Actual source code: htool.cxx

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

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

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

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

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

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

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

     75:   PetscFunctionBegin;
     76:   PetscCall(MatShellGetContext(A, &a));
     77:   PetscCall(VecGetArrayRead(x, &in));
     78:   PetscCall(VecGetArrayWrite(y, &out));
     79:   if (a->permutation == PETSC_TRUE) htool::add_distributed_operator_vector_product_local_to_local<PetscScalar>('N', 1.0, a->distributed_operator_holder->distributed_operator, in, 0.0, out, nullptr);
     80:   else htool::internal_add_distributed_operator_vector_product_local_to_local<PetscScalar>('N', 1.0, a->distributed_operator_holder->distributed_operator, in, 0.0, 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:   if (a->permutation == PETSC_TRUE) htool::add_distributed_operator_vector_product_local_to_local<PetscScalar>('T', 1.0, a->distributed_operator_holder->distributed_operator, in, 0.0, out, nullptr);
     97:   else htool::internal_add_distributed_operator_vector_product_local_to_local<PetscScalar>('T', 1.0, a->distributed_operator_holder->distributed_operator, in, 0.0, out, nullptr);
     98:   PetscCall(VecRestoreArrayRead(x, &in));
     99:   PetscCall(VecRestoreArrayWrite(y, &out));
    100:   PetscFunctionReturn(PETSC_SUCCESS);
    101: }

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

    110:   PetscFunctionBegin;
    111:   PetscCall(MatGetBlockSizes(A, bs, bs + 1));
    112:   if (bs[0] != bs[1]) bs[0] = 1;
    113:   for (PetscInt i = 0; i < is_max; ++i) {
    114:     /* basic implementation that adds indices by shifting an IS by -ov, -ov+1..., -1, 1..., ov-1, ov */
    115:     /* needed to avoid subdomain matrices to replicate A since it is dense                           */
    116:     PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)is[i]), &csize));
    117:     PetscCheck(csize == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "Unsupported parallel IS");
    118:     PetscCall(ISGetSize(is[i], &size));
    119:     PetscCall(ISGetIndices(is[i], &idx));
    120:     for (PetscInt j = 0; j < size; ++j) {
    121:       set.insert(idx[j]);
    122:       for (PetscInt k = 1; k <= ov; ++k) {                                              /* for each layer of overlap      */
    123:         if (idx[j] - k >= 0) set.insert(idx[j] - k);                                    /* do not insert negative indices */
    124:         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 */
    125:       }
    126:     }
    127:     PetscCall(ISRestoreIndices(is[i], &idx));
    128:     PetscCall(ISDestroy(is + i));
    129:     if (bs[0] > 1) {
    130:       for (std::set<PetscInt>::iterator it = set.cbegin(); it != set.cend(); it++) {
    131:         std::vector<PetscInt> block(bs[0]);
    132:         std::iota(block.begin(), block.end(), (*it / bs[0]) * bs[0]);
    133:         set.insert(block.cbegin(), block.cend());
    134:       }
    135:     }
    136:     size = set.size(); /* size with overlap */
    137:     PetscCall(PetscMalloc1(size, &oidx));
    138:     for (const PetscInt j : set) *oidx++ = j;
    139:     oidx -= size;
    140:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, size, oidx, PETSC_OWN_POINTER, is + i));
    141:   }
    142:   PetscFunctionReturn(PETSC_SUCCESS);
    143: }

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

    155:   PetscFunctionBegin;
    156:   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));
    157:   PetscCall(MatShellGetContext(A, &a));
    158:   if (scall != MAT_REUSE_MATRIX) PetscCall(PetscCalloc1(n, submat));
    159:   for (i = 0; i < n; ++i) {
    160:     PetscCall(ISGetLocalSize(irow[i], &nrow));
    161:     PetscCall(ISGetLocalSize(icol[i], &m));
    162:     PetscCall(ISGetIndices(irow[i], &idxr));
    163:     PetscCall(ISGetIndices(icol[i], &idxc));
    164:     if (scall != MAT_REUSE_MATRIX) PetscCall(MatCreateDense(PETSC_COMM_SELF, nrow, m, nrow, m, nullptr, (*submat) + i));
    165:     PetscCall(MatDenseGetArrayWrite((*submat)[i], &ptr));
    166:     if (irow[i] == icol[i]) { /* same row and column IS? */
    167:       PetscCall(MatHasCongruentLayouts(A, &flg));
    168:       if (flg) {
    169:         PetscCall(ISSorted(irow[i], &flg));
    170:         if (flg) { /* sorted IS? */
    171:           it = std::lower_bound(idxr, idxr + nrow, A->rmap->rstart);
    172:           if (it != idxr + nrow && *it == A->rmap->rstart) {    /* rmap->rstart in IS? */
    173:             if (std::distance(idxr, it) + A->rmap->n <= nrow) { /* long enough IS to store the local diagonal block? */
    174:               for (PetscInt j = 0; j < A->rmap->n && flg; ++j)
    175:                 if (PetscUnlikely(it[j] != A->rmap->rstart + j)) flg = PETSC_FALSE;
    176:               if (flg) { /* complete local diagonal block in IS? */
    177:                 /* fast extraction when the local diagonal block is part of the submatrix, e.g., for PCASM or PCHPDDM
    178:                  *      [   B   C   E   ]
    179:                  *  A = [   B   D   E   ]
    180:                  *      [   B   F   E   ]
    181:                  */
    182:                 m = std::distance(idxr, it); /* shift of the coefficient (0,0) of block D from above */
    183:                 PetscCall(MatGetDiagonalBlock(A, &D));
    184:                 PetscCall(MatDenseGetArrayRead(D, &copy));
    185:                 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 */
    186:                 PetscCall(MatDenseRestoreArrayRead(D, &copy));
    187:                 if (m) {
    188:                   a->wrapper->copy_submatrix(nrow, m, idxr, idxc, ptr); /* vertical block B from above */
    189:                   /* entry-wise assembly may be costly, so transpose already-computed entries when possible */
    190:                   if (A->symmetric == PETSC_BOOL3_TRUE || A->hermitian == PETSC_BOOL3_TRUE) {
    191:                     PetscCall(MatCreateDense(PETSC_COMM_SELF, A->rmap->n, m, A->rmap->n, m, ptr + m, &B));
    192:                     PetscCall(MatDenseSetLDA(B, nrow));
    193:                     PetscCall(MatCreateDense(PETSC_COMM_SELF, m, A->rmap->n, m, A->rmap->n, ptr + m * nrow, &BT));
    194:                     PetscCall(MatDenseSetLDA(BT, nrow));
    195:                     if (A->hermitian == PETSC_BOOL3_TRUE && PetscDefined(USE_COMPLEX)) {
    196:                       PetscCall(MatHermitianTranspose(B, MAT_REUSE_MATRIX, &BT));
    197:                     } else {
    198:                       PetscCall(MatTransposeSetPrecursor(B, BT));
    199:                       PetscCall(MatTranspose(B, MAT_REUSE_MATRIX, &BT));
    200:                     }
    201:                     PetscCall(MatDestroy(&B));
    202:                     PetscCall(MatDestroy(&BT));
    203:                   } else {
    204:                     for (PetscInt k = 0; k < A->rmap->n; ++k) { /* block C from above */
    205:                       a->wrapper->copy_submatrix(m, 1, idxr, idxc + m + k, ptr + (m + k) * nrow);
    206:                     }
    207:                   }
    208:                 }
    209:                 if (m + A->rmap->n != nrow) {
    210:                   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 */
    211:                   /* entry-wise assembly may be costly, so transpose already-computed entries when possible */
    212:                   if (A->symmetric == PETSC_BOOL3_TRUE || A->hermitian == PETSC_BOOL3_TRUE) {
    213:                     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));
    214:                     PetscCall(MatDenseSetLDA(B, nrow));
    215:                     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));
    216:                     PetscCall(MatDenseSetLDA(BT, nrow));
    217:                     if (A->hermitian == PETSC_BOOL3_TRUE && PetscDefined(USE_COMPLEX)) {
    218:                       PetscCall(MatHermitianTranspose(B, MAT_REUSE_MATRIX, &BT));
    219:                     } else {
    220:                       PetscCall(MatTransposeSetPrecursor(B, BT));
    221:                       PetscCall(MatTranspose(B, MAT_REUSE_MATRIX, &BT));
    222:                     }
    223:                     PetscCall(MatDestroy(&B));
    224:                     PetscCall(MatDestroy(&BT));
    225:                   } else {
    226:                     for (PetscInt k = 0; k < A->rmap->n; ++k) { /* block F from above */
    227:                       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);
    228:                     }
    229:                   }
    230:                 }
    231:               } /* complete local diagonal block not in IS */
    232:             } else flg = PETSC_FALSE; /* IS not long enough to store the local diagonal block */
    233:           } else flg = PETSC_FALSE;   /* rmap->rstart not in IS */
    234:         } /* unsorted IS */
    235:       }
    236:     } else flg = PETSC_FALSE;                                       /* different row and column IS */
    237:     if (!flg) a->wrapper->copy_submatrix(nrow, m, idxr, idxc, ptr); /* reassemble everything */
    238:     PetscCall(ISRestoreIndices(irow[i], &idxr));
    239:     PetscCall(ISRestoreIndices(icol[i], &idxc));
    240:     PetscCall(MatDenseRestoreArrayWrite((*submat)[i], &ptr));
    241:     PetscCall(MatShift((*submat)[i], shift));
    242:     PetscCall(MatScale((*submat)[i], scale));
    243:   }
    244:   PetscFunctionReturn(PETSC_SUCCESS);
    245: }

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

    253:   PetscFunctionBegin;
    254:   PetscCall(MatShellGetContext(A, &a));
    255:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_htool_seqdense_C", nullptr));
    256:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_htool_mpidense_C", nullptr));
    257:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_htool_seqdense_C", nullptr));
    258:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_htool_mpidense_C", nullptr));
    259:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetHierarchicalMat_C", nullptr));
    260:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolSetKernel_C", nullptr));
    261:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetPermutationSource_C", nullptr));
    262:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetPermutationTarget_C", nullptr));
    263:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolUsePermutation_C", nullptr));
    264:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolUseRecompression_C", nullptr));
    265:   PetscCall(PetscObjectQuery((PetscObject)A, "KernelTranspose", (PetscObject *)&container));
    266:   if (container) { /* created in MatTranspose_Htool() */
    267:     PetscCall(PetscContainerGetPointer(container, (void **)&kernelt));
    268:     PetscCall(MatDestroy(&kernelt->A));
    269:     PetscCall(PetscObjectCompose((PetscObject)A, "KernelTranspose", nullptr));
    270:   }
    271:   if (a->gcoords_source != a->gcoords_target) PetscCall(PetscFree(a->gcoords_source));
    272:   PetscCall(PetscFree(a->gcoords_target));
    273:   delete a->wrapper;
    274:   a->target_cluster.reset();
    275:   a->source_cluster.reset();
    276:   a->distributed_operator_holder.reset();
    277:   PetscCall(PetscFree(a));
    278:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContext_C", nullptr)); // needed to avoid a call to MatShellSetContext_Immutable()
    279:   PetscFunctionReturn(PETSC_SUCCESS);
    280: }

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

    289:   PetscFunctionBegin;
    290:   PetscCall(MatShellGetContext(A, &a));
    291:   hmatrix_information = htool::get_distributed_hmatrix_information(a->distributed_operator_holder->hmatrix, PetscObjectComm((PetscObject)A));
    292:   PetscCall(PetscObjectTypeCompare((PetscObject)pv, PETSCVIEWERASCII, &flg));
    293:   if (flg) {
    294:     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));
    295:     PetscCall(PetscViewerASCIIPrintf(pv, "symmetry: %c\n", a->distributed_operator_holder->block_diagonal_hmatrix->get_symmetry()));
    296:     if (PetscAbsScalar(scale - 1.0) > PETSC_MACHINE_EPSILON) {
    297: #if defined(PETSC_USE_COMPLEX)
    298:       PetscCall(PetscViewerASCIIPrintf(pv, "scaling: %g+%gi\n", (double)PetscRealPart(scale), (double)PetscImaginaryPart(scale)));
    299: #else
    300:       PetscCall(PetscViewerASCIIPrintf(pv, "scaling: %g\n", (double)scale));
    301: #endif
    302:     }
    303:     if (PetscAbsScalar(shift) > PETSC_MACHINE_EPSILON) {
    304: #if defined(PETSC_USE_COMPLEX)
    305:       PetscCall(PetscViewerASCIIPrintf(pv, "shift: %g+%gi\n", (double)PetscRealPart(shift), (double)PetscImaginaryPart(shift)));
    306: #else
    307:       PetscCall(PetscViewerASCIIPrintf(pv, "shift: %g\n", (double)shift));
    308: #endif
    309:     }
    310:     PetscCall(PetscViewerASCIIPrintf(pv, "maximal cluster leaf size: %" PetscInt_FMT "\n", a->max_cluster_leaf_size));
    311:     PetscCall(PetscViewerASCIIPrintf(pv, "epsilon: %g\n", (double)a->epsilon));
    312:     PetscCall(PetscViewerASCIIPrintf(pv, "eta: %g\n", (double)a->eta));
    313:     PetscCall(PetscViewerASCIIPrintf(pv, "minimum target depth: %" PetscInt_FMT "\n", a->depth[0]));
    314:     PetscCall(PetscViewerASCIIPrintf(pv, "minimum source depth: %" PetscInt_FMT "\n", a->depth[1]));
    315:     PetscCall(PetscViewerASCIIPrintf(pv, "compressor: %s\n", MatHtoolCompressorTypes[a->compressor]));
    316:     PetscCall(PetscViewerASCIIPrintf(pv, "clustering: %s\n", MatHtoolClusteringTypes[a->clustering]));
    317:     PetscCall(PetscViewerASCIIPrintf(pv, "compression ratio: %s\n", hmatrix_information["Compression_ratio"].c_str()));
    318:     PetscCall(PetscViewerASCIIPrintf(pv, "space saving: %s\n", hmatrix_information["Space_saving"].c_str()));
    319:     PetscCall(PetscViewerASCIIPrintf(pv, "block tree consistency: %s\n", PetscBools[a->distributed_operator_holder->hmatrix.is_block_tree_consistent()]));
    320:     PetscCall(PetscViewerASCIIPrintf(pv, "recompression: %s\n", PetscBools[a->recompression]));
    321:     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()));
    322:     PetscCall(
    323:       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()));
    324:     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(),
    325:                                      hmatrix_information["Low_rank_block_size_max"].c_str()));
    326:     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()));
    327:   }
    328:   PetscFunctionReturn(PETSC_SUCCESS);
    329: }

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

    339:   PetscFunctionBegin;
    340:   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));
    341:   PetscCall(MatShellGetContext(A, &a));
    342:   if (nz) *nz = A->cmap->N;
    343:   if (idx || v) { /* even if !idx, need to set idxc for htool::copy_submatrix() */
    344:     PetscCall(PetscMalloc1(A->cmap->N, &idxc));
    345:     for (PetscInt i = 0; i < A->cmap->N; ++i) idxc[i] = i;
    346:   }
    347:   if (idx) *idx = idxc;
    348:   if (v) {
    349:     PetscCall(PetscMalloc1(A->cmap->N, v));
    350:     if (a->wrapper) a->wrapper->copy_submatrix(1, A->cmap->N, &row, idxc, *v);
    351:     else reinterpret_cast<htool::VirtualGenerator<PetscScalar> *>(a->kernelctx)->copy_submatrix(1, A->cmap->N, &row, idxc, *v);
    352:     PetscCall(PetscBLASIntCast(A->cmap->N, &bn));
    353:     PetscCallCXX(htool::Blas<PetscScalar>::scal(&bn, &scale, *v, &one));
    354:     if (row < A->cmap->N) (*v)[row] += shift;
    355:   }
    356:   if (!idx) PetscCall(PetscFree(idxc));
    357:   PetscFunctionReturn(PETSC_SUCCESS);
    358: }

    360: static PetscErrorCode MatRestoreRow_Htool(Mat, PetscInt, PetscInt *, PetscInt **idx, PetscScalar **v)
    361: {
    362:   PetscFunctionBegin;
    363:   if (idx) PetscCall(PetscFree(*idx));
    364:   if (v) PetscCall(PetscFree(*v));
    365:   PetscFunctionReturn(PETSC_SUCCESS);
    366: }

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

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

    385:   n = 0;
    386:   PetscCall(PetscOptionsEList("-mat_htool_compressor", "Type of compression", "MatHtoolCompressorType", MatHtoolCompressorTypes, PETSC_STATIC_ARRAY_LENGTH(MatHtoolCompressorTypes), MatHtoolCompressorTypes[MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA], &n, &flg));
    387:   if (flg) a->compressor = MatHtoolCompressorType(n);
    388:   n = 0;
    389:   PetscCall(PetscOptionsEList("-mat_htool_clustering", "Type of clustering", "MatHtoolClusteringType", MatHtoolClusteringTypes, PETSC_STATIC_ARRAY_LENGTH(MatHtoolClusteringTypes), MatHtoolClusteringTypes[MAT_HTOOL_CLUSTERING_PCA_REGULAR], &n, &flg));
    390:   if (flg) a->clustering = MatHtoolClusteringType(n);
    391:   PetscOptionsHeadEnd();
    392:   PetscFunctionReturn(PETSC_SUCCESS);
    393: }

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

    407:   PetscFunctionBegin;
    408:   PetscCall(PetscCitationsRegister(HtoolCitation, &HtoolCite));
    409:   PetscCall(MatShellGetContext(A, &a));
    410:   delete a->wrapper;
    411:   a->target_cluster.reset();
    412:   a->source_cluster.reset();
    413:   a->distributed_operator_holder.reset();
    414:   // clustering
    415:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    416:   PetscCall(PetscMalloc1(2 * size, &offset));
    417:   PetscCall(MatGetOwnershipRanges(A, &ranges));
    418:   for (PetscInt i = 0; i < size; ++i) {
    419:     offset[2 * i]     = ranges[i];
    420:     offset[2 * i + 1] = ranges[i + 1] - ranges[i];
    421:   }
    422:   switch (a->clustering) {
    423:   case MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC:
    424:     recursive_build_strategy.set_partitioning_strategy(std::make_shared<htool::Partitioning<PetscReal, htool::ComputeLargestExtent<PetscReal>, htool::GeometricSplitting<PetscReal>>>());
    425:     break;
    426:   case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC:
    427:     recursive_build_strategy.set_partitioning_strategy(std::make_shared<htool::Partitioning<PetscReal, htool::ComputeBoundingBox<PetscReal>, htool::GeometricSplitting<PetscReal>>>());
    428:     break;
    429:   case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR:
    430:     recursive_build_strategy.set_partitioning_strategy(std::make_shared<htool::Partitioning<PetscReal, htool::ComputeBoundingBox<PetscReal>, htool::RegularSplitting<PetscReal>>>());
    431:     break;
    432:   default:
    433:     recursive_build_strategy.set_partitioning_strategy(std::make_shared<htool::Partitioning<PetscReal, htool::ComputeLargestExtent<PetscReal>, htool::RegularSplitting<PetscReal>>>());
    434:   }
    435:   recursive_build_strategy.set_maximal_leaf_size(a->max_cluster_leaf_size);
    436:   a->target_cluster = std::make_unique<htool::Cluster<PetscReal>>(recursive_build_strategy.create_cluster_tree_from_local_partition(A->rmap->N, a->dim, a->gcoords_target, 2, size, offset));
    437:   if (a->gcoords_target != a->gcoords_source) {
    438:     PetscCall(MatGetOwnershipRangesColumn(A, &ranges));
    439:     for (PetscInt i = 0; i < size; ++i) {
    440:       offset[2 * i]     = ranges[i];
    441:       offset[2 * i + 1] = ranges[i + 1] - ranges[i];
    442:     }
    443:     switch (a->clustering) {
    444:     case MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC:
    445:       recursive_build_strategy.set_partitioning_strategy(std::make_shared<htool::Partitioning<PetscReal, htool::ComputeLargestExtent<PetscReal>, htool::GeometricSplitting<PetscReal>>>());
    446:       break;
    447:     case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC:
    448:       recursive_build_strategy.set_partitioning_strategy(std::make_shared<htool::Partitioning<PetscReal, htool::ComputeBoundingBox<PetscReal>, htool::GeometricSplitting<PetscReal>>>());
    449:       break;
    450:     case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR:
    451:       recursive_build_strategy.set_partitioning_strategy(std::make_shared<htool::Partitioning<PetscReal, htool::ComputeBoundingBox<PetscReal>, htool::RegularSplitting<PetscReal>>>());
    452:       break;
    453:     default:
    454:       recursive_build_strategy.set_partitioning_strategy(std::make_shared<htool::Partitioning<PetscReal, htool::ComputeLargestExtent<PetscReal>, htool::RegularSplitting<PetscReal>>>());
    455:     }
    456:     recursive_build_strategy.set_maximal_leaf_size(a->max_cluster_leaf_size);
    457:     a->source_cluster = std::make_unique<htool::Cluster<PetscReal>>(recursive_build_strategy.create_cluster_tree_from_local_partition(A->cmap->N, a->dim, a->gcoords_source, 2, size, offset));
    458:     S = uplo       = 'N';
    459:     source_cluster = a->source_cluster.get();
    460:   } else source_cluster = a->target_cluster.get();
    461:   PetscCall(PetscFree(offset));
    462:   // generator
    463:   if (a->kernel) a->wrapper = new WrapperHtool(a->dim, a->kernel, a->kernelctx);
    464:   else {
    465:     a->wrapper = nullptr;
    466:     generator  = reinterpret_cast<htool::VirtualGenerator<PetscScalar> *>(a->kernelctx);
    467:   }
    468:   // compressor
    469:   switch (a->compressor) {
    470:   case MAT_HTOOL_COMPRESSOR_FULL_ACA:
    471:     compressor = std::make_shared<htool::fullACA<PetscScalar>>(a->wrapper ? *a->wrapper : *generator, a->target_cluster->get_permutation().data(), source_cluster->get_permutation().data());
    472:     break;
    473:   case MAT_HTOOL_COMPRESSOR_SVD:
    474:     compressor = std::make_shared<htool::SVD<PetscScalar>>(a->wrapper ? *a->wrapper : *generator, a->target_cluster->get_permutation().data(), source_cluster->get_permutation().data());
    475:     break;
    476:   default:
    477:     compressor = std::make_shared<htool::sympartialACA<PetscScalar>>(a->wrapper ? *a->wrapper : *generator, a->target_cluster->get_permutation().data(), source_cluster->get_permutation().data());
    478:   }
    479:   // local hierarchical matrix
    480:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    481:   auto hmatrix_builder = htool::HMatrixTreeBuilder<PetscScalar>(a->epsilon, a->eta, S, uplo);
    482:   if (a->recompression) {
    483:     std::shared_ptr<htool::VirtualInternalLowRankGenerator<PetscScalar>> RecompressedLowRankGenerator = std::make_shared<htool::RecompressedLowRankGenerator<PetscScalar>>(*compressor, std::function<void(htool::LowRankMatrix<PetscScalar> &)>(htool::SVD_recompression<PetscScalar>));
    484:     hmatrix_builder.set_low_rank_generator(RecompressedLowRankGenerator);
    485:   } else {
    486:     hmatrix_builder.set_low_rank_generator(compressor);
    487:   }
    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::DefaultApproximationBuilder<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:     if (a->permutation == PETSC_TRUE) htool::add_distributed_operator_matrix_product_local_to_local<PetscScalar>('N', 1.0, a->distributed_operator_holder->distributed_operator, in, 0.0, out, N, nullptr);
    515:     else htool::internal_add_distributed_operator_matrix_product_local_to_local<PetscScalar>('N', 1.0, a->distributed_operator_holder->distributed_operator, in, 0.0, out, N, nullptr);
    516:     break;
    517:   case MATPRODUCT_AtB:
    518:     if (a->permutation == PETSC_TRUE) htool::add_distributed_operator_matrix_product_local_to_local<PetscScalar>('T', 1.0, a->distributed_operator_holder->distributed_operator, in, 0.0, out, N, nullptr);
    519:     else htool::internal_add_distributed_operator_matrix_product_local_to_local<PetscScalar>('T', 1.0, a->distributed_operator_holder->distributed_operator, in, 0.0, out, N, nullptr);
    520:     break;
    521:   default:
    522:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProductType %s is not supported", MatProductTypes[product->type]);
    523:   }
    524:   PetscCall(MatDenseRestoreArrayWrite(C, &out));
    525:   PetscCall(MatDenseRestoreArrayRead(product->B, &in));
    526:   PetscFunctionReturn(PETSC_SUCCESS);
    527: }

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

    535:   PetscFunctionBegin;
    536:   MatCheckProduct(C, 1);
    537:   A = product->A;
    538:   B = product->B;
    539:   PetscCall(PetscObjectTypeCompareAny((PetscObject)B, &flg, MATSEQDENSE, MATMPIDENSE, ""));
    540:   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);
    541:   if (C->rmap->n == PETSC_DECIDE || C->cmap->n == PETSC_DECIDE || C->rmap->N == PETSC_DECIDE || C->cmap->N == PETSC_DECIDE) {
    542:     if (product->type == MATPRODUCT_AB) PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
    543:     else PetscCall(MatSetSizes(C, A->cmap->n, B->cmap->n, A->cmap->N, B->cmap->N));
    544:   }
    545:   PetscCall(MatSetType(C, MATDENSE));
    546:   PetscCall(MatSetUp(C));
    547:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    548:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    549:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    550:   C->ops->productsymbolic = nullptr;
    551:   C->ops->productnumeric  = MatProductNumeric_Htool;
    552:   PetscFunctionReturn(PETSC_SUCCESS);
    553: }

    555: static PetscErrorCode MatProductSetFromOptions_Htool(Mat C)
    556: {
    557:   PetscFunctionBegin;
    558:   MatCheckProduct(C, 1);
    559:   if (C->product->type == MATPRODUCT_AB || C->product->type == MATPRODUCT_AtB) C->ops->productsymbolic = MatProductSymbolic_Htool;
    560:   PetscFunctionReturn(PETSC_SUCCESS);
    561: }

    563: static PetscErrorCode MatHtoolGetHierarchicalMat_Htool(Mat A, const htool::DistributedOperator<PetscScalar> **distributed_operator)
    564: {
    565:   Mat_Htool *a;

    567:   PetscFunctionBegin;
    568:   PetscCall(MatShellGetContext(A, &a));
    569:   *distributed_operator = &a->distributed_operator_holder->distributed_operator;
    570:   PetscFunctionReturn(PETSC_SUCCESS);
    571: }

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

    576:   No Fortran Support, No C Support

    578:   Input Parameter:
    579: . A - hierarchical matrix

    581:   Output Parameter:
    582: . distributed_operator - opaque pointer to a Htool virtual matrix

    584:   Level: advanced

    586: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`
    587: @*/
    588: PETSC_EXTERN PetscErrorCode MatHtoolGetHierarchicalMat(Mat A, const htool::DistributedOperator<PetscScalar> **distributed_operator)
    589: {
    590:   PetscFunctionBegin;
    592:   PetscAssertPointer(distributed_operator, 2);
    593:   PetscTryMethod(A, "MatHtoolGetHierarchicalMat_C", (Mat, const htool::DistributedOperator<PetscScalar> **), (A, distributed_operator));
    594:   PetscFunctionReturn(PETSC_SUCCESS);
    595: }

    597: static PetscErrorCode MatHtoolSetKernel_Htool(Mat A, MatHtoolKernelFn *kernel, void *kernelctx)
    598: {
    599:   Mat_Htool *a;

    601:   PetscFunctionBegin;
    602:   PetscCall(MatShellGetContext(A, &a));
    603:   a->kernel    = kernel;
    604:   a->kernelctx = kernelctx;
    605:   delete a->wrapper;
    606:   if (a->kernel) a->wrapper = new WrapperHtool(a->dim, a->kernel, a->kernelctx);
    607:   PetscFunctionReturn(PETSC_SUCCESS);
    608: }

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

    613:   Collective, No Fortran Support

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

    620:   Level: advanced

    622: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`, `MatCreateHtoolFromKernel()`
    623: @*/
    624: PetscErrorCode MatHtoolSetKernel(Mat A, MatHtoolKernelFn *kernel, void *kernelctx)
    625: {
    626:   PetscFunctionBegin;
    629:   if (!kernel) PetscAssertPointer(kernelctx, 3);
    630:   PetscTryMethod(A, "MatHtoolSetKernel_C", (Mat, MatHtoolKernelFn *, void *), (A, kernel, kernelctx));
    631:   PetscFunctionReturn(PETSC_SUCCESS);
    632: }

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

    641:   PetscFunctionBegin;
    642:   PetscCall(MatShellGetContext(A, &a));
    643:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    644:   local_source_cluster = a->source_cluster ? &a->source_cluster->get_cluster_on_partition(rank) : &a->target_cluster->get_cluster_on_partition(rank);
    645:   source               = &local_source_cluster->get_permutation();
    646:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), local_source_cluster->get_size(), source->data() + local_source_cluster->get_offset(), PETSC_COPY_VALUES, is));
    647:   PetscCall(ISSetPermutation(*is));
    648:   PetscFunctionReturn(PETSC_SUCCESS);
    649: }

    651: /*@
    652:   MatHtoolGetPermutationSource - Gets the permutation associated to the source cluster for a `MATHTOOL` matrix.

    654:   Input Parameter:
    655: . A - hierarchical matrix

    657:   Output Parameter:
    658: . is - permutation

    660:   Level: advanced

    662: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`, `MatHtoolGetPermutationTarget()`, `MatHtoolUsePermutation()`
    663: @*/
    664: PetscErrorCode MatHtoolGetPermutationSource(Mat A, IS *is)
    665: {
    666:   PetscFunctionBegin;
    668:   if (!is) PetscAssertPointer(is, 2);
    669:   PetscTryMethod(A, "MatHtoolGetPermutationSource_C", (Mat, IS *), (A, is));
    670:   PetscFunctionReturn(PETSC_SUCCESS);
    671: }

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

    679:   PetscFunctionBegin;
    680:   PetscCall(MatShellGetContext(A, &a));
    681:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)A), &rank));
    682:   target = &a->target_cluster->get_permutation();
    683:   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));
    684:   PetscCall(ISSetPermutation(*is));
    685:   PetscFunctionReturn(PETSC_SUCCESS);
    686: }

    688: /*@
    689:   MatHtoolGetPermutationTarget - Gets the permutation associated to the target cluster for a `MATHTOOL` matrix.

    691:   Input Parameter:
    692: . A - hierarchical matrix

    694:   Output Parameter:
    695: . is - permutation

    697:   Level: advanced

    699: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`, `MatHtoolGetPermutationSource()`, `MatHtoolUsePermutation()`
    700: @*/
    701: PetscErrorCode MatHtoolGetPermutationTarget(Mat A, IS *is)
    702: {
    703:   PetscFunctionBegin;
    705:   if (!is) PetscAssertPointer(is, 2);
    706:   PetscTryMethod(A, "MatHtoolGetPermutationTarget_C", (Mat, IS *), (A, is));
    707:   PetscFunctionReturn(PETSC_SUCCESS);
    708: }

    710: static PetscErrorCode MatHtoolUsePermutation_Htool(Mat A, PetscBool use)
    711: {
    712:   Mat_Htool *a;

    714:   PetscFunctionBegin;
    715:   PetscCall(MatShellGetContext(A, &a));
    716:   a->permutation = use;
    717:   PetscFunctionReturn(PETSC_SUCCESS);
    718: }

    720: /*@
    721:   MatHtoolUsePermutation - Sets whether a `MATHTOOL` matrix should permute input (resp. output) vectors following its internal source (resp. target) permutation.

    723:   Input Parameters:
    724: + A   - hierarchical matrix
    725: - use - Boolean value

    727:   Level: advanced

    729: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`, `MatHtoolGetPermutationSource()`, `MatHtoolGetPermutationTarget()`
    730: @*/
    731: PetscErrorCode MatHtoolUsePermutation(Mat A, PetscBool use)
    732: {
    733:   PetscFunctionBegin;
    736:   PetscTryMethod(A, "MatHtoolUsePermutation_C", (Mat, PetscBool), (A, use));
    737:   PetscFunctionReturn(PETSC_SUCCESS);
    738: }

    740: static PetscErrorCode MatHtoolUseRecompression_Htool(Mat A, PetscBool use)
    741: {
    742:   Mat_Htool *a;

    744:   PetscFunctionBegin;
    745:   PetscCall(MatShellGetContext(A, &a));
    746:   a->recompression = use;
    747:   PetscFunctionReturn(PETSC_SUCCESS);
    748: }

    750: /*@
    751:   MatHtoolUseRecompression - Sets whether a `MATHTOOL` matrix should use recompression.

    753:   Input Parameters:
    754: + A   - hierarchical matrix
    755: - use - Boolean value

    757:   Level: advanced

    759: .seealso: [](ch_matrices), `Mat`, `MATHTOOL`
    760: @*/
    761: PetscErrorCode MatHtoolUseRecompression(Mat A, PetscBool use)
    762: {
    763:   PetscFunctionBegin;
    766:   PetscTryMethod(A, "MatHtoolUseRecompression_C", (Mat, PetscBool), (A, use));
    767:   PetscFunctionReturn(PETSC_SUCCESS);
    768: }

    770: static PetscErrorCode MatConvert_Htool_Dense(Mat A, MatType, MatReuse reuse, Mat *B)
    771: {
    772:   Mat          C;
    773:   Mat_Htool   *a;
    774:   PetscScalar *array, shift, scale;
    775:   PetscInt     lda;

    777:   PetscFunctionBegin;
    778:   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));
    779:   PetscCall(MatShellGetContext(A, &a));
    780:   if (reuse == MAT_REUSE_MATRIX) {
    781:     C = *B;
    782:     PetscCheck(C->rmap->n == A->rmap->n && C->cmap->N == A->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible dimensions");
    783:     PetscCall(MatDenseGetLDA(C, &lda));
    784:     PetscCheck(lda == C->rmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported leading dimension (%" PetscInt_FMT " != %" PetscInt_FMT ")", lda, C->rmap->n);
    785:   } else {
    786:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
    787:     PetscCall(MatSetSizes(C, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    788:     PetscCall(MatSetType(C, MATDENSE));
    789:     PetscCall(MatSetUp(C));
    790:     PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    791:   }
    792:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    793:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    794:   PetscCall(MatDenseGetArrayWrite(C, &array));
    795:   htool::copy_to_dense_in_user_numbering(a->distributed_operator_holder->hmatrix, array);
    796:   PetscCall(MatDenseRestoreArrayWrite(C, &array));
    797:   PetscCall(MatShift(C, shift));
    798:   PetscCall(MatScale(C, scale));
    799:   if (reuse == MAT_INPLACE_MATRIX) PetscCall(MatHeaderReplace(A, &C));
    800:   else *B = C;
    801:   PetscFunctionReturn(PETSC_SUCCESS);
    802: }

    804: static PetscErrorCode GenEntriesTranspose(PetscInt sdim, PetscInt M, PetscInt N, const PetscInt *rows, const PetscInt *cols, PetscScalar *ptr, void *ctx)
    805: {
    806:   MatHtoolKernelTranspose *generator = (MatHtoolKernelTranspose *)ctx;
    807:   PetscScalar             *tmp;

    809:   PetscFunctionBegin;
    810:   PetscCall(generator->kernel(sdim, N, M, cols, rows, ptr, generator->kernelctx));
    811:   PetscCall(PetscMalloc1(M * N, &tmp));
    812:   PetscCall(PetscArraycpy(tmp, ptr, M * N));
    813:   for (PetscInt i = 0; i < M; ++i) {
    814:     for (PetscInt j = 0; j < N; ++j) ptr[i + j * M] = tmp[j + i * N];
    815:   }
    816:   PetscCall(PetscFree(tmp));
    817:   PetscFunctionReturn(PETSC_SUCCESS);
    818: }

    820: /* naive implementation which keeps a reference to the original Mat */
    821: static PetscErrorCode MatTranspose_Htool(Mat A, MatReuse reuse, Mat *B)
    822: {
    823:   Mat                      C;
    824:   Mat_Htool               *a, *c;
    825:   PetscScalar              shift, scale;
    826:   PetscInt                 M = A->rmap->N, N = A->cmap->N, m = A->rmap->n, n = A->cmap->n;
    827:   PetscContainer           container;
    828:   MatHtoolKernelTranspose *kernelt;

    830:   PetscFunctionBegin;
    831:   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));
    832:   PetscCall(MatShellGetContext(A, &a));
    833:   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *B));
    834:   PetscCheck(reuse != MAT_INPLACE_MATRIX, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "MatTranspose() with MAT_INPLACE_MATRIX not supported");
    835:   if (reuse == MAT_INITIAL_MATRIX) {
    836:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &C));
    837:     PetscCall(MatSetSizes(C, n, m, N, M));
    838:     PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    839:     PetscCall(MatSetUp(C));
    840:     PetscCall(PetscNew(&kernelt));
    841:     PetscCall(PetscObjectContainerCompose((PetscObject)C, "KernelTranspose", kernelt, PetscCtxDestroyDefault));
    842:   } else {
    843:     C = *B;
    844:     PetscCall(PetscObjectQuery((PetscObject)C, "KernelTranspose", (PetscObject *)&container));
    845:     PetscCheck(container, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Must call MatTranspose() with MAT_INITIAL_MATRIX first");
    846:     PetscCall(PetscContainerGetPointer(container, (void **)&kernelt));
    847:   }
    848:   PetscCall(MatShellGetContext(C, &c));
    849:   c->dim = a->dim;
    850:   PetscCall(MatShift(C, shift));
    851:   PetscCall(MatScale(C, scale));
    852:   c->kernel = GenEntriesTranspose;
    853:   if (kernelt->A != A) {
    854:     PetscCall(MatDestroy(&kernelt->A));
    855:     kernelt->A = A;
    856:     PetscCall(PetscObjectReference((PetscObject)A));
    857:   }
    858:   kernelt->kernel           = a->kernel;
    859:   kernelt->kernelctx        = a->kernelctx;
    860:   c->kernelctx              = kernelt;
    861:   c->max_cluster_leaf_size  = a->max_cluster_leaf_size;
    862:   c->epsilon                = a->epsilon;
    863:   c->eta                    = a->eta;
    864:   c->block_tree_consistency = a->block_tree_consistency;
    865:   c->permutation            = a->permutation;
    866:   c->recompression          = a->recompression;
    867:   c->compressor             = a->compressor;
    868:   c->clustering             = a->clustering;
    869:   if (reuse == MAT_INITIAL_MATRIX) {
    870:     PetscCall(PetscMalloc1(N * c->dim, &c->gcoords_target));
    871:     PetscCall(PetscArraycpy(c->gcoords_target, a->gcoords_source, N * c->dim));
    872:     if (a->gcoords_target != a->gcoords_source) {
    873:       PetscCall(PetscMalloc1(M * c->dim, &c->gcoords_source));
    874:       PetscCall(PetscArraycpy(c->gcoords_source, a->gcoords_target, M * c->dim));
    875:     } else c->gcoords_source = c->gcoords_target;
    876:   }
    877:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    878:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    879:   if (reuse == MAT_INITIAL_MATRIX) *B = C;
    880:   PetscFunctionReturn(PETSC_SUCCESS);
    881: }

    883: static PetscErrorCode MatDestroy_Factor(Mat F)
    884: {
    885:   PetscContainer               container;
    886:   htool::HMatrix<PetscScalar> *A;

    888:   PetscFunctionBegin;
    889:   PetscCall(PetscObjectQuery((PetscObject)F, "HMatrix", (PetscObject *)&container));
    890:   if (container) {
    891:     PetscCall(PetscContainerGetPointer(container, (void **)&A));
    892:     delete A;
    893:     PetscCall(PetscObjectCompose((PetscObject)F, "HMatrix", nullptr));
    894:   }
    895:   PetscCall(PetscObjectComposeFunction((PetscObject)F, "MatFactorGetSolverType_C", nullptr));
    896:   PetscFunctionReturn(PETSC_SUCCESS);
    897: }

    899: static PetscErrorCode MatFactorGetSolverType_Htool(Mat, MatSolverType *type)
    900: {
    901:   PetscFunctionBegin;
    902:   *type = MATSOLVERHTOOL;
    903:   PetscFunctionReturn(PETSC_SUCCESS);
    904: }

    906: template <char trans>
    907: static inline PetscErrorCode MatSolve_Private(Mat A, htool::Matrix<PetscScalar> &X)
    908: {
    909:   PetscContainer               container;
    910:   htool::HMatrix<PetscScalar> *B;

    912:   PetscFunctionBegin;
    913:   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");
    914:   PetscCall(PetscObjectQuery((PetscObject)A, "HMatrix", (PetscObject *)&container));
    915:   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");
    916:   PetscCall(PetscContainerGetPointer(container, (void **)&B));
    917:   if (A->factortype == MAT_FACTOR_LU) htool::lu_solve(trans, *B, X);
    918:   else htool::cholesky_solve('L', *B, X);
    919:   PetscFunctionReturn(PETSC_SUCCESS);
    920: }

    922: template <char trans, class Type, typename std::enable_if<std::is_same<Type, Vec>::value>::type * = nullptr>
    923: static PetscErrorCode MatSolve_Htool(Mat A, Type b, Type x)
    924: {
    925:   PetscInt                   n;
    926:   htool::Matrix<PetscScalar> v;
    927:   PetscScalar               *array;

    929:   PetscFunctionBegin;
    930:   PetscCall(VecGetLocalSize(b, &n));
    931:   PetscCall(VecCopy(b, x));
    932:   PetscCall(VecGetArrayWrite(x, &array));
    933:   v.assign(n, 1, array, false);
    934:   PetscCall(VecRestoreArrayWrite(x, &array));
    935:   PetscCall(MatSolve_Private<trans>(A, v));
    936:   PetscFunctionReturn(PETSC_SUCCESS);
    937: }

    939: template <char trans, class Type, typename std::enable_if<std::is_same<Type, Mat>::value>::type * = nullptr>
    940: static PetscErrorCode MatSolve_Htool(Mat A, Type B, Type X)
    941: {
    942:   PetscInt                   m, N;
    943:   htool::Matrix<PetscScalar> v;
    944:   PetscScalar               *array;

    946:   PetscFunctionBegin;
    947:   PetscCall(MatGetLocalSize(B, &m, nullptr));
    948:   PetscCall(MatGetLocalSize(B, nullptr, &N));
    949:   PetscCall(MatCopy(B, X, SAME_NONZERO_PATTERN));
    950:   PetscCall(MatDenseGetArrayWrite(X, &array));
    951:   v.assign(m, N, array, false);
    952:   PetscCall(MatDenseRestoreArrayWrite(X, &array));
    953:   PetscCall(MatSolve_Private<trans>(A, v));
    954:   PetscFunctionReturn(PETSC_SUCCESS);
    955: }

    957: template <MatFactorType ftype>
    958: static PetscErrorCode MatFactorNumeric_Htool(Mat F, Mat A, const MatFactorInfo *)
    959: {
    960:   Mat_Htool                   *a;
    961:   htool::HMatrix<PetscScalar> *B;

    963:   PetscFunctionBegin;
    964:   PetscCall(MatShellGetContext(A, &a));
    965:   B = new htool::HMatrix<PetscScalar>(a->distributed_operator_holder->hmatrix);
    966:   if (ftype == MAT_FACTOR_LU) htool::sequential_lu_factorization(*B);
    967:   else htool::sequential_cholesky_factorization('L', *B);
    968:   PetscCall(PetscObjectContainerCompose((PetscObject)F, "HMatrix", B, nullptr));
    969:   PetscFunctionReturn(PETSC_SUCCESS);
    970: }

    972: template <MatFactorType ftype>
    973: PetscErrorCode MatFactorSymbolic_Htool(Mat F, Mat)
    974: {
    975:   PetscFunctionBegin;
    976:   F->preallocated  = PETSC_TRUE;
    977:   F->assembled     = PETSC_TRUE;
    978:   F->ops->solve    = MatSolve_Htool<'N', Vec>;
    979:   F->ops->matsolve = MatSolve_Htool<'N', Mat>;
    980:   if (!PetscDefined(USE_COMPLEX) || ftype == MAT_FACTOR_LU) {
    981:     F->ops->solvetranspose    = MatSolve_Htool<'T', Vec>;
    982:     F->ops->matsolvetranspose = MatSolve_Htool<'T', Mat>;
    983:   }
    984:   F->ops->destroy = MatDestroy_Factor;
    985:   if (ftype == MAT_FACTOR_LU) F->ops->lufactornumeric = MatFactorNumeric_Htool<MAT_FACTOR_LU>;
    986:   else F->ops->choleskyfactornumeric = MatFactorNumeric_Htool<MAT_FACTOR_CHOLESKY>;
    987:   PetscFunctionReturn(PETSC_SUCCESS);
    988: }

    990: static PetscErrorCode MatLUFactorSymbolic_Htool(Mat F, Mat A, IS, IS, const MatFactorInfo *)
    991: {
    992:   PetscFunctionBegin;
    993:   PetscCall(MatFactorSymbolic_Htool<MAT_FACTOR_LU>(F, A));
    994:   PetscFunctionReturn(PETSC_SUCCESS);
    995: }

    997: static PetscErrorCode MatCholeskyFactorSymbolic_Htool(Mat F, Mat A, IS, const MatFactorInfo *)
    998: {
    999:   PetscFunctionBegin;
    1000:   PetscCall(MatFactorSymbolic_Htool<MAT_FACTOR_CHOLESKY>(F, A));
    1001:   PetscFunctionReturn(PETSC_SUCCESS);
    1002: }

    1004: static PetscErrorCode MatGetFactor_htool_htool(Mat A, MatFactorType ftype, Mat *F)
    1005: {
    1006:   Mat         B;
    1007:   Mat_Htool  *a;
    1008:   PetscMPIInt size;

    1010:   PetscFunctionBegin;
    1011:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    1012:   PetscCall(MatShellGetContext(A, &a));
    1013:   PetscCheck(size == 1, PetscObjectComm((PetscObject)A), PETSC_ERR_WRONG_MPI_SIZE, "Unsupported parallel MatGetFactor()");
    1014:   PetscCheck(a->block_tree_consistency, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Cannot factor a MatHtool with inconsistent block tree");
    1015:   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    1016:   PetscCall(MatSetSizes(B, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
    1017:   PetscCall(PetscStrallocpy(MATSOLVERHTOOL, &((PetscObject)B)->type_name));
    1018:   PetscCall(MatSetUp(B));

    1020:   B->ops->getinfo    = MatGetInfo_External;
    1021:   B->factortype      = ftype;
    1022:   B->trivialsymbolic = PETSC_TRUE;

    1024:   if (ftype == MAT_FACTOR_LU) B->ops->lufactorsymbolic = MatLUFactorSymbolic_Htool;
    1025:   else if (ftype == MAT_FACTOR_CHOLESKY) B->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_Htool;

    1027:   PetscCall(PetscFree(B->solvertype));
    1028:   PetscCall(PetscStrallocpy(MATSOLVERHTOOL, &B->solvertype));

    1030:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatFactorGetSolverType_C", MatFactorGetSolverType_Htool));
    1031:   *F = B;
    1032:   PetscFunctionReturn(PETSC_SUCCESS);
    1033: }

    1035: PETSC_INTERN PetscErrorCode MatSolverTypeRegister_Htool(void)
    1036: {
    1037:   PetscFunctionBegin;
    1038:   PetscCall(MatSolverTypeRegister(MATSOLVERHTOOL, MATHTOOL, MAT_FACTOR_LU, MatGetFactor_htool_htool));
    1039:   PetscCall(MatSolverTypeRegister(MATSOLVERHTOOL, MATHTOOL, MAT_FACTOR_CHOLESKY, MatGetFactor_htool_htool));
    1040:   PetscFunctionReturn(PETSC_SUCCESS);
    1041: }

    1043: /*@C
    1044:   MatCreateHtoolFromKernel - Creates a `MATHTOOL` from a user-supplied kernel.

    1046:   Collective, No Fortran Support

    1048:   Input Parameters:
    1049: + comm          - MPI communicator
    1050: . m             - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
    1051: . n             - number of local columns (or `PETSC_DECIDE` to have calculated if `N` is given)
    1052: . M             - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    1053: . N             - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    1054: . spacedim      - dimension of the space coordinates
    1055: . coords_target - coordinates of the target
    1056: . coords_source - coordinates of the source
    1057: . kernel        - computational kernel (or `NULL`)
    1058: - kernelctx     - kernel context (if kernel is `NULL`, the pointer must be of type htool::VirtualGenerator<PetscScalar>*)

    1060:   Output Parameter:
    1061: . B - matrix

    1063:   Options Database Keys:
    1064: + -mat_htool_max_cluster_leaf_size <`PetscInt`>                                                - maximal leaf size in cluster tree
    1065: . -mat_htool_epsilon <`PetscReal`>                                                             - relative error in Frobenius norm when approximating a block
    1066: . -mat_htool_eta <`PetscReal`>                                                                 - admissibility condition tolerance
    1067: . -mat_htool_min_target_depth <`PetscInt`>                                                     - minimal cluster tree depth associated with the rows
    1068: . -mat_htool_min_source_depth <`PetscInt`>                                                     - minimal cluster tree depth associated with the columns
    1069: . -mat_htool_block_tree_consistency <`PetscBool`>                                              - block tree consistency
    1070: . -mat_htool_recompression <`PetscBool`>                                                       - use recompression
    1071: . -mat_htool_compressor <sympartialACA, fullACA, SVD>                                          - type of compression
    1072: - -mat_htool_clustering <PCARegular, PCAGeometric, BounbingBox1Regular, BoundingBox1Geometric> - type of clustering

    1074:   Level: intermediate

    1076: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MATHTOOL`, `PCSetCoordinates()`, `MatHtoolSetKernel()`, `MatHtoolCompressorType`, `MATH2OPUS`, `MatCreateH2OpusFromKernel()`
    1077: @*/
    1078: 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)
    1079: {
    1080:   Mat        A;
    1081:   Mat_Htool *a;

    1083:   PetscFunctionBegin;
    1084:   PetscCall(MatCreate(comm, &A));
    1086:   PetscAssertPointer(coords_target, 7);
    1087:   PetscAssertPointer(coords_source, 8);
    1089:   if (!kernel) PetscAssertPointer(kernelctx, 10);
    1090:   PetscCall(MatSetSizes(A, m, n, M, N));
    1091:   PetscCall(MatSetType(A, MATHTOOL));
    1092:   PetscCall(MatSetUp(A));
    1093:   PetscCall(MatShellGetContext(A, &a));
    1094:   a->dim       = spacedim;
    1095:   a->kernel    = kernel;
    1096:   a->kernelctx = kernelctx;
    1097:   PetscCall(PetscCalloc1(A->rmap->N * spacedim, &a->gcoords_target));
    1098:   PetscCall(PetscArraycpy(a->gcoords_target + A->rmap->rstart * spacedim, coords_target, A->rmap->n * spacedim));
    1099:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, a->gcoords_target, A->rmap->N * spacedim, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)A))); /* global target coordinates */
    1100:   if (coords_target != coords_source) {
    1101:     PetscCall(PetscCalloc1(A->cmap->N * spacedim, &a->gcoords_source));
    1102:     PetscCall(PetscArraycpy(a->gcoords_source + A->cmap->rstart * spacedim, coords_source, A->cmap->n * spacedim));
    1103:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, a->gcoords_source, A->cmap->N * spacedim, MPIU_REAL, MPI_SUM, PetscObjectComm((PetscObject)A))); /* global source coordinates */
    1104:   } else a->gcoords_source = a->gcoords_target;
    1105:   *B = A;
    1106:   PetscFunctionReturn(PETSC_SUCCESS);
    1107: }

    1109: /*MC
    1110:      MATHTOOL = "htool" - A matrix type for hierarchical matrices using the Htool package.

    1112:   Use `./configure --download-htool` to install PETSc to use Htool.

    1114:    Options Database Key:
    1115: .     -mat_type htool - matrix type to `MATHTOOL`

    1117:    Level: beginner

    1119: .seealso: [](ch_matrices), `Mat`, `MATH2OPUS`, `MATDENSE`, `MatCreateHtoolFromKernel()`, `MatHtoolSetKernel()`
    1120: M*/
    1121: PETSC_EXTERN PetscErrorCode MatCreate_Htool(Mat A)
    1122: {
    1123:   Mat_Htool *a;

    1125:   PetscFunctionBegin;
    1126:   PetscCall(MatSetType(A, MATSHELL));
    1127:   PetscCall(PetscNew(&a));
    1128:   PetscCall(MatShellSetContext(A, a));
    1129:   PetscCall(MatShellSetOperation(A, MATOP_GET_DIAGONAL, (PetscErrorCodeFn *)MatGetDiagonal_Htool));
    1130:   PetscCall(MatShellSetOperation(A, MATOP_GET_DIAGONAL_BLOCK, (PetscErrorCodeFn *)MatGetDiagonalBlock_Htool));
    1131:   PetscCall(MatShellSetOperation(A, MATOP_MULT, (PetscErrorCodeFn *)MatMult_Htool));
    1132:   PetscCall(MatShellSetOperation(A, MATOP_MULT_TRANSPOSE, (PetscErrorCodeFn *)MatMultTranspose_Htool));
    1133:   if (!PetscDefined(USE_COMPLEX)) PetscCall(MatShellSetOperation(A, MATOP_MULT_HERMITIAN_TRANSPOSE, (PetscErrorCodeFn *)MatMultTranspose_Htool));
    1134:   A->ops->increaseoverlap   = MatIncreaseOverlap_Htool;
    1135:   A->ops->createsubmatrices = MatCreateSubMatrices_Htool;
    1136:   PetscCall(MatShellSetOperation(A, MATOP_VIEW, (PetscErrorCodeFn *)MatView_Htool));
    1137:   PetscCall(MatShellSetOperation(A, MATOP_SET_FROM_OPTIONS, (PetscErrorCodeFn *)MatSetFromOptions_Htool));
    1138:   PetscCall(MatShellSetOperation(A, MATOP_GET_ROW, (PetscErrorCodeFn *)MatGetRow_Htool));
    1139:   PetscCall(MatShellSetOperation(A, MATOP_RESTORE_ROW, (PetscErrorCodeFn *)MatRestoreRow_Htool));
    1140:   PetscCall(MatShellSetOperation(A, MATOP_ASSEMBLY_END, (PetscErrorCodeFn *)MatAssemblyEnd_Htool));
    1141:   PetscCall(MatShellSetOperation(A, MATOP_TRANSPOSE, (PetscErrorCodeFn *)MatTranspose_Htool));
    1142:   PetscCall(MatShellSetOperation(A, MATOP_DESTROY, (PetscErrorCodeFn *)MatDestroy_Htool));
    1143:   a->dim                    = 0;
    1144:   a->gcoords_target         = nullptr;
    1145:   a->gcoords_source         = nullptr;
    1146:   a->max_cluster_leaf_size  = 10;
    1147:   a->epsilon                = PetscSqrtReal(PETSC_SMALL);
    1148:   a->eta                    = 10.0;
    1149:   a->depth[0]               = 0;
    1150:   a->depth[1]               = 0;
    1151:   a->block_tree_consistency = PETSC_TRUE;
    1152:   a->permutation            = PETSC_TRUE;
    1153:   a->recompression          = PETSC_FALSE;
    1154:   a->compressor             = MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA;
    1155:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_htool_seqdense_C", MatProductSetFromOptions_Htool));
    1156:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatProductSetFromOptions_htool_mpidense_C", MatProductSetFromOptions_Htool));
    1157:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_htool_seqdense_C", MatConvert_Htool_Dense));
    1158:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatConvert_htool_mpidense_C", MatConvert_Htool_Dense));
    1159:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetHierarchicalMat_C", MatHtoolGetHierarchicalMat_Htool));
    1160:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolSetKernel_C", MatHtoolSetKernel_Htool));
    1161:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetPermutationSource_C", MatHtoolGetPermutationSource_Htool));
    1162:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolGetPermutationTarget_C", MatHtoolGetPermutationTarget_Htool));
    1163:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolUsePermutation_C", MatHtoolUsePermutation_Htool));
    1164:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatHtoolUseRecompression_C", MatHtoolUseRecompression_Htool));
    1165:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContext_C", MatShellSetContext_Immutable));
    1166:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetContextDestroy_C", MatShellSetContextDestroy_Immutable));
    1167:   PetscCall(PetscObjectComposeFunction((PetscObject)A, "MatShellSetManageScalingShifts_C", MatShellSetManageScalingShifts_Immutable));
    1168:   PetscCall(PetscObjectChangeTypeName((PetscObject)A, MATHTOOL));
    1169:   PetscFunctionReturn(PETSC_SUCCESS);
    1170: }