xref: /petsc/src/mat/impls/dense/mpi/mpidense.c (revision 520136c7e8a9141a0ef59e65a90b8ca416b0ca5f)
1 /*
2    Basic functions for basic parallel dense matrices.
3    Portions of this code are under:
4    Copyright (c) 2022 Advanced Micro Devices, Inc. All rights reserved.
5 */
6 
7 #include <../src/mat/impls/dense/mpi/mpidense.h> /*I   "petscmat.h"  I*/
8 #include <../src/mat/impls/aij/mpi/mpiaij.h>
9 #include <petscblaslapack.h>
10 #include <petsc/private/vecimpl.h>
11 
12 /*@
13   MatDenseGetLocalMatrix - For a `MATMPIDENSE` or `MATSEQDENSE` matrix returns the sequential
14   matrix that represents the operator. For sequential matrices it returns itself.
15 
16   Input Parameter:
17 . A - the sequential or MPI `MATDENSE` matrix
18 
19   Output Parameter:
20 . B - the inner matrix
21 
22   Level: intermediate
23 
24 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MATMPIDENSE`, `MATSEQDENSE`
25 @*/
26 PetscErrorCode MatDenseGetLocalMatrix(Mat A, Mat *B)
27 {
28   Mat_MPIDense *mat = (Mat_MPIDense *)A->data;
29   PetscBool     flg;
30 
31   PetscFunctionBegin;
32   PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
33   PetscAssertPointer(B, 2);
34   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIDENSE, &flg));
35   if (flg) *B = mat->A;
36   else {
37     PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATSEQDENSE, &flg));
38     PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for matrix type %s", ((PetscObject)A)->type_name);
39     *B = A;
40   }
41   PetscFunctionReturn(PETSC_SUCCESS);
42 }
43 
44 static PetscErrorCode MatCopy_MPIDense(Mat A, Mat B, MatStructure s)
45 {
46   Mat_MPIDense *Amat = (Mat_MPIDense *)A->data;
47   Mat_MPIDense *Bmat = (Mat_MPIDense *)B->data;
48 
49   PetscFunctionBegin;
50   PetscCall(MatCopy(Amat->A, Bmat->A, s));
51   PetscFunctionReturn(PETSC_SUCCESS);
52 }
53 
54 PetscErrorCode MatShift_MPIDense(Mat A, PetscScalar alpha)
55 {
56   Mat_MPIDense *mat = (Mat_MPIDense *)A->data;
57   PetscInt      j, lda, rstart = A->rmap->rstart, rend = A->rmap->rend, rend2;
58   PetscScalar  *v;
59 
60   PetscFunctionBegin;
61   PetscCall(MatDenseGetArray(mat->A, &v));
62   PetscCall(MatDenseGetLDA(mat->A, &lda));
63   rend2 = PetscMin(rend, A->cmap->N);
64   if (rend2 > rstart) {
65     for (j = rstart; j < rend2; j++) v[j - rstart + j * lda] += alpha;
66     PetscCall(PetscLogFlops(rend2 - rstart));
67   }
68   PetscCall(MatDenseRestoreArray(mat->A, &v));
69   PetscFunctionReturn(PETSC_SUCCESS);
70 }
71 
72 static PetscErrorCode MatGetRow_MPIDense(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
73 {
74   Mat_MPIDense *mat = (Mat_MPIDense *)A->data;
75   PetscInt      lrow, rstart = A->rmap->rstart, rend = A->rmap->rend;
76 
77   PetscFunctionBegin;
78   PetscCheck(row >= rstart && row < rend, PETSC_COMM_SELF, PETSC_ERR_SUP, "only local rows");
79   lrow = row - rstart;
80   PetscCall(MatGetRow(mat->A, lrow, nz, (const PetscInt **)idx, (const PetscScalar **)v));
81   PetscFunctionReturn(PETSC_SUCCESS);
82 }
83 
84 static PetscErrorCode MatRestoreRow_MPIDense(Mat A, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
85 {
86   Mat_MPIDense *mat = (Mat_MPIDense *)A->data;
87   PetscInt      lrow, rstart = A->rmap->rstart, rend = A->rmap->rend;
88 
89   PetscFunctionBegin;
90   PetscCheck(row >= rstart && row < rend, PETSC_COMM_SELF, PETSC_ERR_SUP, "only local rows");
91   lrow = row - rstart;
92   PetscCall(MatRestoreRow(mat->A, lrow, nz, (const PetscInt **)idx, (const PetscScalar **)v));
93   PetscFunctionReturn(PETSC_SUCCESS);
94 }
95 
96 static PetscErrorCode MatGetDiagonalBlock_MPIDense(Mat A, Mat *a)
97 {
98   Mat_MPIDense *mdn = (Mat_MPIDense *)A->data;
99   PetscInt      m = A->rmap->n, rstart = A->rmap->rstart;
100   PetscScalar  *array;
101   MPI_Comm      comm;
102   PetscBool     flg;
103   Mat           B;
104 
105   PetscFunctionBegin;
106   PetscCall(MatHasCongruentLayouts(A, &flg));
107   PetscCheck(flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only square matrices supported.");
108   PetscCall(PetscObjectQuery((PetscObject)A, "DiagonalBlock", (PetscObject *)&B));
109   if (!B) { /* This should use MatDenseGetSubMatrix (not create), but we would need a call like MatRestoreDiagonalBlock */
110 #if PetscDefined(HAVE_CUDA)
111     PetscCall(PetscObjectTypeCompare((PetscObject)mdn->A, MATSEQDENSECUDA, &flg));
112     PetscCheck(!flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not coded for %s. Send an email to petsc-dev@mcs.anl.gov to request this feature", MATSEQDENSECUDA);
113 #elif PetscDefined(HAVE_HIP)
114     PetscCall(PetscObjectTypeCompare((PetscObject)mdn->A, MATSEQDENSEHIP, &flg));
115     PetscCheck(!flg, PETSC_COMM_SELF, PETSC_ERR_SUP, "Not coded for %s. Send an email to petsc-dev@mcs.anl.gov to request this feature", MATSEQDENSEHIP);
116 #endif
117     PetscCall(PetscObjectGetComm((PetscObject)mdn->A, &comm));
118     PetscCall(MatCreate(comm, &B));
119     PetscCall(MatSetSizes(B, m, m, m, m));
120     PetscCall(MatSetType(B, ((PetscObject)mdn->A)->type_name));
121     PetscCall(MatDenseGetArrayRead(mdn->A, (const PetscScalar **)&array));
122     PetscCall(MatSeqDenseSetPreallocation(B, array + m * rstart));
123     PetscCall(MatDenseRestoreArrayRead(mdn->A, (const PetscScalar **)&array));
124     PetscCall(PetscObjectCompose((PetscObject)A, "DiagonalBlock", (PetscObject)B));
125     *a = B;
126     PetscCall(MatDestroy(&B));
127   } else *a = B;
128   PetscFunctionReturn(PETSC_SUCCESS);
129 }
130 
131 static PetscErrorCode MatSetValues_MPIDense(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], const PetscScalar v[], InsertMode addv)
132 {
133   Mat_MPIDense *A = (Mat_MPIDense *)mat->data;
134   PetscInt      i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend, row;
135   PetscBool     roworiented = A->roworiented;
136 
137   PetscFunctionBegin;
138   for (i = 0; i < m; i++) {
139     if (idxm[i] < 0) continue;
140     PetscCheck(idxm[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large");
141     if (idxm[i] >= rstart && idxm[i] < rend) {
142       row = idxm[i] - rstart;
143       if (roworiented) {
144         PetscCall(MatSetValues(A->A, 1, &row, n, idxn, v ? v + i * n : NULL, addv));
145       } else {
146         for (j = 0; j < n; j++) {
147           if (idxn[j] < 0) continue;
148           PetscCheck(idxn[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large");
149           PetscCall(MatSetValues(A->A, 1, &row, 1, &idxn[j], v ? v + i + j * m : NULL, addv));
150         }
151       }
152     } else if (!A->donotstash) {
153       mat->assembled = PETSC_FALSE;
154       if (roworiented) {
155         PetscCall(MatStashValuesRow_Private(&mat->stash, idxm[i], n, idxn, v ? v + i * n : NULL, PETSC_FALSE));
156       } else {
157         PetscCall(MatStashValuesCol_Private(&mat->stash, idxm[i], n, idxn, v ? v + i : NULL, m, PETSC_FALSE));
158       }
159     }
160   }
161   PetscFunctionReturn(PETSC_SUCCESS);
162 }
163 
164 static PetscErrorCode MatGetValues_MPIDense(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], PetscScalar v[])
165 {
166   Mat_MPIDense *mdn = (Mat_MPIDense *)mat->data;
167   PetscInt      i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend, row;
168 
169   PetscFunctionBegin;
170   for (i = 0; i < m; i++) {
171     if (idxm[i] < 0) continue; /* negative row */
172     PetscCheck(idxm[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large");
173     if (idxm[i] >= rstart && idxm[i] < rend) {
174       row = idxm[i] - rstart;
175       for (j = 0; j < n; j++) {
176         if (idxn[j] < 0) continue; /* negative column */
177         PetscCheck(idxn[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large");
178         PetscCall(MatGetValues(mdn->A, 1, &row, 1, &idxn[j], v + i * n + j));
179       }
180     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Only local values currently supported");
181   }
182   PetscFunctionReturn(PETSC_SUCCESS);
183 }
184 
185 static PetscErrorCode MatDenseGetLDA_MPIDense(Mat A, PetscInt *lda)
186 {
187   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
188 
189   PetscFunctionBegin;
190   PetscCall(MatDenseGetLDA(a->A, lda));
191   PetscFunctionReturn(PETSC_SUCCESS);
192 }
193 
194 static PetscErrorCode MatDenseSetLDA_MPIDense(Mat A, PetscInt lda)
195 {
196   Mat_MPIDense *a     = (Mat_MPIDense *)A->data;
197   MatType       mtype = MATSEQDENSE;
198 
199   PetscFunctionBegin;
200   if (!a->A) {
201     PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
202     PetscCall(PetscLayoutSetUp(A->rmap));
203     PetscCall(PetscLayoutSetUp(A->cmap));
204     PetscCall(MatCreate(PETSC_COMM_SELF, &a->A));
205     PetscCall(MatSetSizes(a->A, A->rmap->n, A->cmap->N, A->rmap->n, A->cmap->N));
206 #if PetscDefined(HAVE_CUDA)
207     PetscBool iscuda;
208     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIDENSECUDA, &iscuda));
209     if (iscuda) mtype = MATSEQDENSECUDA;
210 #elif PetscDefined(HAVE_HIP)
211     PetscBool iship;
212     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIDENSEHIP, &iship));
213     if (iship) mtype = MATSEQDENSEHIP;
214 #endif
215     PetscCall(MatSetType(a->A, mtype));
216   }
217   PetscCall(MatDenseSetLDA(a->A, lda));
218   PetscFunctionReturn(PETSC_SUCCESS);
219 }
220 
221 static PetscErrorCode MatDenseGetArray_MPIDense(Mat A, PetscScalar **array)
222 {
223   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
224 
225   PetscFunctionBegin;
226   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
227   PetscCall(MatDenseGetArray(a->A, array));
228   PetscFunctionReturn(PETSC_SUCCESS);
229 }
230 
231 static PetscErrorCode MatDenseGetArrayRead_MPIDense(Mat A, PetscScalar **array)
232 {
233   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
234 
235   PetscFunctionBegin;
236   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
237   PetscCall(MatDenseGetArrayRead(a->A, (const PetscScalar **)array));
238   PetscFunctionReturn(PETSC_SUCCESS);
239 }
240 
241 static PetscErrorCode MatDenseGetArrayWrite_MPIDense(Mat A, PetscScalar **array)
242 {
243   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
244 
245   PetscFunctionBegin;
246   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
247   PetscCall(MatDenseGetArrayWrite(a->A, array));
248   PetscFunctionReturn(PETSC_SUCCESS);
249 }
250 
251 static PetscErrorCode MatDensePlaceArray_MPIDense(Mat A, const PetscScalar *array)
252 {
253   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
254 
255   PetscFunctionBegin;
256   PetscCheck(!a->vecinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
257   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
258   PetscCall(MatDensePlaceArray(a->A, array));
259   PetscFunctionReturn(PETSC_SUCCESS);
260 }
261 
262 static PetscErrorCode MatDenseResetArray_MPIDense(Mat A)
263 {
264   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
265 
266   PetscFunctionBegin;
267   PetscCheck(!a->vecinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
268   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
269   PetscCall(MatDenseResetArray(a->A));
270   PetscFunctionReturn(PETSC_SUCCESS);
271 }
272 
273 static PetscErrorCode MatDenseReplaceArray_MPIDense(Mat A, const PetscScalar *array)
274 {
275   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
276 
277   PetscFunctionBegin;
278   PetscCheck(!a->vecinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
279   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
280   PetscCall(MatDenseReplaceArray(a->A, array));
281   PetscFunctionReturn(PETSC_SUCCESS);
282 }
283 
284 static PetscErrorCode MatCreateSubMatrix_MPIDense(Mat A, IS isrow, IS iscol, MatReuse scall, Mat *B)
285 {
286   Mat_MPIDense      *mat = (Mat_MPIDense *)A->data, *newmatd;
287   PetscInt           lda, i, j, rstart, rend, nrows, ncols, Ncols, nlrows, nlcols;
288   const PetscInt    *irow, *icol;
289   const PetscScalar *v;
290   PetscScalar       *bv;
291   Mat                newmat;
292   IS                 iscol_local;
293   MPI_Comm           comm_is, comm_mat;
294 
295   PetscFunctionBegin;
296   PetscCall(PetscObjectGetComm((PetscObject)A, &comm_mat));
297   PetscCall(PetscObjectGetComm((PetscObject)iscol, &comm_is));
298   PetscCheck(comm_mat == comm_is, PETSC_COMM_SELF, PETSC_ERR_ARG_NOTSAMECOMM, "IS communicator must match matrix communicator");
299 
300   PetscCall(ISAllGather(iscol, &iscol_local));
301   PetscCall(ISGetIndices(isrow, &irow));
302   PetscCall(ISGetIndices(iscol_local, &icol));
303   PetscCall(ISGetLocalSize(isrow, &nrows));
304   PetscCall(ISGetLocalSize(iscol, &ncols));
305   PetscCall(ISGetSize(iscol, &Ncols)); /* global number of columns, size of iscol_local */
306 
307   /* No parallel redistribution currently supported! Should really check each index set
308      to confirm that it is OK.  ... Currently supports only submatrix same partitioning as
309      original matrix! */
310 
311   PetscCall(MatGetLocalSize(A, &nlrows, &nlcols));
312   PetscCall(MatGetOwnershipRange(A, &rstart, &rend));
313 
314   /* Check submatrix call */
315   if (scall == MAT_REUSE_MATRIX) {
316     /* SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size"); */
317     /* Really need to test rows and column sizes! */
318     newmat = *B;
319   } else {
320     /* Create and fill new matrix */
321     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &newmat));
322     PetscCall(MatSetSizes(newmat, nrows, ncols, PETSC_DECIDE, Ncols));
323     PetscCall(MatSetType(newmat, ((PetscObject)A)->type_name));
324     PetscCall(MatMPIDenseSetPreallocation(newmat, NULL));
325   }
326 
327   /* Now extract the data pointers and do the copy, column at a time */
328   newmatd = (Mat_MPIDense *)newmat->data;
329   PetscCall(MatDenseGetArray(newmatd->A, &bv));
330   PetscCall(MatDenseGetArrayRead(mat->A, &v));
331   PetscCall(MatDenseGetLDA(mat->A, &lda));
332   for (i = 0; i < Ncols; i++) {
333     const PetscScalar *av = v + lda * icol[i];
334     for (j = 0; j < nrows; j++) *bv++ = av[irow[j] - rstart];
335   }
336   PetscCall(MatDenseRestoreArrayRead(mat->A, &v));
337   PetscCall(MatDenseRestoreArray(newmatd->A, &bv));
338 
339   /* Assemble the matrices so that the correct flags are set */
340   PetscCall(MatAssemblyBegin(newmat, MAT_FINAL_ASSEMBLY));
341   PetscCall(MatAssemblyEnd(newmat, MAT_FINAL_ASSEMBLY));
342 
343   /* Free work space */
344   PetscCall(ISRestoreIndices(isrow, &irow));
345   PetscCall(ISRestoreIndices(iscol_local, &icol));
346   PetscCall(ISDestroy(&iscol_local));
347   *B = newmat;
348   PetscFunctionReturn(PETSC_SUCCESS);
349 }
350 
351 static PetscErrorCode MatDenseRestoreArray_MPIDense(Mat A, PetscScalar **array)
352 {
353   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
354 
355   PetscFunctionBegin;
356   PetscCall(MatDenseRestoreArray(a->A, array));
357   PetscFunctionReturn(PETSC_SUCCESS);
358 }
359 
360 static PetscErrorCode MatDenseRestoreArrayRead_MPIDense(Mat A, PetscScalar **array)
361 {
362   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
363 
364   PetscFunctionBegin;
365   PetscCall(MatDenseRestoreArrayRead(a->A, (const PetscScalar **)array));
366   PetscFunctionReturn(PETSC_SUCCESS);
367 }
368 
369 static PetscErrorCode MatDenseRestoreArrayWrite_MPIDense(Mat A, PetscScalar **array)
370 {
371   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
372 
373   PetscFunctionBegin;
374   PetscCall(MatDenseRestoreArrayWrite(a->A, array));
375   PetscFunctionReturn(PETSC_SUCCESS);
376 }
377 
378 static PetscErrorCode MatAssemblyBegin_MPIDense(Mat mat, MatAssemblyType mode)
379 {
380   Mat_MPIDense *mdn = (Mat_MPIDense *)mat->data;
381   PetscInt      nstash, reallocs;
382 
383   PetscFunctionBegin;
384   if (mdn->donotstash || mat->nooffprocentries) PetscFunctionReturn(PETSC_SUCCESS);
385 
386   PetscCall(MatStashScatterBegin_Private(mat, &mat->stash, mat->rmap->range));
387   PetscCall(MatStashGetInfo_Private(&mat->stash, &nstash, &reallocs));
388   PetscCall(PetscInfo(mdn->A, "Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
389   PetscFunctionReturn(PETSC_SUCCESS);
390 }
391 
392 static PetscErrorCode MatAssemblyEnd_MPIDense(Mat mat, MatAssemblyType mode)
393 {
394   Mat_MPIDense *mdn = (Mat_MPIDense *)mat->data;
395   PetscInt      i, *row, *col, flg, j, rstart, ncols;
396   PetscMPIInt   n;
397   PetscScalar  *val;
398 
399   PetscFunctionBegin;
400   if (!mdn->donotstash && !mat->nooffprocentries) {
401     /*  wait on receives */
402     while (1) {
403       PetscCall(MatStashScatterGetMesg_Private(&mat->stash, &n, &row, &col, &val, &flg));
404       if (!flg) break;
405 
406       for (i = 0; i < n;) {
407         /* Now identify the consecutive vals belonging to the same row */
408         for (j = i, rstart = row[j]; j < n; j++) {
409           if (row[j] != rstart) break;
410         }
411         if (j < n) ncols = j - i;
412         else ncols = n - i;
413         /* Now assemble all these values with a single function call */
414         PetscCall(MatSetValues_MPIDense(mat, 1, row + i, ncols, col + i, val + i, mat->insertmode));
415         i = j;
416       }
417     }
418     PetscCall(MatStashScatterEnd_Private(&mat->stash));
419   }
420 
421   PetscCall(MatAssemblyBegin(mdn->A, mode));
422   PetscCall(MatAssemblyEnd(mdn->A, mode));
423   PetscFunctionReturn(PETSC_SUCCESS);
424 }
425 
426 static PetscErrorCode MatZeroEntries_MPIDense(Mat A)
427 {
428   Mat_MPIDense *l = (Mat_MPIDense *)A->data;
429 
430   PetscFunctionBegin;
431   PetscCall(MatZeroEntries(l->A));
432   PetscFunctionReturn(PETSC_SUCCESS);
433 }
434 
435 static PetscErrorCode MatZeroRows_MPIDense(Mat A, PetscInt n, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
436 {
437   Mat_MPIDense *l = (Mat_MPIDense *)A->data;
438   PetscInt      i, len, *lrows;
439 
440   PetscFunctionBegin;
441   /* get locally owned rows */
442   PetscCall(PetscLayoutMapLocal(A->rmap, n, rows, &len, &lrows, NULL));
443   /* fix right-hand side if needed */
444   if (x && b) {
445     const PetscScalar *xx;
446     PetscScalar       *bb;
447 
448     PetscCall(VecGetArrayRead(x, &xx));
449     PetscCall(VecGetArrayWrite(b, &bb));
450     for (i = 0; i < len; ++i) bb[lrows[i]] = diag * xx[lrows[i]];
451     PetscCall(VecRestoreArrayRead(x, &xx));
452     PetscCall(VecRestoreArrayWrite(b, &bb));
453   }
454   PetscCall(MatZeroRows(l->A, len, lrows, 0.0, NULL, NULL));
455   if (diag != 0.0) {
456     Vec d;
457 
458     PetscCall(MatCreateVecs(A, NULL, &d));
459     PetscCall(VecSet(d, diag));
460     PetscCall(MatDiagonalSet(A, d, INSERT_VALUES));
461     PetscCall(VecDestroy(&d));
462   }
463   PetscCall(PetscFree(lrows));
464   PetscFunctionReturn(PETSC_SUCCESS);
465 }
466 
467 PETSC_INTERN PetscErrorCode MatMult_SeqDense(Mat, Vec, Vec);
468 PETSC_INTERN PetscErrorCode MatMultAdd_SeqDense(Mat, Vec, Vec, Vec);
469 PETSC_INTERN PetscErrorCode MatMultTranspose_SeqDense(Mat, Vec, Vec);
470 PETSC_INTERN PetscErrorCode MatMultTransposeAdd_SeqDense(Mat, Vec, Vec, Vec);
471 
472 static PetscErrorCode MatMult_MPIDense(Mat mat, Vec xx, Vec yy)
473 {
474   Mat_MPIDense      *mdn = (Mat_MPIDense *)mat->data;
475   const PetscScalar *ax;
476   PetscScalar       *ay;
477   PetscMemType       axmtype, aymtype;
478 
479   PetscFunctionBegin;
480   if (!mdn->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(mat));
481   PetscCall(VecGetArrayReadAndMemType(xx, &ax, &axmtype));
482   PetscCall(VecGetArrayAndMemType(mdn->lvec, &ay, &aymtype));
483   PetscCall(PetscSFBcastWithMemTypeBegin(mdn->Mvctx, MPIU_SCALAR, axmtype, ax, aymtype, ay, MPI_REPLACE));
484   PetscCall(PetscSFBcastEnd(mdn->Mvctx, MPIU_SCALAR, ax, ay, MPI_REPLACE));
485   PetscCall(VecRestoreArrayAndMemType(mdn->lvec, &ay));
486   PetscCall(VecRestoreArrayReadAndMemType(xx, &ax));
487   PetscCall((*mdn->A->ops->mult)(mdn->A, mdn->lvec, yy));
488   PetscFunctionReturn(PETSC_SUCCESS);
489 }
490 
491 static PetscErrorCode MatMultAddColumnRange_MPIDense(Mat mat, Vec xx, Vec yy, Vec zz, PetscInt c_start, PetscInt c_end)
492 {
493   Mat_MPIDense      *mdn = (Mat_MPIDense *)mat->data;
494   const PetscScalar *ax;
495   PetscScalar       *ay;
496   PetscMemType       axmtype, aymtype;
497 
498   PetscFunctionBegin;
499   if (!mdn->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(mat));
500   PetscCall(VecGetArrayReadAndMemType(xx, &ax, &axmtype));
501   PetscCall(VecGetArrayAndMemType(mdn->lvec, &ay, &aymtype));
502   PetscCall(PetscSFBcastWithMemTypeBegin(mdn->Mvctx, MPIU_SCALAR, axmtype, ax, aymtype, ay, MPI_REPLACE));
503   PetscCall(PetscSFBcastEnd(mdn->Mvctx, MPIU_SCALAR, ax, ay, MPI_REPLACE));
504   PetscCall(VecRestoreArrayAndMemType(mdn->lvec, &ay));
505   PetscCall(VecRestoreArrayReadAndMemType(xx, &ax));
506   PetscUseMethod(mdn->A, "MatMultAddColumnRange_C", (Mat, Vec, Vec, Vec, PetscInt, PetscInt), (mdn->A, mdn->lvec, yy, zz, c_start, c_end));
507   PetscFunctionReturn(PETSC_SUCCESS);
508 }
509 
510 static PetscErrorCode MatMultAdd_MPIDense(Mat mat, Vec xx, Vec yy, Vec zz)
511 {
512   Mat_MPIDense      *mdn = (Mat_MPIDense *)mat->data;
513   const PetscScalar *ax;
514   PetscScalar       *ay;
515   PetscMemType       axmtype, aymtype;
516 
517   PetscFunctionBegin;
518   if (!mdn->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(mat));
519   PetscCall(VecGetArrayReadAndMemType(xx, &ax, &axmtype));
520   PetscCall(VecGetArrayAndMemType(mdn->lvec, &ay, &aymtype));
521   PetscCall(PetscSFBcastWithMemTypeBegin(mdn->Mvctx, MPIU_SCALAR, axmtype, ax, aymtype, ay, MPI_REPLACE));
522   PetscCall(PetscSFBcastEnd(mdn->Mvctx, MPIU_SCALAR, ax, ay, MPI_REPLACE));
523   PetscCall(VecRestoreArrayAndMemType(mdn->lvec, &ay));
524   PetscCall(VecRestoreArrayReadAndMemType(xx, &ax));
525   PetscCall((*mdn->A->ops->multadd)(mdn->A, mdn->lvec, yy, zz));
526   PetscFunctionReturn(PETSC_SUCCESS);
527 }
528 
529 static PetscErrorCode MatMultHermitianTransposeColumnRange_MPIDense(Mat A, Vec xx, Vec yy, PetscInt c_start, PetscInt c_end)
530 {
531   Mat_MPIDense      *a = (Mat_MPIDense *)A->data;
532   const PetscScalar *ax;
533   PetscScalar       *ay;
534   PetscMemType       axmtype, aymtype;
535 
536   PetscFunctionBegin;
537   if (!a->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(A));
538   PetscCall(VecSet(yy, 0.0));
539   PetscUseMethod(a->A, "MatMultHermitianTransposeColumnRange_C", (Mat, Vec, Vec, PetscInt, PetscInt), (a->A, xx, a->lvec, c_start, c_end));
540   PetscCall(VecGetArrayReadAndMemType(a->lvec, &ax, &axmtype));
541   PetscCall(VecGetArrayAndMemType(yy, &ay, &aymtype));
542   PetscCall(PetscSFReduceWithMemTypeBegin(a->Mvctx, MPIU_SCALAR, axmtype, ax, aymtype, ay, MPIU_SUM));
543   PetscCall(PetscSFReduceEnd(a->Mvctx, MPIU_SCALAR, ax, ay, MPIU_SUM));
544   PetscCall(VecRestoreArrayReadAndMemType(a->lvec, &ax));
545   PetscCall(VecRestoreArrayAndMemType(yy, &ay));
546   PetscFunctionReturn(PETSC_SUCCESS);
547 }
548 
549 static PetscErrorCode MatMultTransposeKernel_MPIDense(Mat A, Vec xx, Vec yy, PetscBool herm)
550 {
551   Mat_MPIDense      *a = (Mat_MPIDense *)A->data;
552   const PetscScalar *ax;
553   PetscScalar       *ay;
554   PetscMemType       axmtype, aymtype;
555 
556   PetscFunctionBegin;
557   if (!a->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(A));
558   PetscCall(VecSet(yy, 0.0));
559   if (herm) PetscCall((*a->A->ops->multhermitiantranspose)(a->A, xx, a->lvec));
560   else PetscCall((*a->A->ops->multtranspose)(a->A, xx, a->lvec));
561   PetscCall(VecGetArrayReadAndMemType(a->lvec, &ax, &axmtype));
562   PetscCall(VecGetArrayAndMemType(yy, &ay, &aymtype));
563   PetscCall(PetscSFReduceWithMemTypeBegin(a->Mvctx, MPIU_SCALAR, axmtype, ax, aymtype, ay, MPIU_SUM));
564   PetscCall(PetscSFReduceEnd(a->Mvctx, MPIU_SCALAR, ax, ay, MPIU_SUM));
565   PetscCall(VecRestoreArrayReadAndMemType(a->lvec, &ax));
566   PetscCall(VecRestoreArrayAndMemType(yy, &ay));
567   PetscFunctionReturn(PETSC_SUCCESS);
568 }
569 
570 static PetscErrorCode MatMultHermitianTransposeAddColumnRange_MPIDense(Mat A, Vec xx, Vec yy, Vec zz, PetscInt c_start, PetscInt c_end)
571 {
572   Mat_MPIDense      *a = (Mat_MPIDense *)A->data;
573   const PetscScalar *ax;
574   PetscScalar       *ay;
575   PetscMemType       axmtype, aymtype;
576 
577   PetscFunctionBegin;
578   if (!a->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(A));
579   PetscCall(VecCopy(yy, zz));
580   PetscMPIInt rank;
581   PetscCallMPI(MPI_Comm_rank(MPI_COMM_WORLD, &rank));
582   PetscUseMethod(a->A, "MatMultHermitianTransposeColumnRange_C", (Mat, Vec, Vec, PetscInt, PetscInt), (a->A, xx, a->lvec, c_start, c_end));
583   PetscCall(VecGetArrayReadAndMemType(a->lvec, &ax, &axmtype));
584   PetscCall(VecGetArrayAndMemType(zz, &ay, &aymtype));
585   PetscCall(PetscSFReduceWithMemTypeBegin(a->Mvctx, MPIU_SCALAR, axmtype, ax, aymtype, ay, MPIU_SUM));
586   PetscCall(PetscSFReduceEnd(a->Mvctx, MPIU_SCALAR, ax, ay, MPIU_SUM));
587   PetscCall(VecRestoreArrayReadAndMemType(a->lvec, &ax));
588   PetscCall(VecRestoreArrayAndMemType(zz, &ay));
589   PetscFunctionReturn(PETSC_SUCCESS);
590 }
591 
592 static PetscErrorCode MatMultTransposeAddKernel_MPIDense(Mat A, Vec xx, Vec yy, Vec zz, PetscBool herm)
593 {
594   Mat_MPIDense      *a = (Mat_MPIDense *)A->data;
595   const PetscScalar *ax;
596   PetscScalar       *ay;
597   PetscMemType       axmtype, aymtype;
598 
599   PetscFunctionBegin;
600   if (!a->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(A));
601   PetscCall(VecCopy(yy, zz));
602   if (herm) PetscCall((*a->A->ops->multhermitiantranspose)(a->A, xx, a->lvec));
603   else PetscCall((*a->A->ops->multtranspose)(a->A, xx, a->lvec));
604   PetscCall(VecGetArrayReadAndMemType(a->lvec, &ax, &axmtype));
605   PetscCall(VecGetArrayAndMemType(zz, &ay, &aymtype));
606   PetscCall(PetscSFReduceWithMemTypeBegin(a->Mvctx, MPIU_SCALAR, axmtype, ax, aymtype, ay, MPIU_SUM));
607   PetscCall(PetscSFReduceEnd(a->Mvctx, MPIU_SCALAR, ax, ay, MPIU_SUM));
608   PetscCall(VecRestoreArrayReadAndMemType(a->lvec, &ax));
609   PetscCall(VecRestoreArrayAndMemType(zz, &ay));
610   PetscFunctionReturn(PETSC_SUCCESS);
611 }
612 
613 static PetscErrorCode MatMultTranspose_MPIDense(Mat A, Vec xx, Vec yy)
614 {
615   PetscFunctionBegin;
616   PetscCall(MatMultTransposeKernel_MPIDense(A, xx, yy, PETSC_FALSE));
617   PetscFunctionReturn(PETSC_SUCCESS);
618 }
619 
620 static PetscErrorCode MatMultTransposeAdd_MPIDense(Mat A, Vec xx, Vec yy, Vec zz)
621 {
622   PetscFunctionBegin;
623   PetscCall(MatMultTransposeAddKernel_MPIDense(A, xx, yy, zz, PETSC_FALSE));
624   PetscFunctionReturn(PETSC_SUCCESS);
625 }
626 
627 static PetscErrorCode MatMultHermitianTranspose_MPIDense(Mat A, Vec xx, Vec yy)
628 {
629   PetscFunctionBegin;
630   PetscCall(MatMultTransposeKernel_MPIDense(A, xx, yy, PETSC_TRUE));
631   PetscFunctionReturn(PETSC_SUCCESS);
632 }
633 
634 static PetscErrorCode MatMultHermitianTransposeAdd_MPIDense(Mat A, Vec xx, Vec yy, Vec zz)
635 {
636   PetscFunctionBegin;
637   PetscCall(MatMultTransposeAddKernel_MPIDense(A, xx, yy, zz, PETSC_TRUE));
638   PetscFunctionReturn(PETSC_SUCCESS);
639 }
640 
641 PetscErrorCode MatGetDiagonal_MPIDense(Mat A, Vec v)
642 {
643   Mat_MPIDense      *a = (Mat_MPIDense *)A->data;
644   PetscInt           lda, len, i, nl, ng, m = A->rmap->n, radd;
645   PetscScalar       *x;
646   const PetscScalar *av;
647 
648   PetscFunctionBegin;
649   PetscCall(VecGetArray(v, &x));
650   PetscCall(VecGetSize(v, &ng));
651   PetscCheck(ng == A->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Nonconforming mat and vec");
652   PetscCall(VecGetLocalSize(v, &nl));
653   len  = PetscMin(a->A->rmap->n, a->A->cmap->n);
654   radd = A->rmap->rstart * m;
655   PetscCall(MatDenseGetArrayRead(a->A, &av));
656   PetscCall(MatDenseGetLDA(a->A, &lda));
657   for (i = 0; i < len; i++) x[i] = av[radd + i * lda + i];
658   PetscCall(MatDenseRestoreArrayRead(a->A, &av));
659   if (nl - i > 0) PetscCall(PetscArrayzero(x + i, nl - i));
660   PetscCall(VecRestoreArray(v, &x));
661   PetscFunctionReturn(PETSC_SUCCESS);
662 }
663 
664 static PetscErrorCode MatDestroy_MPIDense(Mat mat)
665 {
666   Mat_MPIDense *mdn = (Mat_MPIDense *)mat->data;
667 
668   PetscFunctionBegin;
669   PetscCall(PetscLogObjectState((PetscObject)mat, "Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT, mat->rmap->N, mat->cmap->N));
670   PetscCall(MatStashDestroy_Private(&mat->stash));
671   PetscCheck(!mdn->vecinuse, PetscObjectComm((PetscObject)mat), PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
672   PetscCheck(!mdn->matinuse, PetscObjectComm((PetscObject)mat), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
673   PetscCall(MatDestroy(&mdn->A));
674   PetscCall(VecDestroy(&mdn->lvec));
675   PetscCall(PetscSFDestroy(&mdn->Mvctx));
676   PetscCall(VecDestroy(&mdn->cvec));
677   PetscCall(MatDestroy(&mdn->cmat));
678 
679   PetscCall(PetscFree(mat->data));
680   PetscCall(PetscObjectChangeTypeName((PetscObject)mat, NULL));
681 
682   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetLDA_C", NULL));
683   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseSetLDA_C", NULL));
684   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArray_C", NULL));
685   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArray_C", NULL));
686   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArrayRead_C", NULL));
687   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArrayRead_C", NULL));
688   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArrayWrite_C", NULL));
689   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArrayWrite_C", NULL));
690   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDensePlaceArray_C", NULL));
691   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseResetArray_C", NULL));
692   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseReplaceArray_C", NULL));
693   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpidense_C", NULL));
694   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_mpiaij_C", NULL));
695 #if defined(PETSC_HAVE_ELEMENTAL)
696   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_elemental_C", NULL));
697 #endif
698 #if defined(PETSC_HAVE_SCALAPACK)
699   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_scalapack_C", NULL));
700 #endif
701   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIDenseSetPreallocation_C", NULL));
702   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaij_mpidense_C", NULL));
703   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidense_mpiaij_C", NULL));
704 #if defined(PETSC_HAVE_CUDA)
705   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaijcusparse_mpidense_C", NULL));
706   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidense_mpiaijcusparse_C", NULL));
707   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_mpidensecuda_C", NULL));
708   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidensecuda_mpidense_C", NULL));
709   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaij_mpidensecuda_C", NULL));
710   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaijcusparse_mpidensecuda_C", NULL));
711   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidensecuda_mpiaij_C", NULL));
712   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidensecuda_mpiaijcusparse_C", NULL));
713   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDAGetArray_C", NULL));
714   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDAGetArrayRead_C", NULL));
715   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDAGetArrayWrite_C", NULL));
716   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDARestoreArray_C", NULL));
717   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDARestoreArrayRead_C", NULL));
718   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDARestoreArrayWrite_C", NULL));
719   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDAPlaceArray_C", NULL));
720   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDAResetArray_C", NULL));
721   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDAReplaceArray_C", NULL));
722   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseCUDASetPreallocation_C", NULL));
723 #endif
724 #if defined(PETSC_HAVE_HIP)
725   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaijhipsparse_mpidense_C", NULL));
726   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidense_mpiaijhipsparse_C", NULL));
727   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_mpidensehip_C", NULL));
728   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidensehip_mpidense_C", NULL));
729   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaij_mpidensehip_C", NULL));
730   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaijhipsparse_mpidensehip_C", NULL));
731   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidensehip_mpiaij_C", NULL));
732   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidensehip_mpiaijhipsparse_C", NULL));
733   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPGetArray_C", NULL));
734   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPGetArrayRead_C", NULL));
735   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPGetArrayWrite_C", NULL));
736   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPRestoreArray_C", NULL));
737   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPRestoreArrayRead_C", NULL));
738   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPRestoreArrayWrite_C", NULL));
739   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPPlaceArray_C", NULL));
740   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPResetArray_C", NULL));
741   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPReplaceArray_C", NULL));
742   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseHIPSetPreallocation_C", NULL));
743 #endif
744   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumn_C", NULL));
745   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumn_C", NULL));
746   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVec_C", NULL));
747   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVec_C", NULL));
748   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVecRead_C", NULL));
749   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVecRead_C", NULL));
750   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVecWrite_C", NULL));
751   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVecWrite_C", NULL));
752   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetSubMatrix_C", NULL));
753   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreSubMatrix_C", NULL));
754   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultAddColumnRange_C", NULL));
755   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultHermitianTransposeColumnRange_C", NULL));
756   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultHermitianTransposeAddColumnRange_C", NULL));
757 
758   PetscCall(PetscObjectCompose((PetscObject)mat, "DiagonalBlock", NULL));
759   PetscFunctionReturn(PETSC_SUCCESS);
760 }
761 
762 #include <petscdraw.h>
763 static PetscErrorCode MatView_MPIDense_ASCIIorDraworSocket(Mat mat, PetscViewer viewer)
764 {
765   Mat_MPIDense     *mdn = (Mat_MPIDense *)mat->data;
766   PetscMPIInt       rank;
767   PetscViewerType   vtype;
768   PetscBool         iascii, isdraw;
769   PetscViewer       sviewer;
770   PetscViewerFormat format;
771 
772   PetscFunctionBegin;
773   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
774   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
775   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
776   if (iascii) {
777     PetscCall(PetscViewerGetType(viewer, &vtype));
778     PetscCall(PetscViewerGetFormat(viewer, &format));
779     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
780       MatInfo info;
781       PetscCall(MatGetInfo(mat, MAT_LOCAL, &info));
782       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
783       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "  [%d] local rows %" PetscInt_FMT " nz %" PetscInt_FMT " nz alloced %" PetscInt_FMT " mem %" PetscInt_FMT " \n", rank, mat->rmap->n, (PetscInt)info.nz_used, (PetscInt)info.nz_allocated,
784                                                    (PetscInt)info.memory));
785       PetscCall(PetscViewerFlush(viewer));
786       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
787       if (mdn->Mvctx) PetscCall(PetscSFView(mdn->Mvctx, viewer));
788       PetscFunctionReturn(PETSC_SUCCESS);
789     } else if (format == PETSC_VIEWER_ASCII_INFO) {
790       PetscFunctionReturn(PETSC_SUCCESS);
791     }
792   } else if (isdraw) {
793     PetscDraw draw;
794     PetscBool isnull;
795 
796     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
797     PetscCall(PetscDrawIsNull(draw, &isnull));
798     if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
799   }
800 
801   {
802     /* assemble the entire matrix onto first processor. */
803     Mat          A;
804     PetscInt     M = mat->rmap->N, N = mat->cmap->N, m, row, i, nz;
805     PetscInt    *cols;
806     PetscScalar *vals;
807 
808     PetscCall(MatCreate(PetscObjectComm((PetscObject)mat), &A));
809     if (rank == 0) {
810       PetscCall(MatSetSizes(A, M, N, M, N));
811     } else {
812       PetscCall(MatSetSizes(A, 0, 0, M, N));
813     }
814     /* Since this is a temporary matrix, MATMPIDENSE instead of ((PetscObject)A)->type_name here is probably acceptable. */
815     PetscCall(MatSetType(A, MATMPIDENSE));
816     PetscCall(MatMPIDenseSetPreallocation(A, NULL));
817 
818     /* Copy the matrix ... This isn't the most efficient means,
819        but it's quick for now */
820     A->insertmode = INSERT_VALUES;
821 
822     row = mat->rmap->rstart;
823     m   = mdn->A->rmap->n;
824     for (i = 0; i < m; i++) {
825       PetscCall(MatGetRow_MPIDense(mat, row, &nz, &cols, &vals));
826       PetscCall(MatSetValues_MPIDense(A, 1, &row, nz, cols, vals, INSERT_VALUES));
827       PetscCall(MatRestoreRow_MPIDense(mat, row, &nz, &cols, &vals));
828       row++;
829     }
830 
831     PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
832     PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
833     PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
834     if (rank == 0) {
835       PetscCall(PetscObjectSetName((PetscObject)((Mat_MPIDense *)A->data)->A, ((PetscObject)mat)->name));
836       PetscCall(MatView_SeqDense(((Mat_MPIDense *)A->data)->A, sviewer));
837     }
838     PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
839     PetscCall(MatDestroy(&A));
840   }
841   PetscFunctionReturn(PETSC_SUCCESS);
842 }
843 
844 static PetscErrorCode MatView_MPIDense(Mat mat, PetscViewer viewer)
845 {
846   PetscBool iascii, isbinary, isdraw, issocket;
847 
848   PetscFunctionBegin;
849   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
850   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
851   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSOCKET, &issocket));
852   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
853 
854   if (iascii || issocket || isdraw) {
855     PetscCall(MatView_MPIDense_ASCIIorDraworSocket(mat, viewer));
856   } else if (isbinary) PetscCall(MatView_Dense_Binary(mat, viewer));
857   PetscFunctionReturn(PETSC_SUCCESS);
858 }
859 
860 static PetscErrorCode MatGetInfo_MPIDense(Mat A, MatInfoType flag, MatInfo *info)
861 {
862   Mat_MPIDense  *mat = (Mat_MPIDense *)A->data;
863   Mat            mdn = mat->A;
864   PetscLogDouble isend[5], irecv[5];
865 
866   PetscFunctionBegin;
867   info->block_size = 1.0;
868 
869   PetscCall(MatGetInfo(mdn, MAT_LOCAL, info));
870 
871   isend[0] = info->nz_used;
872   isend[1] = info->nz_allocated;
873   isend[2] = info->nz_unneeded;
874   isend[3] = info->memory;
875   isend[4] = info->mallocs;
876   if (flag == MAT_LOCAL) {
877     info->nz_used      = isend[0];
878     info->nz_allocated = isend[1];
879     info->nz_unneeded  = isend[2];
880     info->memory       = isend[3];
881     info->mallocs      = isend[4];
882   } else if (flag == MAT_GLOBAL_MAX) {
883     PetscCall(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)A)));
884 
885     info->nz_used      = irecv[0];
886     info->nz_allocated = irecv[1];
887     info->nz_unneeded  = irecv[2];
888     info->memory       = irecv[3];
889     info->mallocs      = irecv[4];
890   } else if (flag == MAT_GLOBAL_SUM) {
891     PetscCall(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)A)));
892 
893     info->nz_used      = irecv[0];
894     info->nz_allocated = irecv[1];
895     info->nz_unneeded  = irecv[2];
896     info->memory       = irecv[3];
897     info->mallocs      = irecv[4];
898   }
899   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
900   info->fill_ratio_needed = 0;
901   info->factor_mallocs    = 0;
902   PetscFunctionReturn(PETSC_SUCCESS);
903 }
904 
905 static PetscErrorCode MatSetOption_MPIDense(Mat A, MatOption op, PetscBool flg)
906 {
907   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
908 
909   PetscFunctionBegin;
910   switch (op) {
911   case MAT_NEW_NONZERO_LOCATIONS:
912   case MAT_NEW_NONZERO_LOCATION_ERR:
913   case MAT_NEW_NONZERO_ALLOCATION_ERR:
914     MatCheckPreallocated(A, 1);
915     PetscCall(MatSetOption(a->A, op, flg));
916     break;
917   case MAT_ROW_ORIENTED:
918     MatCheckPreallocated(A, 1);
919     a->roworiented = flg;
920     PetscCall(MatSetOption(a->A, op, flg));
921     break;
922   case MAT_FORCE_DIAGONAL_ENTRIES:
923   case MAT_KEEP_NONZERO_PATTERN:
924   case MAT_USE_HASH_TABLE:
925   case MAT_SORTED_FULL:
926     PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
927     break;
928   case MAT_IGNORE_OFF_PROC_ENTRIES:
929     a->donotstash = flg;
930     break;
931   case MAT_SYMMETRIC:
932   case MAT_STRUCTURALLY_SYMMETRIC:
933   case MAT_HERMITIAN:
934   case MAT_SYMMETRY_ETERNAL:
935   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
936   case MAT_SPD:
937   case MAT_IGNORE_LOWER_TRIANGULAR:
938   case MAT_IGNORE_ZERO_ENTRIES:
939   case MAT_SPD_ETERNAL:
940     /* if the diagonal matrix is square it inherits some of the properties above */
941     PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
942     break;
943   default:
944     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unknown option %s", MatOptions[op]);
945   }
946   PetscFunctionReturn(PETSC_SUCCESS);
947 }
948 
949 static PetscErrorCode MatDiagonalScale_MPIDense(Mat A, Vec ll, Vec rr)
950 {
951   Mat_MPIDense      *mdn = (Mat_MPIDense *)A->data;
952   const PetscScalar *l;
953   PetscScalar        x, *v, *vv, *r;
954   PetscInt           i, j, s2a, s3a, s2, s3, m = mdn->A->rmap->n, n = mdn->A->cmap->n, lda;
955 
956   PetscFunctionBegin;
957   PetscCall(MatDenseGetArray(mdn->A, &vv));
958   PetscCall(MatDenseGetLDA(mdn->A, &lda));
959   PetscCall(MatGetLocalSize(A, &s2, &s3));
960   if (ll) {
961     PetscCall(VecGetLocalSize(ll, &s2a));
962     PetscCheck(s2a == s2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Left scaling vector non-conforming local size, %" PetscInt_FMT " != %" PetscInt_FMT, s2a, s2);
963     PetscCall(VecGetArrayRead(ll, &l));
964     for (i = 0; i < m; i++) {
965       x = l[i];
966       v = vv + i;
967       for (j = 0; j < n; j++) {
968         (*v) *= x;
969         v += lda;
970       }
971     }
972     PetscCall(VecRestoreArrayRead(ll, &l));
973     PetscCall(PetscLogFlops(1.0 * n * m));
974   }
975   if (rr) {
976     const PetscScalar *ar;
977 
978     PetscCall(VecGetLocalSize(rr, &s3a));
979     PetscCheck(s3a == s3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Right scaling vec non-conforming local size, %" PetscInt_FMT " != %" PetscInt_FMT ".", s3a, s3);
980     PetscCall(VecGetArrayRead(rr, &ar));
981     if (!mdn->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(A));
982     PetscCall(VecGetArray(mdn->lvec, &r));
983     PetscCall(PetscSFBcastBegin(mdn->Mvctx, MPIU_SCALAR, ar, r, MPI_REPLACE));
984     PetscCall(PetscSFBcastEnd(mdn->Mvctx, MPIU_SCALAR, ar, r, MPI_REPLACE));
985     PetscCall(VecRestoreArrayRead(rr, &ar));
986     for (i = 0; i < n; i++) {
987       x = r[i];
988       v = vv + i * lda;
989       for (j = 0; j < m; j++) (*v++) *= x;
990     }
991     PetscCall(VecRestoreArray(mdn->lvec, &r));
992     PetscCall(PetscLogFlops(1.0 * n * m));
993   }
994   PetscCall(MatDenseRestoreArray(mdn->A, &vv));
995   PetscFunctionReturn(PETSC_SUCCESS);
996 }
997 
998 static PetscErrorCode MatNorm_MPIDense(Mat A, NormType type, PetscReal *nrm)
999 {
1000   Mat_MPIDense      *mdn = (Mat_MPIDense *)A->data;
1001   PetscInt           i, j;
1002   PetscMPIInt        size;
1003   PetscReal          sum = 0.0;
1004   const PetscScalar *av, *v;
1005 
1006   PetscFunctionBegin;
1007   PetscCall(MatDenseGetArrayRead(mdn->A, &av));
1008   v = av;
1009   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
1010   if (size == 1) {
1011     PetscCall(MatNorm(mdn->A, type, nrm));
1012   } else {
1013     if (type == NORM_FROBENIUS) {
1014       for (i = 0; i < mdn->A->cmap->n * mdn->A->rmap->n; i++) {
1015         sum += PetscRealPart(PetscConj(*v) * (*v));
1016         v++;
1017       }
1018       PetscCall(MPIU_Allreduce(&sum, nrm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)A)));
1019       *nrm = PetscSqrtReal(*nrm);
1020       PetscCall(PetscLogFlops(2.0 * mdn->A->cmap->n * mdn->A->rmap->n));
1021     } else if (type == NORM_1) {
1022       PetscReal *tmp, *tmp2;
1023       PetscCall(PetscCalloc2(A->cmap->N, &tmp, A->cmap->N, &tmp2));
1024       *nrm = 0.0;
1025       v    = av;
1026       for (j = 0; j < mdn->A->cmap->n; j++) {
1027         for (i = 0; i < mdn->A->rmap->n; i++) {
1028           tmp[j] += PetscAbsScalar(*v);
1029           v++;
1030         }
1031       }
1032       PetscCall(MPIU_Allreduce(tmp, tmp2, A->cmap->N, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)A)));
1033       for (j = 0; j < A->cmap->N; j++) {
1034         if (tmp2[j] > *nrm) *nrm = tmp2[j];
1035       }
1036       PetscCall(PetscFree2(tmp, tmp2));
1037       PetscCall(PetscLogFlops(A->cmap->n * A->rmap->n));
1038     } else if (type == NORM_INFINITY) { /* max row norm */
1039       PetscReal ntemp;
1040       PetscCall(MatNorm(mdn->A, type, &ntemp));
1041       PetscCall(MPIU_Allreduce(&ntemp, nrm, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)A)));
1042     } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "No support for two norm");
1043   }
1044   PetscCall(MatDenseRestoreArrayRead(mdn->A, &av));
1045   PetscFunctionReturn(PETSC_SUCCESS);
1046 }
1047 
1048 static PetscErrorCode MatTranspose_MPIDense(Mat A, MatReuse reuse, Mat *matout)
1049 {
1050   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1051   Mat           B;
1052   PetscInt      M = A->rmap->N, N = A->cmap->N, m, n, *rwork, rstart = A->rmap->rstart;
1053   PetscInt      j, i, lda;
1054   PetscScalar  *v;
1055 
1056   PetscFunctionBegin;
1057   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *matout));
1058   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_INPLACE_MATRIX) {
1059     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
1060     PetscCall(MatSetSizes(B, A->cmap->n, A->rmap->n, N, M));
1061     PetscCall(MatSetType(B, ((PetscObject)A)->type_name));
1062     PetscCall(MatMPIDenseSetPreallocation(B, NULL));
1063   } else B = *matout;
1064 
1065   m = a->A->rmap->n;
1066   n = a->A->cmap->n;
1067   PetscCall(MatDenseGetArrayRead(a->A, (const PetscScalar **)&v));
1068   PetscCall(MatDenseGetLDA(a->A, &lda));
1069   PetscCall(PetscMalloc1(m, &rwork));
1070   for (i = 0; i < m; i++) rwork[i] = rstart + i;
1071   for (j = 0; j < n; j++) {
1072     PetscCall(MatSetValues(B, 1, &j, m, rwork, v, INSERT_VALUES));
1073     v = PetscSafePointerPlusOffset(v, lda);
1074   }
1075   PetscCall(MatDenseRestoreArrayRead(a->A, (const PetscScalar **)&v));
1076   PetscCall(PetscFree(rwork));
1077   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
1078   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
1079   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1080     *matout = B;
1081   } else {
1082     PetscCall(MatHeaderMerge(A, &B));
1083   }
1084   PetscFunctionReturn(PETSC_SUCCESS);
1085 }
1086 
1087 static PetscErrorCode       MatDuplicate_MPIDense(Mat, MatDuplicateOption, Mat *);
1088 PETSC_INTERN PetscErrorCode MatScale_MPIDense(Mat, PetscScalar);
1089 
1090 static PetscErrorCode MatSetUp_MPIDense(Mat A)
1091 {
1092   PetscFunctionBegin;
1093   PetscCall(PetscLayoutSetUp(A->rmap));
1094   PetscCall(PetscLayoutSetUp(A->cmap));
1095   if (!A->preallocated) PetscCall(MatMPIDenseSetPreallocation(A, NULL));
1096   PetscFunctionReturn(PETSC_SUCCESS);
1097 }
1098 
1099 static PetscErrorCode MatAXPY_MPIDense(Mat Y, PetscScalar alpha, Mat X, MatStructure str)
1100 {
1101   Mat_MPIDense *A = (Mat_MPIDense *)Y->data, *B = (Mat_MPIDense *)X->data;
1102 
1103   PetscFunctionBegin;
1104   PetscCall(MatAXPY(A->A, alpha, B->A, str));
1105   PetscFunctionReturn(PETSC_SUCCESS);
1106 }
1107 
1108 static PetscErrorCode MatConjugate_MPIDense(Mat mat)
1109 {
1110   Mat_MPIDense *a = (Mat_MPIDense *)mat->data;
1111 
1112   PetscFunctionBegin;
1113   PetscCall(MatConjugate(a->A));
1114   PetscFunctionReturn(PETSC_SUCCESS);
1115 }
1116 
1117 static PetscErrorCode MatRealPart_MPIDense(Mat A)
1118 {
1119   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1120 
1121   PetscFunctionBegin;
1122   PetscCall(MatRealPart(a->A));
1123   PetscFunctionReturn(PETSC_SUCCESS);
1124 }
1125 
1126 static PetscErrorCode MatImaginaryPart_MPIDense(Mat A)
1127 {
1128   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1129 
1130   PetscFunctionBegin;
1131   PetscCall(MatImaginaryPart(a->A));
1132   PetscFunctionReturn(PETSC_SUCCESS);
1133 }
1134 
1135 static PetscErrorCode MatGetColumnVector_MPIDense(Mat A, Vec v, PetscInt col)
1136 {
1137   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1138 
1139   PetscFunctionBegin;
1140   PetscCheck(a->A, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Missing local matrix");
1141   PetscCheck(a->A->ops->getcolumnvector, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Missing get column operation");
1142   PetscCall((*a->A->ops->getcolumnvector)(a->A, v, col));
1143   PetscFunctionReturn(PETSC_SUCCESS);
1144 }
1145 
1146 PETSC_INTERN PetscErrorCode MatGetColumnReductions_SeqDense(Mat, PetscInt, PetscReal *);
1147 
1148 static PetscErrorCode MatGetColumnReductions_MPIDense(Mat A, PetscInt type, PetscReal *reductions)
1149 {
1150   PetscInt      i, m, n;
1151   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1152   PetscReal    *work;
1153 
1154   PetscFunctionBegin;
1155   PetscCall(MatGetSize(A, &m, &n));
1156   PetscCall(PetscMalloc1(n, &work));
1157   if (type == REDUCTION_MEAN_REALPART) {
1158     PetscCall(MatGetColumnReductions_SeqDense(a->A, (PetscInt)REDUCTION_SUM_REALPART, work));
1159   } else if (type == REDUCTION_MEAN_IMAGINARYPART) {
1160     PetscCall(MatGetColumnReductions_SeqDense(a->A, (PetscInt)REDUCTION_SUM_IMAGINARYPART, work));
1161   } else {
1162     PetscCall(MatGetColumnReductions_SeqDense(a->A, type, work));
1163   }
1164   if (type == NORM_2) {
1165     for (i = 0; i < n; i++) work[i] *= work[i];
1166   }
1167   if (type == NORM_INFINITY) {
1168     PetscCall(MPIU_Allreduce(work, reductions, n, MPIU_REAL, MPIU_MAX, A->hdr.comm));
1169   } else {
1170     PetscCall(MPIU_Allreduce(work, reductions, n, MPIU_REAL, MPIU_SUM, A->hdr.comm));
1171   }
1172   PetscCall(PetscFree(work));
1173   if (type == NORM_2) {
1174     for (i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
1175   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
1176     for (i = 0; i < n; i++) reductions[i] /= m;
1177   }
1178   PetscFunctionReturn(PETSC_SUCCESS);
1179 }
1180 
1181 static PetscErrorCode MatSetRandom_MPIDense(Mat x, PetscRandom rctx)
1182 {
1183   Mat_MPIDense *d = (Mat_MPIDense *)x->data;
1184 
1185   PetscFunctionBegin;
1186   PetscCall(MatSetRandom(d->A, rctx));
1187 #if defined(PETSC_HAVE_DEVICE)
1188   x->offloadmask = d->A->offloadmask;
1189 #endif
1190   PetscFunctionReturn(PETSC_SUCCESS);
1191 }
1192 
1193 static PetscErrorCode MatMissingDiagonal_MPIDense(Mat A, PetscBool *missing, PetscInt *d)
1194 {
1195   PetscFunctionBegin;
1196   *missing = PETSC_FALSE;
1197   PetscFunctionReturn(PETSC_SUCCESS);
1198 }
1199 
1200 static PetscErrorCode MatMatTransposeMultSymbolic_MPIDense_MPIDense(Mat, Mat, PetscReal, Mat);
1201 static PetscErrorCode MatMatTransposeMultNumeric_MPIDense_MPIDense(Mat, Mat, Mat);
1202 static PetscErrorCode MatTransposeMatMultSymbolic_MPIDense_MPIDense(Mat, Mat, PetscReal, Mat);
1203 static PetscErrorCode MatTransposeMatMultNumeric_MPIDense_MPIDense(Mat, Mat, Mat);
1204 static PetscErrorCode MatEqual_MPIDense(Mat, Mat, PetscBool *);
1205 static PetscErrorCode MatLoad_MPIDense(Mat, PetscViewer);
1206 static PetscErrorCode MatProductSetFromOptions_MPIDense(Mat);
1207 
1208 static struct _MatOps MatOps_Values = {MatSetValues_MPIDense,
1209                                        MatGetRow_MPIDense,
1210                                        MatRestoreRow_MPIDense,
1211                                        MatMult_MPIDense,
1212                                        /*  4*/ MatMultAdd_MPIDense,
1213                                        MatMultTranspose_MPIDense,
1214                                        MatMultTransposeAdd_MPIDense,
1215                                        NULL,
1216                                        NULL,
1217                                        NULL,
1218                                        /* 10*/ NULL,
1219                                        NULL,
1220                                        NULL,
1221                                        NULL,
1222                                        MatTranspose_MPIDense,
1223                                        /* 15*/ MatGetInfo_MPIDense,
1224                                        MatEqual_MPIDense,
1225                                        MatGetDiagonal_MPIDense,
1226                                        MatDiagonalScale_MPIDense,
1227                                        MatNorm_MPIDense,
1228                                        /* 20*/ MatAssemblyBegin_MPIDense,
1229                                        MatAssemblyEnd_MPIDense,
1230                                        MatSetOption_MPIDense,
1231                                        MatZeroEntries_MPIDense,
1232                                        /* 24*/ MatZeroRows_MPIDense,
1233                                        NULL,
1234                                        NULL,
1235                                        NULL,
1236                                        NULL,
1237                                        /* 29*/ MatSetUp_MPIDense,
1238                                        NULL,
1239                                        NULL,
1240                                        MatGetDiagonalBlock_MPIDense,
1241                                        NULL,
1242                                        /* 34*/ MatDuplicate_MPIDense,
1243                                        NULL,
1244                                        NULL,
1245                                        NULL,
1246                                        NULL,
1247                                        /* 39*/ MatAXPY_MPIDense,
1248                                        MatCreateSubMatrices_MPIDense,
1249                                        NULL,
1250                                        MatGetValues_MPIDense,
1251                                        MatCopy_MPIDense,
1252                                        /* 44*/ NULL,
1253                                        MatScale_MPIDense,
1254                                        MatShift_MPIDense,
1255                                        NULL,
1256                                        NULL,
1257                                        /* 49*/ MatSetRandom_MPIDense,
1258                                        NULL,
1259                                        NULL,
1260                                        NULL,
1261                                        NULL,
1262                                        /* 54*/ NULL,
1263                                        NULL,
1264                                        NULL,
1265                                        NULL,
1266                                        NULL,
1267                                        /* 59*/ MatCreateSubMatrix_MPIDense,
1268                                        MatDestroy_MPIDense,
1269                                        MatView_MPIDense,
1270                                        NULL,
1271                                        NULL,
1272                                        /* 64*/ NULL,
1273                                        NULL,
1274                                        NULL,
1275                                        NULL,
1276                                        NULL,
1277                                        /* 69*/ NULL,
1278                                        NULL,
1279                                        NULL,
1280                                        NULL,
1281                                        NULL,
1282                                        /* 74*/ NULL,
1283                                        NULL,
1284                                        NULL,
1285                                        NULL,
1286                                        NULL,
1287                                        /* 79*/ NULL,
1288                                        NULL,
1289                                        NULL,
1290                                        NULL,
1291                                        /* 83*/ MatLoad_MPIDense,
1292                                        NULL,
1293                                        NULL,
1294                                        NULL,
1295                                        NULL,
1296                                        NULL,
1297                                        /* 89*/ NULL,
1298                                        NULL,
1299                                        NULL,
1300                                        NULL,
1301                                        NULL,
1302                                        /* 94*/ NULL,
1303                                        NULL,
1304                                        MatMatTransposeMultSymbolic_MPIDense_MPIDense,
1305                                        MatMatTransposeMultNumeric_MPIDense_MPIDense,
1306                                        NULL,
1307                                        /* 99*/ MatProductSetFromOptions_MPIDense,
1308                                        NULL,
1309                                        NULL,
1310                                        MatConjugate_MPIDense,
1311                                        NULL,
1312                                        /*104*/ NULL,
1313                                        MatRealPart_MPIDense,
1314                                        MatImaginaryPart_MPIDense,
1315                                        NULL,
1316                                        NULL,
1317                                        /*109*/ NULL,
1318                                        NULL,
1319                                        NULL,
1320                                        MatGetColumnVector_MPIDense,
1321                                        MatMissingDiagonal_MPIDense,
1322                                        /*114*/ NULL,
1323                                        NULL,
1324                                        NULL,
1325                                        NULL,
1326                                        NULL,
1327                                        /*119*/ NULL,
1328                                        NULL,
1329                                        MatMultHermitianTranspose_MPIDense,
1330                                        MatMultHermitianTransposeAdd_MPIDense,
1331                                        NULL,
1332                                        /*124*/ NULL,
1333                                        MatGetColumnReductions_MPIDense,
1334                                        NULL,
1335                                        NULL,
1336                                        NULL,
1337                                        /*129*/ NULL,
1338                                        NULL,
1339                                        MatTransposeMatMultSymbolic_MPIDense_MPIDense,
1340                                        MatTransposeMatMultNumeric_MPIDense_MPIDense,
1341                                        NULL,
1342                                        /*134*/ NULL,
1343                                        NULL,
1344                                        NULL,
1345                                        NULL,
1346                                        NULL,
1347                                        /*139*/ NULL,
1348                                        NULL,
1349                                        NULL,
1350                                        NULL,
1351                                        NULL,
1352                                        MatCreateMPIMatConcatenateSeqMat_MPIDense,
1353                                        /*145*/ NULL,
1354                                        NULL,
1355                                        NULL,
1356                                        NULL,
1357                                        NULL,
1358                                        /*150*/ NULL,
1359                                        NULL,
1360                                        NULL};
1361 
1362 static PetscErrorCode MatMPIDenseSetPreallocation_MPIDense(Mat mat, PetscScalar *data)
1363 {
1364   Mat_MPIDense *a     = (Mat_MPIDense *)mat->data;
1365   MatType       mtype = MATSEQDENSE;
1366 
1367   PetscFunctionBegin;
1368   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)mat), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1369   PetscCall(PetscLayoutSetUp(mat->rmap));
1370   PetscCall(PetscLayoutSetUp(mat->cmap));
1371   if (!a->A) {
1372     PetscCall(MatCreate(PETSC_COMM_SELF, &a->A));
1373     PetscCall(MatSetSizes(a->A, mat->rmap->n, mat->cmap->N, mat->rmap->n, mat->cmap->N));
1374   }
1375 #if defined(PETSC_HAVE_CUDA)
1376   PetscBool iscuda;
1377   PetscCall(PetscObjectTypeCompare((PetscObject)mat, MATMPIDENSECUDA, &iscuda));
1378   if (iscuda) mtype = MATSEQDENSECUDA;
1379 #endif
1380 #if defined(PETSC_HAVE_HIP)
1381   PetscBool iship;
1382   PetscCall(PetscObjectTypeCompare((PetscObject)mat, MATMPIDENSEHIP, &iship));
1383   if (iship) mtype = MATSEQDENSEHIP;
1384 #endif
1385   PetscCall(MatSetType(a->A, mtype));
1386   PetscCall(MatSeqDenseSetPreallocation(a->A, data));
1387 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1388   mat->offloadmask = a->A->offloadmask;
1389 #endif
1390   mat->preallocated = PETSC_TRUE;
1391   mat->assembled    = PETSC_TRUE;
1392   PetscFunctionReturn(PETSC_SUCCESS);
1393 }
1394 
1395 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIDense(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
1396 {
1397   Mat B, C;
1398 
1399   PetscFunctionBegin;
1400   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &C));
1401   PetscCall(MatConvert_SeqAIJ_SeqDense(C, MATSEQDENSE, MAT_INITIAL_MATRIX, &B));
1402   PetscCall(MatDestroy(&C));
1403   if (reuse == MAT_REUSE_MATRIX) {
1404     C = *newmat;
1405   } else C = NULL;
1406   PetscCall(MatCreateMPIMatConcatenateSeqMat(PetscObjectComm((PetscObject)A), B, A->cmap->n, !C ? MAT_INITIAL_MATRIX : MAT_REUSE_MATRIX, &C));
1407   PetscCall(MatDestroy(&B));
1408   if (reuse == MAT_INPLACE_MATRIX) {
1409     PetscCall(MatHeaderReplace(A, &C));
1410   } else if (reuse == MAT_INITIAL_MATRIX) *newmat = C;
1411   PetscFunctionReturn(PETSC_SUCCESS);
1412 }
1413 
1414 static PetscErrorCode MatConvert_MPIDense_MPIAIJ(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
1415 {
1416   Mat B, C;
1417 
1418   PetscFunctionBegin;
1419   PetscCall(MatDenseGetLocalMatrix(A, &C));
1420   PetscCall(MatConvert_SeqDense_SeqAIJ(C, MATSEQAIJ, MAT_INITIAL_MATRIX, &B));
1421   if (reuse == MAT_REUSE_MATRIX) {
1422     C = *newmat;
1423   } else C = NULL;
1424   PetscCall(MatCreateMPIMatConcatenateSeqMat(PetscObjectComm((PetscObject)A), B, A->cmap->n, !C ? MAT_INITIAL_MATRIX : MAT_REUSE_MATRIX, &C));
1425   PetscCall(MatDestroy(&B));
1426   if (reuse == MAT_INPLACE_MATRIX) {
1427     PetscCall(MatHeaderReplace(A, &C));
1428   } else if (reuse == MAT_INITIAL_MATRIX) *newmat = C;
1429   PetscFunctionReturn(PETSC_SUCCESS);
1430 }
1431 
1432 #if defined(PETSC_HAVE_ELEMENTAL)
1433 PETSC_INTERN PetscErrorCode MatConvert_MPIDense_Elemental(Mat A, MatType newtype, MatReuse reuse, Mat *newmat)
1434 {
1435   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1436   Mat           mat_elemental;
1437   PetscScalar  *v;
1438   PetscInt      m = A->rmap->n, N = A->cmap->N, rstart = A->rmap->rstart, i, *rows, *cols, lda;
1439 
1440   PetscFunctionBegin;
1441   if (reuse == MAT_REUSE_MATRIX) {
1442     mat_elemental = *newmat;
1443     PetscCall(MatZeroEntries(*newmat));
1444   } else {
1445     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &mat_elemental));
1446     PetscCall(MatSetSizes(mat_elemental, PETSC_DECIDE, PETSC_DECIDE, A->rmap->N, A->cmap->N));
1447     PetscCall(MatSetType(mat_elemental, MATELEMENTAL));
1448     PetscCall(MatSetUp(mat_elemental));
1449     PetscCall(MatSetOption(mat_elemental, MAT_ROW_ORIENTED, PETSC_FALSE));
1450   }
1451 
1452   PetscCall(PetscMalloc2(m, &rows, N, &cols));
1453   for (i = 0; i < N; i++) cols[i] = i;
1454   for (i = 0; i < m; i++) rows[i] = rstart + i;
1455 
1456   /* PETSc-Elemental interface uses axpy for setting off-processor entries, only ADD_VALUES is allowed */
1457   PetscCall(MatDenseGetArray(A, &v));
1458   PetscCall(MatDenseGetLDA(a->A, &lda));
1459   if (lda == m) PetscCall(MatSetValues(mat_elemental, m, rows, N, cols, v, ADD_VALUES));
1460   else {
1461     for (i = 0; i < N; i++) PetscCall(MatSetValues(mat_elemental, m, rows, 1, &i, v + lda * i, ADD_VALUES));
1462   }
1463   PetscCall(MatAssemblyBegin(mat_elemental, MAT_FINAL_ASSEMBLY));
1464   PetscCall(MatAssemblyEnd(mat_elemental, MAT_FINAL_ASSEMBLY));
1465   PetscCall(MatDenseRestoreArray(A, &v));
1466   PetscCall(PetscFree2(rows, cols));
1467 
1468   if (reuse == MAT_INPLACE_MATRIX) {
1469     PetscCall(MatHeaderReplace(A, &mat_elemental));
1470   } else {
1471     *newmat = mat_elemental;
1472   }
1473   PetscFunctionReturn(PETSC_SUCCESS);
1474 }
1475 #endif
1476 
1477 static PetscErrorCode MatDenseGetColumn_MPIDense(Mat A, PetscInt col, PetscScalar **vals)
1478 {
1479   Mat_MPIDense *mat = (Mat_MPIDense *)A->data;
1480 
1481   PetscFunctionBegin;
1482   PetscCall(MatDenseGetColumn(mat->A, col, vals));
1483   PetscFunctionReturn(PETSC_SUCCESS);
1484 }
1485 
1486 static PetscErrorCode MatDenseRestoreColumn_MPIDense(Mat A, PetscScalar **vals)
1487 {
1488   Mat_MPIDense *mat = (Mat_MPIDense *)A->data;
1489 
1490   PetscFunctionBegin;
1491   PetscCall(MatDenseRestoreColumn(mat->A, vals));
1492   PetscFunctionReturn(PETSC_SUCCESS);
1493 }
1494 
1495 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIDense(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
1496 {
1497   Mat_MPIDense *mat;
1498   PetscInt      m, nloc, N;
1499 
1500   PetscFunctionBegin;
1501   PetscCall(MatGetSize(inmat, &m, &N));
1502   PetscCall(MatGetLocalSize(inmat, NULL, &nloc));
1503   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
1504     PetscInt sum;
1505 
1506     if (n == PETSC_DECIDE) PetscCall(PetscSplitOwnership(comm, &n, &N));
1507     /* Check sum(n) = N */
1508     PetscCall(MPIU_Allreduce(&n, &sum, 1, MPIU_INT, MPI_SUM, comm));
1509     PetscCheck(sum == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Sum of local columns %" PetscInt_FMT " != global columns %" PetscInt_FMT, sum, N);
1510 
1511     PetscCall(MatCreateDense(comm, m, n, PETSC_DETERMINE, N, NULL, outmat));
1512     PetscCall(MatSetOption(*outmat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
1513   }
1514 
1515   /* numeric phase */
1516   mat = (Mat_MPIDense *)(*outmat)->data;
1517   PetscCall(MatCopy(inmat, mat->A, SAME_NONZERO_PATTERN));
1518   PetscFunctionReturn(PETSC_SUCCESS);
1519 }
1520 
1521 PetscErrorCode MatDenseGetColumnVec_MPIDense(Mat A, PetscInt col, Vec *v)
1522 {
1523   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1524   PetscInt      lda;
1525 
1526   PetscFunctionBegin;
1527   PetscCheck(!a->vecinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
1528   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1529   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
1530   a->vecinuse = col + 1;
1531   PetscCall(MatDenseGetLDA(a->A, &lda));
1532   PetscCall(MatDenseGetArray(a->A, (PetscScalar **)&a->ptrinuse));
1533   PetscCall(VecPlaceArray(a->cvec, PetscSafePointerPlusOffset(a->ptrinuse, (size_t)col * (size_t)lda)));
1534   *v = a->cvec;
1535   PetscFunctionReturn(PETSC_SUCCESS);
1536 }
1537 
1538 PetscErrorCode MatDenseRestoreColumnVec_MPIDense(Mat A, PetscInt col, Vec *v)
1539 {
1540   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1541 
1542   PetscFunctionBegin;
1543   PetscCheck(a->vecinuse, PETSC_COMM_SELF, PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
1544   PetscCheck(a->cvec, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing internal column vector");
1545   VecCheckAssembled(a->cvec);
1546   a->vecinuse = 0;
1547   PetscCall(MatDenseRestoreArray(a->A, (PetscScalar **)&a->ptrinuse));
1548   PetscCall(VecResetArray(a->cvec));
1549   if (v) *v = NULL;
1550   PetscFunctionReturn(PETSC_SUCCESS);
1551 }
1552 
1553 PetscErrorCode MatDenseGetColumnVecRead_MPIDense(Mat A, PetscInt col, Vec *v)
1554 {
1555   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1556   PetscInt      lda;
1557 
1558   PetscFunctionBegin;
1559   PetscCheck(!a->vecinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
1560   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1561   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
1562   a->vecinuse = col + 1;
1563   PetscCall(MatDenseGetLDA(a->A, &lda));
1564   PetscCall(MatDenseGetArrayRead(a->A, &a->ptrinuse));
1565   PetscCall(VecPlaceArray(a->cvec, PetscSafePointerPlusOffset(a->ptrinuse, (size_t)col * (size_t)lda)));
1566   PetscCall(VecLockReadPush(a->cvec));
1567   *v = a->cvec;
1568   PetscFunctionReturn(PETSC_SUCCESS);
1569 }
1570 
1571 PetscErrorCode MatDenseRestoreColumnVecRead_MPIDense(Mat A, PetscInt col, Vec *v)
1572 {
1573   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1574 
1575   PetscFunctionBegin;
1576   PetscCheck(a->vecinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
1577   PetscCheck(a->cvec, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing internal column vector");
1578   VecCheckAssembled(a->cvec);
1579   a->vecinuse = 0;
1580   PetscCall(MatDenseRestoreArrayRead(a->A, &a->ptrinuse));
1581   PetscCall(VecLockReadPop(a->cvec));
1582   PetscCall(VecResetArray(a->cvec));
1583   if (v) *v = NULL;
1584   PetscFunctionReturn(PETSC_SUCCESS);
1585 }
1586 
1587 PetscErrorCode MatDenseGetColumnVecWrite_MPIDense(Mat A, PetscInt col, Vec *v)
1588 {
1589   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1590   PetscInt      lda;
1591 
1592   PetscFunctionBegin;
1593   PetscCheck(!a->vecinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
1594   PetscCheck(!a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1595   if (!a->cvec) PetscCall(MatDenseCreateColumnVec_Private(A, &a->cvec));
1596   a->vecinuse = col + 1;
1597   PetscCall(MatDenseGetLDA(a->A, &lda));
1598   PetscCall(MatDenseGetArrayWrite(a->A, (PetscScalar **)&a->ptrinuse));
1599   PetscCall(VecPlaceArray(a->cvec, PetscSafePointerPlusOffset(a->ptrinuse, (size_t)col * (size_t)lda)));
1600   *v = a->cvec;
1601   PetscFunctionReturn(PETSC_SUCCESS);
1602 }
1603 
1604 PetscErrorCode MatDenseRestoreColumnVecWrite_MPIDense(Mat A, PetscInt col, Vec *v)
1605 {
1606   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1607 
1608   PetscFunctionBegin;
1609   PetscCheck(a->vecinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseGetColumnVec() first");
1610   PetscCheck(a->cvec, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing internal column vector");
1611   VecCheckAssembled(a->cvec);
1612   a->vecinuse = 0;
1613   PetscCall(MatDenseRestoreArrayWrite(a->A, (PetscScalar **)&a->ptrinuse));
1614   PetscCall(VecResetArray(a->cvec));
1615   if (v) *v = NULL;
1616   PetscFunctionReturn(PETSC_SUCCESS);
1617 }
1618 
1619 static PetscErrorCode MatDenseGetSubMatrix_MPIDense(Mat A, PetscInt rbegin, PetscInt rend, PetscInt cbegin, PetscInt cend, Mat *v)
1620 {
1621   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1622   Mat_MPIDense *c;
1623   MPI_Comm      comm;
1624   PetscInt      pbegin, pend;
1625 
1626   PetscFunctionBegin;
1627   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1628   PetscCheck(!a->vecinuse, comm, PETSC_ERR_ORDER, "Need to call MatDenseRestoreColumnVec() first");
1629   PetscCheck(!a->matinuse, comm, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1630   pbegin = PetscMax(0, PetscMin(A->rmap->rend, rbegin) - A->rmap->rstart);
1631   pend   = PetscMin(A->rmap->n, PetscMax(0, rend - A->rmap->rstart));
1632   if (!a->cmat) {
1633     PetscCall(MatCreate(comm, &a->cmat));
1634     PetscCall(MatSetType(a->cmat, ((PetscObject)A)->type_name));
1635     if (rend - rbegin == A->rmap->N) PetscCall(PetscLayoutReference(A->rmap, &a->cmat->rmap));
1636     else {
1637       PetscCall(PetscLayoutSetLocalSize(a->cmat->rmap, pend - pbegin));
1638       PetscCall(PetscLayoutSetSize(a->cmat->rmap, rend - rbegin));
1639       PetscCall(PetscLayoutSetUp(a->cmat->rmap));
1640     }
1641     PetscCall(PetscLayoutSetSize(a->cmat->cmap, cend - cbegin));
1642     PetscCall(PetscLayoutSetUp(a->cmat->cmap));
1643   } else {
1644     PetscBool same = (PetscBool)(rend - rbegin == a->cmat->rmap->N);
1645     if (same && a->cmat->rmap->N != A->rmap->N) {
1646       same = (PetscBool)(pend - pbegin == a->cmat->rmap->n);
1647       PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &same, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
1648     }
1649     if (!same) {
1650       PetscCall(PetscLayoutDestroy(&a->cmat->rmap));
1651       PetscCall(PetscLayoutCreate(comm, &a->cmat->rmap));
1652       PetscCall(PetscLayoutSetLocalSize(a->cmat->rmap, pend - pbegin));
1653       PetscCall(PetscLayoutSetSize(a->cmat->rmap, rend - rbegin));
1654       PetscCall(PetscLayoutSetUp(a->cmat->rmap));
1655     }
1656     if (cend - cbegin != a->cmat->cmap->N) {
1657       PetscCall(PetscLayoutDestroy(&a->cmat->cmap));
1658       PetscCall(PetscLayoutCreate(comm, &a->cmat->cmap));
1659       PetscCall(PetscLayoutSetSize(a->cmat->cmap, cend - cbegin));
1660       PetscCall(PetscLayoutSetUp(a->cmat->cmap));
1661     }
1662   }
1663   c = (Mat_MPIDense *)a->cmat->data;
1664   PetscCheck(!c->A, comm, PETSC_ERR_ORDER, "Need to call MatDenseRestoreSubMatrix() first");
1665   PetscCall(MatDenseGetSubMatrix(a->A, pbegin, pend, cbegin, cend, &c->A));
1666 
1667   a->cmat->preallocated = PETSC_TRUE;
1668   a->cmat->assembled    = PETSC_TRUE;
1669 #if defined(PETSC_HAVE_DEVICE)
1670   a->cmat->offloadmask = c->A->offloadmask;
1671 #endif
1672   a->matinuse = cbegin + 1;
1673   *v          = a->cmat;
1674   PetscFunctionReturn(PETSC_SUCCESS);
1675 }
1676 
1677 static PetscErrorCode MatDenseRestoreSubMatrix_MPIDense(Mat A, Mat *v)
1678 {
1679   Mat_MPIDense *a = (Mat_MPIDense *)A->data;
1680   Mat_MPIDense *c;
1681 
1682   PetscFunctionBegin;
1683   PetscCheck(a->matinuse, PetscObjectComm((PetscObject)A), PETSC_ERR_ORDER, "Need to call MatDenseGetSubMatrix() first");
1684   PetscCheck(a->cmat, PetscObjectComm((PetscObject)A), PETSC_ERR_PLIB, "Missing internal matrix");
1685   PetscCheck(*v == a->cmat, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Not the matrix obtained from MatDenseGetSubMatrix()");
1686   a->matinuse = 0;
1687   c           = (Mat_MPIDense *)a->cmat->data;
1688   PetscCall(MatDenseRestoreSubMatrix(a->A, &c->A));
1689   if (v) *v = NULL;
1690 #if defined(PETSC_HAVE_DEVICE)
1691   A->offloadmask = a->A->offloadmask;
1692 #endif
1693   PetscFunctionReturn(PETSC_SUCCESS);
1694 }
1695 
1696 /*MC
1697    MATMPIDENSE - MATMPIDENSE = "mpidense" - A matrix type to be used for distributed dense matrices.
1698 
1699    Options Database Key:
1700 . -mat_type mpidense - sets the matrix type to `MATMPIDENSE` during a call to `MatSetFromOptions()`
1701 
1702   Level: beginner
1703 
1704 .seealso: [](ch_matrices), `Mat`, `MatCreateDense()`, `MATSEQDENSE`, `MATDENSE`
1705 M*/
1706 PetscErrorCode MatCreate_MPIDense(Mat mat)
1707 {
1708   Mat_MPIDense *a;
1709 
1710   PetscFunctionBegin;
1711   PetscCall(PetscNew(&a));
1712   mat->data   = (void *)a;
1713   mat->ops[0] = MatOps_Values;
1714 
1715   mat->insertmode = NOT_SET_VALUES;
1716 
1717   /* build cache for off array entries formed */
1718   a->donotstash = PETSC_FALSE;
1719 
1720   PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)mat), 1, &mat->stash));
1721 
1722   /* stuff used for matrix vector multiply */
1723   a->lvec        = NULL;
1724   a->Mvctx       = NULL;
1725   a->roworiented = PETSC_TRUE;
1726 
1727   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetLDA_C", MatDenseGetLDA_MPIDense));
1728   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseSetLDA_C", MatDenseSetLDA_MPIDense));
1729   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArray_C", MatDenseGetArray_MPIDense));
1730   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArray_C", MatDenseRestoreArray_MPIDense));
1731   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArrayRead_C", MatDenseGetArrayRead_MPIDense));
1732   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArrayRead_C", MatDenseRestoreArrayRead_MPIDense));
1733   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetArrayWrite_C", MatDenseGetArrayWrite_MPIDense));
1734   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreArrayWrite_C", MatDenseRestoreArrayWrite_MPIDense));
1735   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDensePlaceArray_C", MatDensePlaceArray_MPIDense));
1736   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseResetArray_C", MatDenseResetArray_MPIDense));
1737   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseReplaceArray_C", MatDenseReplaceArray_MPIDense));
1738   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVec_C", MatDenseGetColumnVec_MPIDense));
1739   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVec_C", MatDenseRestoreColumnVec_MPIDense));
1740   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVecRead_C", MatDenseGetColumnVecRead_MPIDense));
1741   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVecRead_C", MatDenseRestoreColumnVecRead_MPIDense));
1742   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumnVecWrite_C", MatDenseGetColumnVecWrite_MPIDense));
1743   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumnVecWrite_C", MatDenseRestoreColumnVecWrite_MPIDense));
1744   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetSubMatrix_C", MatDenseGetSubMatrix_MPIDense));
1745   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreSubMatrix_C", MatDenseRestoreSubMatrix_MPIDense));
1746   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpidense_C", MatConvert_MPIAIJ_MPIDense));
1747   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_mpiaij_C", MatConvert_MPIDense_MPIAIJ));
1748 #if defined(PETSC_HAVE_ELEMENTAL)
1749   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_elemental_C", MatConvert_MPIDense_Elemental));
1750 #endif
1751 #if defined(PETSC_HAVE_SCALAPACK)
1752   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_scalapack_C", MatConvert_Dense_ScaLAPACK));
1753 #endif
1754 #if defined(PETSC_HAVE_CUDA)
1755   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_mpidensecuda_C", MatConvert_MPIDense_MPIDenseCUDA));
1756 #endif
1757   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIDenseSetPreallocation_C", MatMPIDenseSetPreallocation_MPIDense));
1758   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaij_mpidense_C", MatProductSetFromOptions_MPIAIJ_MPIDense));
1759   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidense_mpiaij_C", MatProductSetFromOptions_MPIDense_MPIAIJ));
1760 #if defined(PETSC_HAVE_CUDA)
1761   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaijcusparse_mpidense_C", MatProductSetFromOptions_MPIAIJ_MPIDense));
1762   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidense_mpiaijcusparse_C", MatProductSetFromOptions_MPIDense_MPIAIJ));
1763 #endif
1764 #if defined(PETSC_HAVE_HIP)
1765   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpidense_mpidensehip_C", MatConvert_MPIDense_MPIDenseHIP));
1766   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaijhipsparse_mpidense_C", MatProductSetFromOptions_MPIAIJ_MPIDense));
1767   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpidense_mpiaijhipsparse_C", MatProductSetFromOptions_MPIDense_MPIAIJ));
1768 #endif
1769   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseGetColumn_C", MatDenseGetColumn_MPIDense));
1770   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDenseRestoreColumn_C", MatDenseRestoreColumn_MPIDense));
1771   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultAddColumnRange_C", MatMultAddColumnRange_MPIDense));
1772   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultHermitianTransposeColumnRange_C", MatMultHermitianTransposeColumnRange_MPIDense));
1773   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMultHermitianTransposeAddColumnRange_C", MatMultHermitianTransposeAddColumnRange_MPIDense));
1774   PetscCall(PetscObjectChangeTypeName((PetscObject)mat, MATMPIDENSE));
1775   PetscFunctionReturn(PETSC_SUCCESS);
1776 }
1777 
1778 /*MC
1779    MATDENSE - MATDENSE = "dense" - A matrix type to be used for dense matrices.
1780 
1781    This matrix type is identical to `MATSEQDENSE` when constructed with a single process communicator,
1782    and `MATMPIDENSE` otherwise.
1783 
1784    Options Database Key:
1785 . -mat_type dense - sets the matrix type to `MATDENSE` during a call to `MatSetFromOptions()`
1786 
1787   Level: beginner
1788 
1789 .seealso: [](ch_matrices), `Mat`, `MATSEQDENSE`, `MATMPIDENSE`, `MATDENSECUDA`, `MATDENSEHIP`
1790 M*/
1791 
1792 /*@C
1793   MatMPIDenseSetPreallocation - Sets the array used to store the matrix entries
1794 
1795   Collective
1796 
1797   Input Parameters:
1798 + B    - the matrix
1799 - data - optional location of matrix data.  Set to `NULL` for PETSc
1800          to control all matrix memory allocation.
1801 
1802   Level: intermediate
1803 
1804   Notes:
1805   The dense format is fully compatible with standard Fortran
1806   storage by columns.
1807 
1808   The data input variable is intended primarily for Fortran programmers
1809   who wish to allocate their own matrix memory space.  Most users should
1810   set `data` to `NULL`.
1811 
1812 .seealso: [](ch_matrices), `Mat`, `MATMPIDENSE`, `MatCreate()`, `MatCreateSeqDense()`, `MatSetValues()`
1813 @*/
1814 PetscErrorCode MatMPIDenseSetPreallocation(Mat B, PetscScalar *data)
1815 {
1816   PetscFunctionBegin;
1817   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
1818   PetscTryMethod(B, "MatMPIDenseSetPreallocation_C", (Mat, PetscScalar *), (B, data));
1819   PetscFunctionReturn(PETSC_SUCCESS);
1820 }
1821 
1822 /*@
1823   MatDensePlaceArray - Allows one to replace the array in a `MATDENSE` matrix with an
1824   array provided by the user. This is useful to avoid copying an array
1825   into a matrix
1826 
1827   Not Collective
1828 
1829   Input Parameters:
1830 + mat   - the matrix
1831 - array - the array in column major order
1832 
1833   Level: developer
1834 
1835   Note:
1836   You can return to the original array with a call to `MatDenseResetArray()`. The user is responsible for freeing this array; it will not be
1837   freed when the matrix is destroyed.
1838 
1839 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArray()`, `MatDenseResetArray()`, `VecPlaceArray()`, `VecGetArray()`, `VecRestoreArray()`, `VecReplaceArray()`, `VecResetArray()`,
1840           `MatDenseReplaceArray()`
1841 @*/
1842 PetscErrorCode MatDensePlaceArray(Mat mat, const PetscScalar *array)
1843 {
1844   PetscFunctionBegin;
1845   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1846   PetscUseMethod(mat, "MatDensePlaceArray_C", (Mat, const PetscScalar *), (mat, array));
1847   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
1848 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1849   mat->offloadmask = PETSC_OFFLOAD_CPU;
1850 #endif
1851   PetscFunctionReturn(PETSC_SUCCESS);
1852 }
1853 
1854 /*@
1855   MatDenseResetArray - Resets the matrix array to that it previously had before the call to `MatDensePlaceArray()`
1856 
1857   Not Collective
1858 
1859   Input Parameter:
1860 . mat - the matrix
1861 
1862   Level: developer
1863 
1864   Note:
1865   You can only call this after a call to `MatDensePlaceArray()`
1866 
1867 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatDenseGetArray()`, `MatDensePlaceArray()`, `VecPlaceArray()`, `VecGetArray()`, `VecRestoreArray()`, `VecReplaceArray()`, `VecResetArray()`
1868 @*/
1869 PetscErrorCode MatDenseResetArray(Mat mat)
1870 {
1871   PetscFunctionBegin;
1872   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1873   PetscUseMethod(mat, "MatDenseResetArray_C", (Mat), (mat));
1874   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
1875   PetscFunctionReturn(PETSC_SUCCESS);
1876 }
1877 
1878 /*@
1879   MatDenseReplaceArray - Allows one to replace the array in a dense matrix with an
1880   array provided by the user. This is useful to avoid copying an array
1881   into a matrix
1882 
1883   Not Collective
1884 
1885   Input Parameters:
1886 + mat   - the matrix
1887 - array - the array in column major order
1888 
1889   Level: developer
1890 
1891   Note:
1892   The memory passed in MUST be obtained with `PetscMalloc()` and CANNOT be
1893   freed by the user. It will be freed when the matrix is destroyed.
1894 
1895 .seealso: [](ch_matrices), `Mat`, `MatDensePlaceArray()`, `MatDenseGetArray()`, `VecReplaceArray()`
1896 @*/
1897 PetscErrorCode MatDenseReplaceArray(Mat mat, const PetscScalar *array)
1898 {
1899   PetscFunctionBegin;
1900   PetscValidHeaderSpecific(mat, MAT_CLASSID, 1);
1901   PetscUseMethod(mat, "MatDenseReplaceArray_C", (Mat, const PetscScalar *), (mat, array));
1902   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
1903 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP)
1904   mat->offloadmask = PETSC_OFFLOAD_CPU;
1905 #endif
1906   PetscFunctionReturn(PETSC_SUCCESS);
1907 }
1908 
1909 /*@C
1910   MatCreateDense - Creates a matrix in `MATDENSE` format.
1911 
1912   Collective
1913 
1914   Input Parameters:
1915 + comm - MPI communicator
1916 . m    - number of local rows (or `PETSC_DECIDE` to have calculated if `M` is given)
1917 . n    - number of local columns (or `PETSC_DECIDE` to have calculated if `N` is given)
1918 . M    - number of global rows (or `PETSC_DECIDE` to have calculated if `m` is given)
1919 . N    - number of global columns (or `PETSC_DECIDE` to have calculated if `n` is given)
1920 - data - optional location of matrix data.  Set data to `NULL` (`PETSC_NULL_SCALAR` for Fortran users) for PETSc
1921    to control all matrix memory allocation.
1922 
1923   Output Parameter:
1924 . A - the matrix
1925 
1926   Level: intermediate
1927 
1928   Notes:
1929   The dense format is fully compatible with standard Fortran
1930   storage by columns.
1931 
1932   Although local portions of the matrix are stored in column-major
1933   order, the matrix is partitioned across MPI ranks by row.
1934 
1935   The data input variable is intended primarily for Fortran programmers
1936   who wish to allocate their own matrix memory space.  Most users should
1937   set `data` to `NULL` (`PETSC_NULL_SCALAR` for Fortran users).
1938 
1939   The user MUST specify either the local or global matrix dimensions
1940   (possibly both).
1941 
1942 .seealso: [](ch_matrices), `Mat`, `MATDENSE`, `MatCreate()`, `MatCreateSeqDense()`, `MatSetValues()`
1943 @*/
1944 PetscErrorCode MatCreateDense(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, PetscScalar *data, Mat *A)
1945 {
1946   PetscFunctionBegin;
1947   PetscCall(MatCreate(comm, A));
1948   PetscCall(MatSetSizes(*A, m, n, M, N));
1949   PetscCall(MatSetType(*A, MATDENSE));
1950   PetscCall(MatSeqDenseSetPreallocation(*A, data));
1951   PetscCall(MatMPIDenseSetPreallocation(*A, data));
1952   PetscFunctionReturn(PETSC_SUCCESS);
1953 }
1954 
1955 static PetscErrorCode MatDuplicate_MPIDense(Mat A, MatDuplicateOption cpvalues, Mat *newmat)
1956 {
1957   Mat           mat;
1958   Mat_MPIDense *a, *oldmat = (Mat_MPIDense *)A->data;
1959 
1960   PetscFunctionBegin;
1961   *newmat = NULL;
1962   PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &mat));
1963   PetscCall(MatSetSizes(mat, A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N));
1964   PetscCall(MatSetType(mat, ((PetscObject)A)->type_name));
1965   a = (Mat_MPIDense *)mat->data;
1966 
1967   mat->factortype   = A->factortype;
1968   mat->assembled    = PETSC_TRUE;
1969   mat->preallocated = PETSC_TRUE;
1970 
1971   mat->insertmode = NOT_SET_VALUES;
1972   a->donotstash   = oldmat->donotstash;
1973 
1974   PetscCall(PetscLayoutReference(A->rmap, &mat->rmap));
1975   PetscCall(PetscLayoutReference(A->cmap, &mat->cmap));
1976 
1977   PetscCall(MatDuplicate(oldmat->A, cpvalues, &a->A));
1978 
1979   *newmat = mat;
1980   PetscFunctionReturn(PETSC_SUCCESS);
1981 }
1982 
1983 static PetscErrorCode MatLoad_MPIDense(Mat newMat, PetscViewer viewer)
1984 {
1985   PetscBool isbinary;
1986 #if defined(PETSC_HAVE_HDF5)
1987   PetscBool ishdf5;
1988 #endif
1989 
1990   PetscFunctionBegin;
1991   PetscValidHeaderSpecific(newMat, MAT_CLASSID, 1);
1992   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
1993   /* force binary viewer to load .info file if it has not yet done so */
1994   PetscCall(PetscViewerSetUp(viewer));
1995   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
1996 #if defined(PETSC_HAVE_HDF5)
1997   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
1998 #endif
1999   if (isbinary) {
2000     PetscCall(MatLoad_Dense_Binary(newMat, viewer));
2001 #if defined(PETSC_HAVE_HDF5)
2002   } else if (ishdf5) {
2003     PetscCall(MatLoad_Dense_HDF5(newMat, viewer));
2004 #endif
2005   } else SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "Viewer type %s not yet supported for reading %s matrices", ((PetscObject)viewer)->type_name, ((PetscObject)newMat)->type_name);
2006   PetscFunctionReturn(PETSC_SUCCESS);
2007 }
2008 
2009 static PetscErrorCode MatEqual_MPIDense(Mat A, Mat B, PetscBool *flag)
2010 {
2011   Mat_MPIDense *matB = (Mat_MPIDense *)B->data, *matA = (Mat_MPIDense *)A->data;
2012   Mat           a, b;
2013 
2014   PetscFunctionBegin;
2015   a = matA->A;
2016   b = matB->A;
2017   PetscCall(MatEqual(a, b, flag));
2018   PetscCall(MPIU_Allreduce(MPI_IN_PLACE, flag, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
2019   PetscFunctionReturn(PETSC_SUCCESS);
2020 }
2021 
2022 static PetscErrorCode MatDestroy_MatTransMatMult_MPIDense_MPIDense(void *data)
2023 {
2024   Mat_TransMatMultDense *atb = (Mat_TransMatMultDense *)data;
2025 
2026   PetscFunctionBegin;
2027   PetscCall(PetscFree2(atb->sendbuf, atb->recvcounts));
2028   PetscCall(MatDestroy(&atb->atb));
2029   PetscCall(PetscFree(atb));
2030   PetscFunctionReturn(PETSC_SUCCESS);
2031 }
2032 
2033 static PetscErrorCode MatDestroy_MatMatTransMult_MPIDense_MPIDense(void *data)
2034 {
2035   Mat_MatTransMultDense *abt = (Mat_MatTransMultDense *)data;
2036 
2037   PetscFunctionBegin;
2038   PetscCall(PetscFree2(abt->buf[0], abt->buf[1]));
2039   PetscCall(PetscFree2(abt->recvcounts, abt->recvdispls));
2040   PetscCall(PetscFree(abt));
2041   PetscFunctionReturn(PETSC_SUCCESS);
2042 }
2043 
2044 static PetscErrorCode MatTransposeMatMultNumeric_MPIDense_MPIDense(Mat A, Mat B, Mat C)
2045 {
2046   Mat_MPIDense          *a = (Mat_MPIDense *)A->data, *b = (Mat_MPIDense *)B->data, *c = (Mat_MPIDense *)C->data;
2047   Mat_TransMatMultDense *atb;
2048   MPI_Comm               comm;
2049   PetscMPIInt            size, *recvcounts;
2050   PetscScalar           *carray, *sendbuf;
2051   const PetscScalar     *atbarray;
2052   PetscInt               i, cN = C->cmap->N, proc, k, j, lda;
2053   const PetscInt        *ranges;
2054 
2055   PetscFunctionBegin;
2056   MatCheckProduct(C, 3);
2057   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
2058   atb        = (Mat_TransMatMultDense *)C->product->data;
2059   recvcounts = atb->recvcounts;
2060   sendbuf    = atb->sendbuf;
2061 
2062   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
2063   PetscCallMPI(MPI_Comm_size(comm, &size));
2064 
2065   /* compute atbarray = aseq^T * bseq */
2066   PetscCall(MatTransposeMatMult(a->A, b->A, atb->atb ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX, PETSC_DEFAULT, &atb->atb));
2067 
2068   PetscCall(MatGetOwnershipRanges(C, &ranges));
2069 
2070   /* arrange atbarray into sendbuf */
2071   PetscCall(MatDenseGetArrayRead(atb->atb, &atbarray));
2072   PetscCall(MatDenseGetLDA(atb->atb, &lda));
2073   for (proc = 0, k = 0; proc < size; proc++) {
2074     for (j = 0; j < cN; j++) {
2075       for (i = ranges[proc]; i < ranges[proc + 1]; i++) sendbuf[k++] = atbarray[i + j * lda];
2076     }
2077   }
2078   PetscCall(MatDenseRestoreArrayRead(atb->atb, &atbarray));
2079 
2080   /* sum all atbarray to local values of C */
2081   PetscCall(MatDenseGetArrayWrite(c->A, &carray));
2082   PetscCallMPI(MPI_Reduce_scatter(sendbuf, carray, recvcounts, MPIU_SCALAR, MPIU_SUM, comm));
2083   PetscCall(MatDenseRestoreArrayWrite(c->A, &carray));
2084   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2085   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2086   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2087   PetscFunctionReturn(PETSC_SUCCESS);
2088 }
2089 
2090 static PetscErrorCode MatTransposeMatMultSymbolic_MPIDense_MPIDense(Mat A, Mat B, PetscReal fill, Mat C)
2091 {
2092   MPI_Comm               comm;
2093   PetscMPIInt            size;
2094   PetscInt               cm = A->cmap->n, cM, cN = B->cmap->N;
2095   Mat_TransMatMultDense *atb;
2096   PetscBool              cisdense = PETSC_FALSE;
2097   PetscInt               i;
2098   const PetscInt        *ranges;
2099 
2100   PetscFunctionBegin;
2101   MatCheckProduct(C, 4);
2102   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
2103   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
2104   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend) {
2105     SETERRQ(comm, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != B (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);
2106   }
2107 
2108   /* create matrix product C */
2109   PetscCall(MatSetSizes(C, cm, B->cmap->n, A->cmap->N, B->cmap->N));
2110 #if defined(PETSC_HAVE_CUDA)
2111   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATMPIDENSE, MATMPIDENSECUDA, ""));
2112 #endif
2113 #if defined(PETSC_HAVE_HIP)
2114   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATMPIDENSE, MATMPIDENSEHIP, ""));
2115 #endif
2116   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
2117   PetscCall(MatSetUp(C));
2118 
2119   /* create data structure for reuse C */
2120   PetscCallMPI(MPI_Comm_size(comm, &size));
2121   PetscCall(PetscNew(&atb));
2122   cM = C->rmap->N;
2123   PetscCall(PetscMalloc2(cM * cN, &atb->sendbuf, size, &atb->recvcounts));
2124   PetscCall(MatGetOwnershipRanges(C, &ranges));
2125   for (i = 0; i < size; i++) atb->recvcounts[i] = (ranges[i + 1] - ranges[i]) * cN;
2126 
2127   C->product->data    = atb;
2128   C->product->destroy = MatDestroy_MatTransMatMult_MPIDense_MPIDense;
2129   PetscFunctionReturn(PETSC_SUCCESS);
2130 }
2131 
2132 static PetscErrorCode MatMatTransposeMultSymbolic_MPIDense_MPIDense(Mat A, Mat B, PetscReal fill, Mat C)
2133 {
2134   MPI_Comm               comm;
2135   PetscMPIInt            i, size;
2136   PetscInt               maxRows, bufsiz;
2137   PetscMPIInt            tag;
2138   PetscInt               alg;
2139   Mat_MatTransMultDense *abt;
2140   Mat_Product           *product = C->product;
2141   PetscBool              flg;
2142 
2143   PetscFunctionBegin;
2144   MatCheckProduct(C, 4);
2145   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
2146   /* check local size of A and B */
2147   PetscCheck(A->cmap->n == B->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local column dimensions are incompatible, A (%" PetscInt_FMT ") != B (%" PetscInt_FMT ")", A->cmap->n, B->cmap->n);
2148 
2149   PetscCall(PetscStrcmp(product->alg, "allgatherv", &flg));
2150   alg = flg ? 0 : 1;
2151 
2152   /* setup matrix product C */
2153   PetscCall(MatSetSizes(C, A->rmap->n, B->rmap->n, A->rmap->N, B->rmap->N));
2154   PetscCall(MatSetType(C, MATMPIDENSE));
2155   PetscCall(MatSetUp(C));
2156   PetscCall(PetscObjectGetNewTag((PetscObject)C, &tag));
2157 
2158   /* create data structure for reuse C */
2159   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2160   PetscCallMPI(MPI_Comm_size(comm, &size));
2161   PetscCall(PetscNew(&abt));
2162   abt->tag = tag;
2163   abt->alg = alg;
2164   switch (alg) {
2165   case 1: /* alg: "cyclic" */
2166     for (maxRows = 0, i = 0; i < size; i++) maxRows = PetscMax(maxRows, (B->rmap->range[i + 1] - B->rmap->range[i]));
2167     bufsiz = A->cmap->N * maxRows;
2168     PetscCall(PetscMalloc2(bufsiz, &abt->buf[0], bufsiz, &abt->buf[1]));
2169     break;
2170   default: /* alg: "allgatherv" */
2171     PetscCall(PetscMalloc2(B->rmap->n * B->cmap->N, &abt->buf[0], B->rmap->N * B->cmap->N, &abt->buf[1]));
2172     PetscCall(PetscMalloc2(size, &abt->recvcounts, size + 1, &abt->recvdispls));
2173     for (i = 0; i <= size; i++) abt->recvdispls[i] = B->rmap->range[i] * A->cmap->N;
2174     for (i = 0; i < size; i++) abt->recvcounts[i] = abt->recvdispls[i + 1] - abt->recvdispls[i];
2175     break;
2176   }
2177 
2178   C->product->data                = abt;
2179   C->product->destroy             = MatDestroy_MatMatTransMult_MPIDense_MPIDense;
2180   C->ops->mattransposemultnumeric = MatMatTransposeMultNumeric_MPIDense_MPIDense;
2181   PetscFunctionReturn(PETSC_SUCCESS);
2182 }
2183 
2184 static PetscErrorCode MatMatTransposeMultNumeric_MPIDense_MPIDense_Cyclic(Mat A, Mat B, Mat C)
2185 {
2186   Mat_MPIDense          *a = (Mat_MPIDense *)A->data, *b = (Mat_MPIDense *)B->data, *c = (Mat_MPIDense *)C->data;
2187   Mat_MatTransMultDense *abt;
2188   MPI_Comm               comm;
2189   PetscMPIInt            rank, size, sendsiz, recvsiz, sendto, recvfrom, recvisfrom;
2190   PetscScalar           *sendbuf, *recvbuf = NULL, *cv;
2191   PetscInt               i, cK             = A->cmap->N, k, j, bn;
2192   PetscScalar            _DOne = 1.0, _DZero = 0.0;
2193   const PetscScalar     *av, *bv;
2194   PetscBLASInt           cm, cn, ck, alda, blda = 0, clda;
2195   MPI_Request            reqs[2];
2196   const PetscInt        *ranges;
2197 
2198   PetscFunctionBegin;
2199   MatCheckProduct(C, 3);
2200   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
2201   abt = (Mat_MatTransMultDense *)C->product->data;
2202   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2203   PetscCallMPI(MPI_Comm_rank(comm, &rank));
2204   PetscCallMPI(MPI_Comm_size(comm, &size));
2205   PetscCall(MatDenseGetArrayRead(a->A, &av));
2206   PetscCall(MatDenseGetArrayRead(b->A, &bv));
2207   PetscCall(MatDenseGetArrayWrite(c->A, &cv));
2208   PetscCall(MatDenseGetLDA(a->A, &i));
2209   PetscCall(PetscBLASIntCast(i, &alda));
2210   PetscCall(MatDenseGetLDA(b->A, &i));
2211   PetscCall(PetscBLASIntCast(i, &blda));
2212   PetscCall(MatDenseGetLDA(c->A, &i));
2213   PetscCall(PetscBLASIntCast(i, &clda));
2214   PetscCall(MatGetOwnershipRanges(B, &ranges));
2215   bn = B->rmap->n;
2216   if (blda == bn) {
2217     sendbuf = (PetscScalar *)bv;
2218   } else {
2219     sendbuf = abt->buf[0];
2220     for (k = 0, i = 0; i < cK; i++) {
2221       for (j = 0; j < bn; j++, k++) sendbuf[k] = bv[i * blda + j];
2222     }
2223   }
2224   if (size > 1) {
2225     sendto   = (rank + size - 1) % size;
2226     recvfrom = (rank + size + 1) % size;
2227   } else {
2228     sendto = recvfrom = 0;
2229   }
2230   PetscCall(PetscBLASIntCast(cK, &ck));
2231   PetscCall(PetscBLASIntCast(c->A->rmap->n, &cm));
2232   recvisfrom = rank;
2233   for (i = 0; i < size; i++) {
2234     /* we have finished receiving in sending, bufs can be read/modified */
2235     PetscInt nextrecvisfrom = (recvisfrom + 1) % size; /* which process the next recvbuf will originate on */
2236     PetscInt nextbn         = ranges[nextrecvisfrom + 1] - ranges[nextrecvisfrom];
2237 
2238     if (nextrecvisfrom != rank) {
2239       /* start the cyclic sends from sendbuf, to recvbuf (which will switch to sendbuf) */
2240       sendsiz = cK * bn;
2241       recvsiz = cK * nextbn;
2242       recvbuf = (i & 1) ? abt->buf[0] : abt->buf[1];
2243       PetscCallMPI(MPI_Isend(sendbuf, sendsiz, MPIU_SCALAR, sendto, abt->tag, comm, &reqs[0]));
2244       PetscCallMPI(MPI_Irecv(recvbuf, recvsiz, MPIU_SCALAR, recvfrom, abt->tag, comm, &reqs[1]));
2245     }
2246 
2247     /* local aseq * sendbuf^T */
2248     PetscCall(PetscBLASIntCast(ranges[recvisfrom + 1] - ranges[recvisfrom], &cn));
2249     if (cm && cn && ck) PetscCallBLAS("BLASgemm", BLASgemm_("N", "T", &cm, &cn, &ck, &_DOne, av, &alda, sendbuf, &cn, &_DZero, cv + clda * ranges[recvisfrom], &clda));
2250 
2251     if (nextrecvisfrom != rank) {
2252       /* wait for the sends and receives to complete, swap sendbuf and recvbuf */
2253       PetscCallMPI(MPI_Waitall(2, reqs, MPI_STATUSES_IGNORE));
2254     }
2255     bn         = nextbn;
2256     recvisfrom = nextrecvisfrom;
2257     sendbuf    = recvbuf;
2258   }
2259   PetscCall(MatDenseRestoreArrayRead(a->A, &av));
2260   PetscCall(MatDenseRestoreArrayRead(b->A, &bv));
2261   PetscCall(MatDenseRestoreArrayWrite(c->A, &cv));
2262   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2263   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2264   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2265   PetscFunctionReturn(PETSC_SUCCESS);
2266 }
2267 
2268 static PetscErrorCode MatMatTransposeMultNumeric_MPIDense_MPIDense_Allgatherv(Mat A, Mat B, Mat C)
2269 {
2270   Mat_MPIDense          *a = (Mat_MPIDense *)A->data, *b = (Mat_MPIDense *)B->data, *c = (Mat_MPIDense *)C->data;
2271   Mat_MatTransMultDense *abt;
2272   MPI_Comm               comm;
2273   PetscMPIInt            size;
2274   PetscScalar           *cv, *sendbuf, *recvbuf;
2275   const PetscScalar     *av, *bv;
2276   PetscInt               blda, i, cK = A->cmap->N, k, j, bn;
2277   PetscScalar            _DOne = 1.0, _DZero = 0.0;
2278   PetscBLASInt           cm, cn, ck, alda, clda;
2279 
2280   PetscFunctionBegin;
2281   MatCheckProduct(C, 3);
2282   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
2283   abt = (Mat_MatTransMultDense *)C->product->data;
2284   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
2285   PetscCallMPI(MPI_Comm_size(comm, &size));
2286   PetscCall(MatDenseGetArrayRead(a->A, &av));
2287   PetscCall(MatDenseGetArrayRead(b->A, &bv));
2288   PetscCall(MatDenseGetArrayWrite(c->A, &cv));
2289   PetscCall(MatDenseGetLDA(a->A, &i));
2290   PetscCall(PetscBLASIntCast(i, &alda));
2291   PetscCall(MatDenseGetLDA(b->A, &blda));
2292   PetscCall(MatDenseGetLDA(c->A, &i));
2293   PetscCall(PetscBLASIntCast(i, &clda));
2294   /* copy transpose of B into buf[0] */
2295   bn      = B->rmap->n;
2296   sendbuf = abt->buf[0];
2297   recvbuf = abt->buf[1];
2298   for (k = 0, j = 0; j < bn; j++) {
2299     for (i = 0; i < cK; i++, k++) sendbuf[k] = bv[i * blda + j];
2300   }
2301   PetscCall(MatDenseRestoreArrayRead(b->A, &bv));
2302   PetscCallMPI(MPI_Allgatherv(sendbuf, bn * cK, MPIU_SCALAR, recvbuf, abt->recvcounts, abt->recvdispls, MPIU_SCALAR, comm));
2303   PetscCall(PetscBLASIntCast(cK, &ck));
2304   PetscCall(PetscBLASIntCast(c->A->rmap->n, &cm));
2305   PetscCall(PetscBLASIntCast(c->A->cmap->n, &cn));
2306   if (cm && cn && ck) PetscCallBLAS("BLASgemm", BLASgemm_("N", "N", &cm, &cn, &ck, &_DOne, av, &alda, recvbuf, &ck, &_DZero, cv, &clda));
2307   PetscCall(MatDenseRestoreArrayRead(a->A, &av));
2308   PetscCall(MatDenseRestoreArrayRead(b->A, &bv));
2309   PetscCall(MatDenseRestoreArrayWrite(c->A, &cv));
2310   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2311   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2312   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2313   PetscFunctionReturn(PETSC_SUCCESS);
2314 }
2315 
2316 static PetscErrorCode MatMatTransposeMultNumeric_MPIDense_MPIDense(Mat A, Mat B, Mat C)
2317 {
2318   Mat_MatTransMultDense *abt;
2319 
2320   PetscFunctionBegin;
2321   MatCheckProduct(C, 3);
2322   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
2323   abt = (Mat_MatTransMultDense *)C->product->data;
2324   switch (abt->alg) {
2325   case 1:
2326     PetscCall(MatMatTransposeMultNumeric_MPIDense_MPIDense_Cyclic(A, B, C));
2327     break;
2328   default:
2329     PetscCall(MatMatTransposeMultNumeric_MPIDense_MPIDense_Allgatherv(A, B, C));
2330     break;
2331   }
2332   PetscFunctionReturn(PETSC_SUCCESS);
2333 }
2334 
2335 static PetscErrorCode MatDestroy_MatMatMult_MPIDense_MPIDense(void *data)
2336 {
2337   Mat_MatMultDense *ab = (Mat_MatMultDense *)data;
2338 
2339   PetscFunctionBegin;
2340   PetscCall(MatDestroy(&ab->Ce));
2341   PetscCall(MatDestroy(&ab->Ae));
2342   PetscCall(MatDestroy(&ab->Be));
2343   PetscCall(PetscFree(ab));
2344   PetscFunctionReturn(PETSC_SUCCESS);
2345 }
2346 
2347 static PetscErrorCode MatMatMultNumeric_MPIDense_MPIDense(Mat A, Mat B, Mat C)
2348 {
2349   Mat_MatMultDense *ab;
2350   Mat_MPIDense     *mdn = (Mat_MPIDense *)A->data;
2351 
2352   PetscFunctionBegin;
2353   MatCheckProduct(C, 3);
2354   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Missing product data");
2355   ab = (Mat_MatMultDense *)C->product->data;
2356   if (ab->Ae && ab->Ce) {
2357 #if PetscDefined(HAVE_ELEMENTAL)
2358     PetscCall(MatConvert_MPIDense_Elemental(A, MATELEMENTAL, MAT_REUSE_MATRIX, &ab->Ae));
2359     PetscCall(MatConvert_MPIDense_Elemental(B, MATELEMENTAL, MAT_REUSE_MATRIX, &ab->Be));
2360     PetscCall(MatMatMultNumeric_Elemental(ab->Ae, ab->Be, ab->Ce));
2361     PetscCall(MatConvert(ab->Ce, MATMPIDENSE, MAT_REUSE_MATRIX, &C));
2362 #else
2363     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "PETSC_HAVE_ELEMENTAL not defined");
2364 #endif
2365   } else {
2366     const PetscScalar *read;
2367     PetscScalar       *write;
2368     PetscInt           lda;
2369 
2370     PetscCall(MatDenseGetLDA(B, &lda));
2371     PetscCall(MatDenseGetArrayRead(B, &read));
2372     PetscCall(MatDenseGetArrayWrite(ab->Be, &write));
2373     if (!mdn->Mvctx) PetscCall(MatSetUpMultiply_MPIDense(A)); /* cannot be done during the symbolic phase because of possible calls to MatProductReplaceMats() */
2374     for (PetscInt i = 0; i < C->cmap->N; ++i) {
2375       PetscCall(PetscSFBcastBegin(mdn->Mvctx, MPIU_SCALAR, read + i * lda, write + i * ab->Be->rmap->n, MPI_REPLACE));
2376       PetscCall(PetscSFBcastEnd(mdn->Mvctx, MPIU_SCALAR, read + i * lda, write + i * ab->Be->rmap->n, MPI_REPLACE));
2377     }
2378     PetscCall(MatDenseRestoreArrayWrite(ab->Be, &write));
2379     PetscCall(MatDenseRestoreArrayRead(B, &read));
2380     PetscCall(MatMatMultNumeric_SeqDense_SeqDense(((Mat_MPIDense *)A->data)->A, ab->Be, ((Mat_MPIDense *)C->data)->A));
2381   }
2382   PetscFunctionReturn(PETSC_SUCCESS);
2383 }
2384 
2385 static PetscErrorCode MatMatMultSymbolic_MPIDense_MPIDense(Mat A, Mat B, PetscReal fill, Mat C)
2386 {
2387   Mat_Product      *product = C->product;
2388   PetscInt          alg;
2389   Mat_MatMultDense *ab;
2390   PetscBool         flg;
2391 
2392   PetscFunctionBegin;
2393   MatCheckProduct(C, 4);
2394   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
2395   /* check local size of A and B */
2396   PetscCheck(A->cmap->rstart == B->rmap->rstart && A->cmap->rend == B->rmap->rend, PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != B (%" PetscInt_FMT ", %" PetscInt_FMT ")",
2397              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);
2398 
2399   PetscCall(PetscStrcmp(product->alg, "petsc", &flg));
2400   alg = flg ? 0 : 1;
2401 
2402   /* setup C */
2403   PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
2404   PetscCall(MatSetType(C, MATMPIDENSE));
2405   PetscCall(MatSetUp(C));
2406 
2407   /* create data structure for reuse Cdense */
2408   PetscCall(PetscNew(&ab));
2409 
2410   switch (alg) {
2411   case 1: /* alg: "elemental" */
2412 #if PetscDefined(HAVE_ELEMENTAL)
2413     /* create elemental matrices Ae and Be */
2414     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &ab->Ae));
2415     PetscCall(MatSetSizes(ab->Ae, PETSC_DECIDE, PETSC_DECIDE, A->rmap->N, A->cmap->N));
2416     PetscCall(MatSetType(ab->Ae, MATELEMENTAL));
2417     PetscCall(MatSetUp(ab->Ae));
2418     PetscCall(MatSetOption(ab->Ae, MAT_ROW_ORIENTED, PETSC_FALSE));
2419 
2420     PetscCall(MatCreate(PetscObjectComm((PetscObject)B), &ab->Be));
2421     PetscCall(MatSetSizes(ab->Be, PETSC_DECIDE, PETSC_DECIDE, B->rmap->N, B->cmap->N));
2422     PetscCall(MatSetType(ab->Be, MATELEMENTAL));
2423     PetscCall(MatSetUp(ab->Be));
2424     PetscCall(MatSetOption(ab->Be, MAT_ROW_ORIENTED, PETSC_FALSE));
2425 
2426     /* compute symbolic Ce = Ae*Be */
2427     PetscCall(MatCreate(PetscObjectComm((PetscObject)C), &ab->Ce));
2428     PetscCall(MatMatMultSymbolic_Elemental(ab->Ae, ab->Be, fill, ab->Ce));
2429 #else
2430     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "PETSC_HAVE_ELEMENTAL not defined");
2431 #endif
2432     break;
2433   default: /* alg: "petsc" */
2434     ab->Ae = NULL;
2435     PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, A->cmap->N, B->cmap->N, NULL, &ab->Be));
2436     ab->Ce = NULL;
2437     break;
2438   }
2439 
2440   C->product->data       = ab;
2441   C->product->destroy    = MatDestroy_MatMatMult_MPIDense_MPIDense;
2442   C->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIDense;
2443   PetscFunctionReturn(PETSC_SUCCESS);
2444 }
2445 
2446 static PetscErrorCode MatProductSetFromOptions_MPIDense_AB(Mat C)
2447 {
2448   Mat_Product *product     = C->product;
2449   const char  *algTypes[2] = {"petsc", "elemental"};
2450   PetscInt     alg, nalg = PetscDefined(HAVE_ELEMENTAL) ? 2 : 1;
2451   PetscBool    flg = PETSC_FALSE;
2452 
2453   PetscFunctionBegin;
2454   /* Set default algorithm */
2455   alg = 0; /* default is petsc */
2456   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2457   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2458 
2459   /* Get runtime option */
2460   PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2461   PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AB", algTypes, nalg, algTypes[alg], &alg, &flg));
2462   PetscOptionsEnd();
2463   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2464 
2465   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIDense_MPIDense;
2466   C->ops->productsymbolic = MatProductSymbolic_AB;
2467   PetscFunctionReturn(PETSC_SUCCESS);
2468 }
2469 
2470 static PetscErrorCode MatProductSetFromOptions_MPIDense_AtB(Mat C)
2471 {
2472   Mat_Product *product = C->product;
2473   Mat          A = product->A, B = product->B;
2474 
2475   PetscFunctionBegin;
2476   PetscCheck(A->rmap->rstart == B->rmap->rstart && A->rmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2477              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);
2478   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIDense_MPIDense;
2479   C->ops->productsymbolic          = MatProductSymbolic_AtB;
2480   PetscFunctionReturn(PETSC_SUCCESS);
2481 }
2482 
2483 static PetscErrorCode MatProductSetFromOptions_MPIDense_ABt(Mat C)
2484 {
2485   Mat_Product *product     = C->product;
2486   const char  *algTypes[2] = {"allgatherv", "cyclic"};
2487   PetscInt     alg, nalg = 2;
2488   PetscBool    flg = PETSC_FALSE;
2489 
2490   PetscFunctionBegin;
2491   /* Set default algorithm */
2492   alg = 0; /* default is allgatherv */
2493   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2494   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2495 
2496   /* Get runtime option */
2497   if (product->api_user) {
2498     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatTransposeMult", "Mat");
2499     PetscCall(PetscOptionsEList("-matmattransmult_mpidense_mpidense_via", "Algorithmic approach", "MatMatTransposeMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2500     PetscOptionsEnd();
2501   } else {
2502     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABt", "Mat");
2503     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABt", algTypes, nalg, algTypes[alg], &alg, &flg));
2504     PetscOptionsEnd();
2505   }
2506   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2507 
2508   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_MPIDense_MPIDense;
2509   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2510   PetscFunctionReturn(PETSC_SUCCESS);
2511 }
2512 
2513 static PetscErrorCode MatProductSetFromOptions_MPIDense(Mat C)
2514 {
2515   Mat_Product *product = C->product;
2516 
2517   PetscFunctionBegin;
2518   switch (product->type) {
2519   case MATPRODUCT_AB:
2520     PetscCall(MatProductSetFromOptions_MPIDense_AB(C));
2521     break;
2522   case MATPRODUCT_AtB:
2523     PetscCall(MatProductSetFromOptions_MPIDense_AtB(C));
2524     break;
2525   case MATPRODUCT_ABt:
2526     PetscCall(MatProductSetFromOptions_MPIDense_ABt(C));
2527     break;
2528   default:
2529     break;
2530   }
2531   PetscFunctionReturn(PETSC_SUCCESS);
2532 }
2533