xref: /petsc/src/mat/impls/htool/htool.cxx (revision 8b8ddd11208960f17ab493a4b3eccc5bd1d88bb1)
1 #include <../src/mat/impls/htool/htool.hpp> /*I "petscmat.h" I*/
2 #include <petscblaslapack.h>
3 #include <set>
4 
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;
19 
20 static PetscErrorCode MatGetDiagonal_Htool(Mat A,Vec v)
21 {
22   Mat_Htool      *a = (Mat_Htool*)A->data;
23   PetscScalar    *x;
24   PetscBool      flg;
25   PetscErrorCode ierr;
26 
27   PetscFunctionBegin;
28   ierr = MatHasCongruentLayouts(A,&flg);CHKERRQ(ierr);
29   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Only congruent layouts supported");
30   ierr = VecGetArrayWrite(v,&x);CHKERRQ(ierr);
31   a->hmatrix->copy_local_diagonal(x);
32   ierr = VecRestoreArrayWrite(v,&x);CHKERRQ(ierr);
33   ierr = VecScale(v,a->s);CHKERRQ(ierr);
34   PetscFunctionReturn(0);
35 }
36 
37 static PetscErrorCode MatGetDiagonalBlock_Htool(Mat A,Mat *b)
38 {
39   Mat_Htool      *a = (Mat_Htool*)A->data;
40   Mat            B;
41   PetscScalar    *ptr;
42   PetscBool      flg;
43   PetscErrorCode ierr;
44 
45   PetscFunctionBegin;
46   ierr = MatHasCongruentLayouts(A,&flg);CHKERRQ(ierr);
47   if (!flg) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Only congruent layouts supported");
48   ierr = PetscObjectQuery((PetscObject)A,"DiagonalBlock",(PetscObject*)&B);CHKERRQ(ierr); /* same logic as in MatGetDiagonalBlock_MPIDense() */
49   if (!B) {
50     ierr = MatCreateDense(PETSC_COMM_SELF,A->rmap->n,A->rmap->n,A->rmap->n,A->rmap->n,NULL,&B);CHKERRQ(ierr);
51     ierr = MatDenseGetArrayWrite(B,&ptr);CHKERRQ(ierr);
52     a->hmatrix->copy_local_diagonal_block(ptr);
53     ierr = MatDenseRestoreArrayWrite(B,&ptr);CHKERRQ(ierr);
54     ierr = MatPropagateSymmetryOptions(A,B);CHKERRQ(ierr);
55     ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
56     ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
57     ierr = MatScale(B,a->s);CHKERRQ(ierr);
58     ierr = PetscObjectCompose((PetscObject)A,"DiagonalBlock",(PetscObject)B);CHKERRQ(ierr);
59     *b   = B;
60     ierr = MatDestroy(&B);CHKERRQ(ierr);
61   } else *b = B;
62   PetscFunctionReturn(0);
63 }
64 
65 static PetscErrorCode MatMult_Htool(Mat A,Vec x,Vec y)
66 {
67   Mat_Htool         *a = (Mat_Htool*)A->data;
68   const PetscScalar *in;
69   PetscScalar       *out;
70   PetscErrorCode    ierr;
71 
72   PetscFunctionBegin;
73   ierr = VecGetArrayRead(x,&in);CHKERRQ(ierr);
74   ierr = VecGetArrayWrite(y,&out);CHKERRQ(ierr);
75   a->hmatrix->mvprod_local_to_local(in,out);
76   ierr = VecRestoreArrayRead(x,&in);CHKERRQ(ierr);
77   ierr = VecRestoreArrayWrite(y,&out);CHKERRQ(ierr);
78   ierr = VecScale(y,a->s);CHKERRQ(ierr);
79   PetscFunctionReturn(0);
80 }
81 
82 /* naive implementation of MatMultAdd() needed for FEM-BEM coupling via MATNEST */
83 static PetscErrorCode MatMultAdd_Htool(Mat A,Vec v1,Vec v2,Vec v3)
84 {
85   Mat_Htool         *a = (Mat_Htool*)A->data;
86   Vec               tmp;
87   const PetscScalar scale = a->s;
88   PetscErrorCode    ierr;
89 
90   PetscFunctionBegin;
91   ierr = VecDuplicate(v2,&tmp);CHKERRQ(ierr);
92   ierr = VecCopy(v2,v3);CHKERRQ(ierr); /* no-op in MatMultAdd(bA->m[i][j],bx[j],by[i],by[i]) since VecCopy() checks for x == y */
93   a->s = 1.0; /* set s to 1.0 since VecAXPY() may be used to scale the MatMult() output Vec */
94   ierr = MatMult_Htool(A,v1,tmp);CHKERRQ(ierr);
95   ierr = VecAXPY(v3,scale,tmp);CHKERRQ(ierr);
96   ierr = VecDestroy(&tmp);CHKERRQ(ierr);
97   a->s = scale; /* set s back to its original value */
98   PetscFunctionReturn(0);
99 }
100 
101 static PetscErrorCode MatMultTranspose_Htool(Mat A,Vec x,Vec y)
102 {
103   Mat_Htool         *a = (Mat_Htool*)A->data;
104   const PetscScalar *in;
105   PetscScalar       *out;
106   PetscErrorCode    ierr;
107 
108   PetscFunctionBegin;
109   ierr = VecGetArrayRead(x,&in);CHKERRQ(ierr);
110   ierr = VecGetArrayWrite(y,&out);CHKERRQ(ierr);
111   a->hmatrix->mvprod_transp_local_to_local(in,out);
112   ierr = VecRestoreArrayRead(x,&in);CHKERRQ(ierr);
113   ierr = VecRestoreArrayWrite(y,&out);CHKERRQ(ierr);
114   ierr = VecScale(y,a->s);CHKERRQ(ierr);
115   PetscFunctionReturn(0);
116 }
117 
118 static PetscErrorCode MatIncreaseOverlap_Htool(Mat A,PetscInt is_max,IS is[],PetscInt ov)
119 {
120   std::set<PetscInt> set;
121   const PetscInt     *idx;
122   PetscInt           *oidx,size;
123   PetscMPIInt        csize;
124   PetscErrorCode     ierr;
125 
126   PetscFunctionBegin;
127   for (PetscInt i=0; i<is_max; ++i) {
128     /* basic implementation that adds indices by shifting an IS by -ov, -ov+1..., -1, 1..., ov-1, ov */
129     /* needed to avoid subdomain matrices to replicate A since it is dense                           */
130     ierr = MPI_Comm_size(PetscObjectComm((PetscObject)is[i]),&csize);CHKERRMPI(ierr);
131     if (csize != 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported parallel IS");
132     ierr = ISGetSize(is[i],&size);CHKERRQ(ierr);
133     ierr = ISGetIndices(is[i],&idx);CHKERRQ(ierr);
134     for (PetscInt j=0; j<size; ++j) {
135       set.insert(idx[j]);
136       for (PetscInt k=1; k<=ov; ++k) {               /* for each layer of overlap      */
137         if (idx[j] - k >= 0) set.insert(idx[j] - k); /* do not insert negative indices */
138         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 */
139       }
140     }
141     ierr = ISRestoreIndices(is[i],&idx);CHKERRQ(ierr);
142     ierr = ISDestroy(is+i);CHKERRQ(ierr);
143     size = set.size(); /* size with overlap */
144     ierr = PetscMalloc1(size,&oidx);CHKERRQ(ierr);
145     for (const PetscInt j : set) *oidx++ = j;
146     oidx -= size;
147     ierr = ISCreateGeneral(PETSC_COMM_SELF,size,oidx,PETSC_OWN_POINTER,is+i);CHKERRQ(ierr);
148   }
149   PetscFunctionReturn(0);
150 }
151 
152 static PetscErrorCode MatCreateSubMatrices_Htool(Mat A,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
153 {
154   Mat_Htool         *a = (Mat_Htool*)A->data;
155   Mat               D,B,BT;
156   const PetscScalar *copy;
157   PetscScalar       *ptr;
158   const PetscInt    *idxr,*idxc,*it;
159   PetscInt          nrow,m,i;
160   PetscBool         flg;
161   PetscErrorCode    ierr;
162 
163   PetscFunctionBegin;
164   if (scall != MAT_REUSE_MATRIX) {
165     ierr = PetscCalloc1(n,submat);CHKERRQ(ierr);
166   }
167   for (i=0; i<n; ++i) {
168     ierr = ISGetLocalSize(irow[i],&nrow);CHKERRQ(ierr);
169     ierr = ISGetLocalSize(icol[i],&m);CHKERRQ(ierr);
170     ierr = ISGetIndices(irow[i],&idxr);CHKERRQ(ierr);
171     ierr = ISGetIndices(icol[i],&idxc);CHKERRQ(ierr);
172     if (scall != MAT_REUSE_MATRIX) {
173       ierr = MatCreateDense(PETSC_COMM_SELF,nrow,m,nrow,m,NULL,(*submat)+i);CHKERRQ(ierr);
174     }
175     ierr = MatDenseGetArrayWrite((*submat)[i],&ptr);CHKERRQ(ierr);
176     if (irow[i] == icol[i]) { /* same row and column IS? */
177       ierr = MatHasCongruentLayouts(A,&flg);CHKERRQ(ierr);
178       if (flg) {
179         ierr = ISSorted(irow[i],&flg);CHKERRQ(ierr);
180         if (flg) { /* sorted IS? */
181           it = std::lower_bound(idxr,idxr+nrow,A->rmap->rstart);
182           if (it != idxr+nrow && *it == A->rmap->rstart) { /* rmap->rstart in IS? */
183             if (std::distance(idxr,it) + A->rmap->n <= nrow) { /* long enough IS to store the local diagonal block? */
184               for (PetscInt j=0; j<A->rmap->n && flg; ++j) if (PetscUnlikely(it[j] != A->rmap->rstart+j)) flg = PETSC_FALSE;
185               if (flg) { /* complete local diagonal block in IS? */
186                 /* fast extraction when the local diagonal block is part of the submatrix, e.g., for PCASM or PCHPDDM
187                  *      [   B   C   E   ]
188                  *  A = [   B   D   E   ]
189                  *      [   B   F   E   ]
190                  */
191                 m = std::distance(idxr,it); /* shift of the coefficient (0,0) of block D from above */
192                 ierr = MatGetDiagonalBlock_Htool(A,&D);CHKERRQ(ierr);
193                 ierr = MatDenseGetArrayRead(D,&copy);CHKERRQ(ierr);
194                 for (PetscInt k=0; k<A->rmap->n; ++k) {
195                   ierr = PetscArraycpy(ptr+(m+k)*nrow+m,copy+k*A->rmap->n,A->rmap->n);CHKERRQ(ierr); /* block D from above */
196                 }
197                 ierr = MatDenseRestoreArrayRead(D,&copy);CHKERRQ(ierr);
198                 if (m) {
199                   a->wrapper->copy_submatrix(nrow,m,idxr,idxc,ptr); /* vertical block B from above */
200                   /* entry-wise assembly may be costly, so transpose already-computed entries when possible */
201                   if (A->symmetric || A->hermitian) {
202                     ierr = MatCreateDense(PETSC_COMM_SELF,A->rmap->n,m,A->rmap->n,m,ptr+m,&B);CHKERRQ(ierr);
203                     ierr = MatDenseSetLDA(B,nrow);CHKERRQ(ierr);
204                     ierr = MatCreateDense(PETSC_COMM_SELF,m,A->rmap->n,m,A->rmap->n,ptr+m*nrow,&BT);CHKERRQ(ierr);
205                     ierr = MatDenseSetLDA(BT,nrow);CHKERRQ(ierr);
206                     if (A->hermitian && PetscDefined(USE_COMPLEX)) {
207                       ierr = MatHermitianTranspose(B,MAT_REUSE_MATRIX,&BT);CHKERRQ(ierr);
208                     } else {
209                       ierr = MatTranspose(B,MAT_REUSE_MATRIX,&BT);CHKERRQ(ierr);
210                     }
211                     ierr = MatDestroy(&B);CHKERRQ(ierr);
212                     ierr = MatDestroy(&BT);CHKERRQ(ierr);
213                   } else {
214                     for (PetscInt k=0; k<A->rmap->n; ++k) { /* block C from above */
215                       a->wrapper->copy_submatrix(m,1,idxr,idxc+m+k,ptr+(m+k)*nrow);
216                     }
217                   }
218                 }
219                 if (m+A->rmap->n != nrow) {
220                   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 */
221                   /* entry-wise assembly may be costly, so transpose already-computed entries when possible */
222                   if (A->symmetric || A->hermitian) {
223                     ierr = 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);CHKERRQ(ierr);
224                     ierr = MatDenseSetLDA(B,nrow);CHKERRQ(ierr);
225                     ierr = 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);CHKERRQ(ierr);
226                     ierr = MatDenseSetLDA(BT,nrow);CHKERRQ(ierr);
227                     if (A->hermitian && PetscDefined(USE_COMPLEX)) {
228                       ierr = MatHermitianTranspose(B,MAT_REUSE_MATRIX,&BT);CHKERRQ(ierr);
229                     } else {
230                       ierr = MatTranspose(B,MAT_REUSE_MATRIX,&BT);CHKERRQ(ierr);
231                     }
232                     ierr = MatDestroy(&B);CHKERRQ(ierr);
233                     ierr = MatDestroy(&BT);CHKERRQ(ierr);
234                   } else {
235                     for (PetscInt k=0; k<A->rmap->n; ++k) { /* block F from above */
236                       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);
237                     }
238                   }
239                 }
240               } /* complete local diagonal block not in IS */
241             } else flg = PETSC_FALSE; /* IS not long enough to store the local diagonal block */
242           } else flg = PETSC_FALSE; /* rmap->rstart not in IS */
243         } /* unsorted IS */
244       }
245     } else flg = PETSC_FALSE; /* different row and column IS */
246     if (!flg) a->wrapper->copy_submatrix(nrow,m,idxr,idxc,ptr); /* reassemble everything */
247     ierr = ISRestoreIndices(irow[i],&idxr);CHKERRQ(ierr);
248     ierr = ISRestoreIndices(icol[i],&idxc);CHKERRQ(ierr);
249     ierr = MatDenseRestoreArrayWrite((*submat)[i],&ptr);CHKERRQ(ierr);
250     ierr = MatAssemblyBegin((*submat)[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
251     ierr = MatAssemblyEnd((*submat)[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
252     ierr = MatScale((*submat)[i],a->s);CHKERRQ(ierr);
253   }
254   PetscFunctionReturn(0);
255 }
256 
257 static PetscErrorCode MatDestroy_Htool(Mat A)
258 {
259   Mat_Htool               *a = (Mat_Htool*)A->data;
260   PetscContainer          container;
261   MatHtoolKernelTranspose *kernelt;
262   PetscErrorCode          ierr;
263 
264   PetscFunctionBegin;
265   ierr = PetscObjectChangeTypeName((PetscObject)A,NULL);CHKERRQ(ierr);
266   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_htool_seqdense_C",NULL);CHKERRQ(ierr);
267   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_htool_mpidense_C",NULL);CHKERRQ(ierr);
268   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_htool_seqdense_C",NULL);CHKERRQ(ierr);
269   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_htool_mpidense_C",NULL);CHKERRQ(ierr);
270   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetHierarchicalMat_C",NULL);CHKERRQ(ierr);
271   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolSetKernel_C",NULL);CHKERRQ(ierr);
272   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetPermutationSource_C",NULL);CHKERRQ(ierr);
273   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetPermutationTarget_C",NULL);CHKERRQ(ierr);
274   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolUsePermutation_C",NULL);CHKERRQ(ierr);
275   ierr = PetscObjectQuery((PetscObject)A,"KernelTranspose",(PetscObject*)&container);CHKERRQ(ierr);
276   if (container) { /* created in MatTranspose_Htool() */
277     ierr = PetscContainerGetPointer(container,(void**)&kernelt);CHKERRQ(ierr);
278     ierr = MatDestroy(&kernelt->A);CHKERRQ(ierr);
279     ierr = PetscFree(kernelt);CHKERRQ(ierr);
280     ierr = PetscContainerDestroy(&container);CHKERRQ(ierr);
281     ierr = PetscObjectCompose((PetscObject)A,"KernelTranspose",NULL);CHKERRQ(ierr);
282   }
283   if (a->gcoords_source != a->gcoords_target) {
284     ierr = PetscFree(a->gcoords_source);CHKERRQ(ierr);
285   }
286   ierr = PetscFree(a->gcoords_target);CHKERRQ(ierr);
287   ierr = PetscFree2(a->work_source,a->work_target);CHKERRQ(ierr);
288   delete a->wrapper;
289   delete a->hmatrix;
290   ierr = PetscFree(A->data);CHKERRQ(ierr);
291   PetscFunctionReturn(0);
292 }
293 
294 static PetscErrorCode MatView_Htool(Mat A,PetscViewer pv)
295 {
296   Mat_Htool      *a = (Mat_Htool*)A->data;
297   PetscBool      flg;
298   PetscErrorCode ierr;
299 
300   PetscFunctionBegin;
301   ierr = PetscObjectTypeCompare((PetscObject)pv,PETSCVIEWERASCII,&flg);CHKERRQ(ierr);
302   if (flg) {
303     ierr = PetscViewerASCIIPrintf(pv,"symmetry: %c\n",a->hmatrix->get_symmetry_type());CHKERRQ(ierr);
304     if (PetscAbsScalar(a->s-1.0) > PETSC_MACHINE_EPSILON) {
305 #if defined(PETSC_USE_COMPLEX)
306       ierr = PetscViewerASCIIPrintf(pv,"scaling: %g+%gi\n",(double)PetscRealPart(a->s),(double)PetscImaginaryPart(a->s));CHKERRQ(ierr);
307 #else
308       ierr = PetscViewerASCIIPrintf(pv,"scaling: %g\n",(double)a->s);CHKERRQ(ierr);
309 #endif
310     }
311     ierr = PetscViewerASCIIPrintf(pv,"minimum cluster size: %" PetscInt_FMT "\n",a->bs[0]);CHKERRQ(ierr);
312     ierr = PetscViewerASCIIPrintf(pv,"maximum block size: %" PetscInt_FMT "\n",a->bs[1]);CHKERRQ(ierr);
313     ierr = PetscViewerASCIIPrintf(pv,"epsilon: %g\n",(double)a->epsilon);CHKERRQ(ierr);
314     ierr = PetscViewerASCIIPrintf(pv,"eta: %g\n",(double)a->eta);CHKERRQ(ierr);
315     ierr = PetscViewerASCIIPrintf(pv,"minimum target depth: %" PetscInt_FMT "\n",a->depth[0]);CHKERRQ(ierr);
316     ierr = PetscViewerASCIIPrintf(pv,"minimum source depth: %" PetscInt_FMT "\n",a->depth[1]);CHKERRQ(ierr);
317     ierr = PetscViewerASCIIPrintf(pv,"compressor: %s\n",MatHtoolCompressorTypes[a->compressor]);CHKERRQ(ierr);
318     ierr = PetscViewerASCIIPrintf(pv,"clustering: %s\n",MatHtoolClusteringTypes[a->clustering]);CHKERRQ(ierr);
319     ierr = PetscViewerASCIIPrintf(pv,"compression ratio: %s\n",a->hmatrix->get_infos("Compression_ratio").c_str());CHKERRQ(ierr);
320     ierr = PetscViewerASCIIPrintf(pv,"space saving: %s\n",a->hmatrix->get_infos("Space_saving").c_str());CHKERRQ(ierr);
321     ierr = 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());CHKERRQ(ierr);
322     ierr = 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());CHKERRQ(ierr);
323     ierr = 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());CHKERRQ(ierr);
324     ierr = 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());CHKERRQ(ierr);
325   }
326   PetscFunctionReturn(0);
327 }
328 
329 static PetscErrorCode MatScale_Htool(Mat A,PetscScalar s)
330 {
331   Mat_Htool *a = (Mat_Htool*)A->data;
332 
333   PetscFunctionBegin;
334   a->s *= s;
335   PetscFunctionReturn(0);
336 }
337 
338 /* naive implementation of MatGetRow() needed for MatConvert_Nest_AIJ() */
339 static PetscErrorCode MatGetRow_Htool(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
340 {
341   Mat_Htool      *a = (Mat_Htool*)A->data;
342   PetscInt       *idxc;
343   PetscBLASInt   one = 1,bn;
344   PetscErrorCode ierr;
345 
346   PetscFunctionBegin;
347   if (nz) *nz = A->cmap->N;
348   if (idx || v) { /* even if !idx, need to set idxc for htool::copy_submatrix() */
349     ierr = PetscMalloc1(A->cmap->N,&idxc);CHKERRQ(ierr);
350     for (PetscInt i=0; i<A->cmap->N; ++i) idxc[i] = i;
351   }
352   if (idx) *idx = idxc;
353   if (v) {
354     ierr = PetscMalloc1(A->cmap->N,v);CHKERRQ(ierr);
355     if (a->wrapper) a->wrapper->copy_submatrix(1,A->cmap->N,&row,idxc,*v);
356     else reinterpret_cast<htool::VirtualGenerator<PetscScalar>*>(a->kernelctx)->copy_submatrix(1,A->cmap->N,&row,idxc,*v);
357     ierr = PetscBLASIntCast(A->cmap->N,&bn);CHKERRQ(ierr);
358     PetscStackCallBLAS("BLASscal",BLASscal_(&bn,&a->s,*v,&one));
359   }
360   if (!idx) {
361     ierr = PetscFree(idxc);CHKERRQ(ierr);
362   }
363   PetscFunctionReturn(0);
364 }
365 
366 static PetscErrorCode MatRestoreRow_Htool(Mat A,PetscInt row,PetscInt *nz,PetscInt **idx,PetscScalar **v)
367 {
368   PetscErrorCode ierr;
369 
370   PetscFunctionBegin;
371   if (nz) *nz = 0;
372   if (idx) {
373     ierr = PetscFree(*idx);CHKERRQ(ierr);
374   }
375   if (v) {
376     ierr = PetscFree(*v);CHKERRQ(ierr);
377   }
378   PetscFunctionReturn(0);
379 }
380 
381 static PetscErrorCode MatSetFromOptions_Htool(PetscOptionItems *PetscOptionsObject,Mat A)
382 {
383   Mat_Htool      *a = (Mat_Htool*)A->data;
384   PetscInt       n;
385   PetscBool      flg;
386   PetscErrorCode ierr;
387 
388   PetscFunctionBegin;
389   ierr = PetscOptionsHead(PetscOptionsObject,"Htool options");CHKERRQ(ierr);
390   ierr = PetscOptionsInt("-mat_htool_min_cluster_size","Minimal leaf size in cluster tree",NULL,a->bs[0],a->bs,NULL);CHKERRQ(ierr);
391   ierr = PetscOptionsInt("-mat_htool_max_block_size","Maximal number of coefficients in a dense block",NULL,a->bs[1],a->bs + 1,NULL);CHKERRQ(ierr);
392   ierr = PetscOptionsReal("-mat_htool_epsilon","Relative error in Frobenius norm when approximating a block",NULL,a->epsilon,&a->epsilon,NULL);CHKERRQ(ierr);
393   ierr = PetscOptionsReal("-mat_htool_eta","Admissibility condition tolerance",NULL,a->eta,&a->eta,NULL);CHKERRQ(ierr);
394   ierr = PetscOptionsInt("-mat_htool_min_target_depth","Minimal cluster tree depth associated with the rows",NULL,a->depth[0],a->depth,NULL);CHKERRQ(ierr);
395   ierr = PetscOptionsInt("-mat_htool_min_source_depth","Minimal cluster tree depth associated with the columns",NULL,a->depth[1],a->depth + 1,NULL);CHKERRQ(ierr);
396   n = 0;
397   ierr = PetscOptionsEList("-mat_htool_compressor","Type of compression","MatHtoolCompressorType",MatHtoolCompressorTypes,ALEN(MatHtoolCompressorTypes),MatHtoolCompressorTypes[MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA],&n,&flg);CHKERRQ(ierr);
398   if (flg) a->compressor = MatHtoolCompressorType(n);
399   n = 0;
400   ierr = PetscOptionsEList("-mat_htool_clustering","Type of clustering","MatHtoolClusteringType",MatHtoolClusteringTypes,ALEN(MatHtoolClusteringTypes),MatHtoolClusteringTypes[MAT_HTOOL_CLUSTERING_PCA_REGULAR],&n,&flg);CHKERRQ(ierr);
401   if (flg) a->clustering = MatHtoolClusteringType(n);
402   ierr = PetscOptionsTail();CHKERRQ(ierr);
403   PetscFunctionReturn(0);
404 }
405 
406 static PetscErrorCode MatAssemblyEnd_Htool(Mat A,MatAssemblyType type)
407 {
408   Mat_Htool                                                    *a = (Mat_Htool*)A->data;
409   const PetscInt                                               *ranges;
410   PetscInt                                                     *offset;
411   PetscMPIInt                                                  size;
412   char                                                         S = PetscDefined(USE_COMPLEX) && A->hermitian ? 'H' : (A->symmetric ? 'S' : 'N'),uplo = S == 'N' ? 'N' : 'U';
413   htool::VirtualGenerator<PetscScalar>                         *generator = nullptr;
414   std::shared_ptr<htool::VirtualCluster>                       t,s = nullptr;
415   std::shared_ptr<htool::VirtualLowRankGenerator<PetscScalar>> compressor = nullptr;
416   PetscErrorCode                                               ierr;
417 
418   PetscFunctionBegin;
419   ierr = PetscCitationsRegister(HtoolCitation,&HtoolCite);CHKERRQ(ierr);
420   delete a->wrapper;
421   delete a->hmatrix;
422   ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRMPI(ierr);
423   ierr = PetscMalloc1(2*size,&offset);CHKERRQ(ierr);
424   ierr = MatGetOwnershipRanges(A,&ranges);CHKERRQ(ierr);
425   for (PetscInt i=0; i<size; ++i) {
426     offset[2*i] = ranges[i];
427     offset[2*i+1] = ranges[i+1] - ranges[i];
428   }
429   switch (a->clustering) {
430   case MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC:
431     t = std::make_shared<htool::Cluster<htool::PCA<htool::SplittingTypes::GeometricSplitting>>>(a->dim);
432     break;
433   case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC:
434     t = std::make_shared<htool::Cluster<htool::BoundingBox1<htool::SplittingTypes::GeometricSplitting>>>(a->dim);
435     break;
436   case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR:
437     t = std::make_shared<htool::Cluster<htool::BoundingBox1<htool::SplittingTypes::RegularSplitting>>>(a->dim);
438     break;
439   default:
440     t = std::make_shared<htool::Cluster<htool::PCA<htool::SplittingTypes::RegularSplitting>>>(a->dim);
441   }
442   t->set_minclustersize(a->bs[0]);
443   t->build(A->rmap->N,a->gcoords_target,offset);
444   if (a->kernel) a->wrapper = new WrapperHtool(A->rmap->N,A->cmap->N,a->dim,a->kernel,a->kernelctx);
445   else {
446     a->wrapper = NULL;
447     generator = reinterpret_cast<htool::VirtualGenerator<PetscScalar>*>(a->kernelctx);
448   }
449   if (a->gcoords_target != a->gcoords_source) {
450     ierr = MatGetOwnershipRangesColumn(A,&ranges);CHKERRQ(ierr);
451     for (PetscInt i=0; i<size; ++i) {
452       offset[2*i] = ranges[i];
453       offset[2*i+1] = ranges[i+1] - ranges[i];
454     }
455     switch (a->clustering) {
456     case MAT_HTOOL_CLUSTERING_PCA_GEOMETRIC:
457       s = std::make_shared<htool::Cluster<htool::PCA<htool::SplittingTypes::GeometricSplitting>>>(a->dim);
458       break;
459     case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_GEOMETRIC:
460       s = std::make_shared<htool::Cluster<htool::BoundingBox1<htool::SplittingTypes::GeometricSplitting>>>(a->dim);
461       break;
462     case MAT_HTOOL_CLUSTERING_BOUNDING_BOX_1_REGULAR:
463       s = std::make_shared<htool::Cluster<htool::BoundingBox1<htool::SplittingTypes::RegularSplitting>>>(a->dim);
464       break;
465     default:
466       s = std::make_shared<htool::Cluster<htool::PCA<htool::SplittingTypes::RegularSplitting>>>(a->dim);
467     }
468     s->set_minclustersize(a->bs[0]);
469     s->build(A->cmap->N,a->gcoords_source,offset);
470     S = uplo = 'N';
471   }
472   ierr = PetscFree(offset);CHKERRQ(ierr);
473   switch (a->compressor) {
474   case MAT_HTOOL_COMPRESSOR_FULL_ACA:
475     compressor = std::make_shared<htool::fullACA<PetscScalar>>();
476     break;
477   case MAT_HTOOL_COMPRESSOR_SVD:
478     compressor = std::make_shared<htool::SVD<PetscScalar>>();
479     break;
480   default:
481     compressor = std::make_shared<htool::sympartialACA<PetscScalar>>();
482   }
483   a->hmatrix = dynamic_cast<htool::VirtualHMatrix<PetscScalar>*>(new htool::HMatrix<PetscScalar>(t,s ? s : t,a->epsilon,a->eta,S,uplo));
484   a->hmatrix->set_compression(compressor);
485   a->hmatrix->set_maxblocksize(a->bs[1]);
486   a->hmatrix->set_mintargetdepth(a->depth[0]);
487   a->hmatrix->set_minsourcedepth(a->depth[1]);
488   if (s) a->hmatrix->build(a->wrapper ? *a->wrapper : *generator,a->gcoords_target,a->gcoords_source);
489   else   a->hmatrix->build(a->wrapper ? *a->wrapper : *generator,a->gcoords_target);
490   PetscFunctionReturn(0);
491 }
492 
493 static PetscErrorCode MatProductNumeric_Htool(Mat C)
494 {
495   Mat_Product       *product = C->product;
496   Mat_Htool         *a = (Mat_Htool*)product->A->data;
497   const PetscScalar *in;
498   PetscScalar       *out;
499   PetscInt          N,lda;
500   PetscErrorCode    ierr;
501 
502   PetscFunctionBegin;
503   MatCheckProduct(C,1);
504   ierr = MatGetSize(C,NULL,&N);CHKERRQ(ierr);
505   ierr = MatDenseGetLDA(C,&lda);CHKERRQ(ierr);
506   if (lda != C->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported leading dimension (%" PetscInt_FMT " != %" PetscInt_FMT ")",lda,C->rmap->n);
507   ierr = MatDenseGetArrayRead(product->B,&in);CHKERRQ(ierr);
508   ierr = MatDenseGetArrayWrite(C,&out);CHKERRQ(ierr);
509   switch (product->type) {
510   case MATPRODUCT_AB:
511     a->hmatrix->mvprod_local_to_local(in,out,N);
512     break;
513   case MATPRODUCT_AtB:
514     a->hmatrix->mvprod_transp_local_to_local(in,out,N);
515     break;
516   default:
517     SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProductType %s is not supported",MatProductTypes[product->type]);
518   }
519   ierr = MatDenseRestoreArrayWrite(C,&out);CHKERRQ(ierr);
520   ierr = MatDenseRestoreArrayRead(product->B,&in);CHKERRQ(ierr);
521   ierr = MatScale(C,a->s);CHKERRQ(ierr);
522   PetscFunctionReturn(0);
523 }
524 
525 static PetscErrorCode MatProductSymbolic_Htool(Mat C)
526 {
527   Mat_Product    *product = C->product;
528   Mat            A,B;
529   PetscBool      flg;
530   PetscErrorCode ierr;
531 
532   PetscFunctionBegin;
533   MatCheckProduct(C,1);
534   A = product->A;
535   B = product->B;
536   ierr = PetscObjectTypeCompareAny((PetscObject)B,&flg,MATSEQDENSE,MATMPIDENSE,"");CHKERRQ(ierr);
537   if (!flg) SETERRQ1(PetscObjectComm((PetscObject)B),PETSC_ERR_SUP,"MatProduct_AB not supported for %s",((PetscObject)product->B)->type_name);
538   switch (product->type) {
539   case MATPRODUCT_AB:
540     if (C->rmap->n == PETSC_DECIDE || C->cmap->n == PETSC_DECIDE || C->rmap->N == PETSC_DECIDE || C->cmap->N == PETSC_DECIDE) {
541       ierr = MatSetSizes(C,A->rmap->n,B->cmap->n,A->rmap->N,B->cmap->N);CHKERRQ(ierr);
542     }
543     break;
544   case MATPRODUCT_AtB:
545     if (C->rmap->n == PETSC_DECIDE || C->cmap->n == PETSC_DECIDE || C->rmap->N == PETSC_DECIDE || C->cmap->N == PETSC_DECIDE) {
546       ierr = MatSetSizes(C,A->cmap->n,B->cmap->n,A->cmap->N,B->cmap->N);CHKERRQ(ierr);
547     }
548     break;
549   default:
550     SETERRQ1(PetscObjectComm((PetscObject)B),PETSC_ERR_SUP,"ProductType %s is not supported",MatProductTypes[product->type]);
551   }
552   ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
553   ierr = MatSetUp(C);CHKERRQ(ierr);
554   ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
555   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
556   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
557   C->ops->productsymbolic = NULL;
558   C->ops->productnumeric = MatProductNumeric_Htool;
559   PetscFunctionReturn(0);
560 }
561 
562 static PetscErrorCode MatProductSetFromOptions_Htool(Mat C)
563 {
564   PetscFunctionBegin;
565   MatCheckProduct(C,1);
566   if (C->product->type == MATPRODUCT_AB || C->product->type == MATPRODUCT_AtB) C->ops->productsymbolic = MatProductSymbolic_Htool;
567   PetscFunctionReturn(0);
568 }
569 
570 static PetscErrorCode MatHtoolGetHierarchicalMat_Htool(Mat A,const htool::VirtualHMatrix<PetscScalar> **hmatrix)
571 {
572   Mat_Htool *a = (Mat_Htool*)A->data;
573 
574   PetscFunctionBegin;
575   *hmatrix = a->hmatrix;
576   PetscFunctionReturn(0);
577 }
578 
579 /*@C
580      MatHtoolGetHierarchicalMat - Retrieves the opaque pointer to a Htool virtual matrix stored in a MATHTOOL.
581 
582    Input Parameter:
583 .     A - hierarchical matrix
584 
585    Output Parameter:
586 .     hmatrix - opaque pointer to a Htool virtual matrix
587 
588    Level: advanced
589 
590 .seealso:  MATHTOOL
591 @*/
592 PETSC_EXTERN PetscErrorCode MatHtoolGetHierarchicalMat(Mat A,const htool::VirtualHMatrix<PetscScalar> **hmatrix)
593 {
594   PetscErrorCode ierr;
595 
596   PetscFunctionBegin;
597   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
598   PetscValidPointer(hmatrix,2);
599   ierr = PetscTryMethod(A,"MatHtoolGetHierarchicalMat_C",(Mat,const htool::VirtualHMatrix<PetscScalar>**),(A,hmatrix));CHKERRQ(ierr);
600   PetscFunctionReturn(0);
601 }
602 
603 static PetscErrorCode MatHtoolSetKernel_Htool(Mat A,MatHtoolKernel kernel,void *kernelctx)
604 {
605   Mat_Htool *a = (Mat_Htool*)A->data;
606 
607   PetscFunctionBegin;
608   a->kernel    = kernel;
609   a->kernelctx = kernelctx;
610   delete a->wrapper;
611   if (a->kernel) a->wrapper = new WrapperHtool(A->rmap->N,A->cmap->N,a->dim,a->kernel,a->kernelctx);
612   PetscFunctionReturn(0);
613 }
614 
615 /*@C
616      MatHtoolSetKernel - Sets the kernel and context used for the assembly of a MATHTOOL.
617 
618    Input Parameters:
619 +     A - hierarchical matrix
620 .     kernel - computational kernel (or NULL)
621 -     kernelctx - kernel context (if kernel is NULL, the pointer must be of type htool::VirtualGenerator<PetscScalar>*)
622 
623    Level: advanced
624 
625 .seealso:  MATHTOOL, MatCreateHtoolFromKernel()
626 @*/
627 PETSC_EXTERN PetscErrorCode MatHtoolSetKernel(Mat A,MatHtoolKernel kernel,void *kernelctx)
628 {
629   PetscErrorCode ierr;
630 
631   PetscFunctionBegin;
632   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
633   if (!kernelctx) PetscValidFunction(kernel,2);
634   if (!kernel)    PetscValidPointer(kernelctx,3);
635   ierr = PetscTryMethod(A,"MatHtoolSetKernel_C",(Mat,MatHtoolKernel,void*),(A,kernel,kernelctx));CHKERRQ(ierr);
636   PetscFunctionReturn(0);
637 }
638 
639 static PetscErrorCode MatHtoolGetPermutationSource_Htool(Mat A,IS* is)
640 {
641   Mat_Htool             *a = (Mat_Htool*)A->data;
642   std::vector<PetscInt> source;
643   PetscErrorCode        ierr;
644 
645   PetscFunctionBegin;
646   source = a->hmatrix->get_source_cluster()->get_local_perm();
647   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),source.size(),source.data(),PETSC_COPY_VALUES,is);CHKERRQ(ierr);
648   ierr = ISSetPermutation(*is);CHKERRQ(ierr);
649   PetscFunctionReturn(0);
650 }
651 
652 /*@C
653      MatHtoolGetPermutationSource - Gets the permutation associated to the source cluster.
654 
655    Input Parameter:
656 .     A - hierarchical matrix
657 
658    Output Parameter:
659 .     is - permutation
660 
661    Level: advanced
662 
663 .seealso:  MATHTOOL, MatHtoolGetPermutationTarget(), MatHtoolUsePermutation()
664 @*/
665 PETSC_EXTERN PetscErrorCode MatHtoolGetPermutationSource(Mat A,IS* is)
666 {
667   PetscErrorCode ierr;
668 
669   PetscFunctionBegin;
670   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
671   if (!is) PetscValidPointer(is,2);
672   ierr = PetscTryMethod(A,"MatHtoolGetPermutationSource_C",(Mat,IS*),(A,is));CHKERRQ(ierr);
673   PetscFunctionReturn(0);
674 }
675 
676 static PetscErrorCode MatHtoolGetPermutationTarget_Htool(Mat A,IS* is)
677 {
678   Mat_Htool             *a = (Mat_Htool*)A->data;
679   std::vector<PetscInt> target;
680   PetscErrorCode        ierr;
681 
682   PetscFunctionBegin;
683   target = a->hmatrix->get_target_cluster()->get_local_perm();
684   ierr = ISCreateGeneral(PetscObjectComm((PetscObject)A),target.size(),target.data(),PETSC_COPY_VALUES,is);CHKERRQ(ierr);
685   ierr = ISSetPermutation(*is);CHKERRQ(ierr);
686   PetscFunctionReturn(0);
687 }
688 
689 /*@C
690      MatHtoolGetPermutationTarget - Gets the permutation associated to the target cluster.
691 
692    Input Parameter:
693 .     A - hierarchical matrix
694 
695    Output Parameter:
696 .     is - permutation
697 
698    Level: advanced
699 
700 .seealso:  MATHTOOL, MatHtoolGetPermutationSource(), MatHtoolUsePermutation()
701 @*/
702 PETSC_EXTERN PetscErrorCode MatHtoolGetPermutationTarget(Mat A,IS* is)
703 {
704   PetscErrorCode ierr;
705 
706   PetscFunctionBegin;
707   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
708   if (!is) PetscValidPointer(is,2);
709   ierr = PetscTryMethod(A,"MatHtoolGetPermutationTarget_C",(Mat,IS*),(A,is));CHKERRQ(ierr);
710   PetscFunctionReturn(0);
711 }
712 
713 static PetscErrorCode MatHtoolUsePermutation_Htool(Mat A,PetscBool use)
714 {
715   Mat_Htool *a = (Mat_Htool*)A->data;
716 
717   PetscFunctionBegin;
718   a->hmatrix->set_use_permutation(use);
719   PetscFunctionReturn(0);
720 }
721 
722 /*@C
723      MatHtoolUsePermutation - Sets whether MATHTOOL should permute input (resp. output) vectors following its internal source (resp. target) permutation.
724 
725    Input Parameters:
726 +     A - hierarchical matrix
727 -     use - Boolean value
728 
729    Level: advanced
730 
731 .seealso:  MATHTOOL, MatHtoolGetPermutationSource(), MatHtoolGetPermutationTarget()
732 @*/
733 PETSC_EXTERN PetscErrorCode MatHtoolUsePermutation(Mat A,PetscBool use)
734 {
735   PetscErrorCode ierr;
736 
737   PetscFunctionBegin;
738   PetscValidHeaderSpecific(A,MAT_CLASSID,1);
739   PetscValidLogicalCollectiveBool(A,use,2);
740   ierr = PetscTryMethod(A,"MatHtoolUsePermutation_C",(Mat,PetscBool),(A,use));CHKERRQ(ierr);
741   PetscFunctionReturn(0);
742 }
743 
744 static PetscErrorCode MatConvert_Htool_Dense(Mat A,MatType newtype,MatReuse reuse,Mat *B)
745 {
746   Mat            C;
747   Mat_Htool      *a = (Mat_Htool*)A->data;
748   PetscInt       lda;
749   PetscScalar    *array;
750   PetscErrorCode ierr;
751 
752   PetscFunctionBegin;
753   if (reuse == MAT_REUSE_MATRIX) {
754     C = *B;
755     if (C->rmap->n != A->rmap->n || C->cmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Incompatible dimensions");
756     ierr = MatDenseGetLDA(C,&lda);CHKERRQ(ierr);
757     if (lda != C->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported leading dimension (%" PetscInt_FMT " != %" PetscInt_FMT ")",lda,C->rmap->n);
758   } else {
759     ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
760     ierr = MatSetSizes(C,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
761     ierr = MatSetType(C,MATDENSE);CHKERRQ(ierr);
762     ierr = MatSetUp(C);CHKERRQ(ierr);
763     ierr = MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
764   }
765   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
766   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
767   ierr = MatDenseGetArrayWrite(C,&array);CHKERRQ(ierr);
768   a->hmatrix->copy_local_dense_perm(array);
769   ierr = MatDenseRestoreArrayWrite(C,&array);CHKERRQ(ierr);
770   ierr = MatScale(C,a->s);CHKERRQ(ierr);
771   if (reuse == MAT_INPLACE_MATRIX) {
772     ierr = MatHeaderReplace(A,&C);CHKERRQ(ierr);
773   } else *B = C;
774   PetscFunctionReturn(0);
775 }
776 
777 static PetscErrorCode GenEntriesTranspose(PetscInt sdim,PetscInt M,PetscInt N,const PetscInt *rows,const PetscInt *cols,PetscScalar *ptr,void *ctx)
778 {
779   MatHtoolKernelTranspose *generator = (MatHtoolKernelTranspose*)ctx;
780   PetscScalar             *tmp;
781   PetscErrorCode          ierr;
782 
783   PetscFunctionBegin;
784   generator->kernel(sdim,N,M,cols,rows,ptr,generator->kernelctx);
785   ierr = PetscMalloc1(M*N,&tmp);CHKERRQ(ierr);
786   ierr = PetscArraycpy(tmp,ptr,M*N);CHKERRQ(ierr);
787   for (PetscInt i=0; i<M; ++i) {
788     for (PetscInt j=0; j<N; ++j) ptr[i+j*M] = tmp[j+i*N];
789   }
790   ierr = PetscFree(tmp);CHKERRQ(ierr);
791   PetscFunctionReturn(0);
792 }
793 
794 /* naive implementation which keeps a reference to the original Mat */
795 static PetscErrorCode MatTranspose_Htool(Mat A,MatReuse reuse,Mat *B)
796 {
797   Mat                     C;
798   Mat_Htool               *a = (Mat_Htool*)A->data,*c;
799   PetscInt                M = A->rmap->N,N = A->cmap->N,m = A->rmap->n,n = A->cmap->n;
800   PetscContainer          container;
801   MatHtoolKernelTranspose *kernelt;
802   PetscErrorCode          ierr;
803 
804   PetscFunctionBegin;
805   if (reuse == MAT_INPLACE_MATRIX) SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatTranspose() with MAT_INPLACE_MATRIX not supported");
806   if (reuse == MAT_INITIAL_MATRIX) {
807     ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
808     ierr = MatSetSizes(C,n,m,N,M);CHKERRQ(ierr);
809     ierr = MatSetType(C,((PetscObject)A)->type_name);CHKERRQ(ierr);
810     ierr = MatSetUp(C);CHKERRQ(ierr);
811     ierr = PetscContainerCreate(PetscObjectComm((PetscObject)C),&container);CHKERRQ(ierr);
812     ierr = PetscNew(&kernelt);CHKERRQ(ierr);
813     ierr = PetscContainerSetPointer(container,kernelt);CHKERRQ(ierr);
814     ierr = PetscObjectCompose((PetscObject)C,"KernelTranspose",(PetscObject)container);CHKERRQ(ierr);
815   } else {
816     C = *B;
817     ierr = PetscObjectQuery((PetscObject)C,"KernelTranspose",(PetscObject*)&container);CHKERRQ(ierr);
818     if (!container) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call MatTranspose() with MAT_INITIAL_MATRIX first");
819     ierr = PetscContainerGetPointer(container,(void**)&kernelt);CHKERRQ(ierr);
820   }
821   c                  = (Mat_Htool*)C->data;
822   c->dim             = a->dim;
823   c->s               = a->s;
824   c->kernel          = GenEntriesTranspose;
825   if (kernelt->A != A) {
826     ierr = MatDestroy(&kernelt->A);CHKERRQ(ierr);
827     kernelt->A       = A;
828     ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);
829   }
830   kernelt->kernel    = a->kernel;
831   kernelt->kernelctx = a->kernelctx;
832   c->kernelctx       = kernelt;
833   if (reuse == MAT_INITIAL_MATRIX) {
834     ierr = PetscMalloc1(N*c->dim,&c->gcoords_target);CHKERRQ(ierr);
835     ierr = PetscArraycpy(c->gcoords_target,a->gcoords_source,N*c->dim);CHKERRQ(ierr);
836     if (a->gcoords_target != a->gcoords_source) {
837       ierr = PetscMalloc1(M*c->dim,&c->gcoords_source);CHKERRQ(ierr);
838       ierr = PetscArraycpy(c->gcoords_source,a->gcoords_target,M*c->dim);CHKERRQ(ierr);
839     } else c->gcoords_source = c->gcoords_target;
840     ierr = PetscCalloc2(M,&c->work_source,N,&c->work_target);CHKERRQ(ierr);
841   }
842   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
843   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
844   if (reuse == MAT_INITIAL_MATRIX) *B = C;
845   PetscFunctionReturn(0);
846 }
847 
848 /*@C
849      MatCreateHtoolFromKernel - Creates a MATHTOOL from a user-supplied kernel.
850 
851    Input Parameters:
852 +     comm - MPI communicator
853 .     m - number of local rows (or PETSC_DECIDE to have calculated if M is given)
854 .     n - number of local columns (or PETSC_DECIDE to have calculated if N is given)
855 .     M - number of global rows (or PETSC_DETERMINE to have calculated if m is given)
856 .     N - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
857 .     spacedim - dimension of the space coordinates
858 .     coords_target - coordinates of the target
859 .     coords_source - coordinates of the source
860 .     kernel - computational kernel (or NULL)
861 -     kernelctx - kernel context (if kernel is NULL, the pointer must be of type htool::VirtualGenerator<PetscScalar>*)
862 
863    Output Parameter:
864 .     B - matrix
865 
866    Options Database Keys:
867 +     -mat_htool_min_cluster_size <PetscInt> - minimal leaf size in cluster tree
868 .     -mat_htool_max_block_size <PetscInt> - maximal number of coefficients in a dense block
869 .     -mat_htool_epsilon <PetscReal> - relative error in Frobenius norm when approximating a block
870 .     -mat_htool_eta <PetscReal> - admissibility condition tolerance
871 .     -mat_htool_min_target_depth <PetscInt> - minimal cluster tree depth associated with the rows
872 .     -mat_htool_min_source_depth <PetscInt> - minimal cluster tree depth associated with the columns
873 .     -mat_htool_compressor <sympartialACA, fullACA, SVD> - type of compression
874 -     -mat_htool_clustering <PCARegular, PCAGeometric, BounbingBox1Regular, BoundingBox1Geometric> - type of clustering
875 
876    Level: intermediate
877 
878 .seealso:  MatCreate(), MATHTOOL, PCSetCoordinates(), MatHtoolSetKernel(), MatHtoolCompressorType, MATH2OPUS, MatCreateH2OpusFromKernel()
879 @*/
880 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)
881 {
882   Mat            A;
883   Mat_Htool      *a;
884   PetscErrorCode ierr;
885 
886   PetscFunctionBegin;
887   ierr = MatCreate(comm,&A);CHKERRQ(ierr);
888   PetscValidLogicalCollectiveInt(A,spacedim,6);
889   PetscValidRealPointer(coords_target,7);
890   PetscValidRealPointer(coords_source,8);
891   if (!kernelctx) PetscValidFunction(kernel,9);
892   if (!kernel)    PetscValidPointer(kernelctx,10);
893   ierr = MatSetSizes(A,m,n,M,N);CHKERRQ(ierr);
894   ierr = MatSetType(A,MATHTOOL);CHKERRQ(ierr);
895   ierr = MatSetUp(A);CHKERRQ(ierr);
896   a            = (Mat_Htool*)A->data;
897   a->dim       = spacedim;
898   a->s         = 1.0;
899   a->kernel    = kernel;
900   a->kernelctx = kernelctx;
901   ierr = PetscCalloc1(A->rmap->N*spacedim,&a->gcoords_target);CHKERRQ(ierr);
902   ierr = PetscArraycpy(a->gcoords_target+A->rmap->rstart*spacedim,coords_target,A->rmap->n*spacedim);CHKERRQ(ierr);
903   ierr = MPIU_Allreduce(MPI_IN_PLACE,a->gcoords_target,A->rmap->N*spacedim,MPIU_REAL,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRMPI(ierr); /* global target coordinates */
904   if (coords_target != coords_source) {
905     ierr = PetscCalloc1(A->cmap->N*spacedim,&a->gcoords_source);CHKERRQ(ierr);
906     ierr = PetscArraycpy(a->gcoords_source+A->cmap->rstart*spacedim,coords_source,A->cmap->n*spacedim);CHKERRQ(ierr);
907     ierr = MPIU_Allreduce(MPI_IN_PLACE,a->gcoords_source,A->cmap->N*spacedim,MPIU_REAL,MPI_SUM,PetscObjectComm((PetscObject)A));CHKERRMPI(ierr); /* global source coordinates */
908   } else a->gcoords_source = a->gcoords_target;
909   ierr = PetscCalloc2(A->cmap->N,&a->work_source,A->rmap->N,&a->work_target);CHKERRQ(ierr);
910   *B = A;
911   PetscFunctionReturn(0);
912 }
913 
914 /*MC
915      MATHTOOL = "htool" - A matrix type for hierarchical matrices using the Htool package.
916 
917   Use ./configure --download-htool to install PETSc to use Htool.
918 
919    Options Database Keys:
920 .     -mat_type htool - matrix type to "htool" during a call to MatSetFromOptions()
921 
922    Level: beginner
923 
924 .seealso: MATH2OPUS, MATDENSE, MatCreateHtoolFromKernel(), MatHtoolSetKernel()
925 M*/
926 PETSC_EXTERN PetscErrorCode MatCreate_Htool(Mat A)
927 {
928   Mat_Htool      *a;
929   PetscErrorCode ierr;
930 
931   PetscFunctionBegin;
932   ierr = PetscNewLog(A,&a);CHKERRQ(ierr);
933   A->data = (void*)a;
934   ierr = PetscObjectChangeTypeName((PetscObject)A,MATHTOOL);CHKERRQ(ierr);
935   ierr = PetscMemzero(A->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
936   A->ops->getdiagonal       = MatGetDiagonal_Htool;
937   A->ops->getdiagonalblock  = MatGetDiagonalBlock_Htool;
938   A->ops->mult              = MatMult_Htool;
939   A->ops->multadd           = MatMultAdd_Htool;
940   A->ops->multtranspose     = MatMultTranspose_Htool;
941   if (!PetscDefined(USE_COMPLEX)) A->ops->multhermitiantranspose = MatMultTranspose_Htool;
942   A->ops->increaseoverlap   = MatIncreaseOverlap_Htool;
943   A->ops->createsubmatrices = MatCreateSubMatrices_Htool;
944   A->ops->transpose         = MatTranspose_Htool;
945   A->ops->destroy           = MatDestroy_Htool;
946   A->ops->view              = MatView_Htool;
947   A->ops->setfromoptions    = MatSetFromOptions_Htool;
948   A->ops->scale             = MatScale_Htool;
949   A->ops->getrow            = MatGetRow_Htool;
950   A->ops->restorerow        = MatRestoreRow_Htool;
951   A->ops->assemblyend       = MatAssemblyEnd_Htool;
952   a->dim                    = 0;
953   a->gcoords_target         = NULL;
954   a->gcoords_source         = NULL;
955   a->s                      = 1.0;
956   a->bs[0]                  = 10;
957   a->bs[1]                  = 1000000;
958   a->epsilon                = PetscSqrtReal(PETSC_SMALL);
959   a->eta                    = 10.0;
960   a->depth[0]               = 0;
961   a->depth[1]               = 0;
962   a->compressor             = MAT_HTOOL_COMPRESSOR_SYMPARTIAL_ACA;
963   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_htool_seqdense_C",MatProductSetFromOptions_Htool);CHKERRQ(ierr);
964   ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_htool_mpidense_C",MatProductSetFromOptions_Htool);CHKERRQ(ierr);
965   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_htool_seqdense_C",MatConvert_Htool_Dense);CHKERRQ(ierr);
966   ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_htool_mpidense_C",MatConvert_Htool_Dense);CHKERRQ(ierr);
967   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetHierarchicalMat_C",MatHtoolGetHierarchicalMat_Htool);CHKERRQ(ierr);
968   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolSetKernel_C",MatHtoolSetKernel_Htool);CHKERRQ(ierr);
969   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetPermutationSource_C",MatHtoolGetPermutationSource_Htool);CHKERRQ(ierr);
970   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolGetPermutationTarget_C",MatHtoolGetPermutationTarget_Htool);CHKERRQ(ierr);
971   ierr = PetscObjectComposeFunction((PetscObject)A,"MatHtoolUsePermutation_C",MatHtoolUsePermutation_Htool);CHKERRQ(ierr);
972   PetscFunctionReturn(0);
973 }
974