCall(ISDestroy(&edata->is[i]));
    7787:   PetscCall(PetscFree(edata->is));
    7788:   PetscCall(PetscFree(edata));
    7789:   PetscFunctionReturn(PETSC_SUCCESS);
    7790: }

    7792: /*@
    7793:   MatComputeVariableBlockEnvelope - Given a matrix whose nonzeros are in blocks along the diagonal this computes and stores
    7794:   the sizes of these blocks in the matrix. An individual block may lie over several processes.

    7796:   Collective

    7798:   Input Parameter:
    7799: . mat - the matrix

    7801:   Level: intermediate

    7803:   Notes:
    7804:   There can be zeros within the blocks

    7806:   The blocks can overlap between processes, including laying on more than two processes

    7808: .seealso: [](ch_matrices), `Mat`, `MatInvertVariableBlockEnvelope()`, `MatSetVariableBlockSizes()`
    7809: @*/
    7810: PetscErrorCode MatComputeVariableBlockEnvelope(Mat mat)
    7811: {
    7812:   PetscInt           n, *sizes, *starts, i = 0, env = 0, tbs = 0, lblocks = 0, rstart, II, ln = 0, cnt = 0, cstart, cend;
    7813:   PetscInt          *diag, *odiag, sc;
    7814:   VecScatter         scatter;
    7815:   PetscScalar       *seqv;
    7816:   const PetscScalar *parv;
    7817:   const PetscInt    *ia, *ja;
    7818:   PetscBool          set, flag, done;
    7819:   Mat                AA = mat, A;
    7820:   MPI_Comm           comm;
    7821:   PetscMPIInt        rank, size, tag;
    7822:   MPI_Status         status;
    7823:   PetscContainer     container;
    7824:   EnvelopeData      *edata;
    7825:   Vec                seq, par;
    7826:   IS                 isglobal;

    7828:   PetscFunctionBegin;
    7830:   PetscCall(MatIsSymmetricKnown(mat, &set, &flag));
    7831:   if (!set || !flag) {
    7832:     /* TODO: only needs nonzero structure of transpose */
    7833:     PetscCall(MatTranspose(mat, MAT_INITIAL_MATRIX, &AA));
    7834:     PetscCall(MatAXPY(AA, 1.0, mat, DIFFERENT_NONZERO_PATTERN));
    7835:   }
    7836:   PetscCall(MatAIJGetLocalMat(AA, &A));
    7837:   PetscCall(MatGetRowIJ(A, 0, PETSC_FALSE, PETSC_FALSE, &n, &ia, &ja, &done));
    7838:   PetscCheck(done, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Unable to get IJ structure from matrix");

    7840:   PetscCall(MatGetLocalSize(mat, &n, NULL));
    7841:   PetscCall(PetscObjectGetNewTag((PetscObject)mat, &tag));
    7842:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    7843:   PetscCallMPI(MPI_Comm_size(comm, &size));
    7844:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    7846:   PetscCall(PetscMalloc2(n, &sizes, n, &starts));

    7848:   if (rank > 0) {
    7849:     PetscCallMPI(MPI_Recv(&env, 1, MPIU_INT, rank - 1, tag, comm, &status));
    7850:     PetscCallMPI(MPI_Recv(&tbs, 1, MPIU_INT, rank - 1, tag, comm, &status));
    7851:   }
    7852:   PetscCall(MatGetOwnershipRange(mat, &rstart, NULL));
    7853:   for (i = 0; i < n; i++) {
    7854:     env = PetscMax(env, ja[ia[i + 1] - 1]);
    7855:     II  = rstart + i;
    7856:     if (env == II) {
    7857:       starts[lblocks]  = tbs;
    7858:       sizes[lblocks++] = 1 + II - tbs;
    7859:       tbs              = 1 + II;
    7860:     }
    7861:   }
    7862:   if (rank < size - 1) {
    7863:     PetscCallMPI(MPI_Send(&env, 1, MPIU_INT, rank + 1, tag, comm));
    7864:     PetscCallMPI(MPI_Send(&tbs, 1, MPIU_INT, rank + 1, tag, comm));
    7865:   }

    7867:   PetscCall(MatRestoreRowIJ(A, 0, PETSC_FALSE, PETSC_FALSE, &n, &ia, &ja, &done));
    7868:   if (!set || !flag) PetscCall(MatDestroy(&AA));
    7869:   PetscCall(MatDestroy(&A));

    7871:   PetscCall(PetscNew(&edata));
    7872:   PetscCall(MatGetNonzeroState(mat, &edata->nonzerostate));
    7873:   edata->n = lblocks;
    7874:   /* create IS needed for extracting blocks from the original matrix */
    7875:   PetscCall(PetscMalloc1(lblocks, &edata->is));
    7876:   for (PetscInt i = 0; i < lblocks; i++) PetscCall(ISCreateStride(PETSC_COMM_SELF, sizes[i], starts[i], 1, &edata->is[i]));

    7878:   /* Create the resulting inverse matrix nonzero structure with preallocation information */
    7879:   PetscCall(MatCreate(PetscObjectComm((PetscObject)mat), &edata->C));
    7880:   PetscCall(MatSetSizes(edata->C, mat->rmap->n, mat->cmap->n, mat->rmap->N, mat->cmap->N));
    7881:   PetscCall(MatSetBlockSizesFromMats(edata->C, mat, mat));
    7882:   PetscCall(MatSetType(edata->C, MATAIJ));

    7884:   /* Communicate the start and end of each row, from each block to the correct rank */
    7885:   /* TODO: Use PetscSF instead of VecScatter */
    7886:   for (PetscInt i = 0; i < lblocks; i++) ln += sizes[i];
    7887:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, 2 * ln, &seq));
    7888:   PetscCall(VecGetArrayWrite(seq, &seqv));
    7889:   for (PetscInt i = 0; i < lblocks; i++) {
    7890:     for (PetscInt j = 0; j < sizes[i]; j++) {
    7891:       seqv[cnt]     = starts[i];
    7892:       seqv[cnt + 1] = starts[i] + sizes[i];
    7893:       cnt += 2;
    7894:     }
    7895:   }
    7896:   PetscCall(VecRestoreArrayWrite(seq, &seqv));
    7897:   PetscCallMPI(MPI_Scan(&cnt, &sc, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)mat)));
    7898:   sc -= cnt;
    7899:   PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)mat), 2 * mat->rmap->n, 2 * mat->rmap->N, &par));
    7900:   PetscCall(ISCreateStride(PETSC_COMM_SELF, cnt, sc, 1, &isglobal));
    7901:   PetscCall(VecScatterCreate(seq, NULL, par, isglobal, &scatter));
    7902:   PetscCall(ISDestroy(&isglobal));
    7903:   PetscCall(VecScatterBegin(scatter, seq, par, INSERT_VALUES, SCATTER_FORWARD));
    7904:   PetscCall(VecScatterEnd(scatter, seq, par, INSERT_VALUES, SCATTER_FORWARD));
    7905:   PetscCall(VecScatterDestroy(&scatter));
    7906:   PetscCall(VecDestroy(&seq));
    7907:   PetscCall(MatGetOwnershipRangeColumn(mat, &cstart, &cend));
    7908:   PetscCall(PetscMalloc2(mat->rmap->n, &diag, mat->rmap->n, &odiag));
    7909:   PetscCall(VecGetArrayRead(par, &parv));
    7910:   cnt = 0;
    7911:   PetscCall(MatGetSize(mat, NULL, &n));
    7912:   for (PetscInt i = 0; i < mat->rmap->n; i++) {
    7913:     PetscInt start, end, d = 0, od = 0;

    7915:     start = (PetscInt)PetscRealPart(parv[cnt]);
    7916:     end   = (PetscInt)PetscRealPart(parv[cnt + 1]);
    7917:     cnt += 2;

    7919:     if (start < cstart) {
    7920:       od += cstart - start + n - cend;
    7921:       d += cend - cstart;
    7922:     } else if (start < cend) {
    7923:       od += n - cend;
    7924:       d += cend - start;
    7925:     } else od += n - start;
    7926:     if (end <= cstart) {
    7927:       od -= cstart - end + n - cend;
    7928:       d -= cend - cstart;
    7929:     } else if (end < cend) {
    7930:       od -= n - cend;
    7931:       d -= cend - end;
    7932:     } else od -= n - end;

    7934:     odiag[i] = od;
    7935:     diag[i]  = d;
    7936:   }
    7937:   PetscCall(VecRestoreArrayRead(par, &parv));
    7938:   PetscCall(VecDestroy(&par));
    7939:   PetscCall(MatXAIJSetPreallocation(edata->C, mat->rmap->bs, diag, odiag, NULL, NULL));
    7940:   PetscCall(PetscFree2(diag, odiag));
    7941:   PetscCall(PetscFree2(sizes, starts));

    7943:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    7944:   PetscCall(PetscContainerSetPointer(container, edata));
    7945:   PetscCall(PetscContainerSetCtxDestroy(container, EnvelopeDataDestroy));
    7946:   PetscCall(PetscObjectCompose((PetscObject)mat, "EnvelopeData", (PetscObject)container));
    7947:   PetscCall(PetscObjectDereference((PetscObject)container));
    7948:   PetscFunctionReturn(PETSC_SUCCESS);
    7949: }

    7951: /*@
    7952:   MatInvertVariableBlockEnvelope - set matrix C to be the inverted block diagonal of matrix A

    7954:   Collective

    7956:   Input Parameters:
    7957: + A     - the matrix
    7958: - reuse - indicates if the `C` matrix was obtained from a previous call to this routine

    7960:   Output Parameter:
    7961: . C - matrix with inverted block diagonal of `A`

    7963:   Level: advanced

    7965:   Note:
    7966:   For efficiency the matrix `A` should have all the nonzero entries clustered in smallish blocks along the diagonal.

    7968: .seealso: [](ch_matrices), `Mat`, `MatInvertBlockDiagonal()`, `MatComputeBlockDiagonal()`
    7969: @*/
    7970: PetscErrorCode MatInvertVariableBlockEnvelope(Mat A, MatReuse reuse, Mat *C)
    7971: {
    7972:   PetscContainer   container;
    7973:   EnvelopeData    *edata;
    7974:   PetscObjectState nonzerostate;

    7976:   PetscFunctionBegin;
    7977:   PetscCall(PetscObjectQuery((PetscObject)A, "EnvelopeData", (PetscObject *)&container));
    7978:   if (!container) {
    7979:     PetscCall(MatComputeVariableBlockEnvelope(A));
    7980:     PetscCall(PetscObjectQuery((PetscObject)A, "EnvelopeData", (PetscObject *)&container));
    7981:   }
    7982:   PetscCall(PetscContainerGetPointer(container, &edata));
    7983:   PetscCall(MatGetNonzeroState(A, &nonzerostate));
    7984:   PetscCheck(nonzerostate <= edata->nonzerostate, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot handle changes to matrix nonzero structure");
    7985:   PetscCheck(reuse != MAT_REUSE_MATRIX || *C == edata->C, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "C matrix must be the same as previously output");

    7987:   PetscCall(MatCreateSubMatrices(A, edata->n, edata->is, edata->is, MAT_INITIAL_MATRIX, &edata->mat));
    7988:   *C = edata->C;

    7990:   for (PetscInt i = 0; i < edata->n; i++) {
    7991:     Mat          D;
    7992:     PetscScalar *dvalues;

    7994:     PetscCall(MatConvert(edata->mat[i], MATSEQDENSE, MAT_INITIAL_MATRIX, &D));
    7995:     PetscCall(MatSetOption(*C, MAT_ROW_ORIENTED, PETSC_FALSE));
    7996:     PetscCall(MatSeqDenseInvert(D));
    7997:     PetscCall(MatDenseGetArray(D, &dvalues));
    7998:     PetscCall(MatSetValuesIS(*C, edata->is[i], edata->is[i], dvalues, INSERT_VALUES));
    7999:     PetscCall(MatDestroy(&D));
    8000:   }
    8001:   PetscCall(MatDestroySubMatrices(edata->n, &edata->mat));
    8002:   PetscCall(MatAssemblyBegin(*C, MAT_FINAL_ASSEMBLY));
    8003:   PetscCall(MatAssemblyEnd(*C, MAT_FINAL_ASSEMBLY));
    8004:   PetscFunctionReturn(PETSC_SUCCESS);
    8005: }

    8007: /*@
    8008:   MatSetVariableBlockSizes - Sets diagonal point-blocks of the matrix that need not be of the same size

    8010:   Not Collective

    8012:   Input Parameters:
    8013: + mat     - the matrix
    8014: . nblocks - the number of blocks on this process, each block can only exist on a single process
    8015: - bsizes  - the block sizes

    8017:   Level: intermediate

    8019:   Notes:
    8020:   Currently used by `PCVPBJACOBI` for `MATAIJ` matrices

    8022:   Each variable point-block set of degrees of freedom must live on a single MPI process. That is a point block cannot straddle two MPI processes.

    8024: .seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSizes()`, `MatGetBlockSizes()`, `MatGetVariableBlockSizes()`,
    8025:           `MatComputeVariableBlockEnvelope()`, `PCVPBJACOBI`
    8026: @*/
    8027: PetscErrorCode MatSetVariableBlockSizes(Mat mat, PetscInt nblocks, const PetscInt bsizes[])
    8028: {
    8029:   PetscInt ncnt = 0, nlocal;

    8031:   PetscFunctionBegin;
    8033:   PetscCall(MatGetLocalSize(mat, &nlocal, NULL));
    8034:   PetscCheck(nblocks >= 0 && nblocks <= nlocal, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of local blocks %" PetscInt_FMT " is not in [0, %" PetscInt_FMT "]", nblocks, nlocal);
    8035:   for (PetscInt i = 0; i < nblocks; i++) ncnt += bsizes[i];
    8036:   PetscCheck(ncnt == nlocal, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Sum of local block sizes %" PetscInt_FMT " does not equal local size of matrix %" PetscInt_FMT, ncnt, nlocal);
    8037:   PetscCall(PetscFree(mat->bsizes));
    8038:   mat->nblocks = nblocks;
    8039:   PetscCall(PetscMalloc1(nblocks, &mat->bsizes));
    8040:   PetscCall(PetscArraycpy(mat->bsizes, bsizes, nblocks));
    8041:   PetscFunctionReturn(PETSC_SUCCESS);
    8042: }

    8044: /*@C
    8045:   MatGetVariableBlockSizes - Gets a diagonal blocks of the matrix that need not be of the same size

    8047:   Not Collective; No Fortran Support

    8049:   Input Parameter:
    8050: . mat - the matrix

    8052:   Output Parameters:
    8053: + nblocks - the number of blocks on this process
    8054: - bsizes  - the block sizes

    8056:   Level: intermediate

    8058: .seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSizes()`, `MatGetBlockSizes()`, `MatSetVariableBlockSizes()`, `MatComputeVariableBlockEnvelope()`
    8059: @*/
    8060: PetscErrorCode MatGetVariableBlockSizes(Mat mat, PetscInt *nblocks, const PetscInt *bsizes[])
    8061: {
    8062:   PetscFunctionBegin;
    8064:   if (nblocks) *nblocks = mat->nblocks;
    8065:   if (bsizes) *bsizes = mat->bsizes;
    8066:   PetscFunctionReturn(PETSC_SUCCESS);
    8067: }

    8069: /*@
    8070:   MatSelectVariableBlockSizes - When creating a submatrix, pass on the variable block sizes

    8072:   Not Collective

    8074:   Input Parameter:
    8075: + subA  - the submatrix
    8076: . A     - the original matrix
    8077: - isrow - The `IS` of selected rows for the submatrix, must be sorted

    8079:   Level: developer

    8081:   Notes:
    8082:   If the index set is not sorted or contains off-process entries, this function will do nothing.

    8084: .seealso: [](ch_matrices), `Mat`, `MatSetVariableBlockSizes()`, `MatComputeVariableBlockEnvelope()`
    8085: @*/
    8086: PetscErrorCode MatSelectVariableBlockSizes(Mat subA, Mat A, IS isrow)
    8087: {
    8088:   const PetscInt *rows;
    8089:   PetscInt        n, rStart, rEnd, Nb = 0;
    8090:   PetscBool       flg = A->bsizes ? PETSC_TRUE : PETSC_FALSE;

    8092:   PetscFunctionBegin;
    8093:   // The code for block size extraction does not support an unsorted IS
    8094:   if (flg) PetscCall(ISSorted(isrow, &flg));
    8095:   // We don't support originally off-diagonal blocks
    8096:   if (flg) {
    8097:     PetscCall(MatGetOwnershipRange(A, &rStart, &rEnd));
    8098:     PetscCall(ISGetLocalSize(isrow, &n));
    8099:     PetscCall(ISGetIndices(isrow, &rows));
    8100:     for (PetscInt i = 0; i < n && flg; ++i) {
    8101:       if (rows[i] < rStart || rows[i] >= rEnd) flg = PETSC_FALSE;
    8102:     }
    8103:     PetscCall(ISRestoreIndices(isrow, &rows));
    8104:   }
    8105:   // quiet return if we can't extract block size
    8106:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &flg, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)subA)));
    8107:   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);

    8109:   // extract block sizes
    8110:   PetscCall(ISGetIndices(isrow, &rows));
    8111:   for (PetscInt b = 0, gr = rStart, i = 0; b < A->nblocks; ++b) {
    8112:     PetscBool occupied = PETSC_FALSE;

    8114:     for (PetscInt br = 0; br < A->bsizes[b]; ++br) {
    8115:       const PetscInt row = gr + br;

    8117:       if (i == n) break;
    8118:       if (rows[i] == row) {
    8119:         occupied = PETSC_TRUE;
    8120:         ++i;
    8121:       }
    8122:       while (i < n && rows[i] < row) ++i;
    8123:     }
    8124:     gr += A->bsizes[b];
    8125:     if (occupied) ++Nb;
    8126:   }
    8127:   subA->nblocks = Nb;
    8128:   PetscCall(PetscFree(subA->bsizes));
    8129:   PetscCall(PetscMalloc1(subA->nblocks, &subA->bsizes));
    8130:   PetscInt sb = 0;
    8131:   for (PetscInt b = 0, gr = rStart, i = 0; b < A->nblocks; ++b) {
    8132:     if (sb < subA->nblocks) subA->bsizes[sb] = 0;
    8133:     for (PetscInt br = 0; br < A->bsizes[b]; ++br) {
    8134:       const PetscInt row = gr + br;

    8136:       if (i == n) break;
    8137:       if (rows[i] == row) {
    8138:         ++subA->bsizes[sb];
    8139:         ++i;
    8140:       }
    8141:       while (i < n && rows[i] < row) ++i;
    8142:     }
    8143:     gr += A->bsizes[b];
    8144:     if (sb < subA->nblocks && subA->bsizes[sb]) ++sb;
    8145:   }
    8146:   PetscCheck(sb == subA->nblocks, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of blocks %" PetscInt_FMT " != %" PetscInt_FMT, sb, subA->nblocks);
    8147:   PetscInt nlocal, ncnt = 0;
    8148:   PetscCall(MatGetLocalSize(subA, &nlocal, NULL));
    8149:   PetscCheck(subA->nblocks >= 0 && subA->nblocks <= nlocal, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number of local blocks %" PetscInt_FMT " is not in [0, %" PetscInt_FMT "]", subA->nblocks, nlocal);
    8150:   for (PetscInt i = 0; i < subA->nblocks; i++) ncnt += subA->bsizes[i];
    8151:   PetscCheck(ncnt == nlocal, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Sum of local block sizes %" PetscInt_FMT " does not equal local size of matrix %" PetscInt_FMT, ncnt, nlocal);
    8152:   PetscCall(ISRestoreIndices(isrow, &rows));
    8153:   PetscFunctionReturn(PETSC_SUCCESS);
    8154: }

    8156: /*@
    8157:   MatSetBlockSizes - Sets the matrix block row and column sizes.

    8159:   Logically Collective

    8161:   Input Parameters:
    8162: + mat - the matrix
    8163: . rbs - row block size
    8164: - cbs - column block size

    8166:   Level: intermediate

    8168:   Notes:
    8169:   Block row formats are `MATBAIJ` and  `MATSBAIJ`. These formats ALWAYS have square block storage in the matrix.
    8170:   If you pass a different block size for the columns than the rows, the row block size determines the square block storage.
    8171:   This must be called before `MatSetUp()` or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later.

    8173:   For `MATAIJ` matrix this function can be called at a later stage, provided that the specified block sizes
    8174:   are compatible with the matrix local sizes.

    8176:   The row and column block size determine the blocksize of the "row" and "column" vectors returned by `MatCreateVecs()`.

    8178: .seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSize()`, `MatGetBlockSizes()`
    8179: @*/
    8180: PetscErrorCode MatSetBlockSizes(Mat mat, PetscInt rbs, PetscInt cbs)
    8181: {
    8182:   PetscFunctionBegin;
    8186:   PetscTryTypeMethod(mat, setblocksizes, rbs, cbs);
    8187:   if (mat->rmap->refcnt) {
    8188:     ISLocalToGlobalMapping l2g  = NULL;
    8189:     PetscLayout            nmap = NULL;

    8191:     PetscCall(PetscLayoutDuplicate(mat->rmap, &nmap));
    8192:     if (mat->rmap->mapping) PetscCall(ISLocalToGlobalMappingDuplicate(mat->rmap->mapping, &l2g));
    8193:     PetscCall(PetscLayoutDestroy(&mat->rmap));
    8194:     mat->rmap          = nmap;
    8195:     mat->rmap->mapping = l2g;
    8196:   }
    8197:   if (mat->cmap->refcnt) {
    8198:     ISLocalToGlobalMapping l2g  = NULL;
    8199:     PetscLayout            nmap = NULL;

    8201:     PetscCall(PetscLayoutDuplicate(mat->cmap, &nmap));
    8202:     if (mat->cmap->mapping) PetscCall(ISLocalToGlobalMappingDuplicate(mat->cmap->mapping, &l2g));
    8203:     PetscCall(PetscLayoutDestroy(&mat->cmap));
    8204:     mat->cmap          = nmap;
    8205:     mat->cmap->mapping = l2g;
    8206:   }
    8207:   PetscCall(PetscLayoutSetBlockSize(mat->rmap, rbs));
    8208:   PetscCall(PetscLayoutSetBlockSize(mat->cmap, cbs));
    8209:   PetscFunctionReturn(PETSC_SUCCESS);
    8210: }

    8212: /*@
    8213:   MatSetBlockSizesFromMats - Sets the matrix block row and column sizes to match a pair of matrices

    8215:   Logically Collective

    8217:   Input Parameters:
    8218: + mat     - the matrix
    8219: . fromRow - matrix from which to copy row block size
    8220: - fromCol - matrix from which to copy column block size (can be same as `fromRow`)

    8222:   Level: developer

    8224: .seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSizes()`
    8225: @*/
    8226: PetscErrorCode MatSetBlockSizesFromMats(Mat mat, Mat fromRow, Mat fromCol)
    8227: {
    8228:   PetscFunctionBegin;
    8232:   PetscTryTypeMethod(mat, setblocksizes, fromRow->rmap->bs, fromCol->cmap->bs);
    8233:   PetscCall(PetscLayoutSetBlockSize(mat->rmap, fromRow->rmap->bs));
    8234:   PetscCall(PetscLayoutSetBlockSize(mat->cmap, fromCol->cmap->bs));
    8235:   PetscFunctionReturn(PETSC_SUCCESS);
    8236: }

    8238: /*@
    8239:   MatResidual - Default routine to calculate the residual r = b - Ax

    8241:   Collective

    8243:   Input Parameters:
    8244: + mat - the matrix
    8245: . b   - the right-hand-side
    8246: - x   - the approximate solution

    8248:   Output Parameter:
    8249: . r - location to store the residual

    8251:   Level: developer

    8253: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatMultAdd()`, `PCMGSetResidual()`
    8254: @*/
    8255: PetscErrorCode MatResidual(Mat mat, Vec b, Vec x, Vec r)
    8256: {
    8257:   PetscFunctionBegin;
    8263:   MatCheckPreallocated(mat, 1);
    8264:   PetscCall(PetscLogEventBegin(MAT_Residual, mat, 0, 0, 0));
    8265:   if (!mat->ops->residual) {
    8266:     PetscCall(MatMult(mat, x, r));
    8267:     PetscCall(VecAYPX(r, -1.0, b));
    8268:   } else {
    8269:     PetscUseTypeMethod(mat, residual, b, x, r);
    8270:   }
    8271:   PetscCall(PetscLogEventEnd(MAT_Residual, mat, 0, 0, 0));
    8272:   PetscFunctionReturn(PETSC_SUCCESS);
    8273: }

    8275: /*@C
    8276:   MatGetRowIJ - Returns the compressed row storage i and j indices for the local rows of a sparse matrix

    8278:   Collective

    8280:   Input Parameters:
    8281: + mat             - the matrix
    8282: . shift           - 0 or 1 indicating we want the indices starting at 0 or 1
    8283: . symmetric       - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be symmetrized
    8284: - inodecompressed - `PETSC_TRUE` or `PETSC_FALSE`  indicating if the nonzero structure of the
    8285:                  inodes or the nonzero elements is wanted. For `MATBAIJ` matrices the compressed version is
    8286:                  always used.

    8288:   Output Parameters:
    8289: + n    - number of local rows in the (possibly compressed) matrix, use `NULL` if not needed
    8290: . ia   - the row pointers; that is ia[0] = 0, ia[row] = ia[row-1] + number of elements in that row of the matrix, use `NULL` if not needed
    8291: . ja   - the column indices, use `NULL` if not needed
    8292: - done - indicates if the routine actually worked and returned appropriate ia[] and ja[] arrays; callers
    8293:            are responsible for handling the case when done == `PETSC_FALSE` and ia and ja are not set

    8295:   Level: developer

    8297:   Notes:
    8298:   You CANNOT change any of the ia[] or ja[] values.

    8300:   Use `MatRestoreRowIJ()` when you are finished accessing the ia[] and ja[] values.

    8302:   Fortran Notes:
    8303:   Use
    8304: .vb
    8305:     PetscInt, pointer :: ia(:),ja(:)
    8306:     call MatGetRowIJ(mat,shift,symmetric,inodecompressed,n,ia,ja,done,ierr)
    8307:     ! Access the ith and jth entries via ia(i) and ja(j)
    8308: .ve

    8310: .seealso: [](ch_matrices), `Mat`, `MATAIJ`, `MatGetColumnIJ()`, `MatRestoreRowIJ()`, `MatSeqAIJGetArray()`
    8311: @*/
    8312: PetscErrorCode MatGetRowIJ(Mat mat, PetscInt shift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    8313: {
    8314:   PetscFunctionBegin;
    8317:   if (n) PetscAssertPointer(n, 5);
    8318:   if (ia) PetscAssertPointer(ia, 6);
    8319:   if (ja) PetscAssertPointer(ja, 7);
    8320:   if (done) PetscAssertPointer(done, 8);
    8321:   MatCheckPreallocated(mat, 1);
    8322:   if (!mat->ops->getrowij && done) *done = PETSC_FALSE;
    8323:   else {
    8324:     if (done) *done = PETSC_TRUE;
    8325:     PetscCall(PetscLogEventBegin(MAT_GetRowIJ, mat, 0, 0, 0));
    8326:     PetscUseTypeMethod(mat, getrowij, shift, symmetric, inodecompressed, n, ia, ja, done);
    8327:     PetscCall(PetscLogEventEnd(MAT_GetRowIJ, mat, 0, 0, 0));
    8328:   }
    8329:   PetscFunctionReturn(PETSC_SUCCESS);
    8330: }

    8332: /*@C
    8333:   MatGetColumnIJ - Returns the compressed column storage i and j indices for sequential matrices.

    8335:   Collective

    8337:   Input Parameters:
    8338: + mat             - the matrix
    8339: . shift           - 1 or zero indicating we want the indices starting at 0 or 1
    8340: . symmetric       - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be
    8341:                 symmetrized
    8342: - inodecompressed - `PETSC_TRUE` or `PETSC_FALSE` indicating if the nonzero structure of the
    8343:                  inodes or the nonzero elements is wanted. For `MATBAIJ` matrices the compressed version is
    8344:                  always used.

    8346:   Output Parameters:
    8347: + n    - number of columns in the (possibly compressed) matrix
    8348: . ia   - the column pointers; that is ia[0] = 0, ia[col] = i[col-1] + number of elements in that col of the matrix
    8349: . ja   - the row indices
    8350: - done - `PETSC_TRUE` or `PETSC_FALSE`, indicating whether the values have been returned

    8352:   Level: developer

    8354: .seealso: [](ch_matrices), `Mat`, `MatGetRowIJ()`, `MatRestoreColumnIJ()`
    8355: @*/
    8356: PetscErrorCode MatGetColumnIJ(Mat mat, PetscInt shift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    8357: {
    8358:   PetscFunctionBegin;
    8361:   PetscAssertPointer(n, 5);
    8362:   if (ia) PetscAssertPointer(ia, 6);
    8363:   if (ja) PetscAssertPointer(ja, 7);
    8364:   PetscAssertPointer(done, 8);
    8365:   MatCheckPreallocated(mat, 1);
    8366:   if (!mat->ops->getcolumnij) *done = PETSC_FALSE;
    8367:   else {
    8368:     *done = PETSC_TRUE;
    8369:     PetscUseTypeMethod(mat, getcolumnij, shift, symmetric, inodecompressed, n, ia, ja, done);
    8370:   }
    8371:   PetscFunctionReturn(PETSC_SUCCESS);
    8372: }

    8374: /*@C
    8375:   MatRestoreRowIJ - Call after you are completed with the ia,ja indices obtained with `MatGetRowIJ()`.

    8377:   Collective

    8379:   Input Parameters:
    8380: + mat             - the matrix
    8381: . shift           - 1 or zero indicating we want the indices starting at 0 or 1
    8382: . symmetric       - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be symmetrized
    8383: . inodecompressed - `PETSC_TRUE` or `PETSC_FALSE` indicating if the nonzero structure of the
    8384:                     inodes or the nonzero elements is wanted. For `MATBAIJ` matrices the compressed version is
    8385:                     always used.
    8386: . n               - size of (possibly compressed) matrix
    8387: . ia              - the row pointers
    8388: - ja              - the column indices

    8390:   Output Parameter:
    8391: . done - `PETSC_TRUE` or `PETSC_FALSE` indicated that the values have been returned

    8393:   Level: developer

    8395:   Note:
    8396:   This routine zeros out `n`, `ia`, and `ja`. This is to prevent accidental
    8397:   us of the array after it has been restored. If you pass `NULL`, it will
    8398:   not zero the pointers.  Use of ia or ja after `MatRestoreRowIJ()` is invalid.

    8400: .seealso: [](ch_matrices), `Mat`, `MatGetRowIJ()`, `MatRestoreColumnIJ()`
    8401: @*/
    8402: PetscErrorCode MatRestoreRowIJ(Mat mat, PetscInt shift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    8403: {
    8404:   PetscFunctionBegin;
    8407:   if (ia) PetscAssertPointer(ia, 6);
    8408:   if (ja) PetscAssertPointer(ja, 7);
    8409:   if (done) PetscAssertPointer(done, 8);
    8410:   MatCheckPreallocated(mat, 1);

    8412:   if (!mat->ops->restorerowij && done) *done = PETSC_FALSE;
    8413:   else {
    8414:     if (done) *done = PETSC_TRUE;
    8415:     PetscUseTypeMethod(mat, restorerowij, shift, symmetric, inodecompressed, n, ia, ja, done);
    8416:     if (n) *n = 0;
    8417:     if (ia) *ia = NULL;
    8418:     if (ja) *ja = NULL;
    8419:   }
    8420:   PetscFunctionReturn(PETSC_SUCCESS);
    8421: }

    8423: /*@C
    8424:   MatRestoreColumnIJ - Call after you are completed with the ia,ja indices obtained with `MatGetColumnIJ()`.

    8426:   Collective

    8428:   Input Parameters:
    8429: + mat             - the matrix
    8430: . shift           - 1 or zero indicating we want the indices starting at 0 or 1
    8431: . symmetric       - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be symmetrized
    8432: - inodecompressed - `PETSC_TRUE` or `PETSC_FALSE` indicating if the nonzero structure of the
    8433:                     inodes or the nonzero elements is wanted. For `MATBAIJ` matrices the compressed version is
    8434:                     always used.

    8436:   Output Parameters:
    8437: + n    - size of (possibly compressed) matrix
    8438: . ia   - the column pointers
    8439: . ja   - the row indices
    8440: - done - `PETSC_TRUE` or `PETSC_FALSE` indicated that the values have been returned

    8442:   Level: developer

    8444: .seealso: [](ch_matrices), `Mat`, `MatGetColumnIJ()`, `MatRestoreRowIJ()`
    8445: @*/
    8446: PetscErrorCode MatRestoreColumnIJ(Mat mat, PetscInt shift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    8447: {
    8448:   PetscFunctionBegin;
    8451:   if (ia) PetscAssertPointer(ia, 6);
    8452:   if (ja) PetscAssertPointer(ja, 7);
    8453:   PetscAssertPointer(done, 8);
    8454:   MatCheckPreallocated(mat, 1);

    8456:   if (!mat->ops->restorecolumnij) *done = PETSC_FALSE;
    8457:   else {
    8458:     *done = PETSC_TRUE;
    8459:     PetscUseTypeMethod(mat, restorecolumnij, shift, symmetric, inodecompressed, n, ia, ja, done);
    8460:     if (n) *n = 0;
    8461:     if (ia) *ia = NULL;
    8462:     if (ja) *ja = NULL;
    8463:   }
    8464:   PetscFunctionReturn(PETSC_SUCCESS);
    8465: }

    8467: /*@
    8468:   MatColoringPatch - Used inside matrix coloring routines that use `MatGetRowIJ()` and/or
    8469:   `MatGetColumnIJ()`.

    8471:   Collective

    8473:   Input Parameters:
    8474: + mat        - the matrix
    8475: . ncolors    - maximum color value
    8476: . n          - number of entries in colorarray
    8477: - colorarray - array indicating color for each column

    8479:   Output Parameter:
    8480: . iscoloring - coloring generated using colorarray information

    8482:   Level: developer

    8484: .seealso: [](ch_matrices), `Mat`, `MatGetRowIJ()`, `MatGetColumnIJ()`
    8485: @*/
    8486: PetscErrorCode MatColoringPatch(Mat mat, PetscInt ncolors, PetscInt n, ISColoringValue colorarray[], ISColoring *iscoloring)
    8487: {
    8488:   PetscFunctionBegin;
    8491:   PetscAssertPointer(colorarray, 4);
    8492:   PetscAssertPointer(iscoloring, 5);
    8493:   MatCheckPreallocated(mat, 1);

    8495:   if (!mat->ops->coloringpatch) {
    8496:     PetscCall(ISColoringCreate(PetscObjectComm((PetscObject)mat), ncolors, n, colorarray, PETSC_OWN_POINTER, iscoloring));
    8497:   } else {
    8498:     PetscUseTypeMethod(mat, coloringpatch, ncolors, n, colorarray, iscoloring);
    8499:   }
    8500:   PetscFunctionReturn(PETSC_SUCCESS);
    8501: }

    8503: /*@
    8504:   MatSetUnfactored - Resets a factored matrix to be treated as unfactored.

    8506:   Logically Collective

    8508:   Input Parameter:
    8509: . mat - the factored matrix to be reset

    8511:   Level: developer

    8513:   Notes:
    8514:   This routine should be used only with factored matrices formed by in-place
    8515:   factorization via ILU(0) (or by in-place LU factorization for the `MATSEQDENSE`
    8516:   format).  This option can save memory, for example, when solving nonlinear
    8517:   systems with a matrix-free Newton-Krylov method and a matrix-based, in-place
    8518:   ILU(0) preconditioner.

    8520:   One can specify in-place ILU(0) factorization by calling
    8521: .vb
    8522:      PCType(pc,PCILU);
    8523:      PCFactorSeUseInPlace(pc);
    8524: .ve
    8525:   or by using the options -pc_type ilu -pc_factor_in_place

    8527:   In-place factorization ILU(0) can also be used as a local
    8528:   solver for the blocks within the block Jacobi or additive Schwarz
    8529:   methods (runtime option: -sub_pc_factor_in_place).  See Users-Manual: ch_pc
    8530:   for details on setting local solver options.

    8532:   Most users should employ the `KSP` interface for linear solvers
    8533:   instead of working directly with matrix algebra routines such as this.
    8534:   See, e.g., `KSPCreate()`.

    8536: .seealso: [](ch_matrices), `Mat`, `PCFactorSetUseInPlace()`, `PCFactorGetUseInPlace()`
    8537: @*/
    8538: PetscErrorCode MatSetUnfactored(Mat mat)
    8539: {
    8540:   PetscFunctionBegin;
    8543:   MatCheckPreallocated(mat, 1);
    8544:   mat->factortype = MAT_FACTOR_NONE;
    8545:   if (!mat->ops->setunfactored) PetscFunctionReturn(PETSC_SUCCESS);
    8546:   PetscUseTypeMethod(mat, setunfactored);
    8547:   PetscFunctionReturn(PETSC_SUCCESS);
    8548: }

    8550: /*@
    8551:   MatCreateSubMatrix - Gets a single submatrix on the same number of processors
    8552:   as the original matrix.

    8554:   Collective

    8556:   Input Parameters:
    8557: + mat   - the original matrix
    8558: . isrow - parallel `IS` containing the rows this processor should obtain
    8559: . 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.
    8560: - cll   - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    8562:   Output Parameter:
    8563: . newmat - the new submatrix, of the same type as the original matrix

    8565:   Level: advanced

    8567:   Notes:
    8568:   The submatrix will be able to be multiplied with vectors using the same layout as `iscol`.

    8570:   Some matrix types place restrictions on the row and column indices, such
    8571:   as that they be sorted or that they be equal to each other. For `MATBAIJ` and `MATSBAIJ` matrices the indices must include all rows/columns of a block;
    8572:   for example, if the block size is 3 one cannot select the 0 and 2 rows without selecting the 1 row.

    8574:   The index sets may not have duplicate entries.

    8576:   The first time this is called you should use a cll of `MAT_INITIAL_MATRIX`,
    8577:   the `MatCreateSubMatrix()` routine will create the newmat for you. Any additional calls
    8578:   to this routine with a mat of the same nonzero structure and with a call of `MAT_REUSE_MATRIX`
    8579:   will reuse the matrix generated the first time.  You should call `MatDestroy()` on `newmat` when
    8580:   you are finished using it.

    8582:   The communicator of the newly obtained matrix is ALWAYS the same as the communicator of
    8583:   the input matrix.

    8585:   If `iscol` is `NULL` then all columns are obtained (not supported in Fortran).

    8587:   If `isrow` and `iscol` have a nontrivial block-size, then the resulting matrix has this block-size as well. This feature
    8588:   is used by `PCFIELDSPLIT` to allow easy nesting of its use.

    8590:   Example usage:
    8591:   Consider the following 8x8 matrix with 34 non-zero values, that is
    8592:   assembled across 3 processors. Let's assume that proc0 owns 3 rows,
    8593:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    8594:   as follows
    8595: .vb
    8596:             1  2  0  |  0  3  0  |  0  4
    8597:     Proc0   0  5  6  |  7  0  0  |  8  0
    8598:             9  0 10  | 11  0  0  | 12  0
    8599:     -------------------------------------
    8600:            13  0 14  | 15 16 17  |  0  0
    8601:     Proc1   0 18  0  | 19 20 21  |  0  0
    8602:             0  0  0  | 22 23  0  | 24  0
    8603:     -------------------------------------
    8604:     Proc2  25 26 27  |  0  0 28  | 29  0
    8605:            30  0  0  | 31 32 33  |  0 34
    8606: .ve

    8608:   Suppose `isrow` = [0 1 | 4 | 6 7] and `iscol` = [1 2 | 3 4 5 | 6].  The resulting submatrix is

    8610: .vb
    8611:             2  0  |  0  3  0  |  0
    8612:     Proc0   5  6  |  7  0  0  |  8
    8613:     -------------------------------
    8614:     Proc1  18  0  | 19 20 21  |  0
    8615:     -------------------------------
    8616:     Proc2  26 27  |  0  0 28  | 29
    8617:             0  0  | 31 32 33  |  0
    8618: .ve

    8620: .seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatCreateSubMatricesMPI()`, `MatCreateSubMatrixVirtual()`, `MatSubMatrixVirtualUpdate()`
    8621: @*/
    8622: PetscErrorCode MatCreateSubMatrix(Mat mat, IS isrow, IS iscol, MatReuse cll, Mat *newmat)
    8623: {
    8624:   PetscMPIInt size;
    8625:   Mat        *local;
    8626:   IS          iscoltmp;
    8627:   PetscBool   flg;

    8629:   PetscFunctionBegin;
    8633:   PetscAssertPointer(newmat, 5);
    8636:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    8637:   PetscCheck(cll != MAT_IGNORE_MATRIX, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot use MAT_IGNORE_MATRIX");
    8638:   PetscCheck(cll != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot use MAT_INPLACE_MATRIX");

    8640:   MatCheckPreallocated(mat, 1);
    8641:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));

    8643:   if (!iscol || isrow == iscol) {
    8644:     PetscBool   stride;
    8645:     PetscMPIInt grabentirematrix = 0, grab;
    8646:     PetscCall(PetscObjectTypeCompare((PetscObject)isrow, ISSTRIDE, &stride));
    8647:     if (stride) {
    8648:       PetscInt first, step, n, rstart, rend;
    8649:       PetscCall(ISStrideGetInfo(isrow, &first, &step));
    8650:       if (step == 1) {
    8651:         PetscCall(MatGetOwnershipRange(mat, &rstart, &rend));
    8652:         if (rstart == first) {
    8653:           PetscCall(ISGetLocalSize(isrow, &n));
    8654:           if (n == rend - rstart) grabentirematrix = 1;
    8655:         }
    8656:       }
    8657:     }
    8658:     PetscCallMPI(MPIU_Allreduce(&grabentirematrix, &grab, 1, MPI_INT, MPI_MIN, PetscObjectComm((PetscObject)mat)));
    8659:     if (grab) {
    8660:       PetscCall(PetscInfo(mat, "Getting entire matrix as submatrix\n"));
    8661:       if (cll == MAT_INITIAL_MATRIX) {
    8662:         *newmat = mat;
    8663:         PetscCall(PetscObjectReference((PetscObject)mat));
    8664:       }
    8665:       PetscFunctionReturn(PETSC_SUCCESS);
    8666:     }
    8667:   }

    8669:   if (!iscol) {
    8670:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), mat->cmap->n, mat->cmap->rstart, 1, &iscoltmp));
    8671:   } else {
    8672:     iscoltmp = iscol;
    8673:   }

    8675:   /* if original matrix is on just one processor then use submatrix generated */
    8676:   if (mat->ops->createsubmatrices && !mat->ops->createsubmatrix && size == 1 && cll == MAT_REUSE_MATRIX) {
    8677:     PetscCall(MatCreateSubMatrices(mat, 1, &isrow, &iscoltmp, MAT_REUSE_MATRIX, &newmat));
    8678:     goto setproperties;
    8679:   } else if (mat->ops->createsubmatrices && !mat->ops->createsubmatrix && size == 1) {
    8680:     PetscCall(MatCreateSubMatrices(mat, 1, &isrow, &iscoltmp, MAT_INITIAL_MATRIX, &local));
    8681:     *newmat = *local;
    8682:     PetscCall(PetscFree(local));
    8683:     goto setproperties;
    8684:   } else if (!mat->ops->createsubmatrix) {
    8685:     /* Create a new matrix type that implements the operation using the full matrix */
    8686:     PetscCall(PetscLogEventBegin(MAT_CreateSubMat, mat, 0, 0, 0));
    8687:     switch (cll) {
    8688:     case MAT_INITIAL_MATRIX:
    8689:       PetscCall(MatCreateSubMatrixVirtual(mat, isrow, iscoltmp, newmat));
    8690:       break;
    8691:     case MAT_REUSE_MATRIX:
    8692:       PetscCall(MatSubMatrixVirtualUpdate(*newmat, mat, isrow, iscoltmp));
    8693:       break;
    8694:     default:
    8695:       SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Invalid MatReuse, must be either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX");
    8696:     }
    8697:     PetscCall(PetscLogEventEnd(MAT_CreateSubMat, mat, 0, 0, 0));
    8698:     goto setproperties;
    8699:   }

    8701:   PetscCall(PetscLogEventBegin(MAT_CreateSubMat, mat, 0, 0, 0));
    8702:   PetscUseTypeMethod(mat, createsubmatrix, isrow, iscoltmp, cll, newmat);
    8703:   PetscCall(PetscLogEventEnd(MAT_CreateSubMat, mat, 0, 0, 0));

    8705: setproperties:
    8706:   if ((*newmat)->symmetric == PETSC_BOOL3_UNKNOWN && (*newmat)->structurally_symmetric == PETSC_BOOL3_UNKNOWN && (*newmat)->spd == PETSC_BOOL3_UNKNOWN && (*newmat)->hermitian == PETSC_BOOL3_UNKNOWN) {
    8707:     PetscCall(ISEqualUnsorted(isrow, iscoltmp, &flg));
    8708:     if (flg) PetscCall(MatPropagateSymmetryOptions(mat, *newmat));
    8709:   }
    8710:   if (!iscol) PetscCall(ISDestroy(&iscoltmp));
    8711:   if (*newmat && cll == MAT_INITIAL_MATRIX) PetscCall(PetscObjectStateIncrease((PetscObject)*newmat));
    8712:   if (!iscol || isrow == iscol) PetscCall(MatSelectVariableBlockSizes(*newmat, mat, isrow));
    8713:   PetscFunctionReturn(PETSC_SUCCESS);
    8714: }

    8716: /*@
    8717:   MatPropagateSymmetryOptions - Propagates symmetry options set on a matrix to another matrix

    8719:   Not Collective

    8721:   Input Parameters:
    8722: + A - the matrix we wish to propagate options from
    8723: - B - the matrix we wish to propagate options to

    8725:   Level: beginner

    8727:   Note:
    8728:   Propagates the options associated to `MAT_SYMMETRY_ETERNAL`, `MAT_STRUCTURALLY_SYMMETRIC`, `MAT_HERMITIAN`, `MAT_SPD`, `MAT_SYMMETRIC`, and `MAT_STRUCTURAL_SYMMETRY_ETERNAL`

    8730: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatIsSymmetricKnown()`, `MatIsSPDKnown()`, `MatIsHermitianKnown()`, `MatIsStructurallySymmetricKnown()`
    8731: @*/
    8732: PetscErrorCode MatPropagateSymmetryOptions(Mat A, Mat B)
    8733: {
    8734:   PetscFunctionBegin;
    8737:   B->symmetry_eternal            = A->symmetry_eternal;
    8738:   B->structural_symmetry_eternal = A->structural_symmetry_eternal;
    8739:   B->symmetric                   = A->symmetric;
    8740:   B->structurally_symmetric      = A->structurally_symmetric;
    8741:   B->spd                         = A->spd;
    8742:   B->hermitian                   = A->hermitian;
    8743:   PetscFunctionReturn(PETSC_SUCCESS);
    8744: }

    8746: /*@
    8747:   MatStashSetInitialSize - sets the sizes of the matrix stash, that is
    8748:   used during the assembly process to store values that belong to
    8749:   other processors.

    8751:   Not Collective

    8753:   Input Parameters:
    8754: + mat   - the matrix
    8755: . size  - the initial size of the stash.
    8756: - bsize - the initial size of the block-stash(if used).

    8758:   Options Database Keys:
    8759: + -matstash_initial_size size or size0,size1,...,sizep-1            - set initial size
    8760: - -matstash_block_initial_size bsize  or bsize0,bsize1,...,bsizep-1 - set initial block size

    8762:   Level: intermediate

    8764:   Notes:
    8765:   The block-stash is used for values set with `MatSetValuesBlocked()` while
    8766:   the stash is used for values set with `MatSetValues()`

    8768:   Run with the option -info and look for output of the form
    8769:   MatAssemblyBegin_MPIXXX:Stash has MM entries, uses nn mallocs.
    8770:   to determine the appropriate value, MM, to use for size and
    8771:   MatAssemblyBegin_MPIXXX:Block-Stash has BMM entries, uses nn mallocs.
    8772:   to determine the value, BMM to use for bsize

    8774: .seealso: [](ch_matrices), `MatAssemblyBegin()`, `MatAssemblyEnd()`, `Mat`, `MatStashGetInfo()`
    8775: @*/
    8776: PetscErrorCode MatStashSetInitialSize(Mat mat, PetscInt size, PetscInt bsize)
    8777: {
    8778:   PetscFunctionBegin;
    8781:   PetscCall(MatStashSetInitialSize_Private(&mat->stash, size));
    8782:   PetscCall(MatStashSetInitialSize_Private(&mat->bstash, bsize));
    8783:   PetscFunctionReturn(PETSC_SUCCESS);
    8784: }

    8786: /*@
    8787:   MatInterpolateAdd - $w = y + A*x$ or $A^T*x$ depending on the shape of
    8788:   the matrix

    8790:   Neighbor-wise Collective

    8792:   Input Parameters:
    8793: + A - the matrix
    8794: . x - the vector to be multiplied by the interpolation operator
    8795: - y - the vector to be added to the result

    8797:   Output Parameter:
    8798: . w - the resulting vector

    8800:   Level: intermediate

    8802:   Notes:
    8803:   `w` may be the same vector as `y`.

    8805:   This allows one to use either the restriction or interpolation (its transpose)
    8806:   matrix to do the interpolation

    8808: .seealso: [](ch_matrices), `Mat`, `MatMultAdd()`, `MatMultTransposeAdd()`, `MatRestrict()`, `PCMG`
    8809: @*/
    8810: PetscErrorCode MatInterpolateAdd(Mat A, Vec x, Vec y, Vec w)
    8811: {
    8812:   PetscInt M, N, Ny;

    8814:   PetscFunctionBegin;
    8819:   PetscCall(MatGetSize(A, &M, &N));
    8820:   PetscCall(VecGetSize(y, &Ny));
    8821:   if (M == Ny) PetscCall(MatMultAdd(A, x, y, w));
    8822:   else PetscCall(MatMultTransposeAdd(A, x, y, w));
    8823:   PetscFunctionReturn(PETSC_SUCCESS);
    8824: }

    8826: /*@
    8827:   MatInterpolate - $y = A*x$ or $A^T*x$ depending on the shape of
    8828:   the matrix

    8830:   Neighbor-wise Collective

    8832:   Input Parameters:
    8833: + A - the matrix
    8834: - x - the vector to be interpolated

    8836:   Output Parameter:
    8837: . y - the resulting vector

    8839:   Level: intermediate

    8841:   Note:
    8842:   This allows one to use either the restriction or interpolation (its transpose)
    8843:   matrix to do the interpolation

    8845: .seealso: [](ch_matrices), `Mat`, `MatMultAdd()`, `MatMultTransposeAdd()`, `MatRestrict()`, `PCMG`
    8846: @*/
    8847: PetscErrorCode MatInterpolate(Mat A, Vec x, Vec y)
    8848: {
    8849:   PetscInt M, N, Ny;

    8851:   PetscFunctionBegin;
    8855:   PetscCall(MatGetSize(A, &M, &N));
    8856:   PetscCall(VecGetSize(y, &Ny));
    8857:   if (M == Ny) PetscCall(MatMult(A, x, y));
    8858:   else PetscCall(MatMultTranspose(A, x, y));
    8859:   PetscFunctionReturn(PETSC_SUCCESS);
    8860: }

    8862: /*@
    8863:   MatRestrict - $y = A*x$ or $A^T*x$

    8865:   Neighbor-wise Collective

    8867:   Input Parameters:
    8868: + A - the matrix
    8869: - x - the vector to be restricted

    8871:   Output Parameter:
    8872: . y - the resulting vector

    8874:   Level: intermediate

    8876:   Note:
    8877:   This allows one to use either the restriction or interpolation (its transpose)
    8878:   matrix to do the restriction

    8880: .seealso: [](ch_matrices), `Mat`, `MatMultAdd()`, `MatMultTransposeAdd()`, `MatInterpolate()`, `PCMG`
    8881: @*/
    8882: PetscErrorCode MatRestrict(Mat A, Vec x, Vec y)
    8883: {
    8884:   PetscInt M, N, Nx;

    8886:   PetscFunctionBegin;
    8890:   PetscCall(MatGetSize(A, &M, &N));
    8891:   PetscCall(VecGetSize(x, &Nx));
    8892:   if (M == Nx) PetscCall(MatMultTranspose(A, x, y));
    8893:   else PetscCall(MatMult(A, x, y));
    8894:   PetscFunctionReturn(PETSC_SUCCESS);
    8895: }

    8897: /*@
    8898:   MatMatInterpolateAdd - $Y = W + A*X$ or $W + A^T*X$ depending on the shape of `A`

    8900:   Neighbor-wise Collective

    8902:   Input Parameters:
    8903: + A - the matrix
    8904: . x - the input dense matrix to be multiplied
    8905: - w - the input dense matrix to be added to the result

    8907:   Output Parameter:
    8908: . y - the output dense matrix

    8910:   Level: intermediate

    8912:   Note:
    8913:   This allows one to use either the restriction or interpolation (its transpose)
    8914:   matrix to do the interpolation. `y` matrix can be reused if already created with the proper sizes,
    8915:   otherwise it will be recreated. `y` must be initialized to `NULL` if not supplied.

    8917: .seealso: [](ch_matrices), `Mat`, `MatInterpolateAdd()`, `MatMatInterpolate()`, `MatMatRestrict()`, `PCMG`
    8918: @*/
    8919: PetscErrorCode MatMatInterpolateAdd(Mat A, Mat x, Mat w, Mat *y)
    8920: {
    8921:   PetscInt  M, N, Mx, Nx, Mo, My = 0, Ny = 0;
    8922:   PetscBool trans = PETSC_TRUE;
    8923:   MatReuse  reuse = MAT_INITIAL_MATRIX;

    8925:   PetscFunctionBegin;
    8931:   PetscCall(MatGetSize(A, &M, &N));
    8932:   PetscCall(MatGetSize(x, &Mx, &Nx));
    8933:   if (N == Mx) trans = PETSC_FALSE;
    8934:   else PetscCheck(M == Mx, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Size mismatch: A %" PetscInt_FMT "x%" PetscInt_FMT ", X %" PetscInt_FMT "x%" PetscInt_FMT, M, N, Mx, Nx);
    8935:   Mo = trans ? N : M;
    8936:   if (*y) {
    8937:     PetscCall(MatGetSize(*y, &My, &Ny));
    8938:     if (Mo == My && Nx == Ny) reuse = MAT_REUSE_MATRIX;
    8939:     else {
    8940:       PetscCheck(w || *y != w, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot reuse y and w, size mismatch: A %" PetscInt_FMT "x%" PetscInt_FMT ", X %" PetscInt_FMT "x%" PetscInt_FMT ", Y %" PetscInt_FMT "x%" PetscInt_FMT, M, N, Mx, Nx, My, Ny);
    8941:       PetscCall(MatDestroy(y));
    8942:     }
    8943:   }

    8945:   if (w && *y == w) { /* this is to minimize changes in PCMG */
    8946:     PetscBool flg;

    8948:     PetscCall(PetscObjectQuery((PetscObject)*y, "__MatMatIntAdd_w", (PetscObject *)&w));
    8949:     if (w) {
    8950:       PetscInt My, Ny, Mw, Nw;

    8952:       PetscCall(PetscObjectTypeCompare((PetscObject)*y, ((PetscObject)w)->type_name, &flg));
    8953:       PetscCall(MatGetSize(*y, &My, &Ny));
    8954:       PetscCall(MatGetSize(w, &Mw, &Nw));
    8955:       if (!flg || My != Mw || Ny != Nw) w = NULL;
    8956:     }
    8957:     if (!w) {
    8958:       PetscCall(MatDuplicate(*y, MAT_COPY_VALUES, &w));
    8959:       PetscCall(PetscObjectCompose((PetscObject)*y, "__MatMatIntAdd_w", (PetscObject)w));
    8960:       PetscCall(PetscObjectDereference((PetscObject)w));
    8961:     } else PetscCall(MatCopy(*y, w, UNKNOWN_NONZERO_PATTERN));
    8962:   }
    8963:   if (!trans) PetscCall(MatMatMult(A, x, reuse, PETSC_DETERMINE, y));
    8964:   else PetscCall(MatTransposeMatMult(A, x, reuse, PETSC_DETERMINE, y));
    8965:   if (w) PetscCall(MatAXPY(*y, 1.0, w, UNKNOWN_NONZERO_PATTERN));
    8966:   PetscFunctionReturn(PETSC_SUCCESS);
    8967: }

    8969: /*@
    8970:   MatMatInterpolate - $Y = A*X$ or $A^T*X$ depending on the shape of `A`

    8972:   Neighbor-wise Collective

    8974:   Input Parameters:
    8975: + A - the matrix
    8976: - x - the input dense matrix

    8978:   Output Parameter:
    8979: . y - the output dense matrix

    8981:   Level: intermediate

    8983:   Note:
    8984:   This allows one to use either the restriction or interpolation (its transpose)
    8985:   matrix to do the interpolation. `y` matrix can be reused if already created with the proper sizes,
    8986:   otherwise it will be recreated. `y` must be initialized to `NULL` if not supplied.

    8988: .seealso: [](ch_matrices), `Mat`, `MatInterpolate()`, `MatRestrict()`, `MatMatRestrict()`, `PCMG`
    8989: @*/
    8990: PetscErrorCode MatMatInterpolate(Mat A, Mat x, Mat *y)
    8991: {
    8992:   PetscFunctionBegin;
    8993:   PetscCall(MatMatInterpolateAdd(A, x, NULL, y));
    8994:   PetscFunctionReturn(PETSC_SUCCESS);
    8995: }

    8997: /*@
    8998:   MatMatRestrict - $Y = A*X$ or $A^T*X$ depending on the shape of `A`

    9000:   Neighbor-wise Collective

    9002:   Input Parameters:
    9003: + A - the matrix
    9004: - x - the input dense matrix

    9006:   Output Parameter:
    9007: . y - the output dense matrix

    9009:   Level: intermediate

    9011:   Note:
    9012:   This allows one to use either the restriction or interpolation (its transpose)
    9013:   matrix to do the restriction. `y` matrix can be reused if already created with the proper sizes,
    9014:   otherwise it will be recreated. `y` must be initialized to `NULL` if not supplied.

    9016: .seealso: [](ch_matrices), `Mat`, `MatRestrict()`, `MatInterpolate()`, `MatMatInterpolate()`, `PCMG`
    9017: @*/
    9018: PetscErrorCode MatMatRestrict(Mat A, Mat x, Mat *y)
    9019: {
    9020:   PetscFunctionBegin;
    9021:   PetscCall(MatMatInterpolateAdd(A, x, NULL, y));
    9022:   PetscFunctionReturn(PETSC_SUCCESS);
    9023: }

    9025: /*@
    9026:   MatGetNullSpace - retrieves the null space of a matrix.

    9028:   Logically Collective

    9030:   Input Parameters:
    9031: + mat    - the matrix
    9032: - nullsp - the null space object

    9034:   Level: developer

    9036: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatSetNullSpace()`, `MatNullSpace`
    9037: @*/
    9038: PetscErrorCode MatGetNullSpace(Mat mat, MatNullSpace *nullsp)
    9039: {
    9040:   PetscFunctionBegin;
    9042:   PetscAssertPointer(nullsp, 2);
    9043:   *nullsp = (mat->symmetric == PETSC_BOOL3_TRUE && !mat->nullsp) ? mat->transnullsp : mat->nullsp;
    9044:   PetscFunctionReturn(PETSC_SUCCESS);
    9045: }

    9047: /*@C
    9048:   MatGetNullSpaces - gets the null spaces, transpose null spaces, and near null spaces from an array of matrices

    9050:   Logically Collective

    9052:   Input Parameters:
    9053: + n   - the number of matrices
    9054: - mat - the array of matrices

    9056:   Output Parameters:
    9057: . nullsp - an array of null spaces, `NULL` for each matrix that does not have a null space, length 3 * `n`

    9059:   Level: developer

    9061:   Note:
    9062:   Call `MatRestoreNullspaces()` to provide these to another array of matrices

    9064: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatSetTransposeNullSpace()`, `MatGetTransposeNullSpace()`,
    9065:           `MatNullSpaceRemove()`, `MatRestoreNullSpaces()`
    9066: @*/
    9067: PetscErrorCode MatGetNullSpaces(PetscInt n, Mat mat[], MatNullSpace *nullsp[])
    9068: {
    9069:   PetscFunctionBegin;
    9070:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of matrices %" PetscInt_FMT " must be non-negative", n);
    9071:   PetscAssertPointer(mat, 2);
    9072:   PetscAssertPointer(nullsp, 3);

    9074:   PetscCall(PetscCalloc1(3 * n, nullsp));
    9075:   for (PetscInt i = 0; i < n; i++) {
    9077:     (*nullsp)[i] = mat[i]->nullsp;
    9078:     PetscCall(PetscObjectReference((PetscObject)(*nullsp)[i]));
    9079:     (*nullsp)[n + i] = mat[i]->nearnullsp;
    9080:     PetscCall(PetscObjectReference((PetscObject)(*nullsp)[n + i]));
    9081:     (*nullsp)[2 * n + i] = mat[i]->transnullsp;
    9082:     PetscCall(PetscObjectReference((PetscObject)(*nullsp)[2 * n + i]));
    9083:   }
    9084:   PetscFunctionReturn(PETSC_SUCCESS);
    9085: }

    9087: /*@C
    9088:   MatRestoreNullSpaces - sets the null spaces, transpose null spaces, and near null spaces obtained with `MatGetNullSpaces()` for an array of matrices

    9090:   Logically Collective

    9092:   Input Parameters:
    9093: + n      - the number of matrices
    9094: . mat    - the array of matrices
    9095: - nullsp - an array of null spaces

    9097:   Level: developer

    9099:   Note:
    9100:   Call `MatGetNullSpaces()` to create `nullsp`

    9102: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatSetTransposeNullSpace()`, `MatGetTransposeNullSpace()`,
    9103:           `MatNullSpaceRemove()`, `MatGetNullSpaces()`
    9104: @*/
    9105: PetscErrorCode MatRestoreNullSpaces(PetscInt n, Mat mat[], MatNullSpace *nullsp[])
    9106: {
    9107:   PetscFunctionBegin;
    9108:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of matrices %" PetscInt_FMT " must be non-negative", n);
    9109:   PetscAssertPointer(mat, 2);
    9110:   PetscAssertPointer(nullsp, 3);
    9111:   PetscAssertPointer(*nullsp, 3);

    9113:   for (PetscInt i = 0; i < n; i++) {
    9115:     PetscCall(MatSetNullSpace(mat[i], (*nullsp)[i]));
    9116:     PetscCall(PetscObjectDereference((PetscObject)(*nullsp)[i]));
    9117:     PetscCall(MatSetNearNullSpace(mat[i], (*nullsp)[n + i]));
    9118:     PetscCall(PetscObjectDereference((PetscObject)(*nullsp)[n + i]));
    9119:     PetscCall(MatSetTransposeNullSpace(mat[i], (*nullsp)[2 * n + i]));
    9120:     PetscCall(PetscObjectDereference((PetscObject)(*nullsp)[2 * n + i]));
    9121:   }
    9122:   PetscCall(PetscFree(*nullsp));
    9123:   PetscFunctionReturn(PETSC_SUCCESS);
    9124: }

    9126: /*@
    9127:   MatSetNullSpace - attaches a null space to a matrix.

    9129:   Logically Collective

    9131:   Input Parameters:
    9132: + mat    - the matrix
    9133: - nullsp - the null space object

    9135:   Level: advanced

    9137:   Notes:
    9138:   This null space is used by the `KSP` linear solvers to solve singular systems.

    9140:   Overwrites any previous null space that may have been attached. You can remove the null space from the matrix object by calling this routine with an nullsp of `NULL`

    9142:   For inconsistent singular systems (linear systems where the right-hand side is not in the range of the operator) the `KSP` residuals will not converge
    9143:   to zero but the linear system will still be solved in a least squares sense.

    9145:   The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
    9146:   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 $A$, $n(A)$, plus the range of $A^T$, $R(A^T)$.
    9147:   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
    9148:   $n(A^T))$ 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
    9149:   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 $n(A^T)$.
    9150:   This  $\hat{b}$ can be obtained by calling `MatNullSpaceRemove()` with the null space of the transpose of the matrix.

    9152:   If the matrix is known to be symmetric because it is an `MATSBAIJ` matrix or one has called
    9153:   `MatSetOption`(mat,`MAT_SYMMETRIC` or possibly `MAT_SYMMETRY_ETERNAL`,`PETSC_TRUE`); this
    9154:   routine also automatically calls `MatSetTransposeNullSpace()`.

    9156:   The user should call `MatNullSpaceDestroy()`.

    9158: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatSetTransposeNullSpace()`, `MatGetTransposeNullSpace()`, `MatNullSpaceRemove()`,
    9159:           `KSPSetPCSide()`
    9160: @*/
    9161: PetscErrorCode MatSetNullSpace(Mat mat, MatNullSpace nullsp)
    9162: {
    9163:   PetscFunctionBegin;
    9166:   PetscCall(PetscObjectReference((PetscObject)nullsp));
    9167:   PetscCall(MatNullSpaceDestroy(&mat->nullsp));
    9168:   mat->nullsp = nullsp;
    9169:   if (mat->symmetric == PETSC_BOOL3_TRUE) PetscCall(MatSetTransposeNullSpace(mat, nullsp));
    9170:   PetscFunctionReturn(PETSC_SUCCESS);
    9171: }

    9173: /*@
    9174:   MatGetTransposeNullSpace - retrieves the null space of the transpose of a matrix.

    9176:   Logically Collective

    9178:   Input Parameters:
    9179: + mat    - the matrix
    9180: - nullsp - the null space object

    9182:   Level: developer

    9184: .seealso: [](ch_matrices), `Mat`, `MatNullSpace`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatSetTransposeNullSpace()`, `MatSetNullSpace()`, `MatGetNullSpace()`
    9185: @*/
    9186: PetscErrorCode MatGetTransposeNullSpace(Mat mat, MatNullSpace *nullsp)
    9187: {
    9188:   PetscFunctionBegin;
    9191:   PetscAssertPointer(nullsp, 2);
    9192:   *nullsp = (mat->symmetric == PETSC_BOOL3_TRUE && !mat->transnullsp) ? mat->nullsp : mat->transnullsp;
    9193:   PetscFunctionReturn(PETSC_SUCCESS);
    9194: }

    9196: /*@
    9197:   MatSetTransposeNullSpace - attaches the null space of a transpose of a matrix to the matrix

    9199:   Logically Collective

    9201:   Input Parameters:
    9202: + mat    - the matrix
    9203: - nullsp - the null space object

    9205:   Level: advanced

    9207:   Notes:
    9208:   This allows solving singular linear systems defined by the transpose of the matrix using `KSP` solvers with left preconditioning.

    9210:   See `MatSetNullSpace()`

    9212: .seealso: [](ch_matrices), `Mat`, `MatNullSpace`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatSetNullSpace()`, `MatGetTransposeNullSpace()`, `MatNullSpaceRemove()`, `KSPSetPCSide()`
    9213: @*/
    9214: PetscErrorCode MatSetTransposeNullSpace(Mat mat, MatNullSpace nullsp)
    9215: {
    9216:   PetscFunctionBegin;
    9219:   PetscCall(PetscObjectReference((PetscObject)nullsp));
    9220:   PetscCall(MatNullSpaceDestroy(&mat->transnullsp));
    9221:   mat->transnullsp = nullsp;
    9222:   PetscFunctionReturn(PETSC_SUCCESS);
    9223: }

    9225: /*@
    9226:   MatSetNearNullSpace - attaches a null space to a matrix, which is often the null space (rigid body modes) of the operator without boundary conditions
    9227:   This null space will be used to provide near null space vectors to a multigrid preconditioner built from this matrix.

    9229:   Logically Collective

    9231:   Input Parameters:
    9232: + mat    - the matrix
    9233: - nullsp - the null space object

    9235:   Level: advanced

    9237:   Notes:
    9238:   Overwrites any previous near null space that may have been attached

    9240:   You can remove the null space by calling this routine with an `nullsp` of `NULL`

    9242: .seealso: [](ch_matrices), `Mat`, `MatNullSpace`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNullSpace()`, `MatNullSpaceCreateRigidBody()`, `MatGetNearNullSpace()`
    9243: @*/
    9244: PetscErrorCode MatSetNearNullSpace(Mat mat, MatNullSpace nullsp)
    9245: {
    9246:   PetscFunctionBegin;
    9250:   MatCheckPreallocated(mat, 1);
    9251:   PetscCall(PetscObjectReference((PetscObject)nullsp));
    9252:   PetscCall(MatNullSpaceDestroy(&mat->nearnullsp));
    9253:   mat->nearnullsp = nullsp;
    9254:   PetscFunctionReturn(PETSC_SUCCESS);
    9255: }

    9257: /*@
    9258:   MatGetNearNullSpace - Get null space attached with `MatSetNearNullSpace()`

    9260:   Not Collective

    9262:   Input Parameter:
    9263: . mat - the matrix

    9265:   Output Parameter:
    9266: . nullsp - the null space object, `NULL` if not set

    9268:   Level: advanced

    9270: .seealso: [](ch_matrices), `Mat`, `MatNullSpace`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatNullSpaceCreate()`
    9271: @*/
    9272: PetscErrorCode MatGetNearNullSpace(Mat mat, MatNullSpace *nullsp)
    9273: {
    9274:   PetscFunctionBegin;
    9277:   PetscAssertPointer(nullsp, 2);
    9278:   MatCheckPreallocated(mat, 1);
    9279:   *nullsp = mat->nearnullsp;
    9280:   PetscFunctionReturn(PETSC_SUCCESS);
    9281: }

    9283: /*@
    9284:   MatICCFactor - Performs in-place incomplete Cholesky factorization of matrix.

    9286:   Collective

    9288:   Input Parameters:
    9289: + mat  - the matrix
    9290: . row  - row/column permutation
    9291: - info - information on desired factorization process

    9293:   Level: developer

    9295:   Notes:
    9296:   Probably really in-place only when level of fill is zero, otherwise allocates
    9297:   new space to store factored matrix and deletes previous memory.

    9299:   Most users should employ the `KSP` interface for linear solvers
    9300:   instead of working directly with matrix algebra routines such as this.
    9301:   See, e.g., `KSPCreate()`.

    9303:   Fortran Note:
    9304:   A valid (non-null) `info` argument must be provided

    9306: .seealso: [](ch_matrices), `Mat`, `MatFactorInfo`, `MatGetFactor()`, `MatICCFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`
    9307: @*/
    9308: PetscErrorCode MatICCFactor(Mat mat, IS row, const MatFactorInfo *info)
    9309: {
    9310:   PetscFunctionBegin;
    9314:   PetscAssertPointer(info, 3);
    9315:   PetscCheck(mat->rmap->N == mat->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "matrix must be square");
    9316:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    9317:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    9318:   MatCheckPreallocated(mat, 1);
    9319:   PetscUseTypeMethod(mat, iccfactor, row, info);
    9320:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    9321:   PetscFunctionReturn(PETSC_SUCCESS);
    9322: }

    9324: /*@
    9325:   MatDiagonalScaleLocal - Scales columns of a matrix given the scaling values including the
    9326:   ghosted ones.

    9328:   Not Collective

    9330:   Input Parameters:
    9331: + mat  - the matrix
    9332: - diag - the diagonal values, including ghost ones

    9334:   Level: developer

    9336:   Notes:
    9337:   Works only for `MATMPIAIJ` and `MATMPIBAIJ` matrices

    9339:   This allows one to avoid during communication to perform the scaling that must be done with `MatDiagonalScale()`

    9341: .seealso: [](ch_matrices), `Mat`, `MatDiagonalScale()`
    9342: @*/
    9343: PetscErrorCode MatDiagonalScaleLocal(Mat mat, Vec diag)
    9344: {
    9345:   PetscMPIInt size;

    9347:   PetscFunctionBegin;

    9352:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Matrix must be already assembled");
    9353:   PetscCall(PetscLogEventBegin(MAT_Scale, mat, 0, 0, 0));
    9354:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));
    9355:   if (size == 1) {
    9356:     PetscInt n, m;
    9357:     PetscCall(VecGetSize(diag, &n));
    9358:     PetscCall(MatGetSize(mat, NULL, &m));
    9359:     PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only supported for sequential matrices when no ghost points/periodic conditions");
    9360:     PetscCall(MatDiagonalScale(mat, NULL, diag));
    9361:   } else PetscUseMethod(mat, "MatDiagonalScaleLocal_C", (Mat, Vec), (mat, diag));
    9362:   PetscCall(PetscLogEventEnd(MAT_Scale, mat, 0, 0, 0));
    9363:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    9364:   PetscFunctionReturn(PETSC_SUCCESS);
    9365: }

    9367: /*@
    9368:   MatGetInertia - Gets the inertia from a factored matrix

    9370:   Collective

    9372:   Input Parameter:
    9373: . mat - the matrix

    9375:   Output Parameters:
    9376: + nneg  - number of negative eigenvalues
    9377: . nzero - number of zero eigenvalues
    9378: - npos  - number of positive eigenvalues

    9380:   Level: advanced

    9382:   Note:
    9383:   Matrix must have been factored by `MatCholeskyFactor()`

    9385: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCholeskyFactor()`
    9386: @*/
    9387: PetscErrorCode MatGetInertia(Mat mat, PetscInt *nneg, PetscInt *nzero, PetscInt *npos)
    9388: {
    9389:   PetscFunctionBegin;
    9392:   PetscCheck(mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Unfactored matrix");
    9393:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Numeric factor mat is not assembled");
    9394:   PetscUseTypeMethod(mat, getinertia, nneg, nzero, npos);
    9395:   PetscFunctionReturn(PETSC_SUCCESS);
    9396: }

    9398: /*@C
    9399:   MatSolves - Solves $A x = b$, given a factored matrix, for a collection of vectors

    9401:   Neighbor-wise Collective

    9403:   Input Parameters:
    9404: + mat - the factored matrix obtained with `MatGetFactor()`
    9405: - b   - the right-hand-side vectors

    9407:   Output Parameter:
    9408: . x - the result vectors

    9410:   Level: developer

    9412:   Note:
    9413:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    9414:   call `MatSolves`(A,x,x).

    9416: .seealso: [](ch_matrices), `Mat`, `Vecs`, `MatSolveAdd()`, `MatSolveTranspose()`, `MatSolveTransposeAdd()`, `MatSolve()`
    9417: @*/
    9418: PetscErrorCode MatSolves(Mat mat, Vecs b, Vecs x)
    9419: {
    9420:   PetscFunctionBegin;
    9423:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    9424:   PetscCheck(mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Unfactored matrix");
    9425:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);

    9427:   MatCheckPreallocated(mat, 1);
    9428:   PetscCall(PetscLogEventBegin(MAT_Solves, mat, 0, 0, 0));
    9429:   PetscUseTypeMethod(mat, solves, b, x);
    9430:   PetscCall(PetscLogEventEnd(MAT_Solves, mat, 0, 0, 0));
    9431:   PetscFunctionReturn(PETSC_SUCCESS);
    9432: }

    9434: /*@
    9435:   MatIsSymmetric - Test whether a matrix is symmetric

    9437:   Collective

    9439:   Input Parameters:
    9440: + A   - the matrix to test
    9441: - tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact transpose)

    9443:   Output Parameter:
    9444: . flg - the result

    9446:   Level: intermediate

    9448:   Notes:
    9449:   For real numbers `MatIsSymmetric()` and `MatIsHermitian()` return identical results

    9451:   If the matrix does not yet know if it is symmetric or not this can be an expensive operation, also available `MatIsSymmetricKnown()`

    9453:   One can declare that a matrix is symmetric with `MatSetOption`(mat,`MAT_SYMMETRIC`,`PETSC_TRUE`) and if it is known to remain symmetric
    9454:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9456: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetricKnown()`,
    9457:           `MAT_SYMMETRIC`, `MAT_SYMMETRY_ETERNAL`
    9458: @*/
    9459: PetscErrorCode MatIsSymmetric(Mat A, PetscReal tol, PetscBool *flg)
    9460: {
    9461:   PetscFunctionBegin;
    9463:   PetscAssertPointer(flg, 3);
    9464:   if (A->symmetric != PETSC_BOOL3_UNKNOWN && !tol) *flg = PetscBool3ToBool(A->symmetric);
    9465:   else {
    9466:     if (A->ops->issymmetric) PetscUseTypeMethod(A, issymmetric, tol, flg);
    9467:     else PetscCall(MatIsTranspose(A, A, tol, flg));
    9468:     if (!tol) PetscCall(MatSetOption(A, MAT_SYMMETRIC, *flg));
    9469:   }
    9470:   PetscFunctionReturn(PETSC_SUCCESS);
    9471: }

    9473: /*@
    9474:   MatIsHermitian - Test whether a matrix is Hermitian

    9476:   Collective

    9478:   Input Parameters:
    9479: + A   - the matrix to test
    9480: - tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact Hermitian)

    9482:   Output Parameter:
    9483: . flg - the result

    9485:   Level: intermediate

    9487:   Notes:
    9488:   For real numbers `MatIsSymmetric()` and `MatIsHermitian()` return identical results

    9490:   If the matrix does not yet know if it is Hermitian or not this can be an expensive operation, also available `MatIsHermitianKnown()`

    9492:   One can declare that a matrix is Hermitian with `MatSetOption`(mat,`MAT_HERMITIAN`,`PETSC_TRUE`) and if it is known to remain Hermitian
    9493:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SYMEMTRY_ETERNAL`,`PETSC_TRUE`)

    9495: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitianKnown()`, `MatIsStructurallySymmetric()`, `MatSetOption()`,
    9496:           `MatIsSymmetricKnown()`, `MatIsSymmetric()`, `MAT_HERMITIAN`, `MAT_SYMMETRY_ETERNAL`
    9497: @*/
    9498: PetscErrorCode MatIsHermitian(Mat A, PetscReal tol, PetscBool *flg)
    9499: {
    9500:   PetscFunctionBegin;
    9502:   PetscAssertPointer(flg, 3);
    9503:   if (A->hermitian != PETSC_BOOL3_UNKNOWN && !tol) *flg = PetscBool3ToBool(A->hermitian);
    9504:   else {
    9505:     if (A->ops->ishermitian) PetscUseTypeMethod(A, ishermitian, tol, flg);
    9506:     else PetscCall(MatIsHermitianTranspose(A, A, tol, flg));
    9507:     if (!tol) PetscCall(MatSetOption(A, MAT_HERMITIAN, *flg));
    9508:   }
    9509:   PetscFunctionReturn(PETSC_SUCCESS);
    9510: }

    9512: /*@
    9513:   MatIsSymmetricKnown - Checks if a matrix knows if it is symmetric or not and its symmetric state

    9515:   Not Collective

    9517:   Input Parameter:
    9518: . A - the matrix to check

    9520:   Output Parameters:
    9521: + set - `PETSC_TRUE` if the matrix knows its symmetry state (this tells you if the next flag is valid)
    9522: - flg - the result (only valid if set is `PETSC_TRUE`)

    9524:   Level: advanced

    9526:   Notes:
    9527:   Does not check the matrix values directly, so this may return unknown (set = `PETSC_FALSE`). Use `MatIsSymmetric()`
    9528:   if you want it explicitly checked

    9530:   One can declare that a matrix is symmetric with `MatSetOption`(mat,`MAT_SYMMETRIC`,`PETSC_TRUE`) and if it is known to remain symmetric
    9531:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9533: .seealso: [](ch_matrices), `Mat`, `MAT_SYMMETRY_ETERNAL`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetric()`, `MatIsHermitianKnown()`
    9534: @*/
    9535: PetscErrorCode MatIsSymmetricKnown(Mat A, PetscBool *set, PetscBool *flg)
    9536: {
    9537:   PetscFunctionBegin;
    9539:   PetscAssertPointer(set, 2);
    9540:   PetscAssertPointer(flg, 3);
    9541:   if (A->symmetric != PETSC_BOOL3_UNKNOWN) {
    9542:     *set = PETSC_TRUE;
    9543:     *flg = PetscBool3ToBool(A->symmetric);
    9544:   } else *set = PETSC_FALSE;
    9545:   PetscFunctionReturn(PETSC_SUCCESS);
    9546: }

    9548: /*@
    9549:   MatIsSPDKnown - Checks if a matrix knows if it is symmetric positive definite or not and its symmetric positive definite state

    9551:   Not Collective

    9553:   Input Parameter:
    9554: . A - the matrix to check

    9556:   Output Parameters:
    9557: + set - `PETSC_TRUE` if the matrix knows its symmetric positive definite state (this tells you if the next flag is valid)
    9558: - flg - the result (only valid if set is `PETSC_TRUE`)

    9560:   Level: advanced

    9562:   Notes:
    9563:   Does not check the matrix values directly, so this may return unknown (set = `PETSC_FALSE`).

    9565:   One can declare that a matrix is SPD with `MatSetOption`(mat,`MAT_SPD`,`PETSC_TRUE`) and if it is known to remain SPD
    9566:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SPD_ETERNAL`,`PETSC_TRUE`)

    9568: .seealso: [](ch_matrices), `Mat`, `MAT_SPD_ETERNAL`, `MAT_SPD`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetric()`, `MatIsHermitianKnown()`
    9569: @*/
    9570: PetscErrorCode MatIsSPDKnown(Mat A, PetscBool *set, PetscBool *flg)
    9571: {
    9572:   PetscFunctionBegin;
    9574:   PetscAssertPointer(set, 2);
    9575:   PetscAssertPointer(flg, 3);
    9576:   if (A->spd != PETSC_BOOL3_UNKNOWN) {
    9577:     *set = PETSC_TRUE;
    9578:     *flg = PetscBool3ToBool(A->spd);
    9579:   } else *set = PETSC_FALSE;
    9580:   PetscFunctionReturn(PETSC_SUCCESS);
    9581: }

    9583: /*@
    9584:   MatIsHermitianKnown - Checks if a matrix knows if it is Hermitian or not and its Hermitian state

    9586:   Not Collective

    9588:   Input Parameter:
    9589: . A - the matrix to check

    9591:   Output Parameters:
    9592: + set - `PETSC_TRUE` if the matrix knows its Hermitian state (this tells you if the next flag is valid)
    9593: - flg - the result (only valid if set is `PETSC_TRUE`)

    9595:   Level: advanced

    9597:   Notes:
    9598:   Does not check the matrix values directly, so this may return unknown (set = `PETSC_FALSE`). Use `MatIsHermitian()`
    9599:   if you want it explicitly checked

    9601:   One can declare that a matrix is Hermitian with `MatSetOption`(mat,`MAT_HERMITIAN`,`PETSC_TRUE`) and if it is known to remain Hermitian
    9602:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9604: .seealso: [](ch_matrices), `Mat`, `MAT_SYMMETRY_ETERNAL`, `MAT_HERMITIAN`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetric()`
    9605: @*/
    9606: PetscErrorCode MatIsHermitianKnown(Mat A, PetscBool *set, PetscBool *flg)
    9607: {
    9608:   PetscFunctionBegin;
    9610:   PetscAssertPointer(set, 2);
    9611:   PetscAssertPointer(flg, 3);
    9612:   if (A->hermitian != PETSC_BOOL3_UNKNOWN) {
    9613:     *set = PETSC_TRUE;
    9614:     *flg = PetscBool3ToBool(A->hermitian);
    9615:   } else *set = PETSC_FALSE;
    9616:   PetscFunctionReturn(PETSC_SUCCESS);
    9617: }

    9619: /*@
    9620:   MatIsStructurallySymmetric - Test whether a matrix is structurally symmetric

    9622:   Collective

    9624:   Input Parameter:
    9625: . A - the matrix to test

    9627:   Output Parameter:
    9628: . flg - the result

    9630:   Level: intermediate

    9632:   Notes:
    9633:   If the matrix does yet know it is structurally symmetric this can be an expensive operation, also available `MatIsStructurallySymmetricKnown()`

    9635:   One can declare that a matrix is structurally symmetric with `MatSetOption`(mat,`MAT_STRUCTURALLY_SYMMETRIC`,`PETSC_TRUE`) and if it is known to remain structurally
    9636:   symmetric after changes to the matrices values one can call `MatSetOption`(mat,`MAT_STRUCTURAL_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9638: .seealso: [](ch_matrices), `Mat`, `MAT_STRUCTURALLY_SYMMETRIC`, `MAT_STRUCTURAL_SYMMETRY_ETERNAL`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsSymmetric()`, `MatSetOption()`, `MatIsStructurallySymmetricKnown()`
    9639: @*/
    9640: PetscErrorCode MatIsStructurallySymmetric(Mat A, PetscBool *flg)
    9641: {
    9642:   PetscFunctionBegin;
    9644:   PetscAssertPointer(flg, 2);
    9645:   if (A->structurally_symmetric != PETSC_BOOL3_UNKNOWN) *flg = PetscBool3ToBool(A->structurally_symmetric);
    9646:   else {
    9647:     PetscUseTypeMethod(A, isstructurallysymmetric, flg);
    9648:     PetscCall(MatSetOption(A, MAT_STRUCTURALLY_SYMMETRIC, *flg));
    9649:   }
    9650:   PetscFunctionReturn(PETSC_SUCCESS);
    9651: }

    9653: /*@
    9654:   MatIsStructurallySymmetricKnown - Checks if a matrix knows if it is structurally symmetric or not and its structurally symmetric state

    9656:   Not Collective

    9658:   Input Parameter:
    9659: . A - the matrix to check

    9661:   Output Parameters:
    9662: + set - PETSC_TRUE if the matrix knows its structurally symmetric state (this tells you if the next flag is valid)
    9663: - flg - the result (only valid if set is PETSC_TRUE)

    9665:   Level: advanced

    9667:   Notes:
    9668:   One can declare that a matrix is structurally symmetric with `MatSetOption`(mat,`MAT_STRUCTURALLY_SYMMETRIC`,`PETSC_TRUE`) and if it is known to remain structurally
    9669:   symmetric after changes to the matrices values one can call `MatSetOption`(mat,`MAT_STRUCTURAL_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9671:   Use `MatIsStructurallySymmetric()` to explicitly check if a matrix is structurally symmetric (this is an expensive operation)

    9673: .seealso: [](ch_matrices), `Mat`, `MAT_STRUCTURALLY_SYMMETRIC`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetric()`, `MatIsHermitianKnown()`
    9674: @*/
    9675: PetscErrorCode MatIsStructurallySymmetricKnown(Mat A, PetscBool *set, PetscBool *flg)
    9676: {
    9677:   PetscFunctionBegin;
    9679:   PetscAssertPointer(set, 2);
    9680:   PetscAssertPointer(flg, 3);
    9681:   if (A->structurally_symmetric != PETSC_BOOL3_UNKNOWN) {
    9682:     *set = PETSC_TRUE;
    9683:     *flg = PetscBool3ToBool(A->structurally_symmetric);
    9684:   } else *set = PETSC_FALSE;
    9685:   PetscFunctionReturn(PETSC_SUCCESS);
    9686: }

    9688: /*@
    9689:   MatStashGetInfo - Gets how many values are currently in the matrix stash, i.e. need
    9690:   to be communicated to other processors during the `MatAssemblyBegin()`/`MatAssemblyEnd()` process

    9692:   Not Collective

    9694:   Input Parameter:
    9695: . mat - the matrix

    9697:   Output Parameters:
    9698: + nstash    - the size of the stash
    9699: . reallocs  - the number of additional mallocs incurred.
    9700: . bnstash   - the size of the block stash
    9701: - breallocs - the number of additional mallocs incurred.in the block stash

    9703:   Level: advanced

    9705: .seealso: [](ch_matrices), `MatAssemblyBegin()`, `MatAssemblyEnd()`, `Mat`, `MatStashSetInitialSize()`
    9706: @*/
    9707: PetscErrorCode MatStashGetInfo(Mat mat, PetscInt *nstash, PetscInt *reallocs, PetscInt *bnstash, PetscInt *breallocs)
    9708: {
    9709:   PetscFunctionBegin;
    9710:   PetscCall(MatStashGetInfo_Private(&mat->stash, nstash, reallocs));
    9711:   PetscCall(MatStashGetInfo_Private(&mat->bstash, bnstash, breallocs));
    9712:   PetscFunctionReturn(PETSC_SUCCESS);
    9713: }

    9715: /*@
    9716:   MatCreateVecs - Get vector(s) compatible with the matrix, i.e. with the same
    9717:   parallel layout, `PetscLayout` for rows and columns

    9719:   Collective

    9721:   Input Parameter:
    9722: . mat - the matrix

    9724:   Output Parameters:
    9725: + right - (optional) vector that the matrix can be multiplied against
    9726: - left  - (optional) vector that the matrix vector product can be stored in

    9728:   Options Database Key:
    9729: . -mat_vec_type type - set the `VecType` of the created vectors during `MatSetFromOptions()`

    9731:   Level: advanced

    9733:   Notes:
    9734:   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()`.

    9736:   The `VecType` of the created vectors is determined by the `MatType` of `mat`. This can be overridden by using `MatSetVecType()` or the option `-mat_vec_type`.

    9738:   These are new vectors which are not owned by the `mat`, they should be destroyed with `VecDestroy()` when no longer needed.

    9740:   PETSc `Vec` always have all zero entries when created with `MatCreateVecs()` until routines such as `VecSet()` or `VecSetValues()`
    9741:   are used to change the values. There is no reason to call `VecZeroEntries()` after creation.

    9743: .seealso: [](ch_matrices), `Mat`, `Vec`, `VecCreate()`, `VecDestroy()`, `DMCreateGlobalVector()`, `MatSetVecType()`
    9744: @*/
    9745: PetscErrorCode MatCreateVecs(Mat mat, Vec *right, Vec *left)
    9746: {
    9747:   PetscFunctionBegin;
    9750:   if (mat->ops->getvecs) {
    9751:     PetscUseTypeMethod(mat, getvecs, right, left);
    9752:   } else {
    9753:     if (right) {
    9754:       PetscCheck(mat->cmap->n >= 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "PetscLayout for columns not yet setup");
    9755:       PetscCall(VecCreateWithLayout_Private(mat->cmap, right));
    9756:       PetscCall(VecSetType(*right, mat->defaultvectype));
    9757: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
    9758:       if (mat->boundtocpu && mat->bindingpropagates) {
    9759:         PetscCall(VecSetBindingPropagates(*right, PETSC_TRUE));
    9760:         PetscCall(VecBindToCPU(*right, PETSC_TRUE));
    9761:       }
    9762: #endif
    9763:     }
    9764:     if (left) {
    9765:       PetscCheck(mat->rmap->n >= 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "PetscLayout for rows not yet setup");
    9766:       PetscCall(VecCreateWithLayout_Private(mat->rmap, left));
    9767:       PetscCall(VecSetType(*left, mat->defaultvectype));
    9768: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
    9769:       if (mat->boundtocpu && mat->bindingpropagates) {
    9770:         PetscCall(VecSetBindingPropagates(*left, PETSC_TRUE));
    9771:         PetscCall(VecBindToCPU(*left, PETSC_TRUE));
    9772:       }
    9773: #endif
    9774:     }
    9775:   }
    9776:   PetscFunctionReturn(PETSC_SUCCESS);
    9777: }

    9779: /*@
    9780:   MatFactorInfoInitialize - Initializes a `MatFactorInfo` data structure
    9781:   with default values.

    9783:   Not Collective

    9785:   Input Parameter:
    9786: . info - the `MatFactorInfo` data structure

    9788:   Level: developer

    9790:   Notes:
    9791:   The solvers are generally used through the `KSP` and `PC` objects, for example
    9792:   `PCLU`, `PCILU`, `PCCHOLESKY`, `PCICC`

    9794:   Once the data structure is initialized one may change certain entries as desired for the particular factorization to be performed

    9796: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorInfo`
    9797: @*/
    9798: PetscErrorCode MatFactorInfoInitialize(MatFactorInfo *info)
    9799: {
    9800:   PetscFunctionBegin;
    9801:   PetscCall(PetscMemzero(info, sizeof(MatFactorInfo)));
    9802:   PetscFunctionReturn(PETSC_SUCCESS);
    9803: }

    9805: /*@
    9806:   MatFactorSetSchurIS - Set indices corresponding to the Schur complement you wish to have computed

    9808:   Collective

    9810:   Input Parameters:
    9811: + mat - the factored matrix
    9812: - is  - the index set defining the Schur indices (0-based)

    9814:   Level: advanced

    9816:   Notes:
    9817:   Call `MatFactorSolveSchurComplement()` or `MatFactorSolveSchurComplementTranspose()` after this call to solve a Schur complement system.

    9819:   You can call `MatFactorGetSchurComplement()` or `MatFactorCreateSchurComplement()` after this call.

    9821:   This functionality is only supported for `MATSOLVERMUMPS` and `MATSOLVERMKL_PARDISO`

    9823: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorGetSchurComplement()`, `MatFactorRestoreSchurComplement()`, `MatFactorCreateSchurComplement()`, `MatFactorSolveSchurComplement()`,
    9824:           `MatFactorSolveSchurComplementTranspose()`, `MATSOLVERMUMPS`, `MATSOLVERMKL_PARDISO`
    9825: @*/
    9826: PetscErrorCode MatFactorSetSchurIS(Mat mat, IS is)
    9827: {
    9828:   PetscErrorCode (*f)(Mat, IS);

    9830:   PetscFunctionBegin;
    9835:   PetscCheckSameComm(mat, 1, is, 2);
    9836:   PetscCheck(mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    9837:   PetscCall(PetscObjectQueryFunction((PetscObject)mat, "MatFactorSetSchurIS_C", &f));
    9838:   PetscCheck(f, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "The selected MatSolverType does not support Schur complement computation. You should use MATSOLVERMUMPS or MATSOLVERMKL_PARDISO");
    9839:   PetscCall(MatDestroy(&mat->schur));
    9840:   PetscCall((*f)(mat, is));
    9841:   PetscCheck(mat->schur, PetscObjectComm((PetscObject)mat), PETSC_ERR_PLIB, "Schur complement has not been created");
    9842:   PetscFunctionReturn(PETSC_SUCCESS);
    9843: }

    9845: /*@
    9846:   MatFactorCreateSchurComplement - Create a Schur complement matrix object using Schur data computed during the factorization step

    9848:   Logically Collective

    9850:   Input Parameters:
    9851: + F      - the factored matrix obtained by calling `MatGetFactor()`
    9852: . S      - location where to return the Schur complement, can be `NULL`
    9853: - status - the status of the Schur complement matrix, can be `NULL`

    9855:   Level: advanced

    9857:   Notes:
    9858:   You must call `MatFactorSetSchurIS()` before calling this routine.

    9860:   This functionality is only supported for `MATSOLVERMUMPS` and `MATSOLVERMKL_PARDISO`

    9862:   The routine provides a copy of the Schur matrix stored within the solver data structures.
    9863:   The caller must destroy the object when it is no longer needed.
    9864:   If `MatFactorInvertSchurComplement()` has been called, the routine gets back the inverse.

    9866:   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)

    9868:   See `MatCreateSchurComplement()` or `MatGetSchurComplement()` for ways to create virtual or approximate Schur complements.

    9870:   Developer Note:
    9871:   The reason this routine exists is because the representation of the Schur complement within the factor matrix may be different than a standard PETSc
    9872:   matrix representation and we normally do not want to use the time or memory to make a copy as a regular PETSc matrix.

    9874: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorGetSchurComplement()`, `MatFactorSchurStatus`, `MATSOLVERMUMPS`, `MATSOLVERMKL_PARDISO`
    9875: @*/
    9876: PetscErrorCode MatFactorCreateSchurComplement(Mat F, Mat *S, MatFactorSchurStatus *status)
    9877: {
    9878:   PetscFunctionBegin;
    9880:   if (S) PetscAssertPointer(S, 2);
    9881:   if (status) PetscAssertPointer(status, 3);
    9882:   if (S) {
    9883:     PetscErrorCode (*f)(Mat, Mat *);

    9885:     PetscCall(PetscObjectQueryFunction((PetscObject)F, "MatFactorCreateSchurComplement_C", &f));
    9886:     if (f) PetscCall((*f)(F, S));
    9887:     else PetscCall(MatDuplicate(F->schur, MAT_COPY_VALUES, S));
    9888:   }
    9889:   if (status) *status = F->schur_status;
    9890:   PetscFunctionReturn(PETSC_SUCCESS);
    9891: }

    9893: /*@
    9894:   MatFactorGetSchurComplement - Gets access to a Schur complement matrix using the current Schur data within a factored matrix

    9896:   Logically Collective

    9898:   Input Parameters:
    9899: + F      - the factored matrix obtained by calling `MatGetFactor()`
    9900: . S      - location where to return the Schur complement, can be `NULL`
    9901: - status - the status of the Schur complement matrix, can be `NULL`

    9903:   Level: advanced

    9905:   Notes:
    9906:   You must call `MatFactorSetSchurIS()` before calling this routine.

    9908:   Schur complement mode is currently implemented for sequential matrices with factor type of `MATSOLVERMUMPS`

    9910:   The routine returns a the Schur Complement stored within the data structures of the solver.

    9912:   If `MatFactorInvertSchurComplement()` has previously been called, the returned matrix is actually the inverse of the Schur complement.

    9914:   The returned matrix should not be destroyed; the caller should call `MatFactorRestoreSchurComplement()` when the object is no longer needed.

    9916:   Use `MatFactorCreateSchurComplement()` to create a copy of the Schur complement matrix that is within a factored matrix

    9918:   See `MatCreateSchurComplement()` or `MatGetSchurComplement()` for ways to create virtual or approximate Schur complements.

    9920: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorRestoreSchurComplement()`, `MatFactorCreateSchurComplement()`, `MatFactorSchurStatus`
    9921: @*/
    9922: PetscErrorCode MatFactorGetSchurComplement(Mat F, Mat *S, MatFactorSchurStatus *status)
    9923: {
    9924:   PetscFunctionBegin;
    9926:   if (S) {
    9927:     PetscAssertPointer(S, 2);
    9928:     *S = F->schur;
    9929:   }
    9930:   if (status) {
    9931:     PetscAssertPointer(status, 3);
    9932:     *status = F->schur_status;
    9933:   }
    9934:   PetscFunctionReturn(PETSC_SUCCESS);
    9935: }

    9937: static PetscErrorCode MatFactorUpdateSchurStatus_Private(Mat F)
    9938: {
    9939:   Mat S = F->schur;

    9941:   PetscFunctionBegin;
    9942:   switch (F->schur_status) {
    9943:   case MAT_FACTOR_SCHUR_UNFACTORED: // fall-through
    9944:   case MAT_FACTOR_SCHUR_INVERTED:
    9945:     if (S) {
    9946:       S->ops->solve             = NULL;
    9947:       S->ops->matsolve          = NULL;
    9948:       S->ops->solvetranspose    = NULL;
    9949:       S->ops->matsolvetranspose = NULL;
    9950:       S->ops->solveadd          = NULL;
    9951:       S->ops->solvetransposeadd = NULL;
    9952:       S->factortype             = MAT_FACTOR_NONE;
    9953:       PetscCall(PetscFree(S->solvertype));
    9954:     }
    9955:   case MAT_FACTOR_SCHUR_FACTORED: // fall-through
    9956:     break;
    9957:   default:
    9958:     SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unhandled MatFactorSchurStatus %d", F->schur_status);
    9959:   }
    9960:   PetscFunctionReturn(PETSC_SUCCESS);
    9961: }

    9963: /*@
    9964:   MatFactorRestoreSchurComplement - Restore the Schur complement matrix object obtained from a call to `MatFactorGetSchurComplement()`

    9966:   Logically Collective

    9968:   Input Parameters:
    9969: + F      - the factored matrix obtained by calling `MatGetFactor()`
    9970: . S      - location where the Schur complement is stored
    9971: - status - the status of the Schur complement matrix (see `MatFactorSchurStatus`)

    9973:   Level: advanced

    9975: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorCreateSchurComplement()`, `MatFactorSchurStatus`
    9976: @*/
    9977: PetscErrorCode MatFactorRestoreSchurComplement(Mat F, Mat *S, MatFactorSchurStatus status)
    9978: {
    9979:   PetscFunctionBegin;
    9981:   if (S) {
    9983:     *S = NULL;
    9984:   }
    9985:   F->schur_status = status;
    9986:   PetscCall(MatFactorUpdateSchurStatus_Private(F));
    9987:   PetscFunctionReturn(PETSC_SUCCESS);
    9988: }

    9990: /*@
    9991:   MatFactorSolveSchurComplementTranspose - Solve the transpose of the Schur complement system computed during the factorization step

    9993:   Logically Collective

    9995:   Input Parameters:
    9996: + F   - the factored matrix obtained by calling `MatGetFactor()`
    9997: . rhs - location where the right-hand side of the Schur complement system is stored
    9998: - sol - location where the solution of the Schur complement system has to be returned

    10000:   Level: advanced

    10002:   Notes:
    10003:   The sizes of the vectors should match the size of the Schur complement

    10005:   Must be called after `MatFactorSetSchurIS()`

    10007: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorSolveSchurComplement()`
    10008: @*/
    10009: PetscErrorCode MatFactorSolveSchurComplementTranspose(Mat F, Vec rhs, Vec sol)
    10010: {
    10011:   PetscFunctionBegin;
    10018:   PetscCheckSameComm(F, 1, rhs, 2);
    10019:   PetscCheckSameComm(F, 1, sol, 3);
    10020:   PetscCall(MatFactorFactorizeSchurComplement(F));
    10021:   switch (F->schur_status) {
    10022:   case MAT_FACTOR_SCHUR_FACTORED:
    10023:     PetscCall(MatSolveTranspose(F->schur, rhs, sol));
    10024:     break;
    10025:   case MAT_FACTOR_SCHUR_INVERTED:
    10026:     PetscCall(MatMultTranspose(F->schur, rhs, sol));
    10027:     break;
    10028:   default:
    10029:     SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unhandled MatFactorSchurStatus %d", F->schur_status);
    10030:   }
    10031:   PetscFunctionReturn(PETSC_SUCCESS);
    10032: }

    10034: /*@
    10035:   MatFactorSolveSchurComplement - Solve the Schur complement system computed during the factorization step

    10037:   Logically Collective

    10039:   Input Parameters:
    10040: + F   - the factored matrix obtained by calling `MatGetFactor()`
    10041: . rhs - location where the right-hand side of the Schur complement system is stored
    10042: - sol - location where the solution of the Schur complement system has to be returned

    10044:   Level: advanced

    10046:   Notes:
    10047:   The sizes of the vectors should match the size of the Schur complement

    10049:   Must be called after `MatFactorSetSchurIS()`

    10051: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorSolveSchurComplementTranspose()`
    10052: @*/
    10053: PetscErrorCode MatFactorSolveSchurComplement(Mat F, Vec rhs, Vec sol)
    10054: {
    10055:   PetscFunctionBegin;
    10062:   PetscCheckSameComm(F, 1, rhs, 2);
    10063:   PetscCheckSameComm(F, 1, sol, 3);
    10064:   PetscCall(MatFactorFactorizeSchurComplement(F));
    10065:   switch (F->schur_status) {
    10066:   case MAT_FACTOR_SCHUR_FACTORED:
    10067:     PetscCall(MatSolve(F->schur, rhs, sol));
    10068:     break;
    10069:   case MAT_FACTOR_SCHUR_INVERTED:
    10070:     PetscCall(MatMult(F->schur, rhs, sol));
    10071:     break;
    10072:   default:
    10073:     SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unhandled MatFactorSchurStatus %d", F->schur_status);
    10074:   }
    10075:   PetscFunctionReturn(PETSC_SUCCESS);
    10076: }

    10078: PETSC_SINGLE_LIBRARY_INTERN PetscErrorCode MatSeqDenseInvertFactors_Private(Mat);
    10079: #if PetscDefined(HAVE_CUDA)
    10080: PETSC_SINGLE_LIBRARY_INTERN PetscErrorCode MatSeqDenseCUDAInvertFactors_Internal(Mat);
    10081: #endif

    10083: /* Schur status updated in the interface */
    10084: static PetscErrorCode MatFactorInvertSchurComplement_Private(Mat F)
    10085: {
    10086:   Mat S = F->schur;

    10088:   PetscFunctionBegin;
    10089:   if (S) {
    10090:     PetscMPIInt size;
    10091:     PetscBool   isdense, isdensecuda;

    10093:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)S), &size));
    10094:     PetscCheck(size <= 1, PetscObjectComm((PetscObject)S), PETSC_ERR_SUP, "Not yet implemented");
    10095:     PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSEQDENSE, &isdense));
    10096:     PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSEQDENSECUDA, &isdensecuda));
    10097:     PetscCheck(isdense || isdensecuda, PetscObjectComm((PetscObject)S), PETSC_ERR_SUP, "Not implemented for type %s", ((PetscObject)S)->type_name);
    10098:     PetscCall(PetscLogEventBegin(MAT_FactorInvS, F, 0, 0, 0));
    10099:     if (isdense) {
    10100:       PetscCall(MatSeqDenseInvertFactors_Private(S));
    10101:     } else if (isdensecuda) {
    10102: #if defined(PETSC_HAVE_CUDA)
    10103:       PetscCall(MatSeqDenseCUDAInvertFactors_Internal(S));
    10104: #endif
    10105:     }
    10106:     // HIP??????????????
    10107:     PetscCall(PetscLogEventEnd(MAT_FactorInvS, F, 0, 0, 0));
    10108:   }
    10109:   PetscFunctionReturn(PETSC_SUCCESS);
    10110: }

    10112: /*@
    10113:   MatFactorInvertSchurComplement - Invert the Schur complement matrix computed during the factorization step

    10115:   Logically Collective

    10117:   Input Parameter:
    10118: . F - the factored matrix obtained by calling `MatGetFactor()`

    10120:   Level: advanced

    10122:   Notes:
    10123:   Must be called after `MatFactorSetSchurIS()`.

    10125:   Call `MatFactorGetSchurComplement()` or  `MatFactorCreateSchurComplement()` AFTER this call to actually compute the inverse and get access to it.

    10127: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorGetSchurComplement()`, `MatFactorCreateSchurComplement()`
    10128: @*/
    10129: PetscErrorCode MatFactorInvertSchurComplement(Mat F)
    10130: {
    10131:   PetscFunctionBegin;
    10134:   if (F->schur_status == MAT_FACTOR_SCHUR_INVERTED) PetscFunctionReturn(PETSC_SUCCESS);
    10135:   PetscCall(MatFactorFactorizeSchurComplement(F));
    10136:   PetscCall(MatFactorInvertSchurComplement_Private(F));
    10137:   F->schur_status = MAT_FACTOR_SCHUR_INVERTED;
    10138:   PetscFunctionReturn(PETSC_SUCCESS);
    10139: }

    10141: /*@
    10142:   MatFactorFactorizeSchurComplement - Factorize the Schur complement matrix computed during the factorization step

    10144:   Logically Collective

    10146:   Input Parameter:
    10147: . F - the factored matrix obtained by calling `MatGetFactor()`

    10149:   Level: advanced

    10151:   Note:
    10152:   Must be called after `MatFactorSetSchurIS()`

    10154: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorInvertSchurComplement()`
    10155: @*/
    10156: PetscErrorCode MatFactorFactorizeSchurComplement(Mat F)
    10157: {
    10158:   MatFactorInfo info;

    10160:   PetscFunctionBegin;
    10163:   if (F->schur_status == MAT_FACTOR_SCHUR_INVERTED || F->schur_status == MAT_FACTOR_SCHUR_FACTORED) PetscFunctionReturn(PETSC_SUCCESS);
    10164:   PetscCall(PetscLogEventBegin(MAT_FactorFactS, F, 0, 0, 0));
    10165:   PetscCall(PetscMemzero(&info, sizeof(MatFactorInfo)));
    10166:   if (F->factortype == MAT_FACTOR_CHOLESKY) { /* LDL^t regarded as Cholesky */
    10167:     PetscCall(MatCholeskyFactor(F->schur, NULL, &info));
    10168:   } else {
    10169:     PetscCall(MatLUFactor(F->schur, NULL, NULL, &info));
    10170:   }
    10171:   PetscCall(PetscLogEventEnd(MAT_FactorFactS, F, 0, 0, 0));
    10172:   F->schur_status = MAT_FACTOR_SCHUR_FACTORED;
    10173:   PetscFunctionReturn(PETSC_SUCCESS);
    10174: }

    10176: /*@
    10177:   MatPtAP - Creates the matrix product $C = P^T * A * P$

    10179:   Neighbor-wise Collective

    10181:   Input Parameters:
    10182: + A     - the matrix
    10183: . P     - the projection matrix
    10184: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10185: - fill  - expected fill as ratio of nnz(C)/(nnz(A) + nnz(P)), use `PETSC_DETERMINE` or `PETSC_CURRENT` if you do not have a good estimate
    10186:           if the result is a dense matrix this is irrelevant

    10188:   Output Parameter:
    10189: . C - the product matrix

    10191:   Level: intermediate

    10193:   Notes:
    10194:   `C` will be created and must be destroyed by the user with `MatDestroy()`.

    10196:   This is a convenience routine that wraps the use of the `MatProductCreate()` with a `MatProductType` of `MATPRODUCT_PtAP`
    10197:   functionality into a single function call. For more involved matrix-matrix operations see `MatProductCreate()`.

    10199:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10201:   Developer Note:
    10202:   For matrix types without special implementation the function fallbacks to `MatMatMult()` followed by `MatTransposeMatMult()`.

    10204: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MatMatMult()`, `MatRARt()`
    10205: @*/
    10206: PetscErrorCode MatPtAP(Mat A, Mat P, MatReuse scall, PetscReal fill, Mat *C)
    10207: {
    10208:   PetscFunctionBegin;
    10209:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*C, 5);
    10210:   PetscCheck(scall != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Inplace product not supported");

    10212:   if (scall == MAT_INITIAL_MATRIX) {
    10213:     PetscCall(MatProductCreate(A, P, NULL, C));
    10214:     PetscCall(MatProductSetType(*C, MATPRODUCT_PtAP));
    10215:     PetscCall(MatProductSetAlgorithm(*C, "default"));
    10216:     PetscCall(MatProductSetFill(*C, fill));

    10218:     (*C)->product->api_user = PETSC_TRUE;
    10219:     PetscCall(MatProductSetFromOptions(*C));
    10220:     PetscCheck((*C)->ops->productsymbolic, 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);
    10221:     PetscCall(MatProductSymbolic(*C));
    10222:   } else { /* scall == MAT_REUSE_MATRIX */
    10223:     PetscCall(MatProductReplaceMats(A, P, NULL, *C));
    10224:   }

    10226:   PetscCall(MatProductNumeric(*C));
    10227:   if (A->symmetric == PETSC_BOOL3_TRUE) {
    10228:     PetscCall(MatSetOption(*C, MAT_SYMMETRIC, PETSC_TRUE));
    10229:     (*C)->spd = A->spd;
    10230:   }
    10231:   PetscFunctionReturn(PETSC_SUCCESS);
    10232: }

    10234: /*@
    10235:   MatRARt - Creates the matrix product $C = R * A * R^T$

    10237:   Neighbor-wise Collective

    10239:   Input Parameters:
    10240: + A     - the matrix
    10241: . R     - the projection matrix
    10242: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10243: - fill  - expected fill as ratio of nnz(C)/nnz(A), use `PETSC_DETERMINE` or `PETSC_CURRENT` if you do not have a good estimate
    10244:           if the result is a dense matrix this is irrelevant

    10246:   Output Parameter:
    10247: . C - the product matrix

    10249:   Level: intermediate

    10251:   Notes:
    10252:   `C` will be created and must be destroyed by the user with `MatDestroy()`.

    10254:   This is a convenience routine that wraps the use of the `MatProductCreate()` with a `MatProductType` of `MATPRODUCT_RARt`
    10255:   functionality into a single function call. For more involved matrix-matrix operations see `MatProductCreate()`.

    10257:   This routine is currently only implemented for pairs of `MATAIJ` matrices and classes
    10258:   which inherit from `MATAIJ`. Due to PETSc sparse matrix block row distribution among processes,
    10259:   the parallel `MatRARt()` is implemented computing the explicit transpose of `R`, which can be very expensive.
    10260:   We recommend using `MatPtAP()` when possible.

    10262:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10264: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MatMatMult()`, `MatPtAP()`
    10265: @*/
    10266: PetscErrorCode MatRARt(Mat A, Mat R, MatReuse scall, PetscReal fill, Mat *C)
    10267: {
    10268:   PetscFunctionBegin;
    10269:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*C, 5);
    10270:   PetscCheck(scall != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Inplace product not supported");

    10272:   if (scall == MAT_INITIAL_MATRIX) {
    10273:     PetscCall(MatProductCreate(A, R, NULL, C));
    10274:     PetscCall(MatProductSetType(*C, MATPRODUCT_RARt));
    10275:     PetscCall(MatProductSetAlgorithm(*C, "default"));
    10276:     PetscCall(MatProductSetFill(*C, fill));

    10278:     (*C)->product->api_user = PETSC_TRUE;
    10279:     PetscCall(MatProductSetFromOptions(*C));
    10280:     PetscCheck((*C)->ops->productsymbolic, 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);
    10281:     PetscCall(MatProductSymbolic(*C));
    10282:   } else { /* scall == MAT_REUSE_MATRIX */
    10283:     PetscCall(MatProductReplaceMats(A, R, NULL, *C));
    10284:   }

    10286:   PetscCall(MatProductNumeric(*C));
    10287:   if (A->symmetric == PETSC_BOOL3_TRUE) PetscCall(MatSetOption(*C, MAT_SYMMETRIC, PETSC_TRUE));
    10288:   PetscFunctionReturn(PETSC_SUCCESS);
    10289: }

    10291: static PetscErrorCode MatProduct_Private(Mat A, Mat B, MatReuse scall, PetscReal fill, MatProductType ptype, Mat *C)
    10292: {
    10293:   PetscBool flg = PETSC_TRUE;

    10295:   PetscFunctionBegin;
    10296:   PetscCheck(scall != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MAT_INPLACE_MATRIX product not supported");
    10297:   if (scall == MAT_INITIAL_MATRIX) {
    10298:     PetscCall(PetscInfo(A, "Calling MatProduct API with MAT_INITIAL_MATRIX and product type %s\n", MatProductTypes[ptype]));
    10299:     PetscCall(MatProductCreate(A, B, NULL, C));
    10300:     PetscCall(MatProductSetAlgorithm(*C, MATPRODUCTALGORITHMDEFAULT));
    10301:     PetscCall(MatProductSetFill(*C, fill));
    10302:   } else { /* scall == MAT_REUSE_MATRIX */
    10303:     Mat_Product *product = (*C)->product;

    10305:     PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)*C, &flg, MATSEQDENSE, MATMPIDENSE, ""));
    10306:     if (flg && product && product->type != ptype) {
    10307:       PetscCall(MatProductClear(*C));
    10308:       product = NULL;
    10309:     }
    10310:     PetscCall(PetscInfo(A, "Calling MatProduct API with MAT_REUSE_MATRIX %s product present and product type %s\n", product ? "with" : "without", MatProductTypes[ptype]));
    10311:     if (!product) { /* user provide the dense matrix *C without calling MatProductCreate() or reusing it from previous calls */
    10312:       PetscCheck(flg, PetscObjectComm((PetscObject)*C), PETSC_ERR_SUP, "Call MatProductCreate() first");
    10313:       PetscCall(MatProductCreate_Private(A, B, NULL, *C));
    10314:       product        = (*C)->product;
    10315:       product->fill  = fill;
    10316:       product->clear = PETSC_TRUE;
    10317:     } else { /* user may change input matrices A or B when MAT_REUSE_MATRIX */
    10318:       flg = PETSC_FALSE;
    10319:       PetscCall(MatProductReplaceMats(A, B, NULL, *C));
    10320:     }
    10321:   }
    10322:   if (flg) {
    10323:     (*C)->product->api_user = PETSC_TRUE;
    10324:     PetscCall(MatProductSetType(*C, ptype));
    10325:     PetscCall(MatProductSetFromOptions(*C));
    10326:     PetscCall(MatProductSymbolic(*C));
    10327:   }
    10328:   PetscCall(MatProductNumeric(*C));
    10329:   PetscFunctionReturn(PETSC_SUCCESS);
    10330: }

    10332: /*@
    10333:   MatMatMult - Performs matrix-matrix multiplication $ C=A*B $.

    10335:   Neighbor-wise Collective

    10337:   Input Parameters:
    10338: + A     - the left matrix
    10339: . B     - the right matrix
    10340: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10341: - fill  - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use `PETSC_DETERMINE` or `PETSC_CURRENT` if you do not have a good estimate
    10342:           if the result is a dense matrix this is irrelevant

    10344:   Output Parameter:
    10345: . C - the product matrix

    10347:   Notes:
    10348:   Unless scall is `MAT_REUSE_MATRIX` C will be created.

    10350:   `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
    10351:   call to this function with `MAT_INITIAL_MATRIX`.

    10353:   To determine the correct fill value, run with `-info` and search for the string "Fill ratio" to see the value actually needed.

    10355:   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`,
    10356:   rather than first having `MatMatMult()` create it for you. You can NEVER do this if the matrix `C` is sparse.

    10358:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10360:   This is a convenience routine that wraps the use of the `MatProductCreate()` with a `MatProductType` of `MATPRODUCT_AB`
    10361:   functionality into a single function call. For more involved matrix-matrix operations see `MatProductCreate()`.

    10363:   Example of Usage:
    10364: .vb
    10365:      MatProductCreate(A,B,NULL,&C);
    10366:      MatProductSetType(C,MATPRODUCT_AB);
    10367:      MatProductSymbolic(C);
    10368:      MatProductNumeric(C); // compute C=A * B
    10369:      MatProductReplaceMats(A1,B1,NULL,C); // compute C=A1 * B1
    10370:      MatProductNumeric(C);
    10371:      MatProductReplaceMats(A2,NULL,NULL,C); // compute C=A2 * B1
    10372:      MatProductNumeric(C);
    10373: .ve

    10375:   Level: intermediate

    10377: .seealso: [](ch_matrices), `Mat`, `MatProductType`, `MATPRODUCT_AB`, `MatTransposeMatMult()`, `MatMatTransposeMult()`, `MatPtAP()`, `MatProductCreate()`, `MatProductSymbolic()`, `MatProductReplaceMats()`, `MatProductNumeric()`
    10378: @*/
    10379: PetscErrorCode MatMatMult(Mat A, Mat B, MatReuse scall, PetscReal fill, Mat *C)
    10380: {
    10381:   PetscFunctionBegin;
    10382:   PetscCall(MatProduct_Private(A, B, scall, fill, MATPRODUCT_AB, C));
    10383:   PetscFunctionReturn(PETSC_SUCCESS);
    10384: }

    10386: /*@
    10387:   MatMatTransposeMult - Performs matrix-matrix multiplication $C = A*B^T$.

    10389:   Neighbor-wise Collective

    10391:   Input Parameters:
    10392: + A     - the left matrix
    10393: . B     - the right matrix
    10394: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10395: - fill  - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use `PETSC_DETERMINE` or `PETSC_CURRENT` if not known

    10397:   Output Parameter:
    10398: . C - the product matrix

    10400:   Options Database Key:
    10401: . -matmattransmult_mpidense_mpidense_via {allgatherv,cyclic} - Choose between algorithms for `MATMPIDENSE` matrices: the
    10402:               first redundantly copies the transposed `B` matrix on each process and requires O(log P) communication complexity;
    10403:               the second never stores more than one portion of the `B` matrix at a time but requires O(P) communication complexity.

    10405:   Level: intermediate

    10407:   Notes:
    10408:   C will be created if `MAT_INITIAL_MATRIX` and must be destroyed by the user with `MatDestroy()`.

    10410:   `MAT_REUSE_MATRIX` can only be used if the matrices A and B have the same nonzero pattern as in the previous call

    10412:   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    10413:   actually needed.

    10415:   This routine is currently only implemented for pairs of `MATSEQAIJ` matrices, for the `MATSEQDENSE` class,
    10416:   and for pairs of `MATMPIDENSE` matrices.

    10418:   This is a convenience routine that wraps the use of the `MatProductCreate()` with a `MatProductType` of `MATPRODUCT_ABt`
    10419:   functionality into a single function call. For more involved matrix-matrix operations see `MatProductCreate()`.

    10421:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10423: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MATPRODUCT_ABt`, `MatMatMult()`, `MatTransposeMatMult()`, `MatPtAP()`, `MatProductAlgorithm`, `MatProductType`
    10424: @*/
    10425: PetscErrorCode MatMatTransposeMult(Mat A, Mat B, MatReuse scall, PetscReal fill, Mat *C)
    10426: {
    10427:   PetscFunctionBegin;
    10428:   PetscCall(MatProduct_Private(A, B, scall, fill, MATPRODUCT_ABt, C));
    10429:   if (A == B) PetscCall(MatSetOption(*C, MAT_SYMMETRIC, PETSC_TRUE));
    10430:   PetscFunctionReturn(PETSC_SUCCESS);
    10431: }

    10433: /*@
    10434:   MatTransposeMatMult - Performs matrix-matrix multiplication $C = A^T*B$.

    10436:   Neighbor-wise Collective

    10438:   Input Parameters:
    10439: + A     - the left matrix
    10440: . B     - the right matrix
    10441: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10442: - fill  - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use `PETSC_DETERMINE` or `PETSC_CURRENT` if not known

    10444:   Output Parameter:
    10445: . C - the product matrix

    10447:   Level: intermediate

    10449:   Notes:
    10450:   `C` will be created if `MAT_INITIAL_MATRIX` and must be destroyed by the user with `MatDestroy()`.

    10452:   `MAT_REUSE_MATRIX` can only be used if `A` and `B` have the same nonzero pattern as in the previous call.

    10454:   This is a convenience routine that wraps the use of `MatProductCreate()` with a `MatProductType` of `MATPRODUCT_AtB`
    10455:   functionality into a single function call. For more involved matrix-matrix operations see `MatProductCreate()`.

    10457:   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    10458:   actually needed.

    10460:   This routine is currently implemented for pairs of `MATAIJ` matrices and pairs of `MATSEQDENSE` matrices and classes
    10461:   which inherit from `MATSEQAIJ`.  `C` will be of the same type as the input matrices.

    10463:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10465: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MATPRODUCT_AtB`, `MatMatMult()`, `MatMatTransposeMult()`, `MatPtAP()`
    10466: @*/
    10467: PetscErrorCode MatTransposeMatMult(Mat A, Mat B, MatReuse scall, PetscReal fill, Mat *C)
    10468: {
    10469:   PetscFunctionBegin;
    10470:   PetscCall(MatProduct_Private(A, B, scall, fill, MATPRODUCT_AtB, C));
    10471:   PetscFunctionReturn(PETSC_SUCCESS);
    10472: }

    10474: /*@
    10475:   MatMatMatMult - Performs matrix-matrix-matrix multiplication D=A*B*C.

    10477:   Neighbor-wise Collective

    10479:   Input Parameters:
    10480: + A     - the left matrix
    10481: . B     - the middle matrix
    10482: . C     - the right matrix
    10483: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10484: - fill  - expected fill as ratio of nnz(D)/(nnz(A) + nnz(B)+nnz(C)), use `PETSC_DETERMINE` or `PETSC_CURRENT` if you do not have a good estimate
    10485:           if the result is a dense matrix this is irrelevant

    10487:   Output Parameter:
    10488: . D - the product matrix

    10490:   Level: intermediate

    10492:   Notes:
    10493:   Unless `scall` is `MAT_REUSE_MATRIX` `D` will be created.

    10495:   `MAT_REUSE_MATRIX` can only be used if the matrices `A`, `B`, and `C` have the same nonzero pattern as in the previous call

    10497:   This is a convenience routine that wraps the use of the `MatProductCreate()` with a `MatProductType` of `MATPRODUCT_ABC`
    10498:   functionality into a single function call. For more involved matrix-matrix operations see `MatProductCreate()`.

    10500:   To determine the correct fill value, run with `-info` and search for the string "Fill ratio" to see the value
    10501:   actually needed.

    10503:   If you have many matrices with the same non-zero structure to multiply, you
    10504:   should use `MAT_REUSE_MATRIX` in all calls but the first

    10506:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10508: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MATPRODUCT_ABC`, `MatMatMult`, `MatPtAP()`, `MatMatTransposeMult()`, `MatTransposeMatMult()`
    10509: @*/
    10510: PetscErrorCode MatMatMatMult(Mat A, Mat B, Mat C, MatReuse scall, PetscReal fill, Mat *D)
    10511: {
    10512:   PetscFunctionBegin;
    10513:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*D, 6);
    10514:   PetscCheck(scall != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Inplace product not supported");

    10516:   if (scall == MAT_INITIAL_MATRIX) {
    10517:     PetscCall(MatProductCreate(A, B, C, D));
    10518:     PetscCall(MatProductSetType(*D, MATPRODUCT_ABC));
    10519:     PetscCall(MatProductSetAlgorithm(*D, "default"));
    10520:     PetscCall(MatProductSetFill(*D, fill));

    10522:     (*D)->product->api_user = PETSC_TRUE;
    10523:     PetscCall(MatProductSetFromOptions(*D));
    10524:     PetscCheck((*D)->ops->productsymbolic, 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,
    10525:                ((PetscObject)C)->type_name);
    10526:     PetscCall(MatProductSymbolic(*D));
    10527:   } else { /* user may change input matrices when REUSE */
    10528:     PetscCall(MatProductReplaceMats(A, B, C, *D));
    10529:   }
    10530:   PetscCall(MatProductNumeric(*D));
    10531:   PetscFunctionReturn(PETSC_SUCCESS);
    10532: }

    10534: /*@
    10535:   MatCreateRedundantMatrix - Create redundant matrices and put them into processors of subcommunicators.

    10537:   Collective

    10539:   Input Parameters:
    10540: + mat      - the matrix
    10541: . nsubcomm - the number of subcommunicators (= number of redundant parallel or sequential matrices)
    10542: . subcomm  - MPI communicator split from the communicator where mat resides in (or `MPI_COMM_NULL` if nsubcomm is used)
    10543: - reuse    - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    10545:   Output Parameter:
    10546: . matredundant - redundant matrix

    10548:   Level: advanced

    10550:   Notes:
    10551:   `MAT_REUSE_MATRIX` can only be used when the nonzero structure of the
    10552:   original matrix has not changed from that last call to `MatCreateRedundantMatrix()`.

    10554:   This routine creates the duplicated matrices in the subcommunicators; you should NOT create them before
    10555:   calling it.

    10557:   `PetscSubcommCreate()` can be used to manage the creation of the subcomm but need not be.

    10559: .seealso: [](ch_matrices), `Mat`, `MatDestroy()`, `PetscSubcommCreate()`, `PetscSubcomm`
    10560: @*/
    10561: PetscErrorCode MatCreateRedundantMatrix(Mat mat, PetscInt nsubcomm, MPI_Comm subcomm, MatReuse reuse, Mat *matredundant)
    10562: {
    10563:   MPI_Comm       comm;
    10564:   PetscMPIInt    size;
    10565:   PetscInt       mloc_sub, nloc_sub, rstart, rend, M = mat->rmap->N, N = mat->cmap->N, bs = mat->rmap->bs;
    10566:   Mat_Redundant *redund     = NULL;
    10567:   PetscSubcomm   psubcomm   = NULL;
    10568:   MPI_Comm       subcomm_in = subcomm;
    10569:   Mat           *matseq;
    10570:   IS             isrow, iscol;
    10571:   PetscBool      newsubcomm = PETSC_FALSE;

    10573:   PetscFunctionBegin;
    10575:   if (nsubcomm && reuse == MAT_REUSE_MATRIX) {
    10576:     PetscAssertPointer(*matredundant, 5);
    10578:   }

    10580:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));
    10581:   if (size == 1 || nsubcomm == 1) {
    10582:     if (reuse == MAT_INITIAL_MATRIX) {
    10583:       PetscCall(MatDuplicate(mat, MAT_COPY_VALUES, matredundant));
    10584:     } else {
    10585:       PetscCheck(*matredundant != mat, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MAT_REUSE_MATRIX means reuse the matrix passed in as the final argument, not the original matrix");
    10586:       PetscCall(MatCopy(mat, *matredundant, SAME_NONZERO_PATTERN));
    10587:     }
    10588:     PetscFunctionReturn(PETSC_SUCCESS);
    10589:   }

    10591:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10592:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    10593:   MatCheckPreallocated(mat, 1);

    10595:   PetscCall(PetscLogEventBegin(MAT_RedundantMat, mat, 0, 0, 0));
    10596:   if (subcomm_in == MPI_COMM_NULL && reuse == MAT_INITIAL_MATRIX) { /* get subcomm if user does not provide subcomm */
    10597:     /* create psubcomm, then get subcomm */
    10598:     PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    10599:     PetscCallMPI(MPI_Comm_size(comm, &size));
    10600:     PetscCheck(nsubcomm >= 1 && nsubcomm <= size, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "nsubcomm must between 1 and %d", size);

    10602:     PetscCall(PetscSubcommCreate(comm, &psubcomm));
    10603:     PetscCall(PetscSubcommSetNumber(psubcomm, nsubcomm));
    10604:     PetscCall(PetscSubcommSetType(psubcomm, PETSC_SUBCOMM_CONTIGUOUS));
    10605:     PetscCall(PetscSubcommSetFromOptions(psubcomm));
    10606:     PetscCall(PetscCommDuplicate(PetscSubcommChild(psubcomm), &subcomm, NULL));
    10607:     newsubcomm = PETSC_TRUE;
    10608:     PetscCall(PetscSubcommDestroy(&psubcomm));
    10609:   }

    10611:   /* get isrow, iscol and a local sequential matrix matseq[0] */
    10612:   if (reuse == MAT_INITIAL_MATRIX) {
    10613:     mloc_sub = PETSC_DECIDE;
    10614:     nloc_sub = PETSC_DECIDE;
    10615:     if (bs < 1) {
    10616:       PetscCall(PetscSplitOwnership(subcomm, &mloc_sub, &M));
    10617:       PetscCall(PetscSplitOwnership(subcomm, &nloc_sub, &N));
    10618:     } else {
    10619:       PetscCall(PetscSplitOwnershipBlock(subcomm, bs, &mloc_sub, &M));
    10620:       PetscCall(PetscSplitOwnershipBlock(subcomm, bs, &nloc_sub, &N));
    10621:     }
    10622:     PetscCallMPI(MPI_Scan(&mloc_sub, &rend, 1, MPIU_INT, MPI_SUM, subcomm));
    10623:     rstart = rend - mloc_sub;
    10624:     PetscCall(ISCreateStride(PETSC_COMM_SELF, mloc_sub, rstart, 1, &isrow));
    10625:     PetscCall(ISCreateStride(PETSC_COMM_SELF, N, 0, 1, &iscol));
    10626:     PetscCall(ISSetIdentity(iscol));
    10627:   } else { /* reuse == MAT_REUSE_MATRIX */
    10628:     PetscCheck(*matredundant != mat, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MAT_REUSE_MATRIX means reuse the matrix passed in as the final argument, not the original matrix");
    10629:     /* retrieve subcomm */
    10630:     PetscCall(PetscObjectGetComm((PetscObject)*matredundant, &subcomm));
    10631:     redund = (*matredundant)->redundant;
    10632:     isrow  = redund->isrow;
    10633:     iscol  = redund->iscol;
    10634:     matseq = redund->matseq;
    10635:   }
    10636:   PetscCall(MatCreateSubMatrices(mat, 1, &isrow, &iscol, reuse, &matseq));

    10638:   /* get matredundant over subcomm */
    10639:   if (reuse == MAT_INITIAL_MATRIX) {
    10640:     PetscCall(MatCreateMPIMatConcatenateSeqMat(subcomm, matseq[0], nloc_sub, reuse, matredundant));

    10642:     /* create a supporting struct and attach it to C for reuse */
    10643:     PetscCall(PetscNew(&redund));
    10644:     (*matredundant)->redundant = redund;
    10645:     redund->isrow              = isrow;
    10646:     redund->iscol              = iscol;
    10647:     redund->matseq             = matseq;
    10648:     if (newsubcomm) {
    10649:       redund->subcomm = subcomm;
    10650:     } else {
    10651:       redund->subcomm = MPI_COMM_NULL;
    10652:     }
    10653:   } else {
    10654:     PetscCall(MatCreateMPIMatConcatenateSeqMat(subcomm, matseq[0], PETSC_DECIDE, reuse, matredundant));
    10655:   }
    10656: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
    10657:   if (matseq[0]->boundtocpu && matseq[0]->bindingpropagates) {
    10658:     PetscCall(MatBindToCPU(*matredundant, PETSC_TRUE));
    10659:     PetscCall(MatSetBindingPropagates(*matredundant, PETSC_TRUE));
    10660:   }
    10661: #endif
    10662:   PetscCall(PetscLogEventEnd(MAT_RedundantMat, mat, 0, 0, 0));
    10663:   PetscFunctionReturn(PETSC_SUCCESS);
    10664: }

    10666: /*@C
    10667:   MatGetMultiProcBlock - Create multiple 'parallel submatrices' from
    10668:   a given `Mat`. Each submatrix can span multiple procs.

    10670:   Collective

    10672:   Input Parameters:
    10673: + mat     - the matrix
    10674: . subComm - the sub communicator obtained as if by `MPI_Comm_split(PetscObjectComm((PetscObject)mat))`
    10675: - scall   - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    10677:   Output Parameter:
    10678: . subMat - parallel sub-matrices each spanning a given `subcomm`

    10680:   Level: advanced

    10682:   Notes:
    10683:   The submatrix partition across processors is dictated by `subComm` a
    10684:   communicator obtained by `MPI_comm_split()` or via `PetscSubcommCreate()`. The `subComm`
    10685:   is not restricted to be grouped with consecutive original MPI processes.

    10687:   Due the `MPI_Comm_split()` usage, the parallel layout of the submatrices
    10688:   map directly to the layout of the original matrix [wrt the local
    10689:   row,col partitioning]. So the original 'DiagonalMat' naturally maps
    10690:   into the 'DiagonalMat' of the `subMat`, hence it is used directly from
    10691:   the `subMat`. However the offDiagMat looses some columns - and this is
    10692:   reconstructed with `MatSetValues()`

    10694:   This is used by `PCBJACOBI` when a single block spans multiple MPI processes.

    10696: .seealso: [](ch_matrices), `Mat`, `MatCreateRedundantMatrix()`, `MatCreateSubMatrices()`, `PCBJACOBI`
    10697: @*/
    10698: PetscErrorCode MatGetMultiProcBlock(Mat mat, MPI_Comm subComm, MatReuse scall, Mat *subMat)
    10699: {
    10700:   PetscMPIInt commsize, subCommSize;

    10702:   PetscFunctionBegin;
    10703:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &commsize));
    10704:   PetscCallMPI(MPI_Comm_size(subComm, &subCommSize));
    10705:   PetscCheck(subCommSize <= commsize, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "CommSize %d < SubCommZize %d", commsize, subCommSize);

    10707:   PetscCheck(scall != MAT_REUSE_MATRIX || *subMat != mat, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MAT_REUSE_MATRIX means reuse the matrix passed in as the final argument, not the original matrix");
    10708:   PetscCall(PetscLogEventBegin(MAT_GetMultiProcBlock, mat, 0, 0, 0));
    10709:   PetscUseTypeMethod(mat, getmultiprocblock, subComm, scall, subMat);
    10710:   PetscCall(PetscLogEventEnd(MAT_GetMultiProcBlock, mat, 0, 0, 0));
    10711:   PetscFunctionReturn(PETSC_SUCCESS);
    10712: }

    10714: /*@
    10715:   MatGetLocalSubMatrix - Gets a reference to a submatrix specified in local numbering

    10717:   Not Collective

    10719:   Input Parameters:
    10720: + mat   - matrix to extract local submatrix from
    10721: . isrow - local row indices for submatrix
    10722: - iscol - local column indices for submatrix

    10724:   Output Parameter:
    10725: . submat - the submatrix

    10727:   Level: intermediate

    10729:   Notes:
    10730:   `submat` should be disposed of with `MatRestoreLocalSubMatrix()`.

    10732:   Depending on the format of `mat`, the returned `submat` may not implement `MatMult()`.  Its communicator may be
    10733:   the same as `mat`, it may be `PETSC_COMM_SELF`, or some other sub-communictor of `mat`'s.

    10735:   `submat` always implements `MatSetValuesLocal()`.  If `isrow` and `iscol` have the same block size, then
    10736:   `MatSetValuesBlockedLocal()` will also be implemented.

    10738:   `mat` must have had a `ISLocalToGlobalMapping` provided to it with `MatSetLocalToGlobalMapping()`.
    10739:   Matrices obtained with `DMCreateMatrix()` generally already have the local to global mapping provided.

    10741: .seealso: [](ch_matrices), `Mat`, `MatRestoreLocalSubMatrix()`, `MatCreateLocalRef()`, `MatSetLocalToGlobalMapping()`
    10742: @*/
    10743: PetscErrorCode MatGetLocalSubMatrix(Mat mat, IS isrow, IS iscol, Mat *submat)
    10744: {
    10745:   PetscFunctionBegin;
    10749:   PetscCheckSameComm(isrow, 2, iscol, 3);
    10750:   PetscAssertPointer(submat, 4);
    10751:   PetscCheck(mat->rmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Matrix must have local to global mapping provided before this call");

    10753:   if (mat->ops->getlocalsubmatrix) {
    10754:     PetscUseTypeMethod(mat, getlocalsubmatrix, isrow, iscol, submat);
    10755:   } else {
    10756:     PetscCall(MatCreateLocalRef(mat, isrow, iscol, submat));
    10757:   }
    10758:   (*submat)->assembled = mat->assembled;
    10759:   PetscFunctionReturn(PETSC_SUCCESS);
    10760: }

    10762: /*@
    10763:   MatRestoreLocalSubMatrix - Restores a reference to a submatrix specified in local numbering obtained with `MatGetLocalSubMatrix()`

    10765:   Not Collective

    10767:   Input Parameters:
    10768: + mat    - matrix to extract local submatrix from
    10769: . isrow  - local row indices for submatrix
    10770: . iscol  - local column indices for submatrix
    10771: - submat - the submatrix

    10773:   Level: intermediate

    10775: .seealso: [](ch_matrices), `Mat`, `MatGetLocalSubMatrix()`
    10776: @*/
    10777: PetscErrorCode MatRestoreLocalSubMatrix(Mat mat, IS isrow, IS iscol, Mat *submat)
    10778: {
    10779:   PetscFunctionBegin;
    10783:   PetscCheckSameComm(isrow, 2, iscol, 3);
    10784:   PetscAssertPointer(submat, 4);

    10787:   if (mat->ops->restorelocalsubmatrix) {
    10788:     PetscUseTypeMethod(mat, restorelocalsubmatrix, isrow, iscol, submat);
    10789:   } else {
    10790:     PetscCall(MatDestroy(submat));
    10791:   }
    10792:   *submat = NULL;
    10793:   PetscFunctionReturn(PETSC_SUCCESS);
    10794: }

    10796: /*@
    10797:   MatFindZeroDiagonals - Finds all the rows of a matrix that have zero or no diagonal entry in the matrix

    10799:   Collective

    10801:   Input Parameter:
    10802: . mat - the matrix

    10804:   Output Parameter:
    10805: . is - if any rows have zero diagonals this contains the list of them

    10807:   Level: developer

    10809: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    10810: @*/
    10811: PetscErrorCode MatFindZeroDiagonals(Mat mat, IS *is)
    10812: {
    10813:   PetscFunctionBegin;
    10816:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10817:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");

    10819:   if (!mat->ops->findzerodiagonals) {
    10820:     Vec                diag;
    10821:     const PetscScalar *a;
    10822:     PetscInt          *rows;
    10823:     PetscInt           rStart, rEnd, r, nrow = 0;

    10825:     PetscCall(MatCreateVecs(mat, &diag, NULL));
    10826:     PetscCall(MatGetDiagonal(mat, diag));
    10827:     PetscCall(MatGetOwnershipRange(mat, &rStart, &rEnd));
    10828:     PetscCall(VecGetArrayRead(diag, &a));
    10829:     for (r = 0; r < rEnd - rStart; ++r)
    10830:       if (a[r] == 0.0) ++nrow;
    10831:     PetscCall(PetscMalloc1(nrow, &rows));
    10832:     nrow = 0;
    10833:     for (r = 0; r < rEnd - rStart; ++r)
    10834:       if (a[r] == 0.0) rows[nrow++] = r + rStart;
    10835:     PetscCall(VecRestoreArrayRead(diag, &a));
    10836:     PetscCall(VecDestroy(&diag));
    10837:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)mat), nrow, rows, PETSC_OWN_POINTER, is));
    10838:   } else {
    10839:     PetscUseTypeMethod(mat, findzerodiagonals, is);
    10840:   }
    10841:   PetscFunctionReturn(PETSC_SUCCESS);
    10842: }

    10844: /*@
    10845:   MatFindOffBlockDiagonalEntries - Finds all the rows of a matrix that have entries outside of the main diagonal block (defined by the matrix block size)

    10847:   Collective

    10849:   Input Parameter:
    10850: . mat - the matrix

    10852:   Output Parameter:
    10853: . is - contains the list of rows with off block diagonal entries

    10855:   Level: developer

    10857: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    10858: @*/
    10859: PetscErrorCode MatFindOffBlockDiagonalEntries(Mat mat, IS *is)
    10860: {
    10861:   PetscFunctionBegin;
    10864:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10865:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");

    10867:   PetscUseTypeMethod(mat, findoffblockdiagonalentries, is);
    10868:   PetscFunctionReturn(PETSC_SUCCESS);
    10869: }

    10871: /*@C
    10872:   MatInvertBlockDiagonal - Inverts the block diagonal entries.

    10874:   Collective; No Fortran Support

    10876:   Input Parameter:
    10877: . mat - the matrix

    10879:   Output Parameter:
    10880: . values - the block inverses in column major order (FORTRAN-like)

    10882:   Level: advanced

    10884:   Notes:
    10885:   The size of the blocks is determined by the block size of the matrix.

    10887:   The blocks never overlap between two MPI processes, use `MatInvertVariableBlockEnvelope()` for that case

    10889:   The blocks all have the same size, use `MatInvertVariableBlockDiagonal()` for variable block size

    10891: .seealso: [](ch_matrices), `Mat`, `MatInvertVariableBlockEnvelope()`, `MatInvertBlockDiagonalMat()`
    10892: @*/
    10893: PetscErrorCode MatInvertBlockDiagonal(Mat mat, const PetscScalar *values[])
    10894: {
    10895:   PetscFunctionBegin;
    10897:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10898:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    10899:   PetscUseTypeMethod(mat, invertblockdiagonal, values);
    10900:   PetscFunctionReturn(PETSC_SUCCESS);
    10901: }

    10903: /*@
    10904:   MatInvertVariableBlockDiagonal - Inverts the point block diagonal entries.

    10906:   Collective; No Fortran Support

    10908:   Input Parameters:
    10909: + mat     - the matrix
    10910: . nblocks - the number of blocks on the process, set with `MatSetVariableBlockSizes()`
    10911: - bsizes  - the size of each block on the process, set with `MatSetVariableBlockSizes()`

    10913:   Output Parameter:
    10914: . values - the block inverses in column major order (FORTRAN-like)

    10916:   Level: advanced

    10918:   Notes:
    10919:   Use `MatInvertBlockDiagonal()` if all blocks have the same size

    10921:   The blocks never overlap between two MPI processes, use `MatInvertVariableBlockEnvelope()` for that case

    10923: .seealso: [](ch_matrices), `Mat`, `MatInvertBlockDiagonal()`, `MatSetVariableBlockSizes()`, `MatInvertVariableBlockEnvelope()`
    10924: @*/
    10925: PetscErrorCode MatInvertVariableBlockDiagonal(Mat mat, PetscInt nblocks, const PetscInt bsizes[], PetscScalar values[])
    10926: {
    10927:   PetscFunctionBegin;
    10929:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10930:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    10931:   PetscUseTypeMethod(mat, invertvariableblockdiagonal, nblocks, bsizes, values);
    10932:   PetscFunctionReturn(PETSC_SUCCESS);
    10933: }

    10935: /*@
    10936:   MatInvertBlockDiagonalMat - set the values of matrix C to be the inverted block diagonal of matrix A

    10938:   Collective

    10940:   Input Parameters:
    10941: + A - the matrix
    10942: - C - matrix with inverted block diagonal of `A`.  This matrix should be created and may have its type set.

    10944:   Level: advanced

    10946:   Note:
    10947:   The blocksize of the matrix is used to determine the blocks on the diagonal of `C`

    10949: .seealso: [](ch_matrices), `Mat`, `MatInvertBlockDiagonal()`
    10950: @*/
    10951: PetscErrorCode MatInvertBlockDiagonalMat(Mat A, Mat C)
    10952: {
    10953:   const PetscScalar *vals;
    10954:   PetscInt          *dnnz;
    10955:   PetscInt           m, rstart, rend, bs, i, j;

    10957:   PetscFunctionBegin;
    10958:   PetscCall(MatInvertBlockDiagonal(A, &vals));
    10959:   PetscCall(MatGetBlockSize(A, &bs));
    10960:   PetscCall(MatGetLocalSize(A, &m, NULL));
    10961:   PetscCall(MatSetLayouts(C, A->rmap, A->cmap));
    10962:   PetscCall(MatSetBlockSizes(C, A->rmap->bs, A->cmap->bs));
    10963:   PetscCall(PetscMalloc1(m / bs, &dnnz));
    10964:   for (j = 0; j < m / bs; j++) dnnz[j] = 1;
    10965:   PetscCall(MatXAIJSetPreallocation(C, bs, dnnz, NULL, NULL, NULL));
    10966:   PetscCall(PetscFree(dnnz));
    10967:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));
    10968:   PetscCall(MatSetOption(C, MAT_ROW_ORIENTED, PETSC_FALSE));
    10969:   for (i = rstart / bs; i < rend / bs; i++) PetscCall(MatSetValuesBlocked(C, 1, &i, 1, &i, &vals[(i - rstart / bs) * bs * bs], INSERT_VALUES));
    10970:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    10971:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    10972:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    10973:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    10974:   PetscCall(MatSetOption(C, MAT_ROW_ORIENTED, PETSC_TRUE));
    10975:   PetscFunctionReturn(PETSC_SUCCESS);
    10976: }

    10978: /*@
    10979:   MatTransposeColoringDestroy - Destroys a coloring context for matrix product $C = A*B^T$ that was created
    10980:   via `MatTransposeColoringCreate()`.

    10982:   Collective

    10984:   Input Parameter:
    10985: . c - coloring context

    10987:   Level: intermediate

    10989: .seealso: [](ch_matrices), `Mat`, `MatTransposeColoringCreate()`
    10990: @*/
    10991: PetscErrorCode MatTransposeColoringDestroy(MatTransposeColoring *c)
    10992: {
    10993:   MatTransposeColoring matcolor = *c;

    10995:   PetscFunctionBegin;
    10996:   if (!matcolor) PetscFunctionReturn(PETSC_SUCCESS);
    10997:   if (--((PetscObject)matcolor)->refct > 0) {
    10998:     matcolor = NULL;
    10999:     PetscFunctionReturn(PETSC_SUCCESS);
    11000:   }

    11002:   PetscCall(PetscFree3(matcolor->ncolumns, matcolor->nrows, matcolor->colorforrow));
    11003:   PetscCall(PetscFree(matcolor->rows));
    11004:   PetscCall(PetscFree(matcolor->den2sp));
    11005:   PetscCall(PetscFree(matcolor->colorforcol));
    11006:   PetscCall(PetscFree(matcolor->columns));
    11007:   if (matcolor->brows > 0) PetscCall(PetscFree(matcolor->lstart));
    11008:   PetscCall(PetscHeaderDestroy(c));
    11009:   PetscFunctionReturn(PETSC_SUCCESS);
    11010: }

    11012: /*@
    11013:   MatTransColoringApplySpToDen - Given a symbolic matrix product $C = A*B^T$ for which
    11014:   a `MatTransposeColoring` context has been created, computes a dense $B^T$ by applying
    11015:   `MatTransposeColoring` to sparse `B`.

    11017:   Collective

    11019:   Input Parameters:
    11020: + coloring - coloring context created with `MatTransposeColoringCreate()`
    11021: - B        - sparse matrix

    11023:   Output Parameter:
    11024: . Btdense - dense matrix $B^T$

    11026:   Level: developer

    11028:   Note:
    11029:   These are used internally for some implementations of `MatRARt()`

    11031: .seealso: [](ch_matrices), `Mat`, `MatTransposeColoringCreate()`, `MatTransposeColoringDestroy()`, `MatTransColoringApplyDenToSp()`
    11032: @*/
    11033: PetscErrorCode MatTransColoringApplySpToDen(MatTransposeColoring coloring, Mat B, Mat Btdense)
    11034: {
    11035:   PetscFunctionBegin;

    11040:   PetscCall((*B->ops->transcoloringapplysptoden)(coloring, B, Btdense));
    11041:   PetscFunctionReturn(PETSC_SUCCESS);
    11042: }

    11044: /*@
    11045:   MatTransColoringApplyDenToSp - Given a symbolic matrix product $C_{sp} = A*B^T$ for which
    11046:   a `MatTransposeColoring` context has been created and a dense matrix $C_{den} = A*B^T_{dense}$
    11047:   in which `B^T_{dens}` is obtained from `MatTransColoringApplySpToDen()`, recover sparse matrix
    11048:   $C_{sp}$ from $C_{den}$.

    11050:   Collective

    11052:   Input Parameters:
    11053: + matcoloring - coloring context created with `MatTransposeColoringCreate()`
    11054: - Cden        - matrix product of a sparse matrix and a dense matrix Btdense

    11056:   Output Parameter:
    11057: . Csp - sparse matrix

    11059:   Level: developer

    11061:   Note:
    11062:   These are used internally for some implementations of `MatRARt()`

    11064: .seealso: [](ch_matrices), `Mat`, `MatTransposeColoringCreate()`, `MatTransposeColoringDestroy()`, `MatTransColoringApplySpToDen()`
    11065: @*/
    11066: PetscErrorCode MatTransColoringApplyDenToSp(MatTransposeColoring matcoloring, Mat Cden, Mat Csp)
    11067: {
    11068:   PetscFunctionBegin;

    11073:   PetscCall((*Csp->ops->transcoloringapplydentosp)(matcoloring, Cden, Csp));
    11074:   PetscCall(MatAssemblyBegin(Csp, MAT_FINAL_ASSEMBLY));
    11075:   PetscCall(MatAssemblyEnd(Csp, MAT_FINAL_ASSEMBLY));
    11076:   PetscFunctionReturn(PETSC_SUCCESS);
    11077: }

    11079: /*@
    11080:   MatTransposeColoringCreate - Creates a matrix coloring context for the matrix product $C = A*B^T$.

    11082:   Collective

    11084:   Input Parameters:
    11085: + mat        - the matrix product C
    11086: - iscoloring - the coloring of the matrix; usually obtained with `MatColoringCreate()` or `DMCreateColoring()`

    11088:   Output Parameter:
    11089: . color - the new coloring context

    11091:   Level: intermediate

    11093: .seealso: [](ch_matrices), `Mat`, `MatTransposeColoringDestroy()`, `MatTransColoringApplySpToDen()`,
    11094:           `MatTransColoringApplyDenToSp()`
    11095: @*/
    11096: PetscErrorCode MatTransposeColoringCreate(Mat mat, ISColoring iscoloring, MatTransposeColoring *color)
    11097: {
    11098:   MatTransposeColoring c;
    11099:   MPI_Comm             comm;

    11101:   PetscFunctionBegin;
    11102:   PetscAssertPointer(color, 3);

    11104:   PetscCall(PetscLogEventBegin(MAT_TransposeColoringCreate, mat, 0, 0, 0));
    11105:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    11106:   PetscCall(PetscHeaderCreate(c, MAT_TRANSPOSECOLORING_CLASSID, "MatTransposeColoring", "Matrix product C=A*B^T via coloring", "Mat", comm, MatTransposeColoringDestroy, NULL));
    11107:   c->ctype = iscoloring->ctype;
    11108:   PetscUseTypeMethod(mat, transposecoloringcreate, iscoloring, c);
    11109:   *color = c;
    11110:   PetscCall(PetscLogEventEnd(MAT_TransposeColoringCreate, mat, 0, 0, 0));
    11111:   PetscFunctionReturn(PETSC_SUCCESS);
    11112: }

    11114: /*@
    11115:   MatGetNonzeroState - Returns a 64-bit integer representing the current state of nonzeros in the matrix. If the
    11116:   matrix has had new nonzero locations added to (or removed from) the matrix since the previous call, the value will be larger.

    11118:   Not Collective

    11120:   Input Parameter:
    11121: . mat - the matrix

    11123:   Output Parameter:
    11124: . state - the current state

    11126:   Level: intermediate

    11128:   Notes:
    11129:   You can only compare states from two different calls to the SAME matrix, you cannot compare calls between
    11130:   different matrices

    11132:   Use `PetscObjectStateGet()` to check for changes to the numerical values in a matrix

    11134:   Use the result of `PetscObjectGetId()` to compare if a previously checked matrix is the same as the current matrix, do not compare object pointers.

    11136: .seealso: [](ch_matrices), `Mat`, `PetscObjectStateGet()`, `PetscObjectGetId()`
    11137: @*/
    11138: PetscErrorCode MatGetNonzeroState(Mat mat, PetscObjectState *state)
    11139: {
    11140:   PetscFunctionBegin;
    11142:   *state = mat->nonzerostate;
    11143:   PetscFunctionReturn(PETSC_SUCCESS);
    11144: }

    11146: /*@
    11147:   MatCreateMPIMatConcatenateSeqMat - Creates a single large PETSc matrix by concatenating sequential
    11148:   matrices from each processor

    11150:   Collective

    11152:   Input Parameters:
    11153: + comm   - the communicators the parallel matrix will live on
    11154: . seqmat - the input sequential matrices
    11155: . n      - number of local columns (or `PETSC_DECIDE`)
    11156: - reuse  - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    11158:   Output Parameter:
    11159: . mpimat - the parallel matrix generated

    11161:   Level: developer

    11163:   Note:
    11164:   The number of columns of the matrix in EACH processor MUST be the same.

    11166: .seealso: [](ch_matrices), `Mat`
    11167: @*/
    11168: PetscErrorCode MatCreateMPIMatConcatenateSeqMat(MPI_Comm comm, Mat seqmat, PetscInt n, MatReuse reuse, Mat *mpimat)
    11169: {
    11170:   PetscMPIInt size;

    11172:   PetscFunctionBegin;
    11173:   PetscCallMPI(MPI_Comm_size(comm, &size));
    11174:   if (size == 1) {
    11175:     if (reuse == MAT_INITIAL_MATRIX) {
    11176:       PetscCall(MatDuplicate(seqmat, MAT_COPY_VALUES, mpimat));
    11177:     } else {
    11178:       PetscCall(MatCopy(seqmat, *mpimat, SAME_NONZERO_PATTERN));
    11179:     }
    11180:     PetscFunctionReturn(PETSC_SUCCESS);
    11181:   }

    11183:   PetscCheck(reuse != MAT_REUSE_MATRIX || seqmat != *mpimat, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "MAT_REUSE_MATRIX means reuse the matrix passed in as the final argument, not the original matrix");

    11185:   PetscCall(PetscLogEventBegin(MAT_Merge, seqmat, 0, 0, 0));
    11186:   PetscCall((*seqmat->ops->creatempimatconcatenateseqmat)(comm, seqmat, n, reuse, mpimat));
    11187:   PetscCall(PetscLogEventEnd(MAT_Merge, seqmat, 0, 0, 0));
    11188:   PetscFunctionReturn(PETSC_SUCCESS);
    11189: }

    11191: /*@
    11192:   MatSubdomainsCreateCoalesce - Creates index subdomains by coalescing adjacent MPI processes' ownership ranges.

    11194:   Collective

    11196:   Input Parameters:
    11197: + A - the matrix to create subdomains from
    11198: - N - requested number of subdomains

    11200:   Output Parameters:
    11201: + n   - number of subdomains resulting on this MPI process
    11202: - iss - `IS` list with indices of subdomains on this MPI process

    11204:   Level: advanced

    11206:   Note:
    11207:   The number of subdomains must be smaller than the communicator size

    11209: .seealso: [](ch_matrices), `Mat`, `IS`
    11210: @*/
    11211: PetscErrorCode MatSubdomainsCreateCoalesce(Mat A, PetscInt N, PetscInt *n, IS *iss[])
    11212: {
    11213:   MPI_Comm    comm, subcomm;
    11214:   PetscMPIInt size, rank, color;
    11215:   PetscInt    rstart, rend, k;

    11217:   PetscFunctionBegin;
    11218:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    11219:   PetscCallMPI(MPI_Comm_size(comm, &size));
    11220:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    11221:   PetscCheck(N >= 1 && N < size, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "number of subdomains must be > 0 and < %d, got N = %" PetscInt_FMT, size, N);
    11222:   *n    = 1;
    11223:   k     = size / N + (size % N > 0); /* There are up to k ranks to a color */
    11224:   color = rank / k;
    11225:   PetscCallMPI(MPI_Comm_split(comm, color, rank, &subcomm));
    11226:   PetscCall(PetscMalloc1(1, iss));
    11227:   PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
    11228:   PetscCall(ISCreateStride(subcomm, rend - rstart, rstart, 1, iss[0]));
    11229:   PetscCallMPI(MPI_Comm_free(&subcomm));
    11230:   PetscFunctionReturn(PETSC_SUCCESS);
    11231: }

    11233: /*@
    11234:   MatGalerkin - Constructs the coarse grid problem matrix via Galerkin projection.

    11236:   If the interpolation and restriction operators are the same, uses `MatPtAP()`.
    11237:   If they are not the same, uses `MatMatMatMult()`.

    11239:   Once the coarse grid problem is constructed, correct for interpolation operators
    11240:   that are not of full rank, which can legitimately happen in the case of non-nested
    11241:   geometric multigrid.

    11243:   Input Parameters:
    11244: + restrct     - restriction operator
    11245: . dA          - fine grid matrix
    11246: . interpolate - interpolation operator
    11247: . reuse       - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    11248: - fill        - expected fill, use `PETSC_DETERMINE` or `PETSC_DETERMINE` if you do not have a good estimate

    11250:   Output Parameter:
    11251: . A - the Galerkin coarse matrix

    11253:   Options Database Key:
    11254: . -pc_mg_galerkin (both|pmat|mat|none) - for what matrices the Galerkin process should be used

    11256:   Level: developer

    11258:   Note:
    11259:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    11261: .seealso: [](ch_matrices), `Mat`, `MatPtAP()`, `MatMatMatMult()`
    11262: @*/
    11263: PetscErrorCode MatGalerkin(Mat restrct, Mat dA, Mat interpolate, MatReuse reuse, PetscReal fill, Mat *A)
    11264: {
    11265:   IS  zerorows;
    11266:   Vec diag;

    11268:   PetscFunctionBegin;
    11269:   PetscCheck(reuse != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Inplace product not supported");
    11270:   /* Construct the coarse grid matrix */
    11271:   if (interpolate == restrct) {
    11272:     PetscCall(MatPtAP(dA, interpolate, reuse, fill, A));
    11273:   } else {
    11274:     PetscCall(MatMatMatMult(restrct, dA, interpolate, reuse, fill, A));
    11275:   }

    11277:   /* If the interpolation matrix is not of full rank, A will have zero rows.
    11278:      This can legitimately happen in the case of non-nested geometric multigrid.
    11279:      In that event, we set the rows of the matrix to the rows of the identity,
    11280:      ignoring the equations (as the RHS will also be zero). */

    11282:   PetscCall(MatFindZeroRows(*A, &zerorows));

    11284:   if (zerorows != NULL) { /* if there are any zero rows */
    11285:     PetscCall(MatCreateVecs(*A, &diag, NULL));
    11286:     PetscCall(MatGetDiagonal(*A, diag));
    11287:     PetscCall(VecISSet(diag, zerorows, 1.0));
    11288:     PetscCall(MatDiagonalSet(*A, diag, INSERT_VALUES));
    11289:     PetscCall(VecDestroy(&diag));
    11290:     PetscCall(ISDestroy(&zerorows));
    11291:   }
    11292:   PetscFunctionReturn(PETSC_SUCCESS);
    11293: }

    11295: /*@C
    11296:   MatSetOperation - Allows user to set a matrix operation for any matrix type

    11298:   Logically Collective

    11300:   Input Parameters:
    11301: + mat - the matrix
    11302: . op  - the name of the operation
    11303: - f   - the function that provides the operation

    11305:   Level: developer

    11307:   Example Usage:
    11308: .vb
    11309:   extern PetscErrorCode usermult(Mat, Vec, Vec);

    11311:   PetscCall(MatCreateXXX(comm, ..., &A));
    11312:   PetscCall(MatSetOperation(A, MATOP_MULT, (PetscErrorCodeFn *)usermult));
    11313: .ve

    11315:   Notes:
    11316:   See the file `include/petscmat.h` for a complete list of matrix
    11317:   operations, which all have the form MATOP_<OPERATION>, where
    11318:   <OPERATION> is the name (in all capital letters) of the
    11319:   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).

    11321:   All user-provided functions (except for `MATOP_DESTROY`) should have the same calling
    11322:   sequence as the usual matrix interface routines, since they
    11323:   are intended to be accessed via the usual matrix interface
    11324:   routines, e.g.,
    11325: .vb
    11326:   MatMult(Mat, Vec, Vec) -> usermult(Mat, Vec, Vec)
    11327: .ve

    11329:   In particular each function MUST return `PETSC_SUCCESS` on success and
    11330:   nonzero on failure.

    11332:   This routine is distinct from `MatShellSetOperation()` in that it can be called on any matrix type.

    11334: .seealso: [](ch_matrices), `Mat`, `MatGetOperation()`, `MatCreateShell()`, `MatShellSetContext()`, `MatShellSetOperation()`
    11335: @*/
    11336: PetscErrorCode MatSetOperation(Mat mat, MatOperation op, PetscErrorCodeFn *f)
    11337: {
    11338:   PetscFunctionBegin;
    11340:   if (op == MATOP_VIEW && !mat->ops->viewnative && f != (PetscErrorCodeFn *)mat->ops->view) mat->ops->viewnative = mat->ops->view;
    11341:   (((PetscErrorCodeFn **)mat->ops)[op]) = f;
    11342:   PetscFunctionReturn(PETSC_SUCCESS);
    11343: }

    11345: /*@C
    11346:   MatGetOperation - Gets a matrix operation for any matrix type.

    11348:   Not Collective

    11350:   Input Parameters:
    11351: + mat - the matrix
    11352: - op  - the name of the operation

    11354:   Output Parameter:
    11355: . f - the function that provides the operation

    11357:   Level: developer

    11359:   Example Usage:
    11360: .vb
    11361:   PetscErrorCode (*usermult)(Mat, Vec, Vec);

    11363:   MatGetOperation(A, MATOP_MULT, (PetscErrorCodeFn **)&usermult);
    11364: .ve

    11366:   Notes:
    11367:   See the file `include/petscmat.h` for a complete list of matrix
    11368:   operations, which all have the form MATOP_<OPERATION>, where
    11369:   <OPERATION> is the name (in all capital letters) of the
    11370:   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).

    11372:   This routine is distinct from `MatShellGetOperation()` in that it can be called on any matrix type.

    11374: .seealso: [](ch_matrices), `Mat`, `MatSetOperation()`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`
    11375: @*/
    11376: PetscErrorCode MatGetOperation(Mat mat, MatOperation op, PetscErrorCodeFn **f)
    11377: {
    11378:   PetscFunctionBegin;
    11380:   *f = (((PetscErrorCodeFn **)mat->ops)[op]);
    11381:   PetscFunctionReturn(PETSC_SUCCESS);
    11382: }

    11384: /*@
    11385:   MatHasOperation - Determines whether the given matrix supports the particular operation.

    11387:   Not Collective

    11389:   Input Parameters:
    11390: + mat - the matrix
    11391: - op  - the operation, for example, `MATOP_GET_DIAGONAL`

    11393:   Output Parameter:
    11394: . has - either `PETSC_TRUE` or `PETSC_FALSE`

    11396:   Level: advanced

    11398:   Note:
    11399:   See `MatSetOperation()` for additional discussion on naming convention and usage of `op`.

    11401: .seealso: [](ch_matrices), `Mat`, `MatCreateShell()`, `MatGetOperation()`, `MatSetOperation()`
    11402: @*/
    11403: PetscErrorCode MatHasOperation(Mat mat, MatOperation op, PetscBool *has)
    11404: {
    11405:   PetscFunctionBegin;
    11407:   PetscAssertPointer(has, 3);
    11408:   if (mat->ops->hasoperation) {
    11409:     PetscUseTypeMethod(mat, hasoperation, op, has);
    11410:   } else {
    11411:     if (((void **)mat->ops)[op]) *has = PETSC_TRUE;
    11412:     else {
    11413:       *has = PETSC_FALSE;
    11414:       if (op == MATOP_CREATE_SUBMATRIX) {
    11415:         PetscMPIInt size;

    11417:         PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));
    11418:         if (size == 1) PetscCall(MatHasOperation(mat, MATOP_CREATE_SUBMATRICES, has));
    11419:       }
    11420:     }
    11421:   }
    11422:   PetscFunctionReturn(PETSC_SUCCESS);
    11423: }

    11425: /*@
    11426:   MatHasCongruentLayouts - Determines whether the rows and columns layouts of the matrix are congruent

    11428:   Collective

    11430:   Input Parameter:
    11431: . mat - the matrix

    11433:   Output Parameter:
    11434: . cong - either `PETSC_TRUE` or `PETSC_FALSE`

    11436:   Level: beginner

    11438: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatSetSizes()`, `PetscLayout`
    11439: @*/
    11440: PetscErrorCode MatHasCongruentLayouts(Mat mat, PetscBool *cong)
    11441: {
    11442:   PetscFunctionBegin;
    11445:   PetscAssertPointer(cong, 2);
    11446:   if (!mat->rmap || !mat->cmap) {
    11447:     *cong = mat->rmap == mat->cmap ? PETSC_TRUE : PETSC_FALSE;
    11448:     PetscFunctionReturn(PETSC_SUCCESS);
    11449:   }
    11450:   if (mat->congruentlayouts == PETSC_DECIDE) { /* first time we compare rows and cols layouts */
    11451:     PetscCall(PetscLayoutSetUp(mat->rmap));
    11452:     PetscCall(PetscLayoutSetUp(mat->cmap));
    11453:     PetscCall(PetscLayoutCompare(mat->rmap, mat->cmap, cong));
    11454:     if (*cong) mat->congruentlayouts = 1;
    11455:     else mat->congruentlayouts = 0;
    11456:   } else *cong = mat->congruentlayouts ? PETSC_TRUE : PETSC_FALSE;
    11457:   PetscFunctionReturn(PETSC_SUCCESS);
    11458: }

    11460: PetscErrorCode MatSetInf(Mat A)
    11461: {
    11462:   PetscFunctionBegin;
    11463:   PetscUseTypeMethod(A, setinf);
    11464:   PetscFunctionReturn(PETSC_SUCCESS);
    11465: }

    11467: /*@
    11468:   MatCreateGraph - create a scalar matrix (that is a matrix with one vertex for each block vertex in the original matrix), for use in graph algorithms
    11469:   and possibly removes small values from the graph structure.

    11471:   Collective

    11473:   Input Parameters:
    11474: + A       - the matrix
    11475: . sym     - `PETSC_TRUE` indicates that the graph should be symmetrized
    11476: . scale   - `PETSC_TRUE` indicates that the graph edge weights should be symmetrically scaled with the diagonal entry
    11477: . filter  - filter value - < 0: does nothing; == 0: removes only 0.0 entries; otherwise: removes entries with abs(entries) <= value
    11478: . num_idx - size of `index` array
    11479: - index   - array of block indices to use for graph strength of connection weight

    11481:   Output Parameter:
    11482: . graph - the resulting graph

    11484:   Level: advanced

    11486: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `PCGAMG`
    11487: @*/
    11488: PetscErrorCode MatCreateGraph(Mat A, PetscBool sym, PetscBool scale, PetscReal filter, PetscInt num_idx, PetscInt index[], Mat *graph)
    11489: {
    11490:   PetscFunctionBegin;
    11494:   PetscAssertPointer(graph, 7);
    11495:   PetscCall(PetscLogEventBegin(MAT_CreateGraph, A, 0, 0, 0));
    11496:   PetscUseTypeMethod(A, creategraph, sym, scale, filter, num_idx, index, graph);
    11497:   PetscCall(PetscLogEventEnd(MAT_CreateGraph, A, 0, 0, 0));
    11498:   PetscFunctionReturn(PETSC_SUCCESS);
    11499: }

    11501: /*@
    11502:   MatEliminateZeros - eliminate the nondiagonal zero entries in place from the nonzero structure of a sparse `Mat` in place,
    11503:   meaning the same memory is used for the matrix, and no new memory is allocated.

    11505:   Collective

    11507:   Input Parameters:
    11508: + A    - the matrix
    11509: - keep - if for a given row of `A`, the diagonal coefficient is zero, indicates whether it should be left in the structure or eliminated as well

    11511:   Level: intermediate

    11513:   Developer Note:
    11514:   The entries in the sparse matrix data structure are shifted to fill in the unneeded locations in the data. Thus the end
    11515:   of the arrays in the data structure are unneeded.

    11517: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateGraph()`, `MatFilter()`
    11518: @*/
    11519: PetscErrorCode MatEliminateZeros(Mat A, PetscBool keep)
    11520: {
    11521:   PetscFunctionBegin;
    11523:   PetscUseTypeMethod(A, eliminatezeros, keep);
    11524:   PetscFunctionReturn(PETSC_SUCCESS);
    11525: }

    11527: /*@C
    11528:   MatGetCurrentMemType - Get the memory location of the matrix

    11530:   Not Collective, but the result will be the same on all MPI processes

    11532:   Input Parameter:
    11533: . A - the matrix whose memory type we are checking

    11535:   Output Parameter:
    11536: . m - the memory type

    11538:   Level: intermediate

    11540: .seealso: [](ch_matrices), `Mat`, `MatBoundToCPU()`, `PetscMemType`
    11541: @*/
    11542: PetscErrorCode MatGetCurrentMemType(Mat A, PetscMemType *m)
    11543: {
    11544:   PetscFunctionBegin;
    11546:   PetscAssertPointer(m, 2);
    11547:   if (A->ops->getcurrentmemtype) PetscUseTypeMethod(A, getcurrentmemtype, m);
    11548:   else *m = PETSC_MEMTYPE_HOST;
    11549:   PetscFunctionReturn(PETSC_SUCCESS);
    11550: }