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

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

     51: /*@
     52:   MatSetRandom - Sets all components of a matrix to random numbers.

     54:   Logically Collective

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

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

     68:   Level: intermediate

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

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

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

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

     83:   PetscFunctionBegin;
     87:   MatCheckPreallocated(x, 1);

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

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

    107: /*@
    108:   MatCopyHashToXAIJ - copy hash table entries into an XAIJ matrix type

    110:   Logically Collective

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

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

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

    124:   Level: advanced

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

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

    139: /*@
    140:   MatFactorGetErrorZeroPivot - returns the pivot value that was determined to be zero and the row it occurred in

    142:   Logically Collective

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

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

    152:   Level: advanced

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

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

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

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

    176: /*@
    177:   MatFactorGetError - gets the error code from a factorization

    179:   Logically Collective

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

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

    187:   Level: advanced

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

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

    204: /*@
    205:   MatFactorClearError - clears the error code in a factorization

    207:   Logically Collective

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

    212:   Level: developer

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

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

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

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

    287: /*@
    288:   MatFindNonzeroRows - Locate all rows that are not completely zero in the matrix

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

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

    296:   Level: intermediate

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

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

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

    320: /*@
    321:   MatFindZeroRows - Locate all rows that are completely zero in the matrix

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

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

    329:   Level: intermediate

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

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

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

    359: /*@
    360:   MatGetDiagonalBlock - Returns the part of the matrix associated with the on-process coupling

    362:   Not Collective

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

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

    370:   Level: advanced

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

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

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

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

    397: /*@
    398:   MatGetTrace - Gets the trace of a matrix. The sum of the diagonal entries.

    400:   Collective

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

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

    408:   Level: advanced

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

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

    426: /*@
    427:   MatRealPart - Zeros out the imaginary part of the matrix

    429:   Logically Collective

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

    434:   Level: advanced

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

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

    453:   Collective

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

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

    462:   Level: advanced

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

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

    484: /*@
    485:   MatImaginaryPart - Moves the imaginary part of the matrix to the real part and zeros the imaginary part

    487:   Logically Collective

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

    492:   Level: advanced

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

    508: /*@
    509:   MatMissingDiagonal - Determine if sparse matrix is missing a diagonal entry (or block entry for `MATBAIJ` and `MATSBAIJ` matrices) in the nonzero structure

    511:   Not Collective

    513:   Input Parameter:
    514: . mat - the matrix

    516:   Output Parameters:
    517: + missing - is any diagonal entry missing
    518: - dd      - first diagonal entry that is missing (optional) on this process

    520:   Level: advanced

    522:   Note:
    523:   This does not return diagonal entries that are in the nonzero structure but happen to have a zero numerical value

    525: .seealso: [](ch_matrices), `Mat`
    526: @*/
    527: PetscErrorCode MatMissingDiagonal(Mat mat, PetscBool *missing, PetscInt *dd)
    528: {
    529:   PetscFunctionBegin;
    532:   PetscAssertPointer(missing, 2);
    533:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix %s", ((PetscObject)mat)->type_name);
    534:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    535:   PetscUseTypeMethod(mat, missingdiagonal, missing, dd);
    536:   PetscFunctionReturn(PETSC_SUCCESS);
    537: }

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

    545:   Not Collective

    547:   Input Parameters:
    548: + mat - the matrix
    549: - row - the row to get

    551:   Output Parameters:
    552: + ncols - if not `NULL`, the number of nonzeros in `row`
    553: . cols  - if not `NULL`, the column numbers
    554: - vals  - if not `NULL`, the numerical values

    556:   Level: advanced

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

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

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

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

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

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

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

    584:   Fortran Note:
    585: .vb
    586:   PetscInt, pointer :: cols(:)
    587:   PetscScalar, pointer :: vals(:)
    588: .ve

    590: .seealso: [](ch_matrices), `Mat`, `MatRestoreRow()`, `MatSetValues()`, `MatGetValues()`, `MatCreateSubMatrices()`, `MatGetDiagonal()`, `MatGetRowIJ()`, `MatRestoreRowIJ()`
    591: @*/
    592: PetscErrorCode MatGetRow(Mat mat, PetscInt row, PetscInt *ncols, const PetscInt *cols[], const PetscScalar *vals[])
    593: {
    594:   PetscInt incols;

    596:   PetscFunctionBegin;
    599:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    600:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    601:   MatCheckPreallocated(mat, 1);
    602:   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);
    603:   PetscCall(PetscLogEventBegin(MAT_GetRow, mat, 0, 0, 0));
    604:   PetscUseTypeMethod(mat, getrow, row, &incols, (PetscInt **)cols, (PetscScalar **)vals);
    605:   if (ncols) *ncols = incols;
    606:   PetscCall(PetscLogEventEnd(MAT_GetRow, mat, 0, 0, 0));
    607:   PetscFunctionReturn(PETSC_SUCCESS);
    608: }

    610: /*@
    611:   MatConjugate - replaces the matrix values with their complex conjugates

    613:   Logically Collective

    615:   Input Parameter:
    616: . mat - the matrix

    618:   Level: advanced

    620: .seealso: [](ch_matrices), `Mat`, `MatRealPart()`, `MatImaginaryPart()`, `VecConjugate()`, `MatTranspose()`
    621: @*/
    622: PetscErrorCode MatConjugate(Mat mat)
    623: {
    624:   PetscFunctionBegin;
    626:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    627:   if (PetscDefined(USE_COMPLEX) && !(mat->symmetric == PETSC_BOOL3_TRUE && mat->hermitian == PETSC_BOOL3_TRUE)) {
    628:     PetscUseTypeMethod(mat, conjugate);
    629:     PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    630:   }
    631:   PetscFunctionReturn(PETSC_SUCCESS);
    632: }

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

    637:   Not Collective

    639:   Input Parameters:
    640: + mat   - the matrix
    641: . row   - the row to get
    642: . ncols - the number of nonzeros
    643: . cols  - the columns of the nonzeros
    644: - vals  - if nonzero the column values

    646:   Level: advanced

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

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

    655:   Fortran Note:
    656: .vb
    657:   PetscInt, pointer :: cols(:)
    658:   PetscScalar, pointer :: vals(:)
    659: .ve

    661: .seealso: [](ch_matrices), `Mat`, `MatGetRow()`
    662: @*/
    663: PetscErrorCode MatRestoreRow(Mat mat, PetscInt row, PetscInt *ncols, const PetscInt *cols[], const PetscScalar *vals[])
    664: {
    665:   PetscFunctionBegin;
    667:   if (ncols) PetscAssertPointer(ncols, 3);
    668:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    669:   PetscTryTypeMethod(mat, restorerow, row, ncols, (PetscInt **)cols, (PetscScalar **)vals);
    670:   if (ncols) *ncols = 0;
    671:   if (cols) *cols = NULL;
    672:   if (vals) *vals = NULL;
    673:   PetscFunctionReturn(PETSC_SUCCESS);
    674: }

    676: /*@
    677:   MatGetRowUpperTriangular - Sets a flag to enable calls to `MatGetRow()` for matrix in `MATSBAIJ` format.
    678:   You should call `MatRestoreRowUpperTriangular()` after calling` MatGetRow()` and `MatRestoreRow()` to disable the flag.

    680:   Not Collective

    682:   Input Parameter:
    683: . mat - the matrix

    685:   Level: advanced

    687:   Note:
    688:   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.

    690: .seealso: [](ch_matrices), `Mat`, `MATSBAIJ`, `MatRestoreRowUpperTriangular()`
    691: @*/
    692: PetscErrorCode MatGetRowUpperTriangular(Mat mat)
    693: {
    694:   PetscFunctionBegin;
    697:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    698:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    699:   MatCheckPreallocated(mat, 1);
    700:   PetscTryTypeMethod(mat, getrowuppertriangular);
    701:   PetscFunctionReturn(PETSC_SUCCESS);
    702: }

    704: /*@
    705:   MatRestoreRowUpperTriangular - Disable calls to `MatGetRow()` for matrix in `MATSBAIJ` format.

    707:   Not Collective

    709:   Input Parameter:
    710: . mat - the matrix

    712:   Level: advanced

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

    717: .seealso: [](ch_matrices), `Mat`, `MATSBAIJ`, `MatGetRowUpperTriangular()`
    718: @*/
    719: PetscErrorCode MatRestoreRowUpperTriangular(Mat mat)
    720: {
    721:   PetscFunctionBegin;
    724:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    725:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    726:   MatCheckPreallocated(mat, 1);
    727:   PetscTryTypeMethod(mat, restorerowuppertriangular);
    728:   PetscFunctionReturn(PETSC_SUCCESS);
    729: }

    731: /*@
    732:   MatSetOptionsPrefix - Sets the prefix used for searching for all
    733:   `Mat` options in the database.

    735:   Logically Collective

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

    741:   Level: advanced

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

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

    751: .seealso: [](ch_matrices), `Mat`, `MatSetFromOptions()`, `MatSetOptionsPrefixFactor()`
    752: @*/
    753: PetscErrorCode MatSetOptionsPrefix(Mat A, const char prefix[])
    754: {
    755:   PetscFunctionBegin;
    757:   PetscCall(PetscObjectSetOptionsPrefix((PetscObject)A, prefix));
    758:   PetscTryMethod(A, "MatSetOptionsPrefix_C", (Mat, const char[]), (A, prefix));
    759:   PetscFunctionReturn(PETSC_SUCCESS);
    760: }

    762: /*@
    763:   MatSetOptionsPrefixFactor - Sets the prefix used for searching for all matrix factor options in the database for
    764:   for matrices created with `MatGetFactor()`

    766:   Logically Collective

    768:   Input Parameters:
    769: + A      - the matrix
    770: - prefix - the prefix to prepend to all option names for the factored matrix

    772:   Level: developer

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

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

    781: .seealso: [](ch_matrices), `Mat`,   [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatSetFromOptions()`, `MatSetOptionsPrefix()`, `MatAppendOptionsPrefixFactor()`
    782: @*/
    783: PetscErrorCode MatSetOptionsPrefixFactor(Mat A, const char prefix[])
    784: {
    785:   PetscFunctionBegin;
    787:   if (prefix) {
    788:     PetscAssertPointer(prefix, 2);
    789:     PetscCheck(prefix[0] != '-', PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Options prefix should not begin with a hyphen");
    790:     if (prefix != A->factorprefix) {
    791:       PetscCall(PetscFree(A->factorprefix));
    792:       PetscCall(PetscStrallocpy(prefix, &A->factorprefix));
    793:     }
    794:   } else PetscCall(PetscFree(A->factorprefix));
    795:   PetscFunctionReturn(PETSC_SUCCESS);
    796: }

    798: /*@
    799:   MatAppendOptionsPrefixFactor - Appends to the prefix used for searching for all matrix factor options in the database for
    800:   for matrices created with `MatGetFactor()`

    802:   Logically Collective

    804:   Input Parameters:
    805: + A      - the matrix
    806: - prefix - the prefix to prepend to all option names for the factored matrix

    808:   Level: developer

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

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

    817: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `PetscOptionsCreate()`, `PetscOptionsDestroy()`, `PetscObjectSetOptionsPrefix()`, `PetscObjectPrependOptionsPrefix()`,
    818:           `PetscObjectGetOptionsPrefix()`, `TSAppendOptionsPrefix()`, `SNESAppendOptionsPrefix()`, `KSPAppendOptionsPrefix()`, `MatSetOptionsPrefixFactor()`,
    819:           `MatSetOptionsPrefix()`
    820: @*/
    821: PetscErrorCode MatAppendOptionsPrefixFactor(Mat A, const char prefix[])
    822: {
    823:   size_t len1, len2, new_len;

    825:   PetscFunctionBegin;
    827:   if (!prefix) PetscFunctionReturn(PETSC_SUCCESS);
    828:   if (!A->factorprefix) {
    829:     PetscCall(MatSetOptionsPrefixFactor(A, prefix));
    830:     PetscFunctionReturn(PETSC_SUCCESS);
    831:   }
    832:   PetscCheck(prefix[0] != '-', PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Options prefix should not begin with a hyphen");

    834:   PetscCall(PetscStrlen(A->factorprefix, &len1));
    835:   PetscCall(PetscStrlen(prefix, &len2));
    836:   new_len = len1 + len2 + 1;
    837:   PetscCall(PetscRealloc(new_len * sizeof(*A->factorprefix), &A->factorprefix));
    838:   PetscCall(PetscStrncpy(A->factorprefix + len1, prefix, len2 + 1));
    839:   PetscFunctionReturn(PETSC_SUCCESS);
    840: }

    842: /*@
    843:   MatAppendOptionsPrefix - Appends to the prefix used for searching for all
    844:   matrix options in the database.

    846:   Logically Collective

    848:   Input Parameters:
    849: + A      - the matrix
    850: - prefix - the prefix to prepend to all option names

    852:   Level: advanced

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

    858: .seealso: [](ch_matrices), `Mat`, `MatGetOptionsPrefix()`, `MatAppendOptionsPrefixFactor()`, `MatSetOptionsPrefix()`
    859: @*/
    860: PetscErrorCode MatAppendOptionsPrefix(Mat A, const char prefix[])
    861: {
    862:   PetscFunctionBegin;
    864:   PetscCall(PetscObjectAppendOptionsPrefix((PetscObject)A, prefix));
    865:   PetscTryMethod(A, "MatAppendOptionsPrefix_C", (Mat, const char[]), (A, prefix));
    866:   PetscFunctionReturn(PETSC_SUCCESS);
    867: }

    869: /*@
    870:   MatGetOptionsPrefix - Gets the prefix used for searching for all
    871:   matrix options in the database.

    873:   Not Collective

    875:   Input Parameter:
    876: . A - the matrix

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

    881:   Level: advanced

    883: .seealso: [](ch_matrices), `Mat`, `MatAppendOptionsPrefix()`, `MatSetOptionsPrefix()`, `MatAppendOptionsPrefixFactor()`, `MatSetOptionsPrefixFactor()`
    884: @*/
    885: PetscErrorCode MatGetOptionsPrefix(Mat A, const char *prefix[])
    886: {
    887:   PetscFunctionBegin;
    889:   PetscAssertPointer(prefix, 2);
    890:   PetscCall(PetscObjectGetOptionsPrefix((PetscObject)A, prefix));
    891:   PetscFunctionReturn(PETSC_SUCCESS);
    892: }

    894: /*@
    895:   MatGetState - Gets the state of a `Mat`. Same value as returned by `PetscObjectStateGet()`

    897:   Not Collective

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

    902:   Output Parameter:
    903: . state - the object state

    905:   Level: advanced

    907:   Note:
    908:   Object state is an integer which gets increased every time
    909:   the object is changed. By saving and later querying the object state
    910:   one can determine whether information about the object is still current.

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

    914: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `PetscObjectStateGet()`, `MatGetNonzeroState()`
    915: @*/
    916: PetscErrorCode MatGetState(Mat A, PetscObjectState *state)
    917: {
    918:   PetscFunctionBegin;
    920:   PetscAssertPointer(state, 2);
    921:   PetscCall(PetscObjectStateGet((PetscObject)A, state));
    922:   PetscFunctionReturn(PETSC_SUCCESS);
    923: }

    925: /*@
    926:   MatResetPreallocation - Reset matrix to use the original preallocation values provided by the user, for example with `MatXAIJSetPreallocation()`

    928:   Collective

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

    933:   Level: beginner

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

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

    942:   Currently only supported for  `MATAIJ` matrices.

    944: .seealso: [](ch_matrices), `Mat`, `MatSeqAIJSetPreallocation()`, `MatMPIAIJSetPreallocation()`, `MatXAIJSetPreallocation()`
    945: @*/
    946: PetscErrorCode MatResetPreallocation(Mat A)
    947: {
    948:   PetscFunctionBegin;
    951:   PetscUseMethod(A, "MatResetPreallocation_C", (Mat), (A));
    952:   PetscFunctionReturn(PETSC_SUCCESS);
    953: }

    955: /*@
    956:   MatResetHash - Reset the matrix so that it will use a hash table for the next round of `MatSetValues()` and `MatAssemblyBegin()`/`MatAssemblyEnd()`.

    958:   Collective

    960:   Input Parameter:
    961: . A - the matrix

    963:   Level: intermediate

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

    968:   Currently only supported for `MATAIJ` matrices.

    970: .seealso: [](ch_matrices), `Mat`, `MatResetPreallocation()`
    971: @*/
    972: PetscErrorCode MatResetHash(Mat A)
    973: {
    974:   PetscFunctionBegin;
    977:   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()");
    978:   if (A->num_ass == 0) PetscFunctionReturn(PETSC_SUCCESS);
    979:   PetscUseMethod(A, "MatResetHash_C", (Mat), (A));
    980:   /* These flags are used to determine whether certain setups occur */
    981:   A->was_assembled = PETSC_FALSE;
    982:   A->assembled     = PETSC_FALSE;
    983:   /* Log that the state of this object has changed; this will help guarantee that preconditioners get re-setup */
    984:   PetscCall(PetscObjectStateIncrease((PetscObject)A));
    985:   PetscFunctionReturn(PETSC_SUCCESS);
    986: }

    988: /*@
    989:   MatSetUp - Sets up the internal matrix data structures for later use by the matrix

    991:   Collective

    993:   Input Parameter:
    994: . A - the matrix

    996:   Level: advanced

    998:   Notes:
    999:   If the user has not set preallocation for this matrix then an efficient algorithm will be used for the first round of
    1000:   setting values in the matrix.

    1002:   This routine is called internally by other `Mat` functions when needed so rarely needs to be called by users

    1004: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatCreate()`, `MatDestroy()`, `MatXAIJSetPreallocation()`
    1005: @*/
    1006: PetscErrorCode MatSetUp(Mat A)
    1007: {
    1008:   PetscFunctionBegin;
    1010:   if (!((PetscObject)A)->type_name) {
    1011:     PetscMPIInt size;

    1013:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    1014:     PetscCall(MatSetType(A, size == 1 ? MATSEQAIJ : MATMPIAIJ));
    1015:   }
    1016:   if (!A->preallocated) PetscTryTypeMethod(A, setup);
    1017:   PetscCall(PetscLayoutSetUp(A->rmap));
    1018:   PetscCall(PetscLayoutSetUp(A->cmap));
    1019:   A->preallocated = PETSC_TRUE;
    1020:   PetscFunctionReturn(PETSC_SUCCESS);
    1021: }

    1023: #if defined(PETSC_HAVE_SAWS)
    1024: #include <petscviewersaws.h>
    1025: #endif

    1027: /*
    1028:    If threadsafety is on extraneous matrices may be printed

    1030:    This flag cannot be stored in the matrix because the original matrix in MatView() may assemble a new matrix which is passed into MatViewFromOptions()
    1031: */
    1032: #if !defined(PETSC_HAVE_THREADSAFETY)
    1033: static PetscInt insidematview = 0;
    1034: #endif

    1036: /*@
    1037:   MatViewFromOptions - View properties of the matrix based on options set in the options database

    1039:   Collective

    1041:   Input Parameters:
    1042: + A    - the matrix
    1043: . obj  - optional additional object that provides the options prefix to use
    1044: - name - command line option

    1046:   Options Database Key:
    1047: . -mat_view [viewertype]:... - the viewer and its options

    1049:   Level: intermediate

    1051:   Note:
    1052: .vb
    1053:     If no value is provided ascii:stdout is used
    1054:        ascii[:[filename][:[format][:append]]]    defaults to stdout - format can be one of ascii_info, ascii_info_detail, or ascii_matlab,
    1055:                                                   for example ascii::ascii_info prints just the information about the object not all details
    1056:                                                   unless :append is given filename opens in write mode, overwriting what was already there
    1057:        binary[:[filename][:[format][:append]]]   defaults to the file binaryoutput
    1058:        draw[:drawtype[:filename]]                for example, draw:tikz, draw:tikz:figure.tex  or draw:x
    1059:        socket[:port]                             defaults to the standard output port
    1060:        saws[:communicatorname]                    publishes object to the Scientific Application Webserver (SAWs)
    1061: .ve

    1063: .seealso: [](ch_matrices), `Mat`, `MatView()`, `PetscObjectViewFromOptions()`, `MatCreate()`
    1064: @*/
    1065: PetscErrorCode MatViewFromOptions(Mat A, PetscObject obj, const char name[])
    1066: {
    1067:   PetscFunctionBegin;
    1069: #if !defined(PETSC_HAVE_THREADSAFETY)
    1070:   if (insidematview) PetscFunctionReturn(PETSC_SUCCESS);
    1071: #endif
    1072:   PetscCall(PetscObjectViewFromOptions((PetscObject)A, obj, name));
    1073:   PetscFunctionReturn(PETSC_SUCCESS);
    1074: }

    1076: /*@
    1077:   MatView - display information about a matrix in a variety ways

    1079:   Collective on viewer

    1081:   Input Parameters:
    1082: + mat    - the matrix
    1083: - viewer - visualization context

    1085:   Options Database Keys:
    1086: + -mat_view ::ascii_info           - Prints info on matrix at conclusion of `MatAssemblyEnd()`
    1087: . -mat_view ::ascii_info_detail    - Prints more detailed info
    1088: . -mat_view                        - Prints matrix in ASCII format
    1089: . -mat_view ::ascii_matlab         - Prints matrix in MATLAB format
    1090: . -mat_view draw                   - PetscDraws nonzero structure of matrix, using `MatView()` and `PetscDrawOpenX()`.
    1091: . -display <name>                  - Sets display name (default is host)
    1092: . -draw_pause <sec>                - Sets number of seconds to pause after display
    1093: . -mat_view socket                 - Sends matrix to socket, can be accessed from MATLAB (see Users-Manual: ch_matlab for details)
    1094: . -viewer_socket_machine <machine> - -
    1095: . -viewer_socket_port <port>       - -
    1096: . -mat_view binary                 - save matrix to file in binary format
    1097: - -viewer_binary_filename <name>   - -

    1099:   Level: beginner

    1101:   Notes:
    1102:   The available visualization contexts include
    1103: +    `PETSC_VIEWER_STDOUT_SELF`   - for sequential matrices
    1104: .    `PETSC_VIEWER_STDOUT_WORLD`  - for parallel matrices created on `PETSC_COMM_WORLD`
    1105: .    `PETSC_VIEWER_STDOUT_`(comm) - for matrices created on MPI communicator comm
    1106: -     `PETSC_VIEWER_DRAW_WORLD`   - graphical display of nonzero structure

    1108:   The user can open alternative visualization contexts with
    1109: +    `PetscViewerASCIIOpen()`  - Outputs matrix to a specified file
    1110: .    `PetscViewerBinaryOpen()` - Outputs matrix in binary to a  specified file; corresponding input uses `MatLoad()`
    1111: .    `PetscViewerDrawOpen()`   - Outputs nonzero matrix nonzero structure to an X window display
    1112: -    `PetscViewerSocketOpen()` - Outputs matrix to Socket viewer, `PETSCVIEWERSOCKET`. Only the `MATSEQDENSE` and `MATAIJ` types support this viewer.

    1114:   The user can call `PetscViewerPushFormat()` to specify the output
    1115:   format of ASCII printed objects (when using `PETSC_VIEWER_STDOUT_SELF`,
    1116:   `PETSC_VIEWER_STDOUT_WORLD` and `PetscViewerASCIIOpen()`).  Available formats include
    1117: +    `PETSC_VIEWER_DEFAULT`           - default, prints matrix contents
    1118: .    `PETSC_VIEWER_ASCII_MATLAB`      - prints matrix contents in MATLAB format
    1119: .    `PETSC_VIEWER_ASCII_DENSE`       - prints entire matrix including zeros
    1120: .    `PETSC_VIEWER_ASCII_COMMON`      - prints matrix contents, using a sparse  format common among all matrix types
    1121: .    `PETSC_VIEWER_ASCII_IMPL`        - prints matrix contents, using an implementation-specific format (which is in many cases the same as the default)
    1122: .    `PETSC_VIEWER_ASCII_INFO`        - prints basic information about the matrix size and structure (not the matrix entries)
    1123: -    `PETSC_VIEWER_ASCII_INFO_DETAIL` - prints more detailed information about the matrix nonzero structure (still not vector or matrix entries)

    1125:   The ASCII viewers are only recommended for small matrices on at most a moderate number of processes,
    1126:   the program will seemingly hang and take hours for larger matrices, for larger matrices one should use the binary format.

    1128:   In the debugger you can do "call MatView(mat,0)" to display the matrix. (The same holds for any PETSc object viewer).

    1130:   See the manual page for `MatLoad()` for the exact format of the binary file when the binary
    1131:   viewer is used.

    1133:   See share/petsc/matlab/PetscBinaryRead.m for a MATLAB code that can read in the binary file when the binary
    1134:   viewer is used and lib/petsc/bin/PetscBinaryIO.py for loading them into Python.

    1136:   One can use '-mat_view draw -draw_pause -1' to pause the graphical display of matrix nonzero structure,
    1137:   and then use the following mouse functions.
    1138: .vb
    1139:   left mouse: zoom in
    1140:   middle mouse: zoom out
    1141:   right mouse: continue with the simulation
    1142: .ve

    1144: .seealso: [](ch_matrices), `Mat`, `PetscViewerPushFormat()`, `PetscViewerASCIIOpen()`, `PetscViewerDrawOpen()`, `PetscViewer`,
    1145:           `PetscViewerSocketOpen()`, `PetscViewerBinaryOpen()`, `MatLoad()`, `MatViewFromOptions()`
    1146: @*/
    1147: PetscErrorCode MatView(Mat mat, PetscViewer viewer)
    1148: {
    1149:   PetscInt          rows, cols, rbs, cbs;
    1150:   PetscBool         isascii, isstring, issaws;
    1151:   PetscViewerFormat format;
    1152:   PetscMPIInt       size;

    1154:   PetscFunctionBegin;
    1157:   if (!viewer) PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)mat), &viewer));

    1160:   PetscCall(PetscViewerGetFormat(viewer, &format));
    1161:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)viewer), &size));
    1162:   if (size == 1 && format == PETSC_VIEWER_LOAD_BALANCE) PetscFunctionReturn(PETSC_SUCCESS);

    1164: #if !defined(PETSC_HAVE_THREADSAFETY)
    1165:   insidematview++;
    1166: #endif
    1167:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSTRING, &isstring));
    1168:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    1169:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSAWS, &issaws));
    1170:   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");

    1172:   PetscCall(PetscLogEventBegin(MAT_View, mat, viewer, 0, 0));
    1173:   if (isascii) {
    1174:     if (!mat->preallocated) {
    1175:       PetscCall(PetscViewerASCIIPrintf(viewer, "Matrix has not been preallocated yet\n"));
    1176: #if !defined(PETSC_HAVE_THREADSAFETY)
    1177:       insidematview--;
    1178: #endif
    1179:       PetscCall(PetscLogEventEnd(MAT_View, mat, viewer, 0, 0));
    1180:       PetscFunctionReturn(PETSC_SUCCESS);
    1181:     }
    1182:     if (!mat->assembled) {
    1183:       PetscCall(PetscViewerASCIIPrintf(viewer, "Matrix has not been assembled yet\n"));
    1184: #if !defined(PETSC_HAVE_THREADSAFETY)
    1185:       insidematview--;
    1186: #endif
    1187:       PetscCall(PetscLogEventEnd(MAT_View, mat, viewer, 0, 0));
    1188:       PetscFunctionReturn(PETSC_SUCCESS);
    1189:     }
    1190:     PetscCall(PetscObjectPrintClassNamePrefixType((PetscObject)mat, viewer));
    1191:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1192:       MatNullSpace nullsp, transnullsp;

    1194:       PetscCall(PetscViewerASCIIPushTab(viewer));
    1195:       PetscCall(MatGetSize(mat, &rows, &cols));
    1196:       PetscCall(MatGetBlockSizes(mat, &rbs, &cbs));
    1197:       if (rbs != 1 || cbs != 1) {
    1198:         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" : ""));
    1199:         else PetscCall(PetscViewerASCIIPrintf(viewer, "rows=%" PetscInt_FMT ", cols=%" PetscInt_FMT ", bs=%" PetscInt_FMT "%s\n", rows, cols, rbs, mat->bsizes ? " variable blocks set" : ""));
    1200:       } else PetscCall(PetscViewerASCIIPrintf(viewer, "rows=%" PetscInt_FMT ", cols=%" PetscInt_FMT "\n", rows, cols));
    1201:       if (mat->factortype) {
    1202:         MatSolverType solver;
    1203:         PetscCall(MatFactorGetSolverType(mat, &solver));
    1204:         PetscCall(PetscViewerASCIIPrintf(viewer, "package used to perform factorization: %s\n", solver));
    1205:       }
    1206:       if (mat->ops->getinfo) {
    1207:         PetscBool is_constant_or_diagonal;

    1209:         // Don't print nonzero information for constant or diagonal matrices, it just adds noise to the output
    1210:         PetscCall(PetscObjectTypeCompareAny((PetscObject)mat, &is_constant_or_diagonal, MATCONSTANTDIAGONAL, MATDIAGONAL, ""));
    1211:         if (!is_constant_or_diagonal) {
    1212:           MatInfo info;

    1214:           PetscCall(MatGetInfo(mat, MAT_GLOBAL_SUM, &info));
    1215:           PetscCall(PetscViewerASCIIPrintf(viewer, "total: nonzeros=%.f, allocated nonzeros=%.f\n", info.nz_used, info.nz_allocated));
    1216:           if (!mat->factortype) PetscCall(PetscViewerASCIIPrintf(viewer, "total number of mallocs used during MatSetValues calls=%" PetscInt_FMT "\n", (PetscInt)info.mallocs));
    1217:         }
    1218:       }
    1219:       PetscCall(MatGetNullSpace(mat, &nullsp));
    1220:       PetscCall(MatGetTransposeNullSpace(mat, &transnullsp));
    1221:       if (nullsp) PetscCall(PetscViewerASCIIPrintf(viewer, "  has attached null space\n"));
    1222:       if (transnullsp && transnullsp != nullsp) PetscCall(PetscViewerASCIIPrintf(viewer, "  has attached transposed null space\n"));
    1223:       PetscCall(MatGetNearNullSpace(mat, &nullsp));
    1224:       if (nullsp) PetscCall(PetscViewerASCIIPrintf(viewer, "  has attached near null space\n"));
    1225:       PetscCall(PetscViewerASCIIPushTab(viewer));
    1226:       PetscCall(MatProductView(mat, viewer));
    1227:       PetscCall(PetscViewerASCIIPopTab(viewer));
    1228:       if (mat->bsizes && format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1229:         IS tmp;

    1231:         PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)viewer), mat->nblocks, mat->bsizes, PETSC_USE_POINTER, &tmp));
    1232:         PetscCall(PetscObjectSetName((PetscObject)tmp, "Block Sizes"));
    1233:         PetscCall(PetscViewerASCIIPushTab(viewer));
    1234:         PetscCall(ISView(tmp, viewer));
    1235:         PetscCall(PetscViewerASCIIPopTab(viewer));
    1236:         PetscCall(ISDestroy(&tmp));
    1237:       }
    1238:     }
    1239:   } else if (issaws) {
    1240: #if defined(PETSC_HAVE_SAWS)
    1241:     PetscMPIInt rank;

    1243:     PetscCall(PetscObjectName((PetscObject)mat));
    1244:     PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
    1245:     if (!((PetscObject)mat)->amsmem && rank == 0) PetscCall(PetscObjectViewSAWs((PetscObject)mat, viewer));
    1246: #endif
    1247:   } else if (isstring) {
    1248:     const char *type;
    1249:     PetscCall(MatGetType(mat, &type));
    1250:     PetscCall(PetscViewerStringSPrintf(viewer, " MatType: %-7.7s", type));
    1251:     PetscTryTypeMethod(mat, view, viewer);
    1252:   }
    1253:   if ((format == PETSC_VIEWER_NATIVE || format == PETSC_VIEWER_LOAD_BALANCE) && mat->ops->viewnative) {
    1254:     PetscCall(PetscViewerASCIIPushTab(viewer));
    1255:     PetscUseTypeMethod(mat, viewnative, viewer);
    1256:     PetscCall(PetscViewerASCIIPopTab(viewer));
    1257:   } else if (mat->ops->view) {
    1258:     PetscCall(PetscViewerASCIIPushTab(viewer));
    1259:     PetscUseTypeMethod(mat, view, viewer);
    1260:     PetscCall(PetscViewerASCIIPopTab(viewer));
    1261:   }
    1262:   if (isascii) {
    1263:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1264:     if (format == PETSC_VIEWER_ASCII_INFO || format == PETSC_VIEWER_ASCII_INFO_DETAIL) PetscCall(PetscViewerASCIIPopTab(viewer));
    1265:   }
    1266:   PetscCall(PetscLogEventEnd(MAT_View, mat, viewer, 0, 0));
    1267: #if !defined(PETSC_HAVE_THREADSAFETY)
    1268:   insidematview--;
    1269: #endif
    1270:   PetscFunctionReturn(PETSC_SUCCESS);
    1271: }

    1273: #if defined(PETSC_USE_DEBUG)
    1274: #include <../src/sys/totalview/tv_data_display.h>
    1275: PETSC_UNUSED static int TV_display_type(const struct _p_Mat *mat)
    1276: {
    1277:   TV_add_row("Local rows", "int", &mat->rmap->n);
    1278:   TV_add_row("Local columns", "int", &mat->cmap->n);
    1279:   TV_add_row("Global rows", "int", &mat->rmap->N);
    1280:   TV_add_row("Global columns", "int", &mat->cmap->N);
    1281:   TV_add_row("Typename", TV_ascii_string_type, ((PetscObject)mat)->type_name);
    1282:   return TV_format_OK;
    1283: }
    1284: #endif

    1286: /*@
    1287:   MatLoad - Loads a matrix that has been stored in binary/HDF5 format
    1288:   with `MatView()`.  The matrix format is determined from the options database.
    1289:   Generates a parallel MPI matrix if the communicator has more than one
    1290:   processor.  The default matrix type is `MATAIJ`.

    1292:   Collective

    1294:   Input Parameters:
    1295: + mat    - the newly loaded matrix, this needs to have been created with `MatCreate()`
    1296:             or some related function before a call to `MatLoad()`
    1297: - viewer - `PETSCVIEWERBINARY`/`PETSCVIEWERHDF5` file viewer

    1299:   Options Database Key:
    1300: . -matload_block_size <bs> - set block size

    1302:   Level: beginner

    1304:   Notes:
    1305:   If the `Mat` type has not yet been given then `MATAIJ` is used, call `MatSetFromOptions()` on the
    1306:   `Mat` before calling this routine if you wish to set it from the options database.

    1308:   `MatLoad()` automatically loads into the options database any options
    1309:   given in the file filename.info where filename is the name of the file
    1310:   that was passed to the `PetscViewerBinaryOpen()`. The options in the info
    1311:   file will be ignored if you use the -viewer_binary_skip_info option.

    1313:   If the type or size of mat is not set before a call to `MatLoad()`, PETSc
    1314:   sets the default matrix type AIJ and sets the local and global sizes.
    1315:   If type and/or size is already set, then the same are used.

    1317:   In parallel, each processor can load a subset of rows (or the
    1318:   entire matrix).  This routine is especially useful when a large
    1319:   matrix is stored on disk and only part of it is desired on each
    1320:   processor.  For example, a parallel solver may access only some of
    1321:   the rows from each processor.  The algorithm used here reads
    1322:   relatively small blocks of data rather than reading the entire
    1323:   matrix and then subsetting it.

    1325:   Viewer's `PetscViewerType` must be either `PETSCVIEWERBINARY` or `PETSCVIEWERHDF5`.
    1326:   Such viewer can be created using `PetscViewerBinaryOpen()` or `PetscViewerHDF5Open()`,
    1327:   or the sequence like
    1328: .vb
    1329:     `PetscViewer` v;
    1330:     `PetscViewerCreate`(`PETSC_COMM_WORLD`,&v);
    1331:     `PetscViewerSetType`(v,`PETSCVIEWERBINARY`);
    1332:     `PetscViewerSetFromOptions`(v);
    1333:     `PetscViewerFileSetMode`(v,`FILE_MODE_READ`);
    1334:     `PetscViewerFileSetName`(v,"datafile");
    1335: .ve
    1336:   The optional `PetscViewerSetFromOptions()` call allows overriding `PetscViewerSetType()` using the option
    1337: .vb
    1338:   -viewer_type {binary, hdf5}
    1339: .ve

    1341:   See the example src/ksp/ksp/tutorials/ex27.c with the first approach,
    1342:   and src/mat/tutorials/ex10.c with the second approach.

    1344:   In case of `PETSCVIEWERBINARY`, a native PETSc binary format is used. Each of the blocks
    1345:   is read onto MPI rank 0 and then shipped to its destination MPI rank, one after another.
    1346:   Multiple objects, both matrices and vectors, can be stored within the same file.
    1347:   Their `PetscObject` name is ignored; they are loaded in the order of their storage.

    1349:   Most users should not need to know the details of the binary storage
    1350:   format, since `MatLoad()` and `MatView()` completely hide these details.
    1351:   But for anyone who is interested, the standard binary matrix storage
    1352:   format is

    1354: .vb
    1355:     PetscInt    MAT_FILE_CLASSID
    1356:     PetscInt    number of rows
    1357:     PetscInt    number of columns
    1358:     PetscInt    total number of nonzeros
    1359:     PetscInt    *number nonzeros in each row
    1360:     PetscInt    *column indices of all nonzeros (starting index is zero)
    1361:     PetscScalar *values of all nonzeros
    1362: .ve
    1363:   If PETSc was not configured with `--with-64-bit-indices` then only `MATMPIAIJ` matrices with more than `PETSC_INT_MAX` non-zeros can be
    1364:   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
    1365:   case will not fit in a (32-bit) `PetscInt` the value `PETSC_INT_MAX` is used for the header entry `total number of nonzeros`.

    1367:   PETSc automatically does the byte swapping for
    1368:   machines that store the bytes reversed. Thus if you write your own binary
    1369:   read/write routines you have to swap the bytes; see `PetscBinaryRead()`
    1370:   and `PetscBinaryWrite()` to see how this may be done.

    1372:   In case of `PETSCVIEWERHDF5`, a parallel HDF5 reader is used.
    1373:   Each processor's chunk is loaded independently by its owning MPI process.
    1374:   Multiple objects, both matrices and vectors, can be stored within the same file.
    1375:   They are looked up by their PetscObject name.

    1377:   As the MATLAB MAT-File Version 7.3 format is also a HDF5 flavor, we decided to use
    1378:   by default the same structure and naming of the AIJ arrays and column count
    1379:   within the HDF5 file. This means that a MAT file saved with -v7.3 flag, e.g.
    1380: .vb
    1381:   save example.mat A b -v7.3
    1382: .ve
    1383:   can be directly read by this routine (see Reference 1 for details).

    1385:   Depending on your MATLAB version, this format might be a default,
    1386:   otherwise you can set it as default in Preferences.

    1388:   Unless -nocompression flag is used to save the file in MATLAB,
    1389:   PETSc must be configured with ZLIB package.

    1391:   See also examples src/mat/tutorials/ex10.c and src/ksp/ksp/tutorials/ex27.c

    1393:   This reader currently supports only real `MATSEQAIJ`, `MATMPIAIJ`, `MATSEQDENSE` and `MATMPIDENSE` matrices for `PETSCVIEWERHDF5`

    1395:   Corresponding `MatView()` is not yet implemented.

    1397:   The loaded matrix is actually a transpose of the original one in MATLAB,
    1398:   unless you push `PETSC_VIEWER_HDF5_MAT` format (see examples above).
    1399:   With this format, matrix is automatically transposed by PETSc,
    1400:   unless the matrix is marked as SPD or symmetric
    1401:   (see `MatSetOption()`, `MAT_SPD`, `MAT_SYMMETRIC`).

    1403:   See MATLAB Documentation on `save()`, <https://www.mathworks.com/help/matlab/ref/save.html#btox10b-1-version>

    1405: .seealso: [](ch_matrices), `Mat`, `PetscViewerBinaryOpen()`, `PetscViewerSetType()`, `MatView()`, `VecLoad()`
    1406:  @*/
    1407: PetscErrorCode MatLoad(Mat mat, PetscViewer viewer)
    1408: {
    1409:   PetscBool flg;

    1411:   PetscFunctionBegin;

    1415:   if (!((PetscObject)mat)->type_name) PetscCall(MatSetType(mat, MATAIJ));

    1417:   flg = PETSC_FALSE;
    1418:   PetscCall(PetscOptionsGetBool(((PetscObject)mat)->options, ((PetscObject)mat)->prefix, "-matload_symmetric", &flg, NULL));
    1419:   if (flg) {
    1420:     PetscCall(MatSetOption(mat, MAT_SYMMETRIC, PETSC_TRUE));
    1421:     PetscCall(MatSetOption(mat, MAT_SYMMETRY_ETERNAL, PETSC_TRUE));
    1422:   }
    1423:   flg = PETSC_FALSE;
    1424:   PetscCall(PetscOptionsGetBool(((PetscObject)mat)->options, ((PetscObject)mat)->prefix, "-matload_spd", &flg, NULL));
    1425:   if (flg) PetscCall(MatSetOption(mat, MAT_SPD, PETSC_TRUE));

    1427:   PetscCall(PetscLogEventBegin(MAT_Load, mat, viewer, 0, 0));
    1428:   PetscUseTypeMethod(mat, load, viewer);
    1429:   PetscCall(PetscLogEventEnd(MAT_Load, mat, viewer, 0, 0));
    1430:   PetscFunctionReturn(PETSC_SUCCESS);
    1431: }

    1433: static PetscErrorCode MatDestroy_Redundant(Mat_Redundant **redundant)
    1434: {
    1435:   Mat_Redundant *redund = *redundant;

    1437:   PetscFunctionBegin;
    1438:   if (redund) {
    1439:     if (redund->matseq) { /* via MatCreateSubMatrices()  */
    1440:       PetscCall(ISDestroy(&redund->isrow));
    1441:       PetscCall(ISDestroy(&redund->iscol));
    1442:       PetscCall(MatDestroySubMatrices(1, &redund->matseq));
    1443:     } else {
    1444:       PetscCall(PetscFree2(redund->send_rank, redund->recv_rank));
    1445:       PetscCall(PetscFree(redund->sbuf_j));
    1446:       PetscCall(PetscFree(redund->sbuf_a));
    1447:       for (PetscInt i = 0; i < redund->nrecvs; i++) {
    1448:         PetscCall(PetscFree(redund->rbuf_j[i]));
    1449:         PetscCall(PetscFree(redund->rbuf_a[i]));
    1450:       }
    1451:       PetscCall(PetscFree4(redund->sbuf_nz, redund->rbuf_nz, redund->rbuf_j, redund->rbuf_a));
    1452:     }

    1454:     if (redund->subcomm) PetscCall(PetscCommDestroy(&redund->subcomm));
    1455:     PetscCall(PetscFree(redund));
    1456:   }
    1457:   PetscFunctionReturn(PETSC_SUCCESS);
    1458: }

    1460: /*@
    1461:   MatDestroy - Frees space taken by a matrix.

    1463:   Collective

    1465:   Input Parameter:
    1466: . A - the matrix

    1468:   Level: beginner

    1470:   Developer Note:
    1471:   Some special arrays of matrices are not destroyed in this routine but instead by the routines called by
    1472:   `MatDestroySubMatrices()`. Thus one must be sure that any changes here must also be made in those routines.
    1473:   `MatHeaderMerge()` and `MatHeaderReplace()` also manipulate the data in the `Mat` object and likely need changes
    1474:   if changes are needed here.

    1476: .seealso: [](ch_matrices), `Mat`, `MatCreate()`
    1477: @*/
    1478: PetscErrorCode MatDestroy(Mat *A)
    1479: {
    1480:   PetscFunctionBegin;
    1481:   if (!*A) PetscFunctionReturn(PETSC_SUCCESS);
    1483:   if (--((PetscObject)*A)->refct > 0) {
    1484:     *A = NULL;
    1485:     PetscFunctionReturn(PETSC_SUCCESS);
    1486:   }

    1488:   /* if memory was published with SAWs then destroy it */
    1489:   PetscCall(PetscObjectSAWsViewOff((PetscObject)*A));
    1490:   PetscTryTypeMethod(*A, destroy);

    1492:   PetscCall(PetscFree((*A)->factorprefix));
    1493:   PetscCall(PetscFree((*A)->defaultvectype));
    1494:   PetscCall(PetscFree((*A)->defaultrandtype));
    1495:   PetscCall(PetscFree((*A)->bsizes));
    1496:   PetscCall(PetscFree((*A)->solvertype));
    1497:   for (PetscInt i = 0; i < MAT_FACTOR_NUM_TYPES; i++) PetscCall(PetscFree((*A)->preferredordering[i]));
    1498:   if ((*A)->redundant && (*A)->redundant->matseq[0] == *A) (*A)->redundant->matseq[0] = NULL;
    1499:   PetscCall(MatDestroy_Redundant(&(*A)->redundant));
    1500:   PetscCall(MatProductClear(*A));
    1501:   PetscCall(MatNullSpaceDestroy(&(*A)->nullsp));
    1502:   PetscCall(MatNullSpaceDestroy(&(*A)->transnullsp));
    1503:   PetscCall(MatNullSpaceDestroy(&(*A)->nearnullsp));
    1504:   PetscCall(MatDestroy(&(*A)->schur));
    1505:   PetscCall(PetscLayoutDestroy(&(*A)->rmap));
    1506:   PetscCall(PetscLayoutDestroy(&(*A)->cmap));
    1507:   PetscCall(PetscHeaderDestroy(A));
    1508:   PetscFunctionReturn(PETSC_SUCCESS);
    1509: }

    1511: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    1512: /*@
    1513:   MatSetValues - Inserts or adds a block of values into a matrix.
    1514:   These values may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
    1515:   MUST be called after all calls to `MatSetValues()` have been completed.

    1517:   Not Collective

    1519:   Input Parameters:
    1520: + mat  - the matrix
    1521: . m    - the number of rows
    1522: . idxm - the global indices of the rows
    1523: . n    - the number of columns
    1524: . idxn - the global indices of the columns
    1525: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1526:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1527: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` to replace existing entries with new values

    1529:   Level: beginner

    1531:   Notes:
    1532:   Calls to `MatSetValues()` with the `INSERT_VALUES` and `ADD_VALUES`
    1533:   options cannot be mixed without intervening calls to the assembly
    1534:   routines.

    1536:   `MatSetValues()` uses 0-based row and column numbers in Fortran
    1537:   as well as in C.

    1539:   Negative indices may be passed in `idxm` and `idxn`, these rows and columns are
    1540:   simply ignored. This allows easily inserting element stiffness matrices
    1541:   with homogeneous Dirichlet boundary conditions that you don't want represented
    1542:   in the matrix.

    1544:   Efficiency Alert:
    1545:   The routine `MatSetValuesBlocked()` may offer much better efficiency
    1546:   for users of block sparse formats (`MATSEQBAIJ` and `MATMPIBAIJ`).

    1548:   Fortran Notes:
    1549:   If any of `idxm`, `idxn`, and `v` are scalars pass them using, for example,
    1550: .vb
    1551:   call MatSetValues(mat, one, [idxm], one, [idxn], [v], INSERT_VALUES, ierr)
    1552: .ve

    1554:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1556:   Developer Note:
    1557:   This is labeled with C so does not automatically generate Fortran stubs and interfaces
    1558:   because it requires multiple Fortran interfaces depending on which arguments are scalar or arrays.

    1560: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1561:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`
    1562: @*/
    1563: PetscErrorCode MatSetValues(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], const PetscScalar v[], InsertMode addv)
    1564: {
    1565:   PetscFunctionBeginHot;
    1568:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    1569:   PetscAssertPointer(idxm, 3);
    1570:   PetscAssertPointer(idxn, 5);
    1571:   MatCheckPreallocated(mat, 1);

    1573:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    1574:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");

    1576:   if (PetscDefined(USE_DEBUG)) {
    1577:     PetscInt i, j;

    1579:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    1580:     if (v) {
    1581:       for (i = 0; i < m; i++) {
    1582:         for (j = 0; j < n; j++) {
    1583:           if (mat->erroriffailure && PetscIsInfOrNanScalar(v[i * n + j]))
    1584: #if defined(PETSC_USE_COMPLEX)
    1585:             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]);
    1586: #else
    1587:             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]);
    1588: #endif
    1589:         }
    1590:       }
    1591:     }
    1592:     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);
    1593:     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);
    1594:   }

    1596:   if (mat->assembled) {
    1597:     mat->was_assembled = PETSC_TRUE;
    1598:     mat->assembled     = PETSC_FALSE;
    1599:   }
    1600:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    1601:   PetscUseTypeMethod(mat, setvalues, m, idxm, n, idxn, v, addv);
    1602:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    1603:   PetscFunctionReturn(PETSC_SUCCESS);
    1604: }

    1606: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    1607: /*@
    1608:   MatSetValuesIS - Inserts or adds a block of values into a matrix using an `IS` to indicate the rows and columns
    1609:   These values may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
    1610:   MUST be called after all calls to `MatSetValues()` have been completed.

    1612:   Not Collective

    1614:   Input Parameters:
    1615: + mat  - the matrix
    1616: . ism  - the rows to provide
    1617: . isn  - the columns to provide
    1618: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1619:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1620: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` to replace existing entries with new values

    1622:   Level: beginner

    1624:   Notes:
    1625:   By default, the values, `v`, are stored in row-major order. See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.

    1627:   Calls to `MatSetValues()` with the `INSERT_VALUES` and `ADD_VALUES`
    1628:   options cannot be mixed without intervening calls to the assembly
    1629:   routines.

    1631:   `MatSetValues()` uses 0-based row and column numbers in Fortran
    1632:   as well as in C.

    1634:   Negative indices may be passed in `ism` and `isn`, these rows and columns are
    1635:   simply ignored. This allows easily inserting element stiffness matrices
    1636:   with homogeneous Dirichlet boundary conditions that you don't want represented
    1637:   in the matrix.

    1639:   Fortran Note:
    1640:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1642:   Efficiency Alert:
    1643:   The routine `MatSetValuesBlocked()` may offer much better efficiency
    1644:   for users of block sparse formats (`MATSEQBAIJ` and `MATMPIBAIJ`).

    1646:   This is currently not optimized for any particular `ISType`

    1648: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatSetValues()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1649:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`
    1650: @*/
    1651: PetscErrorCode MatSetValuesIS(Mat mat, IS ism, IS isn, const PetscScalar v[], InsertMode addv)
    1652: {
    1653:   PetscInt        m, n;
    1654:   const PetscInt *rows, *cols;

    1656:   PetscFunctionBeginHot;
    1658:   PetscCall(ISGetIndices(ism, &rows));
    1659:   PetscCall(ISGetIndices(isn, &cols));
    1660:   PetscCall(ISGetLocalSize(ism, &m));
    1661:   PetscCall(ISGetLocalSize(isn, &n));
    1662:   PetscCall(MatSetValues(mat, m, rows, n, cols, v, addv));
    1663:   PetscCall(ISRestoreIndices(ism, &rows));
    1664:   PetscCall(ISRestoreIndices(isn, &cols));
    1665:   PetscFunctionReturn(PETSC_SUCCESS);
    1666: }

    1668: /*@
    1669:   MatSetValuesRowLocal - Inserts a row (block row for `MATBAIJ` matrices) of nonzero
    1670:   values into a matrix

    1672:   Not Collective

    1674:   Input Parameters:
    1675: + mat - the matrix
    1676: . row - the (block) row to set
    1677: - 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.
    1678:         See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.

    1680:   Level: intermediate

    1682:   Notes:
    1683:   The values, `v`, are column-oriented (for the block version) and sorted

    1685:   All the nonzero values in `row` must be provided

    1687:   The matrix must have previously had its column indices set, likely by having been assembled.

    1689:   `row` must belong to this MPI process

    1691:   Fortran Note:
    1692:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1694: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1695:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`, `MatSetValues()`, `MatSetValuesRow()`, `MatSetLocalToGlobalMapping()`
    1696: @*/
    1697: PetscErrorCode MatSetValuesRowLocal(Mat mat, PetscInt row, const PetscScalar v[])
    1698: {
    1699:   PetscInt globalrow;

    1701:   PetscFunctionBegin;
    1704:   PetscAssertPointer(v, 3);
    1705:   PetscCall(ISLocalToGlobalMappingApply(mat->rmap->mapping, 1, &row, &globalrow));
    1706:   PetscCall(MatSetValuesRow(mat, globalrow, v));
    1707:   PetscFunctionReturn(PETSC_SUCCESS);
    1708: }

    1710: /*@
    1711:   MatSetValuesRow - Inserts a row (block row for `MATBAIJ` matrices) of nonzero
    1712:   values into a matrix

    1714:   Not Collective

    1716:   Input Parameters:
    1717: + mat - the matrix
    1718: . row - the (block) row to set
    1719: - 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

    1721:   Level: advanced

    1723:   Notes:
    1724:   The values, `v`, are column-oriented for the block version.

    1726:   All the nonzeros in `row` must be provided

    1728:   THE MATRIX MUST HAVE PREVIOUSLY HAD ITS COLUMN INDICES SET. IT IS RARE THAT THIS ROUTINE IS USED, usually `MatSetValues()` is used.

    1730:   `row` must belong to this process

    1732: .seealso: [](ch_matrices), `Mat`, `MatSetValues()`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    1733:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`
    1734: @*/
    1735: PetscErrorCode MatSetValuesRow(Mat mat, PetscInt row, const PetscScalar v[])
    1736: {
    1737:   PetscFunctionBeginHot;
    1740:   MatCheckPreallocated(mat, 1);
    1741:   PetscAssertPointer(v, 3);
    1742:   PetscCheck(mat->insertmode != ADD_VALUES, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add and insert values");
    1743:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    1744:   mat->insertmode = INSERT_VALUES;

    1746:   if (mat->assembled) {
    1747:     mat->was_assembled = PETSC_TRUE;
    1748:     mat->assembled     = PETSC_FALSE;
    1749:   }
    1750:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    1751:   PetscUseTypeMethod(mat, setvaluesrow, row, v);
    1752:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    1753:   PetscFunctionReturn(PETSC_SUCCESS);
    1754: }

    1756: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    1757: /*@
    1758:   MatSetValuesStencil - Inserts or adds a block of values into a matrix.
    1759:   Using structured grid indexing

    1761:   Not Collective

    1763:   Input Parameters:
    1764: + mat  - the matrix
    1765: . m    - number of rows being entered
    1766: . idxm - grid coordinates (and component number when dof > 1) for matrix rows being entered
    1767: . n    - number of columns being entered
    1768: . idxn - grid coordinates (and component number when dof > 1) for matrix columns being entered
    1769: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1770:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1771: - addv - either `ADD_VALUES` to add to existing entries at that location or `INSERT_VALUES` to replace existing entries with new values

    1773:   Level: beginner

    1775:   Notes:
    1776:   By default the values, `v`, are row-oriented.  See `MatSetOption()` for other options.

    1778:   Calls to `MatSetValuesStencil()` with the `INSERT_VALUES` and `ADD_VALUES`
    1779:   options cannot be mixed without intervening calls to the assembly
    1780:   routines.

    1782:   The grid coordinates are across the entire grid, not just the local portion

    1784:   `MatSetValuesStencil()` uses 0-based row and column numbers in Fortran
    1785:   as well as in C.

    1787:   For setting/accessing vector values via array coordinates you can use the `DMDAVecGetArray()` routine

    1789:   In order to use this routine you must either obtain the matrix with `DMCreateMatrix()`
    1790:   or call `MatSetLocalToGlobalMapping()` and `MatSetStencil()` first.

    1792:   The columns and rows in the stencil passed in MUST be contained within the
    1793:   ghost region of the given process as set with DMDACreateXXX() or `MatSetStencil()`. For example,
    1794:   if you create a `DMDA` with an overlap of one grid level and on a particular process its first
    1795:   local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
    1796:   first i index you can use in your column and row indices in `MatSetStencil()` is 5.

    1798:   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    1799:   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    1800:   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    1801:   `DM_BOUNDARY_PERIODIC` boundary type.

    1803:   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
    1804:   a single value per point) you can skip filling those indices.

    1806:   Inspired by the structured grid interface to the HYPRE package
    1807:   (https://computation.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)

    1809:   Fortran Note:
    1810:   If `y` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1812:   Efficiency Alert:
    1813:   The routine `MatSetValuesBlockedStencil()` may offer much better efficiency
    1814:   for users of block sparse formats (`MATSEQBAIJ` and `MATMPIBAIJ`).

    1816: .seealso: [](ch_matrices), `Mat`, `DMDA`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`
    1817:           `MatSetValues()`, `MatSetValuesBlockedStencil()`, `MatSetStencil()`, `DMCreateMatrix()`, `DMDAVecGetArray()`, `MatStencil`
    1818: @*/
    1819: PetscErrorCode MatSetValuesStencil(Mat mat, PetscInt m, const MatStencil idxm[], PetscInt n, const MatStencil idxn[], const PetscScalar v[], InsertMode addv)
    1820: {
    1821:   PetscInt  buf[8192], *bufm = NULL, *bufn = NULL, *jdxm, *jdxn;
    1822:   PetscInt  j, i, dim = mat->stencil.dim, *dims = mat->stencil.dims + 1, tmp;
    1823:   PetscInt *starts = mat->stencil.starts, *dxm = (PetscInt *)idxm, *dxn = (PetscInt *)idxn, sdim = dim - (1 - (PetscInt)mat->stencil.noc);

    1825:   PetscFunctionBegin;
    1826:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    1829:   PetscAssertPointer(idxm, 3);
    1830:   PetscAssertPointer(idxn, 5);

    1832:   if ((m + n) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    1833:     jdxm = buf;
    1834:     jdxn = buf + m;
    1835:   } else {
    1836:     PetscCall(PetscMalloc2(m, &bufm, n, &bufn));
    1837:     jdxm = bufm;
    1838:     jdxn = bufn;
    1839:   }
    1840:   for (i = 0; i < m; i++) {
    1841:     for (j = 0; j < 3 - sdim; j++) dxm++;
    1842:     tmp = *dxm++ - starts[0];
    1843:     for (j = 0; j < dim - 1; j++) {
    1844:       if ((*dxm++ - starts[j + 1]) < 0 || tmp < 0) tmp = -1;
    1845:       else tmp = tmp * dims[j] + *(dxm - 1) - starts[j + 1];
    1846:     }
    1847:     if (mat->stencil.noc) dxm++;
    1848:     jdxm[i] = tmp;
    1849:   }
    1850:   for (i = 0; i < n; i++) {
    1851:     for (j = 0; j < 3 - sdim; j++) dxn++;
    1852:     tmp = *dxn++ - starts[0];
    1853:     for (j = 0; j < dim - 1; j++) {
    1854:       if ((*dxn++ - starts[j + 1]) < 0 || tmp < 0) tmp = -1;
    1855:       else tmp = tmp * dims[j] + *(dxn - 1) - starts[j + 1];
    1856:     }
    1857:     if (mat->stencil.noc) dxn++;
    1858:     jdxn[i] = tmp;
    1859:   }
    1860:   PetscCall(MatSetValuesLocal(mat, m, jdxm, n, jdxn, v, addv));
    1861:   PetscCall(PetscFree2(bufm, bufn));
    1862:   PetscFunctionReturn(PETSC_SUCCESS);
    1863: }

    1865: /*@
    1866:   MatSetValuesBlockedStencil - Inserts or adds a block of values into a matrix.
    1867:   Using structured grid indexing

    1869:   Not Collective

    1871:   Input Parameters:
    1872: + mat  - the matrix
    1873: . m    - number of rows being entered
    1874: . idxm - grid coordinates for matrix rows being entered
    1875: . n    - number of columns being entered
    1876: . idxn - grid coordinates for matrix columns being entered
    1877: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    1878:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    1879: - addv - either `ADD_VALUES` to add to existing entries or `INSERT_VALUES` to replace existing entries with new values

    1881:   Level: beginner

    1883:   Notes:
    1884:   By default the values, `v`, are row-oriented and unsorted.
    1885:   See `MatSetOption()` for other options.

    1887:   Calls to `MatSetValuesBlockedStencil()` with the `INSERT_VALUES` and `ADD_VALUES`
    1888:   options cannot be mixed without intervening calls to the assembly
    1889:   routines.

    1891:   The grid coordinates are across the entire grid, not just the local portion

    1893:   `MatSetValuesBlockedStencil()` uses 0-based row and column numbers in Fortran
    1894:   as well as in C.

    1896:   For setting/accessing vector values via array coordinates you can use the `DMDAVecGetArray()` routine

    1898:   In order to use this routine you must either obtain the matrix with `DMCreateMatrix()`
    1899:   or call `MatSetBlockSize()`, `MatSetLocalToGlobalMapping()` and `MatSetStencil()` first.

    1901:   The columns and rows in the stencil passed in MUST be contained within the
    1902:   ghost region of the given process as set with DMDACreateXXX() or `MatSetStencil()`. For example,
    1903:   if you create a `DMDA` with an overlap of one grid level and on a particular process its first
    1904:   local nonghost x logical coordinate is 6 (so its first ghost x logical coordinate is 5) the
    1905:   first i index you can use in your column and row indices in `MatSetStencil()` is 5.

    1907:   Negative indices may be passed in `idxm` and `idxn`, these rows and columns are
    1908:   simply ignored. This allows easily inserting element stiffness matrices
    1909:   with homogeneous Dirichlet boundary conditions that you don't want represented
    1910:   in the matrix.

    1912:   Inspired by the structured grid interface to the HYPRE package
    1913:   (https://computation.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)

    1915:   Fortran Notes:
    1916:   `idxm` and `idxn` should be declared as
    1917: .vb
    1918:     MatStencil idxm(4,m),idxn(4,n)
    1919: .ve
    1920:   and the values inserted using
    1921: .vb
    1922:     idxm(MatStencil_i,1) = i
    1923:     idxm(MatStencil_j,1) = j
    1924:     idxm(MatStencil_k,1) = k
    1925:    etc
    1926: .ve

    1928:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    1930: .seealso: [](ch_matrices), `Mat`, `DMDA`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`
    1931:           `MatSetValues()`, `MatSetValuesStencil()`, `MatSetStencil()`, `DMCreateMatrix()`, `DMDAVecGetArray()`, `MatStencil`,
    1932:           `MatSetBlockSize()`, `MatSetLocalToGlobalMapping()`
    1933: @*/
    1934: PetscErrorCode MatSetValuesBlockedStencil(Mat mat, PetscInt m, const MatStencil idxm[], PetscInt n, const MatStencil idxn[], const PetscScalar v[], InsertMode addv)
    1935: {
    1936:   PetscInt  buf[8192], *bufm = NULL, *bufn = NULL, *jdxm, *jdxn;
    1937:   PetscInt  j, i, dim = mat->stencil.dim, *dims = mat->stencil.dims + 1, tmp;
    1938:   PetscInt *starts = mat->stencil.starts, *dxm = (PetscInt *)idxm, *dxn = (PetscInt *)idxn, sdim = dim - (1 - (PetscInt)mat->stencil.noc);

    1940:   PetscFunctionBegin;
    1941:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    1944:   PetscAssertPointer(idxm, 3);
    1945:   PetscAssertPointer(idxn, 5);
    1946:   PetscAssertPointer(v, 6);

    1948:   if ((m + n) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    1949:     jdxm = buf;
    1950:     jdxn = buf + m;
    1951:   } else {
    1952:     PetscCall(PetscMalloc2(m, &bufm, n, &bufn));
    1953:     jdxm = bufm;
    1954:     jdxn = bufn;
    1955:   }
    1956:   for (i = 0; i < m; i++) {
    1957:     for (j = 0; j < 3 - sdim; j++) dxm++;
    1958:     tmp = *dxm++ - starts[0];
    1959:     for (j = 0; j < sdim - 1; j++) {
    1960:       if ((*dxm++ - starts[j + 1]) < 0 || tmp < 0) tmp = -1;
    1961:       else tmp = tmp * dims[j] + *(dxm - 1) - starts[j + 1];
    1962:     }
    1963:     dxm++;
    1964:     jdxm[i] = tmp;
    1965:   }
    1966:   for (i = 0; i < n; i++) {
    1967:     for (j = 0; j < 3 - sdim; j++) dxn++;
    1968:     tmp = *dxn++ - starts[0];
    1969:     for (j = 0; j < sdim - 1; j++) {
    1970:       if ((*dxn++ - starts[j + 1]) < 0 || tmp < 0) tmp = -1;
    1971:       else tmp = tmp * dims[j] + *(dxn - 1) - starts[j + 1];
    1972:     }
    1973:     dxn++;
    1974:     jdxn[i] = tmp;
    1975:   }
    1976:   PetscCall(MatSetValuesBlockedLocal(mat, m, jdxm, n, jdxn, v, addv));
    1977:   PetscCall(PetscFree2(bufm, bufn));
    1978:   PetscFunctionReturn(PETSC_SUCCESS);
    1979: }

    1981: /*@
    1982:   MatSetStencil - Sets the grid information for setting values into a matrix via
    1983:   `MatSetValuesStencil()`

    1985:   Not Collective

    1987:   Input Parameters:
    1988: + mat    - the matrix
    1989: . dim    - dimension of the grid 1, 2, or 3
    1990: . dims   - number of grid points in x, y, and z direction, including ghost points on your processor
    1991: . starts - starting point of ghost nodes on your processor in x, y, and z direction
    1992: - dof    - number of degrees of freedom per node

    1994:   Level: beginner

    1996:   Notes:
    1997:   Inspired by the structured grid interface to the HYPRE package
    1998:   (www.llnl.gov/CASC/hyper)

    2000:   For matrices generated with `DMCreateMatrix()` this routine is automatically called and so not needed by the
    2001:   user.

    2003: .seealso: [](ch_matrices), `Mat`, `MatStencil`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`
    2004:           `MatSetValues()`, `MatSetValuesBlockedStencil()`, `MatSetValuesStencil()`
    2005: @*/
    2006: PetscErrorCode MatSetStencil(Mat mat, PetscInt dim, const PetscInt dims[], const PetscInt starts[], PetscInt dof)
    2007: {
    2008:   PetscFunctionBegin;
    2010:   PetscAssertPointer(dims, 3);
    2011:   PetscAssertPointer(starts, 4);

    2013:   mat->stencil.dim = dim + (dof > 1);
    2014:   for (PetscInt i = 0; i < dim; i++) {
    2015:     mat->stencil.dims[i]   = dims[dim - i - 1]; /* copy the values in backwards */
    2016:     mat->stencil.starts[i] = starts[dim - i - 1];
    2017:   }
    2018:   mat->stencil.dims[dim]   = dof;
    2019:   mat->stencil.starts[dim] = 0;
    2020:   mat->stencil.noc         = (PetscBool)(dof == 1);
    2021:   PetscFunctionReturn(PETSC_SUCCESS);
    2022: }

    2024: /*@
    2025:   MatSetValuesBlocked - Inserts or adds a block of values into a matrix.

    2027:   Not Collective

    2029:   Input Parameters:
    2030: + mat  - the matrix
    2031: . m    - the number of block rows
    2032: . idxm - the global block indices
    2033: . n    - the number of block columns
    2034: . idxn - the global block indices
    2035: . v    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    2036:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    2037: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` replaces existing entries with new values

    2039:   Level: intermediate

    2041:   Notes:
    2042:   If you create the matrix yourself (that is not with a call to `DMCreateMatrix()`) then you MUST call
    2043:   MatXXXXSetPreallocation() or `MatSetUp()` before using this routine.

    2045:   The `m` and `n` count the NUMBER of blocks in the row direction and column direction,
    2046:   NOT the total number of rows/columns; for example, if the block size is 2 and
    2047:   you are passing in values for rows 2,3,4,5  then `m` would be 2 (not 4).
    2048:   The values in `idxm` would be 1 2; that is the first index for each block divided by
    2049:   the block size.

    2051:   You must call `MatSetBlockSize()` when constructing this matrix (before
    2052:   preallocating it).

    2054:   By default, the values, `v`, are stored in row-major order. See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.

    2056:   Calls to `MatSetValuesBlocked()` with the `INSERT_VALUES` and `ADD_VALUES`
    2057:   options cannot be mixed without intervening calls to the assembly
    2058:   routines.

    2060:   `MatSetValuesBlocked()` uses 0-based row and column numbers in Fortran
    2061:   as well as in C.

    2063:   Negative indices may be passed in `idxm` and `idxn`, these rows and columns are
    2064:   simply ignored. This allows easily inserting element stiffness matrices
    2065:   with homogeneous Dirichlet boundary conditions that you don't want represented
    2066:   in the matrix.

    2068:   Each time an entry is set within a sparse matrix via `MatSetValues()`,
    2069:   internal searching must be done to determine where to place the
    2070:   data in the matrix storage space.  By instead inserting blocks of
    2071:   entries via `MatSetValuesBlocked()`, the overhead of matrix assembly is
    2072:   reduced.

    2074:   Example:
    2075: .vb
    2076:    Suppose m=n=2 and block size(bs) = 2 The array is

    2078:    1  2  | 3  4
    2079:    5  6  | 7  8
    2080:    - - - | - - -
    2081:    9  10 | 11 12
    2082:    13 14 | 15 16

    2084:    v[] should be passed in like
    2085:    v[] = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]

    2087:   If you are not using row-oriented storage of v (that is you called MatSetOption(mat,MAT_ROW_ORIENTED,PETSC_FALSE)) then
    2088:    v[] = [1,5,9,13,2,6,10,14,3,7,11,15,4,8,12,16]
    2089: .ve

    2091:   Fortran Notes:
    2092:   If any of `idmx`, `idxn`, and `v` are scalars pass them using, for example,
    2093: .vb
    2094:   call MatSetValuesBlocked(mat, one, [idxm], one, [idxn], [v], INSERT_VALUES, ierr)
    2095: .ve

    2097:   If `v` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    2099: .seealso: [](ch_matrices), `Mat`, `MatSetBlockSize()`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValues()`, `MatSetValuesBlockedLocal()`
    2100: @*/
    2101: PetscErrorCode MatSetValuesBlocked(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], const PetscScalar v[], InsertMode addv)
    2102: {
    2103:   PetscFunctionBeginHot;
    2106:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    2107:   PetscAssertPointer(idxm, 3);
    2108:   PetscAssertPointer(idxn, 5);
    2109:   MatCheckPreallocated(mat, 1);
    2110:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    2111:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    2112:   if (PetscDefined(USE_DEBUG)) {
    2113:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2114:     PetscCheck(mat->ops->setvaluesblocked || mat->ops->setvalues, PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2115:   }
    2116:   if (PetscDefined(USE_DEBUG)) {
    2117:     PetscInt rbs, cbs, M, N, i;
    2118:     PetscCall(MatGetBlockSizes(mat, &rbs, &cbs));
    2119:     PetscCall(MatGetSize(mat, &M, &N));
    2120:     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);
    2121:     for (i = 0; i < n; i++)
    2122:       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);
    2123:   }
    2124:   if (mat->assembled) {
    2125:     mat->was_assembled = PETSC_TRUE;
    2126:     mat->assembled     = PETSC_FALSE;
    2127:   }
    2128:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    2129:   if (mat->ops->setvaluesblocked) {
    2130:     PetscUseTypeMethod(mat, setvaluesblocked, m, idxm, n, idxn, v, addv);
    2131:   } else {
    2132:     PetscInt buf[8192], *bufr = NULL, *bufc = NULL, *iidxm, *iidxn;
    2133:     PetscInt i, j, bs, cbs;

    2135:     PetscCall(MatGetBlockSizes(mat, &bs, &cbs));
    2136:     if ((m * bs + n * cbs) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    2137:       iidxm = buf;
    2138:       iidxn = buf + m * bs;
    2139:     } else {
    2140:       PetscCall(PetscMalloc2(m * bs, &bufr, n * cbs, &bufc));
    2141:       iidxm = bufr;
    2142:       iidxn = bufc;
    2143:     }
    2144:     for (i = 0; i < m; i++) {
    2145:       for (j = 0; j < bs; j++) iidxm[i * bs + j] = bs * idxm[i] + j;
    2146:     }
    2147:     if (m != n || bs != cbs || idxm != idxn) {
    2148:       for (i = 0; i < n; i++) {
    2149:         for (j = 0; j < cbs; j++) iidxn[i * cbs + j] = cbs * idxn[i] + j;
    2150:       }
    2151:     } else iidxn = iidxm;
    2152:     PetscCall(MatSetValues(mat, m * bs, iidxm, n * cbs, iidxn, v, addv));
    2153:     PetscCall(PetscFree2(bufr, bufc));
    2154:   }
    2155:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    2156:   PetscFunctionReturn(PETSC_SUCCESS);
    2157: }

    2159: /*@
    2160:   MatGetValues - Gets a block of local values from a matrix.

    2162:   Not Collective; can only return values that are owned by the give process

    2164:   Input Parameters:
    2165: + mat  - the matrix
    2166: . v    - a logically two-dimensional array for storing the values
    2167: . m    - the number of rows
    2168: . idxm - the  global indices of the rows
    2169: . n    - the number of columns
    2170: - idxn - the global indices of the columns

    2172:   Level: advanced

    2174:   Notes:
    2175:   The user must allocate space (m*n `PetscScalar`s) for the values, `v`.
    2176:   The values, `v`, are then returned in a row-oriented format,
    2177:   analogous to that used by default in `MatSetValues()`.

    2179:   `MatGetValues()` uses 0-based row and column numbers in
    2180:   Fortran as well as in C.

    2182:   `MatGetValues()` requires that the matrix has been assembled
    2183:   with `MatAssemblyBegin()`/`MatAssemblyEnd()`.  Thus, calls to
    2184:   `MatSetValues()` and `MatGetValues()` CANNOT be made in succession
    2185:   without intermediate matrix assembly.

    2187:   Negative row or column indices will be ignored and those locations in `v` will be
    2188:   left unchanged.

    2190:   For the standard row-based matrix formats, `idxm` can only contain rows owned by the requesting MPI process.
    2191:   That is, rows with global index greater than or equal to rstart and less than rend where rstart and rend are obtainable
    2192:   from `MatGetOwnershipRange`(mat,&rstart,&rend).

    2194: .seealso: [](ch_matrices), `Mat`, `MatGetRow()`, `MatCreateSubMatrices()`, `MatSetValues()`, `MatGetOwnershipRange()`, `MatGetValuesLocal()`, `MatGetValue()`
    2195: @*/
    2196: PetscErrorCode MatGetValues(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], PetscScalar v[])
    2197: {
    2198:   PetscFunctionBegin;
    2201:   if (!m || !n) PetscFunctionReturn(PETSC_SUCCESS);
    2202:   PetscAssertPointer(idxm, 3);
    2203:   PetscAssertPointer(idxn, 5);
    2204:   PetscAssertPointer(v, 6);
    2205:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2206:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2207:   MatCheckPreallocated(mat, 1);

    2209:   PetscCall(PetscLogEventBegin(MAT_GetValues, mat, 0, 0, 0));
    2210:   PetscUseTypeMethod(mat, getvalues, m, idxm, n, idxn, v);
    2211:   PetscCall(PetscLogEventEnd(MAT_GetValues, mat, 0, 0, 0));
    2212:   PetscFunctionReturn(PETSC_SUCCESS);
    2213: }

    2215: /*@
    2216:   MatGetValuesLocal - retrieves values from certain locations in a matrix using the local numbering of the indices
    2217:   defined previously by `MatSetLocalToGlobalMapping()`

    2219:   Not Collective

    2221:   Input Parameters:
    2222: + mat  - the matrix
    2223: . nrow - number of rows
    2224: . irow - the row local indices
    2225: . ncol - number of columns
    2226: - icol - the column local indices

    2228:   Output Parameter:
    2229: . y - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    2230:       See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.

    2232:   Level: advanced

    2234:   Notes:
    2235:   If you create the matrix yourself (that is not with a call to `DMCreateMatrix()`) then you MUST call `MatSetLocalToGlobalMapping()` before using this routine.

    2237:   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,
    2238:   are greater than or equal to rstart and less than rend where rstart and rend are obtainable from `MatGetOwnershipRange`(mat,&rstart,&rend). One can
    2239:   determine if the resulting global row associated with the local row r is owned by the requesting MPI process by applying the `ISLocalToGlobalMapping` set
    2240:   with `MatSetLocalToGlobalMapping()`.

    2242: .seealso: [](ch_matrices), `Mat`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValues()`, `MatSetLocalToGlobalMapping()`,
    2243:           `MatSetValuesLocal()`, `MatGetValues()`
    2244: @*/
    2245: PetscErrorCode MatGetValuesLocal(Mat mat, PetscInt nrow, const PetscInt irow[], PetscInt ncol, const PetscInt icol[], PetscScalar y[])
    2246: {
    2247:   PetscFunctionBeginHot;
    2250:   MatCheckPreallocated(mat, 1);
    2251:   if (!nrow || !ncol) PetscFunctionReturn(PETSC_SUCCESS); /* no values to retrieve */
    2252:   PetscAssertPointer(irow, 3);
    2253:   PetscAssertPointer(icol, 5);
    2254:   if (PetscDefined(USE_DEBUG)) {
    2255:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2256:     PetscCheck(mat->ops->getvalueslocal || mat->ops->getvalues, PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2257:   }
    2258:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2259:   PetscCall(PetscLogEventBegin(MAT_GetValues, mat, 0, 0, 0));
    2260:   if (mat->ops->getvalueslocal) PetscUseTypeMethod(mat, getvalueslocal, nrow, irow, ncol, icol, y);
    2261:   else {
    2262:     PetscInt buf[8192], *bufr = NULL, *bufc = NULL, *irowm, *icolm;
    2263:     if ((nrow + ncol) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    2264:       irowm = buf;
    2265:       icolm = buf + nrow;
    2266:     } else {
    2267:       PetscCall(PetscMalloc2(nrow, &bufr, ncol, &bufc));
    2268:       irowm = bufr;
    2269:       icolm = bufc;
    2270:     }
    2271:     PetscCheck(mat->rmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MatGetValuesLocal() cannot proceed without local-to-global row mapping (See MatSetLocalToGlobalMapping()).");
    2272:     PetscCheck(mat->cmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MatGetValuesLocal() cannot proceed without local-to-global column mapping (See MatSetLocalToGlobalMapping()).");
    2273:     PetscCall(ISLocalToGlobalMappingApply(mat->rmap->mapping, nrow, irow, irowm));
    2274:     PetscCall(ISLocalToGlobalMappingApply(mat->cmap->mapping, ncol, icol, icolm));
    2275:     PetscCall(MatGetValues(mat, nrow, irowm, ncol, icolm, y));
    2276:     PetscCall(PetscFree2(bufr, bufc));
    2277:   }
    2278:   PetscCall(PetscLogEventEnd(MAT_GetValues, mat, 0, 0, 0));
    2279:   PetscFunctionReturn(PETSC_SUCCESS);
    2280: }

    2282: /*@
    2283:   MatSetValuesBatch - Adds (`ADD_VALUES`) many blocks of values into a matrix at once. The blocks must all be square and
    2284:   the same size. Currently, this can only be called once and creates the given matrix.

    2286:   Not Collective

    2288:   Input Parameters:
    2289: + mat  - the matrix
    2290: . nb   - the number of blocks
    2291: . bs   - the number of rows (and columns) in each block
    2292: . rows - a concatenation of the rows for each block
    2293: - v    - a concatenation of logically two-dimensional arrays of values

    2295:   Level: advanced

    2297:   Notes:
    2298:   `MatSetPreallocationCOO()` and `MatSetValuesCOO()` may be a better way to provide the values

    2300:   In the future, we will extend this routine to handle rectangular blocks, and to allow multiple calls for a given matrix.

    2302: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValuesBlocked()`, `MatSetValuesLocal()`,
    2303:           `InsertMode`, `INSERT_VALUES`, `ADD_VALUES`, `MatSetValues()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    2304: @*/
    2305: PetscErrorCode MatSetValuesBatch(Mat mat, PetscInt nb, PetscInt bs, PetscInt rows[], const PetscScalar v[])
    2306: {
    2307:   PetscFunctionBegin;
    2310:   PetscAssertPointer(rows, 4);
    2311:   PetscAssertPointer(v, 5);
    2312:   PetscAssert(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");

    2314:   PetscCall(PetscLogEventBegin(MAT_SetValuesBatch, mat, 0, 0, 0));
    2315:   if (mat->ops->setvaluesbatch) PetscUseTypeMethod(mat, setvaluesbatch, nb, bs, rows, v);
    2316:   else {
    2317:     for (PetscInt b = 0; b < nb; ++b) PetscCall(MatSetValues(mat, bs, &rows[b * bs], bs, &rows[b * bs], &v[b * bs * bs], ADD_VALUES));
    2318:   }
    2319:   PetscCall(PetscLogEventEnd(MAT_SetValuesBatch, mat, 0, 0, 0));
    2320:   PetscFunctionReturn(PETSC_SUCCESS);
    2321: }

    2323: /*@
    2324:   MatSetLocalToGlobalMapping - Sets a local-to-global numbering for use by
    2325:   the routine `MatSetValuesLocal()` to allow users to insert matrix entries
    2326:   using a local (per-processor) numbering.

    2328:   Not Collective

    2330:   Input Parameters:
    2331: + x        - the matrix
    2332: . rmapping - row mapping created with `ISLocalToGlobalMappingCreate()` or `ISLocalToGlobalMappingCreateIS()`
    2333: - cmapping - column mapping

    2335:   Level: intermediate

    2337:   Note:
    2338:   If the matrix is obtained with `DMCreateMatrix()` then this may already have been called on the matrix

    2340: .seealso: [](ch_matrices), `Mat`, `DM`, `DMCreateMatrix()`, `MatGetLocalToGlobalMapping()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValues()`, `MatSetValuesLocal()`, `MatGetValuesLocal()`
    2341: @*/
    2342: PetscErrorCode MatSetLocalToGlobalMapping(Mat x, ISLocalToGlobalMapping rmapping, ISLocalToGlobalMapping cmapping)
    2343: {
    2344:   PetscFunctionBegin;
    2349:   if (x->ops->setlocaltoglobalmapping) PetscUseTypeMethod(x, setlocaltoglobalmapping, rmapping, cmapping);
    2350:   else {
    2351:     PetscCall(PetscLayoutSetISLocalToGlobalMapping(x->rmap, rmapping));
    2352:     PetscCall(PetscLayoutSetISLocalToGlobalMapping(x->cmap, cmapping));
    2353:   }
    2354:   PetscFunctionReturn(PETSC_SUCCESS);
    2355: }

    2357: /*@
    2358:   MatGetLocalToGlobalMapping - Gets the local-to-global numbering set by `MatSetLocalToGlobalMapping()`

    2360:   Not Collective

    2362:   Input Parameter:
    2363: . A - the matrix

    2365:   Output Parameters:
    2366: + rmapping - row mapping
    2367: - cmapping - column mapping

    2369:   Level: advanced

    2371: .seealso: [](ch_matrices), `Mat`, `MatSetLocalToGlobalMapping()`, `MatSetValuesLocal()`
    2372: @*/
    2373: PetscErrorCode MatGetLocalToGlobalMapping(Mat A, ISLocalToGlobalMapping *rmapping, ISLocalToGlobalMapping *cmapping)
    2374: {
    2375:   PetscFunctionBegin;
    2378:   if (rmapping) {
    2379:     PetscAssertPointer(rmapping, 2);
    2380:     *rmapping = A->rmap->mapping;
    2381:   }
    2382:   if (cmapping) {
    2383:     PetscAssertPointer(cmapping, 3);
    2384:     *cmapping = A->cmap->mapping;
    2385:   }
    2386:   PetscFunctionReturn(PETSC_SUCCESS);
    2387: }

    2389: /*@
    2390:   MatSetLayouts - Sets the `PetscLayout` objects for rows and columns of a matrix

    2392:   Logically Collective

    2394:   Input Parameters:
    2395: + A    - the matrix
    2396: . rmap - row layout
    2397: - cmap - column layout

    2399:   Level: advanced

    2401:   Note:
    2402:   The `PetscLayout` objects are usually created automatically for the matrix so this routine rarely needs to be called.

    2404: .seealso: [](ch_matrices), `Mat`, `PetscLayout`, `MatCreateVecs()`, `MatGetLocalToGlobalMapping()`, `MatGetLayouts()`
    2405: @*/
    2406: PetscErrorCode MatSetLayouts(Mat A, PetscLayout rmap, PetscLayout cmap)
    2407: {
    2408:   PetscFunctionBegin;
    2410:   PetscCall(PetscLayoutReference(rmap, &A->rmap));
    2411:   PetscCall(PetscLayoutReference(cmap, &A->cmap));
    2412:   PetscFunctionReturn(PETSC_SUCCESS);
    2413: }

    2415: /*@
    2416:   MatGetLayouts - Gets the `PetscLayout` objects for rows and columns

    2418:   Not Collective

    2420:   Input Parameter:
    2421: . A - the matrix

    2423:   Output Parameters:
    2424: + rmap - row layout
    2425: - cmap - column layout

    2427:   Level: advanced

    2429: .seealso: [](ch_matrices), `Mat`, [Matrix Layouts](sec_matlayout), `PetscLayout`, `MatCreateVecs()`, `MatGetLocalToGlobalMapping()`, `MatSetLayouts()`
    2430: @*/
    2431: PetscErrorCode MatGetLayouts(Mat A, PetscLayout *rmap, PetscLayout *cmap)
    2432: {
    2433:   PetscFunctionBegin;
    2436:   if (rmap) {
    2437:     PetscAssertPointer(rmap, 2);
    2438:     *rmap = A->rmap;
    2439:   }
    2440:   if (cmap) {
    2441:     PetscAssertPointer(cmap, 3);
    2442:     *cmap = A->cmap;
    2443:   }
    2444:   PetscFunctionReturn(PETSC_SUCCESS);
    2445: }

    2447: /*@
    2448:   MatSetValuesLocal - Inserts or adds values into certain locations of a matrix,
    2449:   using a local numbering of the rows and columns.

    2451:   Not Collective

    2453:   Input Parameters:
    2454: + mat  - the matrix
    2455: . nrow - number of rows
    2456: . irow - the row local indices
    2457: . ncol - number of columns
    2458: . icol - the column local indices
    2459: . y    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    2460:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    2461: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` to replace existing entries with new values

    2463:   Level: intermediate

    2465:   Notes:
    2466:   If you create the matrix yourself (that is not with a call to `DMCreateMatrix()`) then you MUST call `MatSetLocalToGlobalMapping()` before using this routine

    2468:   Calls to `MatSetValuesLocal()` with the `INSERT_VALUES` and `ADD_VALUES`
    2469:   options cannot be mixed without intervening calls to the assembly
    2470:   routines.

    2472:   These values may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
    2473:   MUST be called after all calls to `MatSetValuesLocal()` have been completed.

    2475:   Fortran Notes:
    2476:   If any of `irow`, `icol`, and `y` are scalars pass them using, for example,
    2477: .vb
    2478:   call MatSetValuesLocal(mat, one, [irow], one, [icol], [y], INSERT_VALUES, ierr)
    2479: .ve

    2481:   If `y` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    2483: .seealso: [](ch_matrices), `Mat`, `MatAssemblyBegin()`, `MatAssemblyEnd()`, `MatSetValues()`, `MatSetLocalToGlobalMapping()`,
    2484:           `MatGetValuesLocal()`
    2485: @*/
    2486: PetscErrorCode MatSetValuesLocal(Mat mat, PetscInt nrow, const PetscInt irow[], PetscInt ncol, const PetscInt icol[], const PetscScalar y[], InsertMode addv)
    2487: {
    2488:   PetscFunctionBeginHot;
    2491:   MatCheckPreallocated(mat, 1);
    2492:   if (!nrow || !ncol) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    2493:   PetscAssertPointer(irow, 3);
    2494:   PetscAssertPointer(icol, 5);
    2495:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    2496:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    2497:   if (PetscDefined(USE_DEBUG)) {
    2498:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2499:     PetscCheck(mat->ops->setvalueslocal || mat->ops->setvalues, PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2500:   }

    2502:   if (mat->assembled) {
    2503:     mat->was_assembled = PETSC_TRUE;
    2504:     mat->assembled     = PETSC_FALSE;
    2505:   }
    2506:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    2507:   if (mat->ops->setvalueslocal) PetscUseTypeMethod(mat, setvalueslocal, nrow, irow, ncol, icol, y, addv);
    2508:   else {
    2509:     PetscInt        buf[8192], *bufr = NULL, *bufc = NULL;
    2510:     const PetscInt *irowm, *icolm;

    2512:     if ((!mat->rmap->mapping && !mat->cmap->mapping) || (nrow + ncol) <= (PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf)) {
    2513:       bufr  = buf;
    2514:       bufc  = buf + nrow;
    2515:       irowm = bufr;
    2516:       icolm = bufc;
    2517:     } else {
    2518:       PetscCall(PetscMalloc2(nrow, &bufr, ncol, &bufc));
    2519:       irowm = bufr;
    2520:       icolm = bufc;
    2521:     }
    2522:     if (mat->rmap->mapping) PetscCall(ISLocalToGlobalMappingApply(mat->rmap->mapping, nrow, irow, bufr));
    2523:     else irowm = irow;
    2524:     if (mat->cmap->mapping) {
    2525:       if (mat->cmap->mapping != mat->rmap->mapping || ncol != nrow || icol != irow) PetscCall(ISLocalToGlobalMappingApply(mat->cmap->mapping, ncol, icol, bufc));
    2526:       else icolm = irowm;
    2527:     } else icolm = icol;
    2528:     PetscCall(MatSetValues(mat, nrow, irowm, ncol, icolm, y, addv));
    2529:     if (bufr != buf) PetscCall(PetscFree2(bufr, bufc));
    2530:   }
    2531:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    2532:   PetscFunctionReturn(PETSC_SUCCESS);
    2533: }

    2535: /*@
    2536:   MatSetValuesBlockedLocal - Inserts or adds values into certain locations of a matrix,
    2537:   using a local ordering of the nodes a block at a time.

    2539:   Not Collective

    2541:   Input Parameters:
    2542: + mat  - the matrix
    2543: . nrow - number of rows
    2544: . irow - the row local indices
    2545: . ncol - number of columns
    2546: . icol - the column local indices
    2547: . y    - a one-dimensional array that contains the values implicitly stored as a two-dimensional array, by default in row-major order.
    2548:          See `MAT_ROW_ORIENTED` in `MatSetOption()` for how to use column-major order.
    2549: - addv - either `ADD_VALUES` to add values to any existing entries, or `INSERT_VALUES` to replace existing entries with new values

    2551:   Level: intermediate

    2553:   Notes:
    2554:   If you create the matrix yourself (that is not with a call to `DMCreateMatrix()`) then you MUST call `MatSetBlockSize()` and `MatSetLocalToGlobalMapping()`
    2555:   before using this routineBefore calling `MatSetValuesLocal()`, the user must first set the

    2557:   Calls to `MatSetValuesBlockedLocal()` with the `INSERT_VALUES` and `ADD_VALUES`
    2558:   options cannot be mixed without intervening calls to the assembly
    2559:   routines.

    2561:   These values may be cached, so `MatAssemblyBegin()` and `MatAssemblyEnd()`
    2562:   MUST be called after all calls to `MatSetValuesBlockedLocal()` have been completed.

    2564:   Fortran Notes:
    2565:   If any of `irow`, `icol`, and `y` are scalars pass them using, for example,
    2566: .vb
    2567:   call MatSetValuesBlockedLocal(mat, one, [irow], one, [icol], [y], INSERT_VALUES, ierr)
    2568: .ve

    2570:   If `y` is a two-dimensional array use `reshape()` to pass it as a one dimensional array

    2572: .seealso: [](ch_matrices), `Mat`, `MatSetBlockSize()`, `MatSetLocalToGlobalMapping()`, `MatAssemblyBegin()`, `MatAssemblyEnd()`,
    2573:           `MatSetValuesLocal()`, `MatSetValuesBlocked()`
    2574: @*/
    2575: PetscErrorCode MatSetValuesBlockedLocal(Mat mat, PetscInt nrow, const PetscInt irow[], PetscInt ncol, const PetscInt icol[], const PetscScalar y[], InsertMode addv)
    2576: {
    2577:   PetscFunctionBeginHot;
    2580:   MatCheckPreallocated(mat, 1);
    2581:   if (!nrow || !ncol) PetscFunctionReturn(PETSC_SUCCESS); /* no values to insert */
    2582:   PetscAssertPointer(irow, 3);
    2583:   PetscAssertPointer(icol, 5);
    2584:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    2585:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    2586:   if (PetscDefined(USE_DEBUG)) {
    2587:     PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2588:     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);
    2589:   }

    2591:   if (mat->assembled) {
    2592:     mat->was_assembled = PETSC_TRUE;
    2593:     mat->assembled     = PETSC_FALSE;
    2594:   }
    2595:   if (PetscUnlikelyDebug(mat->rmap->mapping)) { /* Condition on the mapping existing, because MatSetValuesBlockedLocal_IS does not require it to be set. */
    2596:     PetscInt irbs, rbs;
    2597:     PetscCall(MatGetBlockSizes(mat, &rbs, NULL));
    2598:     PetscCall(ISLocalToGlobalMappingGetBlockSize(mat->rmap->mapping, &irbs));
    2599:     PetscCheck(rbs == irbs, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Different row block sizes! mat %" PetscInt_FMT ", row l2g map %" PetscInt_FMT, rbs, irbs);
    2600:   }
    2601:   if (PetscUnlikelyDebug(mat->cmap->mapping)) {
    2602:     PetscInt icbs, cbs;
    2603:     PetscCall(MatGetBlockSizes(mat, NULL, &cbs));
    2604:     PetscCall(ISLocalToGlobalMappingGetBlockSize(mat->cmap->mapping, &icbs));
    2605:     PetscCheck(cbs == icbs, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Different col block sizes! mat %" PetscInt_FMT ", col l2g map %" PetscInt_FMT, cbs, icbs);
    2606:   }
    2607:   PetscCall(PetscLogEventBegin(MAT_SetValues, mat, 0, 0, 0));
    2608:   if (mat->ops->setvaluesblockedlocal) PetscUseTypeMethod(mat, setvaluesblockedlocal, nrow, irow, ncol, icol, y, addv);
    2609:   else {
    2610:     PetscInt        buf[8192], *bufr = NULL, *bufc = NULL;
    2611:     const PetscInt *irowm, *icolm;

    2613:     if ((!mat->rmap->mapping && !mat->cmap->mapping) || (nrow + ncol) <= ((PetscInt)PETSC_STATIC_ARRAY_LENGTH(buf))) {
    2614:       bufr  = buf;
    2615:       bufc  = buf + nrow;
    2616:       irowm = bufr;
    2617:       icolm = bufc;
    2618:     } else {
    2619:       PetscCall(PetscMalloc2(nrow, &bufr, ncol, &bufc));
    2620:       irowm = bufr;
    2621:       icolm = bufc;
    2622:     }
    2623:     if (mat->rmap->mapping) PetscCall(ISLocalToGlobalMappingApplyBlock(mat->rmap->mapping, nrow, irow, bufr));
    2624:     else irowm = irow;
    2625:     if (mat->cmap->mapping) {
    2626:       if (mat->cmap->mapping != mat->rmap->mapping || ncol != nrow || icol != irow) PetscCall(ISLocalToGlobalMappingApplyBlock(mat->cmap->mapping, ncol, icol, bufc));
    2627:       else icolm = irowm;
    2628:     } else icolm = icol;
    2629:     PetscCall(MatSetValuesBlocked(mat, nrow, irowm, ncol, icolm, y, addv));
    2630:     if (bufr != buf) PetscCall(PetscFree2(bufr, bufc));
    2631:   }
    2632:   PetscCall(PetscLogEventEnd(MAT_SetValues, mat, 0, 0, 0));
    2633:   PetscFunctionReturn(PETSC_SUCCESS);
    2634: }

    2636: /*@
    2637:   MatMultDiagonalBlock - Computes the matrix-vector product, $y = Dx$. Where `D` is defined by the inode or block structure of the diagonal

    2639:   Collective

    2641:   Input Parameters:
    2642: + mat - the matrix
    2643: - x   - the vector to be multiplied

    2645:   Output Parameter:
    2646: . y - the result

    2648:   Level: developer

    2650:   Note:
    2651:   The vectors `x` and `y` cannot be the same.  I.e., one cannot
    2652:   call `MatMultDiagonalBlock`(A,y,y).

    2654: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatMultTranspose()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    2655: @*/
    2656: PetscErrorCode MatMultDiagonalBlock(Mat mat, Vec x, Vec y)
    2657: {
    2658:   PetscFunctionBegin;

    2664:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2665:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2666:   PetscCheck(x != y, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "x and y must be different vectors");
    2667:   MatCheckPreallocated(mat, 1);

    2669:   PetscUseTypeMethod(mat, multdiagonalblock, x, y);
    2670:   PetscCall(PetscObjectStateIncrease((PetscObject)y));
    2671:   PetscFunctionReturn(PETSC_SUCCESS);
    2672: }

    2674: /*@
    2675:   MatMult - Computes the matrix-vector product, $y = Ax$.

    2677:   Neighbor-wise Collective

    2679:   Input Parameters:
    2680: + mat - the matrix
    2681: - x   - the vector to be multiplied

    2683:   Output Parameter:
    2684: . y - the result

    2686:   Level: beginner

    2688:   Note:
    2689:   The vectors `x` and `y` cannot be the same.  I.e., one cannot
    2690:   call `MatMult`(A,y,y).

    2692: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    2693: @*/
    2694: PetscErrorCode MatMult(Mat mat, Vec x, Vec y)
    2695: {
    2696:   PetscFunctionBegin;
    2700:   VecCheckAssembled(x);
    2702:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2703:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2704:   PetscCheck(x != y, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "x and y must be different vectors");
    2705:   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);
    2706:   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);
    2707:   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);
    2708:   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);
    2709:   PetscCall(VecSetErrorIfLocked(y, 3));
    2710:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
    2711:   MatCheckPreallocated(mat, 1);

    2713:   PetscCall(VecLockReadPush(x));
    2714:   PetscCall(PetscLogEventBegin(MAT_Mult, mat, x, y, 0));
    2715:   PetscUseTypeMethod(mat, mult, x, y);
    2716:   PetscCall(PetscLogEventEnd(MAT_Mult, mat, x, y, 0));
    2717:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_FALSE));
    2718:   PetscCall(VecLockReadPop(x));
    2719:   PetscFunctionReturn(PETSC_SUCCESS);
    2720: }

    2722: /*@
    2723:   MatMultTranspose - Computes matrix transpose times a vector $y = A^T * x$.

    2725:   Neighbor-wise Collective

    2727:   Input Parameters:
    2728: + mat - the matrix
    2729: - x   - the vector to be multiplied

    2731:   Output Parameter:
    2732: . y - the result

    2734:   Level: beginner

    2736:   Notes:
    2737:   The vectors `x` and `y` cannot be the same.  I.e., one cannot
    2738:   call `MatMultTranspose`(A,y,y).

    2740:   For complex numbers this does NOT compute the Hermitian (complex conjugate) transpose multiple,
    2741:   use `MatMultHermitianTranspose()`

    2743: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatMultAdd()`, `MatMultTransposeAdd()`, `MatMultHermitianTranspose()`, `MatTranspose()`
    2744: @*/
    2745: PetscErrorCode MatMultTranspose(Mat mat, Vec x, Vec y)
    2746: {
    2747:   PetscErrorCode (*op)(Mat, Vec, Vec) = NULL;

    2749:   PetscFunctionBegin;
    2753:   VecCheckAssembled(x);

    2756:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2757:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2758:   PetscCheck(x != y, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "x and y must be different vectors");
    2759:   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);
    2760:   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);
    2761:   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);
    2762:   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);
    2763:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(x, 2, PETSC_TRUE));
    2764:   MatCheckPreallocated(mat, 1);

    2766:   if (!mat->ops->multtranspose) {
    2767:     if (mat->symmetric == PETSC_BOOL3_TRUE && mat->ops->mult) op = mat->ops->mult;
    2768:     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);
    2769:   } else op = mat->ops->multtranspose;
    2770:   PetscCall(PetscLogEventBegin(MAT_MultTranspose, mat, x, y, 0));
    2771:   PetscCall(VecLockReadPush(x));
    2772:   PetscCall((*op)(mat, x, y));
    2773:   PetscCall(VecLockReadPop(x));
    2774:   PetscCall(PetscLogEventEnd(MAT_MultTranspose, mat, x, y, 0));
    2775:   PetscCall(PetscObjectStateIncrease((PetscObject)y));
    2776:   if (mat->erroriffailure) PetscCall(VecValidValues_Internal(y, 3, PETSC_FALSE));
    2777:   PetscFunctionReturn(PETSC_SUCCESS);
    2778: }

    2780: /*@
    2781:   MatMultHermitianTranspose - Computes matrix Hermitian-transpose times a vector $y = A^H * x$.

    2783:   Neighbor-wise Collective

    2785:   Input Parameters:
    2786: + mat - the matrix
    2787: - x   - the vector to be multiplied

    2789:   Output Parameter:
    2790: . y - the result

    2792:   Level: beginner

    2794:   Notes:
    2795:   The vectors `x` and `y` cannot be the same.  I.e., one cannot
    2796:   call `MatMultHermitianTranspose`(A,y,y).

    2798:   Also called the conjugate transpose, complex conjugate transpose, or adjoint.

    2800:   For real numbers `MatMultTranspose()` and `MatMultHermitianTranspose()` are identical.

    2802: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatMultAdd()`, `MatMultHermitianTransposeAdd()`, `MatMultTranspose()`
    2803: @*/
    2804: PetscErrorCode MatMultHermitianTranspose(Mat mat, Vec x, Vec y)
    2805: {
    2806:   PetscFunctionBegin;

    2812:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2813:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2814:   PetscCheck(x != y, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "x and y must be different vectors");
    2815:   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);
    2816:   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);
    2817:   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);
    2818:   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);
    2819:   MatCheckPreallocated(mat, 1);

    2821:   PetscCall(PetscLogEventBegin(MAT_MultHermitianTranspose, mat, x, y, 0));
    2822: #if defined(PETSC_USE_COMPLEX)
    2823:   if (mat->ops->multhermitiantranspose || (mat->hermitian == PETSC_BOOL3_TRUE && mat->ops->mult)) {
    2824:     PetscCall(VecLockReadPush(x));
    2825:     if (mat->ops->multhermitiantranspose) PetscUseTypeMethod(mat, multhermitiantranspose, x, y);
    2826:     else PetscUseTypeMethod(mat, mult, x, y);
    2827:     PetscCall(VecLockReadPop(x));
    2828:   } else {
    2829:     Vec w;
    2830:     PetscCall(VecDuplicate(x, &w));
    2831:     PetscCall(VecCopy(x, w));
    2832:     PetscCall(VecConjugate(w));
    2833:     PetscCall(MatMultTranspose(mat, w, y));
    2834:     PetscCall(VecDestroy(&w));
    2835:     PetscCall(VecConjugate(y));
    2836:   }
    2837:   PetscCall(PetscObjectStateIncrease((PetscObject)y));
    2838: #else
    2839:   PetscCall(MatMultTranspose(mat, x, y));
    2840: #endif
    2841:   PetscCall(PetscLogEventEnd(MAT_MultHermitianTranspose, mat, x, y, 0));
    2842:   PetscFunctionReturn(PETSC_SUCCESS);
    2843: }

    2845: /*@
    2846:   MatMultAdd -  Computes $v3 = v2 + A * v1$.

    2848:   Neighbor-wise Collective

    2850:   Input Parameters:
    2851: + mat - the matrix
    2852: . v1  - the vector to be multiplied by `mat`
    2853: - v2  - the vector to be added to the result

    2855:   Output Parameter:
    2856: . v3 - the result

    2858:   Level: beginner

    2860:   Note:
    2861:   The vectors `v1` and `v3` cannot be the same.  I.e., one cannot
    2862:   call `MatMultAdd`(A,v1,v2,v1).

    2864: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMult()`, `MatMultTransposeAdd()`
    2865: @*/
    2866: PetscErrorCode MatMultAdd(Mat mat, Vec v1, Vec v2, Vec v3)
    2867: {
    2868:   PetscFunctionBegin;

    2875:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2876:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2877:   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);
    2878:   /* 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);
    2879:      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); */
    2880:   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);
    2881:   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);
    2882:   PetscCheck(v1 != v3, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "v1 and v3 must be different vectors");
    2883:   MatCheckPreallocated(mat, 1);

    2885:   PetscCall(PetscLogEventBegin(MAT_MultAdd, mat, v1, v2, v3));
    2886:   PetscCall(VecLockReadPush(v1));
    2887:   PetscUseTypeMethod(mat, multadd, v1, v2, v3);
    2888:   PetscCall(VecLockReadPop(v1));
    2889:   PetscCall(PetscLogEventEnd(MAT_MultAdd, mat, v1, v2, v3));
    2890:   PetscCall(PetscObjectStateIncrease((PetscObject)v3));
    2891:   PetscFunctionReturn(PETSC_SUCCESS);
    2892: }

    2894: /*@
    2895:   MatMultTransposeAdd - Computes $v3 = v2 + A^T * v1$.

    2897:   Neighbor-wise Collective

    2899:   Input Parameters:
    2900: + mat - the matrix
    2901: . v1  - the vector to be multiplied by the transpose of the matrix
    2902: - v2  - the vector to be added to the result

    2904:   Output Parameter:
    2905: . v3 - the result

    2907:   Level: beginner

    2909:   Note:
    2910:   The vectors `v1` and `v3` cannot be the same.  I.e., one cannot
    2911:   call `MatMultTransposeAdd`(A,v1,v2,v1).

    2913: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMultAdd()`, `MatMult()`
    2914: @*/
    2915: PetscErrorCode MatMultTransposeAdd(Mat mat, Vec v1, Vec v2, Vec v3)
    2916: {
    2917:   PetscErrorCode (*op)(Mat, Vec, Vec, Vec) = (!mat->ops->multtransposeadd && mat->symmetric) ? mat->ops->multadd : mat->ops->multtransposeadd;

    2919:   PetscFunctionBegin;

    2926:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2927:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2928:   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);
    2929:   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);
    2930:   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);
    2931:   PetscCheck(v1 != v3, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "v1 and v3 must be different vectors");
    2932:   PetscCheck(op, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Mat type %s", ((PetscObject)mat)->type_name);
    2933:   MatCheckPreallocated(mat, 1);

    2935:   PetscCall(PetscLogEventBegin(MAT_MultTransposeAdd, mat, v1, v2, v3));
    2936:   PetscCall(VecLockReadPush(v1));
    2937:   PetscCall((*op)(mat, v1, v2, v3));
    2938:   PetscCall(VecLockReadPop(v1));
    2939:   PetscCall(PetscLogEventEnd(MAT_MultTransposeAdd, mat, v1, v2, v3));
    2940:   PetscCall(PetscObjectStateIncrease((PetscObject)v3));
    2941:   PetscFunctionReturn(PETSC_SUCCESS);
    2942: }

    2944: /*@
    2945:   MatMultHermitianTransposeAdd - Computes $v3 = v2 + A^H * v1$.

    2947:   Neighbor-wise Collective

    2949:   Input Parameters:
    2950: + mat - the matrix
    2951: . v1  - the vector to be multiplied by the Hermitian transpose
    2952: - v2  - the vector to be added to the result

    2954:   Output Parameter:
    2955: . v3 - the result

    2957:   Level: beginner

    2959:   Note:
    2960:   The vectors `v1` and `v3` cannot be the same.  I.e., one cannot
    2961:   call `MatMultHermitianTransposeAdd`(A,v1,v2,v1).

    2963: .seealso: [](ch_matrices), `Mat`, `MatMultHermitianTranspose()`, `MatMultTranspose()`, `MatMultAdd()`, `MatMult()`
    2964: @*/
    2965: PetscErrorCode MatMultHermitianTransposeAdd(Mat mat, Vec v1, Vec v2, Vec v3)
    2966: {
    2967:   PetscFunctionBegin;

    2974:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    2975:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    2976:   PetscCheck(v1 != v3, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "v1 and v3 must be different vectors");
    2977:   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);
    2978:   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);
    2979:   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);
    2980:   MatCheckPreallocated(mat, 1);

    2982:   PetscCall(PetscLogEventBegin(MAT_MultHermitianTransposeAdd, mat, v1, v2, v3));
    2983:   PetscCall(VecLockReadPush(v1));
    2984:   if (mat->ops->multhermitiantransposeadd) PetscUseTypeMethod(mat, multhermitiantransposeadd, v1, v2, v3);
    2985:   else {
    2986:     Vec w, z;
    2987:     PetscCall(VecDuplicate(v1, &w));
    2988:     PetscCall(VecCopy(v1, w));
    2989:     PetscCall(VecConjugate(w));
    2990:     PetscCall(VecDuplicate(v3, &z));
    2991:     PetscCall(MatMultTranspose(mat, w, z));
    2992:     PetscCall(VecDestroy(&w));
    2993:     PetscCall(VecConjugate(z));
    2994:     if (v2 != v3) {
    2995:       PetscCall(VecWAXPY(v3, 1.0, v2, z));
    2996:     } else {
    2997:       PetscCall(VecAXPY(v3, 1.0, z));
    2998:     }
    2999:     PetscCall(VecDestroy(&z));
    3000:   }
    3001:   PetscCall(VecLockReadPop(v1));
    3002:   PetscCall(PetscLogEventEnd(MAT_MultHermitianTransposeAdd, mat, v1, v2, v3));
    3003:   PetscCall(PetscObjectStateIncrease((PetscObject)v3));
    3004:   PetscFunctionReturn(PETSC_SUCCESS);
    3005: }

    3007: /*@
    3008:   MatGetFactorType - gets the type of factorization a matrix is

    3010:   Not Collective

    3012:   Input Parameter:
    3013: . mat - the matrix

    3015:   Output Parameter:
    3016: . 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`

    3018:   Level: intermediate

    3020: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorType`, `MatGetFactor()`, `MatSetFactorType()`, `MAT_FACTOR_NONE`, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ILU`,
    3021:           `MAT_FACTOR_ICC`,`MAT_FACTOR_ILUDT`, `MAT_FACTOR_QR`
    3022: @*/
    3023: PetscErrorCode MatGetFactorType(Mat mat, MatFactorType *t)
    3024: {
    3025:   PetscFunctionBegin;
    3028:   PetscAssertPointer(t, 2);
    3029:   *t = mat->factortype;
    3030:   PetscFunctionReturn(PETSC_SUCCESS);
    3031: }

    3033: /*@
    3034:   MatSetFactorType - sets the type of factorization a matrix is

    3036:   Logically Collective

    3038:   Input Parameters:
    3039: + mat - the matrix
    3040: - 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`

    3042:   Level: intermediate

    3044: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorType`, `MatGetFactor()`, `MatGetFactorType()`, `MAT_FACTOR_NONE`, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ILU`,
    3045:           `MAT_FACTOR_ICC`,`MAT_FACTOR_ILUDT`, `MAT_FACTOR_QR`
    3046: @*/
    3047: PetscErrorCode MatSetFactorType(Mat mat, MatFactorType t)
    3048: {
    3049:   PetscFunctionBegin;
    3052:   mat->factortype = t;
    3053:   PetscFunctionReturn(PETSC_SUCCESS);
    3054: }

    3056: /*@
    3057:   MatGetInfo - Returns information about matrix storage (number of
    3058:   nonzeros, memory, etc.).

    3060:   Collective if `MAT_GLOBAL_MAX` or `MAT_GLOBAL_SUM` is used as the flag

    3062:   Input Parameters:
    3063: + mat  - the matrix
    3064: - 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)

    3066:   Output Parameter:
    3067: . info - matrix information context

    3069:   Options Database Key:
    3070: . -mat_view ::ascii_info - print matrix info to `PETSC_STDOUT`

    3072:   Level: intermediate

    3074:   Notes:
    3075:   The `MatInfo` context contains a variety of matrix data, including
    3076:   number of nonzeros allocated and used, number of mallocs during
    3077:   matrix assembly, etc.  Additional information for factored matrices
    3078:   is provided (such as the fill ratio, number of mallocs during
    3079:   factorization, etc.).

    3081:   Example:
    3082:   See the file ${PETSC_DIR}/include/petscmat.h for a complete list of
    3083:   data within the `MatInfo` context.  For example,
    3084: .vb
    3085:       MatInfo info;
    3086:       Mat     A;
    3087:       double  mal, nz_a, nz_u;

    3089:       MatGetInfo(A, MAT_LOCAL, &info);
    3090:       mal  = info.mallocs;
    3091:       nz_a = info.nz_allocated;
    3092: .ve

    3094: .seealso: [](ch_matrices), `Mat`, `MatInfo`, `MatStashGetInfo()`
    3095: @*/
    3096: PetscErrorCode MatGetInfo(Mat mat, MatInfoType flag, MatInfo *info)
    3097: {
    3098:   PetscFunctionBegin;
    3101:   PetscAssertPointer(info, 3);
    3102:   MatCheckPreallocated(mat, 1);
    3103:   PetscUseTypeMethod(mat, getinfo, flag, info);
    3104:   PetscFunctionReturn(PETSC_SUCCESS);
    3105: }

    3107: /*
    3108:    This is used by external packages where it is not easy to get the info from the actual
    3109:    matrix factorization.
    3110: */
    3111: PetscErrorCode MatGetInfo_External(Mat A, MatInfoType flag, MatInfo *info)
    3112: {
    3113:   PetscFunctionBegin;
    3114:   PetscCall(PetscMemzero(info, sizeof(MatInfo)));
    3115:   PetscFunctionReturn(PETSC_SUCCESS);
    3116: }

    3118: /*@
    3119:   MatLUFactor - Performs in-place LU factorization of matrix.

    3121:   Collective

    3123:   Input Parameters:
    3124: + mat  - the matrix
    3125: . row  - row permutation
    3126: . col  - column permutation
    3127: - info - options for factorization, includes
    3128: .vb
    3129:           fill - expected fill as ratio of original fill.
    3130:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3131:                    Run with the option -info to determine an optimal value to use
    3132: .ve

    3134:   Level: developer

    3136:   Notes:
    3137:   Most users should employ the `KSP` interface for linear solvers
    3138:   instead of working directly with matrix algebra routines such as this.
    3139:   See, e.g., `KSPCreate()`.

    3141:   This changes the state of the matrix to a factored matrix; it cannot be used
    3142:   for example with `MatSetValues()` unless one first calls `MatSetUnfactored()`.

    3144:   This is really in-place only for dense matrices, the preferred approach is to use `MatGetFactor()`, `MatLUFactorSymbolic()`, and `MatLUFactorNumeric()`
    3145:   when not using `KSP`.

    3147:   Fortran Note:
    3148:   A valid (non-null) `info` argument must be provided

    3150: .seealso: [](ch_matrices), [Matrix Factorization](sec_matfactor), `Mat`, `MatFactorType`, `MatLUFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`,
    3151:           `MatGetOrdering()`, `MatSetUnfactored()`, `MatFactorInfo`, `MatGetFactor()`
    3152: @*/
    3153: PetscErrorCode MatLUFactor(Mat mat, IS row, IS col, const MatFactorInfo *info)
    3154: {
    3155:   MatFactorInfo tinfo;

    3157:   PetscFunctionBegin;
    3161:   if (info) PetscAssertPointer(info, 4);
    3163:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3164:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3165:   MatCheckPreallocated(mat, 1);
    3166:   if (!info) {
    3167:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3168:     info = &tinfo;
    3169:   }

    3171:   PetscCall(PetscLogEventBegin(MAT_LUFactor, mat, row, col, 0));
    3172:   PetscUseTypeMethod(mat, lufactor, row, col, info);
    3173:   PetscCall(PetscLogEventEnd(MAT_LUFactor, mat, row, col, 0));
    3174:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    3175:   PetscFunctionReturn(PETSC_SUCCESS);
    3176: }

    3178: /*@
    3179:   MatILUFactor - Performs in-place ILU factorization of matrix.

    3181:   Collective

    3183:   Input Parameters:
    3184: + mat  - the matrix
    3185: . row  - row permutation
    3186: . col  - column permutation
    3187: - info - structure containing
    3188: .vb
    3189:       levels - number of levels of fill.
    3190:       expected fill - as ratio of original fill.
    3191:       1 or 0 - indicating force fill on diagonal (improves robustness for matrices
    3192:                 missing diagonal entries)
    3193: .ve

    3195:   Level: developer

    3197:   Notes:
    3198:   Most users should employ the `KSP` interface for linear solvers
    3199:   instead of working directly with matrix algebra routines such as this.
    3200:   See, e.g., `KSPCreate()`.

    3202:   Probably really in-place only when level of fill is zero, otherwise allocates
    3203:   new space to store factored matrix and deletes previous memory. The preferred approach is to use `MatGetFactor()`, `MatILUFactorSymbolic()`, and `MatILUFactorNumeric()`
    3204:   when not using `KSP`.

    3206:   Fortran Note:
    3207:   A valid (non-null) `info` argument must be provided

    3209: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatILUFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`, `MatFactorInfo`
    3210: @*/
    3211: PetscErrorCode MatILUFactor(Mat mat, IS row, IS col, const MatFactorInfo *info)
    3212: {
    3213:   PetscFunctionBegin;
    3217:   PetscAssertPointer(info, 4);
    3219:   PetscCheck(mat->rmap->N == mat->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "matrix must be square");
    3220:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3221:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3222:   MatCheckPreallocated(mat, 1);

    3224:   PetscCall(PetscLogEventBegin(MAT_ILUFactor, mat, row, col, 0));
    3225:   PetscUseTypeMethod(mat, ilufactor, row, col, info);
    3226:   PetscCall(PetscLogEventEnd(MAT_ILUFactor, mat, row, col, 0));
    3227:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    3228:   PetscFunctionReturn(PETSC_SUCCESS);
    3229: }

    3231: /*@
    3232:   MatLUFactorSymbolic - Performs symbolic LU factorization of matrix.
    3233:   Call this routine before calling `MatLUFactorNumeric()` and after `MatGetFactor()`.

    3235:   Collective

    3237:   Input Parameters:
    3238: + fact - the factor matrix obtained with `MatGetFactor()`
    3239: . mat  - the matrix
    3240: . row  - the row permutation
    3241: . col  - the column permutation
    3242: - info - options for factorization, includes
    3243: .vb
    3244:           fill - expected fill as ratio of original fill. Run with the option -info to determine an optimal value to use
    3245:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3246: .ve

    3248:   Level: developer

    3250:   Notes:
    3251:   See [Matrix Factorization](sec_matfactor) for additional information about factorizations

    3253:   Most users should employ the simplified `KSP` interface for linear solvers
    3254:   instead of working directly with matrix algebra routines such as this.
    3255:   See, e.g., `KSPCreate()`.

    3257:   Fortran Note:
    3258:   A valid (non-null) `info` argument must be provided

    3260: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatLUFactor()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`, `MatFactorInfo`, `MatFactorInfoInitialize()`
    3261: @*/
    3262: PetscErrorCode MatLUFactorSymbolic(Mat fact, Mat mat, IS row, IS col, const MatFactorInfo *info)
    3263: {
    3264:   MatFactorInfo tinfo;

    3266:   PetscFunctionBegin;
    3271:   if (info) PetscAssertPointer(info, 5);
    3274:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3275:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3276:   MatCheckPreallocated(mat, 2);
    3277:   if (!info) {
    3278:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3279:     info = &tinfo;
    3280:   }

    3282:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_LUFactorSymbolic, mat, row, col, 0));
    3283:   PetscUseTypeMethod(fact, lufactorsymbolic, mat, row, col, info);
    3284:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_LUFactorSymbolic, mat, row, col, 0));
    3285:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3286:   PetscFunctionReturn(PETSC_SUCCESS);
    3287: }

    3289: /*@
    3290:   MatLUFactorNumeric - Performs numeric LU factorization of a matrix.
    3291:   Call this routine after first calling `MatLUFactorSymbolic()` and `MatGetFactor()`.

    3293:   Collective

    3295:   Input Parameters:
    3296: + fact - the factor matrix obtained with `MatGetFactor()`
    3297: . mat  - the matrix
    3298: - info - options for factorization

    3300:   Level: developer

    3302:   Notes:
    3303:   See `MatLUFactor()` for in-place factorization.  See
    3304:   `MatCholeskyFactorNumeric()` for the symmetric, positive definite case.

    3306:   Most users should employ the `KSP` interface for linear solvers
    3307:   instead of working directly with matrix algebra routines such as this.
    3308:   See, e.g., `KSPCreate()`.

    3310:   Fortran Note:
    3311:   A valid (non-null) `info` argument must be provided

    3313: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatFactorInfo`, `MatLUFactorSymbolic()`, `MatLUFactor()`, `MatCholeskyFactor()`
    3314: @*/
    3315: PetscErrorCode MatLUFactorNumeric(Mat fact, Mat mat, const MatFactorInfo *info)
    3316: {
    3317:   MatFactorInfo tinfo;

    3319:   PetscFunctionBegin;
    3324:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3325:   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,
    3326:              mat->rmap->N, (fact)->rmap->N, mat->cmap->N, (fact)->cmap->N);

    3328:   MatCheckPreallocated(mat, 2);
    3329:   if (!info) {
    3330:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3331:     info = &tinfo;
    3332:   }

    3334:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_LUFactorNumeric, mat, fact, 0, 0));
    3335:   else PetscCall(PetscLogEventBegin(MAT_LUFactor, mat, fact, 0, 0));
    3336:   PetscUseTypeMethod(fact, lufactornumeric, mat, info);
    3337:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_LUFactorNumeric, mat, fact, 0, 0));
    3338:   else PetscCall(PetscLogEventEnd(MAT_LUFactor, mat, fact, 0, 0));
    3339:   PetscCall(MatViewFromOptions(fact, NULL, "-mat_factor_view"));
    3340:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3341:   PetscFunctionReturn(PETSC_SUCCESS);
    3342: }

    3344: /*@
    3345:   MatCholeskyFactor - Performs in-place Cholesky factorization of a
    3346:   symmetric matrix.

    3348:   Collective

    3350:   Input Parameters:
    3351: + mat  - the matrix
    3352: . perm - row and column permutations
    3353: - info - expected fill as ratio of original fill

    3355:   Level: developer

    3357:   Notes:
    3358:   See `MatLUFactor()` for the nonsymmetric case.  See also `MatGetFactor()`,
    3359:   `MatCholeskyFactorSymbolic()`, and `MatCholeskyFactorNumeric()`.

    3361:   Most users should employ the `KSP` interface for linear solvers
    3362:   instead of working directly with matrix algebra routines such as this.
    3363:   See, e.g., `KSPCreate()`.

    3365:   Fortran Note:
    3366:   A valid (non-null) `info` argument must be provided

    3368: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatFactorInfo`, `MatLUFactor()`, `MatCholeskyFactorSymbolic()`, `MatCholeskyFactorNumeric()`
    3369:           `MatGetOrdering()`
    3370: @*/
    3371: PetscErrorCode MatCholeskyFactor(Mat mat, IS perm, const MatFactorInfo *info)
    3372: {
    3373:   MatFactorInfo tinfo;

    3375:   PetscFunctionBegin;
    3378:   if (info) PetscAssertPointer(info, 3);
    3380:   PetscCheck(mat->rmap->N == mat->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "Matrix must be square");
    3381:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3382:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3383:   MatCheckPreallocated(mat, 1);
    3384:   if (!info) {
    3385:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3386:     info = &tinfo;
    3387:   }

    3389:   PetscCall(PetscLogEventBegin(MAT_CholeskyFactor, mat, perm, 0, 0));
    3390:   PetscUseTypeMethod(mat, choleskyfactor, perm, info);
    3391:   PetscCall(PetscLogEventEnd(MAT_CholeskyFactor, mat, perm, 0, 0));
    3392:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    3393:   PetscFunctionReturn(PETSC_SUCCESS);
    3394: }

    3396: /*@
    3397:   MatCholeskyFactorSymbolic - Performs symbolic Cholesky factorization
    3398:   of a symmetric matrix.

    3400:   Collective

    3402:   Input Parameters:
    3403: + fact - the factor matrix obtained with `MatGetFactor()`
    3404: . mat  - the matrix
    3405: . perm - row and column permutations
    3406: - info - options for factorization, includes
    3407: .vb
    3408:           fill - expected fill as ratio of original fill.
    3409:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3410:                    Run with the option -info to determine an optimal value to use
    3411: .ve

    3413:   Level: developer

    3415:   Notes:
    3416:   See `MatLUFactorSymbolic()` for the nonsymmetric case.  See also
    3417:   `MatCholeskyFactor()` and `MatCholeskyFactorNumeric()`.

    3419:   Most users should employ the `KSP` interface for linear solvers
    3420:   instead of working directly with matrix algebra routines such as this.
    3421:   See, e.g., `KSPCreate()`.

    3423:   Fortran Note:
    3424:   A valid (non-null) `info` argument must be provided

    3426: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorInfo`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatCholeskyFactor()`, `MatCholeskyFactorNumeric()`
    3427:           `MatGetOrdering()`
    3428: @*/
    3429: PetscErrorCode MatCholeskyFactorSymbolic(Mat fact, Mat mat, IS perm, const MatFactorInfo *info)
    3430: {
    3431:   MatFactorInfo tinfo;

    3433:   PetscFunctionBegin;
    3437:   if (info) PetscAssertPointer(info, 4);
    3440:   PetscCheck(mat->rmap->N == mat->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "Matrix must be square");
    3441:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3442:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3443:   MatCheckPreallocated(mat, 2);
    3444:   if (!info) {
    3445:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3446:     info = &tinfo;
    3447:   }

    3449:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_CholeskyFactorSymbolic, mat, perm, 0, 0));
    3450:   PetscUseTypeMethod(fact, choleskyfactorsymbolic, mat, perm, info);
    3451:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_CholeskyFactorSymbolic, mat, perm, 0, 0));
    3452:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3453:   PetscFunctionReturn(PETSC_SUCCESS);
    3454: }

    3456: /*@
    3457:   MatCholeskyFactorNumeric - Performs numeric Cholesky factorization
    3458:   of a symmetric matrix. Call this routine after first calling `MatGetFactor()` and
    3459:   `MatCholeskyFactorSymbolic()`.

    3461:   Collective

    3463:   Input Parameters:
    3464: + fact - the factor matrix obtained with `MatGetFactor()`, where the factored values are stored
    3465: . mat  - the initial matrix that is to be factored
    3466: - info - options for factorization

    3468:   Level: developer

    3470:   Note:
    3471:   Most users should employ the `KSP` interface for linear solvers
    3472:   instead of working directly with matrix algebra routines such as this.
    3473:   See, e.g., `KSPCreate()`.

    3475:   Fortran Note:
    3476:   A valid (non-null) `info` argument must be provided

    3478: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorInfo`, `MatGetFactor()`, `MatCholeskyFactorSymbolic()`, `MatCholeskyFactor()`, `MatLUFactorNumeric()`
    3479: @*/
    3480: PetscErrorCode MatCholeskyFactorNumeric(Mat fact, Mat mat, const MatFactorInfo *info)
    3481: {
    3482:   MatFactorInfo tinfo;

    3484:   PetscFunctionBegin;
    3489:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3490:   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,
    3491:              mat->rmap->N, (fact)->rmap->N, mat->cmap->N, (fact)->cmap->N);
    3492:   MatCheckPreallocated(mat, 2);
    3493:   if (!info) {
    3494:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3495:     info = &tinfo;
    3496:   }

    3498:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_CholeskyFactorNumeric, mat, fact, 0, 0));
    3499:   else PetscCall(PetscLogEventBegin(MAT_CholeskyFactor, mat, fact, 0, 0));
    3500:   PetscUseTypeMethod(fact, choleskyfactornumeric, mat, info);
    3501:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_CholeskyFactorNumeric, mat, fact, 0, 0));
    3502:   else PetscCall(PetscLogEventEnd(MAT_CholeskyFactor, mat, fact, 0, 0));
    3503:   PetscCall(MatViewFromOptions(fact, NULL, "-mat_factor_view"));
    3504:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3505:   PetscFunctionReturn(PETSC_SUCCESS);
    3506: }

    3508: /*@
    3509:   MatQRFactor - Performs in-place QR factorization of matrix.

    3511:   Collective

    3513:   Input Parameters:
    3514: + mat  - the matrix
    3515: . col  - column permutation
    3516: - info - options for factorization, includes
    3517: .vb
    3518:           fill - expected fill as ratio of original fill.
    3519:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3520:                    Run with the option -info to determine an optimal value to use
    3521: .ve

    3523:   Level: developer

    3525:   Notes:
    3526:   Most users should employ the `KSP` interface for linear solvers
    3527:   instead of working directly with matrix algebra routines such as this.
    3528:   See, e.g., `KSPCreate()`.

    3530:   This changes the state of the matrix to a factored matrix; it cannot be used
    3531:   for example with `MatSetValues()` unless one first calls `MatSetUnfactored()`.

    3533:   Fortran Note:
    3534:   A valid (non-null) `info` argument must be provided

    3536: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorInfo`, `MatGetFactor()`, `MatQRFactorSymbolic()`, `MatQRFactorNumeric()`, `MatLUFactor()`,
    3537:           `MatSetUnfactored()`
    3538: @*/
    3539: PetscErrorCode MatQRFactor(Mat mat, IS col, const MatFactorInfo *info)
    3540: {
    3541:   PetscFunctionBegin;
    3544:   if (info) PetscAssertPointer(info, 3);
    3546:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3547:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3548:   MatCheckPreallocated(mat, 1);
    3549:   PetscCall(PetscLogEventBegin(MAT_QRFactor, mat, col, 0, 0));
    3550:   PetscUseMethod(mat, "MatQRFactor_C", (Mat, IS, const MatFactorInfo *), (mat, col, info));
    3551:   PetscCall(PetscLogEventEnd(MAT_QRFactor, mat, col, 0, 0));
    3552:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    3553:   PetscFunctionReturn(PETSC_SUCCESS);
    3554: }

    3556: /*@
    3557:   MatQRFactorSymbolic - Performs symbolic QR factorization of matrix.
    3558:   Call this routine after `MatGetFactor()` but before calling `MatQRFactorNumeric()`.

    3560:   Collective

    3562:   Input Parameters:
    3563: + fact - the factor matrix obtained with `MatGetFactor()`
    3564: . mat  - the matrix
    3565: . col  - column permutation
    3566: - info - options for factorization, includes
    3567: .vb
    3568:           fill - expected fill as ratio of original fill.
    3569:           dtcol - pivot tolerance (0 no pivot, 1 full column pivoting)
    3570:                    Run with the option -info to determine an optimal value to use
    3571: .ve

    3573:   Level: developer

    3575:   Note:
    3576:   Most users should employ the `KSP` interface for linear solvers
    3577:   instead of working directly with matrix algebra routines such as this.
    3578:   See, e.g., `KSPCreate()`.

    3580:   Fortran Note:
    3581:   A valid (non-null) `info` argument must be provided

    3583: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatFactorInfo`, `MatQRFactor()`, `MatQRFactorNumeric()`, `MatLUFactor()`, `MatFactorInfoInitialize()`
    3584: @*/
    3585: PetscErrorCode MatQRFactorSymbolic(Mat fact, Mat mat, IS col, const MatFactorInfo *info)
    3586: {
    3587:   MatFactorInfo tinfo;

    3589:   PetscFunctionBegin;
    3593:   if (info) PetscAssertPointer(info, 4);
    3596:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3597:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    3598:   MatCheckPreallocated(mat, 2);
    3599:   if (!info) {
    3600:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3601:     info = &tinfo;
    3602:   }

    3604:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_QRFactorSymbolic, fact, mat, col, 0));
    3605:   PetscUseMethod(fact, "MatQRFactorSymbolic_C", (Mat, Mat, IS, const MatFactorInfo *), (fact, mat, col, info));
    3606:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_QRFactorSymbolic, fact, mat, col, 0));
    3607:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3608:   PetscFunctionReturn(PETSC_SUCCESS);
    3609: }

    3611: /*@
    3612:   MatQRFactorNumeric - Performs numeric QR factorization of a matrix.
    3613:   Call this routine after first calling `MatGetFactor()`, and `MatQRFactorSymbolic()`.

    3615:   Collective

    3617:   Input Parameters:
    3618: + fact - the factor matrix obtained with `MatGetFactor()`
    3619: . mat  - the matrix
    3620: - info - options for factorization

    3622:   Level: developer

    3624:   Notes:
    3625:   See `MatQRFactor()` for in-place factorization.

    3627:   Most users should employ the `KSP` interface for linear solvers
    3628:   instead of working directly with matrix algebra routines such as this.
    3629:   See, e.g., `KSPCreate()`.

    3631:   Fortran Note:
    3632:   A valid (non-null) `info` argument must be provided

    3634: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorInfo`, `MatGetFactor()`, `MatQRFactor()`, `MatQRFactorSymbolic()`, `MatLUFactor()`
    3635: @*/
    3636: PetscErrorCode MatQRFactorNumeric(Mat fact, Mat mat, const MatFactorInfo *info)
    3637: {
    3638:   MatFactorInfo tinfo;

    3640:   PetscFunctionBegin;
    3645:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    3646:   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,
    3647:              mat->rmap->N, (fact)->rmap->N, mat->cmap->N, (fact)->cmap->N);

    3649:   MatCheckPreallocated(mat, 2);
    3650:   if (!info) {
    3651:     PetscCall(MatFactorInfoInitialize(&tinfo));
    3652:     info = &tinfo;
    3653:   }

    3655:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_QRFactorNumeric, mat, fact, 0, 0));
    3656:   else PetscCall(PetscLogEventBegin(MAT_QRFactor, mat, fact, 0, 0));
    3657:   PetscUseMethod(fact, "MatQRFactorNumeric_C", (Mat, Mat, const MatFactorInfo *), (fact, mat, info));
    3658:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_QRFactorNumeric, mat, fact, 0, 0));
    3659:   else PetscCall(PetscLogEventEnd(MAT_QRFactor, mat, fact, 0, 0));
    3660:   PetscCall(MatViewFromOptions(fact, NULL, "-mat_factor_view"));
    3661:   PetscCall(PetscObjectStateIncrease((PetscObject)fact));
    3662:   PetscFunctionReturn(PETSC_SUCCESS);
    3663: }

    3665: /*@
    3666:   MatSolve - Solves $A x = b$, given a factored matrix.

    3668:   Neighbor-wise Collective

    3670:   Input Parameters:
    3671: + mat - the factored matrix
    3672: - b   - the right-hand-side vector

    3674:   Output Parameter:
    3675: . x - the result vector

    3677:   Level: developer

    3679:   Notes:
    3680:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    3681:   call `MatSolve`(A,x,x).

    3683:   Most users should employ the `KSP` interface for linear solvers
    3684:   instead of working directly with matrix algebra routines such as this.
    3685:   See, e.g., `KSPCreate()`.

    3687: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatLUFactor()`, `MatSolveAdd()`, `MatSolveTranspose()`, `MatSolveTransposeAdd()`
    3688: @*/
    3689: PetscErrorCode MatSolve(Mat mat, Vec b, Vec x)
    3690: {
    3691:   PetscFunctionBegin;
    3696:   PetscCheckSameComm(mat, 1, b, 2);
    3697:   PetscCheckSameComm(mat, 1, x, 3);
    3698:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    3699:   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);
    3700:   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);
    3701:   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);
    3702:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3703:   MatCheckPreallocated(mat, 1);

    3705:   PetscCall(PetscLogEventBegin(MAT_Solve, mat, b, x, 0));
    3706:   PetscCall(VecFlag(x, mat->factorerrortype));
    3707:   if (mat->factorerrortype) PetscCall(PetscInfo(mat, "MatFactorError %d\n", mat->factorerrortype));
    3708:   else PetscUseTypeMethod(mat, solve, b, x);
    3709:   PetscCall(PetscLogEventEnd(MAT_Solve, mat, b, x, 0));
    3710:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    3711:   PetscFunctionReturn(PETSC_SUCCESS);
    3712: }

    3714: static PetscErrorCode MatMatSolve_Basic(Mat A, Mat B, Mat X, PetscBool trans)
    3715: {
    3716:   Vec      b, x;
    3717:   PetscInt N, i;
    3718:   PetscErrorCode (*f)(Mat, Vec, Vec);
    3719:   PetscBool Abound, Bneedconv = PETSC_FALSE, Xneedconv = PETSC_FALSE;

    3721:   PetscFunctionBegin;
    3722:   if (A->factorerrortype) {
    3723:     PetscCall(PetscInfo(A, "MatFactorError %d\n", A->factorerrortype));
    3724:     PetscCall(MatSetInf(X));
    3725:     PetscFunctionReturn(PETSC_SUCCESS);
    3726:   }
    3727:   f = (!trans || (!A->ops->solvetranspose && A->symmetric)) ? A->ops->solve : A->ops->solvetranspose;
    3728:   PetscCheck(f, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Mat type %s", ((PetscObject)A)->type_name);
    3729:   PetscCall(MatBoundToCPU(A, &Abound));
    3730:   if (!Abound) {
    3731:     PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &Bneedconv, MATSEQDENSE, MATMPIDENSE, ""));
    3732:     PetscCall(PetscObjectTypeCompareAny((PetscObject)X, &Xneedconv, MATSEQDENSE, MATMPIDENSE, ""));
    3733:   }
    3734: #if PetscDefined(HAVE_CUDA)
    3735:   if (Bneedconv) PetscCall(MatConvert(B, MATDENSECUDA, MAT_INPLACE_MATRIX, &B));
    3736:   if (Xneedconv) PetscCall(MatConvert(X, MATDENSECUDA, MAT_INPLACE_MATRIX, &X));
    3737: #elif PetscDefined(HAVE_HIP)
    3738:   if (Bneedconv) PetscCall(MatConvert(B, MATDENSEHIP, MAT_INPLACE_MATRIX, &B));
    3739:   if (Xneedconv) PetscCall(MatConvert(X, MATDENSEHIP, MAT_INPLACE_MATRIX, &X));
    3740: #endif
    3741:   PetscCall(MatGetSize(B, NULL, &N));
    3742:   for (i = 0; i < N; i++) {
    3743:     PetscCall(MatDenseGetColumnVecRead(B, i, &b));
    3744:     PetscCall(MatDenseGetColumnVecWrite(X, i, &x));
    3745:     PetscCall((*f)(A, b, x));
    3746:     PetscCall(MatDenseRestoreColumnVecWrite(X, i, &x));
    3747:     PetscCall(MatDenseRestoreColumnVecRead(B, i, &b));
    3748:   }
    3749:   if (Bneedconv) PetscCall(MatConvert(B, MATDENSE, MAT_INPLACE_MATRIX, &B));
    3750:   if (Xneedconv) PetscCall(MatConvert(X, MATDENSE, MAT_INPLACE_MATRIX, &X));
    3751:   PetscFunctionReturn(PETSC_SUCCESS);
    3752: }

    3754: /*@
    3755:   MatMatSolve - Solves $A X = B$, given a factored matrix.

    3757:   Neighbor-wise Collective

    3759:   Input Parameters:
    3760: + A - the factored matrix
    3761: - B - the right-hand-side matrix `MATDENSE` (or sparse `MATAIJ`-- when using MUMPS)

    3763:   Output Parameter:
    3764: . X - the result matrix (dense matrix)

    3766:   Level: developer

    3768:   Note:
    3769:   If `B` is a `MATDENSE` matrix then one can call `MatMatSolve`(A,B,B) except with `MATSOLVERMKL_CPARDISO`;
    3770:   otherwise, `B` and `X` cannot be the same.

    3772: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatSolve()`, `MatMatSolveTranspose()`, `MatLUFactor()`, `MatCholeskyFactor()`
    3773: @*/
    3774: PetscErrorCode MatMatSolve(Mat A, Mat B, Mat X)
    3775: {
    3776:   PetscFunctionBegin;
    3781:   PetscCheckSameComm(A, 1, B, 2);
    3782:   PetscCheckSameComm(A, 1, X, 3);
    3783:   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);
    3784:   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);
    3785:   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");
    3786:   if (!A->rmap->N && !A->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3787:   MatCheckPreallocated(A, 1);

    3789:   PetscCall(PetscLogEventBegin(MAT_MatSolve, A, B, X, 0));
    3790:   if (!A->ops->matsolve) {
    3791:     PetscCall(PetscInfo(A, "Mat type %s using basic MatMatSolve\n", ((PetscObject)A)->type_name));
    3792:     PetscCall(MatMatSolve_Basic(A, B, X, PETSC_FALSE));
    3793:   } else PetscUseTypeMethod(A, matsolve, B, X);
    3794:   PetscCall(PetscLogEventEnd(MAT_MatSolve, A, B, X, 0));
    3795:   PetscCall(PetscObjectStateIncrease((PetscObject)X));
    3796:   PetscFunctionReturn(PETSC_SUCCESS);
    3797: }

    3799: /*@
    3800:   MatMatSolveTranspose - Solves $A^T X = B $, given a factored matrix.

    3802:   Neighbor-wise Collective

    3804:   Input Parameters:
    3805: + A - the factored matrix
    3806: - B - the right-hand-side matrix  (`MATDENSE` matrix)

    3808:   Output Parameter:
    3809: . X - the result matrix (dense matrix)

    3811:   Level: developer

    3813:   Note:
    3814:   The matrices `B` and `X` cannot be the same.  I.e., one cannot
    3815:   call `MatMatSolveTranspose`(A,X,X).

    3817: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatSolveTranspose()`, `MatMatSolve()`, `MatLUFactor()`, `MatCholeskyFactor()`
    3818: @*/
    3819: PetscErrorCode MatMatSolveTranspose(Mat A, Mat B, Mat X)
    3820: {
    3821:   PetscFunctionBegin;
    3826:   PetscCheckSameComm(A, 1, B, 2);
    3827:   PetscCheckSameComm(A, 1, X, 3);
    3828:   PetscCheck(X != B, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_IDN, "X and B must be different matrices");
    3829:   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);
    3830:   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);
    3831:   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);
    3832:   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");
    3833:   if (!A->rmap->N && !A->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3834:   MatCheckPreallocated(A, 1);

    3836:   PetscCall(PetscLogEventBegin(MAT_MatSolve, A, B, X, 0));
    3837:   if (!A->ops->matsolvetranspose) {
    3838:     PetscCall(PetscInfo(A, "Mat type %s using basic MatMatSolveTranspose\n", ((PetscObject)A)->type_name));
    3839:     PetscCall(MatMatSolve_Basic(A, B, X, PETSC_TRUE));
    3840:   } else PetscUseTypeMethod(A, matsolvetranspose, B, X);
    3841:   PetscCall(PetscLogEventEnd(MAT_MatSolve, A, B, X, 0));
    3842:   PetscCall(PetscObjectStateIncrease((PetscObject)X));
    3843:   PetscFunctionReturn(PETSC_SUCCESS);
    3844: }

    3846: /*@
    3847:   MatMatTransposeSolve - Solves $A X = B^T$, given a factored matrix.

    3849:   Neighbor-wise Collective

    3851:   Input Parameters:
    3852: + A  - the factored matrix
    3853: - Bt - the transpose of right-hand-side matrix as a `MATDENSE`

    3855:   Output Parameter:
    3856: . X - the result matrix (dense matrix)

    3858:   Level: developer

    3860:   Note:
    3861:   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
    3862:   format on the host processor and call `MatMatTransposeSolve()` to implement MUMPS' `MatMatSolve()`.

    3864: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatMatSolve()`, `MatMatSolveTranspose()`, `MatLUFactor()`, `MatCholeskyFactor()`
    3865: @*/
    3866: PetscErrorCode MatMatTransposeSolve(Mat A, Mat Bt, Mat X)
    3867: {
    3868:   PetscFunctionBegin;
    3873:   PetscCheckSameComm(A, 1, Bt, 2);
    3874:   PetscCheckSameComm(A, 1, X, 3);

    3876:   PetscCheck(X != Bt, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_IDN, "X and B must be different matrices");
    3877:   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);
    3878:   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);
    3879:   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");
    3880:   if (!A->rmap->N && !A->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3881:   PetscCheck(A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Unfactored matrix");
    3882:   MatCheckPreallocated(A, 1);

    3884:   PetscCall(PetscLogEventBegin(MAT_MatTrSolve, A, Bt, X, 0));
    3885:   PetscUseTypeMethod(A, mattransposesolve, Bt, X);
    3886:   PetscCall(PetscLogEventEnd(MAT_MatTrSolve, A, Bt, X, 0));
    3887:   PetscCall(PetscObjectStateIncrease((PetscObject)X));
    3888:   PetscFunctionReturn(PETSC_SUCCESS);
    3889: }

    3891: /*@
    3892:   MatForwardSolve - Solves $ L x = b $, given a factored matrix, $A = LU $, or
    3893:   $U^T*D^(1/2) x = b$, given a factored symmetric matrix, $A = U^T*D*U$,

    3895:   Neighbor-wise Collective

    3897:   Input Parameters:
    3898: + mat - the factored matrix
    3899: - b   - the right-hand-side vector

    3901:   Output Parameter:
    3902: . x - the result vector

    3904:   Level: developer

    3906:   Notes:
    3907:   `MatSolve()` should be used for most applications, as it performs
    3908:   a forward solve followed by a backward solve.

    3910:   The vectors `b` and `x` cannot be the same,  i.e., one cannot
    3911:   call `MatForwardSolve`(A,x,x).

    3913:   For matrix in `MATSEQBAIJ` format with block size larger than 1,
    3914:   the diagonal blocks are not implemented as $D = D^(1/2) * D^(1/2)$ yet.
    3915:   `MatForwardSolve()` solves $U^T*D y = b$, and
    3916:   `MatBackwardSolve()` solves $U x = y$.
    3917:   Thus they do not provide a symmetric preconditioner.

    3919: .seealso: [](ch_matrices), `Mat`, `MatBackwardSolve()`, `MatGetFactor()`, `MatSolve()`
    3920: @*/
    3921: PetscErrorCode MatForwardSolve(Mat mat, Vec b, Vec x)
    3922: {
    3923:   PetscFunctionBegin;
    3928:   PetscCheckSameComm(mat, 1, b, 2);
    3929:   PetscCheckSameComm(mat, 1, x, 3);
    3930:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    3931:   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);
    3932:   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);
    3933:   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);
    3934:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3935:   MatCheckPreallocated(mat, 1);

    3937:   PetscCall(PetscLogEventBegin(MAT_ForwardSolve, mat, b, x, 0));
    3938:   PetscUseTypeMethod(mat, forwardsolve, b, x);
    3939:   PetscCall(PetscLogEventEnd(MAT_ForwardSolve, mat, b, x, 0));
    3940:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    3941:   PetscFunctionReturn(PETSC_SUCCESS);
    3942: }

    3944: /*@
    3945:   MatBackwardSolve - Solves $U x = b$, given a factored matrix, $A = LU$.
    3946:   $D^(1/2) U x = b$, given a factored symmetric matrix, $A = U^T*D*U$,

    3948:   Neighbor-wise Collective

    3950:   Input Parameters:
    3951: + mat - the factored matrix
    3952: - b   - the right-hand-side vector

    3954:   Output Parameter:
    3955: . x - the result vector

    3957:   Level: developer

    3959:   Notes:
    3960:   `MatSolve()` should be used for most applications, as it performs
    3961:   a forward solve followed by a backward solve.

    3963:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    3964:   call `MatBackwardSolve`(A,x,x).

    3966:   For matrix in `MATSEQBAIJ` format with block size larger than 1,
    3967:   the diagonal blocks are not implemented as $D = D^(1/2) * D^(1/2)$ yet.
    3968:   `MatForwardSolve()` solves $U^T*D y = b$, and
    3969:   `MatBackwardSolve()` solves $U x = y$.
    3970:   Thus they do not provide a symmetric preconditioner.

    3972: .seealso: [](ch_matrices), `Mat`, `MatForwardSolve()`, `MatGetFactor()`, `MatSolve()`
    3973: @*/
    3974: PetscErrorCode MatBackwardSolve(Mat mat, Vec b, Vec x)
    3975: {
    3976:   PetscFunctionBegin;
    3981:   PetscCheckSameComm(mat, 1, b, 2);
    3982:   PetscCheckSameComm(mat, 1, x, 3);
    3983:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    3984:   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);
    3985:   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);
    3986:   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);
    3987:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    3988:   MatCheckPreallocated(mat, 1);

    3990:   PetscCall(PetscLogEventBegin(MAT_BackwardSolve, mat, b, x, 0));
    3991:   PetscUseTypeMethod(mat, backwardsolve, b, x);
    3992:   PetscCall(PetscLogEventEnd(MAT_BackwardSolve, mat, b, x, 0));
    3993:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    3994:   PetscFunctionReturn(PETSC_SUCCESS);
    3995: }

    3997: /*@
    3998:   MatSolveAdd - Computes $x = y + A^{-1}*b$, given a factored matrix.

    4000:   Neighbor-wise Collective

    4002:   Input Parameters:
    4003: + mat - the factored matrix
    4004: . b   - the right-hand-side vector
    4005: - y   - the vector to be added to

    4007:   Output Parameter:
    4008: . x - the result vector

    4010:   Level: developer

    4012:   Note:
    4013:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    4014:   call `MatSolveAdd`(A,x,y,x).

    4016: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatSolve()`, `MatGetFactor()`, `MatSolveTranspose()`, `MatSolveTransposeAdd()`
    4017: @*/
    4018: PetscErrorCode MatSolveAdd(Mat mat, Vec b, Vec y, Vec x)
    4019: {
    4020:   PetscScalar one = 1.0;
    4021:   Vec         tmp;

    4023:   PetscFunctionBegin;
    4029:   PetscCheckSameComm(mat, 1, b, 2);
    4030:   PetscCheckSameComm(mat, 1, y, 3);
    4031:   PetscCheckSameComm(mat, 1, x, 4);
    4032:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    4033:   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);
    4034:   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);
    4035:   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);
    4036:   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);
    4037:   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);
    4038:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    4039:   MatCheckPreallocated(mat, 1);

    4041:   PetscCall(PetscLogEventBegin(MAT_SolveAdd, mat, b, x, y));
    4042:   PetscCall(VecFlag(x, mat->factorerrortype));
    4043:   if (mat->factorerrortype) {
    4044:     PetscCall(PetscInfo(mat, "MatFactorError %d\n", mat->factorerrortype));
    4045:   } else if (mat->ops->solveadd) {
    4046:     PetscUseTypeMethod(mat, solveadd, b, y, x);
    4047:   } else {
    4048:     /* do the solve then the add manually */
    4049:     if (x != y) {
    4050:       PetscCall(MatSolve(mat, b, x));
    4051:       PetscCall(VecAXPY(x, one, y));
    4052:     } else {
    4053:       PetscCall(VecDuplicate(x, &tmp));
    4054:       PetscCall(VecCopy(x, tmp));
    4055:       PetscCall(MatSolve(mat, b, x));
    4056:       PetscCall(VecAXPY(x, one, tmp));
    4057:       PetscCall(VecDestroy(&tmp));
    4058:     }
    4059:   }
    4060:   PetscCall(PetscLogEventEnd(MAT_SolveAdd, mat, b, x, y));
    4061:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4062:   PetscFunctionReturn(PETSC_SUCCESS);
    4063: }

    4065: /*@
    4066:   MatSolveTranspose - Solves $A^T x = b$, given a factored matrix.

    4068:   Neighbor-wise Collective

    4070:   Input Parameters:
    4071: + mat - the factored matrix
    4072: - b   - the right-hand-side vector

    4074:   Output Parameter:
    4075: . x - the result vector

    4077:   Level: developer

    4079:   Notes:
    4080:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    4081:   call `MatSolveTranspose`(A,x,x).

    4083:   Most users should employ the `KSP` interface for linear solvers
    4084:   instead of working directly with matrix algebra routines such as this.
    4085:   See, e.g., `KSPCreate()`.

    4087: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `KSP`, `MatSolve()`, `MatSolveAdd()`, `MatSolveTransposeAdd()`
    4088: @*/
    4089: PetscErrorCode MatSolveTranspose(Mat mat, Vec b, Vec x)
    4090: {
    4091:   PetscErrorCode (*f)(Mat, Vec, Vec) = (!mat->ops->solvetranspose && mat->symmetric) ? mat->ops->solve : mat->ops->solvetranspose;

    4093:   PetscFunctionBegin;
    4098:   PetscCheckSameComm(mat, 1, b, 2);
    4099:   PetscCheckSameComm(mat, 1, x, 3);
    4100:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    4101:   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);
    4102:   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);
    4103:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    4104:   MatCheckPreallocated(mat, 1);
    4105:   PetscCall(PetscLogEventBegin(MAT_SolveTranspose, mat, b, x, 0));
    4106:   PetscCall(VecFlag(x, mat->factorerrortype));
    4107:   if (mat->factorerrortype) {
    4108:     PetscCall(PetscInfo(mat, "MatFactorError %d\n", mat->factorerrortype));
    4109:   } else {
    4110:     PetscCheck(f, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Matrix type %s", ((PetscObject)mat)->type_name);
    4111:     PetscCall((*f)(mat, b, x));
    4112:   }
    4113:   PetscCall(PetscLogEventEnd(MAT_SolveTranspose, mat, b, x, 0));
    4114:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4115:   PetscFunctionReturn(PETSC_SUCCESS);
    4116: }

    4118: /*@
    4119:   MatSolveTransposeAdd - Computes $x = y + A^{-T} b$
    4120:   factored matrix.

    4122:   Neighbor-wise Collective

    4124:   Input Parameters:
    4125: + mat - the factored matrix
    4126: . b   - the right-hand-side vector
    4127: - y   - the vector to be added to

    4129:   Output Parameter:
    4130: . x - the result vector

    4132:   Level: developer

    4134:   Note:
    4135:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    4136:   call `MatSolveTransposeAdd`(A,x,y,x).

    4138: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatSolve()`, `MatSolveAdd()`, `MatSolveTranspose()`
    4139: @*/
    4140: PetscErrorCode MatSolveTransposeAdd(Mat mat, Vec b, Vec y, Vec x)
    4141: {
    4142:   PetscScalar one = 1.0;
    4143:   Vec         tmp;
    4144:   PetscErrorCode (*f)(Mat, Vec, Vec, Vec) = (!mat->ops->solvetransposeadd && mat->symmetric) ? mat->ops->solveadd : mat->ops->solvetransposeadd;

    4146:   PetscFunctionBegin;
    4152:   PetscCheckSameComm(mat, 1, b, 2);
    4153:   PetscCheckSameComm(mat, 1, y, 3);
    4154:   PetscCheckSameComm(mat, 1, x, 4);
    4155:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    4156:   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);
    4157:   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);
    4158:   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);
    4159:   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);
    4160:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);
    4161:   MatCheckPreallocated(mat, 1);

    4163:   PetscCall(PetscLogEventBegin(MAT_SolveTransposeAdd, mat, b, x, y));
    4164:   PetscCall(VecFlag(x, mat->factorerrortype));
    4165:   if (mat->factorerrortype) {
    4166:     PetscCall(PetscInfo(mat, "MatFactorError %d\n", mat->factorerrortype));
    4167:   } else if (f) {
    4168:     PetscCall((*f)(mat, b, y, x));
    4169:   } else {
    4170:     /* do the solve then the add manually */
    4171:     if (x != y) {
    4172:       PetscCall(MatSolveTranspose(mat, b, x));
    4173:       PetscCall(VecAXPY(x, one, y));
    4174:     } else {
    4175:       PetscCall(VecDuplicate(x, &tmp));
    4176:       PetscCall(VecCopy(x, tmp));
    4177:       PetscCall(MatSolveTranspose(mat, b, x));
    4178:       PetscCall(VecAXPY(x, one, tmp));
    4179:       PetscCall(VecDestroy(&tmp));
    4180:     }
    4181:   }
    4182:   PetscCall(PetscLogEventEnd(MAT_SolveTransposeAdd, mat, b, x, y));
    4183:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4184:   PetscFunctionReturn(PETSC_SUCCESS);
    4185: }

    4187: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    4188: /*@
    4189:   MatSOR - Computes relaxation (SOR, Gauss-Seidel) sweeps.

    4191:   Neighbor-wise Collective

    4193:   Input Parameters:
    4194: + mat   - the matrix
    4195: . b     - the right-hand side
    4196: . omega - the relaxation factor
    4197: . flag  - flag indicating the type of SOR (see below)
    4198: . shift - diagonal shift
    4199: . its   - the number of iterations
    4200: - lits  - the number of local iterations

    4202:   Output Parameter:
    4203: . x - the solution (can contain an initial guess, use option `SOR_ZERO_INITIAL_GUESS` to indicate no guess)

    4205:   SOR Flags:
    4206: +     `SOR_FORWARD_SWEEP` - forward SOR
    4207: .     `SOR_BACKWARD_SWEEP` - backward SOR
    4208: .     `SOR_SYMMETRIC_SWEEP` - SSOR (symmetric SOR)
    4209: .     `SOR_LOCAL_FORWARD_SWEEP` - local forward SOR
    4210: .     `SOR_LOCAL_BACKWARD_SWEEP` - local forward SOR
    4211: .     `SOR_LOCAL_SYMMETRIC_SWEEP` - local SSOR
    4212: .     `SOR_EISENSTAT` - SOR with Eisenstat trick
    4213: .     `SOR_APPLY_UPPER`, `SOR_APPLY_LOWER` - applies upper/lower triangular part of matrix to vector (with `omega`)
    4214: -     `SOR_ZERO_INITIAL_GUESS` - zero initial guess

    4216:   Level: developer

    4218:   Notes:
    4219:   `SOR_LOCAL_FORWARD_SWEEP`, `SOR_LOCAL_BACKWARD_SWEEP`, and
    4220:   `SOR_LOCAL_SYMMETRIC_SWEEP` perform separate independent smoothings
    4221:   on each processor.

    4223:   Application programmers will not generally use `MatSOR()` directly,
    4224:   but instead will employ `PCSOR` or `PCEISENSTAT`

    4226:   For `MATBAIJ`, `MATSBAIJ`, and `MATAIJ` matrices with inodes, this does a block SOR smoothing, otherwise it does a pointwise smoothing.
    4227:   For `MATAIJ` matrices with inodes, the block sizes are determined by the inode sizes, not the block size set with `MatSetBlockSize()`

    4229:   Vectors `x` and `b` CANNOT be the same

    4231:   The flags are implemented as bitwise inclusive or operations.
    4232:   For example, use (`SOR_ZERO_INITIAL_GUESS` | `SOR_SYMMETRIC_SWEEP`)
    4233:   to specify a zero initial guess for SSOR.

    4235:   Developer Note:
    4236:   We should add block SOR support for `MATAIJ` matrices with block size set to greater than one and no inodes

    4238: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `KSP`, `PC`, `MatGetFactor()`
    4239: @*/
    4240: PetscErrorCode MatSOR(Mat mat, Vec b, PetscReal omega, MatSORType flag, PetscReal shift, PetscInt its, PetscInt lits, Vec x)
    4241: {
    4242:   PetscFunctionBegin;
    4247:   PetscCheckSameComm(mat, 1, b, 2);
    4248:   PetscCheckSameComm(mat, 1, x, 8);
    4249:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    4250:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4251:   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);
    4252:   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);
    4253:   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);
    4254:   PetscCheck(its > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Relaxation requires global its %" PetscInt_FMT " positive", its);
    4255:   PetscCheck(lits > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Relaxation requires local its %" PetscInt_FMT " positive", lits);
    4256:   PetscCheck(b != x, PETSC_COMM_SELF, PETSC_ERR_ARG_IDN, "b and x vector cannot be the same");

    4258:   MatCheckPreallocated(mat, 1);
    4259:   PetscCall(PetscLogEventBegin(MAT_SOR, mat, b, x, 0));
    4260:   PetscUseTypeMethod(mat, sor, b, omega, flag, shift, its, lits, x);
    4261:   PetscCall(PetscLogEventEnd(MAT_SOR, mat, b, x, 0));
    4262:   PetscCall(PetscObjectStateIncrease((PetscObject)x));
    4263:   PetscFunctionReturn(PETSC_SUCCESS);
    4264: }

    4266: /*
    4267:       Default matrix copy routine.
    4268: */
    4269: PetscErrorCode MatCopy_Basic(Mat A, Mat B, MatStructure str)
    4270: {
    4271:   PetscInt           i, rstart = 0, rend = 0, nz;
    4272:   const PetscInt    *cwork;
    4273:   const PetscScalar *vwork;

    4275:   PetscFunctionBegin;
    4276:   if (B->assembled) PetscCall(MatZeroEntries(B));
    4277:   if (str == SAME_NONZERO_PATTERN) {
    4278:     PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
    4279:     for (i = rstart; i < rend; i++) {
    4280:       PetscCall(MatGetRow(A, i, &nz, &cwork, &vwork));
    4281:       PetscCall(MatSetValues(B, 1, &i, nz, cwork, vwork, INSERT_VALUES));
    4282:       PetscCall(MatRestoreRow(A, i, &nz, &cwork, &vwork));
    4283:     }
    4284:   } else {
    4285:     PetscCall(MatAYPX(B, 0.0, A, str));
    4286:   }
    4287:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    4288:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    4289:   PetscFunctionReturn(PETSC_SUCCESS);
    4290: }

    4292: /*@
    4293:   MatCopy - Copies a matrix to another matrix.

    4295:   Collective

    4297:   Input Parameters:
    4298: + A   - the matrix
    4299: - str - `SAME_NONZERO_PATTERN` or `DIFFERENT_NONZERO_PATTERN`

    4301:   Output Parameter:
    4302: . B - where the copy is put

    4304:   Level: intermediate

    4306:   Notes:
    4307:   If you use `SAME_NONZERO_PATTERN`, then the two matrices must have the same nonzero pattern or the routine will crash.

    4309:   `MatCopy()` copies the matrix entries of a matrix to another existing
    4310:   matrix (after first zeroing the second matrix).  A related routine is
    4311:   `MatConvert()`, which first creates a new matrix and then copies the data.

    4313: .seealso: [](ch_matrices), `Mat`, `MatConvert()`, `MatDuplicate()`
    4314: @*/
    4315: PetscErrorCode MatCopy(Mat A, Mat B, MatStructure str)
    4316: {
    4317:   PetscInt i;

    4319:   PetscFunctionBegin;
    4324:   PetscCheckSameComm(A, 1, B, 2);
    4325:   MatCheckPreallocated(B, 2);
    4326:   PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    4327:   PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4328:   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,
    4329:              A->cmap->N, B->cmap->N);
    4330:   MatCheckPreallocated(A, 1);
    4331:   if (A == B) PetscFunctionReturn(PETSC_SUCCESS);

    4333:   PetscCall(PetscLogEventBegin(MAT_Copy, A, B, 0, 0));
    4334:   if (A->ops->copy) PetscUseTypeMethod(A, copy, B, str);
    4335:   else PetscCall(MatCopy_Basic(A, B, str));

    4337:   B->stencil.dim = A->stencil.dim;
    4338:   B->stencil.noc = A->stencil.noc;
    4339:   for (i = 0; i <= A->stencil.dim + (A->stencil.noc ? 0 : -1); i++) {
    4340:     B->stencil.dims[i]   = A->stencil.dims[i];
    4341:     B->stencil.starts[i] = A->stencil.starts[i];
    4342:   }

    4344:   PetscCall(PetscLogEventEnd(MAT_Copy, A, B, 0, 0));
    4345:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    4346:   PetscFunctionReturn(PETSC_SUCCESS);
    4347: }

    4349: /*@
    4350:   MatConvert - Converts a matrix to another matrix, either of the same
    4351:   or different type.

    4353:   Collective

    4355:   Input Parameters:
    4356: + mat     - the matrix
    4357: . newtype - new matrix type.  Use `MATSAME` to create a new matrix of the
    4358:             same type as the original matrix.
    4359: - reuse   - denotes if the destination matrix is to be created or reused.
    4360:             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
    4361:             `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).

    4363:   Output Parameter:
    4364: . M - pointer to place new matrix

    4366:   Level: intermediate

    4368:   Notes:
    4369:   `MatConvert()` first creates a new matrix and then copies the data from
    4370:   the first matrix.  A related routine is `MatCopy()`, which copies the matrix
    4371:   entries of one matrix to another already existing matrix context.

    4373:   Cannot be used to convert a sequential matrix to parallel or parallel to sequential,
    4374:   the MPI communicator of the generated matrix is always the same as the communicator
    4375:   of the input matrix.

    4377: .seealso: [](ch_matrices), `Mat`, `MatCopy()`, `MatDuplicate()`, `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, `MAT_INPLACE_MATRIX`
    4378: @*/
    4379: PetscErrorCode MatConvert(Mat mat, MatType newtype, MatReuse reuse, Mat *M)
    4380: {
    4381:   PetscBool  sametype, issame, flg;
    4382:   PetscBool3 issymmetric, ishermitian, isspd;
    4383:   char       convname[256], mtype[256];
    4384:   Mat        B;

    4386:   PetscFunctionBegin;
    4389:   PetscAssertPointer(M, 4);
    4390:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    4391:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4392:   MatCheckPreallocated(mat, 1);

    4394:   PetscCall(PetscOptionsGetString(((PetscObject)mat)->options, ((PetscObject)mat)->prefix, "-matconvert_type", mtype, sizeof(mtype), &flg));
    4395:   if (flg) newtype = mtype;

    4397:   PetscCall(PetscObjectTypeCompare((PetscObject)mat, newtype, &sametype));
    4398:   PetscCall(PetscStrcmp(newtype, "same", &issame));
    4399:   PetscCheck(!(reuse == MAT_INPLACE_MATRIX) || !(mat != *M), PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "MAT_INPLACE_MATRIX requires same input and output matrix");
    4400:   if (reuse == MAT_REUSE_MATRIX) {
    4402:     PetscCheck(mat != *M, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "MAT_REUSE_MATRIX means reuse matrix in final argument, perhaps you mean MAT_INPLACE_MATRIX");
    4403:   }

    4405:   if ((reuse == MAT_INPLACE_MATRIX) && (issame || sametype)) {
    4406:     PetscCall(PetscInfo(mat, "Early return for inplace %s %d %d\n", ((PetscObject)mat)->type_name, sametype, issame));
    4407:     PetscFunctionReturn(PETSC_SUCCESS);
    4408:   }

    4410:   /* Cache Mat options because some converters use MatHeaderReplace() */
    4411:   issymmetric = mat->symmetric;
    4412:   ishermitian = mat->hermitian;
    4413:   isspd       = mat->spd;

    4415:   if ((sametype || issame) && (reuse == MAT_INITIAL_MATRIX) && mat->ops->duplicate) {
    4416:     PetscCall(PetscInfo(mat, "Calling duplicate for initial matrix %s %d %d\n", ((PetscObject)mat)->type_name, sametype, issame));
    4417:     PetscUseTypeMethod(mat, duplicate, MAT_COPY_VALUES, M);
    4418:   } else {
    4419:     PetscErrorCode (*conv)(Mat, MatType, MatReuse, Mat *) = NULL;
    4420:     const char *prefix[3]                                 = {"seq", "mpi", ""};
    4421:     PetscInt    i;
    4422:     /*
    4423:        Order of precedence:
    4424:        0) See if newtype is a superclass of the current matrix.
    4425:        1) See if a specialized converter is known to the current matrix.
    4426:        2) See if a specialized converter is known to the desired matrix class.
    4427:        3) See if a good general converter is registered for the desired class
    4428:           (as of 6/27/03 only MATMPIADJ falls into this category).
    4429:        4) See if a good general converter is known for the current matrix.
    4430:        5) Use a really basic converter.
    4431:     */

    4433:     /* 0) See if newtype is a superclass of the current matrix.
    4434:           i.e mat is mpiaij and newtype is aij */
    4435:     for (i = 0; i < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(prefix); i++) {
    4436:       PetscCall(PetscStrncpy(convname, prefix[i], sizeof(convname)));
    4437:       PetscCall(PetscStrlcat(convname, newtype, sizeof(convname)));
    4438:       PetscCall(PetscStrcmp(convname, ((PetscObject)mat)->type_name, &flg));
    4439:       PetscCall(PetscInfo(mat, "Check superclass %s %s -> %d\n", convname, ((PetscObject)mat)->type_name, flg));
    4440:       if (flg) {
    4441:         if (reuse == MAT_INPLACE_MATRIX) {
    4442:           PetscCall(PetscInfo(mat, "Early return\n"));
    4443:           PetscFunctionReturn(PETSC_SUCCESS);
    4444:         } else if (reuse == MAT_INITIAL_MATRIX && mat->ops->duplicate) {
    4445:           PetscCall(PetscInfo(mat, "Calling MatDuplicate\n"));
    4446:           PetscUseTypeMethod(mat, duplicate, MAT_COPY_VALUES, M);
    4447:           PetscFunctionReturn(PETSC_SUCCESS);
    4448:         } else if (reuse == MAT_REUSE_MATRIX && mat->ops->copy) {
    4449:           PetscCall(PetscInfo(mat, "Calling MatCopy\n"));
    4450:           PetscCall(MatCopy(mat, *M, SAME_NONZERO_PATTERN));
    4451:           PetscFunctionReturn(PETSC_SUCCESS);
    4452:         }
    4453:       }
    4454:     }
    4455:     /* 1) See if a specialized converter is known to the current matrix and the desired class */
    4456:     for (i = 0; i < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(prefix); i++) {
    4457:       PetscCall(PetscStrncpy(convname, "MatConvert_", sizeof(convname)));
    4458:       PetscCall(PetscStrlcat(convname, ((PetscObject)mat)->type_name, sizeof(convname)));
    4459:       PetscCall(PetscStrlcat(convname, "_", sizeof(convname)));
    4460:       PetscCall(PetscStrlcat(convname, prefix[i], sizeof(convname)));
    4461:       PetscCall(PetscStrlcat(convname, issame ? ((PetscObject)mat)->type_name : newtype, sizeof(convname)));
    4462:       PetscCall(PetscStrlcat(convname, "_C", sizeof(convname)));
    4463:       PetscCall(PetscObjectQueryFunction((PetscObject)mat, convname, &conv));
    4464:       PetscCall(PetscInfo(mat, "Check specialized (1) %s (%s) -> %d\n", convname, ((PetscObject)mat)->type_name, !!conv));
    4465:       if (conv) goto foundconv;
    4466:     }

    4468:     /* 2)  See if a specialized converter is known to the desired matrix class. */
    4469:     PetscCall(MatCreate(PetscObjectComm((PetscObject)mat), &B));
    4470:     PetscCall(MatSetSizes(B, mat->rmap->n, mat->cmap->n, mat->rmap->N, mat->cmap->N));
    4471:     PetscCall(MatSetType(B, newtype));
    4472:     for (i = 0; i < (PetscInt)PETSC_STATIC_ARRAY_LENGTH(prefix); i++) {
    4473:       PetscCall(PetscStrncpy(convname, "MatConvert_", sizeof(convname)));
    4474:       PetscCall(PetscStrlcat(convname, ((PetscObject)mat)->type_name, sizeof(convname)));
    4475:       PetscCall(PetscStrlcat(convname, "_", sizeof(convname)));
    4476:       PetscCall(PetscStrlcat(convname, prefix[i], sizeof(convname)));
    4477:       PetscCall(PetscStrlcat(convname, newtype, sizeof(convname)));
    4478:       PetscCall(PetscStrlcat(convname, "_C", sizeof(convname)));
    4479:       PetscCall(PetscObjectQueryFunction((PetscObject)B, convname, &conv));
    4480:       PetscCall(PetscInfo(mat, "Check specialized (2) %s (%s) -> %d\n", convname, ((PetscObject)B)->type_name, !!conv));
    4481:       if (conv) {
    4482:         PetscCall(MatDestroy(&B));
    4483:         goto foundconv;
    4484:       }
    4485:     }

    4487:     /* 3) See if a good general converter is registered for the desired class */
    4488:     conv = B->ops->convertfrom;
    4489:     PetscCall(PetscInfo(mat, "Check convertfrom (%s) -> %d\n", ((PetscObject)B)->type_name, !!conv));
    4490:     PetscCall(MatDestroy(&B));
    4491:     if (conv) goto foundconv;

    4493:     /* 4) See if a good general converter is known for the current matrix */
    4494:     if (mat->ops->convert) conv = mat->ops->convert;
    4495:     PetscCall(PetscInfo(mat, "Check general convert (%s) -> %d\n", ((PetscObject)mat)->type_name, !!conv));
    4496:     if (conv) goto foundconv;

    4498:     /* 5) Use a really basic converter. */
    4499:     PetscCall(PetscInfo(mat, "Using MatConvert_Basic\n"));
    4500:     conv = MatConvert_Basic;

    4502:   foundconv:
    4503:     PetscCall(PetscLogEventBegin(MAT_Convert, mat, 0, 0, 0));
    4504:     PetscCall((*conv)(mat, newtype, reuse, M));
    4505:     if (mat->rmap->mapping && mat->cmap->mapping && !(*M)->rmap->mapping && !(*M)->cmap->mapping) {
    4506:       /* the block sizes must be same if the mappings are copied over */
    4507:       (*M)->rmap->bs = mat->rmap->bs;
    4508:       (*M)->cmap->bs = mat->cmap->bs;
    4509:       PetscCall(PetscObjectReference((PetscObject)mat->rmap->mapping));
    4510:       PetscCall(PetscObjectReference((PetscObject)mat->cmap->mapping));
    4511:       (*M)->rmap->mapping = mat->rmap->mapping;
    4512:       (*M)->cmap->mapping = mat->cmap->mapping;
    4513:     }
    4514:     (*M)->stencil.dim = mat->stencil.dim;
    4515:     (*M)->stencil.noc = mat->stencil.noc;
    4516:     for (i = 0; i <= mat->stencil.dim + (mat->stencil.noc ? 0 : -1); i++) {
    4517:       (*M)->stencil.dims[i]   = mat->stencil.dims[i];
    4518:       (*M)->stencil.starts[i] = mat->stencil.starts[i];
    4519:     }
    4520:     PetscCall(PetscLogEventEnd(MAT_Convert, mat, 0, 0, 0));
    4521:   }
    4522:   PetscCall(PetscObjectStateIncrease((PetscObject)*M));

    4524:   /* Reset Mat options */
    4525:   if (issymmetric != PETSC_BOOL3_UNKNOWN) PetscCall(MatSetOption(*M, MAT_SYMMETRIC, PetscBool3ToBool(issymmetric)));
    4526:   if (ishermitian != PETSC_BOOL3_UNKNOWN) PetscCall(MatSetOption(*M, MAT_HERMITIAN, PetscBool3ToBool(ishermitian)));
    4527:   if (isspd != PETSC_BOOL3_UNKNOWN) PetscCall(MatSetOption(*M, MAT_SPD, PetscBool3ToBool(isspd)));
    4528:   PetscFunctionReturn(PETSC_SUCCESS);
    4529: }

    4531: /*@
    4532:   MatFactorGetSolverType - Returns name of the package providing the factorization routines

    4534:   Not Collective

    4536:   Input Parameter:
    4537: . mat - the matrix, must be a factored matrix

    4539:   Output Parameter:
    4540: . type - the string name of the package (do not free this string)

    4542:   Level: intermediate

    4544: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatSolverType`, `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`
    4545: @*/
    4546: PetscErrorCode MatFactorGetSolverType(Mat mat, MatSolverType *type)
    4547: {
    4548:   PetscErrorCode (*conv)(Mat, MatSolverType *);

    4550:   PetscFunctionBegin;
    4553:   PetscAssertPointer(type, 2);
    4554:   PetscCheck(mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    4555:   PetscCall(PetscObjectQueryFunction((PetscObject)mat, "MatFactorGetSolverType_C", &conv));
    4556:   if (conv) PetscCall((*conv)(mat, type));
    4557:   else *type = MATSOLVERPETSC;
    4558:   PetscFunctionReturn(PETSC_SUCCESS);
    4559: }

    4561: typedef struct _MatSolverTypeForSpecifcType *MatSolverTypeForSpecifcType;
    4562: struct _MatSolverTypeForSpecifcType {
    4563:   MatType mtype;
    4564:   /* no entry for MAT_FACTOR_NONE */
    4565:   PetscErrorCode (*createfactor[MAT_FACTOR_NUM_TYPES - 1])(Mat, MatFactorType, Mat *);
    4566:   MatSolverTypeForSpecifcType next;
    4567: };

    4569: typedef struct _MatSolverTypeHolder *MatSolverTypeHolder;
    4570: struct _MatSolverTypeHolder {
    4571:   char                       *name;
    4572:   MatSolverTypeForSpecifcType handlers;
    4573:   MatSolverTypeHolder         next;
    4574: };

    4576: static MatSolverTypeHolder MatSolverTypeHolders = NULL;

    4578: /*@C
    4579:   MatSolverTypeRegister - Registers a `MatSolverType` that works for a particular matrix type

    4581:   Logically Collective, No Fortran Support

    4583:   Input Parameters:
    4584: + package      - name of the package, for example `petsc` or `superlu`
    4585: . mtype        - the matrix type that works with this package
    4586: . ftype        - the type of factorization supported by the package
    4587: - createfactor - routine that will create the factored matrix ready to be used

    4589:   Level: developer

    4591: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorGetSolverType()`, `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`,
    4592:   `MatGetFactor()`
    4593: @*/
    4594: PetscErrorCode MatSolverTypeRegister(MatSolverType package, MatType mtype, MatFactorType ftype, PetscErrorCode (*createfactor)(Mat, MatFactorType, Mat *))
    4595: {
    4596:   MatSolverTypeHolder         next = MatSolverTypeHolders, prev = NULL;
    4597:   PetscBool                   flg;
    4598:   MatSolverTypeForSpecifcType inext, iprev = NULL;

    4600:   PetscFunctionBegin;
    4601:   PetscCall(MatInitializePackage());
    4602:   if (!next) {
    4603:     PetscCall(PetscNew(&MatSolverTypeHolders));
    4604:     PetscCall(PetscStrallocpy(package, &MatSolverTypeHolders->name));
    4605:     PetscCall(PetscNew(&MatSolverTypeHolders->handlers));
    4606:     PetscCall(PetscStrallocpy(mtype, (char **)&MatSolverTypeHolders->handlers->mtype));
    4607:     MatSolverTypeHolders->handlers->createfactor[(int)ftype - 1] = createfactor;
    4608:     PetscFunctionReturn(PETSC_SUCCESS);
    4609:   }
    4610:   while (next) {
    4611:     PetscCall(PetscStrcasecmp(package, next->name, &flg));
    4612:     if (flg) {
    4613:       PetscCheck(next->handlers, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MatSolverTypeHolder is missing handlers");
    4614:       inext = next->handlers;
    4615:       while (inext) {
    4616:         PetscCall(PetscStrcasecmp(mtype, inext->mtype, &flg));
    4617:         if (flg) {
    4618:           inext->createfactor[(int)ftype - 1] = createfactor;
    4619:           PetscFunctionReturn(PETSC_SUCCESS);
    4620:         }
    4621:         iprev = inext;
    4622:         inext = inext->next;
    4623:       }
    4624:       PetscCall(PetscNew(&iprev->next));
    4625:       PetscCall(PetscStrallocpy(mtype, (char **)&iprev->next->mtype));
    4626:       iprev->next->createfactor[(int)ftype - 1] = createfactor;
    4627:       PetscFunctionReturn(PETSC_SUCCESS);
    4628:     }
    4629:     prev = next;
    4630:     next = next->next;
    4631:   }
    4632:   PetscCall(PetscNew(&prev->next));
    4633:   PetscCall(PetscStrallocpy(package, &prev->next->name));
    4634:   PetscCall(PetscNew(&prev->next->handlers));
    4635:   PetscCall(PetscStrallocpy(mtype, (char **)&prev->next->handlers->mtype));
    4636:   prev->next->handlers->createfactor[(int)ftype - 1] = createfactor;
    4637:   PetscFunctionReturn(PETSC_SUCCESS);
    4638: }

    4640: /*@C
    4641:   MatSolverTypeGet - Gets the function that creates the factor matrix if it exist

    4643:   Input Parameters:
    4644: + 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
    4645: . ftype - the type of factorization supported by the type
    4646: - mtype - the matrix type that works with this type

    4648:   Output Parameters:
    4649: + foundtype    - `PETSC_TRUE` if the type was registered
    4650: . foundmtype   - `PETSC_TRUE` if the type supports the requested mtype
    4651: - createfactor - routine that will create the factored matrix ready to be used or `NULL` if not found

    4653:   Calling sequence of `createfactor`:
    4654: + A     - the matrix providing the factor matrix
    4655: . ftype - the `MatFactorType` of the factor requested
    4656: - B     - the new factor matrix that responds to MatXXFactorSymbolic,Numeric() functions, such as `MatLUFactorSymbolic()`

    4658:   Level: developer

    4660:   Note:
    4661:   When `type` is `NULL` the available functions are searched for based on the order of the calls to `MatSolverTypeRegister()` in `MatInitializePackage()`.
    4662:   Since different PETSc configurations may have different external solvers, seemingly identical runs with different PETSc configurations may use a different solver.
    4663:   For example if one configuration had `--download-mumps` while a different one had `--download-superlu_dist`.

    4665: .seealso: [](ch_matrices), `Mat`, `MatFactorType`, `MatType`, `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`, `MatSolverTypeRegister()`, `MatGetFactor()`,
    4666:           `MatInitializePackage()`
    4667: @*/
    4668: PetscErrorCode MatSolverTypeGet(MatSolverType type, MatType mtype, MatFactorType ftype, PetscBool *foundtype, PetscBool *foundmtype, PetscErrorCode (**createfactor)(Mat A, MatFactorType ftype, Mat *B))
    4669: {
    4670:   MatSolverTypeHolder         next = MatSolverTypeHolders;
    4671:   PetscBool                   flg;
    4672:   MatSolverTypeForSpecifcType inext;

    4674:   PetscFunctionBegin;
    4675:   if (foundtype) *foundtype = PETSC_FALSE;
    4676:   if (foundmtype) *foundmtype = PETSC_FALSE;
    4677:   if (createfactor) *createfactor = NULL;

    4679:   if (type) {
    4680:     while (next) {
    4681:       PetscCall(PetscStrcasecmp(type, next->name, &flg));
    4682:       if (flg) {
    4683:         if (foundtype) *foundtype = PETSC_TRUE;
    4684:         inext = next->handlers;
    4685:         while (inext) {
    4686:           PetscCall(PetscStrbeginswith(mtype, inext->mtype, &flg));
    4687:           if (flg) {
    4688:             if (foundmtype) *foundmtype = PETSC_TRUE;
    4689:             if (createfactor) *createfactor = inext->createfactor[(int)ftype - 1];
    4690:             PetscFunctionReturn(PETSC_SUCCESS);
    4691:           }
    4692:           inext = inext->next;
    4693:         }
    4694:       }
    4695:       next = next->next;
    4696:     }
    4697:   } else {
    4698:     while (next) {
    4699:       inext = next->handlers;
    4700:       while (inext) {
    4701:         PetscCall(PetscStrcmp(mtype, inext->mtype, &flg));
    4702:         if (flg && inext->createfactor[(int)ftype - 1]) {
    4703:           if (foundtype) *foundtype = PETSC_TRUE;
    4704:           if (foundmtype) *foundmtype = PETSC_TRUE;
    4705:           if (createfactor) *createfactor = inext->createfactor[(int)ftype - 1];
    4706:           PetscFunctionReturn(PETSC_SUCCESS);
    4707:         }
    4708:         inext = inext->next;
    4709:       }
    4710:       next = next->next;
    4711:     }
    4712:     /* try with base classes inext->mtype */
    4713:     next = MatSolverTypeHolders;
    4714:     while (next) {
    4715:       inext = next->handlers;
    4716:       while (inext) {
    4717:         PetscCall(PetscStrbeginswith(mtype, inext->mtype, &flg));
    4718:         if (flg && inext->createfactor[(int)ftype - 1]) {
    4719:           if (foundtype) *foundtype = PETSC_TRUE;
    4720:           if (foundmtype) *foundmtype = PETSC_TRUE;
    4721:           if (createfactor) *createfactor = inext->createfactor[(int)ftype - 1];
    4722:           PetscFunctionReturn(PETSC_SUCCESS);
    4723:         }
    4724:         inext = inext->next;
    4725:       }
    4726:       next = next->next;
    4727:     }
    4728:   }
    4729:   PetscFunctionReturn(PETSC_SUCCESS);
    4730: }

    4732: PetscErrorCode MatSolverTypeDestroy(void)
    4733: {
    4734:   MatSolverTypeHolder         next = MatSolverTypeHolders, prev;
    4735:   MatSolverTypeForSpecifcType inext, iprev;

    4737:   PetscFunctionBegin;
    4738:   while (next) {
    4739:     PetscCall(PetscFree(next->name));
    4740:     inext = next->handlers;
    4741:     while (inext) {
    4742:       PetscCall(PetscFree(inext->mtype));
    4743:       iprev = inext;
    4744:       inext = inext->next;
    4745:       PetscCall(PetscFree(iprev));
    4746:     }
    4747:     prev = next;
    4748:     next = next->next;
    4749:     PetscCall(PetscFree(prev));
    4750:   }
    4751:   MatSolverTypeHolders = NULL;
    4752:   PetscFunctionReturn(PETSC_SUCCESS);
    4753: }

    4755: /*@
    4756:   MatFactorGetCanUseOrdering - Indicates if the factorization can use the ordering provided in `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`

    4758:   Logically Collective

    4760:   Input Parameter:
    4761: . mat - the matrix

    4763:   Output Parameter:
    4764: . flg - `PETSC_TRUE` if uses the ordering

    4766:   Level: developer

    4768:   Note:
    4769:   Most internal PETSc factorizations use the ordering passed to the factorization routine but external
    4770:   packages do not, thus we want to skip generating the ordering when it is not needed or used.

    4772: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`
    4773: @*/
    4774: PetscErrorCode MatFactorGetCanUseOrdering(Mat mat, PetscBool *flg)
    4775: {
    4776:   PetscFunctionBegin;
    4777:   *flg = mat->canuseordering;
    4778:   PetscFunctionReturn(PETSC_SUCCESS);
    4779: }

    4781: /*@
    4782:   MatFactorGetPreferredOrdering - The preferred ordering for a particular matrix factor object

    4784:   Logically Collective

    4786:   Input Parameters:
    4787: + mat   - the matrix obtained with `MatGetFactor()`
    4788: - ftype - the factorization type to be used

    4790:   Output Parameter:
    4791: . otype - the preferred ordering type

    4793:   Level: developer

    4795: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatFactorType`, `MatOrderingType`, `MatCopy()`, `MatDuplicate()`, `MatGetFactorAvailable()`, `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatCholeskyFactorSymbolic()`
    4796: @*/
    4797: PetscErrorCode MatFactorGetPreferredOrdering(Mat mat, MatFactorType ftype, MatOrderingType *otype)
    4798: {
    4799:   PetscFunctionBegin;
    4800:   *otype = mat->preferredordering[ftype];
    4801:   PetscCheck(*otype, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MatFactor did not have a preferred ordering");
    4802:   PetscFunctionReturn(PETSC_SUCCESS);
    4803: }

    4805: /*@
    4806:   MatGetFactor - Returns a matrix suitable to calls to MatXXFactorSymbolic,Numeric()

    4808:   Collective

    4810:   Input Parameters:
    4811: + mat   - the matrix
    4812: . type  - name of solver type, for example, `superlu`, `petsc` (to use PETSc's solver if it is available), if this is 'NULL', then the first result that satisfies
    4813:           the other criteria is returned
    4814: - ftype - factor type, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ICC`, `MAT_FACTOR_ILU`, `MAT_FACTOR_QR`

    4816:   Output Parameter:
    4817: . f - the factor matrix used with MatXXFactorSymbolic,Numeric() calls. Can be `NULL` in some cases, see notes below.

    4819:   Options Database Keys:
    4820: + -pc_factor_mat_solver_type <type>    - choose the type at run time. When using `KSP` solvers
    4821: . -pc_factor_mat_factor_on_host <bool> - do mat factorization on host (with device matrices). Default is doing it on device
    4822: - -pc_factor_mat_solve_on_host <bool>  - do mat solve on host (with device matrices). Default is doing it on device

    4824:   Level: intermediate

    4826:   Notes:
    4827:   The return matrix can be `NULL` if the requested factorization is not available, since some combinations of matrix types and factorization
    4828:   types registered with `MatSolverTypeRegister()` cannot be fully tested if not at runtime.

    4830:   Users usually access the factorization solvers via `KSP`

    4832:   Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
    4833:   such as pastix, superlu, mumps etc. PETSc must have been ./configure to use the external solver, using the option --download-package or --with-package-dir

    4835:   When `type` is `NULL` the available results are searched for based on the order of the calls to `MatSolverTypeRegister()` in `MatInitializePackage()`.
    4836:   Since different PETSc configurations may have different external solvers, seemingly identical runs with different PETSc configurations may use a different solver.
    4837:   For example if one configuration had --download-mumps while a different one had --download-superlu_dist.

    4839:   Some of the packages have options for controlling the factorization, these are in the form -prefix_mat_packagename_packageoption
    4840:   where prefix is normally obtained from the calling `KSP`/`PC`. If `MatGetFactor()` is called directly one can set
    4841:   call `MatSetOptionsPrefixFactor()` on the originating matrix or  `MatSetOptionsPrefix()` on the resulting factor matrix.

    4843:   Developer Note:
    4844:   This should actually be called `MatCreateFactor()` since it creates a new factor object

    4846: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `KSP`, `MatSolverType`, `MatFactorType`, `MatCopy()`, `MatDuplicate()`,
    4847:           `MatGetFactorAvailable()`, `MatFactorGetCanUseOrdering()`, `MatSolverTypeRegister()`, `MatSolverTypeGet()`
    4848:           `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ICC`, `MAT_FACTOR_ILU`, `MAT_FACTOR_QR`, `MatInitializePackage()`
    4849: @*/
    4850: PetscErrorCode MatGetFactor(Mat mat, MatSolverType type, MatFactorType ftype, Mat *f)
    4851: {
    4852:   PetscBool foundtype, foundmtype, shell, hasop = PETSC_FALSE;
    4853:   PetscErrorCode (*conv)(Mat, MatFactorType, Mat *);

    4855:   PetscFunctionBegin;

    4859:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4860:   MatCheckPreallocated(mat, 1);

    4862:   PetscCall(MatIsShell(mat, &shell));
    4863:   if (shell) PetscCall(MatHasOperation(mat, MATOP_GET_FACTOR, &hasop));
    4864:   if (hasop) {
    4865:     PetscUseTypeMethod(mat, getfactor, type, ftype, f);
    4866:     PetscFunctionReturn(PETSC_SUCCESS);
    4867:   }

    4869:   PetscCall(MatSolverTypeGet(type, ((PetscObject)mat)->type_name, ftype, &foundtype, &foundmtype, &conv));
    4870:   if (!foundtype) {
    4871:     if (type) {
    4872:       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],
    4873:               ((PetscObject)mat)->type_name, type);
    4874:     } else {
    4875:       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);
    4876:     }
    4877:   }
    4878:   PetscCheck(foundmtype, PetscObjectComm((PetscObject)mat), PETSC_ERR_MISSING_FACTOR, "MatSolverType %s does not support matrix type %s", type, ((PetscObject)mat)->type_name);
    4879:   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);

    4881:   PetscCall((*conv)(mat, ftype, f));
    4882:   if (mat->factorprefix) PetscCall(MatSetOptionsPrefix(*f, mat->factorprefix));
    4883:   PetscFunctionReturn(PETSC_SUCCESS);
    4884: }

    4886: /*@
    4887:   MatGetFactorAvailable - Returns a flag if matrix supports particular type and factor type

    4889:   Not Collective

    4891:   Input Parameters:
    4892: + mat   - the matrix
    4893: . type  - name of solver type, for example, `superlu`, `petsc` (to use PETSc's default)
    4894: - ftype - factor type, `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ICC`, `MAT_FACTOR_ILU`, `MAT_FACTOR_QR`

    4896:   Output Parameter:
    4897: . flg - PETSC_TRUE if the factorization is available

    4899:   Level: intermediate

    4901:   Notes:
    4902:   Some PETSc matrix formats have alternative solvers available that are contained in alternative packages
    4903:   such as pastix, superlu, mumps etc.

    4905:   PETSc must have been ./configure to use the external solver, using the option --download-package

    4907:   Developer Note:
    4908:   This should actually be called `MatCreateFactorAvailable()` since `MatGetFactor()` creates a new factor object

    4910: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatSolverType`, `MatFactorType`, `MatGetFactor()`, `MatCopy()`, `MatDuplicate()`, `MatSolverTypeRegister()`,
    4911:           `MAT_FACTOR_LU`, `MAT_FACTOR_CHOLESKY`, `MAT_FACTOR_ICC`, `MAT_FACTOR_ILU`, `MAT_FACTOR_QR`, `MatSolverTypeGet()`
    4912: @*/
    4913: PetscErrorCode MatGetFactorAvailable(Mat mat, MatSolverType type, MatFactorType ftype, PetscBool *flg)
    4914: {
    4915:   PetscErrorCode (*gconv)(Mat, MatFactorType, Mat *);

    4917:   PetscFunctionBegin;
    4919:   PetscAssertPointer(flg, 4);

    4921:   *flg = PETSC_FALSE;
    4922:   if (!((PetscObject)mat)->type_name) PetscFunctionReturn(PETSC_SUCCESS);

    4924:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4925:   MatCheckPreallocated(mat, 1);

    4927:   PetscCall(MatSolverTypeGet(type, ((PetscObject)mat)->type_name, ftype, NULL, NULL, &gconv));
    4928:   *flg = gconv ? PETSC_TRUE : PETSC_FALSE;
    4929:   PetscFunctionReturn(PETSC_SUCCESS);
    4930: }

    4932: /*@
    4933:   MatDuplicate - Duplicates a matrix including the non-zero structure.

    4935:   Collective

    4937:   Input Parameters:
    4938: + mat - the matrix
    4939: - op  - One of `MAT_DO_NOT_COPY_VALUES`, `MAT_COPY_VALUES`, or `MAT_SHARE_NONZERO_PATTERN`.
    4940:         See the manual page for `MatDuplicateOption()` for an explanation of these options.

    4942:   Output Parameter:
    4943: . M - pointer to place new matrix

    4945:   Level: intermediate

    4947:   Notes:
    4948:   You cannot change the nonzero pattern for the parent or child matrix later if you use `MAT_SHARE_NONZERO_PATTERN`.

    4950:   If `op` is not `MAT_COPY_VALUES` the numerical values in the new matrix are zeroed.

    4952:   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.

    4954:   When original mat is a product of matrix operation, e.g., an output of `MatMatMult()` or `MatCreateSubMatrix()`, only the matrix data structure of `mat`
    4955:   is duplicated and the internal data structures created for the reuse of previous matrix operations are not duplicated.
    4956:   User should not use `MatDuplicate()` to create new matrix `M` if `M` is intended to be reused as the product of matrix operation.

    4958: .seealso: [](ch_matrices), `Mat`, `MatCopy()`, `MatConvert()`, `MatDuplicateOption`
    4959: @*/
    4960: PetscErrorCode MatDuplicate(Mat mat, MatDuplicateOption op, Mat *M)
    4961: {
    4962:   Mat               B;
    4963:   VecType           vtype;
    4964:   PetscInt          i;
    4965:   PetscObject       dm, container_h, container_d;
    4966:   PetscErrorCodeFn *viewf;

    4968:   PetscFunctionBegin;
    4971:   PetscAssertPointer(M, 3);
    4972:   PetscCheck(op != MAT_COPY_VALUES || mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "MAT_COPY_VALUES not allowed for unassembled matrix");
    4973:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    4974:   MatCheckPreallocated(mat, 1);

    4976:   PetscCall(PetscLogEventBegin(MAT_Convert, mat, 0, 0, 0));
    4977:   PetscUseTypeMethod(mat, duplicate, op, M);
    4978:   PetscCall(PetscLogEventEnd(MAT_Convert, mat, 0, 0, 0));
    4979:   B = *M;

    4981:   PetscCall(MatGetOperation(mat, MATOP_VIEW, &viewf));
    4982:   if (viewf) PetscCall(MatSetOperation(B, MATOP_VIEW, viewf));
    4983:   PetscCall(MatGetVecType(mat, &vtype));
    4984:   PetscCall(MatSetVecType(B, vtype));

    4986:   B->stencil.dim = mat->stencil.dim;
    4987:   B->stencil.noc = mat->stencil.noc;
    4988:   for (i = 0; i <= mat->stencil.dim + (mat->stencil.noc ? 0 : -1); i++) {
    4989:     B->stencil.dims[i]   = mat->stencil.dims[i];
    4990:     B->stencil.starts[i] = mat->stencil.starts[i];
    4991:   }

    4993:   B->nooffproczerorows = mat->nooffproczerorows;
    4994:   B->nooffprocentries  = mat->nooffprocentries;

    4996:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_dm", &dm));
    4997:   if (dm) PetscCall(PetscObjectCompose((PetscObject)B, "__PETSc_dm", dm));
    4998:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", &container_h));
    4999:   if (container_h) PetscCall(PetscObjectCompose((PetscObject)B, "__PETSc_MatCOOStruct_Host", container_h));
    5000:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Device", &container_d));
    5001:   if (container_d) PetscCall(PetscObjectCompose((PetscObject)B, "__PETSc_MatCOOStruct_Device", container_d));
    5002:   if (op == MAT_COPY_VALUES) PetscCall(MatPropagateSymmetryOptions(mat, B));
    5003:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    5004:   PetscFunctionReturn(PETSC_SUCCESS);
    5005: }

    5007: /*@
    5008:   MatGetDiagonal - Gets the diagonal of a matrix as a `Vec`

    5010:   Logically Collective

    5012:   Input Parameter:
    5013: . mat - the matrix

    5015:   Output Parameter:
    5016: . v - the diagonal of the matrix

    5018:   Level: intermediate

    5020:   Note:
    5021:   If `mat` has local sizes `n` x `m`, this routine fills the first `ndiag = min(n, m)` entries
    5022:   of `v` with the diagonal values. Thus `v` must have local size of at least `ndiag`. If `v`
    5023:   is larger than `ndiag`, the values of the remaining entries are unspecified.

    5025:   Currently only correct in parallel for square matrices.

    5027: .seealso: [](ch_matrices), `Mat`, `Vec`, `MatGetRow()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMaxAbs()`
    5028: @*/
    5029: PetscErrorCode MatGetDiagonal(Mat mat, Vec v)
    5030: {
    5031:   PetscFunctionBegin;
    5035:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5036:   MatCheckPreallocated(mat, 1);
    5037:   if (PetscDefined(USE_DEBUG)) {
    5038:     PetscInt nv, row, col, ndiag;

    5040:     PetscCall(VecGetLocalSize(v, &nv));
    5041:     PetscCall(MatGetLocalSize(mat, &row, &col));
    5042:     ndiag = PetscMin(row, col);
    5043:     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);
    5044:   }

    5046:   PetscUseTypeMethod(mat, getdiagonal, v);
    5047:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5048:   PetscFunctionReturn(PETSC_SUCCESS);
    5049: }

    5051: /*@
    5052:   MatGetRowMin - Gets the minimum value (of the real part) of each
    5053:   row of the matrix

    5055:   Logically Collective

    5057:   Input Parameter:
    5058: . mat - the matrix

    5060:   Output Parameters:
    5061: + v   - the vector for storing the maximums
    5062: - idx - the indices of the column found for each row (optional, pass `NULL` if not needed)

    5064:   Level: intermediate

    5066:   Note:
    5067:   The result of this call are the same as if one converted the matrix to dense format
    5068:   and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    5070:   This code is only implemented for a couple of matrix formats.

    5072: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMaxAbs()`, `MatGetRowMinAbs()`,
    5073:           `MatGetRowMax()`
    5074: @*/
    5075: PetscErrorCode MatGetRowMin(Mat mat, Vec v, PetscInt idx[])
    5076: {
    5077:   PetscFunctionBegin;
    5081:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");

    5083:   if (!mat->cmap->N) {
    5084:     PetscCall(VecSet(v, PETSC_MAX_REAL));
    5085:     if (idx) {
    5086:       PetscInt i, m = mat->rmap->n;
    5087:       for (i = 0; i < m; i++) idx[i] = -1;
    5088:     }
    5089:   } else {
    5090:     MatCheckPreallocated(mat, 1);
    5091:   }
    5092:   PetscUseTypeMethod(mat, getrowmin, v, idx);
    5093:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5094:   PetscFunctionReturn(PETSC_SUCCESS);
    5095: }

    5097: /*@
    5098:   MatGetRowMinAbs - Gets the minimum value (in absolute value) of each
    5099:   row of the matrix

    5101:   Logically Collective

    5103:   Input Parameter:
    5104: . mat - the matrix

    5106:   Output Parameters:
    5107: + v   - the vector for storing the minimums
    5108: - idx - the indices of the column found for each row (or `NULL` if not needed)

    5110:   Level: intermediate

    5112:   Notes:
    5113:   if a row is completely empty or has only 0.0 values, then the `idx` value for that
    5114:   row is 0 (the first column).

    5116:   This code is only implemented for a couple of matrix formats.

    5118: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMax()`, `MatGetRowMaxAbs()`, `MatGetRowMin()`
    5119: @*/
    5120: PetscErrorCode MatGetRowMinAbs(Mat mat, Vec v, PetscInt idx[])
    5121: {
    5122:   PetscFunctionBegin;
    5126:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5127:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");

    5129:   if (!mat->cmap->N) {
    5130:     PetscCall(VecSet(v, 0.0));
    5131:     if (idx) {
    5132:       PetscInt i, m = mat->rmap->n;
    5133:       for (i = 0; i < m; i++) idx[i] = -1;
    5134:     }
    5135:   } else {
    5136:     MatCheckPreallocated(mat, 1);
    5137:     if (idx) PetscCall(PetscArrayzero(idx, mat->rmap->n));
    5138:     PetscUseTypeMethod(mat, getrowminabs, v, idx);
    5139:   }
    5140:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5141:   PetscFunctionReturn(PETSC_SUCCESS);
    5142: }

    5144: /*@
    5145:   MatGetRowMax - Gets the maximum value (of the real part) of each
    5146:   row of the matrix

    5148:   Logically Collective

    5150:   Input Parameter:
    5151: . mat - the matrix

    5153:   Output Parameters:
    5154: + v   - the vector for storing the maximums
    5155: - idx - the indices of the column found for each row (optional, otherwise pass `NULL`)

    5157:   Level: intermediate

    5159:   Notes:
    5160:   The result of this call are the same as if one converted the matrix to dense format
    5161:   and found the minimum value in each row (i.e. the implicit zeros are counted as zeros).

    5163:   This code is only implemented for a couple of matrix formats.

    5165: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMaxAbs()`, `MatGetRowMin()`, `MatGetRowMinAbs()`
    5166: @*/
    5167: PetscErrorCode MatGetRowMax(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_MIN_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:     PetscUseTypeMethod(mat, getrowmax, v, idx);
    5184:   }
    5185:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5186:   PetscFunctionReturn(PETSC_SUCCESS);
    5187: }

    5189: /*@
    5190:   MatGetRowMaxAbs - Gets the maximum 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 maximums
    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()`, `MatGetRowSum()`, `MatGetRowMin()`, `MatGetRowMinAbs()`
    5211: @*/
    5212: PetscErrorCode MatGetRowMaxAbs(Mat mat, Vec v, PetscInt idx[])
    5213: {
    5214:   PetscFunctionBegin;
    5218:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");

    5220:   if (!mat->cmap->N) {
    5221:     PetscCall(VecSet(v, 0.0));
    5222:     if (idx) {
    5223:       PetscInt i, m = mat->rmap->n;
    5224:       for (i = 0; i < m; i++) idx[i] = -1;
    5225:     }
    5226:   } else {
    5227:     MatCheckPreallocated(mat, 1);
    5228:     if (idx) PetscCall(PetscArrayzero(idx, mat->rmap->n));
    5229:     PetscUseTypeMethod(mat, getrowmaxabs, v, idx);
    5230:   }
    5231:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5232:   PetscFunctionReturn(PETSC_SUCCESS);
    5233: }

    5235: /*@
    5236:   MatGetRowSumAbs - Gets the sum value (in absolute value) of each row of the matrix

    5238:   Logically Collective

    5240:   Input Parameter:
    5241: . mat - the matrix

    5243:   Output Parameter:
    5244: . v - the vector for storing the sum

    5246:   Level: intermediate

    5248:   This code is only implemented for a couple of matrix formats.

    5250: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMax()`, `MatGetRowMin()`, `MatGetRowMinAbs()`
    5251: @*/
    5252: PetscErrorCode MatGetRowSumAbs(Mat mat, Vec v)
    5253: {
    5254:   PetscFunctionBegin;
    5258:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");

    5260:   if (!mat->cmap->N) {
    5261:     PetscCall(VecSet(v, 0.0));
    5262:   } else {
    5263:     MatCheckPreallocated(mat, 1);
    5264:     PetscUseTypeMethod(mat, getrowsumabs, v);
    5265:   }
    5266:   PetscCall(PetscObjectStateIncrease((PetscObject)v));
    5267:   PetscFunctionReturn(PETSC_SUCCESS);
    5268: }

    5270: /*@
    5271:   MatGetRowSum - Gets the sum of each row of the matrix

    5273:   Logically or Neighborhood Collective

    5275:   Input Parameter:
    5276: . mat - the matrix

    5278:   Output Parameter:
    5279: . v - the vector for storing the sum of rows

    5281:   Level: intermediate

    5283:   Note:
    5284:   This code is slow since it is not currently specialized for different formats

    5286: .seealso: [](ch_matrices), `Mat`, `MatGetDiagonal()`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRowMax()`, `MatGetRowMin()`, `MatGetRowMaxAbs()`, `MatGetRowMinAbs()`, `MatGetRowSumAbs()`
    5287: @*/
    5288: PetscErrorCode MatGetRowSum(Mat mat, Vec v)
    5289: {
    5290:   Vec ones;

    5292:   PetscFunctionBegin;
    5296:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5297:   MatCheckPreallocated(mat, 1);
    5298:   PetscCall(MatCreateVecs(mat, &ones, NULL));
    5299:   PetscCall(VecSet(ones, 1.));
    5300:   PetscCall(MatMult(mat, ones, v));
    5301:   PetscCall(VecDestroy(&ones));
    5302:   PetscFunctionReturn(PETSC_SUCCESS);
    5303: }

    5305: /*@
    5306:   MatTransposeSetPrecursor - Set the matrix from which the second matrix will receive numerical transpose data with a call to `MatTranspose`(A,`MAT_REUSE_MATRIX`,&B)
    5307:   when B was not obtained with `MatTranspose`(A,`MAT_INITIAL_MATRIX`,&B)

    5309:   Collective

    5311:   Input Parameter:
    5312: . mat - the matrix to provide the transpose

    5314:   Output Parameter:
    5315: . 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

    5317:   Level: advanced

    5319:   Note:
    5320:   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
    5321:   routine allows bypassing that call.

    5323: .seealso: [](ch_matrices), `Mat`, `MatTransposeSymbolic()`, `MatTranspose()`, `MatMultTranspose()`, `MatMultTransposeAdd()`, `MatIsTranspose()`, `MatReuse`, `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, `MAT_INPLACE_MATRIX`
    5324: @*/
    5325: PetscErrorCode MatTransposeSetPrecursor(Mat mat, Mat B)
    5326: {
    5327:   MatParentState *rb = NULL;

    5329:   PetscFunctionBegin;
    5330:   PetscCall(PetscNew(&rb));
    5331:   rb->id    = ((PetscObject)mat)->id;
    5332:   rb->state = 0;
    5333:   PetscCall(MatGetNonzeroState(mat, &rb->nonzerostate));
    5334:   PetscCall(PetscObjectContainerCompose((PetscObject)B, "MatTransposeParent", rb, PetscCtxDestroyDefault));
    5335:   PetscFunctionReturn(PETSC_SUCCESS);
    5336: }

    5338: static PetscErrorCode MatTranspose_Private(Mat mat, MatReuse reuse, Mat *B, PetscBool conjugate)
    5339: {
    5340:   PetscContainer  rB                        = NULL;
    5341:   MatParentState *rb                        = NULL;
    5342:   PetscErrorCode (*f)(Mat, MatReuse, Mat *) = NULL;

    5344:   PetscFunctionBegin;
    5347:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5348:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5349:   PetscCheck(reuse != MAT_INPLACE_MATRIX || mat == *B, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "MAT_INPLACE_MATRIX requires last matrix to match first");
    5350:   PetscCheck(reuse != MAT_REUSE_MATRIX || mat != *B, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Perhaps you mean MAT_INPLACE_MATRIX");
    5351:   MatCheckPreallocated(mat, 1);
    5352:   if (reuse == MAT_REUSE_MATRIX) {
    5353:     PetscCall(PetscObjectQuery((PetscObject)*B, "MatTransposeParent", (PetscObject *)&rB));
    5354:     PetscCheck(rB, PetscObjectComm((PetscObject)*B), PETSC_ERR_ARG_WRONG, "Reuse matrix used was not generated from call to MatTranspose(). Suggest MatTransposeSetPrecursor().");
    5355:     PetscCall(PetscContainerGetPointer(rB, (void **)&rb));
    5356:     PetscCheck(rb->id == ((PetscObject)mat)->id, PetscObjectComm((PetscObject)*B), PETSC_ERR_ARG_WRONG, "Reuse matrix used was not generated from input matrix");
    5357:     if (rb->state == ((PetscObject)mat)->state) PetscFunctionReturn(PETSC_SUCCESS);
    5358:   }

    5360:   if (conjugate) {
    5361:     f = mat->ops->hermitiantranspose;
    5362:     if (f) PetscCall((*f)(mat, reuse, B));
    5363:   }
    5364:   if (!f && !(reuse == MAT_INPLACE_MATRIX && mat->hermitian == PETSC_BOOL3_TRUE && conjugate)) {
    5365:     PetscCall(PetscLogEventBegin(MAT_Transpose, mat, 0, 0, 0));
    5366:     if (reuse != MAT_INPLACE_MATRIX || mat->symmetric != PETSC_BOOL3_TRUE) {
    5367:       PetscUseTypeMethod(mat, transpose, reuse, B);
    5368:       PetscCall(PetscObjectStateIncrease((PetscObject)*B));
    5369:     }
    5370:     PetscCall(PetscLogEventEnd(MAT_Transpose, mat, 0, 0, 0));
    5371:     if (conjugate) PetscCall(MatConjugate(*B));
    5372:   }

    5374:   if (reuse == MAT_INITIAL_MATRIX) PetscCall(MatTransposeSetPrecursor(mat, *B));
    5375:   if (reuse != MAT_INPLACE_MATRIX) {
    5376:     PetscCall(PetscObjectQuery((PetscObject)*B, "MatTransposeParent", (PetscObject *)&rB));
    5377:     PetscCall(PetscContainerGetPointer(rB, (void **)&rb));
    5378:     rb->state        = ((PetscObject)mat)->state;
    5379:     rb->nonzerostate = mat->nonzerostate;
    5380:   }
    5381:   PetscFunctionReturn(PETSC_SUCCESS);
    5382: }

    5384: /*@
    5385:   MatTranspose - Computes the transpose of a matrix, either in-place or out-of-place.

    5387:   Collective

    5389:   Input Parameters:
    5390: + mat   - the matrix to transpose
    5391: - reuse - either `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, or `MAT_INPLACE_MATRIX`

    5393:   Output Parameter:
    5394: . B - the transpose of the matrix

    5396:   Level: intermediate

    5398:   Notes:
    5399:   If you use `MAT_INPLACE_MATRIX` then you must pass in `&mat` for `B`

    5401:   `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
    5402:   transpose, call `MatTransposeSetPrecursor(mat, B)` before calling this routine.

    5404:   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.

    5406:   Consider using `MatCreateTranspose()` instead if you only need a matrix that behaves like the transpose but don't need the storage to be changed.
    5407:   For example, the result of `MatCreateTranspose()` will compute the transpose of the given matrix times a vector for matrix-vector products computed with `MatMult()`.

    5409:   If `mat` is unchanged from the last call this function returns immediately without recomputing the result

    5411:   If you only need the symbolic transpose of a matrix, and not the numerical values, use `MatTransposeSymbolic()`

    5413: .seealso: [](ch_matrices), `Mat`, `MatTransposeSetPrecursor()`, `MatMultTranspose()`, `MatMultTransposeAdd()`, `MatIsTranspose()`, `MatReuse`, `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, `MAT_INPLACE_MATRIX`,
    5414:           `MatTransposeSymbolic()`, `MatCreateTranspose()`
    5415: @*/
    5416: PetscErrorCode MatTranspose(Mat mat, MatReuse reuse, Mat *B)
    5417: {
    5418:   PetscFunctionBegin;
    5419:   PetscCall(MatTranspose_Private(mat, reuse, B, PETSC_FALSE));
    5420:   PetscFunctionReturn(PETSC_SUCCESS);
    5421: }

    5423: /*@
    5424:   MatTransposeSymbolic - Computes the symbolic part of the transpose of a matrix.

    5426:   Collective

    5428:   Input Parameter:
    5429: . A - the matrix to transpose

    5431:   Output Parameter:
    5432: . 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
    5433:       numerical portion.

    5435:   Level: intermediate

    5437:   Note:
    5438:   This is not supported for many matrix types, use `MatTranspose()` in those cases

    5440: .seealso: [](ch_matrices), `Mat`, `MatTransposeSetPrecursor()`, `MatTranspose()`, `MatMultTranspose()`, `MatMultTransposeAdd()`, `MatIsTranspose()`, `MatReuse`, `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, `MAT_INPLACE_MATRIX`
    5441: @*/
    5442: PetscErrorCode MatTransposeSymbolic(Mat A, Mat *B)
    5443: {
    5444:   PetscFunctionBegin;
    5447:   PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5448:   PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5449:   PetscCall(PetscLogEventBegin(MAT_Transpose, A, 0, 0, 0));
    5450:   PetscUseTypeMethod(A, transposesymbolic, B);
    5451:   PetscCall(PetscLogEventEnd(MAT_Transpose, A, 0, 0, 0));

    5453:   PetscCall(MatTransposeSetPrecursor(A, *B));
    5454:   PetscFunctionReturn(PETSC_SUCCESS);
    5455: }

    5457: PetscErrorCode MatTransposeCheckNonzeroState_Private(Mat A, Mat B)
    5458: {
    5459:   PetscContainer  rB;
    5460:   MatParentState *rb;

    5462:   PetscFunctionBegin;
    5465:   PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5466:   PetscCheck(!A->factortype, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5467:   PetscCall(PetscObjectQuery((PetscObject)B, "MatTransposeParent", (PetscObject *)&rB));
    5468:   PetscCheck(rB, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONG, "Reuse matrix used was not generated from call to MatTranspose()");
    5469:   PetscCall(PetscContainerGetPointer(rB, (void **)&rb));
    5470:   PetscCheck(rb->id == ((PetscObject)A)->id, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONG, "Reuse matrix used was not generated from input matrix");
    5471:   PetscCheck(rb->nonzerostate == A->nonzerostate, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONGSTATE, "Reuse matrix has changed nonzero structure");
    5472:   PetscFunctionReturn(PETSC_SUCCESS);
    5473: }

    5475: /*@
    5476:   MatIsTranspose - Test whether a matrix is another one's transpose,
    5477:   or its own, in which case it tests symmetry.

    5479:   Collective

    5481:   Input Parameters:
    5482: + A   - the matrix to test
    5483: . B   - the matrix to test against, this can equal the first parameter
    5484: - tol - tolerance, differences between entries smaller than this are counted as zero

    5486:   Output Parameter:
    5487: . flg - the result

    5489:   Level: intermediate

    5491:   Notes:
    5492:   The sequential algorithm has a running time of the order of the number of nonzeros; the parallel
    5493:   test involves parallel copies of the block off-diagonal parts of the matrix.

    5495: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatIsSymmetric()`, `MatIsHermitian()`
    5496: @*/
    5497: PetscErrorCode MatIsTranspose(Mat A, Mat B, PetscReal tol, PetscBool *flg)
    5498: {
    5499:   PetscErrorCode (*f)(Mat, Mat, PetscReal, PetscBool *), (*g)(Mat, Mat, PetscReal, PetscBool *);

    5501:   PetscFunctionBegin;
    5504:   PetscAssertPointer(flg, 4);
    5505:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatIsTranspose_C", &f));
    5506:   PetscCall(PetscObjectQueryFunction((PetscObject)B, "MatIsTranspose_C", &g));
    5507:   *flg = PETSC_FALSE;
    5508:   if (f && g) {
    5509:     PetscCheck(f == g, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_NOTSAMETYPE, "Matrices do not have the same comparator for symmetry test");
    5510:     PetscCall((*f)(A, B, tol, flg));
    5511:   } else {
    5512:     MatType mattype;

    5514:     PetscCall(MatGetType(f ? B : A, &mattype));
    5515:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Matrix of type %s does not support checking for transpose", mattype);
    5516:   }
    5517:   PetscFunctionReturn(PETSC_SUCCESS);
    5518: }

    5520: /*@
    5521:   MatHermitianTranspose - Computes an in-place or out-of-place Hermitian transpose of a matrix in complex conjugate.

    5523:   Collective

    5525:   Input Parameters:
    5526: + mat   - the matrix to transpose and complex conjugate
    5527: - reuse - either `MAT_INITIAL_MATRIX`, `MAT_REUSE_MATRIX`, or `MAT_INPLACE_MATRIX`

    5529:   Output Parameter:
    5530: . B - the Hermitian transpose

    5532:   Level: intermediate

    5534: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatMultTranspose()`, `MatMultTransposeAdd()`, `MatIsTranspose()`, `MatReuse`
    5535: @*/
    5536: PetscErrorCode MatHermitianTranspose(Mat mat, MatReuse reuse, Mat *B)
    5537: {
    5538:   PetscFunctionBegin;
    5539:   PetscCall(MatTranspose_Private(mat, reuse, B, PETSC_TRUE));
    5540:   PetscFunctionReturn(PETSC_SUCCESS);
    5541: }

    5543: /*@
    5544:   MatIsHermitianTranspose - Test whether a matrix is another one's Hermitian transpose,

    5546:   Collective

    5548:   Input Parameters:
    5549: + A   - the matrix to test
    5550: . B   - the matrix to test against, this can equal the first parameter
    5551: - tol - tolerance, differences between entries smaller than this are counted as zero

    5553:   Output Parameter:
    5554: . flg - the result

    5556:   Level: intermediate

    5558:   Notes:
    5559:   Only available for `MATAIJ` matrices.

    5561:   The sequential algorithm
    5562:   has a running time of the order of the number of nonzeros; the parallel
    5563:   test involves parallel copies of the block off-diagonal parts of the matrix.

    5565: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatIsSymmetric()`, `MatIsHermitian()`, `MatIsTranspose()`
    5566: @*/
    5567: PetscErrorCode MatIsHermitianTranspose(Mat A, Mat B, PetscReal tol, PetscBool *flg)
    5568: {
    5569:   PetscErrorCode (*f)(Mat, Mat, PetscReal, PetscBool *), (*g)(Mat, Mat, PetscReal, PetscBool *);

    5571:   PetscFunctionBegin;
    5574:   PetscAssertPointer(flg, 4);
    5575:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatIsHermitianTranspose_C", &f));
    5576:   PetscCall(PetscObjectQueryFunction((PetscObject)B, "MatIsHermitianTranspose_C", &g));
    5577:   if (f && g) {
    5578:     PetscCheck(f == g, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_NOTSAMETYPE, "Matrices do not have the same comparator for Hermitian test");
    5579:     PetscCall((*f)(A, B, tol, flg));
    5580:   } else {
    5581:     MatType mattype;

    5583:     PetscCall(MatGetType(f ? B : A, &mattype));
    5584:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Matrix of type %s does not support checking for Hermitian transpose", mattype);
    5585:   }
    5586:   PetscFunctionReturn(PETSC_SUCCESS);
    5587: }

    5589: /*@
    5590:   MatPermute - Creates a new matrix with rows and columns permuted from the
    5591:   original.

    5593:   Collective

    5595:   Input Parameters:
    5596: + mat - the matrix to permute
    5597: . row - row permutation, each processor supplies only the permutation for its rows
    5598: - col - column permutation, each processor supplies only the permutation for its columns

    5600:   Output Parameter:
    5601: . B - the permuted matrix

    5603:   Level: advanced

    5605:   Note:
    5606:   The index sets map from row/col of permuted matrix to row/col of original matrix.
    5607:   The index sets should be on the same communicator as mat and have the same local sizes.

    5609:   Developer Note:
    5610:   If you want to implement `MatPermute()` for a matrix type, and your approach doesn't
    5611:   exploit the fact that row and col are permutations, consider implementing the
    5612:   more general `MatCreateSubMatrix()` instead.

    5614: .seealso: [](ch_matrices), `Mat`, `MatGetOrdering()`, `ISAllGather()`, `MatCreateSubMatrix()`
    5615: @*/
    5616: PetscErrorCode MatPermute(Mat mat, IS row, IS col, Mat *B)
    5617: {
    5618:   PetscFunctionBegin;
    5623:   PetscAssertPointer(B, 4);
    5624:   PetscCheckSameComm(mat, 1, row, 2);
    5625:   if (row != col) PetscCheckSameComm(row, 2, col, 3);
    5626:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5627:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5628:   PetscCheck(mat->ops->permute || mat->ops->createsubmatrix, PETSC_COMM_SELF, PETSC_ERR_SUP, "MatPermute not available for Mat type %s", ((PetscObject)mat)->type_name);
    5629:   MatCheckPreallocated(mat, 1);

    5631:   if (mat->ops->permute) {
    5632:     PetscUseTypeMethod(mat, permute, row, col, B);
    5633:     PetscCall(PetscObjectStateIncrease((PetscObject)*B));
    5634:   } else {
    5635:     PetscCall(MatCreateSubMatrix(mat, row, col, MAT_INITIAL_MATRIX, B));
    5636:   }
    5637:   PetscFunctionReturn(PETSC_SUCCESS);
    5638: }

    5640: /*@
    5641:   MatEqual - Compares two matrices.

    5643:   Collective

    5645:   Input Parameters:
    5646: + A - the first matrix
    5647: - B - the second matrix

    5649:   Output Parameter:
    5650: . flg - `PETSC_TRUE` if the matrices are equal; `PETSC_FALSE` otherwise.

    5652:   Level: intermediate

    5654:   Note:
    5655:   If either of the matrix is "matrix-free", meaning the matrix entries are not stored explicitly then equality is determined by comparing
    5656:   the results of several matrix-vector product using randomly created vectors, see `MatMultEqual()`.

    5658: .seealso: [](ch_matrices), `Mat`, `MatMultEqual()`
    5659: @*/
    5660: PetscErrorCode MatEqual(Mat A, Mat B, PetscBool *flg)
    5661: {
    5662:   PetscFunctionBegin;
    5667:   PetscAssertPointer(flg, 3);
    5668:   PetscCheckSameComm(A, 1, B, 2);
    5669:   MatCheckPreallocated(A, 1);
    5670:   MatCheckPreallocated(B, 2);
    5671:   PetscCheck(A->assembled, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5672:   PetscCheck(B->assembled, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5673:   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,
    5674:              B->cmap->N);
    5675:   if (A->ops->equal && A->ops->equal == B->ops->equal) {
    5676:     PetscUseTypeMethod(A, equal, B, flg);
    5677:   } else {
    5678:     PetscCall(MatMultEqual(A, B, 10, flg));
    5679:   }
    5680:   PetscFunctionReturn(PETSC_SUCCESS);
    5681: }

    5683: /*@
    5684:   MatDiagonalScale - Scales a matrix on the left and right by diagonal
    5685:   matrices that are stored as vectors.  Either of the two scaling
    5686:   matrices can be `NULL`.

    5688:   Collective

    5690:   Input Parameters:
    5691: + mat - the matrix to be scaled
    5692: . l   - the left scaling vector (or `NULL`)
    5693: - r   - the right scaling vector (or `NULL`)

    5695:   Level: intermediate

    5697:   Note:
    5698:   `MatDiagonalScale()` computes $A = LAR$, where
    5699:   L = a diagonal matrix (stored as a vector), R = a diagonal matrix (stored as a vector)
    5700:   The L scales the rows of the matrix, the R scales the columns of the matrix.

    5702: .seealso: [](ch_matrices), `Mat`, `MatScale()`, `MatShift()`, `MatDiagonalSet()`
    5703: @*/
    5704: PetscErrorCode MatDiagonalScale(Mat mat, Vec l, Vec r)
    5705: {
    5706:   PetscFunctionBegin;
    5709:   if (l) {
    5711:     PetscCheckSameComm(mat, 1, l, 2);
    5712:   }
    5713:   if (r) {
    5715:     PetscCheckSameComm(mat, 1, r, 3);
    5716:   }
    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:   MatCheckPreallocated(mat, 1);
    5720:   if (!l && !r) PetscFunctionReturn(PETSC_SUCCESS);

    5722:   PetscCall(PetscLogEventBegin(MAT_Scale, mat, 0, 0, 0));
    5723:   PetscUseTypeMethod(mat, diagonalscale, l, r);
    5724:   PetscCall(PetscLogEventEnd(MAT_Scale, mat, 0, 0, 0));
    5725:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    5726:   if (l != r) mat->symmetric = PETSC_BOOL3_FALSE;
    5727:   PetscFunctionReturn(PETSC_SUCCESS);
    5728: }

    5730: /*@
    5731:   MatScale - Scales all elements of a matrix by a given number.

    5733:   Logically Collective

    5735:   Input Parameters:
    5736: + mat - the matrix to be scaled
    5737: - a   - the scaling value

    5739:   Level: intermediate

    5741: .seealso: [](ch_matrices), `Mat`, `MatDiagonalScale()`
    5742: @*/
    5743: PetscErrorCode MatScale(Mat mat, PetscScalar a)
    5744: {
    5745:   PetscFunctionBegin;
    5748:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5749:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5751:   MatCheckPreallocated(mat, 1);

    5753:   PetscCall(PetscLogEventBegin(MAT_Scale, mat, 0, 0, 0));
    5754:   if (a != (PetscScalar)1.0) {
    5755:     PetscUseTypeMethod(mat, scale, a);
    5756:     PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    5757:   }
    5758:   PetscCall(PetscLogEventEnd(MAT_Scale, mat, 0, 0, 0));
    5759:   PetscFunctionReturn(PETSC_SUCCESS);
    5760: }

    5762: /*@
    5763:   MatNorm - Calculates various norms of a matrix.

    5765:   Collective

    5767:   Input Parameters:
    5768: + mat  - the matrix
    5769: - type - the type of norm, `NORM_1`, `NORM_FROBENIUS`, `NORM_INFINITY`

    5771:   Output Parameter:
    5772: . nrm - the resulting norm

    5774:   Level: intermediate

    5776: .seealso: [](ch_matrices), `Mat`
    5777: @*/
    5778: PetscErrorCode MatNorm(Mat mat, NormType type, PetscReal *nrm)
    5779: {
    5780:   PetscFunctionBegin;
    5783:   PetscAssertPointer(nrm, 3);

    5785:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    5786:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    5787:   MatCheckPreallocated(mat, 1);

    5789:   PetscUseTypeMethod(mat, norm, type, nrm);
    5790:   PetscFunctionReturn(PETSC_SUCCESS);
    5791: }

    5793: /*
    5794:      This variable is used to prevent counting of MatAssemblyBegin() that
    5795:    are called from within a MatAssemblyEnd().
    5796: */
    5797: static PetscInt MatAssemblyEnd_InUse = 0;
    5798: /*@
    5799:   MatAssemblyBegin - Begins assembling the matrix.  This routine should
    5800:   be called after completing all calls to `MatSetValues()`.

    5802:   Collective

    5804:   Input Parameters:
    5805: + mat  - the matrix
    5806: - type - type of assembly, either `MAT_FLUSH_ASSEMBLY` or `MAT_FINAL_ASSEMBLY`

    5808:   Level: beginner

    5810:   Notes:
    5811:   `MatSetValues()` generally caches the values that belong to other MPI processes.  The matrix is ready to
    5812:   use only after `MatAssemblyBegin()` and `MatAssemblyEnd()` have been called.

    5814:   Use `MAT_FLUSH_ASSEMBLY` when switching between `ADD_VALUES` and `INSERT_VALUES`
    5815:   in `MatSetValues()`; use `MAT_FINAL_ASSEMBLY` for the final assembly before
    5816:   using the matrix.

    5818:   ALL processes that share a matrix MUST call `MatAssemblyBegin()` and `MatAssemblyEnd()` the SAME NUMBER of times, and each time with the
    5819:   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
    5820:   a global collective operation requiring all processes that share the matrix.

    5822:   Space for preallocated nonzeros that is not filled by a call to `MatSetValues()` or a related routine are compressed
    5823:   out by assembly. If you intend to use that extra space on a subsequent assembly, be sure to insert explicit zeros
    5824:   before `MAT_FINAL_ASSEMBLY` so the space is not compressed out.

    5826: .seealso: [](ch_matrices), `Mat`, `MatAssemblyEnd()`, `MatSetValues()`, `MatAssembled()`
    5827: @*/
    5828: PetscErrorCode MatAssemblyBegin(Mat mat, MatAssemblyType type)
    5829: {
    5830:   PetscFunctionBegin;
    5833:   MatCheckPreallocated(mat, 1);
    5834:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix. Did you forget to call MatSetUnfactored()?");
    5835:   if (mat->assembled) {
    5836:     mat->was_assembled = PETSC_TRUE;
    5837:     mat->assembled     = PETSC_FALSE;
    5838:   }

    5840:   if (!MatAssemblyEnd_InUse) {
    5841:     PetscCall(PetscLogEventBegin(MAT_AssemblyBegin, mat, 0, 0, 0));
    5842:     PetscTryTypeMethod(mat, assemblybegin, type);
    5843:     PetscCall(PetscLogEventEnd(MAT_AssemblyBegin, mat, 0, 0, 0));
    5844:   } else PetscTryTypeMethod(mat, assemblybegin, type);
    5845:   PetscFunctionReturn(PETSC_SUCCESS);
    5846: }

    5848: /*@
    5849:   MatAssembled - Indicates if a matrix has been assembled and is ready for
    5850:   use; for example, in matrix-vector product.

    5852:   Not Collective

    5854:   Input Parameter:
    5855: . mat - the matrix

    5857:   Output Parameter:
    5858: . assembled - `PETSC_TRUE` or `PETSC_FALSE`

    5860:   Level: advanced

    5862: .seealso: [](ch_matrices), `Mat`, `MatAssemblyEnd()`, `MatSetValues()`, `MatAssemblyBegin()`
    5863: @*/
    5864: PetscErrorCode MatAssembled(Mat mat, PetscBool *assembled)
    5865: {
    5866:   PetscFunctionBegin;
    5868:   PetscAssertPointer(assembled, 2);
    5869:   *assembled = mat->assembled;
    5870:   PetscFunctionReturn(PETSC_SUCCESS);
    5871: }

    5873: /*@
    5874:   MatAssemblyEnd - Completes assembling the matrix.  This routine should
    5875:   be called after `MatAssemblyBegin()`.

    5877:   Collective

    5879:   Input Parameters:
    5880: + mat  - the matrix
    5881: - type - type of assembly, either `MAT_FLUSH_ASSEMBLY` or `MAT_FINAL_ASSEMBLY`

    5883:   Options Database Keys:
    5884: + -mat_view ::ascii_info             - Prints info on matrix at conclusion of `MatAssemblyEnd()`
    5885: . -mat_view ::ascii_info_detail      - Prints more detailed info
    5886: . -mat_view                          - Prints matrix in ASCII format
    5887: . -mat_view ::ascii_matlab           - Prints matrix in MATLAB format
    5888: . -mat_view draw                     - draws nonzero structure of matrix, using `MatView()` and `PetscDrawOpenX()`.
    5889: . -display <name>                    - Sets display name (default is host)
    5890: . -draw_pause <sec>                  - Sets number of seconds to pause after display
    5891: . -mat_view socket                   - Sends matrix to socket, can be accessed from MATLAB (See [Using MATLAB with PETSc](ch_matlab))
    5892: . -viewer_socket_machine <machine>   - Machine to use for socket
    5893: . -viewer_socket_port <port>         - Port number to use for socket
    5894: - -mat_view binary:filename[:append] - Save matrix to file in binary format

    5896:   Level: beginner

    5898: .seealso: [](ch_matrices), `Mat`, `MatAssemblyBegin()`, `MatSetValues()`, `PetscDrawOpenX()`, `PetscDrawCreate()`, `MatView()`, `MatAssembled()`, `PetscViewerSocketOpen()`
    5899: @*/
    5900: PetscErrorCode MatAssemblyEnd(Mat mat, MatAssemblyType type)
    5901: {
    5902:   static PetscInt inassm = 0;
    5903:   PetscBool       flg    = PETSC_FALSE;

    5905:   PetscFunctionBegin;

    5909:   inassm++;
    5910:   MatAssemblyEnd_InUse++;
    5911:   if (MatAssemblyEnd_InUse == 1) { /* Do the logging only the first time through */
    5912:     PetscCall(PetscLogEventBegin(MAT_AssemblyEnd, mat, 0, 0, 0));
    5913:     PetscTryTypeMethod(mat, assemblyend, type);
    5914:     PetscCall(PetscLogEventEnd(MAT_AssemblyEnd, mat, 0, 0, 0));
    5915:   } else PetscTryTypeMethod(mat, assemblyend, type);

    5917:   /* Flush assembly is not a true assembly */
    5918:   if (type != MAT_FLUSH_ASSEMBLY) {
    5919:     if (mat->num_ass) {
    5920:       if (!mat->symmetry_eternal) {
    5921:         mat->symmetric = PETSC_BOOL3_UNKNOWN;
    5922:         mat->hermitian = PETSC_BOOL3_UNKNOWN;
    5923:       }
    5924:       if (!mat->structural_symmetry_eternal && mat->ass_nonzerostate != mat->nonzerostate) mat->structurally_symmetric = PETSC_BOOL3_UNKNOWN;
    5925:       if (!mat->spd_eternal) mat->spd = PETSC_BOOL3_UNKNOWN;
    5926:     }
    5927:     mat->num_ass++;
    5928:     mat->assembled        = PETSC_TRUE;
    5929:     mat->ass_nonzerostate = mat->nonzerostate;
    5930:   }

    5932:   mat->insertmode = NOT_SET_VALUES;
    5933:   MatAssemblyEnd_InUse--;
    5934:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    5935:   if (inassm == 1 && type != MAT_FLUSH_ASSEMBLY) {
    5936:     PetscCall(MatViewFromOptions(mat, NULL, "-mat_view"));

    5938:     if (mat->checksymmetryonassembly) {
    5939:       PetscCall(MatIsSymmetric(mat, mat->checksymmetrytol, &flg));
    5940:       if (flg) {
    5941:         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "Matrix is symmetric (tolerance %g)\n", (double)mat->checksymmetrytol));
    5942:       } else {
    5943:         PetscCall(PetscPrintf(PetscObjectComm((PetscObject)mat), "Matrix is not symmetric (tolerance %g)\n", (double)mat->checksymmetrytol));
    5944:       }
    5945:     }
    5946:     if (mat->nullsp && mat->checknullspaceonassembly) PetscCall(MatNullSpaceTest(mat->nullsp, mat, NULL));
    5947:   }
    5948:   inassm--;
    5949:   PetscFunctionReturn(PETSC_SUCCESS);
    5950: }

    5952: // PetscClangLinter pragma disable: -fdoc-section-header-unknown
    5953: /*@
    5954:   MatSetOption - Sets a parameter option for a matrix. Some options
    5955:   may be specific to certain storage formats.  Some options
    5956:   determine how values will be inserted (or added). Sorted,
    5957:   row-oriented input will generally assemble the fastest. The default
    5958:   is row-oriented.

    5960:   Logically Collective for certain operations, such as `MAT_SPD`, not collective for `MAT_ROW_ORIENTED`, see `MatOption`

    5962:   Input Parameters:
    5963: + mat - the matrix
    5964: . op  - the option, one of those listed below (and possibly others),
    5965: - flg - turn the option on (`PETSC_TRUE`) or off (`PETSC_FALSE`)

    5967:   Options Describing Matrix Structure:
    5968: + `MAT_SPD`                         - symmetric positive definite
    5969: . `MAT_SYMMETRIC`                   - symmetric in terms of both structure and value
    5970: . `MAT_HERMITIAN`                   - transpose is the complex conjugation
    5971: . `MAT_STRUCTURALLY_SYMMETRIC`      - symmetric nonzero structure
    5972: . `MAT_SYMMETRY_ETERNAL`            - indicates the symmetry (or Hermitian structure) or its absence will persist through any changes to the matrix
    5973: . `MAT_STRUCTURAL_SYMMETRY_ETERNAL` - indicates the structural symmetry or its absence will persist through any changes to the matrix
    5974: . `MAT_SPD_ETERNAL`                 - indicates the value of `MAT_SPD` (true or false) will persist through any changes to the matrix

    5976:    These are not really options of the matrix, they are knowledge about the structure of the matrix that users may provide so that they
    5977:    do not need to be computed (usually at a high cost)

    5979:    Options For Use with `MatSetValues()`:
    5980:    Insert a logically dense subblock, which can be
    5981: . `MAT_ROW_ORIENTED`                - row-oriented (default)

    5983:    These options reflect the data you pass in with `MatSetValues()`; it has
    5984:    nothing to do with how the data is stored internally in the matrix
    5985:    data structure.

    5987:    When (re)assembling a matrix, we can restrict the input for
    5988:    efficiency/debugging purposes.  These options include
    5989: . `MAT_NEW_NONZERO_LOCATIONS`       - additional insertions will be allowed if they generate a new nonzero (slow)
    5990: . `MAT_FORCE_DIAGONAL_ENTRIES`      - forces diagonal entries to be allocated
    5991: . `MAT_IGNORE_OFF_PROC_ENTRIES`     - drops off-processor entries
    5992: . `MAT_NEW_NONZERO_LOCATION_ERR`    - generates an error for new matrix entry
    5993: . `MAT_USE_HASH_TABLE`              - uses a hash table to speed up matrix assembly
    5994: . `MAT_NO_OFF_PROC_ENTRIES`         - you know each process will only set values for its own rows, will generate an error if
    5995:         any process sets values for another process. This avoids all reductions in the MatAssembly routines and thus improves
    5996:         performance for very large process counts.
    5997: - `MAT_SUBSET_OFF_PROC_ENTRIES`     - you know that the first assembly after setting this flag will set a superset
    5998:         of the off-process entries required for all subsequent assemblies. This avoids a rendezvous step in the MatAssembly
    5999:         functions, instead sending only neighbor messages.

    6001:   Level: intermediate

    6003:   Notes:
    6004:   Except for `MAT_UNUSED_NONZERO_LOCATION_ERR` and  `MAT_ROW_ORIENTED` all processes that share the matrix must pass the same value in flg!

    6006:   Some options are relevant only for particular matrix types and
    6007:   are thus ignored by others.  Other options are not supported by
    6008:   certain matrix types and will generate an error message if set.

    6010:   If using Fortran to compute a matrix, one may need to
    6011:   use the column-oriented option (or convert to the row-oriented
    6012:   format).

    6014:   `MAT_NEW_NONZERO_LOCATIONS` set to `PETSC_FALSE` indicates that any add or insertion
    6015:   that would generate a new entry in the nonzero structure is instead
    6016:   ignored.  Thus, if memory has not already been allocated for this particular
    6017:   data, then the insertion is ignored. For dense matrices, in which
    6018:   the entire array is allocated, no entries are ever ignored.
    6019:   Set after the first `MatAssemblyEnd()`. If this option is set, then the `MatAssemblyBegin()`/`MatAssemblyEnd()` processes has one less global reduction

    6021:   `MAT_NEW_NONZERO_LOCATION_ERR` set to PETSC_TRUE indicates that any add or insertion
    6022:   that would generate a new entry in the nonzero structure instead produces
    6023:   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

    6025:   `MAT_NEW_NONZERO_ALLOCATION_ERR` set to `PETSC_TRUE` indicates that any add or insertion
    6026:   that would generate a new entry that has not been preallocated will
    6027:   instead produce an error. (Currently supported for `MATAIJ` and `MATBAIJ` formats
    6028:   only.) This is a useful flag when debugging matrix memory preallocation.
    6029:   If this option is set, then the `MatAssemblyBegin()`/`MatAssemblyEnd()` processes has one less global reduction

    6031:   `MAT_IGNORE_OFF_PROC_ENTRIES` set to `PETSC_TRUE` indicates entries destined for
    6032:   other processors should be dropped, rather than stashed.
    6033:   This is useful if you know that the "owning" processor is also
    6034:   always generating the correct matrix entries, so that PETSc need
    6035:   not transfer duplicate entries generated on another processor.

    6037:   `MAT_USE_HASH_TABLE` indicates that a hash table be used to improve the
    6038:   searches during matrix assembly. When this flag is set, the hash table
    6039:   is created during the first matrix assembly. This hash table is
    6040:   used the next time through, during `MatSetValues()`/`MatSetValuesBlocked()`
    6041:   to improve the searching of indices. `MAT_NEW_NONZERO_LOCATIONS` flag
    6042:   should be used with `MAT_USE_HASH_TABLE` flag. This option is currently
    6043:   supported by `MATMPIBAIJ` format only.

    6045:   `MAT_KEEP_NONZERO_PATTERN` indicates when `MatZeroRows()` is called the zeroed entries
    6046:   are kept in the nonzero structure. This flag is not used for `MatZeroRowsColumns()`

    6048:   `MAT_IGNORE_ZERO_ENTRIES` - for `MATAIJ` and `MATIS` matrices this will stop zero values from creating
    6049:   a zero location in the matrix

    6051:   `MAT_USE_INODES` - indicates using inode version of the code - works with `MATAIJ` matrix types

    6053:   `MAT_NO_OFF_PROC_ZERO_ROWS` - you know each process will only zero its own rows. This avoids all reductions in the
    6054:   zero row routines and thus improves performance for very large process counts.

    6056:   `MAT_IGNORE_LOWER_TRIANGULAR` - For `MATSBAIJ` matrices will ignore any insertions you make in the lower triangular
    6057:   part of the matrix (since they should match the upper triangular part).

    6059:   `MAT_SORTED_FULL` - each process provides exactly its local rows; all column indices for a given row are passed in a
    6060:   single call to `MatSetValues()`, preallocation is perfect, row-oriented, `INSERT_VALUES` is used. Common
    6061:   with finite difference schemes with non-periodic boundary conditions.

    6063:   Developer Note:
    6064:   `MAT_SYMMETRY_ETERNAL`, `MAT_STRUCTURAL_SYMMETRY_ETERNAL`, and `MAT_SPD_ETERNAL` are used by `MatAssemblyEnd()` and in other
    6065:   places where otherwise the value of `MAT_SYMMETRIC`, `MAT_STRUCTURALLY_SYMMETRIC` or `MAT_SPD` would need to be changed back
    6066:   to `PETSC_BOOL3_UNKNOWN` because the matrix values had changed so the code cannot be certain that the related property had
    6067:   not changed.

    6069: .seealso: [](ch_matrices), `MatOption`, `Mat`, `MatGetOption()`
    6070: @*/
    6071: PetscErrorCode MatSetOption(Mat mat, MatOption op, PetscBool flg)
    6072: {
    6073:   PetscFunctionBegin;
    6075:   if (op > 0) {
    6078:   }

    6080:   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);

    6082:   switch (op) {
    6083:   case MAT_FORCE_DIAGONAL_ENTRIES:
    6084:     mat->force_diagonals = flg;
    6085:     PetscFunctionReturn(PETSC_SUCCESS);
    6086:   case MAT_NO_OFF_PROC_ENTRIES:
    6087:     mat->nooffprocentries = flg;
    6088:     PetscFunctionReturn(PETSC_SUCCESS);
    6089:   case MAT_SUBSET_OFF_PROC_ENTRIES:
    6090:     mat->assembly_subset = flg;
    6091:     if (!mat->assembly_subset) { /* See the same logic in VecAssembly wrt VEC_SUBSET_OFF_PROC_ENTRIES */
    6092: #if !defined(PETSC_HAVE_MPIUNI)
    6093:       PetscCall(MatStashScatterDestroy_BTS(&mat->stash));
    6094: #endif
    6095:       mat->stash.first_assembly_done = PETSC_FALSE;
    6096:     }
    6097:     PetscFunctionReturn(PETSC_SUCCESS);
    6098:   case MAT_NO_OFF_PROC_ZERO_ROWS:
    6099:     mat->nooffproczerorows = flg;
    6100:     PetscFunctionReturn(PETSC_SUCCESS);
    6101:   case MAT_SPD:
    6102:     if (flg) {
    6103:       mat->spd                    = PETSC_BOOL3_TRUE;
    6104:       mat->symmetric              = PETSC_BOOL3_TRUE;
    6105:       mat->structurally_symmetric = PETSC_BOOL3_TRUE;
    6106:     } else {
    6107:       mat->spd = PETSC_BOOL3_FALSE;
    6108:     }
    6109:     break;
    6110:   case MAT_SYMMETRIC:
    6111:     mat->symmetric = PetscBoolToBool3(flg);
    6112:     if (flg) mat->structurally_symmetric = PETSC_BOOL3_TRUE;
    6113: #if !defined(PETSC_USE_COMPLEX)
    6114:     mat->hermitian = PetscBoolToBool3(flg);
    6115: #endif
    6116:     break;
    6117:   case MAT_HERMITIAN:
    6118:     mat->hermitian = PetscBoolToBool3(flg);
    6119:     if (flg) mat->structurally_symmetric = PETSC_BOOL3_TRUE;
    6120: #if !defined(PETSC_USE_COMPLEX)
    6121:     mat->symmetric = PetscBoolToBool3(flg);
    6122: #endif
    6123:     break;
    6124:   case MAT_STRUCTURALLY_SYMMETRIC:
    6125:     mat->structurally_symmetric = PetscBoolToBool3(flg);
    6126:     break;
    6127:   case MAT_SYMMETRY_ETERNAL:
    6128:     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");
    6129:     mat->symmetry_eternal = flg;
    6130:     if (flg) mat->structural_symmetry_eternal = PETSC_TRUE;
    6131:     break;
    6132:   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
    6133:     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");
    6134:     mat->structural_symmetry_eternal = flg;
    6135:     break;
    6136:   case MAT_SPD_ETERNAL:
    6137:     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");
    6138:     mat->spd_eternal = flg;
    6139:     if (flg) {
    6140:       mat->structural_symmetry_eternal = PETSC_TRUE;
    6141:       mat->symmetry_eternal            = PETSC_TRUE;
    6142:     }
    6143:     break;
    6144:   case MAT_STRUCTURE_ONLY:
    6145:     mat->structure_only = flg;
    6146:     break;
    6147:   case MAT_SORTED_FULL:
    6148:     mat->sortedfull = flg;
    6149:     break;
    6150:   default:
    6151:     break;
    6152:   }
    6153:   PetscTryTypeMethod(mat, setoption, op, flg);
    6154:   PetscFunctionReturn(PETSC_SUCCESS);
    6155: }

    6157: /*@
    6158:   MatGetOption - Gets a parameter option that has been set for a matrix.

    6160:   Logically Collective

    6162:   Input Parameters:
    6163: + mat - the matrix
    6164: - op  - the option, this only responds to certain options, check the code for which ones

    6166:   Output Parameter:
    6167: . flg - turn the option on (`PETSC_TRUE`) or off (`PETSC_FALSE`)

    6169:   Level: intermediate

    6171:   Notes:
    6172:   Can only be called after `MatSetSizes()` and `MatSetType()` have been set.

    6174:   Certain option values may be unknown, for those use the routines `MatIsSymmetric()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, or
    6175:   `MatIsSymmetricKnown()`, `MatIsHermitianKnown()`, `MatIsStructurallySymmetricKnown()`

    6177: .seealso: [](ch_matrices), `Mat`, `MatOption`, `MatSetOption()`, `MatIsSymmetric()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`,
    6178:     `MatIsSymmetricKnown()`, `MatIsHermitianKnown()`, `MatIsStructurallySymmetricKnown()`
    6179: @*/
    6180: PetscErrorCode MatGetOption(Mat mat, MatOption op, PetscBool *flg)
    6181: {
    6182:   PetscFunctionBegin;

    6186:   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);
    6187:   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()");

    6189:   switch (op) {
    6190:   case MAT_NO_OFF_PROC_ENTRIES:
    6191:     *flg = mat->nooffprocentries;
    6192:     break;
    6193:   case MAT_NO_OFF_PROC_ZERO_ROWS:
    6194:     *flg = mat->nooffproczerorows;
    6195:     break;
    6196:   case MAT_SYMMETRIC:
    6197:     SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Use MatIsSymmetric() or MatIsSymmetricKnown()");
    6198:     break;
    6199:   case MAT_HERMITIAN:
    6200:     SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Use MatIsHermitian() or MatIsHermitianKnown()");
    6201:     break;
    6202:   case MAT_STRUCTURALLY_SYMMETRIC:
    6203:     SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Use MatIsStructurallySymmetric() or MatIsStructurallySymmetricKnown()");
    6204:     break;
    6205:   case MAT_SPD:
    6206:     SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "Use MatIsSPDKnown()");
    6207:     break;
    6208:   case MAT_SYMMETRY_ETERNAL:
    6209:     *flg = mat->symmetry_eternal;
    6210:     break;
    6211:   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
    6212:     *flg = mat->symmetry_eternal;
    6213:     break;
    6214:   default:
    6215:     break;
    6216:   }
    6217:   PetscFunctionReturn(PETSC_SUCCESS);
    6218: }

    6220: /*@
    6221:   MatZeroEntries - Zeros all entries of a matrix.  For sparse matrices
    6222:   this routine retains the old nonzero structure.

    6224:   Logically Collective

    6226:   Input Parameter:
    6227: . mat - the matrix

    6229:   Level: intermediate

    6231:   Note:
    6232:   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.
    6233:   See the Performance chapter of the users manual for information on preallocating matrices.

    6235: .seealso: [](ch_matrices), `Mat`, `MatZeroRows()`, `MatZeroRowsColumns()`
    6236: @*/
    6237: PetscErrorCode MatZeroEntries(Mat mat)
    6238: {
    6239:   PetscFunctionBegin;
    6242:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6243:   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");
    6244:   MatCheckPreallocated(mat, 1);

    6246:   PetscCall(PetscLogEventBegin(MAT_ZeroEntries, mat, 0, 0, 0));
    6247:   PetscUseTypeMethod(mat, zeroentries);
    6248:   PetscCall(PetscLogEventEnd(MAT_ZeroEntries, mat, 0, 0, 0));
    6249:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6250:   PetscFunctionReturn(PETSC_SUCCESS);
    6251: }

    6253: /*@
    6254:   MatZeroRowsColumns - Zeros all entries (except possibly the main diagonal)
    6255:   of a set of rows and columns of a matrix.

    6257:   Collective

    6259:   Input Parameters:
    6260: + mat     - the matrix
    6261: . numRows - the number of rows/columns to zero
    6262: . rows    - the global row indices
    6263: . diag    - value put in the diagonal of the eliminated rows
    6264: . x       - optional vector of the solution for zeroed rows (other entries in vector are not used), these must be set before this call
    6265: - b       - optional vector of the right-hand side, that will be adjusted by provided solution entries

    6267:   Level: intermediate

    6269:   Notes:
    6270:   This routine, along with `MatZeroRows()`, is typically used to eliminate known Dirichlet boundary conditions from a linear system.

    6272:   For each zeroed row, the value of the corresponding `b` is set to diag times the value of the corresponding `x`.
    6273:   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

    6275:   If the resulting linear system is to be solved with `KSP` then one can (but does not have to) call `KSPSetInitialGuessNonzero()` to allow the
    6276:   Krylov method to take advantage of the known solution on the zeroed rows.

    6278:   For the parallel case, all processes that share the matrix (i.e.,
    6279:   those in the communicator used for matrix creation) MUST call this
    6280:   routine, regardless of whether any rows being zeroed are owned by
    6281:   them.

    6283:   Unlike `MatZeroRows()`, this ignores the `MAT_KEEP_NONZERO_PATTERN` option value set with `MatSetOption()`, it merely zeros those entries in the matrix, but never
    6284:   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
    6285:   missing.

    6287:   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6288:   list only rows local to itself).

    6290:   The option `MAT_NO_OFF_PROC_ZERO_ROWS` does not apply to this routine.

    6292: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRows()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6293:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6294: @*/
    6295: PetscErrorCode MatZeroRowsColumns(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    6296: {
    6297:   PetscFunctionBegin;
    6300:   if (numRows) PetscAssertPointer(rows, 3);
    6301:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6302:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6303:   MatCheckPreallocated(mat, 1);

    6305:   PetscUseTypeMethod(mat, zerorowscolumns, numRows, rows, diag, x, b);
    6306:   PetscCall(MatViewFromOptions(mat, NULL, "-mat_view"));
    6307:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6308:   PetscFunctionReturn(PETSC_SUCCESS);
    6309: }

    6311: /*@
    6312:   MatZeroRowsColumnsIS - Zeros all entries (except possibly the main diagonal)
    6313:   of a set of rows and columns of a matrix.

    6315:   Collective

    6317:   Input Parameters:
    6318: + mat  - the matrix
    6319: . is   - the rows to zero
    6320: . diag - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6321: . x    - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6322: - b    - optional vector of right-hand side, that will be adjusted by provided solution

    6324:   Level: intermediate

    6326:   Note:
    6327:   See `MatZeroRowsColumns()` for details on how this routine operates.

    6329: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6330:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRows()`, `MatZeroRowsColumnsStencil()`
    6331: @*/
    6332: PetscErrorCode MatZeroRowsColumnsIS(Mat mat, IS is, PetscScalar diag, Vec x, Vec b)
    6333: {
    6334:   PetscInt        numRows;
    6335:   const PetscInt *rows;

    6337:   PetscFunctionBegin;
    6342:   PetscCall(ISGetLocalSize(is, &numRows));
    6343:   PetscCall(ISGetIndices(is, &rows));
    6344:   PetscCall(MatZeroRowsColumns(mat, numRows, rows, diag, x, b));
    6345:   PetscCall(ISRestoreIndices(is, &rows));
    6346:   PetscFunctionReturn(PETSC_SUCCESS);
    6347: }

    6349: /*@
    6350:   MatZeroRows - Zeros all entries (except possibly the main diagonal)
    6351:   of a set of rows of a matrix.

    6353:   Collective

    6355:   Input Parameters:
    6356: + mat     - the matrix
    6357: . numRows - the number of rows to zero
    6358: . rows    - the global row indices
    6359: . diag    - value put in the diagonal of the zeroed rows
    6360: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used), these must be set before this call
    6361: - b       - optional vector of right-hand side, that will be adjusted by provided solution entries

    6363:   Level: intermediate

    6365:   Notes:
    6366:   This routine, along with `MatZeroRowsColumns()`, is typically used to eliminate known Dirichlet boundary conditions from a linear system.

    6368:   For each zeroed row, the value of the corresponding `b` is set to `diag` times the value of the corresponding `x`.

    6370:   If the resulting linear system is to be solved with `KSP` then one can (but does not have to) call `KSPSetInitialGuessNonzero()` to allow the
    6371:   Krylov method to take advantage of the known solution on the zeroed rows.

    6373:   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)
    6374:   from the matrix.

    6376:   Unlike `MatZeroRowsColumns()` for the `MATAIJ` and `MATBAIJ` matrix formats this removes the old nonzero structure, from the eliminated rows of the matrix
    6377:   but does not release memory.  Because of this removal matrix-vector products with the adjusted matrix will be a bit faster. For the dense
    6378:   formats this does not alter the nonzero structure.

    6380:   If the option `MatSetOption`(mat,`MAT_KEEP_NONZERO_PATTERN`,`PETSC_TRUE`) the nonzero structure
    6381:   of the matrix is not changed the values are
    6382:   merely zeroed.

    6384:   The user can set a value in the diagonal entry (or for the `MATAIJ` format
    6385:   formats can optionally remove the main diagonal entry from the
    6386:   nonzero structure as well, by passing 0.0 as the final argument).

    6388:   For the parallel case, all processes that share the matrix (i.e.,
    6389:   those in the communicator used for matrix creation) MUST call this
    6390:   routine, regardless of whether any rows being zeroed are owned by
    6391:   them.

    6393:   Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
    6394:   list only rows local to itself).

    6396:   You can call `MatSetOption`(mat,`MAT_NO_OFF_PROC_ZERO_ROWS`,`PETSC_TRUE`) if each process indicates only rows it
    6397:   owns that are to be zeroed. This saves a global synchronization in the implementation.

    6399: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6400:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`, `PCREDISTRIBUTE`, `MAT_KEEP_NONZERO_PATTERN`
    6401: @*/
    6402: PetscErrorCode MatZeroRows(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    6403: {
    6404:   PetscFunctionBegin;
    6407:   if (numRows) PetscAssertPointer(rows, 3);
    6408:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6409:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6410:   MatCheckPreallocated(mat, 1);

    6412:   PetscUseTypeMethod(mat, zerorows, numRows, rows, diag, x, b);
    6413:   PetscCall(MatViewFromOptions(mat, NULL, "-mat_view"));
    6414:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6415:   PetscFunctionReturn(PETSC_SUCCESS);
    6416: }

    6418: /*@
    6419:   MatZeroRowsIS - Zeros all entries (except possibly the main diagonal)
    6420:   of a set of rows of a matrix indicated by an `IS`

    6422:   Collective

    6424:   Input Parameters:
    6425: + mat  - the matrix
    6426: . is   - index set, `IS`, of rows to remove (if `NULL` then no row is removed)
    6427: . diag - value put in all diagonals of eliminated rows
    6428: . x    - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6429: - b    - optional vector of right-hand side, that will be adjusted by provided solution

    6431:   Level: intermediate

    6433:   Note:
    6434:   See `MatZeroRows()` for details on how this routine operates.

    6436: .seealso: [](ch_matrices), `Mat`, `MatZeroRows()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6437:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`, `IS`
    6438: @*/
    6439: PetscErrorCode MatZeroRowsIS(Mat mat, IS is, PetscScalar diag, Vec x, Vec b)
    6440: {
    6441:   PetscInt        numRows = 0;
    6442:   const PetscInt *rows    = NULL;

    6444:   PetscFunctionBegin;
    6447:   if (is) {
    6449:     PetscCall(ISGetLocalSize(is, &numRows));
    6450:     PetscCall(ISGetIndices(is, &rows));
    6451:   }
    6452:   PetscCall(MatZeroRows(mat, numRows, rows, diag, x, b));
    6453:   if (is) PetscCall(ISRestoreIndices(is, &rows));
    6454:   PetscFunctionReturn(PETSC_SUCCESS);
    6455: }

    6457: /*@
    6458:   MatZeroRowsStencil - Zeros all entries (except possibly the main diagonal)
    6459:   of a set of rows of a matrix indicated by a `MatStencil`. These rows must be local to the process.

    6461:   Collective

    6463:   Input Parameters:
    6464: + mat     - the matrix
    6465: . numRows - the number of rows to remove
    6466: . rows    - the grid coordinates (and component number when dof > 1) for matrix rows indicated by an array of `MatStencil`
    6467: . diag    - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6468: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6469: - b       - optional vector of right-hand side, that will be adjusted by provided solution

    6471:   Level: intermediate

    6473:   Notes:
    6474:   See `MatZeroRows()` for details on how this routine operates.

    6476:   The grid coordinates are across the entire grid, not just the local portion

    6478:   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    6479:   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    6480:   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    6481:   `DM_BOUNDARY_PERIODIC` boundary type.

    6483:   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
    6484:   a single value per point) you can skip filling those indices.

    6486:   Fortran Note:
    6487:   `idxm` and `idxn` should be declared as
    6488: .vb
    6489:     MatStencil idxm(4, m)
    6490: .ve
    6491:   and the values inserted using
    6492: .vb
    6493:     idxm(MatStencil_i, 1) = i
    6494:     idxm(MatStencil_j, 1) = j
    6495:     idxm(MatStencil_k, 1) = k
    6496:     idxm(MatStencil_c, 1) = c
    6497:    etc
    6498: .ve

    6500: .seealso: [](ch_matrices), `Mat`, `MatStencil`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRows()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6501:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6502: @*/
    6503: PetscErrorCode MatZeroRowsStencil(Mat mat, PetscInt numRows, const MatStencil rows[], PetscScalar diag, Vec x, Vec b)
    6504: {
    6505:   PetscInt  dim    = mat->stencil.dim;
    6506:   PetscInt  sdim   = dim - (1 - (PetscInt)mat->stencil.noc);
    6507:   PetscInt *dims   = mat->stencil.dims + 1;
    6508:   PetscInt *starts = mat->stencil.starts;
    6509:   PetscInt *dxm    = (PetscInt *)rows;
    6510:   PetscInt *jdxm, i, j, tmp, numNewRows = 0;

    6512:   PetscFunctionBegin;
    6515:   if (numRows) PetscAssertPointer(rows, 3);

    6517:   PetscCall(PetscMalloc1(numRows, &jdxm));
    6518:   for (i = 0; i < numRows; ++i) {
    6519:     /* Skip unused dimensions (they are ordered k, j, i, c) */
    6520:     for (j = 0; j < 3 - sdim; ++j) dxm++;
    6521:     /* Local index in X dir */
    6522:     tmp = *dxm++ - starts[0];
    6523:     /* Loop over remaining dimensions */
    6524:     for (j = 0; j < dim - 1; ++j) {
    6525:       /* If nonlocal, set index to be negative */
    6526:       if ((*dxm++ - starts[j + 1]) < 0 || tmp < 0) tmp = PETSC_INT_MIN;
    6527:       /* Update local index */
    6528:       else tmp = tmp * dims[j] + *(dxm - 1) - starts[j + 1];
    6529:     }
    6530:     /* Skip component slot if necessary */
    6531:     if (mat->stencil.noc) dxm++;
    6532:     /* Local row number */
    6533:     if (tmp >= 0) jdxm[numNewRows++] = tmp;
    6534:   }
    6535:   PetscCall(MatZeroRowsLocal(mat, numNewRows, jdxm, diag, x, b));
    6536:   PetscCall(PetscFree(jdxm));
    6537:   PetscFunctionReturn(PETSC_SUCCESS);
    6538: }

    6540: /*@
    6541:   MatZeroRowsColumnsStencil - Zeros all row and column entries (except possibly the main diagonal)
    6542:   of a set of rows and columns of a matrix.

    6544:   Collective

    6546:   Input Parameters:
    6547: + mat     - the matrix
    6548: . numRows - the number of rows/columns to remove
    6549: . rows    - the grid coordinates (and component number when dof > 1) for matrix rows
    6550: . diag    - value put in all diagonals of eliminated rows (0.0 will even eliminate diagonal entry)
    6551: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6552: - b       - optional vector of right-hand side, that will be adjusted by provided solution

    6554:   Level: intermediate

    6556:   Notes:
    6557:   See `MatZeroRowsColumns()` for details on how this routine operates.

    6559:   The grid coordinates are across the entire grid, not just the local portion

    6561:   For periodic boundary conditions use negative indices for values to the left (below 0; that are to be
    6562:   obtained by wrapping values from right edge). For values to the right of the last entry using that index plus one
    6563:   etc to obtain values that obtained by wrapping the values from the left edge. This does not work for anything but the
    6564:   `DM_BOUNDARY_PERIODIC` boundary type.

    6566:   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
    6567:   a single value per point) you can skip filling those indices.

    6569:   Fortran Note:
    6570:   `idxm` and `idxn` should be declared as
    6571: .vb
    6572:     MatStencil idxm(4, m)
    6573: .ve
    6574:   and the values inserted using
    6575: .vb
    6576:     idxm(MatStencil_i, 1) = i
    6577:     idxm(MatStencil_j, 1) = j
    6578:     idxm(MatStencil_k, 1) = k
    6579:     idxm(MatStencil_c, 1) = c
    6580:     etc
    6581: .ve

    6583: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6584:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRows()`
    6585: @*/
    6586: PetscErrorCode MatZeroRowsColumnsStencil(Mat mat, PetscInt numRows, const MatStencil rows[], PetscScalar diag, Vec x, Vec b)
    6587: {
    6588:   PetscInt  dim    = mat->stencil.dim;
    6589:   PetscInt  sdim   = dim - (1 - (PetscInt)mat->stencil.noc);
    6590:   PetscInt *dims   = mat->stencil.dims + 1;
    6591:   PetscInt *starts = mat->stencil.starts;
    6592:   PetscInt *dxm    = (PetscInt *)rows;
    6593:   PetscInt *jdxm, i, j, tmp, numNewRows = 0;

    6595:   PetscFunctionBegin;
    6598:   if (numRows) PetscAssertPointer(rows, 3);

    6600:   PetscCall(PetscMalloc1(numRows, &jdxm));
    6601:   for (i = 0; i < numRows; ++i) {
    6602:     /* Skip unused dimensions (they are ordered k, j, i, c) */
    6603:     for (j = 0; j < 3 - sdim; ++j) dxm++;
    6604:     /* Local index in X dir */
    6605:     tmp = *dxm++ - starts[0];
    6606:     /* Loop over remaining dimensions */
    6607:     for (j = 0; j < dim - 1; ++j) {
    6608:       /* If nonlocal, set index to be negative */
    6609:       if ((*dxm++ - starts[j + 1]) < 0 || tmp < 0) tmp = PETSC_INT_MIN;
    6610:       /* Update local index */
    6611:       else tmp = tmp * dims[j] + *(dxm - 1) - starts[j + 1];
    6612:     }
    6613:     /* Skip component slot if necessary */
    6614:     if (mat->stencil.noc) dxm++;
    6615:     /* Local row number */
    6616:     if (tmp >= 0) jdxm[numNewRows++] = tmp;
    6617:   }
    6618:   PetscCall(MatZeroRowsColumnsLocal(mat, numNewRows, jdxm, diag, x, b));
    6619:   PetscCall(PetscFree(jdxm));
    6620:   PetscFunctionReturn(PETSC_SUCCESS);
    6621: }

    6623: /*@
    6624:   MatZeroRowsLocal - Zeros all entries (except possibly the main diagonal)
    6625:   of a set of rows of a matrix; using local numbering of rows.

    6627:   Collective

    6629:   Input Parameters:
    6630: + mat     - the matrix
    6631: . numRows - the number of rows to remove
    6632: . rows    - the local row indices
    6633: . diag    - value put in all diagonals of eliminated rows
    6634: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6635: - b       - optional vector of right-hand side, that will be adjusted by provided solution

    6637:   Level: intermediate

    6639:   Notes:
    6640:   Before calling `MatZeroRowsLocal()`, the user must first set the
    6641:   local-to-global mapping by calling MatSetLocalToGlobalMapping(), this is often already set for matrices obtained with `DMCreateMatrix()`.

    6643:   See `MatZeroRows()` for details on how this routine operates.

    6645: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRows()`, `MatSetOption()`,
    6646:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6647: @*/
    6648: PetscErrorCode MatZeroRowsLocal(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    6649: {
    6650:   PetscFunctionBegin;
    6653:   if (numRows) PetscAssertPointer(rows, 3);
    6654:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6655:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6656:   MatCheckPreallocated(mat, 1);

    6658:   if (mat->ops->zerorowslocal) {
    6659:     PetscUseTypeMethod(mat, zerorowslocal, numRows, rows, diag, x, b);
    6660:   } else {
    6661:     IS        is, newis;
    6662:     PetscInt *newRows, nl = 0;

    6664:     PetscCheck(mat->rmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Need to provide local to global mapping to matrix first");
    6665:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, numRows, rows, PETSC_USE_POINTER, &is));
    6666:     PetscCall(ISLocalToGlobalMappingApplyIS(mat->rmap->mapping, is, &newis));
    6667:     PetscCall(ISGetIndices(newis, (const PetscInt **)&newRows));
    6668:     for (PetscInt i = 0; i < numRows; i++)
    6669:       if (newRows[i] > -1) newRows[nl++] = newRows[i];
    6670:     PetscUseTypeMethod(mat, zerorows, nl, newRows, diag, x, b);
    6671:     PetscCall(ISRestoreIndices(newis, (const PetscInt **)&newRows));
    6672:     PetscCall(ISDestroy(&newis));
    6673:     PetscCall(ISDestroy(&is));
    6674:   }
    6675:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6676:   PetscFunctionReturn(PETSC_SUCCESS);
    6677: }

    6679: /*@
    6680:   MatZeroRowsLocalIS - Zeros all entries (except possibly the main diagonal)
    6681:   of a set of rows of a matrix; using local numbering of rows.

    6683:   Collective

    6685:   Input Parameters:
    6686: + mat  - the matrix
    6687: . is   - index set of rows to remove
    6688: . diag - value put in all diagonals of eliminated rows
    6689: . x    - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6690: - b    - optional vector of right-hand side, that will be adjusted by provided solution

    6692:   Level: intermediate

    6694:   Notes:
    6695:   Before calling `MatZeroRowsLocalIS()`, the user must first set the
    6696:   local-to-global mapping by calling `MatSetLocalToGlobalMapping()`, this is often already set for matrices obtained with `DMCreateMatrix()`.

    6698:   See `MatZeroRows()` for details on how this routine operates.

    6700: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRows()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6701:           `MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6702: @*/
    6703: PetscErrorCode MatZeroRowsLocalIS(Mat mat, IS is, PetscScalar diag, Vec x, Vec b)
    6704: {
    6705:   PetscInt        numRows;
    6706:   const PetscInt *rows;

    6708:   PetscFunctionBegin;
    6712:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6713:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6714:   MatCheckPreallocated(mat, 1);

    6716:   PetscCall(ISGetLocalSize(is, &numRows));
    6717:   PetscCall(ISGetIndices(is, &rows));
    6718:   PetscCall(MatZeroRowsLocal(mat, numRows, rows, diag, x, b));
    6719:   PetscCall(ISRestoreIndices(is, &rows));
    6720:   PetscFunctionReturn(PETSC_SUCCESS);
    6721: }

    6723: /*@
    6724:   MatZeroRowsColumnsLocal - Zeros all entries (except possibly the main diagonal)
    6725:   of a set of rows and columns of a matrix; using local numbering of rows.

    6727:   Collective

    6729:   Input Parameters:
    6730: + mat     - the matrix
    6731: . numRows - the number of rows to remove
    6732: . rows    - the global row indices
    6733: . diag    - value put in all diagonals of eliminated rows
    6734: . x       - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6735: - b       - optional vector of right-hand side, that will be adjusted by provided solution

    6737:   Level: intermediate

    6739:   Notes:
    6740:   Before calling `MatZeroRowsColumnsLocal()`, the user must first set the
    6741:   local-to-global mapping by calling `MatSetLocalToGlobalMapping()`, this is often already set for matrices obtained with `DMCreateMatrix()`.

    6743:   See `MatZeroRowsColumns()` for details on how this routine operates.

    6745: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6746:           `MatZeroRows()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6747: @*/
    6748: PetscErrorCode MatZeroRowsColumnsLocal(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    6749: {
    6750:   PetscFunctionBegin;
    6753:   if (numRows) PetscAssertPointer(rows, 3);
    6754:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6755:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6756:   MatCheckPreallocated(mat, 1);

    6758:   if (mat->ops->zerorowscolumnslocal) {
    6759:     PetscUseTypeMethod(mat, zerorowscolumnslocal, numRows, rows, diag, x, b);
    6760:   } else {
    6761:     IS        is, newis;
    6762:     PetscInt *newRows, nl = 0;

    6764:     PetscCheck(mat->rmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Need to provide local to global mapping to matrix first");
    6765:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, numRows, rows, PETSC_USE_POINTER, &is));
    6766:     PetscCall(ISLocalToGlobalMappingApplyIS(mat->rmap->mapping, is, &newis));
    6767:     PetscCall(ISGetIndices(newis, (const PetscInt **)&newRows));
    6768:     for (PetscInt i = 0; i < numRows; i++)
    6769:       if (newRows[i] > -1) newRows[nl++] = newRows[i];
    6770:     PetscUseTypeMethod(mat, zerorowscolumns, nl, newRows, diag, x, b);
    6771:     PetscCall(ISRestoreIndices(newis, (const PetscInt **)&newRows));
    6772:     PetscCall(ISDestroy(&newis));
    6773:     PetscCall(ISDestroy(&is));
    6774:   }
    6775:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    6776:   PetscFunctionReturn(PETSC_SUCCESS);
    6777: }

    6779: /*@
    6780:   MatZeroRowsColumnsLocalIS - Zeros all entries (except possibly the main diagonal)
    6781:   of a set of rows and columns of a matrix; using local numbering of rows.

    6783:   Collective

    6785:   Input Parameters:
    6786: + mat  - the matrix
    6787: . is   - index set of rows to remove
    6788: . diag - value put in all diagonals of eliminated rows
    6789: . x    - optional vector of solutions for zeroed rows (other entries in vector are not used)
    6790: - b    - optional vector of right-hand side, that will be adjusted by provided solution

    6792:   Level: intermediate

    6794:   Notes:
    6795:   Before calling `MatZeroRowsColumnsLocalIS()`, the user must first set the
    6796:   local-to-global mapping by calling `MatSetLocalToGlobalMapping()`, this is often already set for matrices obtained with `DMCreateMatrix()`.

    6798:   See `MatZeroRowsColumns()` for details on how this routine operates.

    6800: .seealso: [](ch_matrices), `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
    6801:           `MatZeroRowsColumnsLocal()`, `MatZeroRows()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`
    6802: @*/
    6803: PetscErrorCode MatZeroRowsColumnsLocalIS(Mat mat, IS is, PetscScalar diag, Vec x, Vec b)
    6804: {
    6805:   PetscInt        numRows;
    6806:   const PetscInt *rows;

    6808:   PetscFunctionBegin;
    6812:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    6813:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    6814:   MatCheckPreallocated(mat, 1);

    6816:   PetscCall(ISGetLocalSize(is, &numRows));
    6817:   PetscCall(ISGetIndices(is, &rows));
    6818:   PetscCall(MatZeroRowsColumnsLocal(mat, numRows, rows, diag, x, b));
    6819:   PetscCall(ISRestoreIndices(is, &rows));
    6820:   PetscFunctionReturn(PETSC_SUCCESS);
    6821: }

    6823: /*@
    6824:   MatGetSize - Returns the numbers of rows and columns in a matrix.

    6826:   Not Collective

    6828:   Input Parameter:
    6829: . mat - the matrix

    6831:   Output Parameters:
    6832: + m - the number of global rows
    6833: - n - the number of global columns

    6835:   Level: beginner

    6837:   Note:
    6838:   Both output parameters can be `NULL` on input.

    6840: .seealso: [](ch_matrices), `Mat`, `MatSetSizes()`, `MatGetLocalSize()`
    6841: @*/
    6842: PetscErrorCode MatGetSize(Mat mat, PetscInt *m, PetscInt *n)
    6843: {
    6844:   PetscFunctionBegin;
    6846:   if (m) *m = mat->rmap->N;
    6847:   if (n) *n = mat->cmap->N;
    6848:   PetscFunctionReturn(PETSC_SUCCESS);
    6849: }

    6851: /*@
    6852:   MatGetLocalSize - For most matrix formats, excluding `MATELEMENTAL` and `MATSCALAPACK`, Returns the number of local rows and local columns
    6853:   of a matrix. For all matrices this is the local size of the left and right vectors as returned by `MatCreateVecs()`.

    6855:   Not Collective

    6857:   Input Parameter:
    6858: . mat - the matrix

    6860:   Output Parameters:
    6861: + m - the number of local rows, use `NULL` to not obtain this value
    6862: - n - the number of local columns, use `NULL` to not obtain this value

    6864:   Level: beginner

    6866: .seealso: [](ch_matrices), `Mat`, `MatSetSizes()`, `MatGetSize()`
    6867: @*/
    6868: PetscErrorCode MatGetLocalSize(Mat mat, PetscInt *m, PetscInt *n)
    6869: {
    6870:   PetscFunctionBegin;
    6872:   if (m) PetscAssertPointer(m, 2);
    6873:   if (n) PetscAssertPointer(n, 3);
    6874:   if (m) *m = mat->rmap->n;
    6875:   if (n) *n = mat->cmap->n;
    6876:   PetscFunctionReturn(PETSC_SUCCESS);
    6877: }

    6879: /*@
    6880:   MatGetOwnershipRangeColumn - Returns the range of matrix columns associated with rows of a
    6881:   vector one multiplies this matrix by that are owned by this processor.

    6883:   Not Collective, unless matrix has not been allocated, then collective

    6885:   Input Parameter:
    6886: . mat - the matrix

    6888:   Output Parameters:
    6889: + m - the global index of the first local column, use `NULL` to not obtain this value
    6890: - n - one more than the global index of the last local column, use `NULL` to not obtain this value

    6892:   Level: developer

    6894:   Notes:
    6895:   If the `Mat` was obtained from a `DM` with `DMCreateMatrix()`, then the range values are determined by the specific `DM`.

    6897:   If the `Mat` was created directly the range values are determined by the local size passed to `MatSetSizes()` or `MatCreateAIJ()`.
    6898:   If `PETSC_DECIDE` was passed as the local size, then the vector uses default values for the range using `PetscSplitOwnership()`.

    6900:   For certain `DM`, such as `DMDA`, it is better to use `DM` specific routines, such as `DMDAGetGhostCorners()`, to determine
    6901:   the local values in the matrix.

    6903:   Returns the columns of the "diagonal block" for most sparse matrix formats. See [Matrix
    6904:   Layouts](sec_matlayout) for details on matrix layouts.

    6906: .seealso: [](ch_matrices), `Mat`, `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangesColumn()`, `PetscLayout`,
    6907:           `MatSetSizes()`, `MatCreateAIJ()`, `DMDAGetGhostCorners()`, `DM`
    6908: @*/
    6909: PetscErrorCode MatGetOwnershipRangeColumn(Mat mat, PetscInt *m, PetscInt *n)
    6910: {
    6911:   PetscFunctionBegin;
    6914:   if (m) PetscAssertPointer(m, 2);
    6915:   if (n) PetscAssertPointer(n, 3);
    6916:   MatCheckPreallocated(mat, 1);
    6917:   if (m) *m = mat->cmap->rstart;
    6918:   if (n) *n = mat->cmap->rend;
    6919:   PetscFunctionReturn(PETSC_SUCCESS);
    6920: }

    6922: /*@
    6923:   MatGetOwnershipRange - For matrices that own values by row, excludes `MATELEMENTAL` and `MATSCALAPACK`, returns the range of matrix rows owned by
    6924:   this MPI process.

    6926:   Not Collective

    6928:   Input Parameter:
    6929: . mat - the matrix

    6931:   Output Parameters:
    6932: + m - the global index of the first local row, use `NULL` to not obtain this value
    6933: - n - one more than the global index of the last local row, use `NULL` to not obtain this value

    6935:   Level: beginner

    6937:   Notes:
    6938:   If the `Mat` was obtained from a `DM` with `DMCreateMatrix()`, then the range values are determined by the specific `DM`.

    6940:   If the `Mat` was created directly the range values are determined by the local size passed to `MatSetSizes()` or `MatCreateAIJ()`.
    6941:   If `PETSC_DECIDE` was passed as the local size, then the vector uses default values for the range using `PetscSplitOwnership()`.

    6943:   For certain `DM`, such as `DMDA`, it is better to use `DM` specific routines, such as `DMDAGetGhostCorners()`, to determine
    6944:   the local values in the matrix.

    6946:   The high argument is one more than the last element stored locally.

    6948:   For all matrices  it returns the range of matrix rows associated with rows of a vector that
    6949:   would contain the result of a matrix vector product with this matrix. See [Matrix
    6950:   Layouts](sec_matlayout) for details on matrix layouts.

    6952: .seealso: [](ch_matrices), `Mat`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`, `MatGetOwnershipRangesColumn()`, `PetscSplitOwnership()`,
    6953:           `PetscSplitOwnershipBlock()`, `PetscLayout`, `MatSetSizes()`, `MatCreateAIJ()`, `DMDAGetGhostCorners()`, `DM`
    6954: @*/
    6955: PetscErrorCode MatGetOwnershipRange(Mat mat, PetscInt *m, PetscInt *n)
    6956: {
    6957:   PetscFunctionBegin;
    6960:   if (m) PetscAssertPointer(m, 2);
    6961:   if (n) PetscAssertPointer(n, 3);
    6962:   MatCheckPreallocated(mat, 1);
    6963:   if (m) *m = mat->rmap->rstart;
    6964:   if (n) *n = mat->rmap->rend;
    6965:   PetscFunctionReturn(PETSC_SUCCESS);
    6966: }

    6968: /*@C
    6969:   MatGetOwnershipRanges - For matrices that own values by row, excludes `MATELEMENTAL` and
    6970:   `MATSCALAPACK`, returns the range of matrix rows owned by each process.

    6972:   Not Collective, unless matrix has not been allocated

    6974:   Input Parameter:
    6975: . mat - the matrix

    6977:   Output Parameter:
    6978: . ranges - start of each processors portion plus one more than the total length at the end, of length `size` + 1
    6979:            where `size` is the number of MPI processes used by `mat`

    6981:   Level: beginner

    6983:   Notes:
    6984:   If the `Mat` was obtained from a `DM` with `DMCreateMatrix()`, then the range values are determined by the specific `DM`.

    6986:   If the `Mat` was created directly the range values are determined by the local size passed to `MatSetSizes()` or `MatCreateAIJ()`.
    6987:   If `PETSC_DECIDE` was passed as the local size, then the vector uses default values for the range using `PetscSplitOwnership()`.

    6989:   For certain `DM`, such as `DMDA`, it is better to use `DM` specific routines, such as `DMDAGetGhostCorners()`, to determine
    6990:   the local values in the matrix.

    6992:   For all matrices  it returns the ranges of matrix rows associated with rows of a vector that
    6993:   would contain the result of a matrix vector product with this matrix. See [Matrix
    6994:   Layouts](sec_matlayout) for details on matrix layouts.

    6996: .seealso: [](ch_matrices), `Mat`, `MatGetOwnershipRange()`, `MatGetOwnershipRangeColumn()`, `MatGetOwnershipRangesColumn()`, `PetscLayout`,
    6997:           `PetscSplitOwnership()`, `PetscSplitOwnershipBlock()`, `MatSetSizes()`, `MatCreateAIJ()`,
    6998:           `DMDAGetGhostCorners()`, `DM`
    6999: @*/
    7000: PetscErrorCode MatGetOwnershipRanges(Mat mat, const PetscInt *ranges[])
    7001: {
    7002:   PetscFunctionBegin;
    7005:   MatCheckPreallocated(mat, 1);
    7006:   PetscCall(PetscLayoutGetRanges(mat->rmap, ranges));
    7007:   PetscFunctionReturn(PETSC_SUCCESS);
    7008: }

    7010: /*@C
    7011:   MatGetOwnershipRangesColumn - Returns the ranges of matrix columns associated with rows of a
    7012:   vector one multiplies this vector by that are owned by each processor.

    7014:   Not Collective, unless matrix has not been allocated

    7016:   Input Parameter:
    7017: . mat - the matrix

    7019:   Output Parameter:
    7020: . ranges - start of each processors portion plus one more than the total length at the end

    7022:   Level: beginner

    7024:   Notes:
    7025:   If the `Mat` was obtained from a `DM` with `DMCreateMatrix()`, then the range values are determined by the specific `DM`.

    7027:   If the `Mat` was created directly the range values are determined by the local size passed to `MatSetSizes()` or `MatCreateAIJ()`.
    7028:   If `PETSC_DECIDE` was passed as the local size, then the vector uses default values for the range using `PetscSplitOwnership()`.

    7030:   For certain `DM`, such as `DMDA`, it is better to use `DM` specific routines, such as `DMDAGetGhostCorners()`, to determine
    7031:   the local values in the matrix.

    7033:   Returns the columns of the "diagonal blocks", for most sparse matrix formats. See [Matrix
    7034:   Layouts](sec_matlayout) for details on matrix layouts.

    7036: .seealso: [](ch_matrices), `Mat`, `MatGetOwnershipRange()`, `MatGetOwnershipRangeColumn()`, `MatGetOwnershipRanges()`,
    7037:           `PetscSplitOwnership()`, `PetscSplitOwnershipBlock()`, `PetscLayout`, `MatSetSizes()`, `MatCreateAIJ()`,
    7038:           `DMDAGetGhostCorners()`, `DM`
    7039: @*/
    7040: PetscErrorCode MatGetOwnershipRangesColumn(Mat mat, const PetscInt *ranges[])
    7041: {
    7042:   PetscFunctionBegin;
    7045:   MatCheckPreallocated(mat, 1);
    7046:   PetscCall(PetscLayoutGetRanges(mat->cmap, ranges));
    7047:   PetscFunctionReturn(PETSC_SUCCESS);
    7048: }

    7050: /*@
    7051:   MatGetOwnershipIS - Get row and column ownership of a matrices' values as index sets.

    7053:   Not Collective

    7055:   Input Parameter:
    7056: . A - matrix

    7058:   Output Parameters:
    7059: + rows - rows in which this process owns elements, , use `NULL` to not obtain this value
    7060: - cols - columns in which this process owns elements, use `NULL` to not obtain this value

    7062:   Level: intermediate

    7064:   Note:
    7065:   You should call `ISDestroy()` on the returned `IS`

    7067:   For most matrices, excluding `MATELEMENTAL` and `MATSCALAPACK`, this corresponds to values
    7068:   returned by `MatGetOwnershipRange()`, `MatGetOwnershipRangeColumn()`. For `MATELEMENTAL` and
    7069:   `MATSCALAPACK` the ownership is more complicated. See [Matrix Layouts](sec_matlayout) for
    7070:   details on matrix layouts.

    7072: .seealso: [](ch_matrices), `IS`, `Mat`, `MatGetOwnershipRanges()`, `MatSetValues()`, `MATELEMENTAL`, `MATSCALAPACK`
    7073: @*/
    7074: PetscErrorCode MatGetOwnershipIS(Mat A, IS *rows, IS *cols)
    7075: {
    7076:   PetscErrorCode (*f)(Mat, IS *, IS *);

    7078:   PetscFunctionBegin;
    7081:   MatCheckPreallocated(A, 1);
    7082:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatGetOwnershipIS_C", &f));
    7083:   if (f) {
    7084:     PetscCall((*f)(A, rows, cols));
    7085:   } else { /* Create a standard row-based partition, each process is responsible for ALL columns in their row block */
    7086:     if (rows) PetscCall(ISCreateStride(PETSC_COMM_SELF, A->rmap->n, A->rmap->rstart, 1, rows));
    7087:     if (cols) PetscCall(ISCreateStride(PETSC_COMM_SELF, A->cmap->N, 0, 1, cols));
    7088:   }
    7089:   PetscFunctionReturn(PETSC_SUCCESS);
    7090: }

    7092: /*@
    7093:   MatILUFactorSymbolic - Performs symbolic ILU factorization of a matrix obtained with `MatGetFactor()`
    7094:   Uses levels of fill only, not drop tolerance. Use `MatLUFactorNumeric()`
    7095:   to complete the factorization.

    7097:   Collective

    7099:   Input Parameters:
    7100: + fact - the factorized matrix obtained with `MatGetFactor()`
    7101: . mat  - the matrix
    7102: . row  - row permutation
    7103: . col  - column permutation
    7104: - info - structure containing
    7105: .vb
    7106:       levels - number of levels of fill.
    7107:       expected fill - as ratio of original fill.
    7108:       1 or 0 - indicating force fill on diagonal (improves robustness for matrices
    7109:                 missing diagonal entries)
    7110: .ve

    7112:   Level: developer

    7114:   Notes:
    7115:   See [Matrix Factorization](sec_matfactor) for additional information.

    7117:   Most users should employ the `KSP` interface for linear solvers
    7118:   instead of working directly with matrix algebra routines such as this.
    7119:   See, e.g., `KSPCreate()`.

    7121:   Uses the definition of level of fill as in Y. Saad, {cite}`saad2003`

    7123:   Fortran Note:
    7124:   A valid (non-null) `info` argument must be provided

    7126: .seealso: [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatLUFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`
    7127:           `MatGetOrdering()`, `MatFactorInfo`
    7128: @*/
    7129: PetscErrorCode MatILUFactorSymbolic(Mat fact, Mat mat, IS row, IS col, const MatFactorInfo *info)
    7130: {
    7131:   PetscFunctionBegin;
    7136:   PetscAssertPointer(info, 5);
    7137:   PetscAssertPointer(fact, 1);
    7138:   PetscCheck(info->levels >= 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Levels of fill negative %" PetscInt_FMT, (PetscInt)info->levels);
    7139:   PetscCheck(info->fill >= 1.0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Expected fill less than 1.0 %g", (double)info->fill);
    7140:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7141:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7142:   MatCheckPreallocated(mat, 2);

    7144:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_ILUFactorSymbolic, mat, row, col, 0));
    7145:   PetscUseTypeMethod(fact, ilufactorsymbolic, mat, row, col, info);
    7146:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_ILUFactorSymbolic, mat, row, col, 0));
    7147:   PetscFunctionReturn(PETSC_SUCCESS);
    7148: }

    7150: /*@
    7151:   MatICCFactorSymbolic - Performs symbolic incomplete
    7152:   Cholesky factorization for a symmetric matrix.  Use
    7153:   `MatCholeskyFactorNumeric()` to complete the factorization.

    7155:   Collective

    7157:   Input Parameters:
    7158: + fact - the factorized matrix obtained with `MatGetFactor()`
    7159: . mat  - the matrix to be factored
    7160: . perm - row and column permutation
    7161: - info - structure containing
    7162: .vb
    7163:       levels - number of levels of fill.
    7164:       expected fill - as ratio of original fill.
    7165: .ve

    7167:   Level: developer

    7169:   Notes:
    7170:   Most users should employ the `KSP` interface for linear solvers
    7171:   instead of working directly with matrix algebra routines such as this.
    7172:   See, e.g., `KSPCreate()`.

    7174:   This uses the definition of level of fill as in Y. Saad {cite}`saad2003`

    7176:   Fortran Note:
    7177:   A valid (non-null) `info` argument must be provided

    7179: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCholeskyFactorNumeric()`, `MatCholeskyFactor()`, `MatFactorInfo`
    7180: @*/
    7181: PetscErrorCode MatICCFactorSymbolic(Mat fact, Mat mat, IS perm, const MatFactorInfo *info)
    7182: {
    7183:   PetscFunctionBegin;
    7187:   PetscAssertPointer(info, 4);
    7188:   PetscAssertPointer(fact, 1);
    7189:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7190:   PetscCheck(info->levels >= 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Levels negative %" PetscInt_FMT, (PetscInt)info->levels);
    7191:   PetscCheck(info->fill >= 1.0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Expected fill less than 1.0 %g", (double)info->fill);
    7192:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7193:   MatCheckPreallocated(mat, 2);

    7195:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventBegin(MAT_ICCFactorSymbolic, mat, perm, 0, 0));
    7196:   PetscUseTypeMethod(fact, iccfactorsymbolic, mat, perm, info);
    7197:   if (!fact->trivialsymbolic) PetscCall(PetscLogEventEnd(MAT_ICCFactorSymbolic, mat, perm, 0, 0));
    7198:   PetscFunctionReturn(PETSC_SUCCESS);
    7199: }

    7201: /*@C
    7202:   MatCreateSubMatrices - Extracts several submatrices from a matrix. If submat
    7203:   points to an array of valid matrices, they may be reused to store the new
    7204:   submatrices.

    7206:   Collective

    7208:   Input Parameters:
    7209: + mat   - the matrix
    7210: . n     - the number of submatrixes to be extracted (on this processor, may be zero)
    7211: . irow  - index set of rows to extract
    7212: . icol  - index set of columns to extract
    7213: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    7215:   Output Parameter:
    7216: . submat - the array of submatrices

    7218:   Level: advanced

    7220:   Notes:
    7221:   `MatCreateSubMatrices()` can extract ONLY sequential submatrices
    7222:   (from both sequential and parallel matrices). Use `MatCreateSubMatrix()`
    7223:   to extract a parallel submatrix.

    7225:   Some matrix types place restrictions on the row and column
    7226:   indices, such as that they be sorted or that they be equal to each other.

    7228:   The index sets may not have duplicate entries.

    7230:   When extracting submatrices from a parallel matrix, each processor can
    7231:   form a different submatrix by setting the rows and columns of its
    7232:   individual index sets according to the local submatrix desired.

    7234:   When finished using the submatrices, the user should destroy
    7235:   them with `MatDestroySubMatrices()`.

    7237:   `MAT_REUSE_MATRIX` can only be used when the nonzero structure of the
    7238:   original matrix has not changed from that last call to `MatCreateSubMatrices()`.

    7240:   This routine creates the matrices in submat; you should NOT create them before
    7241:   calling it. It also allocates the array of matrix pointers submat.

    7243:   For `MATBAIJ` matrices the index sets must respect the block structure, that is if they
    7244:   request one row/column in a block, they must request all rows/columns that are in
    7245:   that block. For example, if the block size is 2 you cannot request just row 0 and
    7246:   column 0.

    7248:   Fortran Note:
    7249: .vb
    7250:   Mat, pointer :: submat(:)
    7251: .ve

    7253: .seealso: [](ch_matrices), `Mat`, `MatDestroySubMatrices()`, `MatCreateSubMatrix()`, `MatGetRow()`, `MatGetDiagonal()`, `MatReuse`
    7254: @*/
    7255: PetscErrorCode MatCreateSubMatrices(Mat mat, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
    7256: {
    7257:   PetscInt  i;
    7258:   PetscBool eq;

    7260:   PetscFunctionBegin;
    7263:   if (n) {
    7264:     PetscAssertPointer(irow, 3);
    7266:     PetscAssertPointer(icol, 4);
    7268:   }
    7269:   PetscAssertPointer(submat, 6);
    7270:   if (n && scall == MAT_REUSE_MATRIX) {
    7271:     PetscAssertPointer(*submat, 6);
    7273:   }
    7274:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7275:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7276:   MatCheckPreallocated(mat, 1);
    7277:   PetscCall(PetscLogEventBegin(MAT_CreateSubMats, mat, 0, 0, 0));
    7278:   PetscUseTypeMethod(mat, createsubmatrices, n, irow, icol, scall, submat);
    7279:   PetscCall(PetscLogEventEnd(MAT_CreateSubMats, mat, 0, 0, 0));
    7280:   for (i = 0; i < n; i++) {
    7281:     (*submat)[i]->factortype = MAT_FACTOR_NONE; /* in case in place factorization was previously done on submatrix */
    7282:     PetscCall(ISEqualUnsorted(irow[i], icol[i], &eq));
    7283:     if (eq) PetscCall(MatPropagateSymmetryOptions(mat, (*submat)[i]));
    7284: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
    7285:     if (mat->boundtocpu && mat->bindingpropagates) {
    7286:       PetscCall(MatBindToCPU((*submat)[i], PETSC_TRUE));
    7287:       PetscCall(MatSetBindingPropagates((*submat)[i], PETSC_TRUE));
    7288:     }
    7289: #endif
    7290:   }
    7291:   PetscFunctionReturn(PETSC_SUCCESS);
    7292: }

    7294: /*@C
    7295:   MatCreateSubMatricesMPI - Extracts MPI submatrices across a sub communicator of `mat` (by pairs of `IS` that may live on subcomms).

    7297:   Collective

    7299:   Input Parameters:
    7300: + mat   - the matrix
    7301: . n     - the number of submatrixes to be extracted
    7302: . irow  - index set of rows to extract
    7303: . icol  - index set of columns to extract
    7304: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    7306:   Output Parameter:
    7307: . submat - the array of submatrices

    7309:   Level: advanced

    7311:   Note:
    7312:   This is used by `PCGASM`

    7314: .seealso: [](ch_matrices), `Mat`, `PCGASM`, `MatCreateSubMatrices()`, `MatCreateSubMatrix()`, `MatGetRow()`, `MatGetDiagonal()`, `MatReuse`
    7315: @*/
    7316: PetscErrorCode MatCreateSubMatricesMPI(Mat mat, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
    7317: {
    7318:   PetscInt  i;
    7319:   PetscBool eq;

    7321:   PetscFunctionBegin;
    7324:   if (n) {
    7325:     PetscAssertPointer(irow, 3);
    7327:     PetscAssertPointer(icol, 4);
    7329:   }
    7330:   PetscAssertPointer(submat, 6);
    7331:   if (n && scall == MAT_REUSE_MATRIX) {
    7332:     PetscAssertPointer(*submat, 6);
    7334:   }
    7335:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7336:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7337:   MatCheckPreallocated(mat, 1);

    7339:   PetscCall(PetscLogEventBegin(MAT_CreateSubMats, mat, 0, 0, 0));
    7340:   PetscUseTypeMethod(mat, createsubmatricesmpi, n, irow, icol, scall, submat);
    7341:   PetscCall(PetscLogEventEnd(MAT_CreateSubMats, mat, 0, 0, 0));
    7342:   for (i = 0; i < n; i++) {
    7343:     PetscCall(ISEqualUnsorted(irow[i], icol[i], &eq));
    7344:     if (eq) PetscCall(MatPropagateSymmetryOptions(mat, (*submat)[i]));
    7345:   }
    7346:   PetscFunctionReturn(PETSC_SUCCESS);
    7347: }

    7349: /*@C
    7350:   MatDestroyMatrices - Destroys an array of matrices

    7352:   Collective

    7354:   Input Parameters:
    7355: + n   - the number of local matrices
    7356: - mat - the matrices (this is a pointer to the array of matrices)

    7358:   Level: advanced

    7360:   Notes:
    7361:   Frees not only the matrices, but also the array that contains the matrices

    7363:   For matrices obtained with  `MatCreateSubMatrices()` use `MatDestroySubMatrices()`

    7365: .seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatDestroySubMatrices()`
    7366: @*/
    7367: PetscErrorCode MatDestroyMatrices(PetscInt n, Mat *mat[])
    7368: {
    7369:   PetscInt i;

    7371:   PetscFunctionBegin;
    7372:   if (!*mat) PetscFunctionReturn(PETSC_SUCCESS);
    7373:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Trying to destroy negative number of matrices %" PetscInt_FMT, n);
    7374:   PetscAssertPointer(mat, 2);

    7376:   for (i = 0; i < n; i++) PetscCall(MatDestroy(&(*mat)[i]));

    7378:   /* memory is allocated even if n = 0 */
    7379:   PetscCall(PetscFree(*mat));
    7380:   PetscFunctionReturn(PETSC_SUCCESS);
    7381: }

    7383: /*@C
    7384:   MatDestroySubMatrices - Destroys a set of matrices obtained with `MatCreateSubMatrices()`.

    7386:   Collective

    7388:   Input Parameters:
    7389: + n   - the number of local matrices
    7390: - mat - the matrices (this is a pointer to the array of matrices, to match the calling sequence of `MatCreateSubMatrices()`)

    7392:   Level: advanced

    7394:   Note:
    7395:   Frees not only the matrices, but also the array that contains the matrices

    7397: .seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatDestroyMatrices()`
    7398: @*/
    7399: PetscErrorCode MatDestroySubMatrices(PetscInt n, Mat *mat[])
    7400: {
    7401:   Mat mat0;

    7403:   PetscFunctionBegin;
    7404:   if (!*mat) PetscFunctionReturn(PETSC_SUCCESS);
    7405:   /* mat[] is an array of length n+1, see MatCreateSubMatrices_xxx() */
    7406:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Trying to destroy negative number of matrices %" PetscInt_FMT, n);
    7407:   PetscAssertPointer(mat, 2);

    7409:   mat0 = (*mat)[0];
    7410:   if (mat0 && mat0->ops->destroysubmatrices) {
    7411:     PetscCall((*mat0->ops->destroysubmatrices)(n, mat));
    7412:   } else {
    7413:     PetscCall(MatDestroyMatrices(n, mat));
    7414:   }
    7415:   PetscFunctionReturn(PETSC_SUCCESS);
    7416: }

    7418: /*@
    7419:   MatGetSeqNonzeroStructure - Extracts the nonzero structure from a matrix and stores it, in its entirety, on each process

    7421:   Collective

    7423:   Input Parameter:
    7424: . mat - the matrix

    7426:   Output Parameter:
    7427: . matstruct - the sequential matrix with the nonzero structure of `mat`

    7429:   Level: developer

    7431: .seealso: [](ch_matrices), `Mat`, `MatDestroySeqNonzeroStructure()`, `MatCreateSubMatrices()`, `MatDestroyMatrices()`
    7432: @*/
    7433: PetscErrorCode MatGetSeqNonzeroStructure(Mat mat, Mat *matstruct)
    7434: {
    7435:   PetscFunctionBegin;
    7437:   PetscAssertPointer(matstruct, 2);

    7440:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7441:   MatCheckPreallocated(mat, 1);

    7443:   PetscCall(PetscLogEventBegin(MAT_GetSeqNonzeroStructure, mat, 0, 0, 0));
    7444:   PetscUseTypeMethod(mat, getseqnonzerostructure, matstruct);
    7445:   PetscCall(PetscLogEventEnd(MAT_GetSeqNonzeroStructure, mat, 0, 0, 0));
    7446:   PetscFunctionReturn(PETSC_SUCCESS);
    7447: }

    7449: /*@C
    7450:   MatDestroySeqNonzeroStructure - Destroys matrix obtained with `MatGetSeqNonzeroStructure()`.

    7452:   Collective

    7454:   Input Parameter:
    7455: . mat - the matrix

    7457:   Level: advanced

    7459:   Note:
    7460:   This is not needed, one can just call `MatDestroy()`

    7462: .seealso: [](ch_matrices), `Mat`, `MatGetSeqNonzeroStructure()`
    7463: @*/
    7464: PetscErrorCode MatDestroySeqNonzeroStructure(Mat *mat)
    7465: {
    7466:   PetscFunctionBegin;
    7467:   PetscAssertPointer(mat, 1);
    7468:   PetscCall(MatDestroy(mat));
    7469:   PetscFunctionReturn(PETSC_SUCCESS);
    7470: }

    7472: /*@
    7473:   MatIncreaseOverlap - Given a set of submatrices indicated by index sets,
    7474:   replaces the index sets by larger ones that represent submatrices with
    7475:   additional overlap.

    7477:   Collective

    7479:   Input Parameters:
    7480: + mat - the matrix
    7481: . n   - the number of index sets
    7482: . is  - the array of index sets (these index sets will changed during the call)
    7483: - ov  - the additional overlap requested

    7485:   Options Database Key:
    7486: . -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

    7488:   Level: developer

    7490:   Note:
    7491:   The computed overlap preserves the matrix block sizes when the blocks are square.
    7492:   That is: if a matrix nonzero for a given block would increase the overlap all columns associated with
    7493:   that block are included in the overlap regardless of whether each specific column would increase the overlap.

    7495: .seealso: [](ch_matrices), `Mat`, `PCASM`, `MatSetBlockSize()`, `MatIncreaseOverlapSplit()`, `MatCreateSubMatrices()`
    7496: @*/
    7497: PetscErrorCode MatIncreaseOverlap(Mat mat, PetscInt n, IS is[], PetscInt ov)
    7498: {
    7499:   PetscInt i, bs, cbs;

    7501:   PetscFunctionBegin;
    7505:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have one or more domains, you have %" PetscInt_FMT, n);
    7506:   if (n) {
    7507:     PetscAssertPointer(is, 3);
    7509:   }
    7510:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7511:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7512:   MatCheckPreallocated(mat, 1);

    7514:   if (!ov || !n) PetscFunctionReturn(PETSC_SUCCESS);
    7515:   PetscCall(PetscLogEventBegin(MAT_IncreaseOverlap, mat, 0, 0, 0));
    7516:   PetscUseTypeMethod(mat, increaseoverlap, n, is, ov);
    7517:   PetscCall(PetscLogEventEnd(MAT_IncreaseOverlap, mat, 0, 0, 0));
    7518:   PetscCall(MatGetBlockSizes(mat, &bs, &cbs));
    7519:   if (bs == cbs) {
    7520:     for (i = 0; i < n; i++) PetscCall(ISSetBlockSize(is[i], bs));
    7521:   }
    7522:   PetscFunctionReturn(PETSC_SUCCESS);
    7523: }

    7525: PetscErrorCode MatIncreaseOverlapSplit_Single(Mat, IS *, PetscInt);

    7527: /*@
    7528:   MatIncreaseOverlapSplit - Given a set of submatrices indicated by index sets across
    7529:   a sub communicator, replaces the index sets by larger ones that represent submatrices with
    7530:   additional overlap.

    7532:   Collective

    7534:   Input Parameters:
    7535: + mat - the matrix
    7536: . n   - the number of index sets
    7537: . is  - the array of index sets (these index sets will changed during the call)
    7538: - ov  - the additional overlap requested

    7540:   `   Options Database Key:
    7541: . -mat_increase_overlap_scalable - use a scalable algorithm to compute the overlap (supported by MPIAIJ matrix)

    7543:   Level: developer

    7545: .seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatIncreaseOverlap()`
    7546: @*/
    7547: PetscErrorCode MatIncreaseOverlapSplit(Mat mat, PetscInt n, IS is[], PetscInt ov)
    7548: {
    7549:   PetscInt i;

    7551:   PetscFunctionBegin;
    7554:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must have one or more domains, you have %" PetscInt_FMT, n);
    7555:   if (n) {
    7556:     PetscAssertPointer(is, 3);
    7558:   }
    7559:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    7560:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    7561:   MatCheckPreallocated(mat, 1);
    7562:   if (!ov) PetscFunctionReturn(PETSC_SUCCESS);
    7563:   PetscCall(PetscLogEventBegin(MAT_IncreaseOverlap, mat, 0, 0, 0));
    7564:   for (i = 0; i < n; i++) PetscCall(MatIncreaseOverlapSplit_Single(mat, &is[i], ov));
    7565:   PetscCall(PetscLogEventEnd(MAT_IncreaseOverlap, mat, 0, 0, 0));
    7566:   PetscFunctionReturn(PETSC_SUCCESS);
    7567: }

    7569: /*@
    7570:   MatGetBlockSize - Returns the matrix block size.

    7572:   Not Collective

    7574:   Input Parameter:
    7575: . mat - the matrix

    7577:   Output Parameter:
    7578: . bs - block size

    7580:   Level: intermediate

    7582:   Notes:
    7583:   Block row formats are `MATBAIJ` and `MATSBAIJ` ALWAYS have square block storage in the matrix.

    7585:   If the block size has not been set yet this routine returns 1.

    7587: .seealso: [](ch_matrices), `Mat`, `MATBAIJ`, `MATSBAIJ`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSizes()`
    7588: @*/
    7589: PetscErrorCode MatGetBlockSize(Mat mat, PetscInt *bs)
    7590: {
    7591:   PetscFunctionBegin;
    7593:   PetscAssertPointer(bs, 2);
    7594:   *bs = mat->rmap->bs;
    7595:   PetscFunctionReturn(PETSC_SUCCESS);
    7596: }

    7598: /*@
    7599:   MatGetBlockSizes - Returns the matrix block row and column sizes.

    7601:   Not Collective

    7603:   Input Parameter:
    7604: . mat - the matrix

    7606:   Output Parameters:
    7607: + rbs - row block size
    7608: - cbs - column block size

    7610:   Level: intermediate

    7612:   Notes:
    7613:   Block row formats are `MATBAIJ` and `MATSBAIJ` ALWAYS have square block storage in the matrix.
    7614:   If you pass a different block size for the columns than the rows, the row block size determines the square block storage.

    7616:   If a block size has not been set yet this routine returns 1.

    7618: .seealso: [](ch_matrices), `Mat`, `MATBAIJ`, `MATSBAIJ`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSize()`, `MatSetBlockSizes()`
    7619: @*/
    7620: PetscErrorCode MatGetBlockSizes(Mat mat, PetscInt *rbs, PetscInt *cbs)
    7621: {
    7622:   PetscFunctionBegin;
    7624:   if (rbs) PetscAssertPointer(rbs, 2);
    7625:   if (cbs) PetscAssertPointer(cbs, 3);
    7626:   if (rbs) *rbs = mat->rmap->bs;
    7627:   if (cbs) *cbs = mat->cmap->bs;
    7628:   PetscFunctionReturn(PETSC_SUCCESS);
    7629: }

    7631: /*@
    7632:   MatSetBlockSize - Sets the matrix block size.

    7634:   Logically Collective

    7636:   Input Parameters:
    7637: + mat - the matrix
    7638: - bs  - block size

    7640:   Level: intermediate

    7642:   Notes:
    7643:   Block row formats are `MATBAIJ` and `MATSBAIJ` formats ALWAYS have square block storage in the matrix.
    7644:   This must be called before `MatSetUp()` or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later.

    7646:   For `MATAIJ` matrix format, this function can be called at a later stage, provided that the specified block size
    7647:   is compatible with the matrix local sizes.

    7649: .seealso: [](ch_matrices), `Mat`, `MATBAIJ`, `MATSBAIJ`, `MATAIJ`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSizes()`, `MatGetBlockSizes()`
    7650: @*/
    7651: PetscErrorCode MatSetBlockSize(Mat mat, PetscInt bs)
    7652: {
    7653:   PetscFunctionBegin;
    7656:   PetscCall(MatSetBlockSizes(mat, bs, bs));
    7657:   PetscFunctionReturn(PETSC_SUCCESS);
    7658: }

    7660: typedef struct {
    7661:   PetscInt         n;
    7662:   IS              *is;
    7663:   Mat             *mat;
    7664:   PetscObjectState nonzerostate;
    7665:   Mat              C;
    7666: } EnvelopeData;

    7668: static PetscErrorCode EnvelopeDataDestroy(void **ptr)
    7669: {
    7670:   EnvelopeData *edata = (EnvelopeData *)*ptr;

    7672:   PetscFunctionBegin;
    7673:   for (PetscInt i = 0; i < edata->n; i++) PetscCall(ISDestroy(&edata->is[i]));
    7674:   PetscCall(PetscFree(edata->is));
    7675:   PetscCall(PetscFree(edata));
    7676:   PetscFunctionReturn(PETSC_SUCCESS);
    7677: }

    7679: /*@
    7680:   MatComputeVariableBlockEnvelope - Given a matrix whose nonzeros are in blocks along the diagonal this computes and stores
    7681:   the sizes of these blocks in the matrix. An individual block may lie over several processes.

    7683:   Collective

    7685:   Input Parameter:
    7686: . mat - the matrix

    7688:   Level: intermediate

    7690:   Notes:
    7691:   There can be zeros within the blocks

    7693:   The blocks can overlap between processes, including laying on more than two processes

    7695: .seealso: [](ch_matrices), `Mat`, `MatInvertVariableBlockEnvelope()`, `MatSetVariableBlockSizes()`
    7696: @*/
    7697: PetscErrorCode MatComputeVariableBlockEnvelope(Mat mat)
    7698: {
    7699:   PetscInt           n, *sizes, *starts, i = 0, env = 0, tbs = 0, lblocks = 0, rstart, II, ln = 0, cnt = 0, cstart, cend;
    7700:   PetscInt          *diag, *odiag, sc;
    7701:   VecScatter         scatter;
    7702:   PetscScalar       *seqv;
    7703:   const PetscScalar *parv;
    7704:   const PetscInt    *ia, *ja;
    7705:   PetscBool          set, flag, done;
    7706:   Mat                AA = mat, A;
    7707:   MPI_Comm           comm;
    7708:   PetscMPIInt        rank, size, tag;
    7709:   MPI_Status         status;
    7710:   PetscContainer     container;
    7711:   EnvelopeData      *edata;
    7712:   Vec                seq, par;
    7713:   IS                 isglobal;

    7715:   PetscFunctionBegin;
    7717:   PetscCall(MatIsSymmetricKnown(mat, &set, &flag));
    7718:   if (!set || !flag) {
    7719:     /* TODO: only needs nonzero structure of transpose */
    7720:     PetscCall(MatTranspose(mat, MAT_INITIAL_MATRIX, &AA));
    7721:     PetscCall(MatAXPY(AA, 1.0, mat, DIFFERENT_NONZERO_PATTERN));
    7722:   }
    7723:   PetscCall(MatAIJGetLocalMat(AA, &A));
    7724:   PetscCall(MatGetRowIJ(A, 0, PETSC_FALSE, PETSC_FALSE, &n, &ia, &ja, &done));
    7725:   PetscCheck(done, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Unable to get IJ structure from matrix");

    7727:   PetscCall(MatGetLocalSize(mat, &n, NULL));
    7728:   PetscCall(PetscObjectGetNewTag((PetscObject)mat, &tag));
    7729:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    7730:   PetscCallMPI(MPI_Comm_size(comm, &size));
    7731:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    7733:   PetscCall(PetscMalloc2(n, &sizes, n, &starts));

    7735:   if (rank > 0) {
    7736:     PetscCallMPI(MPI_Recv(&env, 1, MPIU_INT, rank - 1, tag, comm, &status));
    7737:     PetscCallMPI(MPI_Recv(&tbs, 1, MPIU_INT, rank - 1, tag, comm, &status));
    7738:   }
    7739:   PetscCall(MatGetOwnershipRange(mat, &rstart, NULL));
    7740:   for (i = 0; i < n; i++) {
    7741:     env = PetscMax(env, ja[ia[i + 1] - 1]);
    7742:     II  = rstart + i;
    7743:     if (env == II) {
    7744:       starts[lblocks]  = tbs;
    7745:       sizes[lblocks++] = 1 + II - tbs;
    7746:       tbs              = 1 + II;
    7747:     }
    7748:   }
    7749:   if (rank < size - 1) {
    7750:     PetscCallMPI(MPI_Send(&env, 1, MPIU_INT, rank + 1, tag, comm));
    7751:     PetscCallMPI(MPI_Send(&tbs, 1, MPIU_INT, rank + 1, tag, comm));
    7752:   }

    7754:   PetscCall(MatRestoreRowIJ(A, 0, PETSC_FALSE, PETSC_FALSE, &n, &ia, &ja, &done));
    7755:   if (!set || !flag) PetscCall(MatDestroy(&AA));
    7756:   PetscCall(MatDestroy(&A));

    7758:   PetscCall(PetscNew(&edata));
    7759:   PetscCall(MatGetNonzeroState(mat, &edata->nonzerostate));
    7760:   edata->n = lblocks;
    7761:   /* create IS needed for extracting blocks from the original matrix */
    7762:   PetscCall(PetscMalloc1(lblocks, &edata->is));
    7763:   for (PetscInt i = 0; i < lblocks; i++) PetscCall(ISCreateStride(PETSC_COMM_SELF, sizes[i], starts[i], 1, &edata->is[i]));

    7765:   /* Create the resulting inverse matrix nonzero structure with preallocation information */
    7766:   PetscCall(MatCreate(PetscObjectComm((PetscObject)mat), &edata->C));
    7767:   PetscCall(MatSetSizes(edata->C, mat->rmap->n, mat->cmap->n, mat->rmap->N, mat->cmap->N));
    7768:   PetscCall(MatSetBlockSizesFromMats(edata->C, mat, mat));
    7769:   PetscCall(MatSetType(edata->C, MATAIJ));

    7771:   /* Communicate the start and end of each row, from each block to the correct rank */
    7772:   /* TODO: Use PetscSF instead of VecScatter */
    7773:   for (PetscInt i = 0; i < lblocks; i++) ln += sizes[i];
    7774:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, 2 * ln, &seq));
    7775:   PetscCall(VecGetArrayWrite(seq, &seqv));
    7776:   for (PetscInt i = 0; i < lblocks; i++) {
    7777:     for (PetscInt j = 0; j < sizes[i]; j++) {
    7778:       seqv[cnt]     = starts[i];
    7779:       seqv[cnt + 1] = starts[i] + sizes[i];
    7780:       cnt += 2;
    7781:     }
    7782:   }
    7783:   PetscCall(VecRestoreArrayWrite(seq, &seqv));
    7784:   PetscCallMPI(MPI_Scan(&cnt, &sc, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)mat)));
    7785:   sc -= cnt;
    7786:   PetscCall(VecCreateMPI(PetscObjectComm((PetscObject)mat), 2 * mat->rmap->n, 2 * mat->rmap->N, &par));
    7787:   PetscCall(ISCreateStride(PETSC_COMM_SELF, cnt, sc, 1, &isglobal));
    7788:   PetscCall(VecScatterCreate(seq, NULL, par, isglobal, &scatter));
    7789:   PetscCall(ISDestroy(&isglobal));
    7790:   PetscCall(VecScatterBegin(scatter, seq, par, INSERT_VALUES, SCATTER_FORWARD));
    7791:   PetscCall(VecScatterEnd(scatter, seq, par, INSERT_VALUES, SCATTER_FORWARD));
    7792:   PetscCall(VecScatterDestroy(&scatter));
    7793:   PetscCall(VecDestroy(&seq));
    7794:   PetscCall(MatGetOwnershipRangeColumn(mat, &cstart, &cend));
    7795:   PetscCall(PetscMalloc2(mat->rmap->n, &diag, mat->rmap->n, &odiag));
    7796:   PetscCall(VecGetArrayRead(par, &parv));
    7797:   cnt = 0;
    7798:   PetscCall(MatGetSize(mat, NULL, &n));
    7799:   for (PetscInt i = 0; i < mat->rmap->n; i++) {
    7800:     PetscInt start, end, d = 0, od = 0;

    7802:     start = (PetscInt)PetscRealPart(parv[cnt]);
    7803:     end   = (PetscInt)PetscRealPart(parv[cnt + 1]);
    7804:     cnt += 2;

    7806:     if (start < cstart) {
    7807:       od += cstart - start + n - cend;
    7808:       d += cend - cstart;
    7809:     } else if (start < cend) {
    7810:       od += n - cend;
    7811:       d += cend - start;
    7812:     } else od += n - start;
    7813:     if (end <= cstart) {
    7814:       od -= cstart - end + n - cend;
    7815:       d -= cend - cstart;
    7816:     } else if (end < cend) {
    7817:       od -= n - cend;
    7818:       d -= cend - end;
    7819:     } else od -= n - end;

    7821:     odiag[i] = od;
    7822:     diag[i]  = d;
    7823:   }
    7824:   PetscCall(VecRestoreArrayRead(par, &parv));
    7825:   PetscCall(VecDestroy(&par));
    7826:   PetscCall(MatXAIJSetPreallocation(edata->C, mat->rmap->bs, diag, odiag, NULL, NULL));
    7827:   PetscCall(PetscFree2(diag, odiag));
    7828:   PetscCall(PetscFree2(sizes, starts));

    7830:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    7831:   PetscCall(PetscContainerSetPointer(container, edata));
    7832:   PetscCall(PetscContainerSetCtxDestroy(container, EnvelopeDataDestroy));
    7833:   PetscCall(PetscObjectCompose((PetscObject)mat, "EnvelopeData", (PetscObject)container));
    7834:   PetscCall(PetscObjectDereference((PetscObject)container));
    7835:   PetscFunctionReturn(PETSC_SUCCESS);
    7836: }

    7838: /*@
    7839:   MatInvertVariableBlockEnvelope - set matrix C to be the inverted block diagonal of matrix A

    7841:   Collective

    7843:   Input Parameters:
    7844: + A     - the matrix
    7845: - reuse - indicates if the `C` matrix was obtained from a previous call to this routine

    7847:   Output Parameter:
    7848: . C - matrix with inverted block diagonal of `A`

    7850:   Level: advanced

    7852:   Note:
    7853:   For efficiency the matrix `A` should have all the nonzero entries clustered in smallish blocks along the diagonal.

    7855: .seealso: [](ch_matrices), `Mat`, `MatInvertBlockDiagonal()`, `MatComputeBlockDiagonal()`
    7856: @*/
    7857: PetscErrorCode MatInvertVariableBlockEnvelope(Mat A, MatReuse reuse, Mat *C)
    7858: {
    7859:   PetscContainer   container;
    7860:   EnvelopeData    *edata;
    7861:   PetscObjectState nonzerostate;

    7863:   PetscFunctionBegin;
    7864:   PetscCall(PetscObjectQuery((PetscObject)A, "EnvelopeData", (PetscObject *)&container));
    7865:   if (!container) {
    7866:     PetscCall(MatComputeVariableBlockEnvelope(A));
    7867:     PetscCall(PetscObjectQuery((PetscObject)A, "EnvelopeData", (PetscObject *)&container));
    7868:   }
    7869:   PetscCall(PetscContainerGetPointer(container, (void **)&edata));
    7870:   PetscCall(MatGetNonzeroState(A, &nonzerostate));
    7871:   PetscCheck(nonzerostate <= edata->nonzerostate, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot handle changes to matrix nonzero structure");
    7872:   PetscCheck(reuse != MAT_REUSE_MATRIX || *C == edata->C, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "C matrix must be the same as previously output");

    7874:   PetscCall(MatCreateSubMatrices(A, edata->n, edata->is, edata->is, MAT_INITIAL_MATRIX, &edata->mat));
    7875:   *C = edata->C;

    7877:   for (PetscInt i = 0; i < edata->n; i++) {
    7878:     Mat          D;
    7879:     PetscScalar *dvalues;

    7881:     PetscCall(MatConvert(edata->mat[i], MATSEQDENSE, MAT_INITIAL_MATRIX, &D));
    7882:     PetscCall(MatSetOption(*C, MAT_ROW_ORIENTED, PETSC_FALSE));
    7883:     PetscCall(MatSeqDenseInvert(D));
    7884:     PetscCall(MatDenseGetArray(D, &dvalues));
    7885:     PetscCall(MatSetValuesIS(*C, edata->is[i], edata->is[i], dvalues, INSERT_VALUES));
    7886:     PetscCall(MatDestroy(&D));
    7887:   }
    7888:   PetscCall(MatDestroySubMatrices(edata->n, &edata->mat));
    7889:   PetscCall(MatAssemblyBegin(*C, MAT_FINAL_ASSEMBLY));
    7890:   PetscCall(MatAssemblyEnd(*C, MAT_FINAL_ASSEMBLY));
    7891:   PetscFunctionReturn(PETSC_SUCCESS);
    7892: }

    7894: /*@
    7895:   MatSetVariableBlockSizes - Sets diagonal point-blocks of the matrix that need not be of the same size

    7897:   Not Collective

    7899:   Input Parameters:
    7900: + mat     - the matrix
    7901: . nblocks - the number of blocks on this process, each block can only exist on a single process
    7902: - bsizes  - the block sizes

    7904:   Level: intermediate

    7906:   Notes:
    7907:   Currently used by `PCVPBJACOBI` for `MATAIJ` matrices

    7909:   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.

    7911: .seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSizes()`, `MatGetBlockSizes()`, `MatGetVariableBlockSizes()`,
    7912:           `MatComputeVariableBlockEnvelope()`, `PCVPBJACOBI`
    7913: @*/
    7914: PetscErrorCode MatSetVariableBlockSizes(Mat mat, PetscInt nblocks, const PetscInt bsizes[])
    7915: {
    7916:   PetscInt ncnt = 0, nlocal;

    7918:   PetscFunctionBegin;
    7920:   PetscCall(MatGetLocalSize(mat, &nlocal, NULL));
    7921:   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);
    7922:   for (PetscInt i = 0; i < nblocks; i++) ncnt += bsizes[i];
    7923:   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);
    7924:   PetscCall(PetscFree(mat->bsizes));
    7925:   mat->nblocks = nblocks;
    7926:   PetscCall(PetscMalloc1(nblocks, &mat->bsizes));
    7927:   PetscCall(PetscArraycpy(mat->bsizes, bsizes, nblocks));
    7928:   PetscFunctionReturn(PETSC_SUCCESS);
    7929: }

    7931: /*@C
    7932:   MatGetVariableBlockSizes - Gets a diagonal blocks of the matrix that need not be of the same size

    7934:   Not Collective; No Fortran Support

    7936:   Input Parameter:
    7937: . mat - the matrix

    7939:   Output Parameters:
    7940: + nblocks - the number of blocks on this process
    7941: - bsizes  - the block sizes

    7943:   Level: intermediate

    7945: .seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSizes()`, `MatGetBlockSizes()`, `MatSetVariableBlockSizes()`, `MatComputeVariableBlockEnvelope()`
    7946: @*/
    7947: PetscErrorCode MatGetVariableBlockSizes(Mat mat, PetscInt *nblocks, const PetscInt *bsizes[])
    7948: {
    7949:   PetscFunctionBegin;
    7951:   if (nblocks) *nblocks = mat->nblocks;
    7952:   if (bsizes) *bsizes = mat->bsizes;
    7953:   PetscFunctionReturn(PETSC_SUCCESS);
    7954: }

    7956: /*@
    7957:   MatSelectVariableBlockSizes - When creating a submatrix, pass on the variable block sizes

    7959:   Not Collective

    7961:   Input Parameter:
    7962: + subA  - the submatrix
    7963: . A     - the original matrix
    7964: - isrow - The `IS` of selected rows for the submatrix, must be sorted

    7966:   Level: developer

    7968:   Notes:
    7969:   If the index set is not sorted or contains off-process entries, this function will do nothing.

    7971: .seealso: [](ch_matrices), `Mat`, `MatSetVariableBlockSizes()`, `MatComputeVariableBlockEnvelope()`
    7972: @*/
    7973: PetscErrorCode MatSelectVariableBlockSizes(Mat subA, Mat A, IS isrow)
    7974: {
    7975:   const PetscInt *rows;
    7976:   PetscInt        n, rStart, rEnd, Nb = 0;
    7977:   PetscBool       flg = A->bsizes ? PETSC_TRUE : PETSC_FALSE;

    7979:   PetscFunctionBegin;
    7980:   // The code for block size extraction does not support an unsorted IS
    7981:   if (flg) PetscCall(ISSorted(isrow, &flg));
    7982:   // We don't support originally off-diagonal blocks
    7983:   if (flg) {
    7984:     PetscCall(MatGetOwnershipRange(A, &rStart, &rEnd));
    7985:     PetscCall(ISGetLocalSize(isrow, &n));
    7986:     PetscCall(ISGetIndices(isrow, &rows));
    7987:     for (PetscInt i = 0; i < n && flg; ++i) {
    7988:       if (rows[i] < rStart || rows[i] >= rEnd) flg = PETSC_FALSE;
    7989:     }
    7990:     PetscCall(ISRestoreIndices(isrow, &rows));
    7991:   }
    7992:   // quiet return if we can't extract block size
    7993:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &flg, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)subA)));
    7994:   if (!flg) PetscFunctionReturn(PETSC_SUCCESS);

    7996:   // extract block sizes
    7997:   PetscCall(ISGetIndices(isrow, &rows));
    7998:   for (PetscInt b = 0, gr = rStart, i = 0; b < A->nblocks; ++b) {
    7999:     PetscBool occupied = PETSC_FALSE;

    8001:     for (PetscInt br = 0; br < A->bsizes[b]; ++br) {
    8002:       const PetscInt row = gr + br;

    8004:       if (i == n) break;
    8005:       if (rows[i] == row) {
    8006:         occupied = PETSC_TRUE;
    8007:         ++i;
    8008:       }
    8009:       while (i < n && rows[i] < row) ++i;
    8010:     }
    8011:     gr += A->bsizes[b];
    8012:     if (occupied) ++Nb;
    8013:   }
    8014:   subA->nblocks = Nb;
    8015:   PetscCall(PetscFree(subA->bsizes));
    8016:   PetscCall(PetscMalloc1(subA->nblocks, &subA->bsizes));
    8017:   PetscInt sb = 0;
    8018:   for (PetscInt b = 0, gr = rStart, i = 0; b < A->nblocks; ++b) {
    8019:     if (sb < subA->nblocks) subA->bsizes[sb] = 0;
    8020:     for (PetscInt br = 0; br < A->bsizes[b]; ++br) {
    8021:       const PetscInt row = gr + br;

    8023:       if (i == n) break;
    8024:       if (rows[i] == row) {
    8025:         ++subA->bsizes[sb];
    8026:         ++i;
    8027:       }
    8028:       while (i < n && rows[i] < row) ++i;
    8029:     }
    8030:     gr += A->bsizes[b];
    8031:     if (sb < subA->nblocks && subA->bsizes[sb]) ++sb;
    8032:   }
    8033:   PetscCheck(sb == subA->nblocks, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid number of blocks %" PetscInt_FMT " != %" PetscInt_FMT, sb, subA->nblocks);
    8034:   PetscInt nlocal, ncnt = 0;
    8035:   PetscCall(MatGetLocalSize(subA, &nlocal, NULL));
    8036:   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);
    8037:   for (PetscInt i = 0; i < subA->nblocks; i++) ncnt += subA->bsizes[i];
    8038:   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);
    8039:   PetscCall(ISRestoreIndices(isrow, &rows));
    8040:   PetscFunctionReturn(PETSC_SUCCESS);
    8041: }

    8043: /*@
    8044:   MatSetBlockSizes - Sets the matrix block row and column sizes.

    8046:   Logically Collective

    8048:   Input Parameters:
    8049: + mat - the matrix
    8050: . rbs - row block size
    8051: - cbs - column block size

    8053:   Level: intermediate

    8055:   Notes:
    8056:   Block row formats are `MATBAIJ` and  `MATSBAIJ`. These formats ALWAYS have square block storage in the matrix.
    8057:   If you pass a different block size for the columns than the rows, the row block size determines the square block storage.
    8058:   This must be called before `MatSetUp()` or MatXXXSetPreallocation() (or will default to 1) and the block size cannot be changed later.

    8060:   For `MATAIJ` matrix this function can be called at a later stage, provided that the specified block sizes
    8061:   are compatible with the matrix local sizes.

    8063:   The row and column block size determine the blocksize of the "row" and "column" vectors returned by `MatCreateVecs()`.

    8065: .seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSize()`, `MatGetBlockSizes()`
    8066: @*/
    8067: PetscErrorCode MatSetBlockSizes(Mat mat, PetscInt rbs, PetscInt cbs)
    8068: {
    8069:   PetscFunctionBegin;
    8073:   PetscTryTypeMethod(mat, setblocksizes, rbs, cbs);
    8074:   if (mat->rmap->refcnt) {
    8075:     ISLocalToGlobalMapping l2g  = NULL;
    8076:     PetscLayout            nmap = NULL;

    8078:     PetscCall(PetscLayoutDuplicate(mat->rmap, &nmap));
    8079:     if (mat->rmap->mapping) PetscCall(ISLocalToGlobalMappingDuplicate(mat->rmap->mapping, &l2g));
    8080:     PetscCall(PetscLayoutDestroy(&mat->rmap));
    8081:     mat->rmap          = nmap;
    8082:     mat->rmap->mapping = l2g;
    8083:   }
    8084:   if (mat->cmap->refcnt) {
    8085:     ISLocalToGlobalMapping l2g  = NULL;
    8086:     PetscLayout            nmap = NULL;

    8088:     PetscCall(PetscLayoutDuplicate(mat->cmap, &nmap));
    8089:     if (mat->cmap->mapping) PetscCall(ISLocalToGlobalMappingDuplicate(mat->cmap->mapping, &l2g));
    8090:     PetscCall(PetscLayoutDestroy(&mat->cmap));
    8091:     mat->cmap          = nmap;
    8092:     mat->cmap->mapping = l2g;
    8093:   }
    8094:   PetscCall(PetscLayoutSetBlockSize(mat->rmap, rbs));
    8095:   PetscCall(PetscLayoutSetBlockSize(mat->cmap, cbs));
    8096:   PetscFunctionReturn(PETSC_SUCCESS);
    8097: }

    8099: /*@
    8100:   MatSetBlockSizesFromMats - Sets the matrix block row and column sizes to match a pair of matrices

    8102:   Logically Collective

    8104:   Input Parameters:
    8105: + mat     - the matrix
    8106: . fromRow - matrix from which to copy row block size
    8107: - fromCol - matrix from which to copy column block size (can be same as `fromRow`)

    8109:   Level: developer

    8111: .seealso: [](ch_matrices), `Mat`, `MatCreateSeqBAIJ()`, `MatCreateBAIJ()`, `MatGetBlockSize()`, `MatSetBlockSizes()`
    8112: @*/
    8113: PetscErrorCode MatSetBlockSizesFromMats(Mat mat, Mat fromRow, Mat fromCol)
    8114: {
    8115:   PetscFunctionBegin;
    8119:   PetscTryTypeMethod(mat, setblocksizes, fromRow->rmap->bs, fromCol->cmap->bs);
    8120:   PetscCall(PetscLayoutSetBlockSize(mat->rmap, fromRow->rmap->bs));
    8121:   PetscCall(PetscLayoutSetBlockSize(mat->cmap, fromCol->cmap->bs));
    8122:   PetscFunctionReturn(PETSC_SUCCESS);
    8123: }

    8125: /*@
    8126:   MatResidual - Default routine to calculate the residual r = b - Ax

    8128:   Collective

    8130:   Input Parameters:
    8131: + mat - the matrix
    8132: . b   - the right-hand-side
    8133: - x   - the approximate solution

    8135:   Output Parameter:
    8136: . r - location to store the residual

    8138:   Level: developer

    8140: .seealso: [](ch_matrices), `Mat`, `MatMult()`, `MatMultAdd()`, `PCMGSetResidual()`
    8141: @*/
    8142: PetscErrorCode MatResidual(Mat mat, Vec b, Vec x, Vec r)
    8143: {
    8144:   PetscFunctionBegin;
    8150:   MatCheckPreallocated(mat, 1);
    8151:   PetscCall(PetscLogEventBegin(MAT_Residual, mat, 0, 0, 0));
    8152:   if (!mat->ops->residual) {
    8153:     PetscCall(MatMult(mat, x, r));
    8154:     PetscCall(VecAYPX(r, -1.0, b));
    8155:   } else {
    8156:     PetscUseTypeMethod(mat, residual, b, x, r);
    8157:   }
    8158:   PetscCall(PetscLogEventEnd(MAT_Residual, mat, 0, 0, 0));
    8159:   PetscFunctionReturn(PETSC_SUCCESS);
    8160: }

    8162: /*@C
    8163:   MatGetRowIJ - Returns the compressed row storage i and j indices for the local rows of a sparse matrix

    8165:   Collective

    8167:   Input Parameters:
    8168: + mat             - the matrix
    8169: . shift           - 0 or 1 indicating we want the indices starting at 0 or 1
    8170: . symmetric       - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be symmetrized
    8171: - inodecompressed - `PETSC_TRUE` or `PETSC_FALSE`  indicating if the nonzero structure of the
    8172:                  inodes or the nonzero elements is wanted. For `MATBAIJ` matrices the compressed version is
    8173:                  always used.

    8175:   Output Parameters:
    8176: + n    - number of local rows in the (possibly compressed) matrix, use `NULL` if not needed
    8177: . 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
    8178: . ja   - the column indices, use `NULL` if not needed
    8179: - done - indicates if the routine actually worked and returned appropriate ia[] and ja[] arrays; callers
    8180:            are responsible for handling the case when done == `PETSC_FALSE` and ia and ja are not set

    8182:   Level: developer

    8184:   Notes:
    8185:   You CANNOT change any of the ia[] or ja[] values.

    8187:   Use `MatRestoreRowIJ()` when you are finished accessing the ia[] and ja[] values.

    8189:   Fortran Notes:
    8190:   Use
    8191: .vb
    8192:     PetscInt, pointer :: ia(:),ja(:)
    8193:     call MatGetRowIJ(mat,shift,symmetric,inodecompressed,n,ia,ja,done,ierr)
    8194:     ! Access the ith and jth entries via ia(i) and ja(j)
    8195: .ve

    8197: .seealso: [](ch_matrices), `Mat`, `MATAIJ`, `MatGetColumnIJ()`, `MatRestoreRowIJ()`, `MatSeqAIJGetArray()`
    8198: @*/
    8199: PetscErrorCode MatGetRowIJ(Mat mat, PetscInt shift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    8200: {
    8201:   PetscFunctionBegin;
    8204:   if (n) PetscAssertPointer(n, 5);
    8205:   if (ia) PetscAssertPointer(ia, 6);
    8206:   if (ja) PetscAssertPointer(ja, 7);
    8207:   if (done) PetscAssertPointer(done, 8);
    8208:   MatCheckPreallocated(mat, 1);
    8209:   if (!mat->ops->getrowij && done) *done = PETSC_FALSE;
    8210:   else {
    8211:     if (done) *done = PETSC_TRUE;
    8212:     PetscCall(PetscLogEventBegin(MAT_GetRowIJ, mat, 0, 0, 0));
    8213:     PetscUseTypeMethod(mat, getrowij, shift, symmetric, inodecompressed, n, ia, ja, done);
    8214:     PetscCall(PetscLogEventEnd(MAT_GetRowIJ, mat, 0, 0, 0));
    8215:   }
    8216:   PetscFunctionReturn(PETSC_SUCCESS);
    8217: }

    8219: /*@C
    8220:   MatGetColumnIJ - Returns the compressed column storage i and j indices for sequential matrices.

    8222:   Collective

    8224:   Input Parameters:
    8225: + mat             - the matrix
    8226: . shift           - 1 or zero indicating we want the indices starting at 0 or 1
    8227: . symmetric       - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be
    8228:                 symmetrized
    8229: - inodecompressed - `PETSC_TRUE` or `PETSC_FALSE` indicating if the nonzero structure of the
    8230:                  inodes or the nonzero elements is wanted. For `MATBAIJ` matrices the compressed version is
    8231:                  always used.

    8233:   Output Parameters:
    8234: + n    - number of columns in the (possibly compressed) matrix
    8235: . ia   - the column pointers; that is ia[0] = 0, ia[col] = i[col-1] + number of elements in that col of the matrix
    8236: . ja   - the row indices
    8237: - done - `PETSC_TRUE` or `PETSC_FALSE`, indicating whether the values have been returned

    8239:   Level: developer

    8241: .seealso: [](ch_matrices), `Mat`, `MatGetRowIJ()`, `MatRestoreColumnIJ()`
    8242: @*/
    8243: PetscErrorCode MatGetColumnIJ(Mat mat, PetscInt shift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    8244: {
    8245:   PetscFunctionBegin;
    8248:   PetscAssertPointer(n, 5);
    8249:   if (ia) PetscAssertPointer(ia, 6);
    8250:   if (ja) PetscAssertPointer(ja, 7);
    8251:   PetscAssertPointer(done, 8);
    8252:   MatCheckPreallocated(mat, 1);
    8253:   if (!mat->ops->getcolumnij) *done = PETSC_FALSE;
    8254:   else {
    8255:     *done = PETSC_TRUE;
    8256:     PetscUseTypeMethod(mat, getcolumnij, shift, symmetric, inodecompressed, n, ia, ja, done);
    8257:   }
    8258:   PetscFunctionReturn(PETSC_SUCCESS);
    8259: }

    8261: /*@C
    8262:   MatRestoreRowIJ - Call after you are completed with the ia,ja indices obtained with `MatGetRowIJ()`.

    8264:   Collective

    8266:   Input Parameters:
    8267: + mat             - the matrix
    8268: . shift           - 1 or zero indicating we want the indices starting at 0 or 1
    8269: . symmetric       - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be symmetrized
    8270: . inodecompressed - `PETSC_TRUE` or `PETSC_FALSE` indicating if the nonzero structure of the
    8271:                     inodes or the nonzero elements is wanted. For `MATBAIJ` matrices the compressed version is
    8272:                     always used.
    8273: . n               - size of (possibly compressed) matrix
    8274: . ia              - the row pointers
    8275: - ja              - the column indices

    8277:   Output Parameter:
    8278: . done - `PETSC_TRUE` or `PETSC_FALSE` indicated that the values have been returned

    8280:   Level: developer

    8282:   Note:
    8283:   This routine zeros out `n`, `ia`, and `ja`. This is to prevent accidental
    8284:   us of the array after it has been restored. If you pass `NULL`, it will
    8285:   not zero the pointers.  Use of ia or ja after `MatRestoreRowIJ()` is invalid.

    8287: .seealso: [](ch_matrices), `Mat`, `MatGetRowIJ()`, `MatRestoreColumnIJ()`
    8288: @*/
    8289: PetscErrorCode MatRestoreRowIJ(Mat mat, PetscInt shift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    8290: {
    8291:   PetscFunctionBegin;
    8294:   if (ia) PetscAssertPointer(ia, 6);
    8295:   if (ja) PetscAssertPointer(ja, 7);
    8296:   if (done) PetscAssertPointer(done, 8);
    8297:   MatCheckPreallocated(mat, 1);

    8299:   if (!mat->ops->restorerowij && done) *done = PETSC_FALSE;
    8300:   else {
    8301:     if (done) *done = PETSC_TRUE;
    8302:     PetscUseTypeMethod(mat, restorerowij, shift, symmetric, inodecompressed, n, ia, ja, done);
    8303:     if (n) *n = 0;
    8304:     if (ia) *ia = NULL;
    8305:     if (ja) *ja = NULL;
    8306:   }
    8307:   PetscFunctionReturn(PETSC_SUCCESS);
    8308: }

    8310: /*@C
    8311:   MatRestoreColumnIJ - Call after you are completed with the ia,ja indices obtained with `MatGetColumnIJ()`.

    8313:   Collective

    8315:   Input Parameters:
    8316: + mat             - the matrix
    8317: . shift           - 1 or zero indicating we want the indices starting at 0 or 1
    8318: . symmetric       - `PETSC_TRUE` or `PETSC_FALSE` indicating the matrix data structure should be symmetrized
    8319: - inodecompressed - `PETSC_TRUE` or `PETSC_FALSE` indicating if the nonzero structure of the
    8320:                     inodes or the nonzero elements is wanted. For `MATBAIJ` matrices the compressed version is
    8321:                     always used.

    8323:   Output Parameters:
    8324: + n    - size of (possibly compressed) matrix
    8325: . ia   - the column pointers
    8326: . ja   - the row indices
    8327: - done - `PETSC_TRUE` or `PETSC_FALSE` indicated that the values have been returned

    8329:   Level: developer

    8331: .seealso: [](ch_matrices), `Mat`, `MatGetColumnIJ()`, `MatRestoreRowIJ()`
    8332: @*/
    8333: PetscErrorCode MatRestoreColumnIJ(Mat mat, PetscInt shift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *n, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    8334: {
    8335:   PetscFunctionBegin;
    8338:   if (ia) PetscAssertPointer(ia, 6);
    8339:   if (ja) PetscAssertPointer(ja, 7);
    8340:   PetscAssertPointer(done, 8);
    8341:   MatCheckPreallocated(mat, 1);

    8343:   if (!mat->ops->restorecolumnij) *done = PETSC_FALSE;
    8344:   else {
    8345:     *done = PETSC_TRUE;
    8346:     PetscUseTypeMethod(mat, restorecolumnij, shift, symmetric, inodecompressed, n, ia, ja, done);
    8347:     if (n) *n = 0;
    8348:     if (ia) *ia = NULL;
    8349:     if (ja) *ja = NULL;
    8350:   }
    8351:   PetscFunctionReturn(PETSC_SUCCESS);
    8352: }

    8354: /*@
    8355:   MatColoringPatch - Used inside matrix coloring routines that use `MatGetRowIJ()` and/or
    8356:   `MatGetColumnIJ()`.

    8358:   Collective

    8360:   Input Parameters:
    8361: + mat        - the matrix
    8362: . ncolors    - maximum color value
    8363: . n          - number of entries in colorarray
    8364: - colorarray - array indicating color for each column

    8366:   Output Parameter:
    8367: . iscoloring - coloring generated using colorarray information

    8369:   Level: developer

    8371: .seealso: [](ch_matrices), `Mat`, `MatGetRowIJ()`, `MatGetColumnIJ()`
    8372: @*/
    8373: PetscErrorCode MatColoringPatch(Mat mat, PetscInt ncolors, PetscInt n, ISColoringValue colorarray[], ISColoring *iscoloring)
    8374: {
    8375:   PetscFunctionBegin;
    8378:   PetscAssertPointer(colorarray, 4);
    8379:   PetscAssertPointer(iscoloring, 5);
    8380:   MatCheckPreallocated(mat, 1);

    8382:   if (!mat->ops->coloringpatch) {
    8383:     PetscCall(ISColoringCreate(PetscObjectComm((PetscObject)mat), ncolors, n, colorarray, PETSC_OWN_POINTER, iscoloring));
    8384:   } else {
    8385:     PetscUseTypeMethod(mat, coloringpatch, ncolors, n, colorarray, iscoloring);
    8386:   }
    8387:   PetscFunctionReturn(PETSC_SUCCESS);
    8388: }

    8390: /*@
    8391:   MatSetUnfactored - Resets a factored matrix to be treated as unfactored.

    8393:   Logically Collective

    8395:   Input Parameter:
    8396: . mat - the factored matrix to be reset

    8398:   Level: developer

    8400:   Notes:
    8401:   This routine should be used only with factored matrices formed by in-place
    8402:   factorization via ILU(0) (or by in-place LU factorization for the `MATSEQDENSE`
    8403:   format).  This option can save memory, for example, when solving nonlinear
    8404:   systems with a matrix-free Newton-Krylov method and a matrix-based, in-place
    8405:   ILU(0) preconditioner.

    8407:   One can specify in-place ILU(0) factorization by calling
    8408: .vb
    8409:      PCType(pc,PCILU);
    8410:      PCFactorSeUseInPlace(pc);
    8411: .ve
    8412:   or by using the options -pc_type ilu -pc_factor_in_place

    8414:   In-place factorization ILU(0) can also be used as a local
    8415:   solver for the blocks within the block Jacobi or additive Schwarz
    8416:   methods (runtime option: -sub_pc_factor_in_place).  See Users-Manual: ch_pc
    8417:   for details on setting local solver options.

    8419:   Most users should employ the `KSP` interface for linear solvers
    8420:   instead of working directly with matrix algebra routines such as this.
    8421:   See, e.g., `KSPCreate()`.

    8423: .seealso: [](ch_matrices), `Mat`, `PCFactorSetUseInPlace()`, `PCFactorGetUseInPlace()`
    8424: @*/
    8425: PetscErrorCode MatSetUnfactored(Mat mat)
    8426: {
    8427:   PetscFunctionBegin;
    8430:   MatCheckPreallocated(mat, 1);
    8431:   mat->factortype = MAT_FACTOR_NONE;
    8432:   if (!mat->ops->setunfactored) PetscFunctionReturn(PETSC_SUCCESS);
    8433:   PetscUseTypeMethod(mat, setunfactored);
    8434:   PetscFunctionReturn(PETSC_SUCCESS);
    8435: }

    8437: /*@
    8438:   MatCreateSubMatrix - Gets a single submatrix on the same number of processors
    8439:   as the original matrix.

    8441:   Collective

    8443:   Input Parameters:
    8444: + mat   - the original matrix
    8445: . isrow - parallel `IS` containing the rows this processor should obtain
    8446: . 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.
    8447: - cll   - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    8449:   Output Parameter:
    8450: . newmat - the new submatrix, of the same type as the original matrix

    8452:   Level: advanced

    8454:   Notes:
    8455:   The submatrix will be able to be multiplied with vectors using the same layout as `iscol`.

    8457:   Some matrix types place restrictions on the row and column indices, such
    8458:   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;
    8459:   for example, if the block size is 3 one cannot select the 0 and 2 rows without selecting the 1 row.

    8461:   The index sets may not have duplicate entries.

    8463:   The first time this is called you should use a cll of `MAT_INITIAL_MATRIX`,
    8464:   the `MatCreateSubMatrix()` routine will create the newmat for you. Any additional calls
    8465:   to this routine with a mat of the same nonzero structure and with a call of `MAT_REUSE_MATRIX`
    8466:   will reuse the matrix generated the first time.  You should call `MatDestroy()` on `newmat` when
    8467:   you are finished using it.

    8469:   The communicator of the newly obtained matrix is ALWAYS the same as the communicator of
    8470:   the input matrix.

    8472:   If `iscol` is `NULL` then all columns are obtained (not supported in Fortran).

    8474:   If `isrow` and `iscol` have a nontrivial block-size, then the resulting matrix has this block-size as well. This feature
    8475:   is used by `PCFIELDSPLIT` to allow easy nesting of its use.

    8477:   Example usage:
    8478:   Consider the following 8x8 matrix with 34 non-zero values, that is
    8479:   assembled across 3 processors. Let's assume that proc0 owns 3 rows,
    8480:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    8481:   as follows
    8482: .vb
    8483:             1  2  0  |  0  3  0  |  0  4
    8484:     Proc0   0  5  6  |  7  0  0  |  8  0
    8485:             9  0 10  | 11  0  0  | 12  0
    8486:     -------------------------------------
    8487:            13  0 14  | 15 16 17  |  0  0
    8488:     Proc1   0 18  0  | 19 20 21  |  0  0
    8489:             0  0  0  | 22 23  0  | 24  0
    8490:     -------------------------------------
    8491:     Proc2  25 26 27  |  0  0 28  | 29  0
    8492:            30  0  0  | 31 32 33  |  0 34
    8493: .ve

    8495:   Suppose `isrow` = [0 1 | 4 | 6 7] and `iscol` = [1 2 | 3 4 5 | 6].  The resulting submatrix is

    8497: .vb
    8498:             2  0  |  0  3  0  |  0
    8499:     Proc0   5  6  |  7  0  0  |  8
    8500:     -------------------------------
    8501:     Proc1  18  0  | 19 20 21  |  0
    8502:     -------------------------------
    8503:     Proc2  26 27  |  0  0 28  | 29
    8504:             0  0  | 31 32 33  |  0
    8505: .ve

    8507: .seealso: [](ch_matrices), `Mat`, `MatCreateSubMatrices()`, `MatCreateSubMatricesMPI()`, `MatCreateSubMatrixVirtual()`, `MatSubMatrixVirtualUpdate()`
    8508: @*/
    8509: PetscErrorCode MatCreateSubMatrix(Mat mat, IS isrow, IS iscol, MatReuse cll, Mat *newmat)
    8510: {
    8511:   PetscMPIInt size;
    8512:   Mat        *local;
    8513:   IS          iscoltmp;
    8514:   PetscBool   flg;

    8516:   PetscFunctionBegin;
    8520:   PetscAssertPointer(newmat, 5);
    8523:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    8524:   PetscCheck(cll != MAT_IGNORE_MATRIX, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot use MAT_IGNORE_MATRIX");
    8525:   PetscCheck(cll != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Cannot use MAT_INPLACE_MATRIX");

    8527:   MatCheckPreallocated(mat, 1);
    8528:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));

    8530:   if (!iscol || isrow == iscol) {
    8531:     PetscBool   stride;
    8532:     PetscMPIInt grabentirematrix = 0, grab;
    8533:     PetscCall(PetscObjectTypeCompare((PetscObject)isrow, ISSTRIDE, &stride));
    8534:     if (stride) {
    8535:       PetscInt first, step, n, rstart, rend;
    8536:       PetscCall(ISStrideGetInfo(isrow, &first, &step));
    8537:       if (step == 1) {
    8538:         PetscCall(MatGetOwnershipRange(mat, &rstart, &rend));
    8539:         if (rstart == first) {
    8540:           PetscCall(ISGetLocalSize(isrow, &n));
    8541:           if (n == rend - rstart) grabentirematrix = 1;
    8542:         }
    8543:       }
    8544:     }
    8545:     PetscCallMPI(MPIU_Allreduce(&grabentirematrix, &grab, 1, MPI_INT, MPI_MIN, PetscObjectComm((PetscObject)mat)));
    8546:     if (grab) {
    8547:       PetscCall(PetscInfo(mat, "Getting entire matrix as submatrix\n"));
    8548:       if (cll == MAT_INITIAL_MATRIX) {
    8549:         *newmat = mat;
    8550:         PetscCall(PetscObjectReference((PetscObject)mat));
    8551:       }
    8552:       PetscFunctionReturn(PETSC_SUCCESS);
    8553:     }
    8554:   }

    8556:   if (!iscol) {
    8557:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), mat->cmap->n, mat->cmap->rstart, 1, &iscoltmp));
    8558:   } else {
    8559:     iscoltmp = iscol;
    8560:   }

    8562:   /* if original matrix is on just one processor then use submatrix generated */
    8563:   if (mat->ops->createsubmatrices && !mat->ops->createsubmatrix && size == 1 && cll == MAT_REUSE_MATRIX) {
    8564:     PetscCall(MatCreateSubMatrices(mat, 1, &isrow, &iscoltmp, MAT_REUSE_MATRIX, &newmat));
    8565:     goto setproperties;
    8566:   } else if (mat->ops->createsubmatrices && !mat->ops->createsubmatrix && size == 1) {
    8567:     PetscCall(MatCreateSubMatrices(mat, 1, &isrow, &iscoltmp, MAT_INITIAL_MATRIX, &local));
    8568:     *newmat = *local;
    8569:     PetscCall(PetscFree(local));
    8570:     goto setproperties;
    8571:   } else if (!mat->ops->createsubmatrix) {
    8572:     /* Create a new matrix type that implements the operation using the full matrix */
    8573:     PetscCall(PetscLogEventBegin(MAT_CreateSubMat, mat, 0, 0, 0));
    8574:     switch (cll) {
    8575:     case MAT_INITIAL_MATRIX:
    8576:       PetscCall(MatCreateSubMatrixVirtual(mat, isrow, iscoltmp, newmat));
    8577:       break;
    8578:     case MAT_REUSE_MATRIX:
    8579:       PetscCall(MatSubMatrixVirtualUpdate(*newmat, mat, isrow, iscoltmp));
    8580:       break;
    8581:     default:
    8582:       SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "Invalid MatReuse, must be either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX");
    8583:     }
    8584:     PetscCall(PetscLogEventEnd(MAT_CreateSubMat, mat, 0, 0, 0));
    8585:     goto setproperties;
    8586:   }

    8588:   PetscCall(PetscLogEventBegin(MAT_CreateSubMat, mat, 0, 0, 0));
    8589:   PetscUseTypeMethod(mat, createsubmatrix, isrow, iscoltmp, cll, newmat);
    8590:   PetscCall(PetscLogEventEnd(MAT_CreateSubMat, mat, 0, 0, 0));

    8592: setproperties:
    8593:   if ((*newmat)->symmetric == PETSC_BOOL3_UNKNOWN && (*newmat)->structurally_symmetric == PETSC_BOOL3_UNKNOWN && (*newmat)->spd == PETSC_BOOL3_UNKNOWN && (*newmat)->hermitian == PETSC_BOOL3_UNKNOWN) {
    8594:     PetscCall(ISEqualUnsorted(isrow, iscoltmp, &flg));
    8595:     if (flg) PetscCall(MatPropagateSymmetryOptions(mat, *newmat));
    8596:   }
    8597:   if (!iscol) PetscCall(ISDestroy(&iscoltmp));
    8598:   if (*newmat && cll == MAT_INITIAL_MATRIX) PetscCall(PetscObjectStateIncrease((PetscObject)*newmat));
    8599:   if (!iscol || isrow == iscol) PetscCall(MatSelectVariableBlockSizes(*newmat, mat, isrow));
    8600:   PetscFunctionReturn(PETSC_SUCCESS);
    8601: }

    8603: /*@
    8604:   MatPropagateSymmetryOptions - Propagates symmetry options set on a matrix to another matrix

    8606:   Not Collective

    8608:   Input Parameters:
    8609: + A - the matrix we wish to propagate options from
    8610: - B - the matrix we wish to propagate options to

    8612:   Level: beginner

    8614:   Note:
    8615:   Propagates the options associated to `MAT_SYMMETRY_ETERNAL`, `MAT_STRUCTURALLY_SYMMETRIC`, `MAT_HERMITIAN`, `MAT_SPD`, `MAT_SYMMETRIC`, and `MAT_STRUCTURAL_SYMMETRY_ETERNAL`

    8617: .seealso: [](ch_matrices), `Mat`, `MatSetOption()`, `MatIsSymmetricKnown()`, `MatIsSPDKnown()`, `MatIsHermitianKnown()`, `MatIsStructurallySymmetricKnown()`
    8618: @*/
    8619: PetscErrorCode MatPropagateSymmetryOptions(Mat A, Mat B)
    8620: {
    8621:   PetscFunctionBegin;
    8624:   B->symmetry_eternal            = A->symmetry_eternal;
    8625:   B->structural_symmetry_eternal = A->structural_symmetry_eternal;
    8626:   B->symmetric                   = A->symmetric;
    8627:   B->structurally_symmetric      = A->structurally_symmetric;
    8628:   B->spd                         = A->spd;
    8629:   B->hermitian                   = A->hermitian;
    8630:   PetscFunctionReturn(PETSC_SUCCESS);
    8631: }

    8633: /*@
    8634:   MatStashSetInitialSize - sets the sizes of the matrix stash, that is
    8635:   used during the assembly process to store values that belong to
    8636:   other processors.

    8638:   Not Collective

    8640:   Input Parameters:
    8641: + mat   - the matrix
    8642: . size  - the initial size of the stash.
    8643: - bsize - the initial size of the block-stash(if used).

    8645:   Options Database Keys:
    8646: + -matstash_initial_size <size> or <size0,size1,...sizep-1>            - set initial size
    8647: - -matstash_block_initial_size <bsize>  or <bsize0,bsize1,...bsizep-1> - set initial block size

    8649:   Level: intermediate

    8651:   Notes:
    8652:   The block-stash is used for values set with `MatSetValuesBlocked()` while
    8653:   the stash is used for values set with `MatSetValues()`

    8655:   Run with the option -info and look for output of the form
    8656:   MatAssemblyBegin_MPIXXX:Stash has MM entries, uses nn mallocs.
    8657:   to determine the appropriate value, MM, to use for size and
    8658:   MatAssemblyBegin_MPIXXX:Block-Stash has BMM entries, uses nn mallocs.
    8659:   to determine the value, BMM to use for bsize

    8661: .seealso: [](ch_matrices), `MatAssemblyBegin()`, `MatAssemblyEnd()`, `Mat`, `MatStashGetInfo()`
    8662: @*/
    8663: PetscErrorCode MatStashSetInitialSize(Mat mat, PetscInt size, PetscInt bsize)
    8664: {
    8665:   PetscFunctionBegin;
    8668:   PetscCall(MatStashSetInitialSize_Private(&mat->stash, size));
    8669:   PetscCall(MatStashSetInitialSize_Private(&mat->bstash, bsize));
    8670:   PetscFunctionReturn(PETSC_SUCCESS);
    8671: }

    8673: /*@
    8674:   MatInterpolateAdd - $w = y + A*x$ or $A^T*x$ depending on the shape of
    8675:   the matrix

    8677:   Neighbor-wise Collective

    8679:   Input Parameters:
    8680: + A - the matrix
    8681: . x - the vector to be multiplied by the interpolation operator
    8682: - y - the vector to be added to the result

    8684:   Output Parameter:
    8685: . w - the resulting vector

    8687:   Level: intermediate

    8689:   Notes:
    8690:   `w` may be the same vector as `y`.

    8692:   This allows one to use either the restriction or interpolation (its transpose)
    8693:   matrix to do the interpolation

    8695: .seealso: [](ch_matrices), `Mat`, `MatMultAdd()`, `MatMultTransposeAdd()`, `MatRestrict()`, `PCMG`
    8696: @*/
    8697: PetscErrorCode MatInterpolateAdd(Mat A, Vec x, Vec y, Vec w)
    8698: {
    8699:   PetscInt M, N, Ny;

    8701:   PetscFunctionBegin;
    8706:   PetscCall(MatGetSize(A, &M, &N));
    8707:   PetscCall(VecGetSize(y, &Ny));
    8708:   if (M == Ny) {
    8709:     PetscCall(MatMultAdd(A, x, y, w));
    8710:   } else {
    8711:     PetscCall(MatMultTransposeAdd(A, x, y, w));
    8712:   }
    8713:   PetscFunctionReturn(PETSC_SUCCESS);
    8714: }

    8716: /*@
    8717:   MatInterpolate - $y = A*x$ or $A^T*x$ depending on the shape of
    8718:   the matrix

    8720:   Neighbor-wise Collective

    8722:   Input Parameters:
    8723: + A - the matrix
    8724: - x - the vector to be interpolated

    8726:   Output Parameter:
    8727: . y - the resulting vector

    8729:   Level: intermediate

    8731:   Note:
    8732:   This allows one to use either the restriction or interpolation (its transpose)
    8733:   matrix to do the interpolation

    8735: .seealso: [](ch_matrices), `Mat`, `MatMultAdd()`, `MatMultTransposeAdd()`, `MatRestrict()`, `PCMG`
    8736: @*/
    8737: PetscErrorCode MatInterpolate(Mat A, Vec x, Vec y)
    8738: {
    8739:   PetscInt M, N, Ny;

    8741:   PetscFunctionBegin;
    8745:   PetscCall(MatGetSize(A, &M, &N));
    8746:   PetscCall(VecGetSize(y, &Ny));
    8747:   if (M == Ny) {
    8748:     PetscCall(MatMult(A, x, y));
    8749:   } else {
    8750:     PetscCall(MatMultTranspose(A, x, y));
    8751:   }
    8752:   PetscFunctionReturn(PETSC_SUCCESS);
    8753: }

    8755: /*@
    8756:   MatRestrict - $y = A*x$ or $A^T*x$

    8758:   Neighbor-wise Collective

    8760:   Input Parameters:
    8761: + A - the matrix
    8762: - x - the vector to be restricted

    8764:   Output Parameter:
    8765: . y - the resulting vector

    8767:   Level: intermediate

    8769:   Note:
    8770:   This allows one to use either the restriction or interpolation (its transpose)
    8771:   matrix to do the restriction

    8773: .seealso: [](ch_matrices), `Mat`, `MatMultAdd()`, `MatMultTransposeAdd()`, `MatInterpolate()`, `PCMG`
    8774: @*/
    8775: PetscErrorCode MatRestrict(Mat A, Vec x, Vec y)
    8776: {
    8777:   PetscInt M, N, Nx;

    8779:   PetscFunctionBegin;
    8783:   PetscCall(MatGetSize(A, &M, &N));
    8784:   PetscCall(VecGetSize(x, &Nx));
    8785:   if (M == Nx) {
    8786:     PetscCall(MatMultTranspose(A, x, y));
    8787:   } else {
    8788:     PetscCall(MatMult(A, x, y));
    8789:   }
    8790:   PetscFunctionReturn(PETSC_SUCCESS);
    8791: }

    8793: /*@
    8794:   MatMatInterpolateAdd - $Y = W + A*X$ or $W + A^T*X$ depending on the shape of `A`

    8796:   Neighbor-wise Collective

    8798:   Input Parameters:
    8799: + A - the matrix
    8800: . x - the input dense matrix to be multiplied
    8801: - w - the input dense matrix to be added to the result

    8803:   Output Parameter:
    8804: . y - the output dense matrix

    8806:   Level: intermediate

    8808:   Note:
    8809:   This allows one to use either the restriction or interpolation (its transpose)
    8810:   matrix to do the interpolation. `y` matrix can be reused if already created with the proper sizes,
    8811:   otherwise it will be recreated. `y` must be initialized to `NULL` if not supplied.

    8813: .seealso: [](ch_matrices), `Mat`, `MatInterpolateAdd()`, `MatMatInterpolate()`, `MatMatRestrict()`, `PCMG`
    8814: @*/
    8815: PetscErrorCode MatMatInterpolateAdd(Mat A, Mat x, Mat w, Mat *y)
    8816: {
    8817:   PetscInt  M, N, Mx, Nx, Mo, My = 0, Ny = 0;
    8818:   PetscBool trans = PETSC_TRUE;
    8819:   MatReuse  reuse = MAT_INITIAL_MATRIX;

    8821:   PetscFunctionBegin;
    8827:   PetscCall(MatGetSize(A, &M, &N));
    8828:   PetscCall(MatGetSize(x, &Mx, &Nx));
    8829:   if (N == Mx) trans = PETSC_FALSE;
    8830:   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);
    8831:   Mo = trans ? N : M;
    8832:   if (*y) {
    8833:     PetscCall(MatGetSize(*y, &My, &Ny));
    8834:     if (Mo == My && Nx == Ny) {
    8835:       reuse = MAT_REUSE_MATRIX;
    8836:     } else {
    8837:       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);
    8838:       PetscCall(MatDestroy(y));
    8839:     }
    8840:   }

    8842:   if (w && *y == w) { /* this is to minimize changes in PCMG */
    8843:     PetscBool flg;

    8845:     PetscCall(PetscObjectQuery((PetscObject)*y, "__MatMatIntAdd_w", (PetscObject *)&w));
    8846:     if (w) {
    8847:       PetscInt My, Ny, Mw, Nw;

    8849:       PetscCall(PetscObjectTypeCompare((PetscObject)*y, ((PetscObject)w)->type_name, &flg));
    8850:       PetscCall(MatGetSize(*y, &My, &Ny));
    8851:       PetscCall(MatGetSize(w, &Mw, &Nw));
    8852:       if (!flg || My != Mw || Ny != Nw) w = NULL;
    8853:     }
    8854:     if (!w) {
    8855:       PetscCall(MatDuplicate(*y, MAT_COPY_VALUES, &w));
    8856:       PetscCall(PetscObjectCompose((PetscObject)*y, "__MatMatIntAdd_w", (PetscObject)w));
    8857:       PetscCall(PetscObjectDereference((PetscObject)w));
    8858:     } else {
    8859:       PetscCall(MatCopy(*y, w, UNKNOWN_NONZERO_PATTERN));
    8860:     }
    8861:   }
    8862:   if (!trans) {
    8863:     PetscCall(MatMatMult(A, x, reuse, PETSC_DETERMINE, y));
    8864:   } else {
    8865:     PetscCall(MatTransposeMatMult(A, x, reuse, PETSC_DETERMINE, y));
    8866:   }
    8867:   if (w) PetscCall(MatAXPY(*y, 1.0, w, UNKNOWN_NONZERO_PATTERN));
    8868:   PetscFunctionReturn(PETSC_SUCCESS);
    8869: }

    8871: /*@
    8872:   MatMatInterpolate - $Y = A*X$ or $A^T*X$ depending on the shape of `A`

    8874:   Neighbor-wise Collective

    8876:   Input Parameters:
    8877: + A - the matrix
    8878: - x - the input dense matrix

    8880:   Output Parameter:
    8881: . y - the output dense matrix

    8883:   Level: intermediate

    8885:   Note:
    8886:   This allows one to use either the restriction or interpolation (its transpose)
    8887:   matrix to do the interpolation. `y` matrix can be reused if already created with the proper sizes,
    8888:   otherwise it will be recreated. `y` must be initialized to `NULL` if not supplied.

    8890: .seealso: [](ch_matrices), `Mat`, `MatInterpolate()`, `MatRestrict()`, `MatMatRestrict()`, `PCMG`
    8891: @*/
    8892: PetscErrorCode MatMatInterpolate(Mat A, Mat x, Mat *y)
    8893: {
    8894:   PetscFunctionBegin;
    8895:   PetscCall(MatMatInterpolateAdd(A, x, NULL, y));
    8896:   PetscFunctionReturn(PETSC_SUCCESS);
    8897: }

    8899: /*@
    8900:   MatMatRestrict - $Y = A*X$ or $A^T*X$ depending on the shape of `A`

    8902:   Neighbor-wise Collective

    8904:   Input Parameters:
    8905: + A - the matrix
    8906: - x - the input dense matrix

    8908:   Output Parameter:
    8909: . y - the output dense matrix

    8911:   Level: intermediate

    8913:   Note:
    8914:   This allows one to use either the restriction or interpolation (its transpose)
    8915:   matrix to do the restriction. `y` matrix can be reused if already created with the proper sizes,
    8916:   otherwise it will be recreated. `y` must be initialized to `NULL` if not supplied.

    8918: .seealso: [](ch_matrices), `Mat`, `MatRestrict()`, `MatInterpolate()`, `MatMatInterpolate()`, `PCMG`
    8919: @*/
    8920: PetscErrorCode MatMatRestrict(Mat A, Mat x, Mat *y)
    8921: {
    8922:   PetscFunctionBegin;
    8923:   PetscCall(MatMatInterpolateAdd(A, x, NULL, y));
    8924:   PetscFunctionReturn(PETSC_SUCCESS);
    8925: }

    8927: /*@
    8928:   MatGetNullSpace - retrieves the null space of a matrix.

    8930:   Logically Collective

    8932:   Input Parameters:
    8933: + mat    - the matrix
    8934: - nullsp - the null space object

    8936:   Level: developer

    8938: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatSetNullSpace()`, `MatNullSpace`
    8939: @*/
    8940: PetscErrorCode MatGetNullSpace(Mat mat, MatNullSpace *nullsp)
    8941: {
    8942:   PetscFunctionBegin;
    8944:   PetscAssertPointer(nullsp, 2);
    8945:   *nullsp = (mat->symmetric == PETSC_BOOL3_TRUE && !mat->nullsp) ? mat->transnullsp : mat->nullsp;
    8946:   PetscFunctionReturn(PETSC_SUCCESS);
    8947: }

    8949: /*@C
    8950:   MatGetNullSpaces - gets the null spaces, transpose null spaces, and near null spaces from an array of matrices

    8952:   Logically Collective

    8954:   Input Parameters:
    8955: + n   - the number of matrices
    8956: - mat - the array of matrices

    8958:   Output Parameters:
    8959: . nullsp - an array of null spaces, `NULL` for each matrix that does not have a null space, length 3 * `n`

    8961:   Level: developer

    8963:   Note:
    8964:   Call `MatRestoreNullspaces()` to provide these to another array of matrices

    8966: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatSetTransposeNullSpace()`, `MatGetTransposeNullSpace()`,
    8967:           `MatNullSpaceRemove()`, `MatRestoreNullSpaces()`
    8968: @*/
    8969: PetscErrorCode MatGetNullSpaces(PetscInt n, Mat mat[], MatNullSpace *nullsp[])
    8970: {
    8971:   PetscFunctionBegin;
    8972:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of matrices %" PetscInt_FMT " must be non-negative", n);
    8973:   PetscAssertPointer(mat, 2);
    8974:   PetscAssertPointer(nullsp, 3);

    8976:   PetscCall(PetscCalloc1(3 * n, nullsp));
    8977:   for (PetscInt i = 0; i < n; i++) {
    8979:     (*nullsp)[i] = mat[i]->nullsp;
    8980:     PetscCall(PetscObjectReference((PetscObject)(*nullsp)[i]));
    8981:     (*nullsp)[n + i] = mat[i]->nearnullsp;
    8982:     PetscCall(PetscObjectReference((PetscObject)(*nullsp)[n + i]));
    8983:     (*nullsp)[2 * n + i] = mat[i]->transnullsp;
    8984:     PetscCall(PetscObjectReference((PetscObject)(*nullsp)[2 * n + i]));
    8985:   }
    8986:   PetscFunctionReturn(PETSC_SUCCESS);
    8987: }

    8989: /*@C
    8990:   MatRestoreNullSpaces - sets the null spaces, transpose null spaces, and near null spaces obtained with `MatGetNullSpaces()` for an array of matrices

    8992:   Logically Collective

    8994:   Input Parameters:
    8995: + n      - the number of matrices
    8996: . mat    - the array of matrices
    8997: - nullsp - an array of null spaces

    8999:   Level: developer

    9001:   Note:
    9002:   Call `MatGetNullSpaces()` to create `nullsp`

    9004: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatSetTransposeNullSpace()`, `MatGetTransposeNullSpace()`,
    9005:           `MatNullSpaceRemove()`, `MatGetNullSpaces()`
    9006: @*/
    9007: PetscErrorCode MatRestoreNullSpaces(PetscInt n, Mat mat[], MatNullSpace *nullsp[])
    9008: {
    9009:   PetscFunctionBegin;
    9010:   PetscCheck(n >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of matrices %" PetscInt_FMT " must be non-negative", n);
    9011:   PetscAssertPointer(mat, 2);
    9012:   PetscAssertPointer(nullsp, 3);
    9013:   PetscAssertPointer(*nullsp, 3);

    9015:   for (PetscInt i = 0; i < n; i++) {
    9017:     PetscCall(MatSetNullSpace(mat[i], (*nullsp)[i]));
    9018:     PetscCall(PetscObjectDereference((PetscObject)(*nullsp)[i]));
    9019:     PetscCall(MatSetNearNullSpace(mat[i], (*nullsp)[n + i]));
    9020:     PetscCall(PetscObjectDereference((PetscObject)(*nullsp)[n + i]));
    9021:     PetscCall(MatSetTransposeNullSpace(mat[i], (*nullsp)[2 * n + i]));
    9022:     PetscCall(PetscObjectDereference((PetscObject)(*nullsp)[2 * n + i]));
    9023:   }
    9024:   PetscCall(PetscFree(*nullsp));
    9025:   PetscFunctionReturn(PETSC_SUCCESS);
    9026: }

    9028: /*@
    9029:   MatSetNullSpace - attaches a null space to a matrix.

    9031:   Logically Collective

    9033:   Input Parameters:
    9034: + mat    - the matrix
    9035: - nullsp - the null space object

    9037:   Level: advanced

    9039:   Notes:
    9040:   This null space is used by the `KSP` linear solvers to solve singular systems.

    9042:   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`

    9044:   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
    9045:   to zero but the linear system will still be solved in a least squares sense.

    9047:   The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
    9048:   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 $A^T$, $R(A^T)$.
    9049:   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
    9050:   $n(A^T))$ 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
    9051:   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 $n(A^T)$.
    9052:   This  $\hat{b}$ can be obtained by calling `MatNullSpaceRemove()` with the null space of the transpose of the matrix.

    9054:   If the matrix is known to be symmetric because it is an `MATSBAIJ` matrix or one has called
    9055:   `MatSetOption`(mat,`MAT_SYMMETRIC` or possibly `MAT_SYMMETRY_ETERNAL`,`PETSC_TRUE`); this
    9056:   routine also automatically calls `MatSetTransposeNullSpace()`.

    9058:   The user should call `MatNullSpaceDestroy()`.

    9060: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatSetTransposeNullSpace()`, `MatGetTransposeNullSpace()`, `MatNullSpaceRemove()`,
    9061:           `KSPSetPCSide()`
    9062: @*/
    9063: PetscErrorCode MatSetNullSpace(Mat mat, MatNullSpace nullsp)
    9064: {
    9065:   PetscFunctionBegin;
    9068:   if (nullsp) PetscCall(PetscObjectReference((PetscObject)nullsp));
    9069:   PetscCall(MatNullSpaceDestroy(&mat->nullsp));
    9070:   mat->nullsp = nullsp;
    9071:   if (mat->symmetric == PETSC_BOOL3_TRUE) PetscCall(MatSetTransposeNullSpace(mat, nullsp));
    9072:   PetscFunctionReturn(PETSC_SUCCESS);
    9073: }

    9075: /*@
    9076:   MatGetTransposeNullSpace - retrieves the null space of the transpose of a matrix.

    9078:   Logically Collective

    9080:   Input Parameters:
    9081: + mat    - the matrix
    9082: - nullsp - the null space object

    9084:   Level: developer

    9086: .seealso: [](ch_matrices), `Mat`, `MatNullSpace`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatSetTransposeNullSpace()`, `MatSetNullSpace()`, `MatGetNullSpace()`
    9087: @*/
    9088: PetscErrorCode MatGetTransposeNullSpace(Mat mat, MatNullSpace *nullsp)
    9089: {
    9090:   PetscFunctionBegin;
    9093:   PetscAssertPointer(nullsp, 2);
    9094:   *nullsp = (mat->symmetric == PETSC_BOOL3_TRUE && !mat->transnullsp) ? mat->nullsp : mat->transnullsp;
    9095:   PetscFunctionReturn(PETSC_SUCCESS);
    9096: }

    9098: /*@
    9099:   MatSetTransposeNullSpace - attaches the null space of a transpose of a matrix to the matrix

    9101:   Logically Collective

    9103:   Input Parameters:
    9104: + mat    - the matrix
    9105: - nullsp - the null space object

    9107:   Level: advanced

    9109:   Notes:
    9110:   This allows solving singular linear systems defined by the transpose of the matrix using `KSP` solvers with left preconditioning.

    9112:   See `MatSetNullSpace()`

    9114: .seealso: [](ch_matrices), `Mat`, `MatNullSpace`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatSetNullSpace()`, `MatGetTransposeNullSpace()`, `MatNullSpaceRemove()`, `KSPSetPCSide()`
    9115: @*/
    9116: PetscErrorCode MatSetTransposeNullSpace(Mat mat, MatNullSpace nullsp)
    9117: {
    9118:   PetscFunctionBegin;
    9121:   if (nullsp) PetscCall(PetscObjectReference((PetscObject)nullsp));
    9122:   PetscCall(MatNullSpaceDestroy(&mat->transnullsp));
    9123:   mat->transnullsp = nullsp;
    9124:   PetscFunctionReturn(PETSC_SUCCESS);
    9125: }

    9127: /*@
    9128:   MatSetNearNullSpace - attaches a null space to a matrix, which is often the null space (rigid body modes) of the operator without boundary conditions
    9129:   This null space will be used to provide near null space vectors to a multigrid preconditioner built from this matrix.

    9131:   Logically Collective

    9133:   Input Parameters:
    9134: + mat    - the matrix
    9135: - nullsp - the null space object

    9137:   Level: advanced

    9139:   Notes:
    9140:   Overwrites any previous near null space that may have been attached

    9142:   You can remove the null space by calling this routine with an `nullsp` of `NULL`

    9144: .seealso: [](ch_matrices), `Mat`, `MatNullSpace`, `MatCreate()`, `MatNullSpaceCreate()`, `MatSetNullSpace()`, `MatNullSpaceCreateRigidBody()`, `MatGetNearNullSpace()`
    9145: @*/
    9146: PetscErrorCode MatSetNearNullSpace(Mat mat, MatNullSpace nullsp)
    9147: {
    9148:   PetscFunctionBegin;
    9152:   MatCheckPreallocated(mat, 1);
    9153:   if (nullsp) PetscCall(PetscObjectReference((PetscObject)nullsp));
    9154:   PetscCall(MatNullSpaceDestroy(&mat->nearnullsp));
    9155:   mat->nearnullsp = nullsp;
    9156:   PetscFunctionReturn(PETSC_SUCCESS);
    9157: }

    9159: /*@
    9160:   MatGetNearNullSpace - Get null space attached with `MatSetNearNullSpace()`

    9162:   Not Collective

    9164:   Input Parameter:
    9165: . mat - the matrix

    9167:   Output Parameter:
    9168: . nullsp - the null space object, `NULL` if not set

    9170:   Level: advanced

    9172: .seealso: [](ch_matrices), `Mat`, `MatNullSpace`, `MatSetNearNullSpace()`, `MatGetNullSpace()`, `MatNullSpaceCreate()`
    9173: @*/
    9174: PetscErrorCode MatGetNearNullSpace(Mat mat, MatNullSpace *nullsp)
    9175: {
    9176:   PetscFunctionBegin;
    9179:   PetscAssertPointer(nullsp, 2);
    9180:   MatCheckPreallocated(mat, 1);
    9181:   *nullsp = mat->nearnullsp;
    9182:   PetscFunctionReturn(PETSC_SUCCESS);
    9183: }

    9185: /*@
    9186:   MatICCFactor - Performs in-place incomplete Cholesky factorization of matrix.

    9188:   Collective

    9190:   Input Parameters:
    9191: + mat  - the matrix
    9192: . row  - row/column permutation
    9193: - info - information on desired factorization process

    9195:   Level: developer

    9197:   Notes:
    9198:   Probably really in-place only when level of fill is zero, otherwise allocates
    9199:   new space to store factored matrix and deletes previous memory.

    9201:   Most users should employ the `KSP` interface for linear solvers
    9202:   instead of working directly with matrix algebra routines such as this.
    9203:   See, e.g., `KSPCreate()`.

    9205:   Fortran Note:
    9206:   A valid (non-null) `info` argument must be provided

    9208: .seealso: [](ch_matrices), `Mat`, `MatFactorInfo`, `MatGetFactor()`, `MatICCFactorSymbolic()`, `MatLUFactorNumeric()`, `MatCholeskyFactor()`
    9209: @*/
    9210: PetscErrorCode MatICCFactor(Mat mat, IS row, const MatFactorInfo *info)
    9211: {
    9212:   PetscFunctionBegin;
    9216:   PetscAssertPointer(info, 3);
    9217:   PetscCheck(mat->rmap->N == mat->cmap->N, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONG, "matrix must be square");
    9218:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    9219:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    9220:   MatCheckPreallocated(mat, 1);
    9221:   PetscUseTypeMethod(mat, iccfactor, row, info);
    9222:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    9223:   PetscFunctionReturn(PETSC_SUCCESS);
    9224: }

    9226: /*@
    9227:   MatDiagonalScaleLocal - Scales columns of a matrix given the scaling values including the
    9228:   ghosted ones.

    9230:   Not Collective

    9232:   Input Parameters:
    9233: + mat  - the matrix
    9234: - diag - the diagonal values, including ghost ones

    9236:   Level: developer

    9238:   Notes:
    9239:   Works only for `MATMPIAIJ` and `MATMPIBAIJ` matrices

    9241:   This allows one to avoid during communication to perform the scaling that must be done with `MatDiagonalScale()`

    9243: .seealso: [](ch_matrices), `Mat`, `MatDiagonalScale()`
    9244: @*/
    9245: PetscErrorCode MatDiagonalScaleLocal(Mat mat, Vec diag)
    9246: {
    9247:   PetscMPIInt size;

    9249:   PetscFunctionBegin;

    9254:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Matrix must be already assembled");
    9255:   PetscCall(PetscLogEventBegin(MAT_Scale, mat, 0, 0, 0));
    9256:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));
    9257:   if (size == 1) {
    9258:     PetscInt n, m;
    9259:     PetscCall(VecGetSize(diag, &n));
    9260:     PetscCall(MatGetSize(mat, NULL, &m));
    9261:     PetscCheck(m == n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only supported for sequential matrices when no ghost points/periodic conditions");
    9262:     PetscCall(MatDiagonalScale(mat, NULL, diag));
    9263:   } else {
    9264:     PetscUseMethod(mat, "MatDiagonalScaleLocal_C", (Mat, Vec), (mat, diag));
    9265:   }
    9266:   PetscCall(PetscLogEventEnd(MAT_Scale, mat, 0, 0, 0));
    9267:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    9268:   PetscFunctionReturn(PETSC_SUCCESS);
    9269: }

    9271: /*@
    9272:   MatGetInertia - Gets the inertia from a factored matrix

    9274:   Collective

    9276:   Input Parameter:
    9277: . mat - the matrix

    9279:   Output Parameters:
    9280: + nneg  - number of negative eigenvalues
    9281: . nzero - number of zero eigenvalues
    9282: - npos  - number of positive eigenvalues

    9284:   Level: advanced

    9286:   Note:
    9287:   Matrix must have been factored by `MatCholeskyFactor()`

    9289: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatCholeskyFactor()`
    9290: @*/
    9291: PetscErrorCode MatGetInertia(Mat mat, PetscInt *nneg, PetscInt *nzero, PetscInt *npos)
    9292: {
    9293:   PetscFunctionBegin;
    9296:   PetscCheck(mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Unfactored matrix");
    9297:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Numeric factor mat is not assembled");
    9298:   PetscUseTypeMethod(mat, getinertia, nneg, nzero, npos);
    9299:   PetscFunctionReturn(PETSC_SUCCESS);
    9300: }

    9302: /*@C
    9303:   MatSolves - Solves $A x = b$, given a factored matrix, for a collection of vectors

    9305:   Neighbor-wise Collective

    9307:   Input Parameters:
    9308: + mat - the factored matrix obtained with `MatGetFactor()`
    9309: - b   - the right-hand-side vectors

    9311:   Output Parameter:
    9312: . x - the result vectors

    9314:   Level: developer

    9316:   Note:
    9317:   The vectors `b` and `x` cannot be the same.  I.e., one cannot
    9318:   call `MatSolves`(A,x,x).

    9320: .seealso: [](ch_matrices), `Mat`, `Vecs`, `MatSolveAdd()`, `MatSolveTranspose()`, `MatSolveTransposeAdd()`, `MatSolve()`
    9321: @*/
    9322: PetscErrorCode MatSolves(Mat mat, Vecs b, Vecs x)
    9323: {
    9324:   PetscFunctionBegin;
    9327:   PetscCheck(x != b, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_IDN, "x and b must be different vectors");
    9328:   PetscCheck(mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Unfactored matrix");
    9329:   if (!mat->rmap->N && !mat->cmap->N) PetscFunctionReturn(PETSC_SUCCESS);

    9331:   MatCheckPreallocated(mat, 1);
    9332:   PetscCall(PetscLogEventBegin(MAT_Solves, mat, 0, 0, 0));
    9333:   PetscUseTypeMethod(mat, solves, b, x);
    9334:   PetscCall(PetscLogEventEnd(MAT_Solves, mat, 0, 0, 0));
    9335:   PetscFunctionReturn(PETSC_SUCCESS);
    9336: }

    9338: /*@
    9339:   MatIsSymmetric - Test whether a matrix is symmetric

    9341:   Collective

    9343:   Input Parameters:
    9344: + A   - the matrix to test
    9345: - tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact transpose)

    9347:   Output Parameter:
    9348: . flg - the result

    9350:   Level: intermediate

    9352:   Notes:
    9353:   For real numbers `MatIsSymmetric()` and `MatIsHermitian()` return identical results

    9355:   If the matrix does not yet know if it is symmetric or not this can be an expensive operation, also available `MatIsSymmetricKnown()`

    9357:   One can declare that a matrix is symmetric with `MatSetOption`(mat,`MAT_SYMMETRIC`,`PETSC_TRUE`) and if it is known to remain symmetric
    9358:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9360: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetricKnown()`,
    9361:           `MAT_SYMMETRIC`, `MAT_SYMMETRY_ETERNAL`
    9362: @*/
    9363: PetscErrorCode MatIsSymmetric(Mat A, PetscReal tol, PetscBool *flg)
    9364: {
    9365:   PetscFunctionBegin;
    9367:   PetscAssertPointer(flg, 3);
    9368:   if (A->symmetric != PETSC_BOOL3_UNKNOWN && !tol) *flg = PetscBool3ToBool(A->symmetric);
    9369:   else {
    9370:     if (A->ops->issymmetric) PetscUseTypeMethod(A, issymmetric, tol, flg);
    9371:     else PetscCall(MatIsTranspose(A, A, tol, flg));
    9372:     if (!tol) PetscCall(MatSetOption(A, MAT_SYMMETRIC, *flg));
    9373:   }
    9374:   PetscFunctionReturn(PETSC_SUCCESS);
    9375: }

    9377: /*@
    9378:   MatIsHermitian - Test whether a matrix is Hermitian

    9380:   Collective

    9382:   Input Parameters:
    9383: + A   - the matrix to test
    9384: - tol - difference between value and its transpose less than this amount counts as equal (use 0.0 for exact Hermitian)

    9386:   Output Parameter:
    9387: . flg - the result

    9389:   Level: intermediate

    9391:   Notes:
    9392:   For real numbers `MatIsSymmetric()` and `MatIsHermitian()` return identical results

    9394:   If the matrix does not yet know if it is Hermitian or not this can be an expensive operation, also available `MatIsHermitianKnown()`

    9396:   One can declare that a matrix is Hermitian with `MatSetOption`(mat,`MAT_HERMITIAN`,`PETSC_TRUE`) and if it is known to remain Hermitian
    9397:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SYMEMTRY_ETERNAL`,`PETSC_TRUE`)

    9399: .seealso: [](ch_matrices), `Mat`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitianKnown()`, `MatIsStructurallySymmetric()`, `MatSetOption()`,
    9400:           `MatIsSymmetricKnown()`, `MatIsSymmetric()`, `MAT_HERMITIAN`, `MAT_SYMMETRY_ETERNAL`
    9401: @*/
    9402: PetscErrorCode MatIsHermitian(Mat A, PetscReal tol, PetscBool *flg)
    9403: {
    9404:   PetscFunctionBegin;
    9406:   PetscAssertPointer(flg, 3);
    9407:   if (A->hermitian != PETSC_BOOL3_UNKNOWN && !tol) *flg = PetscBool3ToBool(A->hermitian);
    9408:   else {
    9409:     if (A->ops->ishermitian) PetscUseTypeMethod(A, ishermitian, tol, flg);
    9410:     else PetscCall(MatIsHermitianTranspose(A, A, tol, flg));
    9411:     if (!tol) PetscCall(MatSetOption(A, MAT_HERMITIAN, *flg));
    9412:   }
    9413:   PetscFunctionReturn(PETSC_SUCCESS);
    9414: }

    9416: /*@
    9417:   MatIsSymmetricKnown - Checks if a matrix knows if it is symmetric or not and its symmetric state

    9419:   Not Collective

    9421:   Input Parameter:
    9422: . A - the matrix to check

    9424:   Output Parameters:
    9425: + set - `PETSC_TRUE` if the matrix knows its symmetry state (this tells you if the next flag is valid)
    9426: - flg - the result (only valid if set is `PETSC_TRUE`)

    9428:   Level: advanced

    9430:   Notes:
    9431:   Does not check the matrix values directly, so this may return unknown (set = `PETSC_FALSE`). Use `MatIsSymmetric()`
    9432:   if you want it explicitly checked

    9434:   One can declare that a matrix is symmetric with `MatSetOption`(mat,`MAT_SYMMETRIC`,`PETSC_TRUE`) and if it is known to remain symmetric
    9435:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9437: .seealso: [](ch_matrices), `Mat`, `MAT_SYMMETRY_ETERNAL`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetric()`, `MatIsHermitianKnown()`
    9438: @*/
    9439: PetscErrorCode MatIsSymmetricKnown(Mat A, PetscBool *set, PetscBool *flg)
    9440: {
    9441:   PetscFunctionBegin;
    9443:   PetscAssertPointer(set, 2);
    9444:   PetscAssertPointer(flg, 3);
    9445:   if (A->symmetric != PETSC_BOOL3_UNKNOWN) {
    9446:     *set = PETSC_TRUE;
    9447:     *flg = PetscBool3ToBool(A->symmetric);
    9448:   } else {
    9449:     *set = PETSC_FALSE;
    9450:   }
    9451:   PetscFunctionReturn(PETSC_SUCCESS);
    9452: }

    9454: /*@
    9455:   MatIsSPDKnown - Checks if a matrix knows if it is symmetric positive definite or not and its symmetric positive definite state

    9457:   Not Collective

    9459:   Input Parameter:
    9460: . A - the matrix to check

    9462:   Output Parameters:
    9463: + set - `PETSC_TRUE` if the matrix knows its symmetric positive definite state (this tells you if the next flag is valid)
    9464: - flg - the result (only valid if set is `PETSC_TRUE`)

    9466:   Level: advanced

    9468:   Notes:
    9469:   Does not check the matrix values directly, so this may return unknown (set = `PETSC_FALSE`).

    9471:   One can declare that a matrix is SPD with `MatSetOption`(mat,`MAT_SPD`,`PETSC_TRUE`) and if it is known to remain SPD
    9472:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SPD_ETERNAL`,`PETSC_TRUE`)

    9474: .seealso: [](ch_matrices), `Mat`, `MAT_SPD_ETERNAL`, `MAT_SPD`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetric()`, `MatIsHermitianKnown()`
    9475: @*/
    9476: PetscErrorCode MatIsSPDKnown(Mat A, PetscBool *set, PetscBool *flg)
    9477: {
    9478:   PetscFunctionBegin;
    9480:   PetscAssertPointer(set, 2);
    9481:   PetscAssertPointer(flg, 3);
    9482:   if (A->spd != PETSC_BOOL3_UNKNOWN) {
    9483:     *set = PETSC_TRUE;
    9484:     *flg = PetscBool3ToBool(A->spd);
    9485:   } else {
    9486:     *set = PETSC_FALSE;
    9487:   }
    9488:   PetscFunctionReturn(PETSC_SUCCESS);
    9489: }

    9491: /*@
    9492:   MatIsHermitianKnown - Checks if a matrix knows if it is Hermitian or not and its Hermitian state

    9494:   Not Collective

    9496:   Input Parameter:
    9497: . A - the matrix to check

    9499:   Output Parameters:
    9500: + set - `PETSC_TRUE` if the matrix knows its Hermitian state (this tells you if the next flag is valid)
    9501: - flg - the result (only valid if set is `PETSC_TRUE`)

    9503:   Level: advanced

    9505:   Notes:
    9506:   Does not check the matrix values directly, so this may return unknown (set = `PETSC_FALSE`). Use `MatIsHermitian()`
    9507:   if you want it explicitly checked

    9509:   One can declare that a matrix is Hermitian with `MatSetOption`(mat,`MAT_HERMITIAN`,`PETSC_TRUE`) and if it is known to remain Hermitian
    9510:   after changes to the matrices values one can call `MatSetOption`(mat,`MAT_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9512: .seealso: [](ch_matrices), `Mat`, `MAT_SYMMETRY_ETERNAL`, `MAT_HERMITIAN`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetric()`
    9513: @*/
    9514: PetscErrorCode MatIsHermitianKnown(Mat A, PetscBool *set, PetscBool *flg)
    9515: {
    9516:   PetscFunctionBegin;
    9518:   PetscAssertPointer(set, 2);
    9519:   PetscAssertPointer(flg, 3);
    9520:   if (A->hermitian != PETSC_BOOL3_UNKNOWN) {
    9521:     *set = PETSC_TRUE;
    9522:     *flg = PetscBool3ToBool(A->hermitian);
    9523:   } else {
    9524:     *set = PETSC_FALSE;
    9525:   }
    9526:   PetscFunctionReturn(PETSC_SUCCESS);
    9527: }

    9529: /*@
    9530:   MatIsStructurallySymmetric - Test whether a matrix is structurally symmetric

    9532:   Collective

    9534:   Input Parameter:
    9535: . A - the matrix to test

    9537:   Output Parameter:
    9538: . flg - the result

    9540:   Level: intermediate

    9542:   Notes:
    9543:   If the matrix does yet know it is structurally symmetric this can be an expensive operation, also available `MatIsStructurallySymmetricKnown()`

    9545:   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
    9546:   symmetric after changes to the matrices values one can call `MatSetOption`(mat,`MAT_STRUCTURAL_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9548: .seealso: [](ch_matrices), `Mat`, `MAT_STRUCTURALLY_SYMMETRIC`, `MAT_STRUCTURAL_SYMMETRY_ETERNAL`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsSymmetric()`, `MatSetOption()`, `MatIsStructurallySymmetricKnown()`
    9549: @*/
    9550: PetscErrorCode MatIsStructurallySymmetric(Mat A, PetscBool *flg)
    9551: {
    9552:   PetscFunctionBegin;
    9554:   PetscAssertPointer(flg, 2);
    9555:   if (A->structurally_symmetric != PETSC_BOOL3_UNKNOWN) {
    9556:     *flg = PetscBool3ToBool(A->structurally_symmetric);
    9557:   } else {
    9558:     PetscUseTypeMethod(A, isstructurallysymmetric, flg);
    9559:     PetscCall(MatSetOption(A, MAT_STRUCTURALLY_SYMMETRIC, *flg));
    9560:   }
    9561:   PetscFunctionReturn(PETSC_SUCCESS);
    9562: }

    9564: /*@
    9565:   MatIsStructurallySymmetricKnown - Checks if a matrix knows if it is structurally symmetric or not and its structurally symmetric state

    9567:   Not Collective

    9569:   Input Parameter:
    9570: . A - the matrix to check

    9572:   Output Parameters:
    9573: + set - PETSC_TRUE if the matrix knows its structurally symmetric state (this tells you if the next flag is valid)
    9574: - flg - the result (only valid if set is PETSC_TRUE)

    9576:   Level: advanced

    9578:   Notes:
    9579:   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
    9580:   symmetric after changes to the matrices values one can call `MatSetOption`(mat,`MAT_STRUCTURAL_SYMMETRY_ETERNAL`,`PETSC_TRUE`)

    9582:   Use `MatIsStructurallySymmetric()` to explicitly check if a matrix is structurally symmetric (this is an expensive operation)

    9584: .seealso: [](ch_matrices), `Mat`, `MAT_STRUCTURALLY_SYMMETRIC`, `MatTranspose()`, `MatIsTranspose()`, `MatIsHermitian()`, `MatIsStructurallySymmetric()`, `MatSetOption()`, `MatIsSymmetric()`, `MatIsHermitianKnown()`
    9585: @*/
    9586: PetscErrorCode MatIsStructurallySymmetricKnown(Mat A, PetscBool *set, PetscBool *flg)
    9587: {
    9588:   PetscFunctionBegin;
    9590:   PetscAssertPointer(set, 2);
    9591:   PetscAssertPointer(flg, 3);
    9592:   if (A->structurally_symmetric != PETSC_BOOL3_UNKNOWN) {
    9593:     *set = PETSC_TRUE;
    9594:     *flg = PetscBool3ToBool(A->structurally_symmetric);
    9595:   } else {
    9596:     *set = PETSC_FALSE;
    9597:   }
    9598:   PetscFunctionReturn(PETSC_SUCCESS);
    9599: }

    9601: /*@
    9602:   MatStashGetInfo - Gets how many values are currently in the matrix stash, i.e. need
    9603:   to be communicated to other processors during the `MatAssemblyBegin()`/`MatAssemblyEnd()` process

    9605:   Not Collective

    9607:   Input Parameter:
    9608: . mat - the matrix

    9610:   Output Parameters:
    9611: + nstash    - the size of the stash
    9612: . reallocs  - the number of additional mallocs incurred.
    9613: . bnstash   - the size of the block stash
    9614: - breallocs - the number of additional mallocs incurred.in the block stash

    9616:   Level: advanced

    9618: .seealso: [](ch_matrices), `MatAssemblyBegin()`, `MatAssemblyEnd()`, `Mat`, `MatStashSetInitialSize()`
    9619: @*/
    9620: PetscErrorCode MatStashGetInfo(Mat mat, PetscInt *nstash, PetscInt *reallocs, PetscInt *bnstash, PetscInt *breallocs)
    9621: {
    9622:   PetscFunctionBegin;
    9623:   PetscCall(MatStashGetInfo_Private(&mat->stash, nstash, reallocs));
    9624:   PetscCall(MatStashGetInfo_Private(&mat->bstash, bnstash, breallocs));
    9625:   PetscFunctionReturn(PETSC_SUCCESS);
    9626: }

    9628: /*@
    9629:   MatCreateVecs - Get vector(s) compatible with the matrix, i.e. with the same
    9630:   parallel layout, `PetscLayout` for rows and columns

    9632:   Collective

    9634:   Input Parameter:
    9635: . mat - the matrix

    9637:   Output Parameters:
    9638: + right - (optional) vector that the matrix can be multiplied against
    9639: - left  - (optional) vector that the matrix vector product can be stored in

    9641:   Level: advanced

    9643:   Notes:
    9644:   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()`.

    9646:   These are new vectors which are not owned by the mat, they should be destroyed in `VecDestroy()` when no longer needed

    9648: .seealso: [](ch_matrices), `Mat`, `Vec`, `VecCreate()`, `VecDestroy()`, `DMCreateGlobalVector()`
    9649: @*/
    9650: PetscErrorCode MatCreateVecs(Mat mat, Vec *right, Vec *left)
    9651: {
    9652:   PetscFunctionBegin;
    9655:   if (mat->ops->getvecs) {
    9656:     PetscUseTypeMethod(mat, getvecs, right, left);
    9657:   } else {
    9658:     if (right) {
    9659:       PetscCheck(mat->cmap->n >= 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "PetscLayout for columns not yet setup");
    9660:       PetscCall(VecCreateWithLayout_Private(mat->cmap, right));
    9661:       PetscCall(VecSetType(*right, mat->defaultvectype));
    9662: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
    9663:       if (mat->boundtocpu && mat->bindingpropagates) {
    9664:         PetscCall(VecSetBindingPropagates(*right, PETSC_TRUE));
    9665:         PetscCall(VecBindToCPU(*right, PETSC_TRUE));
    9666:       }
    9667: #endif
    9668:     }
    9669:     if (left) {
    9670:       PetscCheck(mat->rmap->n >= 0, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "PetscLayout for rows not yet setup");
    9671:       PetscCall(VecCreateWithLayout_Private(mat->rmap, left));
    9672:       PetscCall(VecSetType(*left, mat->defaultvectype));
    9673: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
    9674:       if (mat->boundtocpu && mat->bindingpropagates) {
    9675:         PetscCall(VecSetBindingPropagates(*left, PETSC_TRUE));
    9676:         PetscCall(VecBindToCPU(*left, PETSC_TRUE));
    9677:       }
    9678: #endif
    9679:     }
    9680:   }
    9681:   PetscFunctionReturn(PETSC_SUCCESS);
    9682: }

    9684: /*@
    9685:   MatFactorInfoInitialize - Initializes a `MatFactorInfo` data structure
    9686:   with default values.

    9688:   Not Collective

    9690:   Input Parameter:
    9691: . info - the `MatFactorInfo` data structure

    9693:   Level: developer

    9695:   Notes:
    9696:   The solvers are generally used through the `KSP` and `PC` objects, for example
    9697:   `PCLU`, `PCILU`, `PCCHOLESKY`, `PCICC`

    9699:   Once the data structure is initialized one may change certain entries as desired for the particular factorization to be performed

    9701: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorInfo`
    9702: @*/
    9703: PetscErrorCode MatFactorInfoInitialize(MatFactorInfo *info)
    9704: {
    9705:   PetscFunctionBegin;
    9706:   PetscCall(PetscMemzero(info, sizeof(MatFactorInfo)));
    9707:   PetscFunctionReturn(PETSC_SUCCESS);
    9708: }

    9710: /*@
    9711:   MatFactorSetSchurIS - Set indices corresponding to the Schur complement you wish to have computed

    9713:   Collective

    9715:   Input Parameters:
    9716: + mat - the factored matrix
    9717: - is  - the index set defining the Schur indices (0-based)

    9719:   Level: advanced

    9721:   Notes:
    9722:   Call `MatFactorSolveSchurComplement()` or `MatFactorSolveSchurComplementTranspose()` after this call to solve a Schur complement system.

    9724:   You can call `MatFactorGetSchurComplement()` or `MatFactorCreateSchurComplement()` after this call.

    9726:   This functionality is only supported for `MATSOLVERMUMPS` and `MATSOLVERMKL_PARDISO`

    9728: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorGetSchurComplement()`, `MatFactorRestoreSchurComplement()`, `MatFactorCreateSchurComplement()`, `MatFactorSolveSchurComplement()`,
    9729:           `MatFactorSolveSchurComplementTranspose()`, `MATSOLVERMUMPS`, `MATSOLVERMKL_PARDISO`
    9730: @*/
    9731: PetscErrorCode MatFactorSetSchurIS(Mat mat, IS is)
    9732: {
    9733:   PetscErrorCode (*f)(Mat, IS);

    9735:   PetscFunctionBegin;
    9740:   PetscCheckSameComm(mat, 1, is, 2);
    9741:   PetscCheck(mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Only for factored matrix");
    9742:   PetscCall(PetscObjectQueryFunction((PetscObject)mat, "MatFactorSetSchurIS_C", &f));
    9743:   PetscCheck(f, PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "The selected MatSolverType does not support Schur complement computation. You should use MATSOLVERMUMPS or MATSOLVERMKL_PARDISO");
    9744:   PetscCall(MatDestroy(&mat->schur));
    9745:   PetscCall((*f)(mat, is));
    9746:   PetscCheck(mat->schur, PetscObjectComm((PetscObject)mat), PETSC_ERR_PLIB, "Schur complement has not been created");
    9747:   PetscFunctionReturn(PETSC_SUCCESS);
    9748: }

    9750: /*@
    9751:   MatFactorCreateSchurComplement - Create a Schur complement matrix object using Schur data computed during the factorization step

    9753:   Logically Collective

    9755:   Input Parameters:
    9756: + F      - the factored matrix obtained by calling `MatGetFactor()`
    9757: . S      - location where to return the Schur complement, can be `NULL`
    9758: - status - the status of the Schur complement matrix, can be `NULL`

    9760:   Level: advanced

    9762:   Notes:
    9763:   You must call `MatFactorSetSchurIS()` before calling this routine.

    9765:   This functionality is only supported for `MATSOLVERMUMPS` and `MATSOLVERMKL_PARDISO`

    9767:   The routine provides a copy of the Schur matrix stored within the solver data structures.
    9768:   The caller must destroy the object when it is no longer needed.
    9769:   If `MatFactorInvertSchurComplement()` has been called, the routine gets back the inverse.

    9771:   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)

    9773:   See `MatCreateSchurComplement()` or `MatGetSchurComplement()` for ways to create virtual or approximate Schur complements.

    9775:   Developer Note:
    9776:   The reason this routine exists is because the representation of the Schur complement within the factor matrix may be different than a standard PETSc
    9777:   matrix representation and we normally do not want to use the time or memory to make a copy as a regular PETSc matrix.

    9779: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorGetSchurComplement()`, `MatFactorSchurStatus`, `MATSOLVERMUMPS`, `MATSOLVERMKL_PARDISO`
    9780: @*/
    9781: PetscErrorCode MatFactorCreateSchurComplement(Mat F, Mat *S, MatFactorSchurStatus *status)
    9782: {
    9783:   PetscFunctionBegin;
    9785:   if (S) PetscAssertPointer(S, 2);
    9786:   if (status) PetscAssertPointer(status, 3);
    9787:   if (S) {
    9788:     PetscErrorCode (*f)(Mat, Mat *);

    9790:     PetscCall(PetscObjectQueryFunction((PetscObject)F, "MatFactorCreateSchurComplement_C", &f));
    9791:     if (f) {
    9792:       PetscCall((*f)(F, S));
    9793:     } else {
    9794:       PetscCall(MatDuplicate(F->schur, MAT_COPY_VALUES, S));
    9795:     }
    9796:   }
    9797:   if (status) *status = F->schur_status;
    9798:   PetscFunctionReturn(PETSC_SUCCESS);
    9799: }

    9801: /*@
    9802:   MatFactorGetSchurComplement - Gets access to a Schur complement matrix using the current Schur data within a factored matrix

    9804:   Logically Collective

    9806:   Input Parameters:
    9807: + F      - the factored matrix obtained by calling `MatGetFactor()`
    9808: . S      - location where to return the Schur complement, can be `NULL`
    9809: - status - the status of the Schur complement matrix, can be `NULL`

    9811:   Level: advanced

    9813:   Notes:
    9814:   You must call `MatFactorSetSchurIS()` before calling this routine.

    9816:   Schur complement mode is currently implemented for sequential matrices with factor type of `MATSOLVERMUMPS`

    9818:   The routine returns a the Schur Complement stored within the data structures of the solver.

    9820:   If `MatFactorInvertSchurComplement()` has previously been called, the returned matrix is actually the inverse of the Schur complement.

    9822:   The returned matrix should not be destroyed; the caller should call `MatFactorRestoreSchurComplement()` when the object is no longer needed.

    9824:   Use `MatFactorCreateSchurComplement()` to create a copy of the Schur complement matrix that is within a factored matrix

    9826:   See `MatCreateSchurComplement()` or `MatGetSchurComplement()` for ways to create virtual or approximate Schur complements.

    9828: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorRestoreSchurComplement()`, `MatFactorCreateSchurComplement()`, `MatFactorSchurStatus`
    9829: @*/
    9830: PetscErrorCode MatFactorGetSchurComplement(Mat F, Mat *S, MatFactorSchurStatus *status)
    9831: {
    9832:   PetscFunctionBegin;
    9834:   if (S) {
    9835:     PetscAssertPointer(S, 2);
    9836:     *S = F->schur;
    9837:   }
    9838:   if (status) {
    9839:     PetscAssertPointer(status, 3);
    9840:     *status = F->schur_status;
    9841:   }
    9842:   PetscFunctionReturn(PETSC_SUCCESS);
    9843: }

    9845: static PetscErrorCode MatFactorUpdateSchurStatus_Private(Mat F)
    9846: {
    9847:   Mat S = F->schur;

    9849:   PetscFunctionBegin;
    9850:   switch (F->schur_status) {
    9851:   case MAT_FACTOR_SCHUR_UNFACTORED: // fall-through
    9852:   case MAT_FACTOR_SCHUR_INVERTED:
    9853:     if (S) {
    9854:       S->ops->solve             = NULL;
    9855:       S->ops->matsolve          = NULL;
    9856:       S->ops->solvetranspose    = NULL;
    9857:       S->ops->matsolvetranspose = NULL;
    9858:       S->ops->solveadd          = NULL;
    9859:       S->ops->solvetransposeadd = NULL;
    9860:       S->factortype             = MAT_FACTOR_NONE;
    9861:       PetscCall(PetscFree(S->solvertype));
    9862:     }
    9863:   case MAT_FACTOR_SCHUR_FACTORED: // fall-through
    9864:     break;
    9865:   default:
    9866:     SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unhandled MatFactorSchurStatus %d", F->schur_status);
    9867:   }
    9868:   PetscFunctionReturn(PETSC_SUCCESS);
    9869: }

    9871: /*@
    9872:   MatFactorRestoreSchurComplement - Restore the Schur complement matrix object obtained from a call to `MatFactorGetSchurComplement()`

    9874:   Logically Collective

    9876:   Input Parameters:
    9877: + F      - the factored matrix obtained by calling `MatGetFactor()`
    9878: . S      - location where the Schur complement is stored
    9879: - status - the status of the Schur complement matrix (see `MatFactorSchurStatus`)

    9881:   Level: advanced

    9883: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorCreateSchurComplement()`, `MatFactorSchurStatus`
    9884: @*/
    9885: PetscErrorCode MatFactorRestoreSchurComplement(Mat F, Mat *S, MatFactorSchurStatus status)
    9886: {
    9887:   PetscFunctionBegin;
    9889:   if (S) {
    9891:     *S = NULL;
    9892:   }
    9893:   F->schur_status = status;
    9894:   PetscCall(MatFactorUpdateSchurStatus_Private(F));
    9895:   PetscFunctionReturn(PETSC_SUCCESS);
    9896: }

    9898: /*@
    9899:   MatFactorSolveSchurComplementTranspose - Solve the transpose of the Schur complement system computed during the factorization step

    9901:   Logically Collective

    9903:   Input Parameters:
    9904: + F   - the factored matrix obtained by calling `MatGetFactor()`
    9905: . rhs - location where the right-hand side of the Schur complement system is stored
    9906: - sol - location where the solution of the Schur complement system has to be returned

    9908:   Level: advanced

    9910:   Notes:
    9911:   The sizes of the vectors should match the size of the Schur complement

    9913:   Must be called after `MatFactorSetSchurIS()`

    9915: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorSolveSchurComplement()`
    9916: @*/
    9917: PetscErrorCode MatFactorSolveSchurComplementTranspose(Mat F, Vec rhs, Vec sol)
    9918: {
    9919:   PetscFunctionBegin;
    9926:   PetscCheckSameComm(F, 1, rhs, 2);
    9927:   PetscCheckSameComm(F, 1, sol, 3);
    9928:   PetscCall(MatFactorFactorizeSchurComplement(F));
    9929:   switch (F->schur_status) {
    9930:   case MAT_FACTOR_SCHUR_FACTORED:
    9931:     PetscCall(MatSolveTranspose(F->schur, rhs, sol));
    9932:     break;
    9933:   case MAT_FACTOR_SCHUR_INVERTED:
    9934:     PetscCall(MatMultTranspose(F->schur, rhs, sol));
    9935:     break;
    9936:   default:
    9937:     SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unhandled MatFactorSchurStatus %d", F->schur_status);
    9938:   }
    9939:   PetscFunctionReturn(PETSC_SUCCESS);
    9940: }

    9942: /*@
    9943:   MatFactorSolveSchurComplement - Solve the Schur complement system computed during the factorization step

    9945:   Logically Collective

    9947:   Input Parameters:
    9948: + F   - the factored matrix obtained by calling `MatGetFactor()`
    9949: . rhs - location where the right-hand side of the Schur complement system is stored
    9950: - sol - location where the solution of the Schur complement system has to be returned

    9952:   Level: advanced

    9954:   Notes:
    9955:   The sizes of the vectors should match the size of the Schur complement

    9957:   Must be called after `MatFactorSetSchurIS()`

    9959: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorSolveSchurComplementTranspose()`
    9960: @*/
    9961: PetscErrorCode MatFactorSolveSchurComplement(Mat F, Vec rhs, Vec sol)
    9962: {
    9963:   PetscFunctionBegin;
    9970:   PetscCheckSameComm(F, 1, rhs, 2);
    9971:   PetscCheckSameComm(F, 1, sol, 3);
    9972:   PetscCall(MatFactorFactorizeSchurComplement(F));
    9973:   switch (F->schur_status) {
    9974:   case MAT_FACTOR_SCHUR_FACTORED:
    9975:     PetscCall(MatSolve(F->schur, rhs, sol));
    9976:     break;
    9977:   case MAT_FACTOR_SCHUR_INVERTED:
    9978:     PetscCall(MatMult(F->schur, rhs, sol));
    9979:     break;
    9980:   default:
    9981:     SETERRQ(PetscObjectComm((PetscObject)F), PETSC_ERR_SUP, "Unhandled MatFactorSchurStatus %d", F->schur_status);
    9982:   }
    9983:   PetscFunctionReturn(PETSC_SUCCESS);
    9984: }

    9986: PETSC_SINGLE_LIBRARY_INTERN PetscErrorCode MatSeqDenseInvertFactors_Private(Mat);
    9987: #if PetscDefined(HAVE_CUDA)
    9988: PETSC_SINGLE_LIBRARY_INTERN PetscErrorCode MatSeqDenseCUDAInvertFactors_Internal(Mat);
    9989: #endif

    9991: /* Schur status updated in the interface */
    9992: static PetscErrorCode MatFactorInvertSchurComplement_Private(Mat F)
    9993: {
    9994:   Mat S = F->schur;

    9996:   PetscFunctionBegin;
    9997:   if (S) {
    9998:     PetscMPIInt size;
    9999:     PetscBool   isdense, isdensecuda;

    10001:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)S), &size));
    10002:     PetscCheck(size <= 1, PetscObjectComm((PetscObject)S), PETSC_ERR_SUP, "Not yet implemented");
    10003:     PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSEQDENSE, &isdense));
    10004:     PetscCall(PetscObjectTypeCompare((PetscObject)S, MATSEQDENSECUDA, &isdensecuda));
    10005:     PetscCheck(isdense || isdensecuda, PetscObjectComm((PetscObject)S), PETSC_ERR_SUP, "Not implemented for type %s", ((PetscObject)S)->type_name);
    10006:     PetscCall(PetscLogEventBegin(MAT_FactorInvS, F, 0, 0, 0));
    10007:     if (isdense) {
    10008:       PetscCall(MatSeqDenseInvertFactors_Private(S));
    10009:     } else if (isdensecuda) {
    10010: #if defined(PETSC_HAVE_CUDA)
    10011:       PetscCall(MatSeqDenseCUDAInvertFactors_Internal(S));
    10012: #endif
    10013:     }
    10014:     // HIP??????????????
    10015:     PetscCall(PetscLogEventEnd(MAT_FactorInvS, F, 0, 0, 0));
    10016:   }
    10017:   PetscFunctionReturn(PETSC_SUCCESS);
    10018: }

    10020: /*@
    10021:   MatFactorInvertSchurComplement - Invert the Schur complement matrix computed during the factorization step

    10023:   Logically Collective

    10025:   Input Parameter:
    10026: . F - the factored matrix obtained by calling `MatGetFactor()`

    10028:   Level: advanced

    10030:   Notes:
    10031:   Must be called after `MatFactorSetSchurIS()`.

    10033:   Call `MatFactorGetSchurComplement()` or  `MatFactorCreateSchurComplement()` AFTER this call to actually compute the inverse and get access to it.

    10035: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorGetSchurComplement()`, `MatFactorCreateSchurComplement()`
    10036: @*/
    10037: PetscErrorCode MatFactorInvertSchurComplement(Mat F)
    10038: {
    10039:   PetscFunctionBegin;
    10042:   if (F->schur_status == MAT_FACTOR_SCHUR_INVERTED) PetscFunctionReturn(PETSC_SUCCESS);
    10043:   PetscCall(MatFactorFactorizeSchurComplement(F));
    10044:   PetscCall(MatFactorInvertSchurComplement_Private(F));
    10045:   F->schur_status = MAT_FACTOR_SCHUR_INVERTED;
    10046:   PetscFunctionReturn(PETSC_SUCCESS);
    10047: }

    10049: /*@
    10050:   MatFactorFactorizeSchurComplement - Factorize the Schur complement matrix computed during the factorization step

    10052:   Logically Collective

    10054:   Input Parameter:
    10055: . F - the factored matrix obtained by calling `MatGetFactor()`

    10057:   Level: advanced

    10059:   Note:
    10060:   Must be called after `MatFactorSetSchurIS()`

    10062: .seealso: [](ch_matrices), `Mat`, `MatGetFactor()`, `MatFactorSetSchurIS()`, `MatFactorInvertSchurComplement()`
    10063: @*/
    10064: PetscErrorCode MatFactorFactorizeSchurComplement(Mat F)
    10065: {
    10066:   MatFactorInfo info;

    10068:   PetscFunctionBegin;
    10071:   if (F->schur_status == MAT_FACTOR_SCHUR_INVERTED || F->schur_status == MAT_FACTOR_SCHUR_FACTORED) PetscFunctionReturn(PETSC_SUCCESS);
    10072:   PetscCall(PetscLogEventBegin(MAT_FactorFactS, F, 0, 0, 0));
    10073:   PetscCall(PetscMemzero(&info, sizeof(MatFactorInfo)));
    10074:   if (F->factortype == MAT_FACTOR_CHOLESKY) { /* LDL^t regarded as Cholesky */
    10075:     PetscCall(MatCholeskyFactor(F->schur, NULL, &info));
    10076:   } else {
    10077:     PetscCall(MatLUFactor(F->schur, NULL, NULL, &info));
    10078:   }
    10079:   PetscCall(PetscLogEventEnd(MAT_FactorFactS, F, 0, 0, 0));
    10080:   F->schur_status = MAT_FACTOR_SCHUR_FACTORED;
    10081:   PetscFunctionReturn(PETSC_SUCCESS);
    10082: }

    10084: /*@
    10085:   MatPtAP - Creates the matrix product $C = P^T * A * P$

    10087:   Neighbor-wise Collective

    10089:   Input Parameters:
    10090: + A     - the matrix
    10091: . P     - the projection matrix
    10092: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10093: - 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
    10094:           if the result is a dense matrix this is irrelevant

    10096:   Output Parameter:
    10097: . C - the product matrix

    10099:   Level: intermediate

    10101:   Notes:
    10102:   C will be created and must be destroyed by the user with `MatDestroy()`.

    10104:   An alternative approach to this function is to use `MatProductCreate()` and set the desired options before the computation is done

    10106:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10108:   Developer Note:
    10109:   For matrix types without special implementation the function fallbacks to `MatMatMult()` followed by `MatTransposeMatMult()`.

    10111: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MatMatMult()`, `MatRARt()`
    10112: @*/
    10113: PetscErrorCode MatPtAP(Mat A, Mat P, MatReuse scall, PetscReal fill, Mat *C)
    10114: {
    10115:   PetscFunctionBegin;
    10116:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*C, 5);
    10117:   PetscCheck(scall != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Inplace product not supported");

    10119:   if (scall == MAT_INITIAL_MATRIX) {
    10120:     PetscCall(MatProductCreate(A, P, NULL, C));
    10121:     PetscCall(MatProductSetType(*C, MATPRODUCT_PtAP));
    10122:     PetscCall(MatProductSetAlgorithm(*C, "default"));
    10123:     PetscCall(MatProductSetFill(*C, fill));

    10125:     (*C)->product->api_user = PETSC_TRUE;
    10126:     PetscCall(MatProductSetFromOptions(*C));
    10127:     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);
    10128:     PetscCall(MatProductSymbolic(*C));
    10129:   } else { /* scall == MAT_REUSE_MATRIX */
    10130:     PetscCall(MatProductReplaceMats(A, P, NULL, *C));
    10131:   }

    10133:   PetscCall(MatProductNumeric(*C));
    10134:   (*C)->symmetric = A->symmetric;
    10135:   (*C)->spd       = A->spd;
    10136:   PetscFunctionReturn(PETSC_SUCCESS);
    10137: }

    10139: /*@
    10140:   MatRARt - Creates the matrix product $C = R * A * R^T$

    10142:   Neighbor-wise Collective

    10144:   Input Parameters:
    10145: + A     - the matrix
    10146: . R     - the projection matrix
    10147: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10148: - fill  - expected fill as ratio of nnz(C)/nnz(A), use `PETSC_DETERMINE` or `PETSC_CURRENT` if you do not have a good estimate
    10149:           if the result is a dense matrix this is irrelevant

    10151:   Output Parameter:
    10152: . C - the product matrix

    10154:   Level: intermediate

    10156:   Notes:
    10157:   `C` will be created and must be destroyed by the user with `MatDestroy()`.

    10159:   An alternative approach to this function is to use `MatProductCreate()` and set the desired options before the computation is done

    10161:   This routine is currently only implemented for pairs of `MATAIJ` matrices and classes
    10162:   which inherit from `MATAIJ`. Due to PETSc sparse matrix block row distribution among processes,
    10163:   the parallel `MatRARt()` is implemented computing the explicit transpose of `R`, which can be very expensive.
    10164:   We recommend using `MatPtAP()` when possible.

    10166:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10168: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MatMatMult()`, `MatPtAP()`
    10169: @*/
    10170: PetscErrorCode MatRARt(Mat A, Mat R, MatReuse scall, PetscReal fill, Mat *C)
    10171: {
    10172:   PetscFunctionBegin;
    10173:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*C, 5);
    10174:   PetscCheck(scall != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Inplace product not supported");

    10176:   if (scall == MAT_INITIAL_MATRIX) {
    10177:     PetscCall(MatProductCreate(A, R, NULL, C));
    10178:     PetscCall(MatProductSetType(*C, MATPRODUCT_RARt));
    10179:     PetscCall(MatProductSetAlgorithm(*C, "default"));
    10180:     PetscCall(MatProductSetFill(*C, fill));

    10182:     (*C)->product->api_user = PETSC_TRUE;
    10183:     PetscCall(MatProductSetFromOptions(*C));
    10184:     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);
    10185:     PetscCall(MatProductSymbolic(*C));
    10186:   } else { /* scall == MAT_REUSE_MATRIX */
    10187:     PetscCall(MatProductReplaceMats(A, R, NULL, *C));
    10188:   }

    10190:   PetscCall(MatProductNumeric(*C));
    10191:   if (A->symmetric == PETSC_BOOL3_TRUE) PetscCall(MatSetOption(*C, MAT_SYMMETRIC, PETSC_TRUE));
    10192:   PetscFunctionReturn(PETSC_SUCCESS);
    10193: }

    10195: static PetscErrorCode MatProduct_Private(Mat A, Mat B, MatReuse scall, PetscReal fill, MatProductType ptype, Mat *C)
    10196: {
    10197:   PetscBool flg = PETSC_TRUE;

    10199:   PetscFunctionBegin;
    10200:   PetscCheck(scall != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MAT_INPLACE_MATRIX product not supported");
    10201:   if (scall == MAT_INITIAL_MATRIX) {
    10202:     PetscCall(PetscInfo(A, "Calling MatProduct API with MAT_INITIAL_MATRIX and product type %s\n", MatProductTypes[ptype]));
    10203:     PetscCall(MatProductCreate(A, B, NULL, C));
    10204:     PetscCall(MatProductSetAlgorithm(*C, MATPRODUCTALGORITHMDEFAULT));
    10205:     PetscCall(MatProductSetFill(*C, fill));
    10206:   } else { /* scall == MAT_REUSE_MATRIX */
    10207:     Mat_Product *product = (*C)->product;

    10209:     PetscCall(PetscObjectBaseTypeCompareAny((PetscObject)*C, &flg, MATSEQDENSE, MATMPIDENSE, ""));
    10210:     if (flg && product && product->type != ptype) {
    10211:       PetscCall(MatProductClear(*C));
    10212:       product = NULL;
    10213:     }
    10214:     PetscCall(PetscInfo(A, "Calling MatProduct API with MAT_REUSE_MATRIX %s product present and product type %s\n", product ? "with" : "without", MatProductTypes[ptype]));
    10215:     if (!product) { /* user provide the dense matrix *C without calling MatProductCreate() or reusing it from previous calls */
    10216:       PetscCheck(flg, PetscObjectComm((PetscObject)*C), PETSC_ERR_SUP, "Call MatProductCreate() first");
    10217:       PetscCall(MatProductCreate_Private(A, B, NULL, *C));
    10218:       product        = (*C)->product;
    10219:       product->fill  = fill;
    10220:       product->clear = PETSC_TRUE;
    10221:     } else { /* user may change input matrices A or B when MAT_REUSE_MATRIX */
    10222:       flg = PETSC_FALSE;
    10223:       PetscCall(MatProductReplaceMats(A, B, NULL, *C));
    10224:     }
    10225:   }
    10226:   if (flg) {
    10227:     (*C)->product->api_user = PETSC_TRUE;
    10228:     PetscCall(MatProductSetType(*C, ptype));
    10229:     PetscCall(MatProductSetFromOptions(*C));
    10230:     PetscCall(MatProductSymbolic(*C));
    10231:   }
    10232:   PetscCall(MatProductNumeric(*C));
    10233:   PetscFunctionReturn(PETSC_SUCCESS);
    10234: }

    10236: /*@
    10237:   MatMatMult - Performs matrix-matrix multiplication C=A*B.

    10239:   Neighbor-wise Collective

    10241:   Input Parameters:
    10242: + A     - the left matrix
    10243: . B     - the right matrix
    10244: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10245: - 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
    10246:           if the result is a dense matrix this is irrelevant

    10248:   Output Parameter:
    10249: . C - the product matrix

    10251:   Notes:
    10252:   Unless scall is `MAT_REUSE_MATRIX` C will be created.

    10254:   `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
    10255:   call to this function with `MAT_INITIAL_MATRIX`.

    10257:   To determine the correct fill value, run with `-info` and search for the string "Fill ratio" to see the value actually needed.

    10259:   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`,
    10260:   rather than first having `MatMatMult()` create it for you. You can NEVER do this if the matrix `C` is sparse.

    10262:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10264:   Example of Usage:
    10265: .vb
    10266:      MatProductCreate(A,B,NULL,&C);
    10267:      MatProductSetType(C,MATPRODUCT_AB);
    10268:      MatProductSymbolic(C);
    10269:      MatProductNumeric(C); // compute C=A * B
    10270:      MatProductReplaceMats(A1,B1,NULL,C); // compute C=A1 * B1
    10271:      MatProductNumeric(C);
    10272:      MatProductReplaceMats(A2,NULL,NULL,C); // compute C=A2 * B1
    10273:      MatProductNumeric(C);
    10274: .ve

    10276:   Level: intermediate

    10278: .seealso: [](ch_matrices), `Mat`, `MatProductType`, `MATPRODUCT_AB`, `MatTransposeMatMult()`, `MatMatTransposeMult()`, `MatPtAP()`, `MatProductCreate()`, `MatProductSymbolic()`, `MatProductReplaceMats()`, `MatProductNumeric()`
    10279: @*/
    10280: PetscErrorCode MatMatMult(Mat A, Mat B, MatReuse scall, PetscReal fill, Mat *C)
    10281: {
    10282:   PetscFunctionBegin;
    10283:   PetscCall(MatProduct_Private(A, B, scall, fill, MATPRODUCT_AB, C));
    10284:   PetscFunctionReturn(PETSC_SUCCESS);
    10285: }

    10287: /*@
    10288:   MatMatTransposeMult - Performs matrix-matrix multiplication $C = A*B^T$.

    10290:   Neighbor-wise Collective

    10292:   Input Parameters:
    10293: + A     - the left matrix
    10294: . B     - the right matrix
    10295: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10296: - fill  - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use `PETSC_DETERMINE` or `PETSC_CURRENT` if not known

    10298:   Output Parameter:
    10299: . C - the product matrix

    10301:   Options Database Key:
    10302: . -matmattransmult_mpidense_mpidense_via {allgatherv,cyclic} - Choose between algorithms for `MATMPIDENSE` matrices: the
    10303:               first redundantly copies the transposed `B` matrix on each process and requires O(log P) communication complexity;
    10304:               the second never stores more than one portion of the `B` matrix at a time but requires O(P) communication complexity.

    10306:   Level: intermediate

    10308:   Notes:
    10309:   C will be created if `MAT_INITIAL_MATRIX` and must be destroyed by the user with `MatDestroy()`.

    10311:   `MAT_REUSE_MATRIX` can only be used if the matrices A and B have the same nonzero pattern as in the previous call

    10313:   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    10314:   actually needed.

    10316:   This routine is currently only implemented for pairs of `MATSEQAIJ` matrices, for the `MATSEQDENSE` class,
    10317:   and for pairs of `MATMPIDENSE` matrices.

    10319:   This routine is shorthand for using `MatProductCreate()` with the `MatProductType` of `MATPRODUCT_ABt`

    10321:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10323: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MATPRODUCT_ABt`, `MatMatMult()`, `MatTransposeMatMult()` `MatPtAP()`, `MatProductAlgorithm`, `MatProductType`
    10324: @*/
    10325: PetscErrorCode MatMatTransposeMult(Mat A, Mat B, MatReuse scall, PetscReal fill, Mat *C)
    10326: {
    10327:   PetscFunctionBegin;
    10328:   PetscCall(MatProduct_Private(A, B, scall, fill, MATPRODUCT_ABt, C));
    10329:   if (A == B) PetscCall(MatSetOption(*C, MAT_SYMMETRIC, PETSC_TRUE));
    10330:   PetscFunctionReturn(PETSC_SUCCESS);
    10331: }

    10333: /*@
    10334:   MatTransposeMatMult - Performs matrix-matrix multiplication $C = A^T*B$.

    10336:   Neighbor-wise Collective

    10338:   Input Parameters:
    10339: + A     - the left matrix
    10340: . B     - the right matrix
    10341: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10342: - fill  - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use `PETSC_DETERMINE` or `PETSC_CURRENT` if not known

    10344:   Output Parameter:
    10345: . C - the product matrix

    10347:   Level: intermediate

    10349:   Notes:
    10350:   `C` will be created if `MAT_INITIAL_MATRIX` and must be destroyed by the user with `MatDestroy()`.

    10352:   `MAT_REUSE_MATRIX` can only be used if the matrices A and B have the same nonzero pattern as in the previous call.

    10354:   This routine is shorthand for using `MatProductCreate()` with the `MatProductType` of `MATPRODUCT_AtB`

    10356:   To determine the correct fill value, run with -info and search for the string "Fill ratio" to see the value
    10357:   actually needed.

    10359:   This routine is currently implemented for pairs of `MATAIJ` matrices and pairs of `MATSEQDENSE` matrices and classes
    10360:   which inherit from `MATSEQAIJ`.  `C` will be of the same type as the input matrices.

    10362:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10364: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MATPRODUCT_AtB`, `MatMatMult()`, `MatMatTransposeMult()`, `MatPtAP()`
    10365: @*/
    10366: PetscErrorCode MatTransposeMatMult(Mat A, Mat B, MatReuse scall, PetscReal fill, Mat *C)
    10367: {
    10368:   PetscFunctionBegin;
    10369:   PetscCall(MatProduct_Private(A, B, scall, fill, MATPRODUCT_AtB, C));
    10370:   PetscFunctionReturn(PETSC_SUCCESS);
    10371: }

    10373: /*@
    10374:   MatMatMatMult - Performs matrix-matrix-matrix multiplication D=A*B*C.

    10376:   Neighbor-wise Collective

    10378:   Input Parameters:
    10379: + A     - the left matrix
    10380: . B     - the middle matrix
    10381: . C     - the right matrix
    10382: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    10383: - 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
    10384:           if the result is a dense matrix this is irrelevant

    10386:   Output Parameter:
    10387: . D - the product matrix

    10389:   Level: intermediate

    10391:   Notes:
    10392:   Unless `scall` is `MAT_REUSE_MATRIX` `D` will be created.

    10394:   `MAT_REUSE_MATRIX` can only be used if the matrices `A`, `B`, and `C` have the same nonzero pattern as in the previous call

    10396:   This routine is shorthand for using `MatProductCreate()` with the `MatProductType` of `MATPRODUCT_ABC`

    10398:   To determine the correct fill value, run with `-info` and search for the string "Fill ratio" to see the value
    10399:   actually needed.

    10401:   If you have many matrices with the same non-zero structure to multiply, you
    10402:   should use `MAT_REUSE_MATRIX` in all calls but the first

    10404:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    10406: .seealso: [](ch_matrices), `Mat`, `MatProductCreate()`, `MATPRODUCT_ABC`, `MatMatMult`, `MatPtAP()`, `MatMatTransposeMult()`, `MatTransposeMatMult()`
    10407: @*/
    10408: PetscErrorCode MatMatMatMult(Mat A, Mat B, Mat C, MatReuse scall, PetscReal fill, Mat *D)
    10409: {
    10410:   PetscFunctionBegin;
    10411:   if (scall == MAT_REUSE_MATRIX) MatCheckProduct(*D, 6);
    10412:   PetscCheck(scall != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Inplace product not supported");

    10414:   if (scall == MAT_INITIAL_MATRIX) {
    10415:     PetscCall(MatProductCreate(A, B, C, D));
    10416:     PetscCall(MatProductSetType(*D, MATPRODUCT_ABC));
    10417:     PetscCall(MatProductSetAlgorithm(*D, "default"));
    10418:     PetscCall(MatProductSetFill(*D, fill));

    10420:     (*D)->product->api_user = PETSC_TRUE;
    10421:     PetscCall(MatProductSetFromOptions(*D));
    10422:     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,
    10423:                ((PetscObject)C)->type_name);
    10424:     PetscCall(MatProductSymbolic(*D));
    10425:   } else { /* user may change input matrices when REUSE */
    10426:     PetscCall(MatProductReplaceMats(A, B, C, *D));
    10427:   }
    10428:   PetscCall(MatProductNumeric(*D));
    10429:   PetscFunctionReturn(PETSC_SUCCESS);
    10430: }

    10432: /*@
    10433:   MatCreateRedundantMatrix - Create redundant matrices and put them into processors of subcommunicators.

    10435:   Collective

    10437:   Input Parameters:
    10438: + mat      - the matrix
    10439: . nsubcomm - the number of subcommunicators (= number of redundant parallel or sequential matrices)
    10440: . subcomm  - MPI communicator split from the communicator where mat resides in (or `MPI_COMM_NULL` if nsubcomm is used)
    10441: - reuse    - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    10443:   Output Parameter:
    10444: . matredundant - redundant matrix

    10446:   Level: advanced

    10448:   Notes:
    10449:   `MAT_REUSE_MATRIX` can only be used when the nonzero structure of the
    10450:   original matrix has not changed from that last call to `MatCreateRedundantMatrix()`.

    10452:   This routine creates the duplicated matrices in the subcommunicators; you should NOT create them before
    10453:   calling it.

    10455:   `PetscSubcommCreate()` can be used to manage the creation of the subcomm but need not be.

    10457: .seealso: [](ch_matrices), `Mat`, `MatDestroy()`, `PetscSubcommCreate()`, `PetscSubcomm`
    10458: @*/
    10459: PetscErrorCode MatCreateRedundantMatrix(Mat mat, PetscInt nsubcomm, MPI_Comm subcomm, MatReuse reuse, Mat *matredundant)
    10460: {
    10461:   MPI_Comm       comm;
    10462:   PetscMPIInt    size;
    10463:   PetscInt       mloc_sub, nloc_sub, rstart, rend, M = mat->rmap->N, N = mat->cmap->N, bs = mat->rmap->bs;
    10464:   Mat_Redundant *redund     = NULL;
    10465:   PetscSubcomm   psubcomm   = NULL;
    10466:   MPI_Comm       subcomm_in = subcomm;
    10467:   Mat           *matseq;
    10468:   IS             isrow, iscol;
    10469:   PetscBool      newsubcomm = PETSC_FALSE;

    10471:   PetscFunctionBegin;
    10473:   if (nsubcomm && reuse == MAT_REUSE_MATRIX) {
    10474:     PetscAssertPointer(*matredundant, 5);
    10476:   }

    10478:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));
    10479:   if (size == 1 || nsubcomm == 1) {
    10480:     if (reuse == MAT_INITIAL_MATRIX) {
    10481:       PetscCall(MatDuplicate(mat, MAT_COPY_VALUES, matredundant));
    10482:     } else {
    10483:       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");
    10484:       PetscCall(MatCopy(mat, *matredundant, SAME_NONZERO_PATTERN));
    10485:     }
    10486:     PetscFunctionReturn(PETSC_SUCCESS);
    10487:   }

    10489:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10490:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    10491:   MatCheckPreallocated(mat, 1);

    10493:   PetscCall(PetscLogEventBegin(MAT_RedundantMat, mat, 0, 0, 0));
    10494:   if (subcomm_in == MPI_COMM_NULL && reuse == MAT_INITIAL_MATRIX) { /* get subcomm if user does not provide subcomm */
    10495:     /* create psubcomm, then get subcomm */
    10496:     PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    10497:     PetscCallMPI(MPI_Comm_size(comm, &size));
    10498:     PetscCheck(nsubcomm >= 1 && nsubcomm <= size, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "nsubcomm must between 1 and %d", size);

    10500:     PetscCall(PetscSubcommCreate(comm, &psubcomm));
    10501:     PetscCall(PetscSubcommSetNumber(psubcomm, nsubcomm));
    10502:     PetscCall(PetscSubcommSetType(psubcomm, PETSC_SUBCOMM_CONTIGUOUS));
    10503:     PetscCall(PetscSubcommSetFromOptions(psubcomm));
    10504:     PetscCall(PetscCommDuplicate(PetscSubcommChild(psubcomm), &subcomm, NULL));
    10505:     newsubcomm = PETSC_TRUE;
    10506:     PetscCall(PetscSubcommDestroy(&psubcomm));
    10507:   }

    10509:   /* get isrow, iscol and a local sequential matrix matseq[0] */
    10510:   if (reuse == MAT_INITIAL_MATRIX) {
    10511:     mloc_sub = PETSC_DECIDE;
    10512:     nloc_sub = PETSC_DECIDE;
    10513:     if (bs < 1) {
    10514:       PetscCall(PetscSplitOwnership(subcomm, &mloc_sub, &M));
    10515:       PetscCall(PetscSplitOwnership(subcomm, &nloc_sub, &N));
    10516:     } else {
    10517:       PetscCall(PetscSplitOwnershipBlock(subcomm, bs, &mloc_sub, &M));
    10518:       PetscCall(PetscSplitOwnershipBlock(subcomm, bs, &nloc_sub, &N));
    10519:     }
    10520:     PetscCallMPI(MPI_Scan(&mloc_sub, &rend, 1, MPIU_INT, MPI_SUM, subcomm));
    10521:     rstart = rend - mloc_sub;
    10522:     PetscCall(ISCreateStride(PETSC_COMM_SELF, mloc_sub, rstart, 1, &isrow));
    10523:     PetscCall(ISCreateStride(PETSC_COMM_SELF, N, 0, 1, &iscol));
    10524:     PetscCall(ISSetIdentity(iscol));
    10525:   } else { /* reuse == MAT_REUSE_MATRIX */
    10526:     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");
    10527:     /* retrieve subcomm */
    10528:     PetscCall(PetscObjectGetComm((PetscObject)*matredundant, &subcomm));
    10529:     redund = (*matredundant)->redundant;
    10530:     isrow  = redund->isrow;
    10531:     iscol  = redund->iscol;
    10532:     matseq = redund->matseq;
    10533:   }
    10534:   PetscCall(MatCreateSubMatrices(mat, 1, &isrow, &iscol, reuse, &matseq));

    10536:   /* get matredundant over subcomm */
    10537:   if (reuse == MAT_INITIAL_MATRIX) {
    10538:     PetscCall(MatCreateMPIMatConcatenateSeqMat(subcomm, matseq[0], nloc_sub, reuse, matredundant));

    10540:     /* create a supporting struct and attach it to C for reuse */
    10541:     PetscCall(PetscNew(&redund));
    10542:     (*matredundant)->redundant = redund;
    10543:     redund->isrow              = isrow;
    10544:     redund->iscol              = iscol;
    10545:     redund->matseq             = matseq;
    10546:     if (newsubcomm) {
    10547:       redund->subcomm = subcomm;
    10548:     } else {
    10549:       redund->subcomm = MPI_COMM_NULL;
    10550:     }
    10551:   } else {
    10552:     PetscCall(MatCreateMPIMatConcatenateSeqMat(subcomm, matseq[0], PETSC_DECIDE, reuse, matredundant));
    10553:   }
    10554: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
    10555:   if (matseq[0]->boundtocpu && matseq[0]->bindingpropagates) {
    10556:     PetscCall(MatBindToCPU(*matredundant, PETSC_TRUE));
    10557:     PetscCall(MatSetBindingPropagates(*matredundant, PETSC_TRUE));
    10558:   }
    10559: #endif
    10560:   PetscCall(PetscLogEventEnd(MAT_RedundantMat, mat, 0, 0, 0));
    10561:   PetscFunctionReturn(PETSC_SUCCESS);
    10562: }

    10564: /*@C
    10565:   MatGetMultiProcBlock - Create multiple 'parallel submatrices' from
    10566:   a given `Mat`. Each submatrix can span multiple procs.

    10568:   Collective

    10570:   Input Parameters:
    10571: + mat     - the matrix
    10572: . subComm - the sub communicator obtained as if by `MPI_Comm_split(PetscObjectComm((PetscObject)mat))`
    10573: - scall   - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    10575:   Output Parameter:
    10576: . subMat - parallel sub-matrices each spanning a given `subcomm`

    10578:   Level: advanced

    10580:   Notes:
    10581:   The submatrix partition across processors is dictated by `subComm` a
    10582:   communicator obtained by `MPI_comm_split()` or via `PetscSubcommCreate()`. The `subComm`
    10583:   is not restricted to be grouped with consecutive original MPI processes.

    10585:   Due the `MPI_Comm_split()` usage, the parallel layout of the submatrices
    10586:   map directly to the layout of the original matrix [wrt the local
    10587:   row,col partitioning]. So the original 'DiagonalMat' naturally maps
    10588:   into the 'DiagonalMat' of the `subMat`, hence it is used directly from
    10589:   the `subMat`. However the offDiagMat looses some columns - and this is
    10590:   reconstructed with `MatSetValues()`

    10592:   This is used by `PCBJACOBI` when a single block spans multiple MPI processes.

    10594: .seealso: [](ch_matrices), `Mat`, `MatCreateRedundantMatrix()`, `MatCreateSubMatrices()`, `PCBJACOBI`
    10595: @*/
    10596: PetscErrorCode MatGetMultiProcBlock(Mat mat, MPI_Comm subComm, MatReuse scall, Mat *subMat)
    10597: {
    10598:   PetscMPIInt commsize, subCommSize;

    10600:   PetscFunctionBegin;
    10601:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &commsize));
    10602:   PetscCallMPI(MPI_Comm_size(subComm, &subCommSize));
    10603:   PetscCheck(subCommSize <= commsize, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_OUTOFRANGE, "CommSize %d < SubCommZize %d", commsize, subCommSize);

    10605:   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");
    10606:   PetscCall(PetscLogEventBegin(MAT_GetMultiProcBlock, mat, 0, 0, 0));
    10607:   PetscUseTypeMethod(mat, getmultiprocblock, subComm, scall, subMat);
    10608:   PetscCall(PetscLogEventEnd(MAT_GetMultiProcBlock, mat, 0, 0, 0));
    10609:   PetscFunctionReturn(PETSC_SUCCESS);
    10610: }

    10612: /*@
    10613:   MatGetLocalSubMatrix - Gets a reference to a submatrix specified in local numbering

    10615:   Not Collective

    10617:   Input Parameters:
    10618: + mat   - matrix to extract local submatrix from
    10619: . isrow - local row indices for submatrix
    10620: - iscol - local column indices for submatrix

    10622:   Output Parameter:
    10623: . submat - the submatrix

    10625:   Level: intermediate

    10627:   Notes:
    10628:   `submat` should be disposed of with `MatRestoreLocalSubMatrix()`.

    10630:   Depending on the format of `mat`, the returned `submat` may not implement `MatMult()`.  Its communicator may be
    10631:   the same as `mat`, it may be `PETSC_COMM_SELF`, or some other sub-communictor of `mat`'s.

    10633:   `submat` always implements `MatSetValuesLocal()`.  If `isrow` and `iscol` have the same block size, then
    10634:   `MatSetValuesBlockedLocal()` will also be implemented.

    10636:   `mat` must have had a `ISLocalToGlobalMapping` provided to it with `MatSetLocalToGlobalMapping()`.
    10637:   Matrices obtained with `DMCreateMatrix()` generally already have the local to global mapping provided.

    10639: .seealso: [](ch_matrices), `Mat`, `MatRestoreLocalSubMatrix()`, `MatCreateLocalRef()`, `MatSetLocalToGlobalMapping()`
    10640: @*/
    10641: PetscErrorCode MatGetLocalSubMatrix(Mat mat, IS isrow, IS iscol, Mat *submat)
    10642: {
    10643:   PetscFunctionBegin;
    10647:   PetscCheckSameComm(isrow, 2, iscol, 3);
    10648:   PetscAssertPointer(submat, 4);
    10649:   PetscCheck(mat->rmap->mapping, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Matrix must have local to global mapping provided before this call");

    10651:   if (mat->ops->getlocalsubmatrix) {
    10652:     PetscUseTypeMethod(mat, getlocalsubmatrix, isrow, iscol, submat);
    10653:   } else {
    10654:     PetscCall(MatCreateLocalRef(mat, isrow, iscol, submat));
    10655:   }
    10656:   (*submat)->assembled = mat->assembled;
    10657:   PetscFunctionReturn(PETSC_SUCCESS);
    10658: }

    10660: /*@
    10661:   MatRestoreLocalSubMatrix - Restores a reference to a submatrix specified in local numbering obtained with `MatGetLocalSubMatrix()`

    10663:   Not Collective

    10665:   Input Parameters:
    10666: + mat    - matrix to extract local submatrix from
    10667: . isrow  - local row indices for submatrix
    10668: . iscol  - local column indices for submatrix
    10669: - submat - the submatrix

    10671:   Level: intermediate

    10673: .seealso: [](ch_matrices), `Mat`, `MatGetLocalSubMatrix()`
    10674: @*/
    10675: PetscErrorCode MatRestoreLocalSubMatrix(Mat mat, IS isrow, IS iscol, Mat *submat)
    10676: {
    10677:   PetscFunctionBegin;
    10681:   PetscCheckSameComm(isrow, 2, iscol, 3);
    10682:   PetscAssertPointer(submat, 4);

    10685:   if (mat->ops->restorelocalsubmatrix) {
    10686:     PetscUseTypeMethod(mat, restorelocalsubmatrix, isrow, iscol, submat);
    10687:   } else {
    10688:     PetscCall(MatDestroy(submat));
    10689:   }
    10690:   *submat = NULL;
    10691:   PetscFunctionReturn(PETSC_SUCCESS);
    10692: }

    10694: /*@
    10695:   MatFindZeroDiagonals - Finds all the rows of a matrix that have zero or no diagonal entry in the matrix

    10697:   Collective

    10699:   Input Parameter:
    10700: . mat - the matrix

    10702:   Output Parameter:
    10703: . is - if any rows have zero diagonals this contains the list of them

    10705:   Level: developer

    10707: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    10708: @*/
    10709: PetscErrorCode MatFindZeroDiagonals(Mat mat, IS *is)
    10710: {
    10711:   PetscFunctionBegin;
    10714:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10715:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");

    10717:   if (!mat->ops->findzerodiagonals) {
    10718:     Vec                diag;
    10719:     const PetscScalar *a;
    10720:     PetscInt          *rows;
    10721:     PetscInt           rStart, rEnd, r, nrow = 0;

    10723:     PetscCall(MatCreateVecs(mat, &diag, NULL));
    10724:     PetscCall(MatGetDiagonal(mat, diag));
    10725:     PetscCall(MatGetOwnershipRange(mat, &rStart, &rEnd));
    10726:     PetscCall(VecGetArrayRead(diag, &a));
    10727:     for (r = 0; r < rEnd - rStart; ++r)
    10728:       if (a[r] == 0.0) ++nrow;
    10729:     PetscCall(PetscMalloc1(nrow, &rows));
    10730:     nrow = 0;
    10731:     for (r = 0; r < rEnd - rStart; ++r)
    10732:       if (a[r] == 0.0) rows[nrow++] = r + rStart;
    10733:     PetscCall(VecRestoreArrayRead(diag, &a));
    10734:     PetscCall(VecDestroy(&diag));
    10735:     PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)mat), nrow, rows, PETSC_OWN_POINTER, is));
    10736:   } else {
    10737:     PetscUseTypeMethod(mat, findzerodiagonals, is);
    10738:   }
    10739:   PetscFunctionReturn(PETSC_SUCCESS);
    10740: }

    10742: /*@
    10743:   MatFindOffBlockDiagonalEntries - Finds all the rows of a matrix that have entries outside of the main diagonal block (defined by the matrix block size)

    10745:   Collective

    10747:   Input Parameter:
    10748: . mat - the matrix

    10750:   Output Parameter:
    10751: . is - contains the list of rows with off block diagonal entries

    10753:   Level: developer

    10755: .seealso: [](ch_matrices), `Mat`, `MatMultTranspose()`, `MatMultAdd()`, `MatMultTransposeAdd()`
    10756: @*/
    10757: PetscErrorCode MatFindOffBlockDiagonalEntries(Mat mat, IS *is)
    10758: {
    10759:   PetscFunctionBegin;
    10762:   PetscCheck(mat->assembled, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10763:   PetscCheck(!mat->factortype, PetscObjectComm((PetscObject)mat), PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");

    10765:   PetscUseTypeMethod(mat, findoffblockdiagonalentries, is);
    10766:   PetscFunctionReturn(PETSC_SUCCESS);
    10767: }

    10769: /*@C
    10770:   MatInvertBlockDiagonal - Inverts the block diagonal entries.

    10772:   Collective; No Fortran Support

    10774:   Input Parameter:
    10775: . mat - the matrix

    10777:   Output Parameter:
    10778: . values - the block inverses in column major order (FORTRAN-like)

    10780:   Level: advanced

    10782:   Notes:
    10783:   The size of the blocks is determined by the block size of the matrix.

    10785:   The blocks never overlap between two MPI processes, use `MatInvertVariableBlockEnvelope()` for that case

    10787:   The blocks all have the same size, use `MatInvertVariableBlockDiagonal()` for variable block size

    10789: .seealso: [](ch_matrices), `Mat`, `MatInvertVariableBlockEnvelope()`, `MatInvertBlockDiagonalMat()`
    10790: @*/
    10791: PetscErrorCode MatInvertBlockDiagonal(Mat mat, const PetscScalar *values[])
    10792: {
    10793:   PetscFunctionBegin;
    10795:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10796:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    10797:   PetscUseTypeMethod(mat, invertblockdiagonal, values);
    10798:   PetscFunctionReturn(PETSC_SUCCESS);
    10799: }

    10801: /*@
    10802:   MatInvertVariableBlockDiagonal - Inverts the point block diagonal entries.

    10804:   Collective; No Fortran Support

    10806:   Input Parameters:
    10807: + mat     - the matrix
    10808: . nblocks - the number of blocks on the process, set with `MatSetVariableBlockSizes()`
    10809: - bsizes  - the size of each block on the process, set with `MatSetVariableBlockSizes()`

    10811:   Output Parameter:
    10812: . values - the block inverses in column major order (FORTRAN-like)

    10814:   Level: advanced

    10816:   Notes:
    10817:   Use `MatInvertBlockDiagonal()` if all blocks have the same size

    10819:   The blocks never overlap between two MPI processes, use `MatInvertVariableBlockEnvelope()` for that case

    10821: .seealso: [](ch_matrices), `Mat`, `MatInvertBlockDiagonal()`, `MatSetVariableBlockSizes()`, `MatInvertVariableBlockEnvelope()`
    10822: @*/
    10823: PetscErrorCode MatInvertVariableBlockDiagonal(Mat mat, PetscInt nblocks, const PetscInt bsizes[], PetscScalar values[])
    10824: {
    10825:   PetscFunctionBegin;
    10827:   PetscCheck(mat->assembled, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for unassembled matrix");
    10828:   PetscCheck(!mat->factortype, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Not for factored matrix");
    10829:   PetscUseTypeMethod(mat, invertvariableblockdiagonal, nblocks, bsizes, values);
    10830:   PetscFunctionReturn(PETSC_SUCCESS);
    10831: }

    10833: /*@
    10834:   MatInvertBlockDiagonalMat - set the values of matrix C to be the inverted block diagonal of matrix A

    10836:   Collective

    10838:   Input Parameters:
    10839: + A - the matrix
    10840: - C - matrix with inverted block diagonal of `A`.  This matrix should be created and may have its type set.

    10842:   Level: advanced

    10844:   Note:
    10845:   The blocksize of the matrix is used to determine the blocks on the diagonal of `C`

    10847: .seealso: [](ch_matrices), `Mat`, `MatInvertBlockDiagonal()`
    10848: @*/
    10849: PetscErrorCode MatInvertBlockDiagonalMat(Mat A, Mat C)
    10850: {
    10851:   const PetscScalar *vals;
    10852:   PetscInt          *dnnz;
    10853:   PetscInt           m, rstart, rend, bs, i, j;

    10855:   PetscFunctionBegin;
    10856:   PetscCall(MatInvertBlockDiagonal(A, &vals));
    10857:   PetscCall(MatGetBlockSize(A, &bs));
    10858:   PetscCall(MatGetLocalSize(A, &m, NULL));
    10859:   PetscCall(MatSetLayouts(C, A->rmap, A->cmap));
    10860:   PetscCall(MatSetBlockSizes(C, A->rmap->bs, A->cmap->bs));
    10861:   PetscCall(PetscMalloc1(m / bs, &dnnz));
    10862:   for (j = 0; j < m / bs; j++) dnnz[j] = 1;
    10863:   PetscCall(MatXAIJSetPreallocation(C, bs, dnnz, NULL, NULL, NULL));
    10864:   PetscCall(PetscFree(dnnz));
    10865:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));
    10866:   PetscCall(MatSetOption(C, MAT_ROW_ORIENTED, PETSC_FALSE));
    10867:   for (i = rstart / bs; i < rend / bs; i++) PetscCall(MatSetValuesBlocked(C, 1, &i, 1, &i, &vals[(i - rstart / bs) * bs * bs], INSERT_VALUES));
    10868:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    10869:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    10870:   PetscCall(MatSetOption(C, MAT_ROW_ORIENTED, PETSC_TRUE));
    10871:   PetscFunctionReturn(PETSC_SUCCESS);
    10872: }

    10874: /*@
    10875:   MatTransposeColoringDestroy - Destroys a coloring context for matrix product $C = A*B^T$ that was created
    10876:   via `MatTransposeColoringCreate()`.

    10878:   Collective

    10880:   Input Parameter:
    10881: . c - coloring context

    10883:   Level: intermediate

    10885: .seealso: [](ch_matrices), `Mat`, `MatTransposeColoringCreate()`
    10886: @*/
    10887: PetscErrorCode MatTransposeColoringDestroy(MatTransposeColoring *c)
    10888: {
    10889:   MatTransposeColoring matcolor = *c;

    10891:   PetscFunctionBegin;
    10892:   if (!matcolor) PetscFunctionReturn(PETSC_SUCCESS);
    10893:   if (--((PetscObject)matcolor)->refct > 0) {
    10894:     matcolor = NULL;
    10895:     PetscFunctionReturn(PETSC_SUCCESS);
    10896:   }

    10898:   PetscCall(PetscFree3(matcolor->ncolumns, matcolor->nrows, matcolor->colorforrow));
    10899:   PetscCall(PetscFree(matcolor->rows));
    10900:   PetscCall(PetscFree(matcolor->den2sp));
    10901:   PetscCall(PetscFree(matcolor->colorforcol));
    10902:   PetscCall(PetscFree(matcolor->columns));
    10903:   if (matcolor->brows > 0) PetscCall(PetscFree(matcolor->lstart));
    10904:   PetscCall(PetscHeaderDestroy(c));
    10905:   PetscFunctionReturn(PETSC_SUCCESS);
    10906: }

    10908: /*@
    10909:   MatTransColoringApplySpToDen - Given a symbolic matrix product $C = A*B^T$ for which
    10910:   a `MatTransposeColoring` context has been created, computes a dense $B^T$ by applying
    10911:   `MatTransposeColoring` to sparse `B`.

    10913:   Collective

    10915:   Input Parameters:
    10916: + coloring - coloring context created with `MatTransposeColoringCreate()`
    10917: - B        - sparse matrix

    10919:   Output Parameter:
    10920: . Btdense - dense matrix $B^T$

    10922:   Level: developer

    10924:   Note:
    10925:   These are used internally for some implementations of `MatRARt()`

    10927: .seealso: [](ch_matrices), `Mat`, `MatTransposeColoringCreate()`, `MatTransposeColoringDestroy()`, `MatTransColoringApplyDenToSp()`
    10928: @*/
    10929: PetscErrorCode MatTransColoringApplySpToDen(MatTransposeColoring coloring, Mat B, Mat Btdense)
    10930: {
    10931:   PetscFunctionBegin;

    10936:   PetscCall((*B->ops->transcoloringapplysptoden)(coloring, B, Btdense));
    10937:   PetscFunctionReturn(PETSC_SUCCESS);
    10938: }

    10940: /*@
    10941:   MatTransColoringApplyDenToSp - Given a symbolic matrix product $C_{sp} = A*B^T$ for which
    10942:   a `MatTransposeColoring` context has been created and a dense matrix $C_{den} = A*B^T_{dense}$
    10943:   in which `B^T_{dens}` is obtained from `MatTransColoringApplySpToDen()`, recover sparse matrix
    10944:   $C_{sp}$ from $C_{den}$.

    10946:   Collective

    10948:   Input Parameters:
    10949: + matcoloring - coloring context created with `MatTransposeColoringCreate()`
    10950: - Cden        - matrix product of a sparse matrix and a dense matrix Btdense

    10952:   Output Parameter:
    10953: . Csp - sparse matrix

    10955:   Level: developer

    10957:   Note:
    10958:   These are used internally for some implementations of `MatRARt()`

    10960: .seealso: [](ch_matrices), `Mat`, `MatTransposeColoringCreate()`, `MatTransposeColoringDestroy()`, `MatTransColoringApplySpToDen()`
    10961: @*/
    10962: PetscErrorCode MatTransColoringApplyDenToSp(MatTransposeColoring matcoloring, Mat Cden, Mat Csp)
    10963: {
    10964:   PetscFunctionBegin;

    10969:   PetscCall((*Csp->ops->transcoloringapplydentosp)(matcoloring, Cden, Csp));
    10970:   PetscCall(MatAssemblyBegin(Csp, MAT_FINAL_ASSEMBLY));
    10971:   PetscCall(MatAssemblyEnd(Csp, MAT_FINAL_ASSEMBLY));
    10972:   PetscFunctionReturn(PETSC_SUCCESS);
    10973: }

    10975: /*@
    10976:   MatTransposeColoringCreate - Creates a matrix coloring context for the matrix product $C = A*B^T$.

    10978:   Collective

    10980:   Input Parameters:
    10981: + mat        - the matrix product C
    10982: - iscoloring - the coloring of the matrix; usually obtained with `MatColoringCreate()` or `DMCreateColoring()`

    10984:   Output Parameter:
    10985: . color - the new coloring context

    10987:   Level: intermediate

    10989: .seealso: [](ch_matrices), `Mat`, `MatTransposeColoringDestroy()`, `MatTransColoringApplySpToDen()`,
    10990:           `MatTransColoringApplyDenToSp()`
    10991: @*/
    10992: PetscErrorCode MatTransposeColoringCreate(Mat mat, ISColoring iscoloring, MatTransposeColoring *color)
    10993: {
    10994:   MatTransposeColoring c;
    10995:   MPI_Comm             comm;

    10997:   PetscFunctionBegin;
    10998:   PetscAssertPointer(color, 3);

    11000:   PetscCall(PetscLogEventBegin(MAT_TransposeColoringCreate, mat, 0, 0, 0));
    11001:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    11002:   PetscCall(PetscHeaderCreate(c, MAT_TRANSPOSECOLORING_CLASSID, "MatTransposeColoring", "Matrix product C=A*B^T via coloring", "Mat", comm, MatTransposeColoringDestroy, NULL));
    11003:   c->ctype = iscoloring->ctype;
    11004:   PetscUseTypeMethod(mat, transposecoloringcreate, iscoloring, c);
    11005:   *color = c;
    11006:   PetscCall(PetscLogEventEnd(MAT_TransposeColoringCreate, mat, 0, 0, 0));
    11007:   PetscFunctionReturn(PETSC_SUCCESS);
    11008: }

    11010: /*@
    11011:   MatGetNonzeroState - Returns a 64-bit integer representing the current state of nonzeros in the matrix. If the
    11012:   matrix has had new nonzero locations added to (or removed from) the matrix since the previous call, the value will be larger.

    11014:   Not Collective

    11016:   Input Parameter:
    11017: . mat - the matrix

    11019:   Output Parameter:
    11020: . state - the current state

    11022:   Level: intermediate

    11024:   Notes:
    11025:   You can only compare states from two different calls to the SAME matrix, you cannot compare calls between
    11026:   different matrices

    11028:   Use `PetscObjectStateGet()` to check for changes to the numerical values in a matrix

    11030:   Use the result of `PetscObjectGetId()` to compare if a previously checked matrix is the same as the current matrix, do not compare object pointers.

    11032: .seealso: [](ch_matrices), `Mat`, `PetscObjectStateGet()`, `PetscObjectGetId()`
    11033: @*/
    11034: PetscErrorCode MatGetNonzeroState(Mat mat, PetscObjectState *state)
    11035: {
    11036:   PetscFunctionBegin;
    11038:   *state = mat->nonzerostate;
    11039:   PetscFunctionReturn(PETSC_SUCCESS);
    11040: }

    11042: /*@
    11043:   MatCreateMPIMatConcatenateSeqMat - Creates a single large PETSc matrix by concatenating sequential
    11044:   matrices from each processor

    11046:   Collective

    11048:   Input Parameters:
    11049: + comm   - the communicators the parallel matrix will live on
    11050: . seqmat - the input sequential matrices
    11051: . n      - number of local columns (or `PETSC_DECIDE`)
    11052: - reuse  - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    11054:   Output Parameter:
    11055: . mpimat - the parallel matrix generated

    11057:   Level: developer

    11059:   Note:
    11060:   The number of columns of the matrix in EACH processor MUST be the same.

    11062: .seealso: [](ch_matrices), `Mat`
    11063: @*/
    11064: PetscErrorCode MatCreateMPIMatConcatenateSeqMat(MPI_Comm comm, Mat seqmat, PetscInt n, MatReuse reuse, Mat *mpimat)
    11065: {
    11066:   PetscMPIInt size;

    11068:   PetscFunctionBegin;
    11069:   PetscCallMPI(MPI_Comm_size(comm, &size));
    11070:   if (size == 1) {
    11071:     if (reuse == MAT_INITIAL_MATRIX) {
    11072:       PetscCall(MatDuplicate(seqmat, MAT_COPY_VALUES, mpimat));
    11073:     } else {
    11074:       PetscCall(MatCopy(seqmat, *mpimat, SAME_NONZERO_PATTERN));
    11075:     }
    11076:     PetscFunctionReturn(PETSC_SUCCESS);
    11077:   }

    11079:   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");

    11081:   PetscCall(PetscLogEventBegin(MAT_Merge, seqmat, 0, 0, 0));
    11082:   PetscCall((*seqmat->ops->creatempimatconcatenateseqmat)(comm, seqmat, n, reuse, mpimat));
    11083:   PetscCall(PetscLogEventEnd(MAT_Merge, seqmat, 0, 0, 0));
    11084:   PetscFunctionReturn(PETSC_SUCCESS);
    11085: }

    11087: /*@
    11088:   MatSubdomainsCreateCoalesce - Creates index subdomains by coalescing adjacent MPI processes' ownership ranges.

    11090:   Collective

    11092:   Input Parameters:
    11093: + A - the matrix to create subdomains from
    11094: - N - requested number of subdomains

    11096:   Output Parameters:
    11097: + n   - number of subdomains resulting on this MPI process
    11098: - iss - `IS` list with indices of subdomains on this MPI process

    11100:   Level: advanced

    11102:   Note:
    11103:   The number of subdomains must be smaller than the communicator size

    11105: .seealso: [](ch_matrices), `Mat`, `IS`
    11106: @*/
    11107: PetscErrorCode MatSubdomainsCreateCoalesce(Mat A, PetscInt N, PetscInt *n, IS *iss[])
    11108: {
    11109:   MPI_Comm    comm, subcomm;
    11110:   PetscMPIInt size, rank, color;
    11111:   PetscInt    rstart, rend, k;

    11113:   PetscFunctionBegin;
    11114:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    11115:   PetscCallMPI(MPI_Comm_size(comm, &size));
    11116:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    11117:   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);
    11118:   *n    = 1;
    11119:   k     = size / N + (size % N > 0); /* There are up to k ranks to a color */
    11120:   color = rank / k;
    11121:   PetscCallMPI(MPI_Comm_split(comm, color, rank, &subcomm));
    11122:   PetscCall(PetscMalloc1(1, iss));
    11123:   PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
    11124:   PetscCall(ISCreateStride(subcomm, rend - rstart, rstart, 1, iss[0]));
    11125:   PetscCallMPI(MPI_Comm_free(&subcomm));
    11126:   PetscFunctionReturn(PETSC_SUCCESS);
    11127: }

    11129: /*@
    11130:   MatGalerkin - Constructs the coarse grid problem matrix via Galerkin projection.

    11132:   If the interpolation and restriction operators are the same, uses `MatPtAP()`.
    11133:   If they are not the same, uses `MatMatMatMult()`.

    11135:   Once the coarse grid problem is constructed, correct for interpolation operators
    11136:   that are not of full rank, which can legitimately happen in the case of non-nested
    11137:   geometric multigrid.

    11139:   Input Parameters:
    11140: + restrct     - restriction operator
    11141: . dA          - fine grid matrix
    11142: . interpolate - interpolation operator
    11143: . reuse       - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    11144: - fill        - expected fill, use `PETSC_DETERMINE` or `PETSC_DETERMINE` if you do not have a good estimate

    11146:   Output Parameter:
    11147: . A - the Galerkin coarse matrix

    11149:   Options Database Key:
    11150: . -pc_mg_galerkin <both,pmat,mat,none> - for what matrices the Galerkin process should be used

    11152:   Level: developer

    11154:   Note:
    11155:   The deprecated `PETSC_DEFAULT` in `fill` also means use the current value

    11157: .seealso: [](ch_matrices), `Mat`, `MatPtAP()`, `MatMatMatMult()`
    11158: @*/
    11159: PetscErrorCode MatGalerkin(Mat restrct, Mat dA, Mat interpolate, MatReuse reuse, PetscReal fill, Mat *A)
    11160: {
    11161:   IS  zerorows;
    11162:   Vec diag;

    11164:   PetscFunctionBegin;
    11165:   PetscCheck(reuse != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Inplace product not supported");
    11166:   /* Construct the coarse grid matrix */
    11167:   if (interpolate == restrct) {
    11168:     PetscCall(MatPtAP(dA, interpolate, reuse, fill, A));
    11169:   } else {
    11170:     PetscCall(MatMatMatMult(restrct, dA, interpolate, reuse, fill, A));
    11171:   }

    11173:   /* If the interpolation matrix is not of full rank, A will have zero rows.
    11174:      This can legitimately happen in the case of non-nested geometric multigrid.
    11175:      In that event, we set the rows of the matrix to the rows of the identity,
    11176:      ignoring the equations (as the RHS will also be zero). */

    11178:   PetscCall(MatFindZeroRows(*A, &zerorows));

    11180:   if (zerorows != NULL) { /* if there are any zero rows */
    11181:     PetscCall(MatCreateVecs(*A, &diag, NULL));
    11182:     PetscCall(MatGetDiagonal(*A, diag));
    11183:     PetscCall(VecISSet(diag, zerorows, 1.0));
    11184:     PetscCall(MatDiagonalSet(*A, diag, INSERT_VALUES));
    11185:     PetscCall(VecDestroy(&diag));
    11186:     PetscCall(ISDestroy(&zerorows));
    11187:   }
    11188:   PetscFunctionReturn(PETSC_SUCCESS);
    11189: }

    11191: /*@C
    11192:   MatSetOperation - Allows user to set a matrix operation for any matrix type

    11194:   Logically Collective

    11196:   Input Parameters:
    11197: + mat - the matrix
    11198: . op  - the name of the operation
    11199: - f   - the function that provides the operation

    11201:   Level: developer

    11203:   Example Usage:
    11204: .vb
    11205:   extern PetscErrorCode usermult(Mat, Vec, Vec);

    11207:   PetscCall(MatCreateXXX(comm, ..., &A));
    11208:   PetscCall(MatSetOperation(A, MATOP_MULT, (PetscErrorCodeFn *)usermult));
    11209: .ve

    11211:   Notes:
    11212:   See the file `include/petscmat.h` for a complete list of matrix
    11213:   operations, which all have the form MATOP_<OPERATION>, where
    11214:   <OPERATION> is the name (in all capital letters) of the
    11215:   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).

    11217:   All user-provided functions (except for `MATOP_DESTROY`) should have the same calling
    11218:   sequence as the usual matrix interface routines, since they
    11219:   are intended to be accessed via the usual matrix interface
    11220:   routines, e.g.,
    11221: .vb
    11222:   MatMult(Mat, Vec, Vec) -> usermult(Mat, Vec, Vec)
    11223: .ve

    11225:   In particular each function MUST return `PETSC_SUCCESS` on success and
    11226:   nonzero on failure.

    11228:   This routine is distinct from `MatShellSetOperation()` in that it can be called on any matrix type.

    11230: .seealso: [](ch_matrices), `Mat`, `MatGetOperation()`, `MatCreateShell()`, `MatShellSetContext()`, `MatShellSetOperation()`
    11231: @*/
    11232: PetscErrorCode MatSetOperation(Mat mat, MatOperation op, PetscErrorCodeFn *f)
    11233: {
    11234:   PetscFunctionBegin;
    11236:   if (op == MATOP_VIEW && !mat->ops->viewnative && f != (PetscErrorCodeFn *)mat->ops->view) mat->ops->viewnative = mat->ops->view;
    11237:   (((PetscErrorCodeFn **)mat->ops)[op]) = f;
    11238:   PetscFunctionReturn(PETSC_SUCCESS);
    11239: }

    11241: /*@C
    11242:   MatGetOperation - Gets a matrix operation for any matrix type.

    11244:   Not Collective

    11246:   Input Parameters:
    11247: + mat - the matrix
    11248: - op  - the name of the operation

    11250:   Output Parameter:
    11251: . f - the function that provides the operation

    11253:   Level: developer

    11255:   Example Usage:
    11256: .vb
    11257:   PetscErrorCode (*usermult)(Mat, Vec, Vec);

    11259:   MatGetOperation(A, MATOP_MULT, (PetscErrorCodeFn **)&usermult);
    11260: .ve

    11262:   Notes:
    11263:   See the file `include/petscmat.h` for a complete list of matrix
    11264:   operations, which all have the form MATOP_<OPERATION>, where
    11265:   <OPERATION> is the name (in all capital letters) of the
    11266:   user interface routine (e.g., `MatMult()` -> `MATOP_MULT`).

    11268:   This routine is distinct from `MatShellGetOperation()` in that it can be called on any matrix type.

    11270: .seealso: [](ch_matrices), `Mat`, `MatSetOperation()`, `MatCreateShell()`, `MatShellGetContext()`, `MatShellGetOperation()`
    11271: @*/
    11272: PetscErrorCode MatGetOperation(Mat mat, MatOperation op, PetscErrorCodeFn **f)
    11273: {
    11274:   PetscFunctionBegin;
    11276:   *f = (((PetscErrorCodeFn **)mat->ops)[op]);
    11277:   PetscFunctionReturn(PETSC_SUCCESS);
    11278: }

    11280: /*@
    11281:   MatHasOperation - Determines whether the given matrix supports the particular operation.

    11283:   Not Collective

    11285:   Input Parameters:
    11286: + mat - the matrix
    11287: - op  - the operation, for example, `MATOP_GET_DIAGONAL`

    11289:   Output Parameter:
    11290: . has - either `PETSC_TRUE` or `PETSC_FALSE`

    11292:   Level: advanced

    11294:   Note:
    11295:   See `MatSetOperation()` for additional discussion on naming convention and usage of `op`.

    11297: .seealso: [](ch_matrices), `Mat`, `MatCreateShell()`, `MatGetOperation()`, `MatSetOperation()`
    11298: @*/
    11299: PetscErrorCode MatHasOperation(Mat mat, MatOperation op, PetscBool *has)
    11300: {
    11301:   PetscFunctionBegin;
    11303:   PetscAssertPointer(has, 3);
    11304:   if (mat->ops->hasoperation) {
    11305:     PetscUseTypeMethod(mat, hasoperation, op, has);
    11306:   } else {
    11307:     if (((void **)mat->ops)[op]) *has = PETSC_TRUE;
    11308:     else {
    11309:       *has = PETSC_FALSE;
    11310:       if (op == MATOP_CREATE_SUBMATRIX) {
    11311:         PetscMPIInt size;

    11313:         PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)mat), &size));
    11314:         if (size == 1) PetscCall(MatHasOperation(mat, MATOP_CREATE_SUBMATRICES, has));
    11315:       }
    11316:     }
    11317:   }
    11318:   PetscFunctionReturn(PETSC_SUCCESS);
    11319: }

    11321: /*@
    11322:   MatHasCongruentLayouts - Determines whether the rows and columns layouts of the matrix are congruent

    11324:   Collective

    11326:   Input Parameter:
    11327: . mat - the matrix

    11329:   Output Parameter:
    11330: . cong - either `PETSC_TRUE` or `PETSC_FALSE`

    11332:   Level: beginner

    11334: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatSetSizes()`, `PetscLayout`
    11335: @*/
    11336: PetscErrorCode MatHasCongruentLayouts(Mat mat, PetscBool *cong)
    11337: {
    11338:   PetscFunctionBegin;
    11341:   PetscAssertPointer(cong, 2);
    11342:   if (!mat->rmap || !mat->cmap) {
    11343:     *cong = mat->rmap == mat->cmap ? PETSC_TRUE : PETSC_FALSE;
    11344:     PetscFunctionReturn(PETSC_SUCCESS);
    11345:   }
    11346:   if (mat->congruentlayouts == PETSC_DECIDE) { /* first time we compare rows and cols layouts */
    11347:     PetscCall(PetscLayoutSetUp(mat->rmap));
    11348:     PetscCall(PetscLayoutSetUp(mat->cmap));
    11349:     PetscCall(PetscLayoutCompare(mat->rmap, mat->cmap, cong));
    11350:     if (*cong) mat->congruentlayouts = 1;
    11351:     else mat->congruentlayouts = 0;
    11352:   } else *cong = mat->congruentlayouts ? PETSC_TRUE : PETSC_FALSE;
    11353:   PetscFunctionReturn(PETSC_SUCCESS);
    11354: }

    11356: PetscErrorCode MatSetInf(Mat A)
    11357: {
    11358:   PetscFunctionBegin;
    11359:   PetscUseTypeMethod(A, setinf);
    11360:   PetscFunctionReturn(PETSC_SUCCESS);
    11361: }

    11363: /*@
    11364:   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
    11365:   and possibly removes small values from the graph structure.

    11367:   Collective

    11369:   Input Parameters:
    11370: + A       - the matrix
    11371: . sym     - `PETSC_TRUE` indicates that the graph should be symmetrized
    11372: . scale   - `PETSC_TRUE` indicates that the graph edge weights should be symmetrically scaled with the diagonal entry
    11373: . filter  - filter value - < 0: does nothing; == 0: removes only 0.0 entries; otherwise: removes entries with abs(entries) <= value
    11374: . num_idx - size of 'index' array
    11375: - index   - array of block indices to use for graph strength of connection weight

    11377:   Output Parameter:
    11378: . graph - the resulting graph

    11380:   Level: advanced

    11382: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `PCGAMG`
    11383: @*/
    11384: PetscErrorCode MatCreateGraph(Mat A, PetscBool sym, PetscBool scale, PetscReal filter, PetscInt num_idx, PetscInt index[], Mat *graph)
    11385: {
    11386:   PetscFunctionBegin;
    11390:   PetscAssertPointer(graph, 7);
    11391:   PetscCall(PetscLogEventBegin(MAT_CreateGraph, A, 0, 0, 0));
    11392:   PetscUseTypeMethod(A, creategraph, sym, scale, filter, num_idx, index, graph);
    11393:   PetscCall(PetscLogEventEnd(MAT_CreateGraph, A, 0, 0, 0));
    11394:   PetscFunctionReturn(PETSC_SUCCESS);
    11395: }

    11397: /*@
    11398:   MatEliminateZeros - eliminate the nondiagonal zero entries in place from the nonzero structure of a sparse `Mat` in place,
    11399:   meaning the same memory is used for the matrix, and no new memory is allocated.

    11401:   Collective

    11403:   Input Parameters:
    11404: + A    - the matrix
    11405: - 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

    11407:   Level: intermediate

    11409:   Developer Note:
    11410:   The entries in the sparse matrix data structure are shifted to fill in the unneeded locations in the data. Thus the end
    11411:   of the arrays in the data structure are unneeded.

    11413: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateGraph()`, `MatFilter()`
    11414: @*/
    11415: PetscErrorCode MatEliminateZeros(Mat A, PetscBool keep)
    11416: {
    11417:   PetscFunctionBegin;
    11419:   PetscUseTypeMethod(A, eliminatezeros, keep);
    11420:   PetscFunctionReturn(PETSC_SUCCESS);
    11421: }

    11423: /*@C
    11424:   MatGetCurrentMemType - Get the memory location of the matrix

    11426:   Not Collective, but the result will be the same on all MPI processes

    11428:   Input Parameter:
    11429: . A - the matrix whose memory type we are checking

    11431:   Output Parameter:
    11432: . m - the memory type

    11434:   Level: intermediate

    11436: .seealso: [](ch_matrices), `Mat`, `MatBoundToCPU()`, `PetscMemType`
    11437: @*/
    11438: PetscErrorCode MatGetCurrentMemType(Mat A, PetscMemType *m)
    11439: {
    11440:   PetscFunctionBegin;
    11442:   PetscAssertPointer(m, 2);
    11443:   if (A->ops->getcurrentmemtype) PetscUseTypeMethod(A, getcurrentmemtype, m);
    11444:   else *m = PETSC_MEMTYPE_HOST;
    11445:   PetscFunctionReturn(PETSC_SUCCESS);
    11446: }