Date: 2022-03-31T04:47:00+00:00

Actual source code: htool.cxx

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

      5: #define ALEN(a) (sizeof(a)/sizeof((a)[0]))
      6: const char *const MatHtoolCompressorTypes[] = { "sympartialACA", "fullACA", "SVD" };
      7: const char *const MatHtoolClusteringTypes[] = { "PCARegular", "PCAGeometric", "BoundingBox1Regular", "BoundingBox1Geometric" };
      8: const char HtoolCitation[] = "@article{marchand2020two,\n"
      9: "  Author = {Marchand, Pierre and Claeys, Xavier and Jolivet, Pierre and Nataf, Fr\\'ed\\'eric and Tournier, Pierre-Henri},\n"
     10: "  Title = {Two-level preconditioning for $h$-version boundary element approximation of hypersingular operator with {GenEO}},\n"
     11: "  Year = {2020},\n"
     12: "  Publisher = {Elsevier},\n"
     13: "  Journal = {Numerische Mathematik},\n"
     14: "  Volume = {146},\n"
     15: "  Pages = {597--628},\n"
     16: "  Url = {https://github.com/htool-ddm/htool}\n"
     17: "}\n";
     18: static PetscBool HtoolCite = PETSC_FALSE;

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

     26:   MatHasCongruentLayouts(A,&flg);
     28:   VecGetArrayWrite(v,&x);
     29:   a->hmatrix->copy_local_diagonal(x);
     30:   VecRestoreArrayWrite(v,&x);
     31:   VecScale(v,a->s);
     32:   return 0;
     33: }

     35: static PetscErrorCode MatGetDiagonalBlock_Htool(Mat A,Mat *b)
     36: {
     37:   Mat_Htool      *a = (Mat_Htool*)A->data;
     38:   Mat            B;
     39:   PetscScalar    *ptr;
     40:   PetscBool      flg;

     42:   MatHasCongruentLayouts(A,&flg);
     44:   PetscObjectQuery((PetscObject)A,"DiagonalBlock",(PetscObject*)&B); /* same logic as in MatGetDiagonalBlock_MPIDense() */
     45:   if (!B) {
     46:     MatCreateDense(PETSC_COMM_SELF,A->rmap->n,A->rmap->n,A->rmap->n,A->rmap->n,NULL,&B);
     47:     MatDenseGetArrayWrite(B,&ptr);
     48:     a->hmatrix->copy_local_diagonal_block(ptr);
     49:     MatDenseRestoreArrayWrite(B,&ptr);
     50:     MatPropagateSymmetryOptions(A,B);
     51:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
     52:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
     53:     MatScale(B,a->s);
     54:     PetscObjectCompose((PetscObject)A,"DiagonalBlock",(PetscObject)B);
     55:     *b   = B;
     56:     MatDestroy(&B);
     57:   } else *b = B;
     58:   return 0;
     59: }

     61: static PetscErrorCode MatMult_Htool(Mat A,Vec x,Vec y)
     62: {
     63:   Mat_Htool         *a = (Mat_Htool*)A->data;
     64:   const PetscScalar *in;
     65:   PetscScalar       *out;

     67:   VecGetArrayRead(x,&in);
     68:   VecGetArrayWrite(y,&out);
     69:   a->hmatrix->mvprod_local_to_local(in,out);
     70:   VecRestoreArrayRead(x,&in);
     71:   VecRestoreArrayWrite(y,&out);
     72:   VecScale(y,a->s);
     73:   return 0;
     74: }

     76: /* naive implementation of MatMultAdd() needed for FEM-BEM coupling via MATNEST */
     77: static PetscErrorCode MatMultAdd_Htool(Mat A,Vec v1,Vec v2,Vec v3)
     78: {
     79:   Mat_Htool         *a = (Mat_Htool*)A->data;
     80:   Vec               tmp;
     81:   const PetscScalar scale = a->s;

     83:   VecDuplicate(v2,&tmp);
     84:   VecCopy(v2,v3); /* no-op in MatMultAdd(bA->m[i][j],bx[j],by[i],by[i]) since VecCopy() checks for x == y */
     85:   a->s = 1.0; /* set s to 1.0 since VecAXPY() may be used to scale the MatMult() output Vec */
     86:   MatMult_Htool(A,v1,tmp);
     87:   VecAXPY(v3,scale,tmp);
     88:   VecDestroy(&tmp);
     89:   a->s = scale; /* set s back to its original value */
     90:   return 0;
     91: }

     93: static PetscErrorCode MatMultTranspose_Htool(Mat A,Vec x,Vec y)
     94: {
     95:   Mat_Htool         *a = (Mat_Htool*)A->data;
     96:   const PetscScalar *in;
     97:   PetscScalar       *out;

     99:   VecGetArrayRead(x,&in);
    100:   VecGetArrayWrite(y,&out);
    101:   a->hmatrix->mvprod_transp_local_to_local(in,out);
    102:   VecRestoreArrayRead(x,&in);
    103:   VecRestoreArrayWrite(y,&out);
    104:   VecScale(y,a->s);
    105:   return 0;
    106: }

    108: static PetscErrorCode MatIncreaseOverlap_Htool(Mat A,PetscInt is_max,IS is[],PetscInt ov)
    109: {
    110:   std::set<PetscInt> set;
    111:   const PetscInt     *idx;
    112:   PetscInt           *oidx,size,bs[2];
    113:   PetscMPIInt        csize;

    115:   MatGetBlockSizes(A,bs,bs+1);
    116:   if (bs[0] != bs[1]) bs[0] = 1;
    117:   for (PetscInt i=0; i<is_max; ++i) {
    118:     /* basic implementation that adds indices by shifting an IS by -ov, -ov+1..., -1, 1..., ov-1, ov */
    119:     /* needed to avoid subdomain matrices to replicate A since it is dense                           */
    120:     MPI_Comm_size(PetscObjectComm((PetscObject)is[i]),&csize);
    122:     ISGetSize(is[i],&size);
    123:     ISGetIndices(is[i],&idx);
    124:     for (PetscInt j=0; j<size; ++j) {
    125:       set.insert(idx[j]);
    126:       for (PetscInt k=1; k<=ov; ++k) {               /* for each layer of overlap      */
    127:         if (idx[j] - k >= 0) set.insert(idx[j] - k); /* do not insert negative indices */
    128:         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 */
    129:       }
    130:     }
    131:     ISRestoreIndices(is[i],&idx);
    132:     ISDestroy(is+i);
    133:     if (bs[0] > 1) {
    134:       for (std::set<PetscInt>::iterator it=set.cbegin(); it!=set.cend(); it++) {
    135:         std::vector<PetscInt> block(bs[0]);
    136:         std::iota(block.begin(),block.end(),(*it/bs[0])*bs[0]);
    137:         set.insert(block.cbegin(),block.cend());
    138:       }
    139:     }
    140:     size = set.size(); /* size with overlap */
    141:     PetscMalloc1(size,&oidx);
    142:     for (const PetscInt j : set) *oidx++ = j;
    143:     oidx -= size;
    144:     ISCreateGeneral(PETSC_COMM_SELF,size,oidx,PETSC_OWN_POINTER,is+i);
    145:   }
    146:   return 0;
    147: }

    149: static PetscErrorCode MatCreateSubMatrices_Htool(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
    150: {
    151:   Mat_Htool         *a = (Mat_Htool*)A->data;
    152:   Mat               D,B,BT;
    153:   const PetscScalar *copy;
    154:   PetscScalar       *ptr;
    155:   const PetscInt    *idxr,*idxc,*it;
    156:   PetscInt          nrow,m,i;
    157:   PetscBool         flg;

    159:   if (scall != MAT_REUSE_MATRIX) {
    160:     PetscCalloc1(n,submat);
    161:   }
    162:   for (i=0; i<n; ++i) {
    163:     ISGetLocalSize(irow[i],&nrow);
    164:     ISGetLocalSize(icol[i],&m);
    165:     ISGetIndices(irow[i],&idxr);
    166:     ISGetIndices(icol[i],&idxc);
    167:     if (scall != MAT_REUSE_MATRIX) {
    168:       MatCreateDense(PETSC_COMM_SELF,nrow,m,nrow,m,NULL,(*submat)+i);
    169:     }
    170:     MatDenseGetArrayWrite((*submat)[i],&ptr);
    171:     if (irow[i] == icol[i]) { /* same row and column IS? */
    172:       MatHasCongruentLayouts(A,&flg);
    173:       if (flg) {
    174:         ISSorted(irow[i],&flg);
    175:         if (flg) { /* sorted IS? */
    176:           it = std::lower_bound(idxr,idxr+nrow,A->rmap->rstart);
    177:           if (it != idxr+nrow && *it == A->rmap->rstart) { /* rmap->rstart in IS? */
    178:             if (std::distance(idxr,it) + A->rmap->n <= nrow) { /* long enough IS to store the local diagonal block? */
    179:               for (PetscInt j=0; j<A->rmap->n && flg; ++j) if (PetscUnlikely(it[j] != A->rmap->rstart+j)) flg = PETSC_FALSE;
    180:               if (flg) { /* complete local diagonal block in IS? */
    181:                 /* fast extraction when the local diagonal block is part of the submatrix, e.g., for PCASM or PCHPDDM
    182:                  *      [   B   C   E   ]
    183:                  *  A = [   B   D   E   ]
    184:                  *      [   B   F   E   ]
    185:                  */
    186:                 m = std::distance(idxr,it); /* shift of the coefficient (0,0) of block D from above */
    187:                 MatGetDiagonalBlock_Htool(A,&D);
    188:                 MatDenseGetArrayRead(D,&copy);
    189:                 for (PetscInt k=0; k<A->rmap->n; ++k) {
    190:                   PetscArraycpy(ptr+(m+k)*nrow+m,copy+k*A->rmap->n,A->rmap->n); /* block D from above */
    191:                 }
    192:                 MatDenseRestoreArrayRead(D,&copy);
    193:                 if (m) {
    194:                   a->wrapper->copy_submatrix(nrow,m,idxr,idxc,ptr); /* vertical block B from above */
    195:                   /* entry-wise assembly may be costly, so transpose already-computed entries when possible */
    196:                   if (A->symmetric || A->hermitian) {
    197:                     MatCreateDense(PETSC_COMM_SELF,A->rmap->n,m,A->rmap->n,m,ptr+m,&B);
    198:                     MatDenseSetLDA(B,nrow);
    199:                     MatCreateDense(PETSC_COMM_SELF,m,A->rmap->n,m,A->rmap->n,ptr+m*nrow,&BT);
    200:                     MatDenseSetLDA(BT,nrow);
    201:                     if (A->hermitian && PetscDefined(USE_COMPLEX)) {
    202:                       MatHermitianTranspose(B,MAT_REUSE_MATRIX,&BT);
    203:                     } else {
    204:                       MatTranspose(B,MAT_REUSE_MATRIX,&BT);
    205:                     }
    206:                     MatDestroy(&B);
    207:                     MatDestroy(&BT);
    208:                   } else {
    209:                     for (PetscInt k=0; k<A->rmap->n; ++k) { /* block C from above */
    210:                       a->wrapper->copy_submatrix(m,1,idxr,idxc+m+k,ptr+(m+k)*nrow);
    211:                     }
    212:                   }
    213:                 }
    214:                 if (m+A->rmap->n != nrow) {
    215:                   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 */
    216:                   /* entry-wise assembly may be costly, so transpose already-computed entries when possible */
    217:                   if (A->symmetric || A->hermitian) {
    218:                     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);
    219:                     MatDenseSetLDA(B,nrow);
    220:                     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);
    221:                     MatDenseSetLDA(BT,nrow);
    222:                     if (A->hermitian && PetscDefined(USE_COMPLEX)) {
    223:                       MatHermitianTranspose(B,MAT_REUSE_MATRIX,&BT);
    224:                     } else {
    225:                       MatTranspose(B,MAT_REUSE_MATRIX,&BT);
    226:                     }
    227:                     MatDestroy(&B);
    228:                     MatDestroy(&BT);
    229:                   } else {
    230:                     for (PetscInt k=0; k<A->rmap->n; ++k) { /* block F from above */
    231:                       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);
    232:                     }
    233:                   }
    234:                 }
    235:               } /* complete local diagonal block not in IS */
    236:             } else flg = PETSC_FALSE; /* IS not long enough to store the local diagonal block */
    237:           } else flg = PETSC_FALSE; /* rmap->rstart not in IS */
    238:         } /* unsorted IS */
    239:       }
    240:     } else flg = PETSC_FALSE; /* different row and column IS */
    241:     if (!flg) a->wrapper->copy_submatrix(nrow,m,idxr,idxc,ptr); /* reassemble everything */
    242:     ISRestoreIndices(irow[i],&idxr);
    243:     ISRestoreIndices(icol[i],&idxc);
    244:     MatDenseRestoreArrayWrite((*submat)[i],&ptr);
    245:     MatAssemblyBegin((*submat)[i],MAT_FINAL_ASSEMBLY);
    246:     MatAssemblyEnd((*submat)[i],MAT_FINAL_ASSEMBLY);
    247:     MatScale((*submat)[i],a->s);
    248:   }
    249:   return 0;
    250: }

    252: static PetscErrorCode MatDestroy_Htool(Mat A)
    253: {
    254:   Mat_Htool               *a = (Mat_Htool*)A->data;
    255:   PetscContainer          container;
    256:   MatHtoolKernelTranspose *kernelt;

    258:   PetscObjectChangeTypeName((PetscObject)A,NULL);
    259:   PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_htool_seqdense_C",NULL);
    260:   PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_htool_mpidense_C",NULL);
    261:   PetscObjectComposeFunction((PetscObject)A,"MatConvert_htool_seqdense_C",NULL);
    262:   PetscObjectComposeFunction((PetscObject)A,"MatConvert_htool_mpidense_C",NULL);
    263:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetHierarchicalMat_C",NULL);
    264:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolSetKernel_C",NULL);
    265:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetPermutationSource_C",NULL);
    266:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetPermutationTarget_C",NULL);
    267:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolUsePermutation_C",NULL);
    268:   PetscObjectQuery((PetscObject)A,"KernelTranspose",(PetscObject*)&container);
    269:   if (container) { /* created in MatTranspose_Htool() */
    270:     PetscContainerGetPointer(container,(void**)&kernelt);
    271:     MatDestroy(&kernelt->A);
    272:     PetscFree(kernelt);
    273:     PetscContainerDestroy(&container);
    274:     PetscObjectCompose((PetscObject)A,"KernelTranspose",NULL);
    275:   }
    276:   if (a->gcoords_source != a->gcoords_target) {
    277:     PetscFree(a->gcoords_source);
    278:   }
    279:   PetscFree(a->gcoords_target);
    280:   PetscFree2(a->work_source,a->work_target);
    281:   delete a->wrapper;
    282:   delete a->hmatrix;
    283:   PetscFree(A->data);
    284:   return 0;
    285: }

    287: static PetscErrorCode MatView_Htool(Mat A,PetscViewer pv)
    288: {
    289:   Mat_Htool      *a = (Mat_Htool*)A->data;
    290:   PetscBool      flg;

    292:   PetscObjectTypeCompare((PetscObject)pv,PETSCVIEWERASCII,&flg);
    293:   if (flg) {
    294:     PetscViewerASCIIPrintf(pv,"symmetry: %c\n",a->hmatrix->get_symmetry_type());
    295:     if (PetscAbsScalar(a->s-1.0) > PETSC_MACHINE_EPSILON) {
    296: #if defined(PETSC_USE_COMPLEX)
    297:       PetscViewerASCIIPrintf(pv,"scaling: %g+%gi\n",(double)PetscRealPart(a->s),(double)PetscImaginaryPart(a->s));
    298: #else
    299:       PetscViewerASCIIPrintf(pv,"scaling: %g\n",(double)a->s);
    300: #endif
    301:     }
    302:     PetscViewerASCIIPrintf(pv,"minimum cluster size: %" PetscInt_FMT "\n",a->bs[0]);
    303:     PetscViewerASCIIPrintf(pv,"maximum block size: %" PetscInt_FMT "\n",a->bs[1]);
    304:     PetscViewerASCIIPrintf(pv,"epsilon: %g\n",(double)a->epsilon);
    305:     PetscViewerASCIIPrintf(pv,"eta: %g\n",(double)a->eta);
    306:     PetscViewerASCIIPrintf(pv,"minimum target depth: %" PetscInt_FMT "\n",a->depth[0]);
    307:     PetscViewerASCIIPrintf(pv,"minimum source depth: %" PetscInt_FMT "\n",a->depth[1]);
    308:     PetscViewerASCIIPrintf(pv,"compressor: %s\n",MatHtoolCompressorTypes[a->compressor]);
    309:     PetscViewerASCIIPrintf(pv,"clustering: %s\n",MatHtoolClusteringTypes[a->clustering]);
    310:     PetscViewerASCIIPrintf(pv,"compression ratio: %s\n",a->hmatrix->get_infos("Compression_ratio").c_str());
    311:     PetscViewerASCIIPrintf(pv,"space saving: %s\n",a->hmatrix->get_infos("Space_saving").c_str());
    312:     PetscViewerASCIIPrintf(pv,"number of dense (resp. low rank) matrices: %s (resp. %s)\n",a->hmatrix->get_infos("Number_of_dmat").c_str(),a->hmatrix->get_infos("Number_of_lrmat").c_str());
    313:     PetscViewerASCIIPrintf(pv,"(minimum, mean, maximum) dense block sizes: (%s, %s, %s)\n",a->hmatrix->get_infos("Dense_block_size_min").c_str(),a->hmatrix->get_infos("Dense_block_size_mean").c_str(),a->hmatrix->get_infos("Dense_block_size_max").c_str());
    314:     PetscViewerASCIIPrintf(pv,"(minimum, mean, maximum) low rank block sizes: (%s, %s, %s)\n",a->hmatrix->get_infos("Low_rank_block_size_min").c_str(),a->hmatrix->get_infos("Low_rank_block_size_mean").c_str(),a->hmatrix->get_infos("Low_rank_block_size_max").c_str());
    315:     PetscViewerASCIIPrintf(pv,"(minimum, mean, maximum) ranks: (%s, %s, %s)\n",a->hmatrix->get_infos("Rank_min").c_str(),a->hmatrix->get_infos("Rank_mean").c_str(),a->hmatrix->get_infos("Rank_max").c_str());
    316:   }
    317:   return 0;
    318: }

    320: static PetscErrorCode MatScale_Htool(Mat A,PetscScalar s)
    321: {
    322:   Mat_Htool *a = (Mat_Htool*)A->data;

    324:   a->s *= s;
    325:   return 0;
    326: }

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

    335:   if (nz) *nz = A->cmap->N;
    336:   if (idx || v) { /* even if !idx, need to set idxc for htool::copy_submatrix() */
    337:     PetscMalloc1(A->cmap->N,&idxc);
    338:     for (PetscInt i=0; i<A->cmap->N; ++i) idxc[i] = i;
    339:   }
    340:   if (idx) *idx = idxc;
    341:   if (v) {
    342:     PetscMalloc1(A->cmap->N,v);
    343:     if (a->wrapper) a->wrapper->copy_submatrix(1,A->cmap->N,&row,idxc,*v);
    344:     else reinterpret_cast<htool::VirtualGenerator<PetscScalar>*>(a->kernelctx)->copy_submatrix(1,A->cmap->N,&row,idxc,*v);
    345:     PetscBLASIntCast(A->cmap->N,&bn);
    346:     PetscStackCallBLAS("BLASscal",BLASscal_(&bn,&a->s,*v,&one));
    347:   }
    348:   if (!idx) {
    349:     PetscFree(idxc);
    350:   }
    351:   return 0;
    352: }

    354: static PetscErrorCode MatRestoreRow_Htool(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
    355: {
    356:   if (nz) *nz = 0;
    357:   if (idx) {
    358:     PetscFree(*idx);
    359:   }
    360:   if (v) {
    361:     PetscFree(*v);
    362:   }
    363:   return 0;
    364: }

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

    372:   PetscOptionsHead(PetscOptionsObject,"Htool options");
    373:   PetscOptionsInt("-mat_htool_min_cluster_size","Minimal leaf size in cluster tree",NULL,a->bs[0],a->bs,NULL);
    374:   PetscOptionsInt("-mat_htool_max_block_size","Maximal number of coefficients in a dense block",NULL,a->bs[1],a->bs + 1,NULL);
    375:   PetscOptionsReal("-mat_htool_epsilon","Relative error in Frobenius norm when approximating a block",NULL,a->epsilon,&a->epsilon,NULL);
    376:   PetscOptionsReal("-mat_htool_eta","Admissibility condition tolerance",NULL,a->eta,&a->eta,NULL);
    377:   PetscOptionsInt("-mat_htool_min_target_depth","Minimal cluster tree depth associated with the rows",NULL,a->depth[0],a->depth,NULL);
    378:   PetscOptionsInt("-mat_htool_min_source_depth","Minimal cluster tree depth associated with the columns",NULL,a->depth[1],a->depth + 1,NULL);
    379:   n = 0;
    380:   PetscOptionsEList("-mat_htool_compressor","Type of compression","MatHtoolCompressorType",MatHtoolCompressorTypes,ALEN(MatHtoolCompressorTypes),MatHtoolCompressorTypes[MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA],&n,&flg);
    381:   if (flg) a->compressor = MatHtoolCompressorType(n);
    382:   n = 0;
    383:   PetscOptionsEList("-mat_htool_clustering","Type of clustering","MatHtoolClusteringType",MatHtoolClusteringTypes,ALEN(MatHtoolClusteringTypes),MatHtoolClusteringTypes[MAT_HTOOL_CLUSTERING_PCA_REGULAR],&n,&flg);
    384:   if (flg) a->clustering = MatHtoolClusteringType(n);
    385:   PetscOptionsTail();
    386:   return 0;
    387: }

    389: static PetscErrorCode MatAssemblyEnd_Htool(Mat A,MatAssemblyType type)
    390: {
    391:   Mat_Htool                                                    *a = (Mat_Htool*)A->data;
    392:   const PetscInt                                               *ranges;
    393:   PetscInt                                                     *offset;
    394:   PetscMPIInt                                                  size;
    395:   char                                                         S = PetscDefined(USE_COMPLEX) && A->hermitian ? 'H' : (A->symmetric ? 'S' : 'N'),uplo = S == 'N' ? 'N' : 'U';
    396:   htool::VirtualGenerator<PetscScalar>                         *generator = nullptr;
    397:   std::shared_ptr<htool::VirtualCluster>                       t,s = nullptr;
    398:   std::shared_ptr<htool::VirtualLowRankGenerator<PetscScalar>> compressor = nullptr;

    400:   PetscCitationsRegister(HtoolCitation,&HtoolCite);
    401:   delete a->wrapper;
    402:   delete a->hmatrix;
    403:   MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);
    404:   PetscMalloc1(2*size,&offset);
    405:   MatGetOwnershipRanges(A,&ranges);
    406:   for (PetscInt i=0; i<size; ++i) {
    407:     offset[2*i] = ranges[i];
    408:     offset[2*i+1] = ranges[i+1] - ranges[i];
    409:   }
    410:   switch (a->clustering) {
    411:   case MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC:
    412:     t = std::make_shared<htool::Cluster<htool::PCA<htool::SplittingTypes::GeometricSplitting>>>(a->dim);
    413:     break;
    414:   case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC:
    415:     t = std::make_shared<htool::Cluster<htool::BoundingBox1<htool::SplittingTypes::GeometricSplitting>>>(a->dim);
    416:     break;
    417:   case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR:
    418:     t = std::make_shared<htool::Cluster<htool::BoundingBox1<htool::SplittingTypes::RegularSplitting>>>(a->dim);
    419:     break;
    420:   default:
    421:     t = std::make_shared<htool::Cluster<htool::PCA<htool::SplittingTypes::RegularSplitting>>>(a->dim);
    422:   }
    423:   t->set_minclustersize(a->bs[0]);
    424:   t->build(A->rmap->N,a->gcoords_target,offset);
    425:   if (a->kernel) a->wrapper = new WrapperHtool(A->rmap->N,A->cmap->N,a->dim,a->kernel,a->kernelctx);
    426:   else {
    427:     a->wrapper = NULL;
    428:     generator = reinterpret_cast<htool::VirtualGenerator<PetscScalar>*>(a->kernelctx);
    429:   }
    430:   if (a->gcoords_target != a->gcoords_source) {
    431:     MatGetOwnershipRangesColumn(A,&ranges);
    432:     for (PetscInt i=0; i<size; ++i) {
    433:       offset[2*i] = ranges[i];
    434:       offset[2*i+1] = ranges[i+1] - ranges[i];
    435:     }
    436:     switch (a->clustering) {
    437:     case MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC:
    438:       s = std::make_shared<htool::Cluster<htool::PCA<htool::SplittingTypes::GeometricSplitting>>>(a->dim);
    439:       break;
    440:     case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC:
    441:       s = std::make_shared<htool::Cluster<htool::BoundingBox1<htool::SplittingTypes::GeometricSplitting>>>(a->dim);
    442:       break;
    443:     case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR:
    444:       s = std::make_shared<htool::Cluster<htool::BoundingBox1<htool::SplittingTypes::RegularSplitting>>>(a->dim);
    445:       break;
    446:     default:
    447:       s = std::make_shared<htool::Cluster<htool::PCA<htool::SplittingTypes::RegularSplitting>>>(a->dim);
    448:     }
    449:     s->set_minclustersize(a->bs[0]);
    450:     s->build(A->cmap->N,a->gcoords_source,offset);
    451:     S = uplo = 'N';
    452:   }
    453:   PetscFree(offset);
    454:   switch (a->compressor) {
    455:   case MAT_HTOOL_COMPRESSOR_FULL_ACA:
    456:     compressor = std::make_shared<htool::fullACA<PetscScalar>>();
    457:     break;
    458:   case MAT_HTOOL_COMPRESSOR_SVD:
    459:     compressor = std::make_shared<htool::SVD<PetscScalar>>();
    460:     break;
    461:   default:
    462:     compressor = std::make_shared<htool::sympartialACA<PetscScalar>>();
    463:   }
    464:   a->hmatrix = dynamic_cast<htool::VirtualHMatrix<PetscScalar>*>(new htool::HMatrix<PetscScalar>(t,s ? s : t,a->epsilon,a->eta,S,uplo));
    465:   a->hmatrix->set_compression(compressor);
    466:   a->hmatrix->set_maxblocksize(a->bs[1]);
    467:   a->hmatrix->set_mintargetdepth(a->depth[0]);
    468:   a->hmatrix->set_minsourcedepth(a->depth[1]);
    469:   if (s) a->hmatrix->build(a->wrapper ? *a->wrapper : *generator,a->gcoords_target,a->gcoords_source);
    470:   else   a->hmatrix->build(a->wrapper ? *a->wrapper : *generator,a->gcoords_target);
    471:   return 0;
    472: }

    474: static PetscErrorCode MatProductNumeric_Htool(Mat C)
    475: {
    476:   Mat_Product       *product = C->product;
    477:   Mat_Htool         *a = (Mat_Htool*)product->A->data;
    478:   const PetscScalar *in;
    479:   PetscScalar       *out;
    480:   PetscInt          N,lda;

    482:   MatCheckProduct(C,1);
    483:   MatGetSize(C,NULL,&N);
    484:   MatDenseGetLDA(C,&lda);
    486:   MatDenseGetArrayRead(product->B,&in);
    487:   MatDenseGetArrayWrite(C,&out);
    488:   switch (product->type) {
    489:   case MATPRODUCT_AB:
    490:     a->hmatrix->mvprod_local_to_local(in,out,N);
    491:     break;
    492:   case MATPRODUCT_AtB:
    493:     a->hmatrix->mvprod_transp_local_to_local(in,out,N);
    494:     break;
    495:   default:
    496:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProductType %s is not supported",MatProductTypes[product->type]);
    497:   }
    498:   MatDenseRestoreArrayWrite(C,&out);
    499:   MatDenseRestoreArrayRead(product->B,&in);
    500:   MatScale(C,a->s);
    501:   return 0;
    502: }

    504: static PetscErrorCode MatProductSymbolic_Htool(Mat C)
    505: {
    506:   Mat_Product    *product = C->product;
    507:   Mat            A,B;
    508:   PetscBool      flg;

    510:   MatCheckProduct(C,1);
    511:   A = product->A;
    512:   B = product->B;
    513:   PetscObjectTypeCompareAny((PetscObject)B,&flg,MATSEQDENSE,MATMPIDENSE,"");
    515:   switch (product->type) {
    516:   case MATPRODUCT_AB:
    517:     if (C->rmap->n == PETSC_DECIDE || C->cmap->n == PETSC_DECIDE || C->rmap->N == PETSC_DECIDE || C->cmap->N == PETSC_DECIDE) {
    518:       MatSetSizes(C,A->rmap->n,B->cmap->n,A->rmap->N,B->cmap->N);
    519:     }
    520:     break;
    521:   case MATPRODUCT_AtB:
    522:     if (C->rmap->n == PETSC_DECIDE || C->cmap->n == PETSC_DECIDE || C->rmap->N == PETSC_DECIDE || C->cmap->N == PETSC_DECIDE) {
    523:       MatSetSizes(C,A->cmap->n,B->cmap->n,A->cmap->N,B->cmap->N);
    524:     }
    525:     break;
    526:   default:
    527:     SETERRQ(PetscObjectComm((PetscObject)B),PETSC_ERR_SUP,"ProductType %s is not supported",MatProductTypes[product->type]);
    528:   }
    529:   MatSetType(C,MATDENSE);
    530:   MatSetUp(C);
    531:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    532:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    533:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    534:   C->ops->productsymbolic = NULL;
    535:   C->ops->productnumeric = MatProductNumeric_Htool;
    536:   return 0;
    537: }

    539: static PetscErrorCode MatProductSetFromOptions_Htool(Mat C)
    540: {
    541:   MatCheckProduct(C,1);
    542:   if (C->product->type == MATPRODUCT_AB || C->product->type == MATPRODUCT_AtB) C->ops->productsymbolic = MatProductSymbolic_Htool;
    543:   return 0;
    544: }

    546: static PetscErrorCode MatHtoolGetHierarchicalMat_Htool(Mat A,const htool::VirtualHMatrix<PetscScalar> **hmatrix)
    547: {
    548:   Mat_Htool *a = (Mat_Htool*)A->data;

    550:   *hmatrix = a->hmatrix;
    551:   return 0;
    552: }

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

    557:    Input Parameter:
    558: .     A - hierarchical matrix

    560:    Output Parameter:
    561: .     hmatrix - opaque pointer to a Htool virtual matrix

    563:    Level: advanced

    565: .seealso:  MATHTOOL
    566: @*/
    567: PETSC_EXTERN PetscErrorCode MatHtoolGetHierarchicalMat(Mat A,const htool::VirtualHMatrix<PetscScalar> **hmatrix)
    568: {
    571:   PetscTryMethod(A,"MatHtoolGetHierarchicalMat_C",(Mat,const htool::VirtualHMatrix<PetscScalar>**),(A,hmatrix));
    572:   return 0;
    573: }

    575: static PetscErrorCode MatHtoolSetKernel_Htool(Mat A,MatHtoolKernel kernel,void *kernelctx)
    576: {
    577:   Mat_Htool *a = (Mat_Htool*)A->data;

    579:   a->kernel    = kernel;
    580:   a->kernelctx = kernelctx;
    581:   delete a->wrapper;
    582:   if (a->kernel) a->wrapper = new WrapperHtool(A->rmap->N,A->cmap->N,a->dim,a->kernel,a->kernelctx);
    583:   return 0;
    584: }

    586: /*@C
    587:      MatHtoolSetKernel - Sets the kernel and context used for the assembly of a MATHTOOL.

    589:    Input Parameters:
    590: +     A - hierarchical matrix
    591: .     kernel - computational kernel (or NULL)
    592: -     kernelctx - kernel context (if kernel is NULL, the pointer must be of type htool::VirtualGenerator<PetscScalar>*)

    594:    Level: advanced

    596: .seealso:  MATHTOOL, MatCreateHtoolFromKernel()
    597: @*/
    598: PETSC_EXTERN PetscErrorCode MatHtoolSetKernel(Mat A,MatHtoolKernel kernel,void *kernelctx)
    599: {
    603:   PetscTryMethod(A,"MatHtoolSetKernel_C",(Mat,MatHtoolKernel,void*),(A,kernel,kernelctx));
    604:   return 0;
    605: }

    607: static PetscErrorCode MatHtoolGetPermutationSource_Htool(Mat A,IS* is)
    608: {
    609:   Mat_Htool             *a = (Mat_Htool*)A->data;
    610:   std::vector<PetscInt> source;

    612:   source = a->hmatrix->get_source_cluster()->get_local_perm();
    613:   ISCreateGeneral(PetscObjectComm((PetscObject)A),source.size(),source.data(),PETSC_COPY_VALUES,is);
    614:   ISSetPermutation(*is);
    615:   return 0;
    616: }

    618: /*@C
    619:      MatHtoolGetPermutationSource - Gets the permutation associated to the source cluster.

    621:    Input Parameter:
    622: .     A - hierarchical matrix

    624:    Output Parameter:
    625: .     is - permutation

    627:    Level: advanced

    629: .seealso:  MATHTOOL, MatHtoolGetPermutationTarget(), MatHtoolUsePermutation()
    630: @*/
    631: PETSC_EXTERN PetscErrorCode MatHtoolGetPermutationSource(Mat A,IS* is)
    632: {
    635:   PetscTryMethod(A,"MatHtoolGetPermutationSource_C",(Mat,IS*),(A,is));
    636:   return 0;
    637: }

    639: static PetscErrorCode MatHtoolGetPermutationTarget_Htool(Mat A,IS* is)
    640: {
    641:   Mat_Htool             *a = (Mat_Htool*)A->data;
    642:   std::vector<PetscInt> target;

    644:   target = a->hmatrix->get_target_cluster()->get_local_perm();
    645:   ISCreateGeneral(PetscObjectComm((PetscObject)A),target.size(),target.data(),PETSC_COPY_VALUES,is);
    646:   ISSetPermutation(*is);
    647:   return 0;
    648: }

    650: /*@C
    651:      MatHtoolGetPermutationTarget - Gets the permutation associated to the target cluster.

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

    656:    Output Parameter:
    657: .     is - permutation

    659:    Level: advanced

    661: .seealso:  MATHTOOL, MatHtoolGetPermutationSource(), MatHtoolUsePermutation()
    662: @*/
    663: PETSC_EXTERN PetscErrorCode MatHtoolGetPermutationTarget(Mat A,IS* is)
    664: {
    667:   PetscTryMethod(A,"MatHtoolGetPermutationTarget_C",(Mat,IS*),(A,is));
    668:   return 0;
    669: }

    671: static PetscErrorCode MatHtoolUsePermutation_Htool(Mat A,PetscBool use)
    672: {
    673:   Mat_Htool *a = (Mat_Htool*)A->data;

    675:   a->hmatrix->set_use_permutation(use);
    676:   return 0;
    677: }

    679: /*@C
    680:      MatHtoolUsePermutation - Sets whether MATHTOOL should permute input (resp. output) vectors following its internal source (resp. target) permutation.

    682:    Input Parameters:
    683: +     A - hierarchical matrix
    684: -     use - Boolean value

    686:    Level: advanced

    688: .seealso:  MATHTOOL, MatHtoolGetPermutationSource(), MatHtoolGetPermutationTarget()
    689: @*/
    690: PETSC_EXTERN PetscErrorCode MatHtoolUsePermutation(Mat A,PetscBool use)
    691: {
    694:   PetscTryMethod(A,"MatHtoolUsePermutation_C",(Mat,PetscBool),(A,use));
    695:   return 0;
    696: }

    698: static PetscErrorCode MatConvert_Htool_Dense(Mat A,MatType newtype,MatReuse reuse,Mat *B)
    699: {
    700:   Mat            C;
    701:   Mat_Htool      *a = (Mat_Htool*)A->data;
    702:   PetscInt       lda;
    703:   PetscScalar    *array;

    705:   if (reuse == MAT_REUSE_MATRIX) {
    706:     C = *B;
    708:     MatDenseGetLDA(C,&lda);
    710:   } else {
    711:     MatCreate(PetscObjectComm((PetscObject)A),&C);
    712:     MatSetSizes(C,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);
    713:     MatSetType(C,MATDENSE);
    714:     MatSetUp(C);
    715:     MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    716:   }
    717:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    718:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    719:   MatDenseGetArrayWrite(C,&array);
    720:   a->hmatrix->copy_local_dense_perm(array);
    721:   MatDenseRestoreArrayWrite(C,&array);
    722:   MatScale(C,a->s);
    723:   if (reuse == MAT_INPLACE_MATRIX) {
    724:     MatHeaderReplace(A,&C);
    725:   } else *B = C;
    726:   return 0;
    727: }

    729: static PetscErrorCode GenEntriesTranspose(PetscInt sdim,PetscInt M,PetscInt N,const PetscInt *rows,const PetscInt *cols,PetscScalar *ptr,void *ctx)
    730: {
    731:   MatHtoolKernelTranspose *generator = (MatHtoolKernelTranspose*)ctx;
    732:   PetscScalar             *tmp;

    734:   generator->kernel(sdim,N,M,cols,rows,ptr,generator->kernelctx);
    735:   PetscMalloc1(M*N,&tmp);
    736:   PetscArraycpy(tmp,ptr,M*N);
    737:   for (PetscInt i=0; i<M; ++i) {
    738:     for (PetscInt j=0; j<N; ++j) ptr[i+j*M] = tmp[j+i*N];
    739:   }
    740:   PetscFree(tmp);
    741:   return 0;
    742: }

    744: /* naive implementation which keeps a reference to the original Mat */
    745: static PetscErrorCode MatTranspose_Htool(Mat A,MatReuse reuse,Mat *B)
    746: {
    747:   Mat                     C;
    748:   Mat_Htool               *a = (Mat_Htool*)A->data,*c;
    749:   PetscInt                M = A->rmap->N,N = A->cmap->N,m = A->rmap->n,n = A->cmap->n;
    750:   PetscContainer          container;
    751:   MatHtoolKernelTranspose *kernelt;

    754:   if (reuse == MAT_INITIAL_MATRIX) {
    755:     MatCreate(PetscObjectComm((PetscObject)A),&C);
    756:     MatSetSizes(C,n,m,N,M);
    757:     MatSetType(C,((PetscObject)A)->type_name);
    758:     MatSetUp(C);
    759:     PetscContainerCreate(PetscObjectComm((PetscObject)C),&container);
    760:     PetscNew(&kernelt);
    761:     PetscContainerSetPointer(container,kernelt);
    762:     PetscObjectCompose((PetscObject)C,"KernelTranspose",(PetscObject)container);
    763:   } else {
    764:     C = *B;
    765:     PetscObjectQuery((PetscObject)C,"KernelTranspose",(PetscObject*)&container);
    767:     PetscContainerGetPointer(container,(void**)&kernelt);
    768:   }
    769:   c                  = (Mat_Htool*)C->data;
    770:   c->dim             = a->dim;
    771:   c->s               = a->s;
    772:   c->kernel          = GenEntriesTranspose;
    773:   if (kernelt->A != A) {
    774:     MatDestroy(&kernelt->A);
    775:     kernelt->A       = A;
    776:     PetscObjectReference((PetscObject)A);
    777:   }
    778:   kernelt->kernel    = a->kernel;
    779:   kernelt->kernelctx = a->kernelctx;
    780:   c->kernelctx       = kernelt;
    781:   if (reuse == MAT_INITIAL_MATRIX) {
    782:     PetscMalloc1(N*c->dim,&c->gcoords_target);
    783:     PetscArraycpy(c->gcoords_target,a->gcoords_source,N*c->dim);
    784:     if (a->gcoords_target != a->gcoords_source) {
    785:       PetscMalloc1(M*c->dim,&c->gcoords_source);
    786:       PetscArraycpy(c->gcoords_source,a->gcoords_target,M*c->dim);
    787:     } else c->gcoords_source = c->gcoords_target;
    788:     PetscCalloc2(M,&c->work_source,N,&c->work_target);
    789:   }
    790:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    791:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    792:   if (reuse == MAT_INITIAL_MATRIX) *B = C;
    793:   return 0;
    794: }

    796: /*@C
    797:      MatCreateHtoolFromKernel - Creates a MATHTOOL from a user-supplied kernel.

    799:    Input Parameters:
    800: +     comm - MPI communicator
    801: .     m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
    802: .     n - number of local columns (or PETSC_DECIDE to have calculated if N is given)
    803: .     M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
    804: .     N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
    805: .     spacedim - dimension of the space coordinates
    806: .     coords_target - coordinates of the target
    807: .     coords_source - coordinates of the source
    808: .     kernel - computational kernel (or NULL)
    809: -     kernelctx - kernel context (if kernel is NULL, the pointer must be of type htool::VirtualGenerator<PetscScalar>*)

    811:    Output Parameter:
    812: .     B - matrix

    814:    Options Database Keys:
    815: +     -mat_htool_min_cluster_size <PetscInt> - minimal leaf size in cluster tree
    816: .     -mat_htool_max_block_size <PetscInt> - maximal number of coefficients in a dense block
    817: .     -mat_htool_epsilon <PetscReal> - relative error in Frobenius norm when approximating a block
    818: .     -mat_htool_eta <PetscReal> - admissibility condition tolerance
    819: .     -mat_htool_min_target_depth <PetscInt> - minimal cluster tree depth associated with the rows
    820: .     -mat_htool_min_source_depth <PetscInt> - minimal cluster tree depth associated with the columns
    821: .     -mat_htool_compressor <sympartialACA, fullACA, SVD> - type of compression
    822: -     -mat_htool_clustering <PCARegular, PCAGeometric, BounbingBox1Regular, BoundingBox1Geometric> - type of clustering

    824:    Level: intermediate

    826: .seealso:  MatCreate(), MATHTOOL, PCSetCoordinates(), MatHtoolSetKernel(), MatHtoolCompressorType, MATH2OPUS, MatCreateH2OpusFromKernel()
    827: @*/
    828: PetscErrorCode MatCreateHtoolFromKernel(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt spacedim,const PetscReal coords_target[],const PetscReal coords_source[],MatHtoolKernel kernel,void *kernelctx,Mat *B)
    829: {
    830:   Mat            A;
    831:   Mat_Htool      *a;

    833:   MatCreate(comm,&A);
    839:   MatSetSizes(A,m,n,M,N);
    840:   MatSetType(A,MATHTOOL);
    841:   MatSetUp(A);
    842:   a            = (Mat_Htool*)A->data;
    843:   a->dim       = spacedim;
    844:   a->s         = 1.0;
    845:   a->kernel    = kernel;
    846:   a->kernelctx = kernelctx;
    847:   PetscCalloc1(A->rmap->N*spacedim,&a->gcoords_target);
    848:   PetscArraycpy(a->gcoords_target+A->rmap->rstart*spacedim,coords_target,A->rmap->n*spacedim);
    849:   MPIU_Allreduce(MPI_IN_PLACE,a->gcoords_target,A->rmap->N*spacedim,MPIU_REAL,MPI_SUM,PetscObjectComm((PetscObject)A)); /* global target coordinates */
    850:   if (coords_target != coords_source) {
    851:     PetscCalloc1(A->cmap->N*spacedim,&a->gcoords_source);
    852:     PetscArraycpy(a->gcoords_source+A->cmap->rstart*spacedim,coords_source,A->cmap->n*spacedim);
    853:     MPIU_Allreduce(MPI_IN_PLACE,a->gcoords_source,A->cmap->N*spacedim,MPIU_REAL,MPI_SUM,PetscObjectComm((PetscObject)A)); /* global source coordinates */
    854:   } else a->gcoords_source = a->gcoords_target;
    855:   PetscCalloc2(A->cmap->N,&a->work_source,A->rmap->N,&a->work_target);
    856:   *B = A;
    857:   return 0;
    858: }

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

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

    865:    Options Database Keys:
    866: .     -mat_type htool - matrix type to "htool" during a call to MatSetFromOptions()

    868:    Level: beginner

    870: .seealso: MATH2OPUS, MATDENSE, MatCreateHtoolFromKernel(), MatHtoolSetKernel()
    871: M*/
    872: PETSC_EXTERN PetscErrorCode MatCreate_Htool(Mat A)
    873: {
    874:   Mat_Htool *a;

    876:   PetscNewLog(A,&a);
    877:   A->data = (void*)a;
    878:   PetscObjectChangeTypeName((PetscObject)A,MATHTOOL);
    879:   PetscMemzero(A->ops,sizeof(struct _MatOps));
    880:   A->ops->getdiagonal       = MatGetDiagonal_Htool;
    881:   A->ops->getdiagonalblock  = MatGetDiagonalBlock_Htool;
    882:   A->ops->mult              = MatMult_Htool;
    883:   A->ops->multadd           = MatMultAdd_Htool;
    884:   A->ops->multtranspose     = MatMultTranspose_Htool;
    885:   if (!PetscDefined(USE_COMPLEX)) A->ops->multhermitiantranspose = MatMultTranspose_Htool;
    886:   A->ops->increaseoverlap   = MatIncreaseOverlap_Htool;
    887:   A->ops->createsubmatrices = MatCreateSubMatrices_Htool;
    888:   A->ops->transpose         = MatTranspose_Htool;
    889:   A->ops->destroy           = MatDestroy_Htool;
    890:   A->ops->view              = MatView_Htool;
    891:   A->ops->setfromoptions    = MatSetFromOptions_Htool;
    892:   A->ops->scale             = MatScale_Htool;
    893:   A->ops->getrow            = MatGetRow_Htool;
    894:   A->ops->restorerow        = MatRestoreRow_Htool;
    895:   A->ops->assemblyend       = MatAssemblyEnd_Htool;
    896:   a->dim                    = 0;
    897:   a->gcoords_target         = NULL;
    898:   a->gcoords_source         = NULL;
    899:   a->s                      = 1.0;
    900:   a->bs[0]                  = 10;
    901:   a->bs[1]                  = 1000000;
    902:   a->epsilon                = PetscSqrtReal(PETSC_SMALL);
    903:   a->eta                    = 10.0;
    904:   a->depth[0]               = 0;
    905:   a->depth[1]               = 0;
    906:   a->compressor             = MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA;
    907:   PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_htool_seqdense_C",MatProductSetFromOptions_Htool);
    908:   PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_htool_mpidense_C",MatProductSetFromOptions_Htool);
    909:   PetscObjectComposeFunction((PetscObject)A,"MatConvert_htool_seqdense_C",MatConvert_Htool_Dense);
    910:   PetscObjectComposeFunction((PetscObject)A,"MatConvert_htool_mpidense_C",MatConvert_Htool_Dense);
    911:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetHierarchicalMat_C",MatHtoolGetHierarchicalMat_Htool);
    912:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolSetKernel_C",MatHtoolSetKernel_Htool);
    913:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetPermutationSource_C",MatHtoolGetPermutationSource_Htool);
    914:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetPermutationTarget_C",MatHtoolGetPermutationTarget_Htool);
    915:   PetscObjectComposeFunction((PetscObject)A,"MatHtoolUsePermutation_C",MatHtoolUsePermutation_Htool);
    916:   return 0;
    917: }