Actual source code: htool.cxx

      1: #include <../src/mat/impls/htool/htool.hpp>
      2: #include <petscblaslapack.h>
      3: #include <set>

      5: const char *const MatHtoolCompressorTypes[] = {"sympartialACA", "fullACA", "SVD"};
      6: const char *const MatHtoolClusteringTypes[] = {"PCARegular", "PCAGeometric", "BoundingBox1Regular", "BoundingBox1Geometric"};
      7: const char        HtoolCitation[]           = "@article{marchand2020two,\n"
      8:                                               "  Author = {Marchand, Pierre and Claeys, Xavier and Jolivet, Pierre and Nataf, Fr\\'ed\\'eric and Tournier, Pierre-Henri},\n"
      9:                                               "  Title = {Two-level preconditioning for $h$-version boundary element approximation of hypersingular operator with {GenEO}},\n"
     10:                                               "  Year = {2020},\n"
     11:                                               "  Publisher = {Elsevier},\n"
     12:                                               "  Journal = {Numerische Mathematik},\n"
     13:                                               "  Volume = {146},\n"
     14:                                               "  Pages = {597--628},\n"
     15:                                               "  Url = {https://github.com/htool-ddm/htool}\n"
     16:                                               "}\n";
     17: static PetscBool  HtoolCite                 = PETSC_FALSE;

     19: static PetscErrorCode MatGetDiagonal_Htool(Mat A, Vec v)
     20: {
     21:   Mat_Htool   *a;
     22:   PetscScalar *x;
     23:   PetscBool    flg;

     25:   PetscFunctionBegin;
     26:   PetscCall(MatHasCongruentLayouts(A, &flg));
     27:   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Only congruent layouts supported");
     28:   PetscCall(MatShellGetContext(A, &a));
     29:   PetscCall(VecGetArrayWrite(v, &x));
     30:   PetscStackCallExternalVoid("copy_diagonal_in_user_numbering", htool::copy_diagonal_in_user_numbering(a->distributed_operator_holder->hmatrix, x));
     31:   PetscCall(VecRestoreArrayWrite(v, &x));
     32:   PetscFunctionReturn(PETSC_SUCCESS);
     33: }

     35: static PetscErrorCode MatGetDiagonalBlock_Htool(Mat A, Mat *b)
     36: {
     37:   Mat_Htool                 *a;
     38:   Mat                        B;
     39:   PetscScalar               *ptr, shift, scale;
     40:   PetscBool                  flg;
     41:   PetscMPIInt                rank;
     42:   htool::Cluster<PetscReal> *source_cluster = nullptr;

     44:   PetscFunctionBegin;
     45:   PetscCall(MatHasCongruentLayouts(A, &flg));
     46:   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Only congruent layouts supported");
     47:   PetscCall(MatShellGetContext(A, &a));
     48:   PetscCall(PetscObjectQuery((PetscObject)A, "DiagonalBlock", (PetscObject *)&B)); /* same logic as in MatGetDiagonalBlock_MPIDense() */
     49:   if (!B) {
     50:     PetscCall(MatShellGetScalingShifts(A, &shift, &scale, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
     51:     PetscCall(MatCreateDense(PETSC_COMM_SELF, A->rmap->n, A->rmap->n, A->rmap->n, A->rmap->n, nullptr, &B));
     52:     PetscCall(MatDenseGetArrayWrite(B, &ptr));
     53:     PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
     54:     source_cluster = a->source_cluster ? a->source_cluster.get() : a->target_cluster.get();
     55:     PetscStackCallExternalVoid("copy_to_dense_in_user_numbering", htool::copy_to_dense_in_user_numbering(*a->distributed_operator_holder->hmatrix.get_sub_hmatrix(a->target_cluster->get_cluster_on_partition(rank), source_cluster->get_cluster_on_partition(rank)), ptr));
     56:     PetscCall(MatDenseRestoreArrayWrite(B, &ptr));
     57:     PetscCall(MatPropagateSymmetryOptions(A, B));
     58:     PetscCall(PetscObjectCompose((PetscObject)A, "DiagonalBlock", (PetscObject)B));
     59:     *b = B;
     60:     PetscCall(MatDestroy(&B));
     61:     PetscCall(MatShift(*b, shift));
     62:     PetscCall(MatScale(*b, scale));
     63:   } else {
     64:     PetscCall(MatShellGetScalingShifts(A, (PetscScalar *)MAT_SHELL_NOT_ALLOWED, (PetscScalar *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
     65:     *b = B;
     66:   }
     67:   PetscFunctionReturn(PETSC_SUCCESS);
     68: }

     70: static PetscErrorCode MatMult_Htool(Mat A, Vec x, Vec y)
     71: {
     72:   Mat_Htool         *a;
     73:   const PetscScalar *in;
     74:   PetscScalar       *out;

     76:   PetscFunctionBegin;
     77:   PetscCall(MatShellGetContext(A, &a));
     78:   PetscCall(VecGetArrayRead(x, &in));
     79:   PetscCall(VecGetArrayWrite(y, &out));
     80:   a->distributed_operator_holder->distributed_operator.vector_product_local_to_local(in, out, nullptr);
     81:   PetscCall(VecRestoreArrayRead(x, &in));
     82:   PetscCall(VecRestoreArrayWrite(y, &out));
     83:   PetscFunctionReturn(PETSC_SUCCESS);
     84: }

     86: static PetscErrorCode MatMultTranspose_Htool(Mat A, Vec x, Vec y)
     87: {
     88:   Mat_Htool         *a;
     89:   const PetscScalar *in;
     90:   PetscScalar       *out;

     92:   PetscFunctionBegin;
     93:   PetscCall(MatShellGetContext(A, &a));
     94:   PetscCall(VecGetArrayRead(x, &in));
     95:   PetscCall(VecGetArrayWrite(y, &out));
     96:   a->distributed_operator_holder->distributed_operator.vector_product_transp_local_to_local(in, out, nullptr);
     97:   PetscCall(VecRestoreArrayRead(x, &in));
     98:   PetscCall(VecRestoreArrayWrite(y, &out));
     99:   PetscFunctionReturn(PETSC_SUCCESS);
    100: }

    102: static PetscErrorCode MatIncreaseOverlap_Htool(Mat A, PetscInt is_max, IS is[], PetscInt ov)
    103: {
    104:   std::set<PetscInt> set;
    105:   const PetscInt    *idx;
    106:   PetscInt          *oidx, size, bs[2];
    107:   PetscMPIInt        csize;

    109:   PetscFunctionBegin;
    110:   PetscCall(MatGetBlockSizes(A, bs, bs + 1));
    111:   if (bs[0] != bs[1]) bs[0] = 1;
    112:   for (PetscInt i = 0; i < is_max; ++i) {
    113:     /* basic implementation that adds indices by shifting an IS by -ov, -ov+1..., -1, 1..., ov-1, ov */
    114:     /* needed to avoid subdomain matrices to replicate A since it is dense                           */
    115:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)is[i]), &csize));
    116:     PetscCheck(csize == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "Unsupported parallel IS");
    117:     PetscCall(ISGetSize(is[i], &size));
    118:     PetscCall(ISGetIndices(is[i], &idx));
    119:     for (PetscInt j = 0; j < size; ++j) {
    120:       set.insert(idx[j]);
    121:       for (PetscInt k = 1; k <= ov; ++k) {                                              /* for each layer of overlap      */
    122:         if (idx[j] - k >= 0) set.insert(idx[j] - k);                                    /* do not insert negative indices */
    123:         if (idx[j] + k < A->rmap->N && idx[j] + k < A->cmap->N) set.insert(idx[j] + k); /* do not insert indices greater than the dimension of A */
    124:       }
    125:     }
    126:     PetscCall(ISRestoreIndices(is[i], &idx));
    127:     PetscCall(ISDestroy(is + i));
    128:     if (bs[0] > 1) {
    129:       for (std::set<PetscInt>::iterator it = set.cbegin(); it != set.cend(); it++) {
    130:         std::vector<PetscInt> block(bs[0]);
    131:         std::iota(block.begin(), block.end(), (*it / bs[0]) * bs[0]);
    132:         set.insert(block.cbegin(), block.cend());
    133:       }
    134:     }
    135:     size = set.size(); /* size with overlap */
    136:     PetscCall(PetscMalloc1(size, &oidx));
    137:     for (const PetscInt j : set) *oidx++ = j;
    138:     oidx -= size;
    139:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, size, oidx, PETSC_OWN_POINTER, is + i));
    140:   }
    141:   PetscFunctionReturn(PETSC_SUCCESS);
    142: }

    144: static PetscErrorCode MatCreateSubMatrices_Htool(Mat A, PetscInt n, const IS irow[], const IS icol[], MatReuse scall, Mat *submat[])
    145: {
    146:   Mat_Htool         *a;
    147:   Mat                D, B, BT;
    148:   const PetscScalar *copy;
    149:   PetscScalar       *ptr, shift, scale;
    150:   const PetscInt    *idxr, *idxc, *it;
    151:   PetscInt           nrow, m, i;
    152:   PetscBool          flg;

    154:   PetscFunctionBegin;
    155:   PetscCall(MatShellGetScalingShifts(A, &shift, &scale, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
    156:   PetscCall(MatShellGetContext(A, &a));
    157:   if (scall != MAT_REUSE_MATRIX) PetscCall(PetscCalloc1(n, submat));
    158:   for (i = 0; i < n; ++i) {
    159:     PetscCall(ISGetLocalSize(irow[i], &nrow));
    160:     PetscCall(ISGetLocalSize(icol[i], &m));
    161:     PetscCall(ISGetIndices(irow[i], &idxr));
    162:     PetscCall(ISGetIndices(icol[i], &idxc));
    163:     if (scall != MAT_REUSE_MATRIX) PetscCall(MatCreateDense(PETSC_COMM_SELF, nrow, m, nrow, m, nullptr, (*submat) + i));
    164:     PetscCall(MatDenseGetArrayWrite((*submat)[i], &ptr));
    165:     if (irow[i] == icol[i]) { /* same row and column IS? */
    166:       PetscCall(MatHasCongruentLayouts(A, &flg));
    167:       if (flg) {
    168:         PetscCall(ISSorted(irow[i], &flg));
    169:         if (flg) { /* sorted IS? */
    170:           it = std::lower_bound(idxr, idxr + nrow, A->rmap->rstart);
    171:           if (it != idxr + nrow && *it == A->rmap->rstart) {    /* rmap->rstart in IS? */
    172:             if (std::distance(idxr, it) + A->rmap->n <= nrow) { /* long enough IS to store the local diagonal block? */
    173:               for (PetscInt j = 0; j < A->rmap->n && flg; ++j)
    174:                 if (PetscUnlikely(it[j] != A->rmap->rstart + j)) flg = PETSC_FALSE;
    175:               if (flg) { /* complete local diagonal block in IS? */
    176:                 /* fast extraction when the local diagonal block is part of the submatrix, e.g., for PCASM or PCHPDDM
    177:                  *      [   B   C   E   ]
    178:                  *  A = [   B   D   E   ]
    179:                  *      [   B   F   E   ]
    180:                  */
    181:                 m = std::distance(idxr, it); /* shift of the coefficient (0,0) of block D from above */
    182:                 PetscCall(MatGetDiagonalBlock(A, &D));
    183:                 PetscCall(MatDenseGetArrayRead(D, &copy));
    184:                 for (PetscInt k = 0; k < A->rmap->n; ++k) { PetscCall(PetscArraycpy(ptr + (m + k) * nrow + m, copy + k * A->rmap->n, A->rmap->n)); /* block D from above */ }
    185:                 PetscCall(MatDenseRestoreArrayRead(D, &copy));
    186:                 if (m) {
    187:                   a->wrapper->copy_submatrix(nrow, m, idxr, idxc, ptr); /* vertical block B from above */
    188:                   /* entry-wise assembly may be costly, so transpose already-computed entries when possible */
    189:                   if (A->symmetric == PETSC_BOOL3_TRUE || A->hermitian == PETSC_BOOL3_TRUE) {
    190:                     PetscCall(MatCreateDense(PETSC_COMM_SELF, A->rmap->n, m, A->rmap->n, m, ptr + m, &B));
    191:                     PetscCall(MatDenseSetLDA(B, nrow));
    192:                     PetscCall(MatCreateDense(PETSC_COMM_SELF, m, A->rmap->n, m, A->rmap->n, ptr + m * nrow, &BT));
    193:                     PetscCall(MatDenseSetLDA(BT, nrow));
    194:                     if (A->hermitian == PETSC_BOOL3_TRUE && PetscDefined(USE_COMPLEX)) {
    195:                       PetscCall(MatHermitianTranspose(B, MAT_REUSE_MATRIX, &BT));
    196:                     } else {
    197:                       PetscCall(MatTransposeSetPrecursor(B, BT));
    198:                       PetscCall(MatTranspose(B, MAT_REUSE_MATRIX, &BT));
    199:                     }
    200:                     PetscCall(MatDestroy(&B));
    201:                     PetscCall(MatDestroy(&BT));
    202:                   } else {
    203:                     for (PetscInt k = 0; k < A->rmap->n; ++k) { /* block C from above */
    204:                       a->wrapper->copy_submatrix(m, 1, idxr, idxc + m + k, ptr + (m + k) * nrow);
    205:                     }
    206:                   }
    207:                 }
    208:                 if (m + A->rmap->n != nrow) {
    209:                   a->wrapper->copy_submatrix(nrow, std::distance(it + A->rmap->n, idxr + nrow), idxr, idxc + m + A->rmap->n, ptr + (m + A->rmap->n) * nrow); /* vertical block E from above */
    210:                   /* entry-wise assembly may be costly, so transpose already-computed entries when possible */
    211:                   if (A->symmetric == PETSC_BOOL3_TRUE || A->hermitian == PETSC_BOOL3_TRUE) {
    212:                     PetscCall(MatCreateDense(PETSC_COMM_SELF, A->rmap->n, nrow - (m + A->rmap->n), A->rmap->n, nrow - (m + A->rmap->n), ptr + (m + A->rmap->n) * nrow + m, &B));
    213:                     PetscCall(MatDenseSetLDA(B, nrow));
    214:                     PetscCall(MatCreateDense(PETSC_COMM_SELF, nrow - (m + A->rmap->n), A->rmap->n, nrow - (m + A->rmap->n), A->rmap->n, ptr + m * nrow + m + A->rmap->n, &BT));
    215:                     PetscCall(MatDenseSetLDA(BT, nrow));
    216:                     if (A->hermitian == PETSC_BOOL3_TRUE && PetscDefined(USE_COMPLEX)) {
    217:                       PetscCall(MatHermitianTranspose(B, MAT_REUSE_MATRIX, &BT));
    218:                     } else {
    219:                       PetscCall(MatTransposeSetPrecursor(B, BT));
    220:                       PetscCall(MatTranspose(B, MAT_REUSE_MATRIX, &BT));
    221:                     }
    222:                     PetscCall(MatDestroy(&B));
    223:                     PetscCall(MatDestroy(&BT));
    224:                   } else {
    225:                     for (PetscInt k = 0; k < A->rmap->n; ++k) { /* block F from above */
    226:                       a->wrapper->copy_submatrix(std::distance(it + A->rmap->n, idxr + nrow), 1, it + A->rmap->n, idxc + m + k, ptr + (m + k) * nrow + m + A->rmap->n);
    227:                     }
    228:                   }
    229:                 }
    230:               } /* complete local diagonal block not in IS */
    231:             } else flg = PETSC_FALSE; /* IS not long enough to store the local diagonal block */
    232:           } else flg = PETSC_FALSE;   /* rmap->rstart not in IS */
    233:         } /* unsorted IS */
    234:       }
    235:     } else flg = PETSC_FALSE;                                       /* different row and column IS */
    236:     if (!flg) a->wrapper->copy_submatrix(nrow, m, idxr, idxc, ptr); /* reassemble everything */
    237:     PetscCall(ISRestoreIndices(irow[i], &idxr));
    238:     PetscCall(ISRestoreIndices(icol[i], &idxc));
    239:     PetscCall(MatDenseRestoreArrayWrite((*submat)[i], &ptr));
    240:     PetscCall(MatShift((*submat)[i], shift));
    241:     PetscCall(MatScale((*submat)[i], scale));
    242:   }
    243:   PetscFunctionReturn(PETSC_SUCCESS);
    244: }

    246: static PetscErrorCode MatDestroy_Htool(Mat A)
    247: {
    248:   Mat_Htool               *a;
    249:   PetscContainer           container;
    250:   MatHtoolKernelTranspose *kernelt;

    252:   PetscFunctionBegin;
    253:   PetscCall(MatShellGetContext(A, &a));
    254:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_htool_seqdense_C", nullptr));
    255:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_htool_mpidense_C", nullptr));
    256:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_htool_seqdense_C", nullptr));
    257:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_htool_mpidense_C", nullptr));
    258:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetHierarchicalMat_C", nullptr));
    259:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolSetKernel_C", nullptr));
    260:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetPermutationSource_C", nullptr));
    261:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetPermutationTarget_C", nullptr));
    262:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolUsePermutation_C", nullptr));
    263:   PetscCall(PetscObjectQuery((PetscObject)A, "KernelTranspose", (PetscObject *)&container));
    264:   if (container) { /* created in MatTranspose_Htool() */
    265:     PetscCall(PetscContainerGetPointer(container, (void **)&kernelt));
    266:     PetscCall(MatDestroy(&kernelt->A));
    267:     PetscCall(PetscObjectCompose((PetscObject)A, "KernelTranspose", nullptr));
    268:   }
    269:   if (a->gcoords_source != a->gcoords_target) PetscCall(PetscFree(a->gcoords_source));
    270:   PetscCall(PetscFree(a->gcoords_target));
    271:   PetscCall(PetscFree2(a->work_source, a->work_target));
    272:   delete a->wrapper;
    273:   a->target_cluster.reset();
    274:   a->source_cluster.reset();
    275:   a->distributed_operator_holder.reset();
    276:   PetscCall(PetscFree(a));
    277:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContext_C", nullptr)); // needed to avoid a call to MatShellSetContext_Immutable()
    278:   PetscFunctionReturn(PETSC_SUCCESS);
    279: }

    281: static PetscErrorCode MatView_Htool(Mat A, PetscViewer pv)
    282: {
    283:   Mat_Htool                         *a;
    284:   PetscScalar                        shift, scale;
    285:   PetscBool                          flg;
    286:   std::map<std::string, std::string> hmatrix_information;

    288:   PetscFunctionBegin;
    289:   PetscCall(MatShellGetContext(A, &a));
    290:   hmatrix_information = htool::get_distributed_hmatrix_information(a->distributed_operator_holder->hmatrix, PetscObjectComm((PetscObject)A));
    291:   PetscCall(PetscObjectTypeCompare((PetscObject)pv, PETSCVIEWERASCII, &flg));
    292:   if (flg) {
    293:     PetscCall(MatShellGetScalingShifts(A, &shift, &scale, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
    294:     PetscCall(PetscViewerASCIIPrintf(pv, "symmetry: %c\n", a->distributed_operator_holder->distributed_operator.get_symmetry_type()));
    295:     if (PetscAbsScalar(scale - 1.0) > PETSC_MACHINE_EPSILON) {
    296: #if defined(PETSC_USE_COMPLEX)
    297:       PetscCall(PetscViewerASCIIPrintf(pv, "scaling: %g+%gi\n", (double)PetscRealPart(scale), (double)PetscImaginaryPart(scale)));
    298: #else
    299:       PetscCall(PetscViewerASCIIPrintf(pv, "scaling: %g\n", (double)scale));
    300: #endif
    301:     }
    302:     if (PetscAbsScalar(shift) > PETSC_MACHINE_EPSILON) {
    303: #if defined(PETSC_USE_COMPLEX)
    304:       PetscCall(PetscViewerASCIIPrintf(pv, "shift: %g+%gi\n", (double)PetscRealPart(shift), (double)PetscImaginaryPart(shift)));
    305: #else
    306:       PetscCall(PetscViewerASCIIPrintf(pv, "shift: %g\n", (double)shift));
    307: #endif
    308:     }
    309:     PetscCall(PetscViewerASCIIPrintf(pv, "minimum cluster size: %" PetscInt_FMT "\n", a->min_cluster_size));
    310:     PetscCall(PetscViewerASCIIPrintf(pv, "epsilon: %g\n", (double)a->epsilon));
    311:     PetscCall(PetscViewerASCIIPrintf(pv, "eta: %g\n", (double)a->eta));
    312:     PetscCall(PetscViewerASCIIPrintf(pv, "minimum target depth: %" PetscInt_FMT "\n", a->depth[0]));
    313:     PetscCall(PetscViewerASCIIPrintf(pv, "minimum source depth: %" PetscInt_FMT "\n", a->depth[1]));
    314:     PetscCall(PetscViewerASCIIPrintf(pv, "compressor: %s\n", MatHtoolCompressorTypes[a->compressor]));
    315:     PetscCall(PetscViewerASCIIPrintf(pv, "clustering: %s\n", MatHtoolClusteringTypes[a->clustering]));
    316:     PetscCall(PetscViewerASCIIPrintf(pv, "compression ratio: %s\n", hmatrix_information["Compression_ratio"].c_str()));
    317:     PetscCall(PetscViewerASCIIPrintf(pv, "space saving: %s\n", hmatrix_information["Space_saving"].c_str()));
    318:     PetscCall(PetscViewerASCIIPrintf(pv, "block tree consistency: %s\n", PetscBools[a->distributed_operator_holder->hmatrix.is_block_tree_consistent()]));
    319:     PetscCall(PetscViewerASCIIPrintf(pv, "number of dense (resp. low rank) matrices: %s (resp. %s)\n", hmatrix_information["Number_of_dense_blocks"].c_str(), hmatrix_information["Number_of_low_rank_blocks"].c_str()));
    320:     PetscCall(
    321:       PetscViewerASCIIPrintf(pv, "(minimum, mean, maximum) dense block sizes: (%s, %s, %s)\n", hmatrix_information["Dense_block_size_min"].c_str(), hmatrix_information["Dense_block_size_mean"].c_str(), hmatrix_information["Dense_block_size_max"].c_str()));
    322:     PetscCall(PetscViewerASCIIPrintf(pv, "(minimum, mean, maximum) low rank block sizes: (%s, %s, %s)\n", hmatrix_information["Low_rank_block_size_min"].c_str(), hmatrix_information["Low_rank_block_size_mean"].c_str(),
    323:                                      hmatrix_information["Low_rank_block_size_max"].c_str()));
    324:     PetscCall(PetscViewerASCIIPrintf(pv, "(minimum, mean, maximum) ranks: (%s, %s, %s)\n", hmatrix_information["Rank_min"].c_str(), hmatrix_information["Rank_mean"].c_str(), hmatrix_information["Rank_max"].c_str()));
    325:   }
    326:   PetscFunctionReturn(PETSC_SUCCESS);
    327: }

    329: /* naive implementation of MatGetRow() needed for MatConvert_Nest_AIJ() */
    330: static PetscErrorCode MatGetRow_Htool(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    331: {
    332:   Mat_Htool   *a;
    333:   PetscScalar  shift, scale;
    334:   PetscInt    *idxc;
    335:   PetscBLASInt one = 1, bn;

    337:   PetscFunctionBegin;
    338:   PetscCall(MatShellGetScalingShifts(A, &shift, &scale, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
    339:   PetscCall(MatShellGetContext(A, &a));
    340:   if (nz) *nz = A->cmap->N;
    341:   if (idx || v) { /* even if !idx, need to set idxc for htool::copy_submatrix() */
    342:     PetscCall(PetscMalloc1(A->cmap->N, &idxc));
    343:     for (PetscInt i = 0; i < A->cmap->N; ++i) idxc[i] = i;
    344:   }
    345:   if (idx) *idx = idxc;
    346:   if (v) {
    347:     PetscCall(PetscMalloc1(A->cmap->N, v));
    348:     if (a->wrapper) a->wrapper->copy_submatrix(1, A->cmap->N, &row, idxc, *v);
    349:     else reinterpret_cast<htool::VirtualGenerator<PetscScalar> *>(a->kernelctx)->copy_submatrix(1, A->cmap->N, &row, idxc, *v);
    350:     PetscCall(PetscBLASIntCast(A->cmap->N, &bn));
    351:     PetscCallBLAS("BLASscal", BLASscal_(&bn, &scale, *v, &one));
    352:     if (row < A->cmap->N) (*v)[row] += shift;
    353:   }
    354:   if (!idx) PetscCall(PetscFree(idxc));
    355:   PetscFunctionReturn(PETSC_SUCCESS);
    356: }

    358: static PetscErrorCode MatRestoreRow_Htool(Mat, PetscInt, PetscInt *, PetscInt **idx, PetscScalar **v)
    359: {
    360:   PetscFunctionBegin;
    361:   if (idx) PetscCall(PetscFree(*idx));
    362:   if (v) PetscCall(PetscFree(*v));
    363:   PetscFunctionReturn(PETSC_SUCCESS);
    364: }

    366: static PetscErrorCode MatSetFromOptions_Htool(Mat A, PetscOptionItems *PetscOptionsObject)
    367: {
    368:   Mat_Htool *a;
    369:   PetscInt   n;
    370:   PetscBool  flg;

    372:   PetscFunctionBegin;
    373:   PetscCall(MatShellGetContext(A, &a));
    374:   PetscOptionsHeadBegin(PetscOptionsObject, "Htool options");
    375:   PetscCall(PetscOptionsBoundedInt("-mat_htool_min_cluster_size", "Minimal leaf size in cluster tree", nullptr, a->min_cluster_size, &a->min_cluster_size, nullptr, 0));
    376:   PetscCall(PetscOptionsBoundedReal("-mat_htool_epsilon", "Relative error in Frobenius norm when approximating a block", nullptr, a->epsilon, &a->epsilon, nullptr, 0.0));
    377:   PetscCall(PetscOptionsReal("-mat_htool_eta", "Admissibility condition tolerance", nullptr, a->eta, &a->eta, nullptr));
    378:   PetscCall(PetscOptionsBoundedInt("-mat_htool_min_target_depth", "Minimal cluster tree depth associated with the rows", nullptr, a->depth[0], a->depth, nullptr, 0));
    379:   PetscCall(PetscOptionsBoundedInt("-mat_htool_min_source_depth", "Minimal cluster tree depth associated with the columns", nullptr, a->depth[1], a->depth + 1, nullptr, 0));
    380:   PetscCall(PetscOptionsBool("-mat_htool_block_tree_consistency", "Block tree consistency", nullptr, a->block_tree_consistency, &a->block_tree_consistency, nullptr));

    382:   n = 0;
    383:   PetscCall(PetscOptionsEList("-mat_htool_compressor", "Type of compression", "MatHtoolCompressorType", MatHtoolCompressorTypes, PETSC_STATIC_ARRAY_LENGTH(MatHtoolCompressorTypes), MatHtoolCompressorTypes[MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA], &n, &flg));
    384:   if (flg) a->compressor = MatHtoolCompressorType(n);
    385:   n = 0;
    386:   PetscCall(PetscOptionsEList("-mat_htool_clustering", "Type of clustering", "MatHtoolClusteringType", MatHtoolClusteringTypes, PETSC_STATIC_ARRAY_LENGTH(MatHtoolClusteringTypes), MatHtoolClusteringTypes[MAT_HTOOL_CLUSTERING_PCA_REGULAR], &n, &flg));
    387:   if (flg) a->clustering = MatHtoolClusteringType(n);
    388:   PetscOptionsHeadEnd();
    389:   PetscFunctionReturn(PETSC_SUCCESS);
    390: }

    392: static PetscErrorCode MatAssemblyEnd_Htool(Mat A, MatAssemblyType)
    393: {
    394:   Mat_Htool                                                   *a;
    395:   const PetscInt                                              *ranges;
    396:   PetscInt                                                    *offset;
    397:   PetscMPIInt                                                  size, rank;
    398:   char                                                         S = PetscDefined(USE_COMPLEX) && A->hermitian == PETSC_BOOL3_TRUE ? 'H' : (A->symmetric == PETSC_BOOL3_TRUE ? 'S' : 'N'), uplo = S == 'N' ? 'N' : 'U';
    399:   htool::VirtualGenerator<PetscScalar>                        *generator = nullptr;
    400:   htool::ClusterTreeBuilder<PetscReal>                         recursive_build_strategy;
    401:   htool::Cluster<PetscReal>                                   *source_cluster;
    402:   std::shared_ptr<htool::VirtualLowRankGenerator<PetscScalar>> compressor;

    404:   PetscFunctionBegin;
    405:   PetscCall(PetscCitationsRegister(HtoolCitation, &HtoolCite));
    406:   PetscCall(MatShellGetContext(A, &a));
    407:   delete a->wrapper;
    408:   a->target_cluster.reset();
    409:   a->source_cluster.reset();
    410:   a->distributed_operator_holder.reset();
    411:   // clustering
    412:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    413:   PetscCall(PetscMalloc1(2 * size, &offset));
    414:   PetscCall(MatGetOwnershipRanges(A, &ranges));
    415:   for (PetscInt i = 0; i < size; ++i) {
    416:     offset[2 * i]     = ranges[i];
    417:     offset[2 * i + 1] = ranges[i + 1] - ranges[i];
    418:   }
    419:   switch (a->clustering) {
    420:   case MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC:
    421:     recursive_build_strategy.set_direction_computation_strategy(std::make_shared<htool::ComputeLargestExtent<PetscReal>>());
    422:     recursive_build_strategy.set_splitting_strategy(std::make_shared<htool::GeometricSplitting<PetscReal>>());
    423:     break;
    424:   case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC:
    425:     recursive_build_strategy.set_direction_computation_strategy(std::make_shared<htool::ComputeBoundingBox<PetscReal>>());
    426:     recursive_build_strategy.set_splitting_strategy(std::make_shared<htool::GeometricSplitting<PetscReal>>());
    427:     break;
    428:   case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR:
    429:     recursive_build_strategy.set_direction_computation_strategy(std::make_shared<htool::ComputeBoundingBox<PetscReal>>());
    430:     recursive_build_strategy.set_splitting_strategy(std::make_shared<htool::RegularSplitting<PetscReal>>());
    431:     break;
    432:   default:
    433:     recursive_build_strategy.set_direction_computation_strategy(std::make_shared<htool::ComputeLargestExtent<PetscReal>>());
    434:     recursive_build_strategy.set_splitting_strategy(std::make_shared<htool::RegularSplitting<PetscReal>>());
    435:   }
    436:   recursive_build_strategy.set_minclustersize(a->min_cluster_size);
    437:   a->target_cluster = std::make_unique<htool::Cluster<PetscReal>>(recursive_build_strategy.create_cluster_tree(A->rmap->N, a->dim, a->gcoords_target, 2, size, offset));
    438:   if (a->gcoords_target != a->gcoords_source) {
    439:     PetscCall(MatGetOwnershipRangesColumn(A, &ranges));
    440:     for (PetscInt i = 0; i < size; ++i) {
    441:       offset[2 * i]     = ranges[i];
    442:       offset[2 * i + 1] = ranges[i + 1] - ranges[i];
    443:     }
    444:     switch (a->clustering) {
    445:     case MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC:
    446:       recursive_build_strategy.set_direction_computation_strategy(std::make_shared<htool::ComputeLargestExtent<PetscReal>>());
    447:       recursive_build_strategy.set_splitting_strategy(std::make_shared<htool::GeometricSplitting<PetscReal>>());
    448:       break;
    449:     case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC:
    450:       recursive_build_strategy.set_direction_computation_strategy(std::make_shared<htool::ComputeBoundingBox<PetscReal>>());
    451:       recursive_build_strategy.set_splitting_strategy(std::make_shared<htool::GeometricSplitting<PetscReal>>());
    452:       break;
    453:     case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR:
    454:       recursive_build_strategy.set_direction_computation_strategy(std::make_shared<htool::ComputeBoundingBox<PetscReal>>());
    455:       recursive_build_strategy.set_splitting_strategy(std::make_shared<htool::RegularSplitting<PetscReal>>());
    456:       break;
    457:     default:
    458:       recursive_build_strategy.set_direction_computation_strategy(std::make_shared<htool::ComputeLargestExtent<PetscReal>>());
    459:       recursive_build_strategy.set_splitting_strategy(std::make_shared<htool::RegularSplitting<PetscReal>>());
    460:     }
    461:     recursive_build_strategy.set_minclustersize(a->min_cluster_size);
    462:     a->source_cluster = std::make_unique<htool::Cluster<PetscReal>>(recursive_build_strategy.create_cluster_tree(A->cmap->N, a->dim, a->gcoords_source, 2, size, offset));
    463:     S = uplo       = 'N';
    464:     source_cluster = a->source_cluster.get();
    465:   } else source_cluster = a->target_cluster.get();
    466:   PetscCall(PetscFree(offset));
    467:   // generator
    468:   if (a->kernel) a->wrapper = new WrapperHtool(a->dim, a->kernel, a->kernelctx);
    469:   else {
    470:     a->wrapper = nullptr;
    471:     generator  = reinterpret_cast<htool::VirtualGenerator<PetscScalar> *>(a->kernelctx);
    472:   }
    473:   // compressor
    474:   switch (a->compressor) {
    475:   case MAT_HTOOL_COMPRESSOR_FULL_ACA:
    476:     compressor = std::make_shared<htool::fullACA<PetscScalar>>();
    477:     break;
    478:   case MAT_HTOOL_COMPRESSOR_SVD:
    479:     compressor = std::make_shared<htool::SVD<PetscScalar>>();
    480:     break;
    481:   default:
    482:     compressor = std::make_shared<htool::sympartialACA<PetscScalar>>();
    483:   }
    484:   // local hierarchical matrix
    485:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    486:   auto hmatrix_builder = htool::HMatrixTreeBuilder<PetscScalar>(*a->target_cluster, *source_cluster, a->epsilon, a->eta, S, uplo, -1, rank, rank);
    487:   hmatrix_builder.set_low_rank_generator(compressor);
    488:   hmatrix_builder.set_minimal_target_depth(a->depth[0]);
    489:   hmatrix_builder.set_minimal_source_depth(a->depth[1]);
    490:   PetscCheck(a->block_tree_consistency || (!a->block_tree_consistency && !(A->symmetric == PETSC_BOOL3_TRUE || A->hermitian == PETSC_BOOL3_TRUE)), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot have a MatHtool with inconsistent block tree which is either symmetric or Hermitian");
    491:   hmatrix_builder.set_block_tree_consistency(a->block_tree_consistency);
    492:   a->distributed_operator_holder = std::make_unique<htool::DistributedOperatorFromHMatrix<PetscScalar>>(a->wrapper ? *a->wrapper : *generator, *a->target_cluster, *source_cluster, hmatrix_builder, PetscObjectComm((PetscObject)A));
    493:   PetscFunctionReturn(PETSC_SUCCESS);
    494: }

    496: static PetscErrorCode MatProductNumeric_Htool(Mat C)
    497: {
    498:   Mat_Product       *product = C->product;
    499:   Mat_Htool         *a;
    500:   const PetscScalar *in;
    501:   PetscScalar       *out;
    502:   PetscInt           N, lda;

    504:   PetscFunctionBegin;
    505:   MatCheckProduct(C, 1);
    506:   PetscCall(MatGetSize(C, nullptr, &N));
    507:   PetscCall(MatDenseGetLDA(C, &lda));
    508:   PetscCheck(lda == C->rmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported leading dimension (%" PetscInt_FMT " != %" PetscInt_FMT ")", lda, C->rmap->n);
    509:   PetscCall(MatDenseGetArrayRead(product->B, &in));
    510:   PetscCall(MatDenseGetArrayWrite(C, &out));
    511:   PetscCall(MatShellGetContext(product->A, &a));
    512:   switch (product->type) {
    513:   case MATPRODUCT_AB:
    514:     a->distributed_operator_holder->distributed_operator.matrix_product_local_to_local(in, out, N, nullptr);
    515:     break;
    516:   case MATPRODUCT_AtB:
    517:     a->distributed_operator_holder->distributed_operator.matrix_product_transp_local_to_local(in, out, N, nullptr);
    518:     break;
    519:   default:
    520:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProductType %s is not supported", MatProductTypes[product->type]);
    521:   }
    522:   PetscCall(MatDenseRestoreArrayWrite(C, &out));
    523:   PetscCall(MatDenseRestoreArrayRead(product->B, &in));
    524:   PetscFunctionReturn(PETSC_SUCCESS);
    525: }

    527: static PetscErrorCode MatProductSymbolic_Htool(Mat C)
    528: {
    529:   Mat_Product *product = C->product;
    530:   Mat          A, B;
    531:   PetscBool    flg;

    533:   PetscFunctionBegin;
    534:   MatCheckProduct(C, 1);
    535:   A = product->A;
    536:   B = product->B;
    537:   PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &flg, MATSEQDENSE, MATMPIDENSE, ""));
    538:   PetscCheck(flg && (product->type == MATPRODUCT_AB || product->type == MATPRODUCT_AtB), PetscObjectComm((PetscObject)B), PETSC_ERR_SUP, "ProductType %s not supported for %s", MatProductTypes[product->type], ((PetscObject)product->B)->type_name);
    539:   if (C->rmap->n == PETSC_DECIDE || C->cmap->n == PETSC_DECIDE || C->rmap->N == PETSC_DECIDE || C->cmap->N == PETSC_DECIDE) {
    540:     if (product->type == MATPRODUCT_AB) PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
    541:     else PetscCall(MatSetSizes(C, A->cmap->n, B->cmap->n, A->cmap->N, B->cmap->N));
    542:   }
    543:   PetscCall(MatSetType(C, MATDENSE));
    544:   PetscCall(MatSetUp(C));
    545:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    546:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    547:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    548:   C->ops->productsymbolic = nullptr;
    549:   C->ops->productnumeric  = MatProductNumeric_Htool;
    550:   PetscFunctionReturn(PETSC_SUCCESS);
    551: }

    553: static PetscErrorCode MatProductSetFromOptions_Htool(Mat C)
    554: {
    555:   PetscFunctionBegin;
    556:   MatCheckProduct(C, 1);
    557:   if (C->product->type == MATPRODUCT_AB || C->product->type == MATPRODUCT_AtB) C->ops->productsymbolic = MatProductSymbolic_Htool;
    558:   PetscFunctionReturn(PETSC_SUCCESS);
    559: }

    561: static PetscErrorCode MatHtoolGetHierarchicalMat_Htool(Mat A, const htool::DistributedOperator<PetscScalar> **distributed_operator)
    562: {
    563:   Mat_Htool *a;

    565:   PetscFunctionBegin;
    566:   PetscCall(MatShellGetContext(A, &a));
    567:   *distributed_operator = &a->distributed_operator_holder->distributed_operator;
    568:   PetscFunctionReturn(PETSC_SUCCESS);
    569: }

    571: /*@C
    572:   MatHtoolGetHierarchicalMat - Retrieves the opaque pointer to a Htool virtual matrix stored in a `MATHTOOL`.

    574:   No Fortran Support, No C Support

    576:   Input Parameter:
    577: . A - hierarchical matrix

    579:   Output Parameter:
    580: . distributed_operator - opaque pointer to a Htool virtual matrix

    582:   Level: advanced

    584: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`
    585: @*/
    586: PETSC_EXTERN PetscErrorCode MatHtoolGetHierarchicalMat(Mat A, const htool::DistributedOperator<PetscScalar> **distributed_operator)
    587: {
    588:   PetscFunctionBegin;
    590:   PetscAssertPointer(distributed_operator, 2);
    591:   PetscTryMethod(A, "MatHtoolGetHierarchicalMat_C", (Mat, const htool::DistributedOperator<PetscScalar> **), (A, distributed_operator));
    592:   PetscFunctionReturn(PETSC_SUCCESS);
    593: }

    595: static PetscErrorCode MatHtoolSetKernel_Htool(Mat A, MatHtoolKernelFn *kernel, void *kernelctx)
    596: {
    597:   Mat_Htool *a;

    599:   PetscFunctionBegin;
    600:   PetscCall(MatShellGetContext(A, &a));
    601:   a->kernel    = kernel;
    602:   a->kernelctx = kernelctx;
    603:   delete a->wrapper;
    604:   if (a->kernel) a->wrapper = new WrapperHtool(a->dim, a->kernel, a->kernelctx);
    605:   PetscFunctionReturn(PETSC_SUCCESS);
    606: }

    608: /*@C
    609:   MatHtoolSetKernel - Sets the kernel and context used for the assembly of a `MATHTOOL`.

    611:   Collective, No Fortran Support

    613:   Input Parameters:
    614: + A         - hierarchical matrix
    615: . kernel    - computational kernel (or `NULL`)
    616: - kernelctx - kernel context (if kernel is `NULL`, the pointer must be of type htool::VirtualGenerator<PetscScalar>*)

    618:   Level: advanced

    620: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`, `MatCreateHtoolFromKernel()`
    621: @*/
    622: PetscErrorCode MatHtoolSetKernel(Mat A, MatHtoolKernelFn *kernel, void *kernelctx)
    623: {
    624:   PetscFunctionBegin;
    627:   if (!kernel) PetscAssertPointer(kernelctx, 3);
    628:   PetscTryMethod(A, "MatHtoolSetKernel_C", (Mat, MatHtoolKernelFn *, void *), (A, kernel, kernelctx));
    629:   PetscFunctionReturn(PETSC_SUCCESS);
    630: }

    632: static PetscErrorCode MatHtoolGetPermutationSource_Htool(Mat A, IS *is)
    633: {
    634:   Mat_Htool                       *a;
    635:   PetscMPIInt                      rank;
    636:   const std::vector<PetscInt>     *source;
    637:   const htool::Cluster<PetscReal> *local_source_cluster;

    639:   PetscFunctionBegin;
    640:   PetscCall(MatShellGetContext(A, &a));
    641:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    642:   local_source_cluster = a->source_cluster ? &a->source_cluster->get_cluster_on_partition(rank) : &a->target_cluster->get_cluster_on_partition(rank);
    643:   source               = &local_source_cluster->get_permutation();
    644:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), local_source_cluster->get_size(), source->data() + local_source_cluster->get_offset(), PETSC_COPY_VALUES, is));
    645:   PetscCall(ISSetPermutation(*is));
    646:   PetscFunctionReturn(PETSC_SUCCESS);
    647: }

    649: /*@
    650:   MatHtoolGetPermutationSource - Gets the permutation associated to the source cluster for a `MATHTOOL` matrix.

    652:   Input Parameter:
    653: . A - hierarchical matrix

    655:   Output Parameter:
    656: . is - permutation

    658:   Level: advanced

    660: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`, `MatHtoolGetPermutationTarget()`, `MatHtoolUsePermutation()`
    661: @*/
    662: PetscErrorCode MatHtoolGetPermutationSource(Mat A, IS *is)
    663: {
    664:   PetscFunctionBegin;
    666:   if (!is) PetscAssertPointer(is, 2);
    667:   PetscTryMethod(A, "MatHtoolGetPermutationSource_C", (Mat, IS *), (A, is));
    668:   PetscFunctionReturn(PETSC_SUCCESS);
    669: }

    671: static PetscErrorCode MatHtoolGetPermutationTarget_Htool(Mat A, IS *is)
    672: {
    673:   Mat_Htool                   *a;
    674:   const std::vector<PetscInt> *target;
    675:   PetscMPIInt                  rank;

    677:   PetscFunctionBegin;
    678:   PetscCall(MatShellGetContext(A, &a));
    679:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    680:   target = &a->target_cluster->get_permutation();
    681:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), a->target_cluster->get_cluster_on_partition(rank).get_size(), target->data() + a->target_cluster->get_cluster_on_partition(rank).get_offset(), PETSC_COPY_VALUES, is));
    682:   PetscCall(ISSetPermutation(*is));
    683:   PetscFunctionReturn(PETSC_SUCCESS);
    684: }

    686: /*@
    687:   MatHtoolGetPermutationTarget - Gets the permutation associated to the target cluster for a `MATHTOOL` matrix.

    689:   Input Parameter:
    690: . A - hierarchical matrix

    692:   Output Parameter:
    693: . is - permutation

    695:   Level: advanced

    697: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`, `MatHtoolGetPermutationSource()`, `MatHtoolUsePermutation()`
    698: @*/
    699: PetscErrorCode MatHtoolGetPermutationTarget(Mat A, IS *is)
    700: {
    701:   PetscFunctionBegin;
    703:   if (!is) PetscAssertPointer(is, 2);
    704:   PetscTryMethod(A, "MatHtoolGetPermutationTarget_C", (Mat, IS *), (A, is));
    705:   PetscFunctionReturn(PETSC_SUCCESS);
    706: }

    708: static PetscErrorCode MatHtoolUsePermutation_Htool(Mat A, PetscBool use)
    709: {
    710:   Mat_Htool *a;

    712:   PetscFunctionBegin;
    713:   PetscCall(MatShellGetContext(A, &a));
    714:   a->distributed_operator_holder->distributed_operator.use_permutation() = use;
    715:   PetscFunctionReturn(PETSC_SUCCESS);
    716: }

    718: /*@
    719:   MatHtoolUsePermutation - Sets whether a `MATHTOOL` matrix should permute input (resp. output) vectors following its internal source (resp. target) permutation.

    721:   Input Parameters:
    722: + A   - hierarchical matrix
    723: - use - Boolean value

    725:   Level: advanced

    727: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`, `MatHtoolGetPermutationSource()`, `MatHtoolGetPermutationTarget()`
    728: @*/
    729: PetscErrorCode MatHtoolUsePermutation(Mat A, PetscBool use)
    730: {
    731:   PetscFunctionBegin;
    734:   PetscTryMethod(A, "MatHtoolUsePermutation_C", (Mat, PetscBool), (A, use));
    735:   PetscFunctionReturn(PETSC_SUCCESS);
    736: }

    738: static PetscErrorCode MatConvert_Htool_Dense(Mat A, MatType, MatReuse reuse, Mat *B)
    739: {
    740:   Mat          C;
    741:   Mat_Htool   *a;
    742:   PetscScalar *array, shift, scale;
    743:   PetscInt     lda;

    745:   PetscFunctionBegin;
    746:   PetscCall(MatShellGetScalingShifts(A, &shift, &scale, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
    747:   PetscCall(MatShellGetContext(A, &a));
    748:   if (reuse == MAT_REUSE_MATRIX) {
    749:     C = *B;
    750:     PetscCheck(C->rmap->n == A->rmap->n && C->cmap->N == A->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible dimensions");
    751:     PetscCall(MatDenseGetLDA(C, &lda));
    752:     PetscCheck(lda == C->rmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported leading dimension (%" PetscInt_FMT " != %" PetscInt_FMT ")", lda, C->rmap->n);
    753:   } else {
    754:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
    755:     PetscCall(MatSetSizes(C, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    756:     PetscCall(MatSetType(C, MATDENSE));
    757:     PetscCall(MatSetUp(C));
    758:     PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    759:   }
    760:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    761:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    762:   PetscCall(MatDenseGetArrayWrite(C, &array));
    763:   htool::copy_to_dense_in_user_numbering(a->distributed_operator_holder->hmatrix, array);
    764:   PetscCall(MatDenseRestoreArrayWrite(C, &array));
    765:   PetscCall(MatShift(C, shift));
    766:   PetscCall(MatScale(C, scale));
    767:   if (reuse == MAT_INPLACE_MATRIX) {
    768:     PetscCall(MatHeaderReplace(A, &C));
    769:   } else *B = C;
    770:   PetscFunctionReturn(PETSC_SUCCESS);
    771: }

    773: static PetscErrorCode GenEntriesTranspose(PetscInt sdim, PetscInt M, PetscInt N, const PetscInt *rows, const PetscInt *cols, PetscScalar *ptr, void *ctx)
    774: {
    775:   MatHtoolKernelTranspose *generator = (MatHtoolKernelTranspose *)ctx;
    776:   PetscScalar             *tmp;

    778:   PetscFunctionBegin;
    779:   PetscCall(generator->kernel(sdim, N, M, cols, rows, ptr, generator->kernelctx));
    780:   PetscCall(PetscMalloc1(M * N, &tmp));
    781:   PetscCall(PetscArraycpy(tmp, ptr, M * N));
    782:   for (PetscInt i = 0; i < M; ++i) {
    783:     for (PetscInt j = 0; j < N; ++j) ptr[i + j * M] = tmp[j + i * N];
    784:   }
    785:   PetscCall(PetscFree(tmp));
    786:   PetscFunctionReturn(PETSC_SUCCESS);
    787: }

    789: /* naive implementation which keeps a reference to the original Mat */
    790: static PetscErrorCode MatTranspose_Htool(Mat A, MatReuse reuse, Mat *B)
    791: {
    792:   Mat                      C;
    793:   Mat_Htool               *a, *c;
    794:   PetscScalar              shift, scale;
    795:   PetscInt                 M = A->rmap->N, N = A->cmap->N, m = A->rmap->n, n = A->cmap->n;
    796:   PetscContainer           container;
    797:   MatHtoolKernelTranspose *kernelt;

    799:   PetscFunctionBegin;
    800:   PetscCall(MatShellGetScalingShifts(A, &shift, &scale, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Vec *)MAT_SHELL_NOT_ALLOWED, (Mat *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED, (IS *)MAT_SHELL_NOT_ALLOWED));
    801:   PetscCall(MatShellGetContext(A, &a));
    802:   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *B));
    803:   PetscCheck(reuse != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MatTranspose() with MAT_INPLACE_MATRIX not supported");
    804:   if (reuse == MAT_INITIAL_MATRIX) {
    805:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
    806:     PetscCall(MatSetSizes(C, n, m, N, M));
    807:     PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    808:     PetscCall(MatSetUp(C));
    809:     PetscCall(PetscNew(&kernelt));
    810:     PetscCall(PetscObjectContainerCompose((PetscObject)C, "KernelTranspose", kernelt, PetscContainerUserDestroyDefault));
    811:   } else {
    812:     C = *B;
    813:     PetscCall(PetscObjectQuery((PetscObject)C, "KernelTranspose", (PetscObject *)&container));
    814:     PetscCheck(container, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call MatTranspose() with MAT_INITIAL_MATRIX first");
    815:     PetscCall(PetscContainerGetPointer(container, (void **)&kernelt));
    816:   }
    817:   PetscCall(MatShellGetContext(C, &c));
    818:   c->dim = a->dim;
    819:   PetscCall(MatShift(C, shift));
    820:   PetscCall(MatScale(C, scale));
    821:   c->kernel = GenEntriesTranspose;
    822:   if (kernelt->A != A) {
    823:     PetscCall(MatDestroy(&kernelt->A));
    824:     kernelt->A = A;
    825:     PetscCall(PetscObjectReference((PetscObject)A));
    826:   }
    827:   kernelt->kernel    = a->kernel;
    828:   kernelt->kernelctx = a->kernelctx;
    829:   c->kernelctx       = kernelt;
    830:   if (reuse == MAT_INITIAL_MATRIX) {
    831:     PetscCall(PetscMalloc1(N * c->dim, &c->gcoords_target));
    832:     PetscCall(PetscArraycpy(c->gcoords_target, a->gcoords_source, N * c->dim));
    833:     if (a->gcoords_target != a->gcoords_source) {
    834:       PetscCall(PetscMalloc1(M * c->dim, &c->gcoords_source));
    835:       PetscCall(PetscArraycpy(c->gcoords_source, a->gcoords_target, M * c->dim));
    836:     } else c->gcoords_source = c->gcoords_target;
    837:     PetscCall(PetscCalloc2(M, &c->work_source, N, &c->work_target));
    838:   }
    839:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    840:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    841:   if (reuse == MAT_INITIAL_MATRIX) *B = C;
    842:   PetscFunctionReturn(PETSC_SUCCESS);
    843: }

    845: static PetscErrorCode MatDestroy_Factor(Mat F)
    846: {
    847:   PetscContainer               container;
    848:   htool::HMatrix<PetscScalar> *A;

    850:   PetscFunctionBegin;
    851:   PetscCall(PetscObjectQuery((PetscObject)F, "HMatrix", (PetscObject *)&container));
    852:   if (container) {
    853:     PetscCall(PetscContainerGetPointer(container, (void **)&A));
    854:     delete A;
    855:     PetscCall(PetscObjectCompose((PetscObject)F, "HMatrix", nullptr));
    856:   }
    857:   PetscCall(PetscObjectComposeFunction((PetscObject)F, "MatFactorGetSolverType_C", nullptr));
    858:   PetscFunctionReturn(PETSC_SUCCESS);
    859: }

    861: static PetscErrorCode MatFactorGetSolverType_Htool(Mat, MatSolverType *type)
    862: {
    863:   PetscFunctionBegin;
    864:   *type = MATSOLVERHTOOL;
    865:   PetscFunctionReturn(PETSC_SUCCESS);
    866: }

    868: template <char trans>
    869: static inline PetscErrorCode MatSolve_Private(Mat A, htool::Matrix<PetscScalar> &X)
    870: {
    871:   PetscContainer               container;
    872:   htool::HMatrix<PetscScalar> *B;

    874:   PetscFunctionBegin;
    875:   PetscCheck(A->factortype == MAT_FACTOR_LU || A->factortype == MAT_FACTOR_CHOLESKY, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_UNKNOWN_TYPE, "Only MAT_LU_FACTOR and MAT_CHOLESKY_FACTOR are supported");
    876:   PetscCall(PetscObjectQuery((PetscObject)A, "HMatrix", (PetscObject *)&container));
    877:   PetscCheck(container, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call Mat%sFactorNumeric() before Mat%sSolve%s()", A->factortype == MAT_FACTOR_LU ? "LU" : "Cholesky", X.nb_cols() == 1 ? "" : "Mat", trans == 'N' ? "" : "Transpose");
    878:   PetscCall(PetscContainerGetPointer(container, (void **)&B));
    879:   if (A->factortype == MAT_FACTOR_LU) htool::lu_solve(trans, *B, X);
    880:   else htool::cholesky_solve('L', *B, X);
    881:   PetscFunctionReturn(PETSC_SUCCESS);
    882: }

    884: template <char trans, class Type, typename std::enable_if<std::is_same<Type, Vec>::value>::type * = nullptr>
    885: static PetscErrorCode MatSolve_Htool(Mat A, Type b, Type x)
    886: {
    887:   PetscInt                   n;
    888:   htool::Matrix<PetscScalar> v;
    889:   PetscScalar               *array;

    891:   PetscFunctionBegin;
    892:   PetscCall(VecGetLocalSize(b, &n));
    893:   PetscCall(VecCopy(b, x));
    894:   PetscCall(VecGetArrayWrite(x, &array));
    895:   v.assign(n, 1, array, false);
    896:   PetscCall(VecRestoreArrayWrite(x, &array));
    897:   PetscCall(MatSolve_Private<trans>(A, v));
    898:   PetscFunctionReturn(PETSC_SUCCESS);
    899: }

    901: template <char trans, class Type, typename std::enable_if<std::is_same<Type, Mat>::value>::type * = nullptr>
    902: static PetscErrorCode MatSolve_Htool(Mat A, Type B, Type X)
    903: {
    904:   PetscInt                   m, N;
    905:   htool::Matrix<PetscScalar> v;
    906:   PetscScalar               *array;

    908:   PetscFunctionBegin;
    909:   PetscCall(MatGetLocalSize(B, &m, nullptr));
    910:   PetscCall(MatGetLocalSize(B, nullptr, &N));
    911:   PetscCall(MatCopy(B, X, SAME_NONZERO_PATTERN));
    912:   PetscCall(MatDenseGetArrayWrite(X, &array));
    913:   v.assign(m, N, array, false);
    914:   PetscCall(MatDenseRestoreArrayWrite(X, &array));
    915:   PetscCall(MatSolve_Private<trans>(A, v));
    916:   PetscFunctionReturn(PETSC_SUCCESS);
    917: }

    919: template <MatFactorType ftype>
    920: static PetscErrorCode MatFactorNumeric_Htool(Mat F, Mat A, const MatFactorInfo *)
    921: {
    922:   Mat_Htool                   *a;
    923:   htool::HMatrix<PetscScalar> *B;

    925:   PetscFunctionBegin;
    926:   PetscCall(MatShellGetContext(A, &a));
    927:   B = new htool::HMatrix<PetscScalar>(a->distributed_operator_holder->hmatrix);
    928:   if (ftype == MAT_FACTOR_LU) htool::lu_factorization(*B);
    929:   else htool::cholesky_factorization('L', *B);
    930:   PetscCall(PetscObjectContainerCompose((PetscObject)F, "HMatrix", B, nullptr));
    931:   PetscFunctionReturn(PETSC_SUCCESS);
    932: }

    934: template <MatFactorType ftype>
    935: PetscErrorCode MatFactorSymbolic_Htool(Mat F, Mat)
    936: {
    937:   PetscFunctionBegin;
    938:   F->preallocated  = PETSC_TRUE;
    939:   F->assembled     = PETSC_TRUE;
    940:   F->ops->solve    = MatSolve_Htool<'N', Vec>;
    941:   F->ops->matsolve = MatSolve_Htool<'N', Mat>;
    942:   if (!PetscDefined(USE_COMPLEX) || ftype == MAT_FACTOR_LU) {
    943:     F->ops->solvetranspose    = MatSolve_Htool<'T', Vec>;
    944:     F->ops->matsolvetranspose = MatSolve_Htool<'T', Mat>;
    945:   }
    946:   F->ops->destroy = MatDestroy_Factor;
    947:   if (ftype == MAT_FACTOR_LU) F->ops->lufactornumeric = MatFactorNumeric_Htool<MAT_FACTOR_LU>;
    948:   else F->ops->choleskyfactornumeric = MatFactorNumeric_Htool<MAT_FACTOR_CHOLESKY>;
    949:   PetscFunctionReturn(PETSC_SUCCESS);
    950: }

    952: static PetscErrorCode MatLUFactorSymbolic_Htool(Mat F, Mat A, IS, IS, const MatFactorInfo *)
    953: {
    954:   PetscFunctionBegin;
    955:   PetscCall(MatFactorSymbolic_Htool<MAT_FACTOR_LU>(F, A));
    956:   PetscFunctionReturn(PETSC_SUCCESS);
    957: }

    959: static PetscErrorCode MatCholeskyFactorSymbolic_Htool(Mat F, Mat A, IS, const MatFactorInfo *)
    960: {
    961:   PetscFunctionBegin;
    962:   PetscCall(MatFactorSymbolic_Htool<MAT_FACTOR_CHOLESKY>(F, A));
    963:   PetscFunctionReturn(PETSC_SUCCESS);
    964: }

    966: static PetscErrorCode MatGetFactor_htool_htool(Mat A, MatFactorType ftype, Mat *F)
    967: {
    968:   Mat         B;
    969:   Mat_Htool  *a;
    970:   PetscMPIInt size;

    972:   PetscFunctionBegin;
    973:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    974:   PetscCall(MatShellGetContext(A, &a));
    975:   PetscCheck(size == 1, PetscObjectComm((PetscObject)A), PETSC_ERR_WRONG_MPI_SIZE, "Unsupported parallel MatGetFactor()");
    976:   PetscCheck(a->block_tree_consistency, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot factor a MatHtool with inconsistent block tree");
    977:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    978:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    979:   PetscCall(PetscStrallocpy(MATSOLVERHTOOL, &((PetscObject)B)->type_name));
    980:   PetscCall(MatSetUp(B));

    982:   B->ops->getinfo    = MatGetInfo_External;
    983:   B->factortype      = ftype;
    984:   B->trivialsymbolic = PETSC_TRUE;

    986:   if (ftype == MAT_FACTOR_LU) B->ops->lufactorsymbolic = MatLUFactorSymbolic_Htool;
    987:   else if (ftype == MAT_FACTOR_CHOLESKY) B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_Htool;

    989:   PetscCall(PetscFree(B->solvertype));
    990:   PetscCall(PetscStrallocpy(MATSOLVERHTOOL, &B->solvertype));

    992:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_Htool));
    993:   *F = B;
    994:   PetscFunctionReturn(PETSC_SUCCESS);
    995: }

    997: PETSC_INTERN PetscErrorCode MatSolverTypeRegister_Htool(void)
    998: {
    999:   PetscFunctionBegin;
    1000:   PetscCall(MatSolverTypeRegister(MATSOLVERHTOOL, MATHTOOL, MAT_FACTOR_LU, MatGetFactor_htool_htool));
    1001:   PetscCall(MatSolverTypeRegister(MATSOLVERHTOOL, MATHTOOL, MAT_FACTOR_CHOLESKY, MatGetFactor_htool_htool));
    1002:   PetscFunctionReturn(PETSC_SUCCESS);
    1003: }

    1005: /*@C
    1006:   MatCreateHtoolFromKernel - Creates a `MATHTOOL` from a user-supplied kernel.

    1008:   Collective, No Fortran Support

    1010:   Input Parameters:
    1011: + comm          - MPI communicator
    1012: . m             - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
    1013: . n             - number of local columns (or `PETSC_DECIDE` to have calculated if `N` is given)
    1014: . M             - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    1015: . N             - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    1016: . spacedim      - dimension of the space coordinates
    1017: . coords_target - coordinates of the target
    1018: . coords_source - coordinates of the source
    1019: . kernel        - computational kernel (or `NULL`)
    1020: - kernelctx     - kernel context (if kernel is `NULL`, the pointer must be of type htool::VirtualGenerator<PetscScalar>*)

    1022:   Output Parameter:
    1023: . B - matrix

    1025:   Options Database Keys:
    1026: + -mat_htool_min_cluster_size <`PetscInt`>                                                     - minimal leaf size in cluster tree
    1027: . -mat_htool_epsilon <`PetscReal`>                                                             - relative error in Frobenius norm when approximating a block
    1028: . -mat_htool_eta <`PetscReal`>                                                                 - admissibility condition tolerance
    1029: . -mat_htool_min_target_depth <`PetscInt`>                                                     - minimal cluster tree depth associated with the rows
    1030: . -mat_htool_min_source_depth <`PetscInt`>                                                     - minimal cluster tree depth associated with the columns
    1031: . -mat_htool_block_tree_consistency <`PetscBool`>                                              - block tree consistency
    1032: . -mat_htool_compressor <sympartialACA, fullACA, SVD>                                          - type of compression
    1033: - -mat_htool_clustering <PCARegular, PCAGeometric, BounbingBox1Regular, BoundingBox1Geometric> - type of clustering

    1035:   Level: intermediate

    1037: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATHTOOL`, `PCSetCoordinates()`, `MatHtoolSetKernel()`, `MatHtoolCompressorType`, `MATH2OPUS`, `MatCreateH2OpusFromKernel()`
    1038: @*/
    1039: PetscErrorCode MatCreateHtoolFromKernel(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, PetscInt spacedim, const PetscReal coords_target[], const PetscReal coords_source[], MatHtoolKernelFn *kernel, void *kernelctx, Mat *B)
    1040: {
    1041:   Mat        A;
    1042:   Mat_Htool *a;

    1044:   PetscFunctionBegin;
    1045:   PetscCall(MatCreate(comm, &A));
    1047:   PetscAssertPointer(coords_target, 7);
    1048:   PetscAssertPointer(coords_source, 8);
    1050:   if (!kernel) PetscAssertPointer(kernelctx, 10);
    1051:   PetscCall(MatSetSizes(A, m, n, M, N));
    1052:   PetscCall(MatSetType(A, MATHTOOL));
    1053:   PetscCall(MatSetUp(A));
    1054:   PetscCall(MatShellGetContext(A, &a));
    1055:   a->dim       = spacedim;
    1056:   a->kernel    = kernel;
    1057:   a->kernelctx = kernelctx;
    1058:   PetscCall(PetscCalloc1(A->rmap->N * spacedim, &a->gcoords_target));
    1059:   PetscCall(PetscArraycpy(a->gcoords_target + A->rmap->rstart * spacedim, coords_target, A->rmap->n * spacedim));
    1060:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, a->gcoords_target, A->rmap->N * spacedim, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)A))); /* global target coordinates */
    1061:   if (coords_target != coords_source) {
    1062:     PetscCall(PetscCalloc1(A->cmap->N * spacedim, &a->gcoords_source));
    1063:     PetscCall(PetscArraycpy(a->gcoords_source + A->cmap->rstart * spacedim, coords_source, A->cmap->n * spacedim));
    1064:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, a->gcoords_source, A->cmap->N * spacedim, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)A))); /* global source coordinates */
    1065:   } else a->gcoords_source = a->gcoords_target;
    1066:   PetscCall(PetscCalloc2(A->cmap->N, &a->work_source, A->rmap->N, &a->work_target));
    1067:   *B = A;
    1068:   PetscFunctionReturn(PETSC_SUCCESS);
    1069: }

    1071: /*MC
    1072:      MATHTOOL = "htool" - A matrix type for hierarchical matrices using the Htool package.

    1074:   Use `./configure --download-htool` to install PETSc to use Htool.

    1076:    Options Database Key:
    1077: .     -mat_type htool - matrix type to `MATHTOOL`

    1079:    Level: beginner

    1081: .seealso: [](ch_matrices), `Mat`, `MATH2OPUS`, `MATDENSE`, `MatCreateHtoolFromKernel()`, `MatHtoolSetKernel()`
    1082: M*/
    1083: PETSC_EXTERN PetscErrorCode MatCreate_Htool(Mat A)
    1084: {
    1085:   Mat_Htool *a;

    1087:   PetscFunctionBegin;
    1088:   PetscCall(MatSetType(A, MATSHELL));
    1089:   PetscCall(PetscNew(&a));
    1090:   PetscCall(MatShellSetContext(A, a));
    1091:   PetscCall(MatShellSetOperation(A, MATOP_GET_DIAGONAL, (void (*)(void))MatGetDiagonal_Htool));
    1092:   PetscCall(MatShellSetOperation(A, MATOP_GET_DIAGONAL_BLOCK, (void (*)(void))MatGetDiagonalBlock_Htool));
    1093:   PetscCall(MatShellSetOperation(A, MATOP_MULT, (void (*)(void))MatMult_Htool));
    1094:   PetscCall(MatShellSetOperation(A, MATOP_MULT_TRANSPOSE, (void (*)(void))MatMultTranspose_Htool));
    1095:   if (!PetscDefined(USE_COMPLEX)) PetscCall(MatShellSetOperation(A, MATOP_MULT_HERMITIAN_TRANSPOSE, (void (*)(void))MatMultTranspose_Htool));
    1096:   A->ops->increaseoverlap   = MatIncreaseOverlap_Htool;
    1097:   A->ops->createsubmatrices = MatCreateSubMatrices_Htool;
    1098:   PetscCall(MatShellSetOperation(A, MATOP_VIEW, (void (*)(void))MatView_Htool));
    1099:   PetscCall(MatShellSetOperation(A, MATOP_SET_FROM_OPTIONS, (void (*)(void))MatSetFromOptions_Htool));
    1100:   PetscCall(MatShellSetOperation(A, MATOP_GET_ROW, (void (*)(void))MatGetRow_Htool));
    1101:   PetscCall(MatShellSetOperation(A, MATOP_RESTORE_ROW, (void (*)(void))MatRestoreRow_Htool));
    1102:   PetscCall(MatShellSetOperation(A, MATOP_ASSEMBLY_END, (void (*)(void))MatAssemblyEnd_Htool));
    1103:   PetscCall(MatShellSetOperation(A, MATOP_TRANSPOSE, (void (*)(void))MatTranspose_Htool));
    1104:   PetscCall(MatShellSetOperation(A, MATOP_DESTROY, (void (*)(void))MatDestroy_Htool));
    1105:   a->dim                    = 0;
    1106:   a->gcoords_target         = nullptr;
    1107:   a->gcoords_source         = nullptr;
    1108:   a->min_cluster_size       = 10;
    1109:   a->epsilon                = PetscSqrtReal(PETSC_SMALL);
    1110:   a->eta                    = 10.0;
    1111:   a->depth[0]               = 0;
    1112:   a->depth[1]               = 0;
    1113:   a->block_tree_consistency = PETSC_TRUE;
    1114:   a->compressor             = MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA;
    1115:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_htool_seqdense_C", MatProductSetFromOptions_Htool));
    1116:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_htool_mpidense_C", MatProductSetFromOptions_Htool));
    1117:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_htool_seqdense_C", MatConvert_Htool_Dense));
    1118:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_htool_mpidense_C", MatConvert_Htool_Dense));
    1119:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetHierarchicalMat_C", MatHtoolGetHierarchicalMat_Htool));
    1120:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolSetKernel_C", MatHtoolSetKernel_Htool));
    1121:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetPermutationSource_C", MatHtoolGetPermutationSource_Htool));
    1122:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetPermutationTarget_C", MatHtoolGetPermutationTarget_Htool));
    1123:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolUsePermutation_C", MatHtoolUsePermutation_Htool));
    1124:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContext_C", MatShellSetContext_Immutable));
    1125:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContextDestroy_C", MatShellSetContextDestroy_Immutable));
    1126:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetManageScalingShifts_C", MatShellSetManageScalingShifts_Immutable));
    1127:   PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATHTOOL));
    1128:   PetscFunctionReturn(PETSC_SUCCESS);
    1129: }