xref: /petsc/src/mat/impls/aij/mpi/mpiaij.c (revision 4c17f1ccc7b2164a69cf463ab430260cd6f52f71)
1 #include <../src/mat/impls/aij/mpi/mpiaij.h> /*I "petscmat.h" I*/
2 #include <petsc/private/vecimpl.h>
3 #include <petsc/private/sfimpl.h>
4 #include <petsc/private/isimpl.h>
5 #include <petscblaslapack.h>
6 #include <petscsf.h>
7 #include <petsc/private/hashmapi.h>
8 
9 PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
10 {
11   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
12 
13   PetscFunctionBegin;
14   PetscCall(PetscLogObjectState((PetscObject)mat, "Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT, mat->rmap->N, mat->cmap->N));
15   PetscCall(MatStashDestroy_Private(&mat->stash));
16   PetscCall(VecDestroy(&aij->diag));
17   PetscCall(MatDestroy(&aij->A));
18   PetscCall(MatDestroy(&aij->B));
19 #if defined(PETSC_USE_CTABLE)
20   PetscCall(PetscHMapIDestroy(&aij->colmap));
21 #else
22   PetscCall(PetscFree(aij->colmap));
23 #endif
24   PetscCall(PetscFree(aij->garray));
25   PetscCall(VecDestroy(&aij->lvec));
26   PetscCall(VecScatterDestroy(&aij->Mvctx));
27   PetscCall(PetscFree2(aij->rowvalues, aij->rowindices));
28   PetscCall(PetscFree(aij->ld));
29 
30   PetscCall(PetscFree(mat->data));
31 
32   /* may be created by MatCreateMPIAIJSumSeqAIJSymbolic */
33   PetscCall(PetscObjectCompose((PetscObject)mat, "MatMergeSeqsToMPI", NULL));
34 
35   PetscCall(PetscObjectChangeTypeName((PetscObject)mat, NULL));
36   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatStoreValues_C", NULL));
37   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatRetrieveValues_C", NULL));
38   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatIsTranspose_C", NULL));
39   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetPreallocation_C", NULL));
40   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatResetPreallocation_C", NULL));
41   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetPreallocationCSR_C", NULL));
42   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDiagonalScaleLocal_C", NULL));
43   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpibaij_C", NULL));
44   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpisbaij_C", NULL));
45 #if defined(PETSC_HAVE_CUDA)
46   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijcusparse_C", NULL));
47 #endif
48 #if defined(PETSC_HAVE_HIP)
49   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijhipsparse_C", NULL));
50 #endif
51 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
52   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijkokkos_C", NULL));
53 #endif
54   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpidense_C", NULL));
55 #if defined(PETSC_HAVE_ELEMENTAL)
56   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_elemental_C", NULL));
57 #endif
58 #if defined(PETSC_HAVE_SCALAPACK)
59   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_scalapack_C", NULL));
60 #endif
61 #if defined(PETSC_HAVE_HYPRE)
62   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_hypre_C", NULL));
63   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", NULL));
64 #endif
65   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_is_C", NULL));
66   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_is_mpiaij_C", NULL));
67   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaij_mpiaij_C", NULL));
68   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetUseScalableIncreaseOverlap_C", NULL));
69   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijperm_C", NULL));
70   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijsell_C", NULL));
71 #if defined(PETSC_HAVE_MKL_SPARSE)
72   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijmkl_C", NULL));
73 #endif
74   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijcrl_C", NULL));
75   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_is_C", NULL));
76   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpisell_C", NULL));
77   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetPreallocationCOO_C", NULL));
78   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetValuesCOO_C", NULL));
79   PetscFunctionReturn(PETSC_SUCCESS);
80 }
81 
82 /* defines MatSetValues_MPI_Hash(), MatAssemblyBegin_MPI_Hash(), and  MatAssemblyEnd_MPI_Hash() */
83 #define TYPE AIJ
84 #define TYPE_AIJ
85 #include "../src/mat/impls/aij/mpi/mpihashmat.h"
86 #undef TYPE
87 #undef TYPE_AIJ
88 
89 static PetscErrorCode MatGetRowIJ_MPIAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *m, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
90 {
91   Mat B;
92 
93   PetscFunctionBegin;
94   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &B));
95   PetscCall(PetscObjectCompose((PetscObject)A, "MatGetRowIJ_MPIAIJ", (PetscObject)B));
96   PetscCall(MatGetRowIJ(B, oshift, symmetric, inodecompressed, m, ia, ja, done));
97   PetscCall(MatDestroy(&B));
98   PetscFunctionReturn(PETSC_SUCCESS);
99 }
100 
101 static PetscErrorCode MatRestoreRowIJ_MPIAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *m, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
102 {
103   Mat B;
104 
105   PetscFunctionBegin;
106   PetscCall(PetscObjectQuery((PetscObject)A, "MatGetRowIJ_MPIAIJ", (PetscObject *)&B));
107   PetscCall(MatRestoreRowIJ(B, oshift, symmetric, inodecompressed, m, ia, ja, done));
108   PetscCall(PetscObjectCompose((PetscObject)A, "MatGetRowIJ_MPIAIJ", NULL));
109   PetscFunctionReturn(PETSC_SUCCESS);
110 }
111 
112 /*MC
113    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.
114 
115    This matrix type is identical to` MATSEQAIJ` when constructed with a single process communicator,
116    and `MATMPIAIJ` otherwise.  As a result, for single process communicators,
117   `MatSeqAIJSetPreallocation()` is supported, and similarly `MatMPIAIJSetPreallocation()` is supported
118   for communicators controlling multiple processes.  It is recommended that you call both of
119   the above preallocation routines for simplicity.
120 
121    Options Database Key:
122 . -mat_type aij - sets the matrix type to `MATAIJ` during a call to `MatSetFromOptions()`
123 
124   Developer Note:
125   Level: beginner
126 
127     Subclasses include `MATAIJCUSPARSE`, `MATAIJPERM`, `MATAIJSELL`, `MATAIJMKL`, `MATAIJCRL`, `MATAIJKOKKOS`,and also automatically switches over to use inodes when
128    enough exist.
129 
130 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MATSEQAIJ`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATMPIAIJ`
131 M*/
132 
133 /*MC
134    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.
135 
136    This matrix type is identical to `MATSEQAIJCRL` when constructed with a single process communicator,
137    and `MATMPIAIJCRL` otherwise.  As a result, for single process communicators,
138    `MatSeqAIJSetPreallocation()` is supported, and similarly `MatMPIAIJSetPreallocation()` is supported
139   for communicators controlling multiple processes.  It is recommended that you call both of
140   the above preallocation routines for simplicity.
141 
142    Options Database Key:
143 . -mat_type aijcrl - sets the matrix type to `MATMPIAIJCRL` during a call to `MatSetFromOptions()`
144 
145   Level: beginner
146 
147 .seealso: [](ch_matrices), `Mat`, `MatCreateMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`
148 M*/
149 
150 static PetscErrorCode MatBindToCPU_MPIAIJ(Mat A, PetscBool flg)
151 {
152   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
153 
154   PetscFunctionBegin;
155 #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP) || defined(PETSC_HAVE_VIENNACL)
156   A->boundtocpu = flg;
157 #endif
158   if (a->A) PetscCall(MatBindToCPU(a->A, flg));
159   if (a->B) PetscCall(MatBindToCPU(a->B, flg));
160 
161   /* In addition to binding the diagonal and off-diagonal matrices, bind the local vectors used for matrix-vector products.
162    * This maybe seems a little odd for a MatBindToCPU() call to do, but it makes no sense for the binding of these vectors
163    * to differ from the parent matrix. */
164   if (a->lvec) PetscCall(VecBindToCPU(a->lvec, flg));
165   if (a->diag) PetscCall(VecBindToCPU(a->diag, flg));
166 
167   PetscFunctionReturn(PETSC_SUCCESS);
168 }
169 
170 static PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
171 {
172   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)M->data;
173 
174   PetscFunctionBegin;
175   if (mat->A) {
176     PetscCall(MatSetBlockSizes(mat->A, rbs, cbs));
177     PetscCall(MatSetBlockSizes(mat->B, rbs, 1));
178   }
179   PetscFunctionReturn(PETSC_SUCCESS);
180 }
181 
182 static PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M, IS *keptrows)
183 {
184   Mat_MPIAIJ      *mat = (Mat_MPIAIJ *)M->data;
185   Mat_SeqAIJ      *a   = (Mat_SeqAIJ *)mat->A->data;
186   Mat_SeqAIJ      *b   = (Mat_SeqAIJ *)mat->B->data;
187   const PetscInt  *ia, *ib;
188   const MatScalar *aa, *bb, *aav, *bav;
189   PetscInt         na, nb, i, j, *rows, cnt = 0, n0rows;
190   PetscInt         m = M->rmap->n, rstart = M->rmap->rstart;
191 
192   PetscFunctionBegin;
193   *keptrows = NULL;
194 
195   ia = a->i;
196   ib = b->i;
197   PetscCall(MatSeqAIJGetArrayRead(mat->A, &aav));
198   PetscCall(MatSeqAIJGetArrayRead(mat->B, &bav));
199   for (i = 0; i < m; i++) {
200     na = ia[i + 1] - ia[i];
201     nb = ib[i + 1] - ib[i];
202     if (!na && !nb) {
203       cnt++;
204       goto ok1;
205     }
206     aa = aav + ia[i];
207     for (j = 0; j < na; j++) {
208       if (aa[j] != 0.0) goto ok1;
209     }
210     bb = bav ? bav + ib[i] : NULL;
211     for (j = 0; j < nb; j++) {
212       if (bb[j] != 0.0) goto ok1;
213     }
214     cnt++;
215   ok1:;
216   }
217   PetscCall(MPIU_Allreduce(&cnt, &n0rows, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)M)));
218   if (!n0rows) {
219     PetscCall(MatSeqAIJRestoreArrayRead(mat->A, &aav));
220     PetscCall(MatSeqAIJRestoreArrayRead(mat->B, &bav));
221     PetscFunctionReturn(PETSC_SUCCESS);
222   }
223   PetscCall(PetscMalloc1(M->rmap->n - cnt, &rows));
224   cnt = 0;
225   for (i = 0; i < m; i++) {
226     na = ia[i + 1] - ia[i];
227     nb = ib[i + 1] - ib[i];
228     if (!na && !nb) continue;
229     aa = aav + ia[i];
230     for (j = 0; j < na; j++) {
231       if (aa[j] != 0.0) {
232         rows[cnt++] = rstart + i;
233         goto ok2;
234       }
235     }
236     bb = bav ? bav + ib[i] : NULL;
237     for (j = 0; j < nb; j++) {
238       if (bb[j] != 0.0) {
239         rows[cnt++] = rstart + i;
240         goto ok2;
241       }
242     }
243   ok2:;
244   }
245   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)M), cnt, rows, PETSC_OWN_POINTER, keptrows));
246   PetscCall(MatSeqAIJRestoreArrayRead(mat->A, &aav));
247   PetscCall(MatSeqAIJRestoreArrayRead(mat->B, &bav));
248   PetscFunctionReturn(PETSC_SUCCESS);
249 }
250 
251 static PetscErrorCode MatDiagonalSet_MPIAIJ(Mat Y, Vec D, InsertMode is)
252 {
253   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)Y->data;
254   PetscBool   cong;
255 
256   PetscFunctionBegin;
257   PetscCall(MatHasCongruentLayouts(Y, &cong));
258   if (Y->assembled && cong) {
259     PetscCall(MatDiagonalSet(aij->A, D, is));
260   } else {
261     PetscCall(MatDiagonalSet_Default(Y, D, is));
262   }
263   PetscFunctionReturn(PETSC_SUCCESS);
264 }
265 
266 static PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M, IS *zrows)
267 {
268   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)M->data;
269   PetscInt    i, rstart, nrows, *rows;
270 
271   PetscFunctionBegin;
272   *zrows = NULL;
273   PetscCall(MatFindZeroDiagonals_SeqAIJ_Private(aij->A, &nrows, &rows));
274   PetscCall(MatGetOwnershipRange(M, &rstart, NULL));
275   for (i = 0; i < nrows; i++) rows[i] += rstart;
276   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)M), nrows, rows, PETSC_OWN_POINTER, zrows));
277   PetscFunctionReturn(PETSC_SUCCESS);
278 }
279 
280 static PetscErrorCode MatGetColumnReductions_MPIAIJ(Mat A, PetscInt type, PetscReal *reductions)
281 {
282   Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)A->data;
283   PetscInt           i, m, n, *garray = aij->garray;
284   Mat_SeqAIJ        *a_aij = (Mat_SeqAIJ *)aij->A->data;
285   Mat_SeqAIJ        *b_aij = (Mat_SeqAIJ *)aij->B->data;
286   PetscReal         *work;
287   const PetscScalar *dummy;
288 
289   PetscFunctionBegin;
290   PetscCall(MatGetSize(A, &m, &n));
291   PetscCall(PetscCalloc1(n, &work));
292   PetscCall(MatSeqAIJGetArrayRead(aij->A, &dummy));
293   PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &dummy));
294   PetscCall(MatSeqAIJGetArrayRead(aij->B, &dummy));
295   PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &dummy));
296   if (type == NORM_2) {
297     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i] * a_aij->a[i]);
298     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i] * b_aij->a[i]);
299   } else if (type == NORM_1) {
300     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
301     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
302   } else if (type == NORM_INFINITY) {
303     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
304     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]), work[garray[b_aij->j[i]]]);
305   } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
306     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] += PetscRealPart(a_aij->a[i]);
307     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscRealPart(b_aij->a[i]);
308   } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
309     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] += PetscImaginaryPart(a_aij->a[i]);
310     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscImaginaryPart(b_aij->a[i]);
311   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unknown reduction type");
312   if (type == NORM_INFINITY) {
313     PetscCall(MPIU_Allreduce(work, reductions, n, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)A)));
314   } else {
315     PetscCall(MPIU_Allreduce(work, reductions, n, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)A)));
316   }
317   PetscCall(PetscFree(work));
318   if (type == NORM_2) {
319     for (i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
320   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
321     for (i = 0; i < n; i++) reductions[i] /= m;
322   }
323   PetscFunctionReturn(PETSC_SUCCESS);
324 }
325 
326 static PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A, IS *is)
327 {
328   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)A->data;
329   IS              sis, gis;
330   const PetscInt *isis, *igis;
331   PetscInt        n, *iis, nsis, ngis, rstart, i;
332 
333   PetscFunctionBegin;
334   PetscCall(MatFindOffBlockDiagonalEntries(a->A, &sis));
335   PetscCall(MatFindNonzeroRows(a->B, &gis));
336   PetscCall(ISGetSize(gis, &ngis));
337   PetscCall(ISGetSize(sis, &nsis));
338   PetscCall(ISGetIndices(sis, &isis));
339   PetscCall(ISGetIndices(gis, &igis));
340 
341   PetscCall(PetscMalloc1(ngis + nsis, &iis));
342   PetscCall(PetscArraycpy(iis, igis, ngis));
343   PetscCall(PetscArraycpy(iis + ngis, isis, nsis));
344   n = ngis + nsis;
345   PetscCall(PetscSortRemoveDupsInt(&n, iis));
346   PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
347   for (i = 0; i < n; i++) iis[i] += rstart;
348   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), n, iis, PETSC_OWN_POINTER, is));
349 
350   PetscCall(ISRestoreIndices(sis, &isis));
351   PetscCall(ISRestoreIndices(gis, &igis));
352   PetscCall(ISDestroy(&sis));
353   PetscCall(ISDestroy(&gis));
354   PetscFunctionReturn(PETSC_SUCCESS);
355 }
356 
357 /*
358   Local utility routine that creates a mapping from the global column
359 number to the local number in the off-diagonal part of the local
360 storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
361 a slightly higher hash table cost; without it it is not scalable (each processor
362 has an order N integer array but is fast to access.
363 */
364 PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
365 {
366   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
367   PetscInt    n   = aij->B->cmap->n, i;
368 
369   PetscFunctionBegin;
370   PetscCheck(!n || aij->garray, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MPIAIJ Matrix was assembled but is missing garray");
371 #if defined(PETSC_USE_CTABLE)
372   PetscCall(PetscHMapICreateWithSize(n, &aij->colmap));
373   for (i = 0; i < n; i++) PetscCall(PetscHMapISet(aij->colmap, aij->garray[i] + 1, i + 1));
374 #else
375   PetscCall(PetscCalloc1(mat->cmap->N + 1, &aij->colmap));
376   for (i = 0; i < n; i++) aij->colmap[aij->garray[i]] = i + 1;
377 #endif
378   PetscFunctionReturn(PETSC_SUCCESS);
379 }
380 
381 #define MatSetValues_SeqAIJ_A_Private(row, col, value, addv, orow, ocol) \
382   do { \
383     if (col <= lastcol1) low1 = 0; \
384     else high1 = nrow1; \
385     lastcol1 = col; \
386     while (high1 - low1 > 5) { \
387       t = (low1 + high1) / 2; \
388       if (rp1[t] > col) high1 = t; \
389       else low1 = t; \
390     } \
391     for (_i = low1; _i < high1; _i++) { \
392       if (rp1[_i] > col) break; \
393       if (rp1[_i] == col) { \
394         if (addv == ADD_VALUES) { \
395           ap1[_i] += value; \
396           /* Not sure LogFlops will slow dow the code or not */ \
397           (void)PetscLogFlops(1.0); \
398         } else ap1[_i] = value; \
399         goto a_noinsert; \
400       } \
401     } \
402     if (value == 0.0 && ignorezeroentries && row != col) { \
403       low1  = 0; \
404       high1 = nrow1; \
405       goto a_noinsert; \
406     } \
407     if (nonew == 1) { \
408       low1  = 0; \
409       high1 = nrow1; \
410       goto a_noinsert; \
411     } \
412     PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", orow, ocol); \
413     MatSeqXAIJReallocateAIJ(A, am, 1, nrow1, row, col, rmax1, aa, ai, aj, rp1, ap1, aimax, nonew, MatScalar); \
414     N = nrow1++ - 1; \
415     a->nz++; \
416     high1++; \
417     /* shift up all the later entries in this row */ \
418     PetscCall(PetscArraymove(rp1 + _i + 1, rp1 + _i, N - _i + 1)); \
419     PetscCall(PetscArraymove(ap1 + _i + 1, ap1 + _i, N - _i + 1)); \
420     rp1[_i] = col; \
421     ap1[_i] = value; \
422     A->nonzerostate++; \
423   a_noinsert:; \
424     ailen[row] = nrow1; \
425   } while (0)
426 
427 #define MatSetValues_SeqAIJ_B_Private(row, col, value, addv, orow, ocol) \
428   do { \
429     if (col <= lastcol2) low2 = 0; \
430     else high2 = nrow2; \
431     lastcol2 = col; \
432     while (high2 - low2 > 5) { \
433       t = (low2 + high2) / 2; \
434       if (rp2[t] > col) high2 = t; \
435       else low2 = t; \
436     } \
437     for (_i = low2; _i < high2; _i++) { \
438       if (rp2[_i] > col) break; \
439       if (rp2[_i] == col) { \
440         if (addv == ADD_VALUES) { \
441           ap2[_i] += value; \
442           (void)PetscLogFlops(1.0); \
443         } else ap2[_i] = value; \
444         goto b_noinsert; \
445       } \
446     } \
447     if (value == 0.0 && ignorezeroentries) { \
448       low2  = 0; \
449       high2 = nrow2; \
450       goto b_noinsert; \
451     } \
452     if (nonew == 1) { \
453       low2  = 0; \
454       high2 = nrow2; \
455       goto b_noinsert; \
456     } \
457     PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", orow, ocol); \
458     MatSeqXAIJReallocateAIJ(B, bm, 1, nrow2, row, col, rmax2, ba, bi, bj, rp2, ap2, bimax, nonew, MatScalar); \
459     N = nrow2++ - 1; \
460     b->nz++; \
461     high2++; \
462     /* shift up all the later entries in this row */ \
463     PetscCall(PetscArraymove(rp2 + _i + 1, rp2 + _i, N - _i + 1)); \
464     PetscCall(PetscArraymove(ap2 + _i + 1, ap2 + _i, N - _i + 1)); \
465     rp2[_i] = col; \
466     ap2[_i] = value; \
467     B->nonzerostate++; \
468   b_noinsert:; \
469     bilen[row] = nrow2; \
470   } while (0)
471 
472 static PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A, PetscInt row, const PetscScalar v[])
473 {
474   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)A->data;
475   Mat_SeqAIJ  *a = (Mat_SeqAIJ *)mat->A->data, *b = (Mat_SeqAIJ *)mat->B->data;
476   PetscInt     l, *garray                         = mat->garray, diag;
477   PetscScalar *aa, *ba;
478 
479   PetscFunctionBegin;
480   /* code only works for square matrices A */
481 
482   /* find size of row to the left of the diagonal part */
483   PetscCall(MatGetOwnershipRange(A, &diag, NULL));
484   row = row - diag;
485   for (l = 0; l < b->i[row + 1] - b->i[row]; l++) {
486     if (garray[b->j[b->i[row] + l]] > diag) break;
487   }
488   if (l) {
489     PetscCall(MatSeqAIJGetArray(mat->B, &ba));
490     PetscCall(PetscArraycpy(ba + b->i[row], v, l));
491     PetscCall(MatSeqAIJRestoreArray(mat->B, &ba));
492   }
493 
494   /* diagonal part */
495   if (a->i[row + 1] - a->i[row]) {
496     PetscCall(MatSeqAIJGetArray(mat->A, &aa));
497     PetscCall(PetscArraycpy(aa + a->i[row], v + l, (a->i[row + 1] - a->i[row])));
498     PetscCall(MatSeqAIJRestoreArray(mat->A, &aa));
499   }
500 
501   /* right of diagonal part */
502   if (b->i[row + 1] - b->i[row] - l) {
503     PetscCall(MatSeqAIJGetArray(mat->B, &ba));
504     PetscCall(PetscArraycpy(ba + b->i[row] + l, v + l + a->i[row + 1] - a->i[row], b->i[row + 1] - b->i[row] - l));
505     PetscCall(MatSeqAIJRestoreArray(mat->B, &ba));
506   }
507   PetscFunctionReturn(PETSC_SUCCESS);
508 }
509 
510 PetscErrorCode MatSetValues_MPIAIJ(Mat mat, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode addv)
511 {
512   Mat_MPIAIJ *aij   = (Mat_MPIAIJ *)mat->data;
513   PetscScalar value = 0.0;
514   PetscInt    i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
515   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
516   PetscBool   roworiented = aij->roworiented;
517 
518   /* Some Variables required in the macro */
519   Mat         A     = aij->A;
520   Mat_SeqAIJ *a     = (Mat_SeqAIJ *)A->data;
521   PetscInt   *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
522   PetscBool   ignorezeroentries = a->ignorezeroentries;
523   Mat         B                 = aij->B;
524   Mat_SeqAIJ *b                 = (Mat_SeqAIJ *)B->data;
525   PetscInt   *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j, bm = aij->B->rmap->n, am = aij->A->rmap->n;
526   MatScalar  *aa, *ba;
527   PetscInt   *rp1, *rp2, ii, nrow1, nrow2, _i, rmax1, rmax2, N, low1, high1, low2, high2, t, lastcol1, lastcol2;
528   PetscInt    nonew;
529   MatScalar  *ap1, *ap2;
530 
531   PetscFunctionBegin;
532   PetscCall(MatSeqAIJGetArray(A, &aa));
533   PetscCall(MatSeqAIJGetArray(B, &ba));
534   for (i = 0; i < m; i++) {
535     if (im[i] < 0) continue;
536     PetscCheck(im[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, im[i], mat->rmap->N - 1);
537     if (im[i] >= rstart && im[i] < rend) {
538       row      = im[i] - rstart;
539       lastcol1 = -1;
540       rp1      = aj ? aj + ai[row] : NULL;
541       ap1      = aa ? aa + ai[row] : NULL;
542       rmax1    = aimax[row];
543       nrow1    = ailen[row];
544       low1     = 0;
545       high1    = nrow1;
546       lastcol2 = -1;
547       rp2      = bj ? bj + bi[row] : NULL;
548       ap2      = ba ? ba + bi[row] : NULL;
549       rmax2    = bimax[row];
550       nrow2    = bilen[row];
551       low2     = 0;
552       high2    = nrow2;
553 
554       for (j = 0; j < n; j++) {
555         if (v) value = roworiented ? v[i * n + j] : v[i + j * m];
556         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
557         if (in[j] >= cstart && in[j] < cend) {
558           col   = in[j] - cstart;
559           nonew = a->nonew;
560           MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
561         } else if (in[j] < 0) {
562           continue;
563         } else {
564           PetscCheck(in[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
565           if (mat->was_assembled) {
566             if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
567 #if defined(PETSC_USE_CTABLE)
568             PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col)); /* map global col ids to local ones */
569             col--;
570 #else
571             col = aij->colmap[in[j]] - 1;
572 #endif
573             if (col < 0 && !((Mat_SeqAIJ *)(aij->B->data))->nonew) { /* col < 0 means in[j] is a new col for B */
574               PetscCall(MatDisAssemble_MPIAIJ(mat));                 /* Change aij->B from reduced/local format to expanded/global format */
575               col = in[j];
576               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
577               B     = aij->B;
578               b     = (Mat_SeqAIJ *)B->data;
579               bimax = b->imax;
580               bi    = b->i;
581               bilen = b->ilen;
582               bj    = b->j;
583               ba    = b->a;
584               rp2   = bj + bi[row];
585               ap2   = ba + bi[row];
586               rmax2 = bimax[row];
587               nrow2 = bilen[row];
588               low2  = 0;
589               high2 = nrow2;
590               bm    = aij->B->rmap->n;
591               ba    = b->a;
592             } else if (col < 0 && !(ignorezeroentries && value == 0.0)) {
593               if (1 == ((Mat_SeqAIJ *)(aij->B->data))->nonew) {
594                 PetscCall(PetscInfo(mat, "Skipping of insertion of new nonzero location in off-diagonal portion of matrix %g(%" PetscInt_FMT ",%" PetscInt_FMT ")\n", (double)PetscRealPart(value), im[i], in[j]));
595               } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", im[i], in[j]);
596             }
597           } else col = in[j];
598           nonew = b->nonew;
599           MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
600         }
601       }
602     } else {
603       PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Setting off process row %" PetscInt_FMT " even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set", im[i]);
604       if (!aij->donotstash) {
605         mat->assembled = PETSC_FALSE;
606         if (roworiented) {
607           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, v ? v + i * n : NULL, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
608         } else {
609           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, v ? v + i : NULL, m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
610         }
611       }
612     }
613   }
614   PetscCall(MatSeqAIJRestoreArray(A, &aa)); /* aa, bb might have been free'd due to reallocation above. But we don't access them here */
615   PetscCall(MatSeqAIJRestoreArray(B, &ba));
616   PetscFunctionReturn(PETSC_SUCCESS);
617 }
618 
619 /*
620     This function sets the j and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
621     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
622     No off-processor parts off the matrix are allowed here and mat->was_assembled has to be PETSC_FALSE.
623 */
624 PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Mat mat, const PetscInt mat_j[], const PetscInt mat_i[])
625 {
626   Mat_MPIAIJ *aij    = (Mat_MPIAIJ *)mat->data;
627   Mat         A      = aij->A; /* diagonal part of the matrix */
628   Mat         B      = aij->B; /* off-diagonal part of the matrix */
629   Mat_SeqAIJ *a      = (Mat_SeqAIJ *)A->data;
630   Mat_SeqAIJ *b      = (Mat_SeqAIJ *)B->data;
631   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, col;
632   PetscInt   *ailen = a->ilen, *aj = a->j;
633   PetscInt   *bilen = b->ilen, *bj = b->j;
634   PetscInt    am          = aij->A->rmap->n, j;
635   PetscInt    diag_so_far = 0, dnz;
636   PetscInt    offd_so_far = 0, onz;
637 
638   PetscFunctionBegin;
639   /* Iterate over all rows of the matrix */
640   for (j = 0; j < am; j++) {
641     dnz = onz = 0;
642     /*  Iterate over all non-zero columns of the current row */
643     for (col = mat_i[j]; col < mat_i[j + 1]; col++) {
644       /* If column is in the diagonal */
645       if (mat_j[col] >= cstart && mat_j[col] < cend) {
646         aj[diag_so_far++] = mat_j[col] - cstart;
647         dnz++;
648       } else { /* off-diagonal entries */
649         bj[offd_so_far++] = mat_j[col];
650         onz++;
651       }
652     }
653     ailen[j] = dnz;
654     bilen[j] = onz;
655   }
656   PetscFunctionReturn(PETSC_SUCCESS);
657 }
658 
659 /*
660     This function sets the local j, a and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
661     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
662     No off-processor parts off the matrix are allowed here, they are set at a later point by MatSetValues_MPIAIJ.
663     Also, mat->was_assembled has to be false, otherwise the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart;
664     would not be true and the more complex MatSetValues_MPIAIJ has to be used.
665 */
666 PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat(Mat mat, const PetscInt mat_j[], const PetscInt mat_i[], const PetscScalar mat_a[])
667 {
668   Mat_MPIAIJ  *aij  = (Mat_MPIAIJ *)mat->data;
669   Mat          A    = aij->A; /* diagonal part of the matrix */
670   Mat          B    = aij->B; /* off-diagonal part of the matrix */
671   Mat_SeqAIJ  *aijd = (Mat_SeqAIJ *)(aij->A)->data, *aijo = (Mat_SeqAIJ *)(aij->B)->data;
672   Mat_SeqAIJ  *a      = (Mat_SeqAIJ *)A->data;
673   Mat_SeqAIJ  *b      = (Mat_SeqAIJ *)B->data;
674   PetscInt     cstart = mat->cmap->rstart, cend = mat->cmap->rend;
675   PetscInt    *ailen = a->ilen, *aj = a->j;
676   PetscInt    *bilen = b->ilen, *bj = b->j;
677   PetscInt     am          = aij->A->rmap->n, j;
678   PetscInt    *full_diag_i = aijd->i, *full_offd_i = aijo->i; /* These variables can also include non-local elements, which are set at a later point. */
679   PetscInt     col, dnz_row, onz_row, rowstart_diag, rowstart_offd;
680   PetscScalar *aa = a->a, *ba = b->a;
681 
682   PetscFunctionBegin;
683   /* Iterate over all rows of the matrix */
684   for (j = 0; j < am; j++) {
685     dnz_row = onz_row = 0;
686     rowstart_offd     = full_offd_i[j];
687     rowstart_diag     = full_diag_i[j];
688     /*  Iterate over all non-zero columns of the current row */
689     for (col = mat_i[j]; col < mat_i[j + 1]; col++) {
690       /* If column is in the diagonal */
691       if (mat_j[col] >= cstart && mat_j[col] < cend) {
692         aj[rowstart_diag + dnz_row] = mat_j[col] - cstart;
693         aa[rowstart_diag + dnz_row] = mat_a[col];
694         dnz_row++;
695       } else { /* off-diagonal entries */
696         bj[rowstart_offd + onz_row] = mat_j[col];
697         ba[rowstart_offd + onz_row] = mat_a[col];
698         onz_row++;
699       }
700     }
701     ailen[j] = dnz_row;
702     bilen[j] = onz_row;
703   }
704   PetscFunctionReturn(PETSC_SUCCESS);
705 }
706 
707 static PetscErrorCode MatGetValues_MPIAIJ(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], PetscScalar v[])
708 {
709   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
710   PetscInt    i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
711   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
712 
713   PetscFunctionBegin;
714   for (i = 0; i < m; i++) {
715     if (idxm[i] < 0) continue; /* negative row */
716     PetscCheck(idxm[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, idxm[i], mat->rmap->N - 1);
717     PetscCheck(idxm[i] >= rstart && idxm[i] < rend, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only local values currently supported, row requested %" PetscInt_FMT " range [%" PetscInt_FMT " %" PetscInt_FMT ")", idxm[i], rstart, rend);
718     row = idxm[i] - rstart;
719     for (j = 0; j < n; j++) {
720       if (idxn[j] < 0) continue; /* negative column */
721       PetscCheck(idxn[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, idxn[j], mat->cmap->N - 1);
722       if (idxn[j] >= cstart && idxn[j] < cend) {
723         col = idxn[j] - cstart;
724         PetscCall(MatGetValues(aij->A, 1, &row, 1, &col, v + i * n + j));
725       } else {
726         if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
727 #if defined(PETSC_USE_CTABLE)
728         PetscCall(PetscHMapIGetWithDefault(aij->colmap, idxn[j] + 1, 0, &col));
729         col--;
730 #else
731         col = aij->colmap[idxn[j]] - 1;
732 #endif
733         if ((col < 0) || (aij->garray[col] != idxn[j])) *(v + i * n + j) = 0.0;
734         else PetscCall(MatGetValues(aij->B, 1, &row, 1, &col, v + i * n + j));
735       }
736     }
737   }
738   PetscFunctionReturn(PETSC_SUCCESS);
739 }
740 
741 static PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat, MatAssemblyType mode)
742 {
743   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
744   PetscInt    nstash, reallocs;
745 
746   PetscFunctionBegin;
747   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(PETSC_SUCCESS);
748 
749   PetscCall(MatStashScatterBegin_Private(mat, &mat->stash, mat->rmap->range));
750   PetscCall(MatStashGetInfo_Private(&mat->stash, &nstash, &reallocs));
751   PetscCall(PetscInfo(aij->A, "Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
752   PetscFunctionReturn(PETSC_SUCCESS);
753 }
754 
755 PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat, MatAssemblyType mode)
756 {
757   Mat_MPIAIJ  *aij = (Mat_MPIAIJ *)mat->data;
758   PetscMPIInt  n;
759   PetscInt     i, j, rstart, ncols, flg;
760   PetscInt    *row, *col;
761   PetscBool    other_disassembled;
762   PetscScalar *val;
763 
764   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */
765 
766   PetscFunctionBegin;
767   if (!aij->donotstash && !mat->nooffprocentries) {
768     while (1) {
769       PetscCall(MatStashScatterGetMesg_Private(&mat->stash, &n, &row, &col, &val, &flg));
770       if (!flg) break;
771 
772       for (i = 0; i < n;) {
773         /* Now identify the consecutive vals belonging to the same row */
774         for (j = i, rstart = row[j]; j < n; j++) {
775           if (row[j] != rstart) break;
776         }
777         if (j < n) ncols = j - i;
778         else ncols = n - i;
779         /* Now assemble all these values with a single function call */
780         PetscCall(MatSetValues_MPIAIJ(mat, 1, row + i, ncols, col + i, val + i, mat->insertmode));
781         i = j;
782       }
783     }
784     PetscCall(MatStashScatterEnd_Private(&mat->stash));
785   }
786 #if defined(PETSC_HAVE_DEVICE)
787   if (mat->offloadmask == PETSC_OFFLOAD_CPU) aij->A->offloadmask = PETSC_OFFLOAD_CPU;
788   /* We call MatBindToCPU() on aij->A and aij->B here, because if MatBindToCPU_MPIAIJ() is called before assembly, it cannot bind these. */
789   if (mat->boundtocpu) {
790     PetscCall(MatBindToCPU(aij->A, PETSC_TRUE));
791     PetscCall(MatBindToCPU(aij->B, PETSC_TRUE));
792   }
793 #endif
794   PetscCall(MatAssemblyBegin(aij->A, mode));
795   PetscCall(MatAssemblyEnd(aij->A, mode));
796 
797   /* determine if any processor has disassembled, if so we must
798      also disassemble ourself, in order that we may reassemble. */
799   /*
800      if nonzero structure of submatrix B cannot change then we know that
801      no processor disassembled thus we can skip this stuff
802   */
803   if (!((Mat_SeqAIJ *)aij->B->data)->nonew) {
804     PetscCall(MPIU_Allreduce(&mat->was_assembled, &other_disassembled, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
805     if (mat->was_assembled && !other_disassembled) { /* mat on this rank has reduced off-diag B with local col ids, but globally it does not */
806       PetscCall(MatDisAssemble_MPIAIJ(mat));
807     }
808   }
809   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) PetscCall(MatSetUpMultiply_MPIAIJ(mat));
810   PetscCall(MatSetOption(aij->B, MAT_USE_INODES, PETSC_FALSE));
811 #if defined(PETSC_HAVE_DEVICE)
812   if (mat->offloadmask == PETSC_OFFLOAD_CPU && aij->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) aij->B->offloadmask = PETSC_OFFLOAD_CPU;
813 #endif
814   PetscCall(MatAssemblyBegin(aij->B, mode));
815   PetscCall(MatAssemblyEnd(aij->B, mode));
816 
817   PetscCall(PetscFree2(aij->rowvalues, aij->rowindices));
818 
819   aij->rowvalues = NULL;
820 
821   PetscCall(VecDestroy(&aij->diag));
822 
823   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
824   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ *)(aij->A->data))->nonew) {
825     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
826     PetscCall(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));
827   }
828 #if defined(PETSC_HAVE_DEVICE)
829   mat->offloadmask = PETSC_OFFLOAD_BOTH;
830 #endif
831   PetscFunctionReturn(PETSC_SUCCESS);
832 }
833 
834 static PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
835 {
836   Mat_MPIAIJ *l = (Mat_MPIAIJ *)A->data;
837 
838   PetscFunctionBegin;
839   PetscCall(MatZeroEntries(l->A));
840   PetscCall(MatZeroEntries(l->B));
841   PetscFunctionReturn(PETSC_SUCCESS);
842 }
843 
844 static PetscErrorCode MatZeroRows_MPIAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
845 {
846   Mat_MPIAIJ      *mat = (Mat_MPIAIJ *)A->data;
847   PetscObjectState sA, sB;
848   PetscInt        *lrows;
849   PetscInt         r, len;
850   PetscBool        cong, lch, gch;
851 
852   PetscFunctionBegin;
853   /* get locally owned rows */
854   PetscCall(MatZeroRowsMapLocal_Private(A, N, rows, &len, &lrows));
855   PetscCall(MatHasCongruentLayouts(A, &cong));
856   /* fix right hand side if needed */
857   if (x && b) {
858     const PetscScalar *xx;
859     PetscScalar       *bb;
860 
861     PetscCheck(cong, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Need matching row/col layout");
862     PetscCall(VecGetArrayRead(x, &xx));
863     PetscCall(VecGetArray(b, &bb));
864     for (r = 0; r < len; ++r) bb[lrows[r]] = diag * xx[lrows[r]];
865     PetscCall(VecRestoreArrayRead(x, &xx));
866     PetscCall(VecRestoreArray(b, &bb));
867   }
868 
869   sA = mat->A->nonzerostate;
870   sB = mat->B->nonzerostate;
871 
872   if (diag != 0.0 && cong) {
873     PetscCall(MatZeroRows(mat->A, len, lrows, diag, NULL, NULL));
874     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
875   } else if (diag != 0.0) { /* non-square or non congruent layouts -> if keepnonzeropattern is false, we allow for new insertion */
876     Mat_SeqAIJ *aijA = (Mat_SeqAIJ *)mat->A->data;
877     Mat_SeqAIJ *aijB = (Mat_SeqAIJ *)mat->B->data;
878     PetscInt    nnwA, nnwB;
879     PetscBool   nnzA, nnzB;
880 
881     nnwA = aijA->nonew;
882     nnwB = aijB->nonew;
883     nnzA = aijA->keepnonzeropattern;
884     nnzB = aijB->keepnonzeropattern;
885     if (!nnzA) {
886       PetscCall(PetscInfo(mat->A, "Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on diagonal block.\n"));
887       aijA->nonew = 0;
888     }
889     if (!nnzB) {
890       PetscCall(PetscInfo(mat->B, "Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on off-diagonal block.\n"));
891       aijB->nonew = 0;
892     }
893     /* Must zero here before the next loop */
894     PetscCall(MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL));
895     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
896     for (r = 0; r < len; ++r) {
897       const PetscInt row = lrows[r] + A->rmap->rstart;
898       if (row >= A->cmap->N) continue;
899       PetscCall(MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES));
900     }
901     aijA->nonew = nnwA;
902     aijB->nonew = nnwB;
903   } else {
904     PetscCall(MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL));
905     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
906   }
907   PetscCall(PetscFree(lrows));
908   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
909   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
910 
911   /* reduce nonzerostate */
912   lch = (PetscBool)(sA != mat->A->nonzerostate || sB != mat->B->nonzerostate);
913   PetscCall(MPIU_Allreduce(&lch, &gch, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)A)));
914   if (gch) A->nonzerostate++;
915   PetscFunctionReturn(PETSC_SUCCESS);
916 }
917 
918 static PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
919 {
920   Mat_MPIAIJ        *l = (Mat_MPIAIJ *)A->data;
921   PetscMPIInt        n = A->rmap->n;
922   PetscInt           i, j, r, m, len = 0;
923   PetscInt          *lrows, *owners = A->rmap->range;
924   PetscMPIInt        p = 0;
925   PetscSFNode       *rrows;
926   PetscSF            sf;
927   const PetscScalar *xx;
928   PetscScalar       *bb, *mask, *aij_a;
929   Vec                xmask, lmask;
930   Mat_SeqAIJ        *aij = (Mat_SeqAIJ *)l->B->data;
931   const PetscInt    *aj, *ii, *ridx;
932   PetscScalar       *aa;
933 
934   PetscFunctionBegin;
935   /* Create SF where leaves are input rows and roots are owned rows */
936   PetscCall(PetscMalloc1(n, &lrows));
937   for (r = 0; r < n; ++r) lrows[r] = -1;
938   PetscCall(PetscMalloc1(N, &rrows));
939   for (r = 0; r < N; ++r) {
940     const PetscInt idx = rows[r];
941     PetscCheck(idx >= 0 && A->rmap->N > idx, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row %" PetscInt_FMT " out of range [0,%" PetscInt_FMT ")", idx, A->rmap->N);
942     if (idx < owners[p] || owners[p + 1] <= idx) { /* short-circuit the search if the last p owns this row too */
943       PetscCall(PetscLayoutFindOwner(A->rmap, idx, &p));
944     }
945     rrows[r].rank  = p;
946     rrows[r].index = rows[r] - owners[p];
947   }
948   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
949   PetscCall(PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER));
950   /* Collect flags for rows to be zeroed */
951   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *)rows, lrows, MPI_LOR));
952   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *)rows, lrows, MPI_LOR));
953   PetscCall(PetscSFDestroy(&sf));
954   /* Compress and put in row numbers */
955   for (r = 0; r < n; ++r)
956     if (lrows[r] >= 0) lrows[len++] = r;
957   /* zero diagonal part of matrix */
958   PetscCall(MatZeroRowsColumns(l->A, len, lrows, diag, x, b));
959   /* handle off-diagonal part of matrix */
960   PetscCall(MatCreateVecs(A, &xmask, NULL));
961   PetscCall(VecDuplicate(l->lvec, &lmask));
962   PetscCall(VecGetArray(xmask, &bb));
963   for (i = 0; i < len; i++) bb[lrows[i]] = 1;
964   PetscCall(VecRestoreArray(xmask, &bb));
965   PetscCall(VecScatterBegin(l->Mvctx, xmask, lmask, ADD_VALUES, SCATTER_FORWARD));
966   PetscCall(VecScatterEnd(l->Mvctx, xmask, lmask, ADD_VALUES, SCATTER_FORWARD));
967   PetscCall(VecDestroy(&xmask));
968   if (x && b) { /* this code is buggy when the row and column layout don't match */
969     PetscBool cong;
970 
971     PetscCall(MatHasCongruentLayouts(A, &cong));
972     PetscCheck(cong, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Need matching row/col layout");
973     PetscCall(VecScatterBegin(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
974     PetscCall(VecScatterEnd(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
975     PetscCall(VecGetArrayRead(l->lvec, &xx));
976     PetscCall(VecGetArray(b, &bb));
977   }
978   PetscCall(VecGetArray(lmask, &mask));
979   /* remove zeroed rows of off-diagonal matrix */
980   PetscCall(MatSeqAIJGetArray(l->B, &aij_a));
981   ii = aij->i;
982   for (i = 0; i < len; i++) PetscCall(PetscArrayzero(aij_a + ii[lrows[i]], ii[lrows[i] + 1] - ii[lrows[i]]));
983   /* loop over all elements of off process part of matrix zeroing removed columns*/
984   if (aij->compressedrow.use) {
985     m    = aij->compressedrow.nrows;
986     ii   = aij->compressedrow.i;
987     ridx = aij->compressedrow.rindex;
988     for (i = 0; i < m; i++) {
989       n  = ii[i + 1] - ii[i];
990       aj = aij->j + ii[i];
991       aa = aij_a + ii[i];
992 
993       for (j = 0; j < n; j++) {
994         if (PetscAbsScalar(mask[*aj])) {
995           if (b) bb[*ridx] -= *aa * xx[*aj];
996           *aa = 0.0;
997         }
998         aa++;
999         aj++;
1000       }
1001       ridx++;
1002     }
1003   } else { /* do not use compressed row format */
1004     m = l->B->rmap->n;
1005     for (i = 0; i < m; i++) {
1006       n  = ii[i + 1] - ii[i];
1007       aj = aij->j + ii[i];
1008       aa = aij_a + ii[i];
1009       for (j = 0; j < n; j++) {
1010         if (PetscAbsScalar(mask[*aj])) {
1011           if (b) bb[i] -= *aa * xx[*aj];
1012           *aa = 0.0;
1013         }
1014         aa++;
1015         aj++;
1016       }
1017     }
1018   }
1019   if (x && b) {
1020     PetscCall(VecRestoreArray(b, &bb));
1021     PetscCall(VecRestoreArrayRead(l->lvec, &xx));
1022   }
1023   PetscCall(MatSeqAIJRestoreArray(l->B, &aij_a));
1024   PetscCall(VecRestoreArray(lmask, &mask));
1025   PetscCall(VecDestroy(&lmask));
1026   PetscCall(PetscFree(lrows));
1027 
1028   /* only change matrix nonzero state if pattern was allowed to be changed */
1029   if (!((Mat_SeqAIJ *)(l->A->data))->keepnonzeropattern) {
1030     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
1031     PetscCall(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
1032   }
1033   PetscFunctionReturn(PETSC_SUCCESS);
1034 }
1035 
1036 static PetscErrorCode MatMult_MPIAIJ(Mat A, Vec xx, Vec yy)
1037 {
1038   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1039   PetscInt    nt;
1040   VecScatter  Mvctx = a->Mvctx;
1041 
1042   PetscFunctionBegin;
1043   PetscCall(VecGetLocalSize(xx, &nt));
1044   PetscCheck(nt == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible partition of A (%" PetscInt_FMT ") and xx (%" PetscInt_FMT ")", A->cmap->n, nt);
1045   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
1046   PetscUseTypeMethod(a->A, mult, xx, yy);
1047   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
1048   PetscUseTypeMethod(a->B, multadd, a->lvec, yy, yy);
1049   PetscFunctionReturn(PETSC_SUCCESS);
1050 }
1051 
1052 static PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A, Vec bb, Vec xx)
1053 {
1054   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1055 
1056   PetscFunctionBegin;
1057   PetscCall(MatMultDiagonalBlock(a->A, bb, xx));
1058   PetscFunctionReturn(PETSC_SUCCESS);
1059 }
1060 
1061 static PetscErrorCode MatMultAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
1062 {
1063   Mat_MPIAIJ *a     = (Mat_MPIAIJ *)A->data;
1064   VecScatter  Mvctx = a->Mvctx;
1065 
1066   PetscFunctionBegin;
1067   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
1068   PetscCall((*a->A->ops->multadd)(a->A, xx, yy, zz));
1069   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
1070   PetscCall((*a->B->ops->multadd)(a->B, a->lvec, zz, zz));
1071   PetscFunctionReturn(PETSC_SUCCESS);
1072 }
1073 
1074 static PetscErrorCode MatMultTranspose_MPIAIJ(Mat A, Vec xx, Vec yy)
1075 {
1076   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1077 
1078   PetscFunctionBegin;
1079   /* do nondiagonal part */
1080   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
1081   /* do local part */
1082   PetscCall((*a->A->ops->multtranspose)(a->A, xx, yy));
1083   /* add partial results together */
1084   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
1085   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
1086   PetscFunctionReturn(PETSC_SUCCESS);
1087 }
1088 
1089 static PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat, Mat Bmat, PetscReal tol, PetscBool *f)
1090 {
1091   MPI_Comm    comm;
1092   Mat_MPIAIJ *Aij = (Mat_MPIAIJ *)Amat->data, *Bij = (Mat_MPIAIJ *)Bmat->data;
1093   Mat         Adia = Aij->A, Bdia = Bij->A, Aoff, Boff, *Aoffs, *Boffs;
1094   IS          Me, Notme;
1095   PetscInt    M, N, first, last, *notme, i;
1096   PetscBool   lf;
1097   PetscMPIInt size;
1098 
1099   PetscFunctionBegin;
1100   /* Easy test: symmetric diagonal block */
1101   PetscCall(MatIsTranspose(Adia, Bdia, tol, &lf));
1102   PetscCall(MPIU_Allreduce(&lf, f, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)Amat)));
1103   if (!*f) PetscFunctionReturn(PETSC_SUCCESS);
1104   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
1105   PetscCallMPI(MPI_Comm_size(comm, &size));
1106   if (size == 1) PetscFunctionReturn(PETSC_SUCCESS);
1107 
1108   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
1109   PetscCall(MatGetSize(Amat, &M, &N));
1110   PetscCall(MatGetOwnershipRange(Amat, &first, &last));
1111   PetscCall(PetscMalloc1(N - last + first, &notme));
1112   for (i = 0; i < first; i++) notme[i] = i;
1113   for (i = last; i < M; i++) notme[i - last + first] = i;
1114   PetscCall(ISCreateGeneral(MPI_COMM_SELF, N - last + first, notme, PETSC_COPY_VALUES, &Notme));
1115   PetscCall(ISCreateStride(MPI_COMM_SELF, last - first, first, 1, &Me));
1116   PetscCall(MatCreateSubMatrices(Amat, 1, &Me, &Notme, MAT_INITIAL_MATRIX, &Aoffs));
1117   Aoff = Aoffs[0];
1118   PetscCall(MatCreateSubMatrices(Bmat, 1, &Notme, &Me, MAT_INITIAL_MATRIX, &Boffs));
1119   Boff = Boffs[0];
1120   PetscCall(MatIsTranspose(Aoff, Boff, tol, f));
1121   PetscCall(MatDestroyMatrices(1, &Aoffs));
1122   PetscCall(MatDestroyMatrices(1, &Boffs));
1123   PetscCall(ISDestroy(&Me));
1124   PetscCall(ISDestroy(&Notme));
1125   PetscCall(PetscFree(notme));
1126   PetscFunctionReturn(PETSC_SUCCESS);
1127 }
1128 
1129 static PetscErrorCode MatIsSymmetric_MPIAIJ(Mat A, PetscReal tol, PetscBool *f)
1130 {
1131   PetscFunctionBegin;
1132   PetscCall(MatIsTranspose_MPIAIJ(A, A, tol, f));
1133   PetscFunctionReturn(PETSC_SUCCESS);
1134 }
1135 
1136 static PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
1137 {
1138   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1139 
1140   PetscFunctionBegin;
1141   /* do nondiagonal part */
1142   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
1143   /* do local part */
1144   PetscCall((*a->A->ops->multtransposeadd)(a->A, xx, yy, zz));
1145   /* add partial results together */
1146   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
1147   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
1148   PetscFunctionReturn(PETSC_SUCCESS);
1149 }
1150 
1151 /*
1152   This only works correctly for square matrices where the subblock A->A is the
1153    diagonal block
1154 */
1155 static PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A, Vec v)
1156 {
1157   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1158 
1159   PetscFunctionBegin;
1160   PetscCheck(A->rmap->N == A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Supports only square matrix where A->A is diag block");
1161   PetscCheck(A->rmap->rstart == A->cmap->rstart && A->rmap->rend == A->cmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "row partition must equal col partition");
1162   PetscCall(MatGetDiagonal(a->A, v));
1163   PetscFunctionReturn(PETSC_SUCCESS);
1164 }
1165 
1166 static PetscErrorCode MatScale_MPIAIJ(Mat A, PetscScalar aa)
1167 {
1168   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1169 
1170   PetscFunctionBegin;
1171   PetscCall(MatScale(a->A, aa));
1172   PetscCall(MatScale(a->B, aa));
1173   PetscFunctionReturn(PETSC_SUCCESS);
1174 }
1175 
1176 static PetscErrorCode MatView_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
1177 {
1178   Mat_MPIAIJ        *aij    = (Mat_MPIAIJ *)mat->data;
1179   Mat_SeqAIJ        *A      = (Mat_SeqAIJ *)aij->A->data;
1180   Mat_SeqAIJ        *B      = (Mat_SeqAIJ *)aij->B->data;
1181   const PetscInt    *garray = aij->garray;
1182   const PetscScalar *aa, *ba;
1183   PetscInt           header[4], M, N, m, rs, cs, cnt, i, ja, jb;
1184   PetscInt64         nz, hnz;
1185   PetscInt          *rowlens;
1186   PetscInt          *colidxs;
1187   PetscScalar       *matvals;
1188   PetscMPIInt        rank;
1189 
1190   PetscFunctionBegin;
1191   PetscCall(PetscViewerSetUp(viewer));
1192 
1193   M  = mat->rmap->N;
1194   N  = mat->cmap->N;
1195   m  = mat->rmap->n;
1196   rs = mat->rmap->rstart;
1197   cs = mat->cmap->rstart;
1198   nz = A->nz + B->nz;
1199 
1200   /* write matrix header */
1201   header[0] = MAT_FILE_CLASSID;
1202   header[1] = M;
1203   header[2] = N;
1204   PetscCallMPI(MPI_Reduce(&nz, &hnz, 1, MPIU_INT64, MPI_SUM, 0, PetscObjectComm((PetscObject)mat)));
1205   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
1206   if (rank == 0) {
1207     if (hnz > PETSC_MAX_INT) header[3] = PETSC_MAX_INT;
1208     else header[3] = (PetscInt)hnz;
1209   }
1210   PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));
1211 
1212   /* fill in and store row lengths  */
1213   PetscCall(PetscMalloc1(m, &rowlens));
1214   for (i = 0; i < m; i++) rowlens[i] = A->i[i + 1] - A->i[i] + B->i[i + 1] - B->i[i];
1215   PetscCall(PetscViewerBinaryWriteAll(viewer, rowlens, m, rs, M, PETSC_INT));
1216   PetscCall(PetscFree(rowlens));
1217 
1218   /* fill in and store column indices */
1219   PetscCall(PetscMalloc1(nz, &colidxs));
1220   for (cnt = 0, i = 0; i < m; i++) {
1221     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
1222       if (garray[B->j[jb]] > cs) break;
1223       colidxs[cnt++] = garray[B->j[jb]];
1224     }
1225     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) colidxs[cnt++] = A->j[ja] + cs;
1226     for (; jb < B->i[i + 1]; jb++) colidxs[cnt++] = garray[B->j[jb]];
1227   }
1228   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
1229   PetscCall(PetscViewerBinaryWriteAll(viewer, colidxs, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
1230   PetscCall(PetscFree(colidxs));
1231 
1232   /* fill in and store nonzero values */
1233   PetscCall(MatSeqAIJGetArrayRead(aij->A, &aa));
1234   PetscCall(MatSeqAIJGetArrayRead(aij->B, &ba));
1235   PetscCall(PetscMalloc1(nz, &matvals));
1236   for (cnt = 0, i = 0; i < m; i++) {
1237     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
1238       if (garray[B->j[jb]] > cs) break;
1239       matvals[cnt++] = ba[jb];
1240     }
1241     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) matvals[cnt++] = aa[ja];
1242     for (; jb < B->i[i + 1]; jb++) matvals[cnt++] = ba[jb];
1243   }
1244   PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &aa));
1245   PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &ba));
1246   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_LIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
1247   PetscCall(PetscViewerBinaryWriteAll(viewer, matvals, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
1248   PetscCall(PetscFree(matvals));
1249 
1250   /* write block size option to the viewer's .info file */
1251   PetscCall(MatView_Binary_BlockSizes(mat, viewer));
1252   PetscFunctionReturn(PETSC_SUCCESS);
1253 }
1254 
1255 #include <petscdraw.h>
1256 static PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat, PetscViewer viewer)
1257 {
1258   Mat_MPIAIJ       *aij  = (Mat_MPIAIJ *)mat->data;
1259   PetscMPIInt       rank = aij->rank, size = aij->size;
1260   PetscBool         isdraw, iascii, isbinary;
1261   PetscViewer       sviewer;
1262   PetscViewerFormat format;
1263 
1264   PetscFunctionBegin;
1265   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
1266   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1267   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
1268   if (iascii) {
1269     PetscCall(PetscViewerGetFormat(viewer, &format));
1270     if (format == PETSC_VIEWER_LOAD_BALANCE) {
1271       PetscInt i, nmax = 0, nmin = PETSC_MAX_INT, navg = 0, *nz, nzlocal = ((Mat_SeqAIJ *)(aij->A->data))->nz + ((Mat_SeqAIJ *)(aij->B->data))->nz;
1272       PetscCall(PetscMalloc1(size, &nz));
1273       PetscCallMPI(MPI_Allgather(&nzlocal, 1, MPIU_INT, nz, 1, MPIU_INT, PetscObjectComm((PetscObject)mat)));
1274       for (i = 0; i < (PetscInt)size; i++) {
1275         nmax = PetscMax(nmax, nz[i]);
1276         nmin = PetscMin(nmin, nz[i]);
1277         navg += nz[i];
1278       }
1279       PetscCall(PetscFree(nz));
1280       navg = navg / size;
1281       PetscCall(PetscViewerASCIIPrintf(viewer, "Load Balance - Nonzeros: Min %" PetscInt_FMT "  avg %" PetscInt_FMT "  max %" PetscInt_FMT "\n", nmin, navg, nmax));
1282       PetscFunctionReturn(PETSC_SUCCESS);
1283     }
1284     PetscCall(PetscViewerGetFormat(viewer, &format));
1285     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
1286       MatInfo   info;
1287       PetscInt *inodes = NULL;
1288 
1289       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
1290       PetscCall(MatGetInfo(mat, MAT_LOCAL, &info));
1291       PetscCall(MatInodeGetInodeSizes(aij->A, NULL, &inodes, NULL));
1292       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
1293       if (!inodes) {
1294         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] Local rows %" PetscInt_FMT " nz %" PetscInt_FMT " nz alloced %" PetscInt_FMT " mem %g, not using I-node routines\n", rank, mat->rmap->n, (PetscInt)info.nz_used, (PetscInt)info.nz_allocated,
1295                                                      (double)info.memory));
1296       } else {
1297         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] Local rows %" PetscInt_FMT " nz %" PetscInt_FMT " nz alloced %" PetscInt_FMT " mem %g, using I-node routines\n", rank, mat->rmap->n, (PetscInt)info.nz_used, (PetscInt)info.nz_allocated,
1298                                                      (double)info.memory));
1299       }
1300       PetscCall(MatGetInfo(aij->A, MAT_LOCAL, &info));
1301       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] on-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
1302       PetscCall(MatGetInfo(aij->B, MAT_LOCAL, &info));
1303       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] off-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
1304       PetscCall(PetscViewerFlush(viewer));
1305       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
1306       PetscCall(PetscViewerASCIIPrintf(viewer, "Information on VecScatter used in matrix-vector product: \n"));
1307       PetscCall(VecScatterView(aij->Mvctx, viewer));
1308       PetscFunctionReturn(PETSC_SUCCESS);
1309     } else if (format == PETSC_VIEWER_ASCII_INFO) {
1310       PetscInt inodecount, inodelimit, *inodes;
1311       PetscCall(MatInodeGetInodeSizes(aij->A, &inodecount, &inodes, &inodelimit));
1312       if (inodes) {
1313         PetscCall(PetscViewerASCIIPrintf(viewer, "using I-node (on process 0) routines: found %" PetscInt_FMT " nodes, limit used is %" PetscInt_FMT "\n", inodecount, inodelimit));
1314       } else {
1315         PetscCall(PetscViewerASCIIPrintf(viewer, "not using I-node (on process 0) routines\n"));
1316       }
1317       PetscFunctionReturn(PETSC_SUCCESS);
1318     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
1319       PetscFunctionReturn(PETSC_SUCCESS);
1320     }
1321   } else if (isbinary) {
1322     if (size == 1) {
1323       PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
1324       PetscCall(MatView(aij->A, viewer));
1325     } else {
1326       PetscCall(MatView_MPIAIJ_Binary(mat, viewer));
1327     }
1328     PetscFunctionReturn(PETSC_SUCCESS);
1329   } else if (iascii && size == 1) {
1330     PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
1331     PetscCall(MatView(aij->A, viewer));
1332     PetscFunctionReturn(PETSC_SUCCESS);
1333   } else if (isdraw) {
1334     PetscDraw draw;
1335     PetscBool isnull;
1336     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
1337     PetscCall(PetscDrawIsNull(draw, &isnull));
1338     if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
1339   }
1340 
1341   { /* assemble the entire matrix onto first processor */
1342     Mat A = NULL, Av;
1343     IS  isrow, iscol;
1344 
1345     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->rmap->N : 0, 0, 1, &isrow));
1346     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->cmap->N : 0, 0, 1, &iscol));
1347     PetscCall(MatCreateSubMatrix(mat, isrow, iscol, MAT_INITIAL_MATRIX, &A));
1348     PetscCall(MatMPIAIJGetSeqAIJ(A, &Av, NULL, NULL));
1349     /*  The commented code uses MatCreateSubMatrices instead */
1350     /*
1351     Mat *AA, A = NULL, Av;
1352     IS  isrow,iscol;
1353 
1354     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->rmap->N : 0,0,1,&isrow));
1355     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->cmap->N : 0,0,1,&iscol));
1356     PetscCall(MatCreateSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&AA));
1357     if (rank == 0) {
1358        PetscCall(PetscObjectReference((PetscObject)AA[0]));
1359        A    = AA[0];
1360        Av   = AA[0];
1361     }
1362     PetscCall(MatDestroySubMatrices(1,&AA));
1363 */
1364     PetscCall(ISDestroy(&iscol));
1365     PetscCall(ISDestroy(&isrow));
1366     /*
1367        Everyone has to call to draw the matrix since the graphics waits are
1368        synchronized across all processors that share the PetscDraw object
1369     */
1370     PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
1371     if (rank == 0) {
1372       if (((PetscObject)mat)->name) PetscCall(PetscObjectSetName((PetscObject)Av, ((PetscObject)mat)->name));
1373       PetscCall(MatView_SeqAIJ(Av, sviewer));
1374     }
1375     PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
1376     PetscCall(PetscViewerFlush(viewer));
1377     PetscCall(MatDestroy(&A));
1378   }
1379   PetscFunctionReturn(PETSC_SUCCESS);
1380 }
1381 
1382 PetscErrorCode MatView_MPIAIJ(Mat mat, PetscViewer viewer)
1383 {
1384   PetscBool iascii, isdraw, issocket, isbinary;
1385 
1386   PetscFunctionBegin;
1387   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
1388   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
1389   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
1390   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSOCKET, &issocket));
1391   if (iascii || isdraw || isbinary || issocket) PetscCall(MatView_MPIAIJ_ASCIIorDraworSocket(mat, viewer));
1392   PetscFunctionReturn(PETSC_SUCCESS);
1393 }
1394 
1395 static PetscErrorCode MatSOR_MPIAIJ(Mat matin, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
1396 {
1397   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)matin->data;
1398   Vec         bb1 = NULL;
1399   PetscBool   hasop;
1400 
1401   PetscFunctionBegin;
1402   if (flag == SOR_APPLY_UPPER) {
1403     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
1404     PetscFunctionReturn(PETSC_SUCCESS);
1405   }
1406 
1407   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) PetscCall(VecDuplicate(bb, &bb1));
1408 
1409   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
1410     if (flag & SOR_ZERO_INITIAL_GUESS) {
1411       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
1412       its--;
1413     }
1414 
1415     while (its--) {
1416       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
1417       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
1418 
1419       /* update rhs: bb1 = bb - B*x */
1420       PetscCall(VecScale(mat->lvec, -1.0));
1421       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));
1422 
1423       /* local sweep */
1424       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_SYMMETRIC_SWEEP, fshift, lits, 1, xx));
1425     }
1426   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
1427     if (flag & SOR_ZERO_INITIAL_GUESS) {
1428       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
1429       its--;
1430     }
1431     while (its--) {
1432       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
1433       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
1434 
1435       /* update rhs: bb1 = bb - B*x */
1436       PetscCall(VecScale(mat->lvec, -1.0));
1437       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));
1438 
1439       /* local sweep */
1440       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_FORWARD_SWEEP, fshift, lits, 1, xx));
1441     }
1442   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
1443     if (flag & SOR_ZERO_INITIAL_GUESS) {
1444       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
1445       its--;
1446     }
1447     while (its--) {
1448       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
1449       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
1450 
1451       /* update rhs: bb1 = bb - B*x */
1452       PetscCall(VecScale(mat->lvec, -1.0));
1453       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));
1454 
1455       /* local sweep */
1456       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_BACKWARD_SWEEP, fshift, lits, 1, xx));
1457     }
1458   } else if (flag & SOR_EISENSTAT) {
1459     Vec xx1;
1460 
1461     PetscCall(VecDuplicate(bb, &xx1));
1462     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP), fshift, lits, 1, xx));
1463 
1464     PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
1465     PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
1466     if (!mat->diag) {
1467       PetscCall(MatCreateVecs(matin, &mat->diag, NULL));
1468       PetscCall(MatGetDiagonal(matin, mat->diag));
1469     }
1470     PetscCall(MatHasOperation(matin, MATOP_MULT_DIAGONAL_BLOCK, &hasop));
1471     if (hasop) {
1472       PetscCall(MatMultDiagonalBlock(matin, xx, bb1));
1473     } else {
1474       PetscCall(VecPointwiseMult(bb1, mat->diag, xx));
1475     }
1476     PetscCall(VecAYPX(bb1, (omega - 2.0) / omega, bb));
1477 
1478     PetscCall(MatMultAdd(mat->B, mat->lvec, bb1, bb1));
1479 
1480     /* local sweep */
1481     PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP), fshift, lits, 1, xx1));
1482     PetscCall(VecAXPY(xx, 1.0, xx1));
1483     PetscCall(VecDestroy(&xx1));
1484   } else SETERRQ(PetscObjectComm((PetscObject)matin), PETSC_ERR_SUP, "Parallel SOR not supported");
1485 
1486   PetscCall(VecDestroy(&bb1));
1487 
1488   matin->factorerrortype = mat->A->factorerrortype;
1489   PetscFunctionReturn(PETSC_SUCCESS);
1490 }
1491 
1492 static PetscErrorCode MatPermute_MPIAIJ(Mat A, IS rowp, IS colp, Mat *B)
1493 {
1494   Mat             aA, aB, Aperm;
1495   const PetscInt *rwant, *cwant, *gcols, *ai, *bi, *aj, *bj;
1496   PetscScalar    *aa, *ba;
1497   PetscInt        i, j, m, n, ng, anz, bnz, *dnnz, *onnz, *tdnnz, *tonnz, *rdest, *cdest, *work, *gcdest;
1498   PetscSF         rowsf, sf;
1499   IS              parcolp = NULL;
1500   PetscBool       done;
1501 
1502   PetscFunctionBegin;
1503   PetscCall(MatGetLocalSize(A, &m, &n));
1504   PetscCall(ISGetIndices(rowp, &rwant));
1505   PetscCall(ISGetIndices(colp, &cwant));
1506   PetscCall(PetscMalloc3(PetscMax(m, n), &work, m, &rdest, n, &cdest));
1507 
1508   /* Invert row permutation to find out where my rows should go */
1509   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &rowsf));
1510   PetscCall(PetscSFSetGraphLayout(rowsf, A->rmap, A->rmap->n, NULL, PETSC_OWN_POINTER, rwant));
1511   PetscCall(PetscSFSetFromOptions(rowsf));
1512   for (i = 0; i < m; i++) work[i] = A->rmap->rstart + i;
1513   PetscCall(PetscSFReduceBegin(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));
1514   PetscCall(PetscSFReduceEnd(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));
1515 
1516   /* Invert column permutation to find out where my columns should go */
1517   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
1518   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, A->cmap->n, NULL, PETSC_OWN_POINTER, cwant));
1519   PetscCall(PetscSFSetFromOptions(sf));
1520   for (i = 0; i < n; i++) work[i] = A->cmap->rstart + i;
1521   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, work, cdest, MPI_REPLACE));
1522   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, work, cdest, MPI_REPLACE));
1523   PetscCall(PetscSFDestroy(&sf));
1524 
1525   PetscCall(ISRestoreIndices(rowp, &rwant));
1526   PetscCall(ISRestoreIndices(colp, &cwant));
1527   PetscCall(MatMPIAIJGetSeqAIJ(A, &aA, &aB, &gcols));
1528 
1529   /* Find out where my gcols should go */
1530   PetscCall(MatGetSize(aB, NULL, &ng));
1531   PetscCall(PetscMalloc1(ng, &gcdest));
1532   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
1533   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, ng, NULL, PETSC_OWN_POINTER, gcols));
1534   PetscCall(PetscSFSetFromOptions(sf));
1535   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
1536   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
1537   PetscCall(PetscSFDestroy(&sf));
1538 
1539   PetscCall(PetscCalloc4(m, &dnnz, m, &onnz, m, &tdnnz, m, &tonnz));
1540   PetscCall(MatGetRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
1541   PetscCall(MatGetRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
1542   for (i = 0; i < m; i++) {
1543     PetscInt    row = rdest[i];
1544     PetscMPIInt rowner;
1545     PetscCall(PetscLayoutFindOwner(A->rmap, row, &rowner));
1546     for (j = ai[i]; j < ai[i + 1]; j++) {
1547       PetscInt    col = cdest[aj[j]];
1548       PetscMPIInt cowner;
1549       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner)); /* Could build an index for the columns to eliminate this search */
1550       if (rowner == cowner) dnnz[i]++;
1551       else onnz[i]++;
1552     }
1553     for (j = bi[i]; j < bi[i + 1]; j++) {
1554       PetscInt    col = gcdest[bj[j]];
1555       PetscMPIInt cowner;
1556       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner));
1557       if (rowner == cowner) dnnz[i]++;
1558       else onnz[i]++;
1559     }
1560   }
1561   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
1562   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
1563   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
1564   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
1565   PetscCall(PetscSFDestroy(&rowsf));
1566 
1567   PetscCall(MatCreateAIJ(PetscObjectComm((PetscObject)A), A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N, 0, tdnnz, 0, tonnz, &Aperm));
1568   PetscCall(MatSeqAIJGetArray(aA, &aa));
1569   PetscCall(MatSeqAIJGetArray(aB, &ba));
1570   for (i = 0; i < m; i++) {
1571     PetscInt *acols = dnnz, *bcols = onnz; /* Repurpose now-unneeded arrays */
1572     PetscInt  j0, rowlen;
1573     rowlen = ai[i + 1] - ai[i];
1574     for (j0 = j = 0; j < rowlen; j0 = j) { /* rowlen could be larger than number of rows m, so sum in batches */
1575       for (; j < PetscMin(rowlen, j0 + m); j++) acols[j - j0] = cdest[aj[ai[i] + j]];
1576       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, acols, aa + ai[i] + j0, INSERT_VALUES));
1577     }
1578     rowlen = bi[i + 1] - bi[i];
1579     for (j0 = j = 0; j < rowlen; j0 = j) {
1580       for (; j < PetscMin(rowlen, j0 + m); j++) bcols[j - j0] = gcdest[bj[bi[i] + j]];
1581       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, bcols, ba + bi[i] + j0, INSERT_VALUES));
1582     }
1583   }
1584   PetscCall(MatAssemblyBegin(Aperm, MAT_FINAL_ASSEMBLY));
1585   PetscCall(MatAssemblyEnd(Aperm, MAT_FINAL_ASSEMBLY));
1586   PetscCall(MatRestoreRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
1587   PetscCall(MatRestoreRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
1588   PetscCall(MatSeqAIJRestoreArray(aA, &aa));
1589   PetscCall(MatSeqAIJRestoreArray(aB, &ba));
1590   PetscCall(PetscFree4(dnnz, onnz, tdnnz, tonnz));
1591   PetscCall(PetscFree3(work, rdest, cdest));
1592   PetscCall(PetscFree(gcdest));
1593   if (parcolp) PetscCall(ISDestroy(&colp));
1594   *B = Aperm;
1595   PetscFunctionReturn(PETSC_SUCCESS);
1596 }
1597 
1598 static PetscErrorCode MatGetGhosts_MPIAIJ(Mat mat, PetscInt *nghosts, const PetscInt *ghosts[])
1599 {
1600   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
1601 
1602   PetscFunctionBegin;
1603   PetscCall(MatGetSize(aij->B, NULL, nghosts));
1604   if (ghosts) *ghosts = aij->garray;
1605   PetscFunctionReturn(PETSC_SUCCESS);
1606 }
1607 
1608 static PetscErrorCode MatGetInfo_MPIAIJ(Mat matin, MatInfoType flag, MatInfo *info)
1609 {
1610   Mat_MPIAIJ    *mat = (Mat_MPIAIJ *)matin->data;
1611   Mat            A = mat->A, B = mat->B;
1612   PetscLogDouble isend[5], irecv[5];
1613 
1614   PetscFunctionBegin;
1615   info->block_size = 1.0;
1616   PetscCall(MatGetInfo(A, MAT_LOCAL, info));
1617 
1618   isend[0] = info->nz_used;
1619   isend[1] = info->nz_allocated;
1620   isend[2] = info->nz_unneeded;
1621   isend[3] = info->memory;
1622   isend[4] = info->mallocs;
1623 
1624   PetscCall(MatGetInfo(B, MAT_LOCAL, info));
1625 
1626   isend[0] += info->nz_used;
1627   isend[1] += info->nz_allocated;
1628   isend[2] += info->nz_unneeded;
1629   isend[3] += info->memory;
1630   isend[4] += info->mallocs;
1631   if (flag == MAT_LOCAL) {
1632     info->nz_used      = isend[0];
1633     info->nz_allocated = isend[1];
1634     info->nz_unneeded  = isend[2];
1635     info->memory       = isend[3];
1636     info->mallocs      = isend[4];
1637   } else if (flag == MAT_GLOBAL_MAX) {
1638     PetscCall(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)matin)));
1639 
1640     info->nz_used      = irecv[0];
1641     info->nz_allocated = irecv[1];
1642     info->nz_unneeded  = irecv[2];
1643     info->memory       = irecv[3];
1644     info->mallocs      = irecv[4];
1645   } else if (flag == MAT_GLOBAL_SUM) {
1646     PetscCall(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)matin)));
1647 
1648     info->nz_used      = irecv[0];
1649     info->nz_allocated = irecv[1];
1650     info->nz_unneeded  = irecv[2];
1651     info->memory       = irecv[3];
1652     info->mallocs      = irecv[4];
1653   }
1654   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
1655   info->fill_ratio_needed = 0;
1656   info->factor_mallocs    = 0;
1657   PetscFunctionReturn(PETSC_SUCCESS);
1658 }
1659 
1660 PetscErrorCode MatSetOption_MPIAIJ(Mat A, MatOption op, PetscBool flg)
1661 {
1662   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
1663 
1664   PetscFunctionBegin;
1665   switch (op) {
1666   case MAT_NEW_NONZERO_LOCATIONS:
1667   case MAT_NEW_NONZERO_ALLOCATION_ERR:
1668   case MAT_UNUSED_NONZERO_LOCATION_ERR:
1669   case MAT_KEEP_NONZERO_PATTERN:
1670   case MAT_NEW_NONZERO_LOCATION_ERR:
1671   case MAT_USE_INODES:
1672   case MAT_IGNORE_ZERO_ENTRIES:
1673   case MAT_FORM_EXPLICIT_TRANSPOSE:
1674     MatCheckPreallocated(A, 1);
1675     PetscCall(MatSetOption(a->A, op, flg));
1676     PetscCall(MatSetOption(a->B, op, flg));
1677     break;
1678   case MAT_ROW_ORIENTED:
1679     MatCheckPreallocated(A, 1);
1680     a->roworiented = flg;
1681 
1682     PetscCall(MatSetOption(a->A, op, flg));
1683     PetscCall(MatSetOption(a->B, op, flg));
1684     break;
1685   case MAT_FORCE_DIAGONAL_ENTRIES:
1686   case MAT_SORTED_FULL:
1687     PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
1688     break;
1689   case MAT_IGNORE_OFF_PROC_ENTRIES:
1690     a->donotstash = flg;
1691     break;
1692   /* Symmetry flags are handled directly by MatSetOption() and they don't affect preallocation */
1693   case MAT_SPD:
1694   case MAT_SYMMETRIC:
1695   case MAT_STRUCTURALLY_SYMMETRIC:
1696   case MAT_HERMITIAN:
1697   case MAT_SYMMETRY_ETERNAL:
1698   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
1699   case MAT_SPD_ETERNAL:
1700     /* if the diagonal matrix is square it inherits some of the properties above */
1701     break;
1702   case MAT_SUBMAT_SINGLEIS:
1703     A->submat_singleis = flg;
1704     break;
1705   case MAT_STRUCTURE_ONLY:
1706     /* The option is handled directly by MatSetOption() */
1707     break;
1708   default:
1709     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unknown option %d", op);
1710   }
1711   PetscFunctionReturn(PETSC_SUCCESS);
1712 }
1713 
1714 PetscErrorCode MatGetRow_MPIAIJ(Mat matin, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
1715 {
1716   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)matin->data;
1717   PetscScalar *vworkA, *vworkB, **pvA, **pvB, *v_p;
1718   PetscInt     i, *cworkA, *cworkB, **pcA, **pcB, cstart = matin->cmap->rstart;
1719   PetscInt     nztot, nzA, nzB, lrow, rstart = matin->rmap->rstart, rend = matin->rmap->rend;
1720   PetscInt    *cmap, *idx_p;
1721 
1722   PetscFunctionBegin;
1723   PetscCheck(!mat->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Already active");
1724   mat->getrowactive = PETSC_TRUE;
1725 
1726   if (!mat->rowvalues && (idx || v)) {
1727     /*
1728         allocate enough space to hold information from the longest row.
1729     */
1730     Mat_SeqAIJ *Aa = (Mat_SeqAIJ *)mat->A->data, *Ba = (Mat_SeqAIJ *)mat->B->data;
1731     PetscInt    max = 1, tmp;
1732     for (i = 0; i < matin->rmap->n; i++) {
1733       tmp = Aa->i[i + 1] - Aa->i[i] + Ba->i[i + 1] - Ba->i[i];
1734       if (max < tmp) max = tmp;
1735     }
1736     PetscCall(PetscMalloc2(max, &mat->rowvalues, max, &mat->rowindices));
1737   }
1738 
1739   PetscCheck(row >= rstart && row < rend, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Only local rows");
1740   lrow = row - rstart;
1741 
1742   pvA = &vworkA;
1743   pcA = &cworkA;
1744   pvB = &vworkB;
1745   pcB = &cworkB;
1746   if (!v) {
1747     pvA = NULL;
1748     pvB = NULL;
1749   }
1750   if (!idx) {
1751     pcA = NULL;
1752     if (!v) pcB = NULL;
1753   }
1754   PetscCall((*mat->A->ops->getrow)(mat->A, lrow, &nzA, pcA, pvA));
1755   PetscCall((*mat->B->ops->getrow)(mat->B, lrow, &nzB, pcB, pvB));
1756   nztot = nzA + nzB;
1757 
1758   cmap = mat->garray;
1759   if (v || idx) {
1760     if (nztot) {
1761       /* Sort by increasing column numbers, assuming A and B already sorted */
1762       PetscInt imark = -1;
1763       if (v) {
1764         *v = v_p = mat->rowvalues;
1765         for (i = 0; i < nzB; i++) {
1766           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
1767           else break;
1768         }
1769         imark = i;
1770         for (i = 0; i < nzA; i++) v_p[imark + i] = vworkA[i];
1771         for (i = imark; i < nzB; i++) v_p[nzA + i] = vworkB[i];
1772       }
1773       if (idx) {
1774         *idx = idx_p = mat->rowindices;
1775         if (imark > -1) {
1776           for (i = 0; i < imark; i++) idx_p[i] = cmap[cworkB[i]];
1777         } else {
1778           for (i = 0; i < nzB; i++) {
1779             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
1780             else break;
1781           }
1782           imark = i;
1783         }
1784         for (i = 0; i < nzA; i++) idx_p[imark + i] = cstart + cworkA[i];
1785         for (i = imark; i < nzB; i++) idx_p[nzA + i] = cmap[cworkB[i]];
1786       }
1787     } else {
1788       if (idx) *idx = NULL;
1789       if (v) *v = NULL;
1790     }
1791   }
1792   *nz = nztot;
1793   PetscCall((*mat->A->ops->restorerow)(mat->A, lrow, &nzA, pcA, pvA));
1794   PetscCall((*mat->B->ops->restorerow)(mat->B, lrow, &nzB, pcB, pvB));
1795   PetscFunctionReturn(PETSC_SUCCESS);
1796 }
1797 
1798 PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
1799 {
1800   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
1801 
1802   PetscFunctionBegin;
1803   PetscCheck(aij->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "MatGetRow() must be called first");
1804   aij->getrowactive = PETSC_FALSE;
1805   PetscFunctionReturn(PETSC_SUCCESS);
1806 }
1807 
1808 static PetscErrorCode MatNorm_MPIAIJ(Mat mat, NormType type, PetscReal *norm)
1809 {
1810   Mat_MPIAIJ      *aij  = (Mat_MPIAIJ *)mat->data;
1811   Mat_SeqAIJ      *amat = (Mat_SeqAIJ *)aij->A->data, *bmat = (Mat_SeqAIJ *)aij->B->data;
1812   PetscInt         i, j, cstart = mat->cmap->rstart;
1813   PetscReal        sum = 0.0;
1814   const MatScalar *v, *amata, *bmata;
1815 
1816   PetscFunctionBegin;
1817   if (aij->size == 1) {
1818     PetscCall(MatNorm(aij->A, type, norm));
1819   } else {
1820     PetscCall(MatSeqAIJGetArrayRead(aij->A, &amata));
1821     PetscCall(MatSeqAIJGetArrayRead(aij->B, &bmata));
1822     if (type == NORM_FROBENIUS) {
1823       v = amata;
1824       for (i = 0; i < amat->nz; i++) {
1825         sum += PetscRealPart(PetscConj(*v) * (*v));
1826         v++;
1827       }
1828       v = bmata;
1829       for (i = 0; i < bmat->nz; i++) {
1830         sum += PetscRealPart(PetscConj(*v) * (*v));
1831         v++;
1832       }
1833       PetscCall(MPIU_Allreduce(&sum, norm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
1834       *norm = PetscSqrtReal(*norm);
1835       PetscCall(PetscLogFlops(2.0 * amat->nz + 2.0 * bmat->nz));
1836     } else if (type == NORM_1) { /* max column norm */
1837       PetscReal *tmp, *tmp2;
1838       PetscInt  *jj, *garray = aij->garray;
1839       PetscCall(PetscCalloc1(mat->cmap->N + 1, &tmp));
1840       PetscCall(PetscMalloc1(mat->cmap->N + 1, &tmp2));
1841       *norm = 0.0;
1842       v     = amata;
1843       jj    = amat->j;
1844       for (j = 0; j < amat->nz; j++) {
1845         tmp[cstart + *jj++] += PetscAbsScalar(*v);
1846         v++;
1847       }
1848       v  = bmata;
1849       jj = bmat->j;
1850       for (j = 0; j < bmat->nz; j++) {
1851         tmp[garray[*jj++]] += PetscAbsScalar(*v);
1852         v++;
1853       }
1854       PetscCall(MPIU_Allreduce(tmp, tmp2, mat->cmap->N, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
1855       for (j = 0; j < mat->cmap->N; j++) {
1856         if (tmp2[j] > *norm) *norm = tmp2[j];
1857       }
1858       PetscCall(PetscFree(tmp));
1859       PetscCall(PetscFree(tmp2));
1860       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
1861     } else if (type == NORM_INFINITY) { /* max row norm */
1862       PetscReal ntemp = 0.0;
1863       for (j = 0; j < aij->A->rmap->n; j++) {
1864         v   = amata + amat->i[j];
1865         sum = 0.0;
1866         for (i = 0; i < amat->i[j + 1] - amat->i[j]; i++) {
1867           sum += PetscAbsScalar(*v);
1868           v++;
1869         }
1870         v = bmata + bmat->i[j];
1871         for (i = 0; i < bmat->i[j + 1] - bmat->i[j]; i++) {
1872           sum += PetscAbsScalar(*v);
1873           v++;
1874         }
1875         if (sum > ntemp) ntemp = sum;
1876       }
1877       PetscCall(MPIU_Allreduce(&ntemp, norm, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)mat)));
1878       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
1879     } else SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "No support for two norm");
1880     PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &amata));
1881     PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &bmata));
1882   }
1883   PetscFunctionReturn(PETSC_SUCCESS);
1884 }
1885 
1886 static PetscErrorCode MatTranspose_MPIAIJ(Mat A, MatReuse reuse, Mat *matout)
1887 {
1888   Mat_MPIAIJ      *a    = (Mat_MPIAIJ *)A->data, *b;
1889   Mat_SeqAIJ      *Aloc = (Mat_SeqAIJ *)a->A->data, *Bloc = (Mat_SeqAIJ *)a->B->data, *sub_B_diag;
1890   PetscInt         M = A->rmap->N, N = A->cmap->N, ma, na, mb, nb, row, *cols, *cols_tmp, *B_diag_ilen, i, ncol, A_diag_ncol;
1891   const PetscInt  *ai, *aj, *bi, *bj, *B_diag_i;
1892   Mat              B, A_diag, *B_diag;
1893   const MatScalar *pbv, *bv;
1894 
1895   PetscFunctionBegin;
1896   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *matout));
1897   ma = A->rmap->n;
1898   na = A->cmap->n;
1899   mb = a->B->rmap->n;
1900   nb = a->B->cmap->n;
1901   ai = Aloc->i;
1902   aj = Aloc->j;
1903   bi = Bloc->i;
1904   bj = Bloc->j;
1905   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
1906     PetscInt            *d_nnz, *g_nnz, *o_nnz;
1907     PetscSFNode         *oloc;
1908     PETSC_UNUSED PetscSF sf;
1909 
1910     PetscCall(PetscMalloc4(na, &d_nnz, na, &o_nnz, nb, &g_nnz, nb, &oloc));
1911     /* compute d_nnz for preallocation */
1912     PetscCall(PetscArrayzero(d_nnz, na));
1913     for (i = 0; i < ai[ma]; i++) d_nnz[aj[i]]++;
1914     /* compute local off-diagonal contributions */
1915     PetscCall(PetscArrayzero(g_nnz, nb));
1916     for (i = 0; i < bi[ma]; i++) g_nnz[bj[i]]++;
1917     /* map those to global */
1918     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
1919     PetscCall(PetscSFSetGraphLayout(sf, A->cmap, nb, NULL, PETSC_USE_POINTER, a->garray));
1920     PetscCall(PetscSFSetFromOptions(sf));
1921     PetscCall(PetscArrayzero(o_nnz, na));
1922     PetscCall(PetscSFReduceBegin(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
1923     PetscCall(PetscSFReduceEnd(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
1924     PetscCall(PetscSFDestroy(&sf));
1925 
1926     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
1927     PetscCall(MatSetSizes(B, A->cmap->n, A->rmap->n, N, M));
1928     PetscCall(MatSetBlockSizes(B, PetscAbs(A->cmap->bs), PetscAbs(A->rmap->bs)));
1929     PetscCall(MatSetType(B, ((PetscObject)A)->type_name));
1930     PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
1931     PetscCall(PetscFree4(d_nnz, o_nnz, g_nnz, oloc));
1932   } else {
1933     B = *matout;
1934     PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
1935   }
1936 
1937   b           = (Mat_MPIAIJ *)B->data;
1938   A_diag      = a->A;
1939   B_diag      = &b->A;
1940   sub_B_diag  = (Mat_SeqAIJ *)(*B_diag)->data;
1941   A_diag_ncol = A_diag->cmap->N;
1942   B_diag_ilen = sub_B_diag->ilen;
1943   B_diag_i    = sub_B_diag->i;
1944 
1945   /* Set ilen for diagonal of B */
1946   for (i = 0; i < A_diag_ncol; i++) B_diag_ilen[i] = B_diag_i[i + 1] - B_diag_i[i];
1947 
1948   /* Transpose the diagonal part of the matrix. In contrast to the off-diagonal part, this can be done
1949   very quickly (=without using MatSetValues), because all writes are local. */
1950   PetscCall(MatTransposeSetPrecursor(A_diag, *B_diag));
1951   PetscCall(MatTranspose(A_diag, MAT_REUSE_MATRIX, B_diag));
1952 
1953   /* copy over the B part */
1954   PetscCall(PetscMalloc1(bi[mb], &cols));
1955   PetscCall(MatSeqAIJGetArrayRead(a->B, &bv));
1956   pbv = bv;
1957   row = A->rmap->rstart;
1958   for (i = 0; i < bi[mb]; i++) cols[i] = a->garray[bj[i]];
1959   cols_tmp = cols;
1960   for (i = 0; i < mb; i++) {
1961     ncol = bi[i + 1] - bi[i];
1962     PetscCall(MatSetValues(B, ncol, cols_tmp, 1, &row, pbv, INSERT_VALUES));
1963     row++;
1964     if (pbv) pbv += ncol;
1965     if (cols_tmp) cols_tmp += ncol;
1966   }
1967   PetscCall(PetscFree(cols));
1968   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &bv));
1969 
1970   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
1971   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
1972   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
1973     *matout = B;
1974   } else {
1975     PetscCall(MatHeaderMerge(A, &B));
1976   }
1977   PetscFunctionReturn(PETSC_SUCCESS);
1978 }
1979 
1980 static PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat, Vec ll, Vec rr)
1981 {
1982   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
1983   Mat         a = aij->A, b = aij->B;
1984   PetscInt    s1, s2, s3;
1985 
1986   PetscFunctionBegin;
1987   PetscCall(MatGetLocalSize(mat, &s2, &s3));
1988   if (rr) {
1989     PetscCall(VecGetLocalSize(rr, &s1));
1990     PetscCheck(s1 == s3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "right vector non-conforming local size");
1991     /* Overlap communication with computation. */
1992     PetscCall(VecScatterBegin(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
1993   }
1994   if (ll) {
1995     PetscCall(VecGetLocalSize(ll, &s1));
1996     PetscCheck(s1 == s2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "left vector non-conforming local size");
1997     PetscUseTypeMethod(b, diagonalscale, ll, NULL);
1998   }
1999   /* scale  the diagonal block */
2000   PetscUseTypeMethod(a, diagonalscale, ll, rr);
2001 
2002   if (rr) {
2003     /* Do a scatter end and then right scale the off-diagonal block */
2004     PetscCall(VecScatterEnd(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
2005     PetscUseTypeMethod(b, diagonalscale, NULL, aij->lvec);
2006   }
2007   PetscFunctionReturn(PETSC_SUCCESS);
2008 }
2009 
2010 static PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
2011 {
2012   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2013 
2014   PetscFunctionBegin;
2015   PetscCall(MatSetUnfactored(a->A));
2016   PetscFunctionReturn(PETSC_SUCCESS);
2017 }
2018 
2019 static PetscErrorCode MatEqual_MPIAIJ(Mat A, Mat B, PetscBool *flag)
2020 {
2021   Mat_MPIAIJ *matB = (Mat_MPIAIJ *)B->data, *matA = (Mat_MPIAIJ *)A->data;
2022   Mat         a, b, c, d;
2023   PetscBool   flg;
2024 
2025   PetscFunctionBegin;
2026   a = matA->A;
2027   b = matA->B;
2028   c = matB->A;
2029   d = matB->B;
2030 
2031   PetscCall(MatEqual(a, c, &flg));
2032   if (flg) PetscCall(MatEqual(b, d, &flg));
2033   PetscCall(MPIU_Allreduce(&flg, flag, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
2034   PetscFunctionReturn(PETSC_SUCCESS);
2035 }
2036 
2037 static PetscErrorCode MatCopy_MPIAIJ(Mat A, Mat B, MatStructure str)
2038 {
2039   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2040   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
2041 
2042   PetscFunctionBegin;
2043   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
2044   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
2045     /* because of the column compression in the off-processor part of the matrix a->B,
2046        the number of columns in a->B and b->B may be different, hence we cannot call
2047        the MatCopy() directly on the two parts. If need be, we can provide a more
2048        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
2049        then copying the submatrices */
2050     PetscCall(MatCopy_Basic(A, B, str));
2051   } else {
2052     PetscCall(MatCopy(a->A, b->A, str));
2053     PetscCall(MatCopy(a->B, b->B, str));
2054   }
2055   PetscCall(PetscObjectStateIncrease((PetscObject)B));
2056   PetscFunctionReturn(PETSC_SUCCESS);
2057 }
2058 
2059 /*
2060    Computes the number of nonzeros per row needed for preallocation when X and Y
2061    have different nonzero structure.
2062 */
2063 PetscErrorCode MatAXPYGetPreallocation_MPIX_private(PetscInt m, const PetscInt *xi, const PetscInt *xj, const PetscInt *xltog, const PetscInt *yi, const PetscInt *yj, const PetscInt *yltog, PetscInt *nnz)
2064 {
2065   PetscInt i, j, k, nzx, nzy;
2066 
2067   PetscFunctionBegin;
2068   /* Set the number of nonzeros in the new matrix */
2069   for (i = 0; i < m; i++) {
2070     const PetscInt *xjj = xj + xi[i], *yjj = yj + yi[i];
2071     nzx    = xi[i + 1] - xi[i];
2072     nzy    = yi[i + 1] - yi[i];
2073     nnz[i] = 0;
2074     for (j = 0, k = 0; j < nzx; j++) {                                /* Point in X */
2075       for (; k < nzy && yltog[yjj[k]] < xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
2076       if (k < nzy && yltog[yjj[k]] == xltog[xjj[j]]) k++;             /* Skip duplicate */
2077       nnz[i]++;
2078     }
2079     for (; k < nzy; k++) nnz[i]++;
2080   }
2081   PetscFunctionReturn(PETSC_SUCCESS);
2082 }
2083 
2084 /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
2085 static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y, const PetscInt *yltog, Mat X, const PetscInt *xltog, PetscInt *nnz)
2086 {
2087   PetscInt    m = Y->rmap->N;
2088   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data;
2089   Mat_SeqAIJ *y = (Mat_SeqAIJ *)Y->data;
2090 
2091   PetscFunctionBegin;
2092   PetscCall(MatAXPYGetPreallocation_MPIX_private(m, x->i, x->j, xltog, y->i, y->j, yltog, nnz));
2093   PetscFunctionReturn(PETSC_SUCCESS);
2094 }
2095 
2096 static PetscErrorCode MatAXPY_MPIAIJ(Mat Y, PetscScalar a, Mat X, MatStructure str)
2097 {
2098   Mat_MPIAIJ *xx = (Mat_MPIAIJ *)X->data, *yy = (Mat_MPIAIJ *)Y->data;
2099 
2100   PetscFunctionBegin;
2101   if (str == SAME_NONZERO_PATTERN) {
2102     PetscCall(MatAXPY(yy->A, a, xx->A, str));
2103     PetscCall(MatAXPY(yy->B, a, xx->B, str));
2104   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
2105     PetscCall(MatAXPY_Basic(Y, a, X, str));
2106   } else {
2107     Mat       B;
2108     PetscInt *nnz_d, *nnz_o;
2109 
2110     PetscCall(PetscMalloc1(yy->A->rmap->N, &nnz_d));
2111     PetscCall(PetscMalloc1(yy->B->rmap->N, &nnz_o));
2112     PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
2113     PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
2114     PetscCall(MatSetLayouts(B, Y->rmap, Y->cmap));
2115     PetscCall(MatSetType(B, ((PetscObject)Y)->type_name));
2116     PetscCall(MatAXPYGetPreallocation_SeqAIJ(yy->A, xx->A, nnz_d));
2117     PetscCall(MatAXPYGetPreallocation_MPIAIJ(yy->B, yy->garray, xx->B, xx->garray, nnz_o));
2118     PetscCall(MatMPIAIJSetPreallocation(B, 0, nnz_d, 0, nnz_o));
2119     PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
2120     PetscCall(MatHeaderMerge(Y, &B));
2121     PetscCall(PetscFree(nnz_d));
2122     PetscCall(PetscFree(nnz_o));
2123   }
2124   PetscFunctionReturn(PETSC_SUCCESS);
2125 }
2126 
2127 PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat);
2128 
2129 static PetscErrorCode MatConjugate_MPIAIJ(Mat mat)
2130 {
2131   PetscFunctionBegin;
2132   if (PetscDefined(USE_COMPLEX)) {
2133     Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
2134 
2135     PetscCall(MatConjugate_SeqAIJ(aij->A));
2136     PetscCall(MatConjugate_SeqAIJ(aij->B));
2137   }
2138   PetscFunctionReturn(PETSC_SUCCESS);
2139 }
2140 
2141 static PetscErrorCode MatRealPart_MPIAIJ(Mat A)
2142 {
2143   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2144 
2145   PetscFunctionBegin;
2146   PetscCall(MatRealPart(a->A));
2147   PetscCall(MatRealPart(a->B));
2148   PetscFunctionReturn(PETSC_SUCCESS);
2149 }
2150 
2151 static PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
2152 {
2153   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2154 
2155   PetscFunctionBegin;
2156   PetscCall(MatImaginaryPart(a->A));
2157   PetscCall(MatImaginaryPart(a->B));
2158   PetscFunctionReturn(PETSC_SUCCESS);
2159 }
2160 
2161 static PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2162 {
2163   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
2164   PetscInt           i, *idxb = NULL, m = A->rmap->n;
2165   PetscScalar       *va, *vv;
2166   Vec                vB, vA;
2167   const PetscScalar *vb;
2168 
2169   PetscFunctionBegin;
2170   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &vA));
2171   PetscCall(MatGetRowMaxAbs(a->A, vA, idx));
2172 
2173   PetscCall(VecGetArrayWrite(vA, &va));
2174   if (idx) {
2175     for (i = 0; i < m; i++) {
2176       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
2177     }
2178   }
2179 
2180   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &vB));
2181   PetscCall(PetscMalloc1(m, &idxb));
2182   PetscCall(MatGetRowMaxAbs(a->B, vB, idxb));
2183 
2184   PetscCall(VecGetArrayWrite(v, &vv));
2185   PetscCall(VecGetArrayRead(vB, &vb));
2186   for (i = 0; i < m; i++) {
2187     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
2188       vv[i] = vb[i];
2189       if (idx) idx[i] = a->garray[idxb[i]];
2190     } else {
2191       vv[i] = va[i];
2192       if (idx && PetscAbsScalar(va[i]) == PetscAbsScalar(vb[i]) && idxb[i] != -1 && idx[i] > a->garray[idxb[i]]) idx[i] = a->garray[idxb[i]];
2193     }
2194   }
2195   PetscCall(VecRestoreArrayWrite(vA, &vv));
2196   PetscCall(VecRestoreArrayWrite(vA, &va));
2197   PetscCall(VecRestoreArrayRead(vB, &vb));
2198   PetscCall(PetscFree(idxb));
2199   PetscCall(VecDestroy(&vA));
2200   PetscCall(VecDestroy(&vB));
2201   PetscFunctionReturn(PETSC_SUCCESS);
2202 }
2203 
2204 static PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2205 {
2206   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
2207   PetscInt           m = A->rmap->n, n = A->cmap->n;
2208   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
2209   PetscInt          *cmap = mat->garray;
2210   PetscInt          *diagIdx, *offdiagIdx;
2211   Vec                diagV, offdiagV;
2212   PetscScalar       *a, *diagA, *offdiagA;
2213   const PetscScalar *ba, *bav;
2214   PetscInt           r, j, col, ncols, *bi, *bj;
2215   Mat                B = mat->B;
2216   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;
2217 
2218   PetscFunctionBegin;
2219   /* When a process holds entire A and other processes have no entry */
2220   if (A->cmap->N == n) {
2221     PetscCall(VecGetArrayWrite(v, &diagA));
2222     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
2223     PetscCall(MatGetRowMinAbs(mat->A, diagV, idx));
2224     PetscCall(VecDestroy(&diagV));
2225     PetscCall(VecRestoreArrayWrite(v, &diagA));
2226     PetscFunctionReturn(PETSC_SUCCESS);
2227   } else if (n == 0) {
2228     if (m) {
2229       PetscCall(VecGetArrayWrite(v, &a));
2230       for (r = 0; r < m; r++) {
2231         a[r] = 0.0;
2232         if (idx) idx[r] = -1;
2233       }
2234       PetscCall(VecRestoreArrayWrite(v, &a));
2235     }
2236     PetscFunctionReturn(PETSC_SUCCESS);
2237   }
2238 
2239   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
2240   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
2241   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
2242   PetscCall(MatGetRowMinAbs(mat->A, diagV, diagIdx));
2243 
2244   /* Get offdiagIdx[] for implicit 0.0 */
2245   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
2246   ba = bav;
2247   bi = b->i;
2248   bj = b->j;
2249   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
2250   for (r = 0; r < m; r++) {
2251     ncols = bi[r + 1] - bi[r];
2252     if (ncols == A->cmap->N - n) { /* Brow is dense */
2253       offdiagA[r]   = *ba;
2254       offdiagIdx[r] = cmap[0];
2255     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
2256       offdiagA[r] = 0.0;
2257 
2258       /* Find first hole in the cmap */
2259       for (j = 0; j < ncols; j++) {
2260         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
2261         if (col > j && j < cstart) {
2262           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
2263           break;
2264         } else if (col > j + n && j >= cstart) {
2265           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
2266           break;
2267         }
2268       }
2269       if (j == ncols && ncols < A->cmap->N - n) {
2270         /* a hole is outside compressed Bcols */
2271         if (ncols == 0) {
2272           if (cstart) {
2273             offdiagIdx[r] = 0;
2274           } else offdiagIdx[r] = cend;
2275         } else { /* ncols > 0 */
2276           offdiagIdx[r] = cmap[ncols - 1] + 1;
2277           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
2278         }
2279       }
2280     }
2281 
2282     for (j = 0; j < ncols; j++) {
2283       if (PetscAbsScalar(offdiagA[r]) > PetscAbsScalar(*ba)) {
2284         offdiagA[r]   = *ba;
2285         offdiagIdx[r] = cmap[*bj];
2286       }
2287       ba++;
2288       bj++;
2289     }
2290   }
2291 
2292   PetscCall(VecGetArrayWrite(v, &a));
2293   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
2294   for (r = 0; r < m; ++r) {
2295     if (PetscAbsScalar(diagA[r]) < PetscAbsScalar(offdiagA[r])) {
2296       a[r] = diagA[r];
2297       if (idx) idx[r] = cstart + diagIdx[r];
2298     } else if (PetscAbsScalar(diagA[r]) == PetscAbsScalar(offdiagA[r])) {
2299       a[r] = diagA[r];
2300       if (idx) {
2301         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
2302           idx[r] = cstart + diagIdx[r];
2303         } else idx[r] = offdiagIdx[r];
2304       }
2305     } else {
2306       a[r] = offdiagA[r];
2307       if (idx) idx[r] = offdiagIdx[r];
2308     }
2309   }
2310   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
2311   PetscCall(VecRestoreArrayWrite(v, &a));
2312   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
2313   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
2314   PetscCall(VecDestroy(&diagV));
2315   PetscCall(VecDestroy(&offdiagV));
2316   PetscCall(PetscFree2(diagIdx, offdiagIdx));
2317   PetscFunctionReturn(PETSC_SUCCESS);
2318 }
2319 
2320 static PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2321 {
2322   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
2323   PetscInt           m = A->rmap->n, n = A->cmap->n;
2324   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
2325   PetscInt          *cmap = mat->garray;
2326   PetscInt          *diagIdx, *offdiagIdx;
2327   Vec                diagV, offdiagV;
2328   PetscScalar       *a, *diagA, *offdiagA;
2329   const PetscScalar *ba, *bav;
2330   PetscInt           r, j, col, ncols, *bi, *bj;
2331   Mat                B = mat->B;
2332   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;
2333 
2334   PetscFunctionBegin;
2335   /* When a process holds entire A and other processes have no entry */
2336   if (A->cmap->N == n) {
2337     PetscCall(VecGetArrayWrite(v, &diagA));
2338     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
2339     PetscCall(MatGetRowMin(mat->A, diagV, idx));
2340     PetscCall(VecDestroy(&diagV));
2341     PetscCall(VecRestoreArrayWrite(v, &diagA));
2342     PetscFunctionReturn(PETSC_SUCCESS);
2343   } else if (n == 0) {
2344     if (m) {
2345       PetscCall(VecGetArrayWrite(v, &a));
2346       for (r = 0; r < m; r++) {
2347         a[r] = PETSC_MAX_REAL;
2348         if (idx) idx[r] = -1;
2349       }
2350       PetscCall(VecRestoreArrayWrite(v, &a));
2351     }
2352     PetscFunctionReturn(PETSC_SUCCESS);
2353   }
2354 
2355   PetscCall(PetscCalloc2(m, &diagIdx, m, &offdiagIdx));
2356   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
2357   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
2358   PetscCall(MatGetRowMin(mat->A, diagV, diagIdx));
2359 
2360   /* Get offdiagIdx[] for implicit 0.0 */
2361   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
2362   ba = bav;
2363   bi = b->i;
2364   bj = b->j;
2365   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
2366   for (r = 0; r < m; r++) {
2367     ncols = bi[r + 1] - bi[r];
2368     if (ncols == A->cmap->N - n) { /* Brow is dense */
2369       offdiagA[r]   = *ba;
2370       offdiagIdx[r] = cmap[0];
2371     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
2372       offdiagA[r] = 0.0;
2373 
2374       /* Find first hole in the cmap */
2375       for (j = 0; j < ncols; j++) {
2376         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
2377         if (col > j && j < cstart) {
2378           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
2379           break;
2380         } else if (col > j + n && j >= cstart) {
2381           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
2382           break;
2383         }
2384       }
2385       if (j == ncols && ncols < A->cmap->N - n) {
2386         /* a hole is outside compressed Bcols */
2387         if (ncols == 0) {
2388           if (cstart) {
2389             offdiagIdx[r] = 0;
2390           } else offdiagIdx[r] = cend;
2391         } else { /* ncols > 0 */
2392           offdiagIdx[r] = cmap[ncols - 1] + 1;
2393           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
2394         }
2395       }
2396     }
2397 
2398     for (j = 0; j < ncols; j++) {
2399       if (PetscRealPart(offdiagA[r]) > PetscRealPart(*ba)) {
2400         offdiagA[r]   = *ba;
2401         offdiagIdx[r] = cmap[*bj];
2402       }
2403       ba++;
2404       bj++;
2405     }
2406   }
2407 
2408   PetscCall(VecGetArrayWrite(v, &a));
2409   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
2410   for (r = 0; r < m; ++r) {
2411     if (PetscRealPart(diagA[r]) < PetscRealPart(offdiagA[r])) {
2412       a[r] = diagA[r];
2413       if (idx) idx[r] = cstart + diagIdx[r];
2414     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
2415       a[r] = diagA[r];
2416       if (idx) {
2417         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
2418           idx[r] = cstart + diagIdx[r];
2419         } else idx[r] = offdiagIdx[r];
2420       }
2421     } else {
2422       a[r] = offdiagA[r];
2423       if (idx) idx[r] = offdiagIdx[r];
2424     }
2425   }
2426   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
2427   PetscCall(VecRestoreArrayWrite(v, &a));
2428   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
2429   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
2430   PetscCall(VecDestroy(&diagV));
2431   PetscCall(VecDestroy(&offdiagV));
2432   PetscCall(PetscFree2(diagIdx, offdiagIdx));
2433   PetscFunctionReturn(PETSC_SUCCESS);
2434 }
2435 
2436 static PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
2437 {
2438   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
2439   PetscInt           m = A->rmap->n, n = A->cmap->n;
2440   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
2441   PetscInt          *cmap = mat->garray;
2442   PetscInt          *diagIdx, *offdiagIdx;
2443   Vec                diagV, offdiagV;
2444   PetscScalar       *a, *diagA, *offdiagA;
2445   const PetscScalar *ba, *bav;
2446   PetscInt           r, j, col, ncols, *bi, *bj;
2447   Mat                B = mat->B;
2448   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;
2449 
2450   PetscFunctionBegin;
2451   /* When a process holds entire A and other processes have no entry */
2452   if (A->cmap->N == n) {
2453     PetscCall(VecGetArrayWrite(v, &diagA));
2454     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
2455     PetscCall(MatGetRowMax(mat->A, diagV, idx));
2456     PetscCall(VecDestroy(&diagV));
2457     PetscCall(VecRestoreArrayWrite(v, &diagA));
2458     PetscFunctionReturn(PETSC_SUCCESS);
2459   } else if (n == 0) {
2460     if (m) {
2461       PetscCall(VecGetArrayWrite(v, &a));
2462       for (r = 0; r < m; r++) {
2463         a[r] = PETSC_MIN_REAL;
2464         if (idx) idx[r] = -1;
2465       }
2466       PetscCall(VecRestoreArrayWrite(v, &a));
2467     }
2468     PetscFunctionReturn(PETSC_SUCCESS);
2469   }
2470 
2471   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
2472   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
2473   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
2474   PetscCall(MatGetRowMax(mat->A, diagV, diagIdx));
2475 
2476   /* Get offdiagIdx[] for implicit 0.0 */
2477   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
2478   ba = bav;
2479   bi = b->i;
2480   bj = b->j;
2481   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
2482   for (r = 0; r < m; r++) {
2483     ncols = bi[r + 1] - bi[r];
2484     if (ncols == A->cmap->N - n) { /* Brow is dense */
2485       offdiagA[r]   = *ba;
2486       offdiagIdx[r] = cmap[0];
2487     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
2488       offdiagA[r] = 0.0;
2489 
2490       /* Find first hole in the cmap */
2491       for (j = 0; j < ncols; j++) {
2492         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
2493         if (col > j && j < cstart) {
2494           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
2495           break;
2496         } else if (col > j + n && j >= cstart) {
2497           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
2498           break;
2499         }
2500       }
2501       if (j == ncols && ncols < A->cmap->N - n) {
2502         /* a hole is outside compressed Bcols */
2503         if (ncols == 0) {
2504           if (cstart) {
2505             offdiagIdx[r] = 0;
2506           } else offdiagIdx[r] = cend;
2507         } else { /* ncols > 0 */
2508           offdiagIdx[r] = cmap[ncols - 1] + 1;
2509           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
2510         }
2511       }
2512     }
2513 
2514     for (j = 0; j < ncols; j++) {
2515       if (PetscRealPart(offdiagA[r]) < PetscRealPart(*ba)) {
2516         offdiagA[r]   = *ba;
2517         offdiagIdx[r] = cmap[*bj];
2518       }
2519       ba++;
2520       bj++;
2521     }
2522   }
2523 
2524   PetscCall(VecGetArrayWrite(v, &a));
2525   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
2526   for (r = 0; r < m; ++r) {
2527     if (PetscRealPart(diagA[r]) > PetscRealPart(offdiagA[r])) {
2528       a[r] = diagA[r];
2529       if (idx) idx[r] = cstart + diagIdx[r];
2530     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
2531       a[r] = diagA[r];
2532       if (idx) {
2533         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
2534           idx[r] = cstart + diagIdx[r];
2535         } else idx[r] = offdiagIdx[r];
2536       }
2537     } else {
2538       a[r] = offdiagA[r];
2539       if (idx) idx[r] = offdiagIdx[r];
2540     }
2541   }
2542   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
2543   PetscCall(VecRestoreArrayWrite(v, &a));
2544   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
2545   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
2546   PetscCall(VecDestroy(&diagV));
2547   PetscCall(VecDestroy(&offdiagV));
2548   PetscCall(PetscFree2(diagIdx, offdiagIdx));
2549   PetscFunctionReturn(PETSC_SUCCESS);
2550 }
2551 
2552 PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat, Mat *newmat)
2553 {
2554   Mat *dummy;
2555 
2556   PetscFunctionBegin;
2557   PetscCall(MatCreateSubMatrix_MPIAIJ_All(mat, MAT_DO_NOT_GET_VALUES, MAT_INITIAL_MATRIX, &dummy));
2558   *newmat = *dummy;
2559   PetscCall(PetscFree(dummy));
2560   PetscFunctionReturn(PETSC_SUCCESS);
2561 }
2562 
2563 static PetscErrorCode MatInvertBlockDiagonal_MPIAIJ(Mat A, const PetscScalar **values)
2564 {
2565   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2566 
2567   PetscFunctionBegin;
2568   PetscCall(MatInvertBlockDiagonal(a->A, values));
2569   A->factorerrortype = a->A->factorerrortype;
2570   PetscFunctionReturn(PETSC_SUCCESS);
2571 }
2572 
2573 static PetscErrorCode MatSetRandom_MPIAIJ(Mat x, PetscRandom rctx)
2574 {
2575   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)x->data;
2576 
2577   PetscFunctionBegin;
2578   PetscCheck(x->assembled || x->preallocated, PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_WRONGSTATE, "MatSetRandom on an unassembled and unpreallocated MATMPIAIJ is not allowed");
2579   PetscCall(MatSetRandom(aij->A, rctx));
2580   if (x->assembled) {
2581     PetscCall(MatSetRandom(aij->B, rctx));
2582   } else {
2583     PetscCall(MatSetRandomSkipColumnRange_SeqAIJ_Private(aij->B, x->cmap->rstart, x->cmap->rend, rctx));
2584   }
2585   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
2586   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
2587   PetscFunctionReturn(PETSC_SUCCESS);
2588 }
2589 
2590 static PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A, PetscBool sc)
2591 {
2592   PetscFunctionBegin;
2593   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
2594   else A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ;
2595   PetscFunctionReturn(PETSC_SUCCESS);
2596 }
2597 
2598 /*@
2599   MatMPIAIJGetNumberNonzeros - gets the number of nonzeros in the matrix on this MPI rank
2600 
2601   Not Collective
2602 
2603   Input Parameter:
2604 . A - the matrix
2605 
2606   Output Parameter:
2607 . nz - the number of nonzeros
2608 
2609   Level: advanced
2610 
2611 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
2612 @*/
2613 PetscErrorCode MatMPIAIJGetNumberNonzeros(Mat A, PetscCount *nz)
2614 {
2615   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)A->data;
2616   Mat_SeqAIJ *aaij = (Mat_SeqAIJ *)maij->A->data, *baij = (Mat_SeqAIJ *)maij->B->data;
2617   PetscBool   isaij;
2618 
2619   PetscFunctionBegin;
2620   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIAIJ, &isaij));
2621   PetscCheck(isaij, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for type %s", ((PetscObject)A)->type_name);
2622   *nz = aaij->i[A->rmap->n] + baij->i[A->rmap->n];
2623   PetscFunctionReturn(PETSC_SUCCESS);
2624 }
2625 
2626 /*@
2627   MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap
2628 
2629   Collective
2630 
2631   Input Parameters:
2632 + A  - the matrix
2633 - sc - `PETSC_TRUE` indicates use the scalable algorithm (default is not to use the scalable algorithm)
2634 
2635   Level: advanced
2636 
2637 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
2638 @*/
2639 PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A, PetscBool sc)
2640 {
2641   PetscFunctionBegin;
2642   PetscTryMethod(A, "MatMPIAIJSetUseScalableIncreaseOverlap_C", (Mat, PetscBool), (A, sc));
2643   PetscFunctionReturn(PETSC_SUCCESS);
2644 }
2645 
2646 PetscErrorCode MatSetFromOptions_MPIAIJ(Mat A, PetscOptionItems *PetscOptionsObject)
2647 {
2648   PetscBool sc = PETSC_FALSE, flg;
2649 
2650   PetscFunctionBegin;
2651   PetscOptionsHeadBegin(PetscOptionsObject, "MPIAIJ options");
2652   if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
2653   PetscCall(PetscOptionsBool("-mat_increase_overlap_scalable", "Use a scalable algorithm to compute the overlap", "MatIncreaseOverlap", sc, &sc, &flg));
2654   if (flg) PetscCall(MatMPIAIJSetUseScalableIncreaseOverlap(A, sc));
2655   PetscOptionsHeadEnd();
2656   PetscFunctionReturn(PETSC_SUCCESS);
2657 }
2658 
2659 static PetscErrorCode MatShift_MPIAIJ(Mat Y, PetscScalar a)
2660 {
2661   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)Y->data;
2662   Mat_SeqAIJ *aij  = (Mat_SeqAIJ *)maij->A->data;
2663 
2664   PetscFunctionBegin;
2665   if (!Y->preallocated) {
2666     PetscCall(MatMPIAIJSetPreallocation(Y, 1, NULL, 0, NULL));
2667   } else if (!aij->nz) { /* It does not matter if diagonals of Y only partially lie in maij->A. We just need an estimated preallocation. */
2668     PetscInt nonew = aij->nonew;
2669     PetscCall(MatSeqAIJSetPreallocation(maij->A, 1, NULL));
2670     aij->nonew = nonew;
2671   }
2672   PetscCall(MatShift_Basic(Y, a));
2673   PetscFunctionReturn(PETSC_SUCCESS);
2674 }
2675 
2676 static PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A, PetscBool *missing, PetscInt *d)
2677 {
2678   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2679 
2680   PetscFunctionBegin;
2681   PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only works for square matrices");
2682   PetscCall(MatMissingDiagonal(a->A, missing, d));
2683   if (d) {
2684     PetscInt rstart;
2685     PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
2686     *d += rstart;
2687   }
2688   PetscFunctionReturn(PETSC_SUCCESS);
2689 }
2690 
2691 static PetscErrorCode MatInvertVariableBlockDiagonal_MPIAIJ(Mat A, PetscInt nblocks, const PetscInt *bsizes, PetscScalar *diag)
2692 {
2693   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2694 
2695   PetscFunctionBegin;
2696   PetscCall(MatInvertVariableBlockDiagonal(a->A, nblocks, bsizes, diag));
2697   PetscFunctionReturn(PETSC_SUCCESS);
2698 }
2699 
2700 static PetscErrorCode MatEliminateZeros_MPIAIJ(Mat A, PetscBool keep)
2701 {
2702   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
2703 
2704   PetscFunctionBegin;
2705   PetscCall(MatEliminateZeros_SeqAIJ(a->A, keep));        // possibly keep zero diagonal coefficients
2706   PetscCall(MatEliminateZeros_SeqAIJ(a->B, PETSC_FALSE)); // never keep zero diagonal coefficients
2707   PetscFunctionReturn(PETSC_SUCCESS);
2708 }
2709 
2710 static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
2711                                        MatGetRow_MPIAIJ,
2712                                        MatRestoreRow_MPIAIJ,
2713                                        MatMult_MPIAIJ,
2714                                        /* 4*/ MatMultAdd_MPIAIJ,
2715                                        MatMultTranspose_MPIAIJ,
2716                                        MatMultTransposeAdd_MPIAIJ,
2717                                        NULL,
2718                                        NULL,
2719                                        NULL,
2720                                        /*10*/ NULL,
2721                                        NULL,
2722                                        NULL,
2723                                        MatSOR_MPIAIJ,
2724                                        MatTranspose_MPIAIJ,
2725                                        /*15*/ MatGetInfo_MPIAIJ,
2726                                        MatEqual_MPIAIJ,
2727                                        MatGetDiagonal_MPIAIJ,
2728                                        MatDiagonalScale_MPIAIJ,
2729                                        MatNorm_MPIAIJ,
2730                                        /*20*/ MatAssemblyBegin_MPIAIJ,
2731                                        MatAssemblyEnd_MPIAIJ,
2732                                        MatSetOption_MPIAIJ,
2733                                        MatZeroEntries_MPIAIJ,
2734                                        /*24*/ MatZeroRows_MPIAIJ,
2735                                        NULL,
2736                                        NULL,
2737                                        NULL,
2738                                        NULL,
2739                                        /*29*/ MatSetUp_MPI_Hash,
2740                                        NULL,
2741                                        NULL,
2742                                        MatGetDiagonalBlock_MPIAIJ,
2743                                        NULL,
2744                                        /*34*/ MatDuplicate_MPIAIJ,
2745                                        NULL,
2746                                        NULL,
2747                                        NULL,
2748                                        NULL,
2749                                        /*39*/ MatAXPY_MPIAIJ,
2750                                        MatCreateSubMatrices_MPIAIJ,
2751                                        MatIncreaseOverlap_MPIAIJ,
2752                                        MatGetValues_MPIAIJ,
2753                                        MatCopy_MPIAIJ,
2754                                        /*44*/ MatGetRowMax_MPIAIJ,
2755                                        MatScale_MPIAIJ,
2756                                        MatShift_MPIAIJ,
2757                                        MatDiagonalSet_MPIAIJ,
2758                                        MatZeroRowsColumns_MPIAIJ,
2759                                        /*49*/ MatSetRandom_MPIAIJ,
2760                                        MatGetRowIJ_MPIAIJ,
2761                                        MatRestoreRowIJ_MPIAIJ,
2762                                        NULL,
2763                                        NULL,
2764                                        /*54*/ MatFDColoringCreate_MPIXAIJ,
2765                                        NULL,
2766                                        MatSetUnfactored_MPIAIJ,
2767                                        MatPermute_MPIAIJ,
2768                                        NULL,
2769                                        /*59*/ MatCreateSubMatrix_MPIAIJ,
2770                                        MatDestroy_MPIAIJ,
2771                                        MatView_MPIAIJ,
2772                                        NULL,
2773                                        NULL,
2774                                        /*64*/ NULL,
2775                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
2776                                        NULL,
2777                                        NULL,
2778                                        NULL,
2779                                        /*69*/ MatGetRowMaxAbs_MPIAIJ,
2780                                        MatGetRowMinAbs_MPIAIJ,
2781                                        NULL,
2782                                        NULL,
2783                                        NULL,
2784                                        NULL,
2785                                        /*75*/ MatFDColoringApply_AIJ,
2786                                        MatSetFromOptions_MPIAIJ,
2787                                        NULL,
2788                                        NULL,
2789                                        MatFindZeroDiagonals_MPIAIJ,
2790                                        /*80*/ NULL,
2791                                        NULL,
2792                                        NULL,
2793                                        /*83*/ MatLoad_MPIAIJ,
2794                                        MatIsSymmetric_MPIAIJ,
2795                                        NULL,
2796                                        NULL,
2797                                        NULL,
2798                                        NULL,
2799                                        /*89*/ NULL,
2800                                        NULL,
2801                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
2802                                        NULL,
2803                                        NULL,
2804                                        /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
2805                                        NULL,
2806                                        NULL,
2807                                        NULL,
2808                                        MatBindToCPU_MPIAIJ,
2809                                        /*99*/ MatProductSetFromOptions_MPIAIJ,
2810                                        NULL,
2811                                        NULL,
2812                                        MatConjugate_MPIAIJ,
2813                                        NULL,
2814                                        /*104*/ MatSetValuesRow_MPIAIJ,
2815                                        MatRealPart_MPIAIJ,
2816                                        MatImaginaryPart_MPIAIJ,
2817                                        NULL,
2818                                        NULL,
2819                                        /*109*/ NULL,
2820                                        NULL,
2821                                        MatGetRowMin_MPIAIJ,
2822                                        NULL,
2823                                        MatMissingDiagonal_MPIAIJ,
2824                                        /*114*/ MatGetSeqNonzeroStructure_MPIAIJ,
2825                                        NULL,
2826                                        MatGetGhosts_MPIAIJ,
2827                                        NULL,
2828                                        NULL,
2829                                        /*119*/ MatMultDiagonalBlock_MPIAIJ,
2830                                        NULL,
2831                                        NULL,
2832                                        NULL,
2833                                        MatGetMultiProcBlock_MPIAIJ,
2834                                        /*124*/ MatFindNonzeroRows_MPIAIJ,
2835                                        MatGetColumnReductions_MPIAIJ,
2836                                        MatInvertBlockDiagonal_MPIAIJ,
2837                                        MatInvertVariableBlockDiagonal_MPIAIJ,
2838                                        MatCreateSubMatricesMPI_MPIAIJ,
2839                                        /*129*/ NULL,
2840                                        NULL,
2841                                        NULL,
2842                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
2843                                        NULL,
2844                                        /*134*/ NULL,
2845                                        NULL,
2846                                        NULL,
2847                                        NULL,
2848                                        NULL,
2849                                        /*139*/ MatSetBlockSizes_MPIAIJ,
2850                                        NULL,
2851                                        NULL,
2852                                        MatFDColoringSetUp_MPIXAIJ,
2853                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
2854                                        MatCreateMPIMatConcatenateSeqMat_MPIAIJ,
2855                                        /*145*/ NULL,
2856                                        NULL,
2857                                        NULL,
2858                                        MatCreateGraph_Simple_AIJ,
2859                                        NULL,
2860                                        /*150*/ NULL,
2861                                        MatEliminateZeros_MPIAIJ};
2862 
2863 static PetscErrorCode MatStoreValues_MPIAIJ(Mat mat)
2864 {
2865   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
2866 
2867   PetscFunctionBegin;
2868   PetscCall(MatStoreValues(aij->A));
2869   PetscCall(MatStoreValues(aij->B));
2870   PetscFunctionReturn(PETSC_SUCCESS);
2871 }
2872 
2873 static PetscErrorCode MatRetrieveValues_MPIAIJ(Mat mat)
2874 {
2875   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
2876 
2877   PetscFunctionBegin;
2878   PetscCall(MatRetrieveValues(aij->A));
2879   PetscCall(MatRetrieveValues(aij->B));
2880   PetscFunctionReturn(PETSC_SUCCESS);
2881 }
2882 
2883 PetscErrorCode MatMPIAIJSetPreallocation_MPIAIJ(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
2884 {
2885   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
2886   PetscMPIInt size;
2887 
2888   PetscFunctionBegin;
2889   if (B->hash_active) {
2890     B->ops[0]      = b->cops;
2891     B->hash_active = PETSC_FALSE;
2892   }
2893   PetscCall(PetscLayoutSetUp(B->rmap));
2894   PetscCall(PetscLayoutSetUp(B->cmap));
2895 
2896 #if defined(PETSC_USE_CTABLE)
2897   PetscCall(PetscHMapIDestroy(&b->colmap));
2898 #else
2899   PetscCall(PetscFree(b->colmap));
2900 #endif
2901   PetscCall(PetscFree(b->garray));
2902   PetscCall(VecDestroy(&b->lvec));
2903   PetscCall(VecScatterDestroy(&b->Mvctx));
2904 
2905   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));
2906   PetscCall(MatDestroy(&b->B));
2907   PetscCall(MatCreate(PETSC_COMM_SELF, &b->B));
2908   PetscCall(MatSetSizes(b->B, B->rmap->n, size > 1 ? B->cmap->N : 0, B->rmap->n, size > 1 ? B->cmap->N : 0));
2909   PetscCall(MatSetBlockSizesFromMats(b->B, B, B));
2910   PetscCall(MatSetType(b->B, MATSEQAIJ));
2911 
2912   PetscCall(MatDestroy(&b->A));
2913   PetscCall(MatCreate(PETSC_COMM_SELF, &b->A));
2914   PetscCall(MatSetSizes(b->A, B->rmap->n, B->cmap->n, B->rmap->n, B->cmap->n));
2915   PetscCall(MatSetBlockSizesFromMats(b->A, B, B));
2916   PetscCall(MatSetType(b->A, MATSEQAIJ));
2917 
2918   PetscCall(MatSeqAIJSetPreallocation(b->A, d_nz, d_nnz));
2919   PetscCall(MatSeqAIJSetPreallocation(b->B, o_nz, o_nnz));
2920   B->preallocated  = PETSC_TRUE;
2921   B->was_assembled = PETSC_FALSE;
2922   B->assembled     = PETSC_FALSE;
2923   PetscFunctionReturn(PETSC_SUCCESS);
2924 }
2925 
2926 static PetscErrorCode MatResetPreallocation_MPIAIJ(Mat B)
2927 {
2928   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
2929 
2930   PetscFunctionBegin;
2931   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
2932   PetscCall(PetscLayoutSetUp(B->rmap));
2933   PetscCall(PetscLayoutSetUp(B->cmap));
2934 
2935 #if defined(PETSC_USE_CTABLE)
2936   PetscCall(PetscHMapIDestroy(&b->colmap));
2937 #else
2938   PetscCall(PetscFree(b->colmap));
2939 #endif
2940   PetscCall(PetscFree(b->garray));
2941   PetscCall(VecDestroy(&b->lvec));
2942   PetscCall(VecScatterDestroy(&b->Mvctx));
2943 
2944   PetscCall(MatResetPreallocation(b->A));
2945   PetscCall(MatResetPreallocation(b->B));
2946   B->preallocated  = PETSC_TRUE;
2947   B->was_assembled = PETSC_FALSE;
2948   B->assembled     = PETSC_FALSE;
2949   PetscFunctionReturn(PETSC_SUCCESS);
2950 }
2951 
2952 PetscErrorCode MatDuplicate_MPIAIJ(Mat matin, MatDuplicateOption cpvalues, Mat *newmat)
2953 {
2954   Mat         mat;
2955   Mat_MPIAIJ *a, *oldmat = (Mat_MPIAIJ *)matin->data;
2956 
2957   PetscFunctionBegin;
2958   *newmat = NULL;
2959   PetscCall(MatCreate(PetscObjectComm((PetscObject)matin), &mat));
2960   PetscCall(MatSetSizes(mat, matin->rmap->n, matin->cmap->n, matin->rmap->N, matin->cmap->N));
2961   PetscCall(MatSetBlockSizesFromMats(mat, matin, matin));
2962   PetscCall(MatSetType(mat, ((PetscObject)matin)->type_name));
2963   a = (Mat_MPIAIJ *)mat->data;
2964 
2965   mat->factortype = matin->factortype;
2966   mat->assembled  = matin->assembled;
2967   mat->insertmode = NOT_SET_VALUES;
2968 
2969   a->size         = oldmat->size;
2970   a->rank         = oldmat->rank;
2971   a->donotstash   = oldmat->donotstash;
2972   a->roworiented  = oldmat->roworiented;
2973   a->rowindices   = NULL;
2974   a->rowvalues    = NULL;
2975   a->getrowactive = PETSC_FALSE;
2976 
2977   PetscCall(PetscLayoutReference(matin->rmap, &mat->rmap));
2978   PetscCall(PetscLayoutReference(matin->cmap, &mat->cmap));
2979   if (matin->hash_active) {
2980     PetscCall(MatSetUp(mat));
2981   } else {
2982     mat->preallocated = matin->preallocated;
2983     if (oldmat->colmap) {
2984 #if defined(PETSC_USE_CTABLE)
2985       PetscCall(PetscHMapIDuplicate(oldmat->colmap, &a->colmap));
2986 #else
2987       PetscCall(PetscMalloc1(mat->cmap->N, &a->colmap));
2988       PetscCall(PetscArraycpy(a->colmap, oldmat->colmap, mat->cmap->N));
2989 #endif
2990     } else a->colmap = NULL;
2991     if (oldmat->garray) {
2992       PetscInt len;
2993       len = oldmat->B->cmap->n;
2994       PetscCall(PetscMalloc1(len + 1, &a->garray));
2995       if (len) PetscCall(PetscArraycpy(a->garray, oldmat->garray, len));
2996     } else a->garray = NULL;
2997 
2998     /* It may happen MatDuplicate is called with a non-assembled matrix
2999       In fact, MatDuplicate only requires the matrix to be preallocated
3000       This may happen inside a DMCreateMatrix_Shell */
3001     if (oldmat->lvec) PetscCall(VecDuplicate(oldmat->lvec, &a->lvec));
3002     if (oldmat->Mvctx) PetscCall(VecScatterCopy(oldmat->Mvctx, &a->Mvctx));
3003     PetscCall(MatDuplicate(oldmat->A, cpvalues, &a->A));
3004     PetscCall(MatDuplicate(oldmat->B, cpvalues, &a->B));
3005   }
3006   PetscCall(PetscFunctionListDuplicate(((PetscObject)matin)->qlist, &((PetscObject)mat)->qlist));
3007   *newmat = mat;
3008   PetscFunctionReturn(PETSC_SUCCESS);
3009 }
3010 
3011 PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
3012 {
3013   PetscBool isbinary, ishdf5;
3014 
3015   PetscFunctionBegin;
3016   PetscValidHeaderSpecific(newMat, MAT_CLASSID, 1);
3017   PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
3018   /* force binary viewer to load .info file if it has not yet done so */
3019   PetscCall(PetscViewerSetUp(viewer));
3020   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
3021   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
3022   if (isbinary) {
3023     PetscCall(MatLoad_MPIAIJ_Binary(newMat, viewer));
3024   } else if (ishdf5) {
3025 #if defined(PETSC_HAVE_HDF5)
3026     PetscCall(MatLoad_AIJ_HDF5(newMat, viewer));
3027 #else
3028     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
3029 #endif
3030   } else {
3031     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);
3032   }
3033   PetscFunctionReturn(PETSC_SUCCESS);
3034 }
3035 
3036 PetscErrorCode MatLoad_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
3037 {
3038   PetscInt     header[4], M, N, m, nz, rows, cols, sum, i;
3039   PetscInt    *rowidxs, *colidxs;
3040   PetscScalar *matvals;
3041 
3042   PetscFunctionBegin;
3043   PetscCall(PetscViewerSetUp(viewer));
3044 
3045   /* read in matrix header */
3046   PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
3047   PetscCheck(header[0] == MAT_FILE_CLASSID, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Not a matrix object in file");
3048   M  = header[1];
3049   N  = header[2];
3050   nz = header[3];
3051   PetscCheck(M >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix row size (%" PetscInt_FMT ") in file is negative", M);
3052   PetscCheck(N >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix column size (%" PetscInt_FMT ") in file is negative", N);
3053   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix stored in special format on disk, cannot load as MPIAIJ");
3054 
3055   /* set block sizes from the viewer's .info file */
3056   PetscCall(MatLoad_Binary_BlockSizes(mat, viewer));
3057   /* set global sizes if not set already */
3058   if (mat->rmap->N < 0) mat->rmap->N = M;
3059   if (mat->cmap->N < 0) mat->cmap->N = N;
3060   PetscCall(PetscLayoutSetUp(mat->rmap));
3061   PetscCall(PetscLayoutSetUp(mat->cmap));
3062 
3063   /* check if the matrix sizes are correct */
3064   PetscCall(MatGetSize(mat, &rows, &cols));
3065   PetscCheck(M == rows && N == cols, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different sizes (%" PetscInt_FMT ", %" PetscInt_FMT ") than the input matrix (%" PetscInt_FMT ", %" PetscInt_FMT ")", M, N, rows, cols);
3066 
3067   /* read in row lengths and build row indices */
3068   PetscCall(MatGetLocalSize(mat, &m, NULL));
3069   PetscCall(PetscMalloc1(m + 1, &rowidxs));
3070   PetscCall(PetscViewerBinaryReadAll(viewer, rowidxs + 1, m, PETSC_DECIDE, M, PETSC_INT));
3071   rowidxs[0] = 0;
3072   for (i = 0; i < m; i++) rowidxs[i + 1] += rowidxs[i];
3073   if (nz != PETSC_MAX_INT) {
3074     PetscCall(MPIU_Allreduce(&rowidxs[m], &sum, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)viewer)));
3075     PetscCheck(sum == nz, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Inconsistent matrix data in file: nonzeros = %" PetscInt_FMT ", sum-row-lengths = %" PetscInt_FMT, nz, sum);
3076   }
3077 
3078   /* read in column indices and matrix values */
3079   PetscCall(PetscMalloc2(rowidxs[m], &colidxs, rowidxs[m], &matvals));
3080   PetscCall(PetscViewerBinaryReadAll(viewer, colidxs, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
3081   PetscCall(PetscViewerBinaryReadAll(viewer, matvals, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
3082   /* store matrix indices and values */
3083   PetscCall(MatMPIAIJSetPreallocationCSR(mat, rowidxs, colidxs, matvals));
3084   PetscCall(PetscFree(rowidxs));
3085   PetscCall(PetscFree2(colidxs, matvals));
3086   PetscFunctionReturn(PETSC_SUCCESS);
3087 }
3088 
3089 /* Not scalable because of ISAllGather() unless getting all columns. */
3090 static PetscErrorCode ISGetSeqIS_Private(Mat mat, IS iscol, IS *isseq)
3091 {
3092   IS          iscol_local;
3093   PetscBool   isstride;
3094   PetscMPIInt lisstride = 0, gisstride;
3095 
3096   PetscFunctionBegin;
3097   /* check if we are grabbing all columns*/
3098   PetscCall(PetscObjectTypeCompare((PetscObject)iscol, ISSTRIDE, &isstride));
3099 
3100   if (isstride) {
3101     PetscInt start, len, mstart, mlen;
3102     PetscCall(ISStrideGetInfo(iscol, &start, NULL));
3103     PetscCall(ISGetLocalSize(iscol, &len));
3104     PetscCall(MatGetOwnershipRangeColumn(mat, &mstart, &mlen));
3105     if (mstart == start && mlen - mstart == len) lisstride = 1;
3106   }
3107 
3108   PetscCall(MPIU_Allreduce(&lisstride, &gisstride, 1, MPI_INT, MPI_MIN, PetscObjectComm((PetscObject)mat)));
3109   if (gisstride) {
3110     PetscInt N;
3111     PetscCall(MatGetSize(mat, NULL, &N));
3112     PetscCall(ISCreateStride(PETSC_COMM_SELF, N, 0, 1, &iscol_local));
3113     PetscCall(ISSetIdentity(iscol_local));
3114     PetscCall(PetscInfo(mat, "Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n"));
3115   } else {
3116     PetscInt cbs;
3117     PetscCall(ISGetBlockSize(iscol, &cbs));
3118     PetscCall(ISAllGather(iscol, &iscol_local));
3119     PetscCall(ISSetBlockSize(iscol_local, cbs));
3120   }
3121 
3122   *isseq = iscol_local;
3123   PetscFunctionReturn(PETSC_SUCCESS);
3124 }
3125 
3126 /*
3127  Used by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
3128  (see MatCreateSubMatrix_MPIAIJ_nonscalable)
3129 
3130  Input Parameters:
3131 +   mat - matrix
3132 .   isrow - parallel row index set; its local indices are a subset of local columns of `mat`,
3133            i.e., mat->rstart <= isrow[i] < mat->rend
3134 -   iscol - parallel column index set; its local indices are a subset of local columns of `mat`,
3135            i.e., mat->cstart <= iscol[i] < mat->cend
3136 
3137  Output Parameters:
3138 +   isrow_d - sequential row index set for retrieving mat->A
3139 .   iscol_d - sequential  column index set for retrieving mat->A
3140 .   iscol_o - sequential column index set for retrieving mat->B
3141 -   garray - column map; garray[i] indicates global location of iscol_o[i] in `iscol`
3142  */
3143 static PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat, IS isrow, IS iscol, IS *isrow_d, IS *iscol_d, IS *iscol_o, const PetscInt *garray[])
3144 {
3145   Vec             x, cmap;
3146   const PetscInt *is_idx;
3147   PetscScalar    *xarray, *cmaparray;
3148   PetscInt        ncols, isstart, *idx, m, rstart, *cmap1, count;
3149   Mat_MPIAIJ     *a    = (Mat_MPIAIJ *)mat->data;
3150   Mat             B    = a->B;
3151   Vec             lvec = a->lvec, lcmap;
3152   PetscInt        i, cstart, cend, Bn = B->cmap->N;
3153   MPI_Comm        comm;
3154   VecScatter      Mvctx = a->Mvctx;
3155 
3156   PetscFunctionBegin;
3157   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
3158   PetscCall(ISGetLocalSize(iscol, &ncols));
3159 
3160   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
3161   PetscCall(MatCreateVecs(mat, &x, NULL));
3162   PetscCall(VecSet(x, -1.0));
3163   PetscCall(VecDuplicate(x, &cmap));
3164   PetscCall(VecSet(cmap, -1.0));
3165 
3166   /* Get start indices */
3167   PetscCallMPI(MPI_Scan(&ncols, &isstart, 1, MPIU_INT, MPI_SUM, comm));
3168   isstart -= ncols;
3169   PetscCall(MatGetOwnershipRangeColumn(mat, &cstart, &cend));
3170 
3171   PetscCall(ISGetIndices(iscol, &is_idx));
3172   PetscCall(VecGetArray(x, &xarray));
3173   PetscCall(VecGetArray(cmap, &cmaparray));
3174   PetscCall(PetscMalloc1(ncols, &idx));
3175   for (i = 0; i < ncols; i++) {
3176     xarray[is_idx[i] - cstart]    = (PetscScalar)is_idx[i];
3177     cmaparray[is_idx[i] - cstart] = i + isstart;        /* global index of iscol[i] */
3178     idx[i]                        = is_idx[i] - cstart; /* local index of iscol[i]  */
3179   }
3180   PetscCall(VecRestoreArray(x, &xarray));
3181   PetscCall(VecRestoreArray(cmap, &cmaparray));
3182   PetscCall(ISRestoreIndices(iscol, &is_idx));
3183 
3184   /* Get iscol_d */
3185   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, iscol_d));
3186   PetscCall(ISGetBlockSize(iscol, &i));
3187   PetscCall(ISSetBlockSize(*iscol_d, i));
3188 
3189   /* Get isrow_d */
3190   PetscCall(ISGetLocalSize(isrow, &m));
3191   rstart = mat->rmap->rstart;
3192   PetscCall(PetscMalloc1(m, &idx));
3193   PetscCall(ISGetIndices(isrow, &is_idx));
3194   for (i = 0; i < m; i++) idx[i] = is_idx[i] - rstart;
3195   PetscCall(ISRestoreIndices(isrow, &is_idx));
3196 
3197   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, idx, PETSC_OWN_POINTER, isrow_d));
3198   PetscCall(ISGetBlockSize(isrow, &i));
3199   PetscCall(ISSetBlockSize(*isrow_d, i));
3200 
3201   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
3202   PetscCall(VecScatterBegin(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));
3203   PetscCall(VecScatterEnd(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));
3204 
3205   PetscCall(VecDuplicate(lvec, &lcmap));
3206 
3207   PetscCall(VecScatterBegin(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));
3208   PetscCall(VecScatterEnd(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));
3209 
3210   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
3211   /* off-process column indices */
3212   count = 0;
3213   PetscCall(PetscMalloc1(Bn, &idx));
3214   PetscCall(PetscMalloc1(Bn, &cmap1));
3215 
3216   PetscCall(VecGetArray(lvec, &xarray));
3217   PetscCall(VecGetArray(lcmap, &cmaparray));
3218   for (i = 0; i < Bn; i++) {
3219     if (PetscRealPart(xarray[i]) > -1.0) {
3220       idx[count]   = i;                                     /* local column index in off-diagonal part B */
3221       cmap1[count] = (PetscInt)PetscRealPart(cmaparray[i]); /* column index in submat */
3222       count++;
3223     }
3224   }
3225   PetscCall(VecRestoreArray(lvec, &xarray));
3226   PetscCall(VecRestoreArray(lcmap, &cmaparray));
3227 
3228   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_COPY_VALUES, iscol_o));
3229   /* cannot ensure iscol_o has same blocksize as iscol! */
3230 
3231   PetscCall(PetscFree(idx));
3232   *garray = cmap1;
3233 
3234   PetscCall(VecDestroy(&x));
3235   PetscCall(VecDestroy(&cmap));
3236   PetscCall(VecDestroy(&lcmap));
3237   PetscFunctionReturn(PETSC_SUCCESS);
3238 }
3239 
3240 /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
3241 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *submat)
3242 {
3243   Mat_MPIAIJ *a = (Mat_MPIAIJ *)mat->data, *asub;
3244   Mat         M = NULL;
3245   MPI_Comm    comm;
3246   IS          iscol_d, isrow_d, iscol_o;
3247   Mat         Asub = NULL, Bsub = NULL;
3248   PetscInt    n;
3249 
3250   PetscFunctionBegin;
3251   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
3252 
3253   if (call == MAT_REUSE_MATRIX) {
3254     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
3255     PetscCall(PetscObjectQuery((PetscObject)*submat, "isrow_d", (PetscObject *)&isrow_d));
3256     PetscCheck(isrow_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "isrow_d passed in was not used before, cannot reuse");
3257 
3258     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_d", (PetscObject *)&iscol_d));
3259     PetscCheck(iscol_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_d passed in was not used before, cannot reuse");
3260 
3261     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_o", (PetscObject *)&iscol_o));
3262     PetscCheck(iscol_o, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_o passed in was not used before, cannot reuse");
3263 
3264     /* Update diagonal and off-diagonal portions of submat */
3265     asub = (Mat_MPIAIJ *)(*submat)->data;
3266     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->A));
3267     PetscCall(ISGetLocalSize(iscol_o, &n));
3268     if (n) PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->B));
3269     PetscCall(MatAssemblyBegin(*submat, MAT_FINAL_ASSEMBLY));
3270     PetscCall(MatAssemblyEnd(*submat, MAT_FINAL_ASSEMBLY));
3271 
3272   } else { /* call == MAT_INITIAL_MATRIX) */
3273     const PetscInt *garray;
3274     PetscInt        BsubN;
3275 
3276     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
3277     PetscCall(ISGetSeqIS_SameColDist_Private(mat, isrow, iscol, &isrow_d, &iscol_d, &iscol_o, &garray));
3278 
3279     /* Create local submatrices Asub and Bsub */
3280     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Asub));
3281     PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Bsub));
3282 
3283     /* Create submatrix M */
3284     PetscCall(MatCreateMPIAIJWithSeqAIJ(comm, Asub, Bsub, garray, &M));
3285 
3286     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
3287     asub = (Mat_MPIAIJ *)M->data;
3288 
3289     PetscCall(ISGetLocalSize(iscol_o, &BsubN));
3290     n = asub->B->cmap->N;
3291     if (BsubN > n) {
3292       /* This case can be tested using ~petsc/src/tao/bound/tutorials/runplate2_3 */
3293       const PetscInt *idx;
3294       PetscInt        i, j, *idx_new, *subgarray = asub->garray;
3295       PetscCall(PetscInfo(M, "submatrix Bn %" PetscInt_FMT " != BsubN %" PetscInt_FMT ", update iscol_o\n", n, BsubN));
3296 
3297       PetscCall(PetscMalloc1(n, &idx_new));
3298       j = 0;
3299       PetscCall(ISGetIndices(iscol_o, &idx));
3300       for (i = 0; i < n; i++) {
3301         if (j >= BsubN) break;
3302         while (subgarray[i] > garray[j]) j++;
3303 
3304         if (subgarray[i] == garray[j]) {
3305           idx_new[i] = idx[j++];
3306         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "subgarray[%" PetscInt_FMT "]=%" PetscInt_FMT " cannot < garray[%" PetscInt_FMT "]=%" PetscInt_FMT, i, subgarray[i], j, garray[j]);
3307       }
3308       PetscCall(ISRestoreIndices(iscol_o, &idx));
3309 
3310       PetscCall(ISDestroy(&iscol_o));
3311       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, idx_new, PETSC_OWN_POINTER, &iscol_o));
3312 
3313     } else if (BsubN < n) {
3314       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Columns of Bsub (%" PetscInt_FMT ") cannot be smaller than B's (%" PetscInt_FMT ")", BsubN, asub->B->cmap->N);
3315     }
3316 
3317     PetscCall(PetscFree(garray));
3318     *submat = M;
3319 
3320     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
3321     PetscCall(PetscObjectCompose((PetscObject)M, "isrow_d", (PetscObject)isrow_d));
3322     PetscCall(ISDestroy(&isrow_d));
3323 
3324     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_d", (PetscObject)iscol_d));
3325     PetscCall(ISDestroy(&iscol_d));
3326 
3327     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_o", (PetscObject)iscol_o));
3328     PetscCall(ISDestroy(&iscol_o));
3329   }
3330   PetscFunctionReturn(PETSC_SUCCESS);
3331 }
3332 
3333 PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *newmat)
3334 {
3335   IS        iscol_local = NULL, isrow_d;
3336   PetscInt  csize;
3337   PetscInt  n, i, j, start, end;
3338   PetscBool sameRowDist = PETSC_FALSE, sameDist[2], tsameDist[2];
3339   MPI_Comm  comm;
3340 
3341   PetscFunctionBegin;
3342   /* If isrow has same processor distribution as mat,
3343      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
3344   if (call == MAT_REUSE_MATRIX) {
3345     PetscCall(PetscObjectQuery((PetscObject)*newmat, "isrow_d", (PetscObject *)&isrow_d));
3346     if (isrow_d) {
3347       sameRowDist  = PETSC_TRUE;
3348       tsameDist[1] = PETSC_TRUE; /* sameColDist */
3349     } else {
3350       PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_local));
3351       if (iscol_local) {
3352         sameRowDist  = PETSC_TRUE;
3353         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
3354       }
3355     }
3356   } else {
3357     /* Check if isrow has same processor distribution as mat */
3358     sameDist[0] = PETSC_FALSE;
3359     PetscCall(ISGetLocalSize(isrow, &n));
3360     if (!n) {
3361       sameDist[0] = PETSC_TRUE;
3362     } else {
3363       PetscCall(ISGetMinMax(isrow, &i, &j));
3364       PetscCall(MatGetOwnershipRange(mat, &start, &end));
3365       if (i >= start && j < end) sameDist[0] = PETSC_TRUE;
3366     }
3367 
3368     /* Check if iscol has same processor distribution as mat */
3369     sameDist[1] = PETSC_FALSE;
3370     PetscCall(ISGetLocalSize(iscol, &n));
3371     if (!n) {
3372       sameDist[1] = PETSC_TRUE;
3373     } else {
3374       PetscCall(ISGetMinMax(iscol, &i, &j));
3375       PetscCall(MatGetOwnershipRangeColumn(mat, &start, &end));
3376       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
3377     }
3378 
3379     PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
3380     PetscCall(MPIU_Allreduce(&sameDist, &tsameDist, 2, MPIU_BOOL, MPI_LAND, comm));
3381     sameRowDist = tsameDist[0];
3382   }
3383 
3384   if (sameRowDist) {
3385     if (tsameDist[1]) { /* sameRowDist & sameColDist */
3386       /* isrow and iscol have same processor distribution as mat */
3387       PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat, isrow, iscol, call, newmat));
3388       PetscFunctionReturn(PETSC_SUCCESS);
3389     } else { /* sameRowDist */
3390       /* isrow has same processor distribution as mat */
3391       if (call == MAT_INITIAL_MATRIX) {
3392         PetscBool sorted;
3393         PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
3394         PetscCall(ISGetLocalSize(iscol_local, &n)); /* local size of iscol_local = global columns of newmat */
3395         PetscCall(ISGetSize(iscol, &i));
3396         PetscCheck(n == i, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "n %" PetscInt_FMT " != size of iscol %" PetscInt_FMT, n, i);
3397 
3398         PetscCall(ISSorted(iscol_local, &sorted));
3399         if (sorted) {
3400           /* MatCreateSubMatrix_MPIAIJ_SameRowDist() requires iscol_local be sorted; it can have duplicate indices */
3401           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, iscol_local, MAT_INITIAL_MATRIX, newmat));
3402           PetscFunctionReturn(PETSC_SUCCESS);
3403         }
3404       } else { /* call == MAT_REUSE_MATRIX */
3405         IS iscol_sub;
3406         PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
3407         if (iscol_sub) {
3408           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, NULL, call, newmat));
3409           PetscFunctionReturn(PETSC_SUCCESS);
3410         }
3411       }
3412     }
3413   }
3414 
3415   /* General case: iscol -> iscol_local which has global size of iscol */
3416   if (call == MAT_REUSE_MATRIX) {
3417     PetscCall(PetscObjectQuery((PetscObject)*newmat, "ISAllGather", (PetscObject *)&iscol_local));
3418     PetscCheck(iscol_local, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
3419   } else {
3420     if (!iscol_local) PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
3421   }
3422 
3423   PetscCall(ISGetLocalSize(iscol, &csize));
3424   PetscCall(MatCreateSubMatrix_MPIAIJ_nonscalable(mat, isrow, iscol_local, csize, call, newmat));
3425 
3426   if (call == MAT_INITIAL_MATRIX) {
3427     PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
3428     PetscCall(ISDestroy(&iscol_local));
3429   }
3430   PetscFunctionReturn(PETSC_SUCCESS);
3431 }
3432 
3433 /*@C
3434   MatCreateMPIAIJWithSeqAIJ - creates a `MATMPIAIJ` matrix using `MATSEQAIJ` matrices that contain the "diagonal"
3435   and "off-diagonal" part of the matrix in CSR format.
3436 
3437   Collective
3438 
3439   Input Parameters:
3440 + comm   - MPI communicator
3441 . A      - "diagonal" portion of matrix
3442 . B      - "off-diagonal" portion of matrix, may have empty columns, will be destroyed by this routine
3443 - garray - global index of `B` columns
3444 
3445   Output Parameter:
3446 . mat - the matrix, with input `A` as its local diagonal matrix
3447 
3448   Level: advanced
3449 
3450   Notes:
3451   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix.
3452 
3453   `A` becomes part of output mat, `B` is destroyed by this routine. The user cannot use `A` and `B` anymore.
3454 
3455 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MATSEQAIJ`, `MatCreateMPIAIJWithSplitArrays()`
3456 @*/
3457 PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm, Mat A, Mat B, const PetscInt garray[], Mat *mat)
3458 {
3459   Mat_MPIAIJ        *maij;
3460   Mat_SeqAIJ        *b  = (Mat_SeqAIJ *)B->data, *bnew;
3461   PetscInt          *oi = b->i, *oj = b->j, i, nz, col;
3462   const PetscScalar *oa;
3463   Mat                Bnew;
3464   PetscInt           m, n, N;
3465   MatType            mpi_mat_type;
3466 
3467   PetscFunctionBegin;
3468   PetscCall(MatCreate(comm, mat));
3469   PetscCall(MatGetSize(A, &m, &n));
3470   PetscCheck(m == B->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Am %" PetscInt_FMT " != Bm %" PetscInt_FMT, m, B->rmap->N);
3471   PetscCheck(PetscAbs(A->rmap->bs) == PetscAbs(B->rmap->bs), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "A row bs %" PetscInt_FMT " != B row bs %" PetscInt_FMT, A->rmap->bs, B->rmap->bs);
3472   /* remove check below; When B is created using iscol_o from ISGetSeqIS_SameColDist_Private(), its bs may not be same as A */
3473   /* PetscCheck(A->cmap->bs == B->cmap->bs,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A column bs %" PetscInt_FMT " != B column bs %" PetscInt_FMT,A->cmap->bs,B->cmap->bs); */
3474 
3475   /* Get global columns of mat */
3476   PetscCall(MPIU_Allreduce(&n, &N, 1, MPIU_INT, MPI_SUM, comm));
3477 
3478   PetscCall(MatSetSizes(*mat, m, n, PETSC_DECIDE, N));
3479   /* Determine the type of MPI matrix that should be created from the type of matrix A, which holds the "diagonal" portion. */
3480   PetscCall(MatGetMPIMatType_Private(A, &mpi_mat_type));
3481   PetscCall(MatSetType(*mat, mpi_mat_type));
3482 
3483   if (A->rmap->bs > 1 || A->cmap->bs > 1) PetscCall(MatSetBlockSizes(*mat, A->rmap->bs, A->cmap->bs));
3484   maij = (Mat_MPIAIJ *)(*mat)->data;
3485 
3486   (*mat)->preallocated = PETSC_TRUE;
3487 
3488   PetscCall(PetscLayoutSetUp((*mat)->rmap));
3489   PetscCall(PetscLayoutSetUp((*mat)->cmap));
3490 
3491   /* Set A as diagonal portion of *mat */
3492   maij->A = A;
3493 
3494   nz = oi[m];
3495   for (i = 0; i < nz; i++) {
3496     col   = oj[i];
3497     oj[i] = garray[col];
3498   }
3499 
3500   /* Set Bnew as off-diagonal portion of *mat */
3501   PetscCall(MatSeqAIJGetArrayRead(B, &oa));
3502   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, N, oi, oj, (PetscScalar *)oa, &Bnew));
3503   PetscCall(MatSeqAIJRestoreArrayRead(B, &oa));
3504   bnew        = (Mat_SeqAIJ *)Bnew->data;
3505   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
3506   maij->B     = Bnew;
3507 
3508   PetscCheck(B->rmap->N == Bnew->rmap->N, PETSC_COMM_SELF, PETSC_ERR_PLIB, "BN %" PetscInt_FMT " != BnewN %" PetscInt_FMT, B->rmap->N, Bnew->rmap->N);
3509 
3510   b->singlemalloc = PETSC_FALSE; /* B arrays are shared by Bnew */
3511   b->free_a       = PETSC_FALSE;
3512   b->free_ij      = PETSC_FALSE;
3513   PetscCall(MatDestroy(&B));
3514 
3515   bnew->singlemalloc = PETSC_TRUE; /* arrays will be freed by MatDestroy(&Bnew) */
3516   bnew->free_a       = PETSC_TRUE;
3517   bnew->free_ij      = PETSC_TRUE;
3518 
3519   /* condense columns of maij->B */
3520   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
3521   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
3522   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
3523   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
3524   PetscCall(MatSetOption(*mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
3525   PetscFunctionReturn(PETSC_SUCCESS);
3526 }
3527 
3528 extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat, PetscInt, const IS[], const IS[], MatReuse, PetscBool, Mat *);
3529 
3530 PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat, IS isrow, IS iscol, IS iscol_local, MatReuse call, Mat *newmat)
3531 {
3532   PetscInt        i, m, n, rstart, row, rend, nz, j, bs, cbs;
3533   PetscInt       *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
3534   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)mat->data;
3535   Mat             M, Msub, B = a->B;
3536   MatScalar      *aa;
3537   Mat_SeqAIJ     *aij;
3538   PetscInt       *garray = a->garray, *colsub, Ncols;
3539   PetscInt        count, Bn = B->cmap->N, cstart = mat->cmap->rstart, cend = mat->cmap->rend;
3540   IS              iscol_sub, iscmap;
3541   const PetscInt *is_idx, *cmap;
3542   PetscBool       allcolumns = PETSC_FALSE;
3543   MPI_Comm        comm;
3544 
3545   PetscFunctionBegin;
3546   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
3547   if (call == MAT_REUSE_MATRIX) {
3548     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
3549     PetscCheck(iscol_sub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "SubIScol passed in was not used before, cannot reuse");
3550     PetscCall(ISGetLocalSize(iscol_sub, &count));
3551 
3552     PetscCall(PetscObjectQuery((PetscObject)*newmat, "Subcmap", (PetscObject *)&iscmap));
3553     PetscCheck(iscmap, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Subcmap passed in was not used before, cannot reuse");
3554 
3555     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Msub));
3556     PetscCheck(Msub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
3557 
3558     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_REUSE_MATRIX, PETSC_FALSE, &Msub));
3559 
3560   } else { /* call == MAT_INITIAL_MATRIX) */
3561     PetscBool flg;
3562 
3563     PetscCall(ISGetLocalSize(iscol, &n));
3564     PetscCall(ISGetSize(iscol, &Ncols));
3565 
3566     /* (1) iscol -> nonscalable iscol_local */
3567     /* Check for special case: each processor gets entire matrix columns */
3568     PetscCall(ISIdentity(iscol_local, &flg));
3569     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3570     PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
3571     if (allcolumns) {
3572       iscol_sub = iscol_local;
3573       PetscCall(PetscObjectReference((PetscObject)iscol_local));
3574       PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &iscmap));
3575 
3576     } else {
3577       /* (2) iscol_local -> iscol_sub and iscmap. Implementation below requires iscol_local be sorted, it can have duplicate indices */
3578       PetscInt *idx, *cmap1, k;
3579       PetscCall(PetscMalloc1(Ncols, &idx));
3580       PetscCall(PetscMalloc1(Ncols, &cmap1));
3581       PetscCall(ISGetIndices(iscol_local, &is_idx));
3582       count = 0;
3583       k     = 0;
3584       for (i = 0; i < Ncols; i++) {
3585         j = is_idx[i];
3586         if (j >= cstart && j < cend) {
3587           /* diagonal part of mat */
3588           idx[count]     = j;
3589           cmap1[count++] = i; /* column index in submat */
3590         } else if (Bn) {
3591           /* off-diagonal part of mat */
3592           if (j == garray[k]) {
3593             idx[count]     = j;
3594             cmap1[count++] = i; /* column index in submat */
3595           } else if (j > garray[k]) {
3596             while (j > garray[k] && k < Bn - 1) k++;
3597             if (j == garray[k]) {
3598               idx[count]     = j;
3599               cmap1[count++] = i; /* column index in submat */
3600             }
3601           }
3602         }
3603       }
3604       PetscCall(ISRestoreIndices(iscol_local, &is_idx));
3605 
3606       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_OWN_POINTER, &iscol_sub));
3607       PetscCall(ISGetBlockSize(iscol, &cbs));
3608       PetscCall(ISSetBlockSize(iscol_sub, cbs));
3609 
3610       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local), count, cmap1, PETSC_OWN_POINTER, &iscmap));
3611     }
3612 
3613     /* (3) Create sequential Msub */
3614     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_INITIAL_MATRIX, allcolumns, &Msub));
3615   }
3616 
3617   PetscCall(ISGetLocalSize(iscol_sub, &count));
3618   aij = (Mat_SeqAIJ *)(Msub)->data;
3619   ii  = aij->i;
3620   PetscCall(ISGetIndices(iscmap, &cmap));
3621 
3622   /*
3623       m - number of local rows
3624       Ncols - number of columns (same on all processors)
3625       rstart - first row in new global matrix generated
3626   */
3627   PetscCall(MatGetSize(Msub, &m, NULL));
3628 
3629   if (call == MAT_INITIAL_MATRIX) {
3630     /* (4) Create parallel newmat */
3631     PetscMPIInt rank, size;
3632     PetscInt    csize;
3633 
3634     PetscCallMPI(MPI_Comm_size(comm, &size));
3635     PetscCallMPI(MPI_Comm_rank(comm, &rank));
3636 
3637     /*
3638         Determine the number of non-zeros in the diagonal and off-diagonal
3639         portions of the matrix in order to do correct preallocation
3640     */
3641 
3642     /* first get start and end of "diagonal" columns */
3643     PetscCall(ISGetLocalSize(iscol, &csize));
3644     if (csize == PETSC_DECIDE) {
3645       PetscCall(ISGetSize(isrow, &mglobal));
3646       if (mglobal == Ncols) { /* square matrix */
3647         nlocal = m;
3648       } else {
3649         nlocal = Ncols / size + ((Ncols % size) > rank);
3650       }
3651     } else {
3652       nlocal = csize;
3653     }
3654     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
3655     rstart = rend - nlocal;
3656     PetscCheck(rank != size - 1 || rend == Ncols, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local column sizes %" PetscInt_FMT " do not add up to total number of columns %" PetscInt_FMT, rend, Ncols);
3657 
3658     /* next, compute all the lengths */
3659     jj = aij->j;
3660     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
3661     olens = dlens + m;
3662     for (i = 0; i < m; i++) {
3663       jend = ii[i + 1] - ii[i];
3664       olen = 0;
3665       dlen = 0;
3666       for (j = 0; j < jend; j++) {
3667         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
3668         else dlen++;
3669         jj++;
3670       }
3671       olens[i] = olen;
3672       dlens[i] = dlen;
3673     }
3674 
3675     PetscCall(ISGetBlockSize(isrow, &bs));
3676     PetscCall(ISGetBlockSize(iscol, &cbs));
3677 
3678     PetscCall(MatCreate(comm, &M));
3679     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, Ncols));
3680     PetscCall(MatSetBlockSizes(M, bs, cbs));
3681     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
3682     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
3683     PetscCall(PetscFree(dlens));
3684 
3685   } else { /* call == MAT_REUSE_MATRIX */
3686     M = *newmat;
3687     PetscCall(MatGetLocalSize(M, &i, NULL));
3688     PetscCheck(i == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
3689     PetscCall(MatZeroEntries(M));
3690     /*
3691          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3692        rather than the slower MatSetValues().
3693     */
3694     M->was_assembled = PETSC_TRUE;
3695     M->assembled     = PETSC_FALSE;
3696   }
3697 
3698   /* (5) Set values of Msub to *newmat */
3699   PetscCall(PetscMalloc1(count, &colsub));
3700   PetscCall(MatGetOwnershipRange(M, &rstart, NULL));
3701 
3702   jj = aij->j;
3703   PetscCall(MatSeqAIJGetArrayRead(Msub, (const PetscScalar **)&aa));
3704   for (i = 0; i < m; i++) {
3705     row = rstart + i;
3706     nz  = ii[i + 1] - ii[i];
3707     for (j = 0; j < nz; j++) colsub[j] = cmap[jj[j]];
3708     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, colsub, aa, INSERT_VALUES));
3709     jj += nz;
3710     aa += nz;
3711   }
3712   PetscCall(MatSeqAIJRestoreArrayRead(Msub, (const PetscScalar **)&aa));
3713   PetscCall(ISRestoreIndices(iscmap, &cmap));
3714 
3715   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
3716   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
3717 
3718   PetscCall(PetscFree(colsub));
3719 
3720   /* save Msub, iscol_sub and iscmap used in processor for next request */
3721   if (call == MAT_INITIAL_MATRIX) {
3722     *newmat = M;
3723     PetscCall(PetscObjectCompose((PetscObject)(*newmat), "SubMatrix", (PetscObject)Msub));
3724     PetscCall(MatDestroy(&Msub));
3725 
3726     PetscCall(PetscObjectCompose((PetscObject)(*newmat), "SubIScol", (PetscObject)iscol_sub));
3727     PetscCall(ISDestroy(&iscol_sub));
3728 
3729     PetscCall(PetscObjectCompose((PetscObject)(*newmat), "Subcmap", (PetscObject)iscmap));
3730     PetscCall(ISDestroy(&iscmap));
3731 
3732     if (iscol_local) {
3733       PetscCall(PetscObjectCompose((PetscObject)(*newmat), "ISAllGather", (PetscObject)iscol_local));
3734       PetscCall(ISDestroy(&iscol_local));
3735     }
3736   }
3737   PetscFunctionReturn(PETSC_SUCCESS);
3738 }
3739 
3740 /*
3741     Not great since it makes two copies of the submatrix, first an SeqAIJ
3742   in local and then by concatenating the local matrices the end result.
3743   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()
3744 
3745   This requires a sequential iscol with all indices.
3746 */
3747 PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat, IS isrow, IS iscol, PetscInt csize, MatReuse call, Mat *newmat)
3748 {
3749   PetscMPIInt rank, size;
3750   PetscInt    i, m, n, rstart, row, rend, nz, *cwork, j, bs, cbs;
3751   PetscInt   *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
3752   Mat         M, Mreuse;
3753   MatScalar  *aa, *vwork;
3754   MPI_Comm    comm;
3755   Mat_SeqAIJ *aij;
3756   PetscBool   colflag, allcolumns = PETSC_FALSE;
3757 
3758   PetscFunctionBegin;
3759   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
3760   PetscCallMPI(MPI_Comm_rank(comm, &rank));
3761   PetscCallMPI(MPI_Comm_size(comm, &size));
3762 
3763   /* Check for special case: each processor gets entire matrix columns */
3764   PetscCall(ISIdentity(iscol, &colflag));
3765   PetscCall(ISGetLocalSize(iscol, &n));
3766   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
3767   PetscCall(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
3768 
3769   if (call == MAT_REUSE_MATRIX) {
3770     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Mreuse));
3771     PetscCheck(Mreuse, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
3772     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_REUSE_MATRIX, allcolumns, &Mreuse));
3773   } else {
3774     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_INITIAL_MATRIX, allcolumns, &Mreuse));
3775   }
3776 
3777   /*
3778       m - number of local rows
3779       n - number of columns (same on all processors)
3780       rstart - first row in new global matrix generated
3781   */
3782   PetscCall(MatGetSize(Mreuse, &m, &n));
3783   PetscCall(MatGetBlockSizes(Mreuse, &bs, &cbs));
3784   if (call == MAT_INITIAL_MATRIX) {
3785     aij = (Mat_SeqAIJ *)(Mreuse)->data;
3786     ii  = aij->i;
3787     jj  = aij->j;
3788 
3789     /*
3790         Determine the number of non-zeros in the diagonal and off-diagonal
3791         portions of the matrix in order to do correct preallocation
3792     */
3793 
3794     /* first get start and end of "diagonal" columns */
3795     if (csize == PETSC_DECIDE) {
3796       PetscCall(ISGetSize(isrow, &mglobal));
3797       if (mglobal == n) { /* square matrix */
3798         nlocal = m;
3799       } else {
3800         nlocal = n / size + ((n % size) > rank);
3801       }
3802     } else {
3803       nlocal = csize;
3804     }
3805     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
3806     rstart = rend - nlocal;
3807     PetscCheck(rank != size - 1 || rend == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local column sizes %" PetscInt_FMT " do not add up to total number of columns %" PetscInt_FMT, rend, n);
3808 
3809     /* next, compute all the lengths */
3810     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
3811     olens = dlens + m;
3812     for (i = 0; i < m; i++) {
3813       jend = ii[i + 1] - ii[i];
3814       olen = 0;
3815       dlen = 0;
3816       for (j = 0; j < jend; j++) {
3817         if (*jj < rstart || *jj >= rend) olen++;
3818         else dlen++;
3819         jj++;
3820       }
3821       olens[i] = olen;
3822       dlens[i] = dlen;
3823     }
3824     PetscCall(MatCreate(comm, &M));
3825     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, n));
3826     PetscCall(MatSetBlockSizes(M, bs, cbs));
3827     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
3828     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
3829     PetscCall(PetscFree(dlens));
3830   } else {
3831     PetscInt ml, nl;
3832 
3833     M = *newmat;
3834     PetscCall(MatGetLocalSize(M, &ml, &nl));
3835     PetscCheck(ml == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
3836     PetscCall(MatZeroEntries(M));
3837     /*
3838          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
3839        rather than the slower MatSetValues().
3840     */
3841     M->was_assembled = PETSC_TRUE;
3842     M->assembled     = PETSC_FALSE;
3843   }
3844   PetscCall(MatGetOwnershipRange(M, &rstart, &rend));
3845   aij = (Mat_SeqAIJ *)(Mreuse)->data;
3846   ii  = aij->i;
3847   jj  = aij->j;
3848 
3849   /* trigger copy to CPU if needed */
3850   PetscCall(MatSeqAIJGetArrayRead(Mreuse, (const PetscScalar **)&aa));
3851   for (i = 0; i < m; i++) {
3852     row   = rstart + i;
3853     nz    = ii[i + 1] - ii[i];
3854     cwork = jj;
3855     jj += nz;
3856     vwork = aa;
3857     aa += nz;
3858     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, cwork, vwork, INSERT_VALUES));
3859   }
3860   PetscCall(MatSeqAIJRestoreArrayRead(Mreuse, (const PetscScalar **)&aa));
3861 
3862   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
3863   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
3864   *newmat = M;
3865 
3866   /* save submatrix used in processor for next request */
3867   if (call == MAT_INITIAL_MATRIX) {
3868     PetscCall(PetscObjectCompose((PetscObject)M, "SubMatrix", (PetscObject)Mreuse));
3869     PetscCall(MatDestroy(&Mreuse));
3870   }
3871   PetscFunctionReturn(PETSC_SUCCESS);
3872 }
3873 
3874 static PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
3875 {
3876   PetscInt        m, cstart, cend, j, nnz, i, d, *ld;
3877   PetscInt       *d_nnz, *o_nnz, nnz_max = 0, rstart, ii;
3878   const PetscInt *JJ;
3879   PetscBool       nooffprocentries;
3880   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)B->data;
3881 
3882   PetscFunctionBegin;
3883   PetscCheck(Ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Ii[0] must be 0 it is %" PetscInt_FMT, Ii[0]);
3884 
3885   PetscCall(PetscLayoutSetUp(B->rmap));
3886   PetscCall(PetscLayoutSetUp(B->cmap));
3887   m      = B->rmap->n;
3888   cstart = B->cmap->rstart;
3889   cend   = B->cmap->rend;
3890   rstart = B->rmap->rstart;
3891 
3892   PetscCall(PetscCalloc2(m, &d_nnz, m, &o_nnz));
3893 
3894   if (PetscDefined(USE_DEBUG)) {
3895     for (i = 0; i < m; i++) {
3896       nnz = Ii[i + 1] - Ii[i];
3897       JJ  = J ? J + Ii[i] : NULL;
3898       PetscCheck(nnz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative %" PetscInt_FMT " number of columns", i, nnz);
3899       PetscCheck(!nnz || !(JJ[0] < 0), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Row %" PetscInt_FMT " starts with negative column index %" PetscInt_FMT, i, JJ[0]);
3900       PetscCheck(!nnz || !(JJ[nnz - 1] >= B->cmap->N), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Row %" PetscInt_FMT " ends with too large a column index %" PetscInt_FMT " (max allowed %" PetscInt_FMT ")", i, JJ[nnz - 1], B->cmap->N);
3901     }
3902   }
3903 
3904   for (i = 0; i < m; i++) {
3905     nnz     = Ii[i + 1] - Ii[i];
3906     JJ      = J ? J + Ii[i] : NULL;
3907     nnz_max = PetscMax(nnz_max, nnz);
3908     d       = 0;
3909     for (j = 0; j < nnz; j++) {
3910       if (cstart <= JJ[j] && JJ[j] < cend) d++;
3911     }
3912     d_nnz[i] = d;
3913     o_nnz[i] = nnz - d;
3914   }
3915   PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
3916   PetscCall(PetscFree2(d_nnz, o_nnz));
3917 
3918   for (i = 0; i < m; i++) {
3919     ii = i + rstart;
3920     PetscCall(MatSetValues_MPIAIJ(B, 1, &ii, Ii[i + 1] - Ii[i], J ? J + Ii[i] : NULL, v ? v + Ii[i] : NULL, INSERT_VALUES));
3921   }
3922   nooffprocentries    = B->nooffprocentries;
3923   B->nooffprocentries = PETSC_TRUE;
3924   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
3925   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
3926   B->nooffprocentries = nooffprocentries;
3927 
3928   /* count number of entries below block diagonal */
3929   PetscCall(PetscFree(Aij->ld));
3930   PetscCall(PetscCalloc1(m, &ld));
3931   Aij->ld = ld;
3932   for (i = 0; i < m; i++) {
3933     nnz = Ii[i + 1] - Ii[i];
3934     j   = 0;
3935     while (j < nnz && J[j] < cstart) j++;
3936     ld[i] = j;
3937     if (J) J += nnz;
3938   }
3939 
3940   PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
3941   PetscFunctionReturn(PETSC_SUCCESS);
3942 }
3943 
3944 /*@
3945   MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in `MATAIJ` format
3946   (the default parallel PETSc format).
3947 
3948   Collective
3949 
3950   Input Parameters:
3951 + B - the matrix
3952 . i - the indices into j for the start of each local row (starts with zero)
3953 . j - the column indices for each local row (starts with zero)
3954 - v - optional values in the matrix
3955 
3956   Level: developer
3957 
3958   Notes:
3959   The `i`, `j`, and `v` arrays ARE copied by this routine into the internal format used by PETSc;
3960   thus you CANNOT change the matrix entries by changing the values of `v` after you have
3961   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.
3962 
3963   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.
3964 
3965   The format which is used for the sparse matrix input, is equivalent to a
3966   row-major ordering.. i.e for the following matrix, the input data expected is
3967   as shown
3968 
3969 .vb
3970         1 0 0
3971         2 0 3     P0
3972        -------
3973         4 5 6     P1
3974 
3975      Process0 [P0] rows_owned=[0,1]
3976         i =  {0,1,3}  [size = nrow+1  = 2+1]
3977         j =  {0,0,2}  [size = 3]
3978         v =  {1,2,3}  [size = 3]
3979 
3980      Process1 [P1] rows_owned=[2]
3981         i =  {0,3}    [size = nrow+1  = 1+1]
3982         j =  {0,1,2}  [size = 3]
3983         v =  {4,5,6}  [size = 3]
3984 .ve
3985 
3986 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatCreateAIJ()`,
3987           `MatCreateSeqAIJWithArrays()`, `MatCreateMPIAIJWithSplitArrays()`
3988 @*/
3989 PetscErrorCode MatMPIAIJSetPreallocationCSR(Mat B, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
3990 {
3991   PetscFunctionBegin;
3992   PetscTryMethod(B, "MatMPIAIJSetPreallocationCSR_C", (Mat, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, i, j, v));
3993   PetscFunctionReturn(PETSC_SUCCESS);
3994 }
3995 
3996 /*@C
3997   MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in `MATMPIAIJ` format
3998   (the default parallel PETSc format).  For good matrix assembly performance
3999   the user should preallocate the matrix storage by setting the parameters
4000   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).
4001 
4002   Collective
4003 
4004   Input Parameters:
4005 + B     - the matrix
4006 . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4007            (same value is used for all local rows)
4008 . d_nnz - array containing the number of nonzeros in the various rows of the
4009            DIAGONAL portion of the local submatrix (possibly different for each row)
4010            or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `d_nz` is used to specify the nonzero structure.
4011            The size of this array is equal to the number of local rows, i.e 'm'.
4012            For matrices that will be factored, you must leave room for (and set)
4013            the diagonal entry even if it is zero.
4014 . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4015            submatrix (same value is used for all local rows).
4016 - o_nnz - array containing the number of nonzeros in the various rows of the
4017            OFF-DIAGONAL portion of the local submatrix (possibly different for
4018            each row) or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `o_nz` is used to specify the nonzero
4019            structure. The size of this array is equal to the number
4020            of local rows, i.e 'm'.
4021 
4022   Example Usage:
4023   Consider the following 8x8 matrix with 34 non-zero values, that is
4024   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4025   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4026   as follows
4027 
4028 .vb
4029             1  2  0  |  0  3  0  |  0  4
4030     Proc0   0  5  6  |  7  0  0  |  8  0
4031             9  0 10  | 11  0  0  | 12  0
4032     -------------------------------------
4033            13  0 14  | 15 16 17  |  0  0
4034     Proc1   0 18  0  | 19 20 21  |  0  0
4035             0  0  0  | 22 23  0  | 24  0
4036     -------------------------------------
4037     Proc2  25 26 27  |  0  0 28  | 29  0
4038            30  0  0  | 31 32 33  |  0 34
4039 .ve
4040 
4041   This can be represented as a collection of submatrices as
4042 .vb
4043       A B C
4044       D E F
4045       G H I
4046 .ve
4047 
4048   Where the submatrices A,B,C are owned by proc0, D,E,F are
4049   owned by proc1, G,H,I are owned by proc2.
4050 
4051   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4052   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4053   The 'M','N' parameters are 8,8, and have the same values on all procs.
4054 
4055   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4056   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4057   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4058   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4059   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
4060   matrix, ans [DF] as another `MATSEQAIJ` matrix.
4061 
4062   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
4063   allocated for every row of the local diagonal submatrix, and `o_nz`
4064   storage locations are allocated for every row of the OFF-DIAGONAL submat.
4065   One way to choose `d_nz` and `o_nz` is to use the max nonzerors per local
4066   rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4067   In this case, the values of `d_nz`, `o_nz` are
4068 .vb
4069      proc0  dnz = 2, o_nz = 2
4070      proc1  dnz = 3, o_nz = 2
4071      proc2  dnz = 1, o_nz = 4
4072 .ve
4073   We are allocating `m`*(`d_nz`+`o_nz`) storage locations for every proc. This
4074   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4075   for proc3. i.e we are using 12+15+10=37 storage locations to store
4076   34 values.
4077 
4078   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
4079   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4080   In the above case the values for `d_nnz`, `o_nnz` are
4081 .vb
4082      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
4083      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
4084      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
4085 .ve
4086   Here the space allocated is sum of all the above values i.e 34, and
4087   hence pre-allocation is perfect.
4088 
4089   Level: intermediate
4090 
4091   Notes:
4092   If the *_nnz parameter is given then the *_nz parameter is ignored
4093 
4094   The `MATAIJ` format, also called compressed row storage (CSR), is compatible with standard Fortran
4095   storage.  The stored row and column indices begin with zero.
4096   See [Sparse Matrices](sec_matsparse) for details.
4097 
4098   The parallel matrix is partitioned such that the first m0 rows belong to
4099   process 0, the next m1 rows belong to process 1, the next m2 rows belong
4100   to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.
4101 
4102   The DIAGONAL portion of the local submatrix of a processor can be defined
4103   as the submatrix which is obtained by extraction the part corresponding to
4104   the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
4105   first row that belongs to the processor, r2 is the last row belonging to
4106   the this processor, and c1-c2 is range of indices of the local part of a
4107   vector suitable for applying the matrix to.  This is an mxn matrix.  In the
4108   common case of a square matrix, the row and column ranges are the same and
4109   the DIAGONAL part is also square. The remaining portion of the local
4110   submatrix (mxN) constitute the OFF-DIAGONAL portion.
4111 
4112   If `o_nnz` and `d_nnz` are specified, then `o_nz` and `d_nz` are ignored.
4113 
4114   You can call `MatGetInfo()` to get information on how effective the preallocation was;
4115   for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
4116   You can also run with the option `-info` and look for messages with the string
4117   malloc in them to see if additional memory allocation was needed.
4118 
4119 .seealso: [](ch_matrices), `Mat`, [Sparse Matrices](sec_matsparse), `MATMPIAIJ`, `MATAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatCreateAIJ()`, `MatMPIAIJSetPreallocationCSR()`,
4120           `MatGetInfo()`, `PetscSplitOwnership()`
4121 @*/
4122 PetscErrorCode MatMPIAIJSetPreallocation(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
4123 {
4124   PetscFunctionBegin;
4125   PetscValidHeaderSpecific(B, MAT_CLASSID, 1);
4126   PetscValidType(B, 1);
4127   PetscTryMethod(B, "MatMPIAIJSetPreallocation_C", (Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]), (B, d_nz, d_nnz, o_nz, o_nnz));
4128   PetscFunctionReturn(PETSC_SUCCESS);
4129 }
4130 
4131 /*@
4132   MatCreateMPIAIJWithArrays - creates a `MATMPIAIJ` matrix using arrays that contain in standard
4133   CSR format for the local rows.
4134 
4135   Collective
4136 
4137   Input Parameters:
4138 + comm - MPI communicator
4139 . m    - number of local rows (Cannot be `PETSC_DECIDE`)
4140 . n    - This value should be the same as the local size used in creating the
4141        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
4142        calculated if N is given) For square matrices n is almost always m.
4143 . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
4144 . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
4145 . i    - row indices; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
4146 . j    - column indices
4147 - a    - optional matrix values
4148 
4149   Output Parameter:
4150 . mat - the matrix
4151 
4152   Level: intermediate
4153 
4154   Notes:
4155   The `i`, `j`, and `a` arrays ARE copied by this routine into the internal format used by PETSc;
4156   thus you CANNOT change the matrix entries by changing the values of a[] after you have
4157   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.
4158 
4159   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.
4160 
4161   The format which is used for the sparse matrix input, is equivalent to a
4162   row-major ordering.. i.e for the following matrix, the input data expected is
4163   as shown
4164 
4165   Once you have created the matrix you can update it with new numerical values using MatUpdateMPIAIJWithArrays
4166 .vb
4167         1 0 0
4168         2 0 3     P0
4169        -------
4170         4 5 6     P1
4171 
4172      Process0 [P0] rows_owned=[0,1]
4173         i =  {0,1,3}  [size = nrow+1  = 2+1]
4174         j =  {0,0,2}  [size = 3]
4175         v =  {1,2,3}  [size = 3]
4176 
4177      Process1 [P1] rows_owned=[2]
4178         i =  {0,3}    [size = nrow+1  = 1+1]
4179         j =  {0,1,2}  [size = 3]
4180         v =  {4,5,6}  [size = 3]
4181 .ve
4182 
4183 .seealso: [](ch_matrices), `Mat`, `MATMPIAIK`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
4184           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArrays()`
4185 @*/
4186 PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt i[], const PetscInt j[], const PetscScalar a[], Mat *mat)
4187 {
4188   PetscFunctionBegin;
4189   PetscCheck(!i || !i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
4190   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
4191   PetscCall(MatCreate(comm, mat));
4192   PetscCall(MatSetSizes(*mat, m, n, M, N));
4193   /* PetscCall(MatSetBlockSizes(M,bs,cbs)); */
4194   PetscCall(MatSetType(*mat, MATMPIAIJ));
4195   PetscCall(MatMPIAIJSetPreallocationCSR(*mat, i, j, a));
4196   PetscFunctionReturn(PETSC_SUCCESS);
4197 }
4198 
4199 /*@
4200   MatUpdateMPIAIJWithArrays - updates a `MATMPIAIJ` matrix using arrays that contain in standard
4201   CSR format for the local rows. Only the numerical values are updated the other arrays must be identical to what was passed
4202   from `MatCreateMPIAIJWithArrays()`
4203 
4204   Deprecated: Use `MatUpdateMPIAIJWithArray()`
4205 
4206   Collective
4207 
4208   Input Parameters:
4209 + mat - the matrix
4210 . m   - number of local rows (Cannot be `PETSC_DECIDE`)
4211 . n   - This value should be the same as the local size used in creating the
4212        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
4213        calculated if N is given) For square matrices n is almost always m.
4214 . M   - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
4215 . N   - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
4216 . Ii  - row indices; that is Ii[0] = 0, Ii[row] = Ii[row-1] + number of elements in that row of the matrix
4217 . J   - column indices
4218 - v   - matrix values
4219 
4220   Level: deprecated
4221 
4222 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
4223           `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`
4224 @*/
4225 PetscErrorCode MatUpdateMPIAIJWithArrays(Mat mat, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
4226 {
4227   PetscInt        nnz, i;
4228   PetscBool       nooffprocentries;
4229   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
4230   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
4231   PetscScalar    *ad, *ao;
4232   PetscInt        ldi, Iii, md;
4233   const PetscInt *Adi = Ad->i;
4234   PetscInt       *ld  = Aij->ld;
4235 
4236   PetscFunctionBegin;
4237   PetscCheck(Ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
4238   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
4239   PetscCheck(m == mat->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of rows cannot change from call to MatUpdateMPIAIJWithArrays()");
4240   PetscCheck(n == mat->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of columns cannot change from call to MatUpdateMPIAIJWithArrays()");
4241 
4242   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
4243   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));
4244 
4245   for (i = 0; i < m; i++) {
4246     if (PetscDefined(USE_DEBUG)) {
4247       for (PetscInt j = Ii[i] + 1; j < Ii[i + 1]; ++j) {
4248         PetscCheck(J[j] >= J[j - 1], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column entry number %" PetscInt_FMT " (actual column %" PetscInt_FMT ") in row %" PetscInt_FMT " is not sorted", j - Ii[i], J[j], i);
4249         PetscCheck(J[j] != J[j - 1], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column entry number %" PetscInt_FMT " (actual column %" PetscInt_FMT ") in row %" PetscInt_FMT " is identical to previous entry", j - Ii[i], J[j], i);
4250       }
4251     }
4252     nnz = Ii[i + 1] - Ii[i];
4253     Iii = Ii[i];
4254     ldi = ld[i];
4255     md  = Adi[i + 1] - Adi[i];
4256     PetscCall(PetscArraycpy(ao, v + Iii, ldi));
4257     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
4258     PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
4259     ad += md;
4260     ao += nnz - md;
4261   }
4262   nooffprocentries      = mat->nooffprocentries;
4263   mat->nooffprocentries = PETSC_TRUE;
4264   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
4265   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
4266   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
4267   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
4268   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
4269   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
4270   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
4271   mat->nooffprocentries = nooffprocentries;
4272   PetscFunctionReturn(PETSC_SUCCESS);
4273 }
4274 
4275 /*@
4276   MatUpdateMPIAIJWithArray - updates an `MATMPIAIJ` matrix using an array that contains the nonzero values
4277 
4278   Collective
4279 
4280   Input Parameters:
4281 + mat - the matrix
4282 - v   - matrix values, stored by row
4283 
4284   Level: intermediate
4285 
4286   Note:
4287   The matrix must have been obtained with `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()`
4288 
4289 .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
4290           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArrays()`
4291 @*/
4292 PetscErrorCode MatUpdateMPIAIJWithArray(Mat mat, const PetscScalar v[])
4293 {
4294   PetscInt        nnz, i, m;
4295   PetscBool       nooffprocentries;
4296   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
4297   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
4298   Mat_SeqAIJ     *Ao  = (Mat_SeqAIJ *)Aij->B->data;
4299   PetscScalar    *ad, *ao;
4300   const PetscInt *Adi = Ad->i, *Adj = Ao->i;
4301   PetscInt        ldi, Iii, md;
4302   PetscInt       *ld = Aij->ld;
4303 
4304   PetscFunctionBegin;
4305   m = mat->rmap->n;
4306 
4307   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
4308   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));
4309   Iii = 0;
4310   for (i = 0; i < m; i++) {
4311     nnz = Adi[i + 1] - Adi[i] + Adj[i + 1] - Adj[i];
4312     ldi = ld[i];
4313     md  = Adi[i + 1] - Adi[i];
4314     PetscCall(PetscArraycpy(ao, v + Iii, ldi));
4315     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
4316     PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
4317     ad += md;
4318     ao += nnz - md;
4319     Iii += nnz;
4320   }
4321   nooffprocentries      = mat->nooffprocentries;
4322   mat->nooffprocentries = PETSC_TRUE;
4323   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
4324   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
4325   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
4326   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
4327   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
4328   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
4329   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
4330   mat->nooffprocentries = nooffprocentries;
4331   PetscFunctionReturn(PETSC_SUCCESS);
4332 }
4333 
4334 /*@C
4335   MatCreateAIJ - Creates a sparse parallel matrix in `MATAIJ` format
4336   (the default parallel PETSc format).  For good matrix assembly performance
4337   the user should preallocate the matrix storage by setting the parameters
4338   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).
4339 
4340   Collective
4341 
4342   Input Parameters:
4343 + comm  - MPI communicator
4344 . m     - number of local rows (or `PETSC_DECIDE` to have calculated if M is given)
4345            This value should be the same as the local size used in creating the
4346            y vector for the matrix-vector product y = Ax.
4347 . n     - This value should be the same as the local size used in creating the
4348        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
4349        calculated if N is given) For square matrices n is almost always m.
4350 . M     - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
4351 . N     - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
4352 . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
4353            (same value is used for all local rows)
4354 . d_nnz - array containing the number of nonzeros in the various rows of the
4355            DIAGONAL portion of the local submatrix (possibly different for each row)
4356            or `NULL`, if `d_nz` is used to specify the nonzero structure.
4357            The size of this array is equal to the number of local rows, i.e 'm'.
4358 . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
4359            submatrix (same value is used for all local rows).
4360 - o_nnz - array containing the number of nonzeros in the various rows of the
4361            OFF-DIAGONAL portion of the local submatrix (possibly different for
4362            each row) or `NULL`, if `o_nz` is used to specify the nonzero
4363            structure. The size of this array is equal to the number
4364            of local rows, i.e 'm'.
4365 
4366   Output Parameter:
4367 . A - the matrix
4368 
4369   Options Database Keys:
4370 + -mat_no_inode                     - Do not use inodes
4371 . -mat_inode_limit <limit>          - Sets inode limit (max limit=5)
4372 - -matmult_vecscatter_view <viewer> - View the vecscatter (i.e., communication pattern) used in `MatMult()` of sparse parallel matrices.
4373         See viewer types in manual of `MatView()`. Of them, ascii_matlab, draw or binary cause the vecscatter be viewed as a matrix.
4374         Entry (i,j) is the size of message (in bytes) rank i sends to rank j in one `MatMult()` call.
4375 
4376   Level: intermediate
4377 
4378   Notes:
4379   It is recommended that one use `MatCreateFromOptions()` or the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
4380   MatXXXXSetPreallocation() paradigm instead of this routine directly.
4381   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]
4382 
4383   If the *_nnz parameter is given then the *_nz parameter is ignored
4384 
4385   The `m`,`n`,`M`,`N` parameters specify the size of the matrix, and its partitioning across
4386   processors, while `d_nz`,`d_nnz`,`o_nz`,`o_nnz` parameters specify the approximate
4387   storage requirements for this matrix.
4388 
4389   If `PETSC_DECIDE` or  `PETSC_DETERMINE` is used for a particular argument on one
4390   processor than it must be used on all processors that share the object for
4391   that argument.
4392 
4393   The user MUST specify either the local or global matrix dimensions
4394   (possibly both).
4395 
4396   The parallel matrix is partitioned across processors such that the
4397   first m0 rows belong to process 0, the next m1 rows belong to
4398   process 1, the next m2 rows belong to process 2 etc.. where
4399   m0,m1,m2,.. are the input parameter 'm'. i.e each processor stores
4400   values corresponding to [m x N] submatrix.
4401 
4402   The columns are logically partitioned with the n0 columns belonging
4403   to 0th partition, the next n1 columns belonging to the next
4404   partition etc.. where n0,n1,n2... are the input parameter 'n'.
4405 
4406   The DIAGONAL portion of the local submatrix on any given processor
4407   is the submatrix corresponding to the rows and columns m,n
4408   corresponding to the given processor. i.e diagonal matrix on
4409   process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
4410   etc. The remaining portion of the local submatrix [m x (N-n)]
4411   constitute the OFF-DIAGONAL portion. The example below better
4412   illustrates this concept.
4413 
4414   For a square global matrix we define each processor's diagonal portion
4415   to be its local rows and the corresponding columns (a square submatrix);
4416   each processor's off-diagonal portion encompasses the remainder of the
4417   local matrix (a rectangular submatrix).
4418 
4419   If `o_nnz`, `d_nnz` are specified, then `o_nz`, and `d_nz` are ignored.
4420 
4421   When calling this routine with a single process communicator, a matrix of
4422   type `MATSEQAIJ` is returned.  If a matrix of type `MATMPIAIJ` is desired for this
4423   type of communicator, use the construction mechanism
4424 .vb
4425   MatCreate(..., &A);
4426   MatSetType(A, MATMPIAIJ);
4427   MatSetSizes(A, m, n, M, N);
4428   MatMPIAIJSetPreallocation(A, ...);
4429 .ve
4430 
4431   By default, this format uses inodes (identical nodes) when possible.
4432   We search for consecutive rows with the same nonzero structure, thereby
4433   reusing matrix information to achieve increased efficiency.
4434 
4435   Example Usage:
4436   Consider the following 8x8 matrix with 34 non-zero values, that is
4437   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
4438   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
4439   as follows
4440 
4441 .vb
4442             1  2  0  |  0  3  0  |  0  4
4443     Proc0   0  5  6  |  7  0  0  |  8  0
4444             9  0 10  | 11  0  0  | 12  0
4445     -------------------------------------
4446            13  0 14  | 15 16 17  |  0  0
4447     Proc1   0 18  0  | 19 20 21  |  0  0
4448             0  0  0  | 22 23  0  | 24  0
4449     -------------------------------------
4450     Proc2  25 26 27  |  0  0 28  | 29  0
4451            30  0  0  | 31 32 33  |  0 34
4452 .ve
4453 
4454   This can be represented as a collection of submatrices as
4455 
4456 .vb
4457       A B C
4458       D E F
4459       G H I
4460 .ve
4461 
4462   Where the submatrices A,B,C are owned by proc0, D,E,F are
4463   owned by proc1, G,H,I are owned by proc2.
4464 
4465   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4466   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
4467   The 'M','N' parameters are 8,8, and have the same values on all procs.
4468 
4469   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
4470   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
4471   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
4472   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
4473   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
4474   matrix, ans [DF] as another SeqAIJ matrix.
4475 
4476   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
4477   allocated for every row of the local diagonal submatrix, and `o_nz`
4478   storage locations are allocated for every row of the OFF-DIAGONAL submat.
4479   One way to choose `d_nz` and `o_nz` is to use the max nonzerors per local
4480   rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
4481   In this case, the values of `d_nz`,`o_nz` are
4482 .vb
4483      proc0  dnz = 2, o_nz = 2
4484      proc1  dnz = 3, o_nz = 2
4485      proc2  dnz = 1, o_nz = 4
4486 .ve
4487   We are allocating m*(`d_nz`+`o_nz`) storage locations for every proc. This
4488   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
4489   for proc3. i.e we are using 12+15+10=37 storage locations to store
4490   34 values.
4491 
4492   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
4493   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
4494   In the above case the values for d_nnz,o_nnz are
4495 .vb
4496      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
4497      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
4498      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
4499 .ve
4500   Here the space allocated is sum of all the above values i.e 34, and
4501   hence pre-allocation is perfect.
4502 
4503 .seealso: [](ch_matrices), `Mat`, [Sparse Matrix Creation](sec_matsparse), `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
4504           `MATMPIAIJ`, `MatCreateMPIAIJWithArrays()`
4505 @*/
4506 PetscErrorCode MatCreateAIJ(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[], Mat *A)
4507 {
4508   PetscMPIInt size;
4509 
4510   PetscFunctionBegin;
4511   PetscCall(MatCreate(comm, A));
4512   PetscCall(MatSetSizes(*A, m, n, M, N));
4513   PetscCallMPI(MPI_Comm_size(comm, &size));
4514   if (size > 1) {
4515     PetscCall(MatSetType(*A, MATMPIAIJ));
4516     PetscCall(MatMPIAIJSetPreallocation(*A, d_nz, d_nnz, o_nz, o_nnz));
4517   } else {
4518     PetscCall(MatSetType(*A, MATSEQAIJ));
4519     PetscCall(MatSeqAIJSetPreallocation(*A, d_nz, d_nnz));
4520   }
4521   PetscFunctionReturn(PETSC_SUCCESS);
4522 }
4523 
4524 /*MC
4525     MatMPIAIJGetSeqAIJF90 - Returns the local pieces of this distributed matrix
4526 
4527     Synopsis:
4528     MatMPIAIJGetSeqAIJF90(Mat A, Mat Ad, Mat Ao, {PetscInt, pointer :: colmap(:)},integer ierr)
4529 
4530     Not Collective
4531 
4532     Input Parameter:
4533 .   A - the `MATMPIAIJ` matrix
4534 
4535     Output Parameters:
4536 +   Ad - the diagonal portion of the matrix
4537 .   Ao - the off-diagonal portion of the matrix
4538 .   colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix
4539 -   ierr - error code
4540 
4541      Level: advanced
4542 
4543     Note:
4544     Use  `MatMPIAIJRestoreSeqAIJF90()` when you no longer need access to the matrices and `colmap`
4545 
4546 .seealso: [](ch_matrices), `Mat`, [](sec_fortranarrays), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetSeqAIJ()`, `MatMPIAIJRestoreSeqAIJF90()`
4547 M*/
4548 
4549 /*MC
4550     MatMPIAIJRestoreSeqAIJF90 - call after `MatMPIAIJGetSeqAIJF90()` when you no longer need access to the matrices and `colmap`
4551 
4552     Synopsis:
4553     MatMPIAIJRestoreSeqAIJF90(Mat A, Mat Ad, Mat Ao, {PetscInt, pointer :: colmap(:)},integer ierr)
4554 
4555     Not Collective
4556 
4557     Input Parameters:
4558 +   A - the `MATMPIAIJ` matrix
4559 .   Ad - the diagonal portion of the matrix
4560 .   Ao - the off-diagonal portion of the matrix
4561 .   colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix
4562 -   ierr - error code
4563 
4564      Level: advanced
4565 
4566 .seealso: [](ch_matrices), `Mat`, [](sec_fortranarrays), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetSeqAIJ()`, `MatMPIAIJGetSeqAIJF90()`
4567 M*/
4568 
4569 /*@C
4570   MatMPIAIJGetSeqAIJ - Returns the local pieces of this distributed matrix
4571 
4572   Not Collective
4573 
4574   Input Parameter:
4575 . A - The `MATMPIAIJ` matrix
4576 
4577   Output Parameters:
4578 + Ad     - The local diagonal block as a `MATSEQAIJ` matrix
4579 . Ao     - The local off-diagonal block as a `MATSEQAIJ` matrix
4580 - colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix
4581 
4582   Level: intermediate
4583 
4584   Note:
4585   The rows in `Ad` and `Ao` are in [0, Nr), where Nr is the number of local rows on this process. The columns
4586   in `Ad` are in [0, Nc) where Nc is the number of local columns. The columns are `Ao` are in [0, Nco), where Nco is
4587   the number of nonzero columns in the local off-diagonal piece of the matrix `A`. The array colmap maps these
4588   local column numbers to global column numbers in the original matrix.
4589 
4590   Fortran Notes:
4591   `MatMPIAIJGetSeqAIJ()` Fortran binding is deprecated (since PETSc 3.19), use `MatMPIAIJGetSeqAIJF90()`
4592 
4593 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetSeqAIJF90()`, `MatMPIAIJRestoreSeqAIJF90()`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`, `MatCreateAIJ()`, `MATSEQAIJ`
4594 @*/
4595 PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A, Mat *Ad, Mat *Ao, const PetscInt *colmap[])
4596 {
4597   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
4598   PetscBool   flg;
4599 
4600   PetscFunctionBegin;
4601   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &flg));
4602   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "This function requires a MATMPIAIJ matrix as input");
4603   if (Ad) *Ad = a->A;
4604   if (Ao) *Ao = a->B;
4605   if (colmap) *colmap = a->garray;
4606   PetscFunctionReturn(PETSC_SUCCESS);
4607 }
4608 
4609 PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
4610 {
4611   PetscInt     m, N, i, rstart, nnz, Ii;
4612   PetscInt    *indx;
4613   PetscScalar *values;
4614   MatType      rootType;
4615 
4616   PetscFunctionBegin;
4617   PetscCall(MatGetSize(inmat, &m, &N));
4618   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
4619     PetscInt *dnz, *onz, sum, bs, cbs;
4620 
4621     if (n == PETSC_DECIDE) PetscCall(PetscSplitOwnership(comm, &n, &N));
4622     /* Check sum(n) = N */
4623     PetscCall(MPIU_Allreduce(&n, &sum, 1, MPIU_INT, MPI_SUM, comm));
4624     PetscCheck(sum == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Sum of local columns %" PetscInt_FMT " != global columns %" PetscInt_FMT, sum, N);
4625 
4626     PetscCallMPI(MPI_Scan(&m, &rstart, 1, MPIU_INT, MPI_SUM, comm));
4627     rstart -= m;
4628 
4629     MatPreallocateBegin(comm, m, n, dnz, onz);
4630     for (i = 0; i < m; i++) {
4631       PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
4632       PetscCall(MatPreallocateSet(i + rstart, nnz, indx, dnz, onz));
4633       PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
4634     }
4635 
4636     PetscCall(MatCreate(comm, outmat));
4637     PetscCall(MatSetSizes(*outmat, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
4638     PetscCall(MatGetBlockSizes(inmat, &bs, &cbs));
4639     PetscCall(MatSetBlockSizes(*outmat, bs, cbs));
4640     PetscCall(MatGetRootType_Private(inmat, &rootType));
4641     PetscCall(MatSetType(*outmat, rootType));
4642     PetscCall(MatSeqAIJSetPreallocation(*outmat, 0, dnz));
4643     PetscCall(MatMPIAIJSetPreallocation(*outmat, 0, dnz, 0, onz));
4644     MatPreallocateEnd(dnz, onz);
4645     PetscCall(MatSetOption(*outmat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
4646   }
4647 
4648   /* numeric phase */
4649   PetscCall(MatGetOwnershipRange(*outmat, &rstart, NULL));
4650   for (i = 0; i < m; i++) {
4651     PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
4652     Ii = i + rstart;
4653     PetscCall(MatSetValues(*outmat, 1, &Ii, nnz, indx, values, INSERT_VALUES));
4654     PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
4655   }
4656   PetscCall(MatAssemblyBegin(*outmat, MAT_FINAL_ASSEMBLY));
4657   PetscCall(MatAssemblyEnd(*outmat, MAT_FINAL_ASSEMBLY));
4658   PetscFunctionReturn(PETSC_SUCCESS);
4659 }
4660 
4661 static PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(void *data)
4662 {
4663   Mat_Merge_SeqsToMPI *merge = (Mat_Merge_SeqsToMPI *)data;
4664 
4665   PetscFunctionBegin;
4666   if (!merge) PetscFunctionReturn(PETSC_SUCCESS);
4667   PetscCall(PetscFree(merge->id_r));
4668   PetscCall(PetscFree(merge->len_s));
4669   PetscCall(PetscFree(merge->len_r));
4670   PetscCall(PetscFree(merge->bi));
4671   PetscCall(PetscFree(merge->bj));
4672   PetscCall(PetscFree(merge->buf_ri[0]));
4673   PetscCall(PetscFree(merge->buf_ri));
4674   PetscCall(PetscFree(merge->buf_rj[0]));
4675   PetscCall(PetscFree(merge->buf_rj));
4676   PetscCall(PetscFree(merge->coi));
4677   PetscCall(PetscFree(merge->coj));
4678   PetscCall(PetscFree(merge->owners_co));
4679   PetscCall(PetscLayoutDestroy(&merge->rowmap));
4680   PetscCall(PetscFree(merge));
4681   PetscFunctionReturn(PETSC_SUCCESS);
4682 }
4683 
4684 #include <../src/mat/utils/freespace.h>
4685 #include <petscbt.h>
4686 
4687 PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat, Mat mpimat)
4688 {
4689   MPI_Comm             comm;
4690   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)seqmat->data;
4691   PetscMPIInt          size, rank, taga, *len_s;
4692   PetscInt             N = mpimat->cmap->N, i, j, *owners, *ai = a->i, *aj;
4693   PetscInt             proc, m;
4694   PetscInt           **buf_ri, **buf_rj;
4695   PetscInt             k, anzi, *bj_i, *bi, *bj, arow, bnzi, nextaj;
4696   PetscInt             nrows, **buf_ri_k, **nextrow, **nextai;
4697   MPI_Request         *s_waits, *r_waits;
4698   MPI_Status          *status;
4699   const MatScalar     *aa, *a_a;
4700   MatScalar          **abuf_r, *ba_i;
4701   Mat_Merge_SeqsToMPI *merge;
4702   PetscContainer       container;
4703 
4704   PetscFunctionBegin;
4705   PetscCall(PetscObjectGetComm((PetscObject)mpimat, &comm));
4706   PetscCall(PetscLogEventBegin(MAT_Seqstompinum, seqmat, 0, 0, 0));
4707 
4708   PetscCallMPI(MPI_Comm_size(comm, &size));
4709   PetscCallMPI(MPI_Comm_rank(comm, &rank));
4710 
4711   PetscCall(PetscObjectQuery((PetscObject)mpimat, "MatMergeSeqsToMPI", (PetscObject *)&container));
4712   PetscCheck(container, PetscObjectComm((PetscObject)mpimat), PETSC_ERR_PLIB, "Mat not created from MatCreateMPIAIJSumSeqAIJSymbolic");
4713   PetscCall(PetscContainerGetPointer(container, (void **)&merge));
4714   PetscCall(MatSeqAIJGetArrayRead(seqmat, &a_a));
4715   aa = a_a;
4716 
4717   bi     = merge->bi;
4718   bj     = merge->bj;
4719   buf_ri = merge->buf_ri;
4720   buf_rj = merge->buf_rj;
4721 
4722   PetscCall(PetscMalloc1(size, &status));
4723   owners = merge->rowmap->range;
4724   len_s  = merge->len_s;
4725 
4726   /* send and recv matrix values */
4727   PetscCall(PetscObjectGetNewTag((PetscObject)mpimat, &taga));
4728   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));
4729 
4730   PetscCall(PetscMalloc1(merge->nsend + 1, &s_waits));
4731   for (proc = 0, k = 0; proc < size; proc++) {
4732     if (!len_s[proc]) continue;
4733     i = owners[proc];
4734     PetscCallMPI(MPI_Isend(aa + ai[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
4735     k++;
4736   }
4737 
4738   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
4739   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));
4740   PetscCall(PetscFree(status));
4741 
4742   PetscCall(PetscFree(s_waits));
4743   PetscCall(PetscFree(r_waits));
4744 
4745   /* insert mat values of mpimat */
4746   PetscCall(PetscMalloc1(N, &ba_i));
4747   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));
4748 
4749   for (k = 0; k < merge->nrecv; k++) {
4750     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4751     nrows       = *(buf_ri_k[k]);
4752     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
4753     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
4754   }
4755 
4756   /* set values of ba */
4757   m = merge->rowmap->n;
4758   for (i = 0; i < m; i++) {
4759     arow = owners[rank] + i;
4760     bj_i = bj + bi[i]; /* col indices of the i-th row of mpimat */
4761     bnzi = bi[i + 1] - bi[i];
4762     PetscCall(PetscArrayzero(ba_i, bnzi));
4763 
4764     /* add local non-zero vals of this proc's seqmat into ba */
4765     anzi   = ai[arow + 1] - ai[arow];
4766     aj     = a->j + ai[arow];
4767     aa     = a_a + ai[arow];
4768     nextaj = 0;
4769     for (j = 0; nextaj < anzi; j++) {
4770       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4771         ba_i[j] += aa[nextaj++];
4772       }
4773     }
4774 
4775     /* add received vals into ba */
4776     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
4777       /* i-th row */
4778       if (i == *nextrow[k]) {
4779         anzi   = *(nextai[k] + 1) - *nextai[k];
4780         aj     = buf_rj[k] + *(nextai[k]);
4781         aa     = abuf_r[k] + *(nextai[k]);
4782         nextaj = 0;
4783         for (j = 0; nextaj < anzi; j++) {
4784           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
4785             ba_i[j] += aa[nextaj++];
4786           }
4787         }
4788         nextrow[k]++;
4789         nextai[k]++;
4790       }
4791     }
4792     PetscCall(MatSetValues(mpimat, 1, &arow, bnzi, bj_i, ba_i, INSERT_VALUES));
4793   }
4794   PetscCall(MatSeqAIJRestoreArrayRead(seqmat, &a_a));
4795   PetscCall(MatAssemblyBegin(mpimat, MAT_FINAL_ASSEMBLY));
4796   PetscCall(MatAssemblyEnd(mpimat, MAT_FINAL_ASSEMBLY));
4797 
4798   PetscCall(PetscFree(abuf_r[0]));
4799   PetscCall(PetscFree(abuf_r));
4800   PetscCall(PetscFree(ba_i));
4801   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));
4802   PetscCall(PetscLogEventEnd(MAT_Seqstompinum, seqmat, 0, 0, 0));
4803   PetscFunctionReturn(PETSC_SUCCESS);
4804 }
4805 
4806 PetscErrorCode MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, Mat *mpimat)
4807 {
4808   Mat                  B_mpi;
4809   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)seqmat->data;
4810   PetscMPIInt          size, rank, tagi, tagj, *len_s, *len_si, *len_ri;
4811   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
4812   PetscInt             M = seqmat->rmap->n, N = seqmat->cmap->n, i, *owners, *ai = a->i, *aj = a->j;
4813   PetscInt             len, proc, *dnz, *onz, bs, cbs;
4814   PetscInt             k, anzi, *bi, *bj, *lnk, nlnk, arow, bnzi;
4815   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextai;
4816   MPI_Request         *si_waits, *sj_waits, *ri_waits, *rj_waits;
4817   MPI_Status          *status;
4818   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
4819   PetscBT              lnkbt;
4820   Mat_Merge_SeqsToMPI *merge;
4821   PetscContainer       container;
4822 
4823   PetscFunctionBegin;
4824   PetscCall(PetscLogEventBegin(MAT_Seqstompisym, seqmat, 0, 0, 0));
4825 
4826   /* make sure it is a PETSc comm */
4827   PetscCall(PetscCommDuplicate(comm, &comm, NULL));
4828   PetscCallMPI(MPI_Comm_size(comm, &size));
4829   PetscCallMPI(MPI_Comm_rank(comm, &rank));
4830 
4831   PetscCall(PetscNew(&merge));
4832   PetscCall(PetscMalloc1(size, &status));
4833 
4834   /* determine row ownership */
4835   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));
4836   PetscCall(PetscLayoutSetLocalSize(merge->rowmap, m));
4837   PetscCall(PetscLayoutSetSize(merge->rowmap, M));
4838   PetscCall(PetscLayoutSetBlockSize(merge->rowmap, 1));
4839   PetscCall(PetscLayoutSetUp(merge->rowmap));
4840   PetscCall(PetscMalloc1(size, &len_si));
4841   PetscCall(PetscMalloc1(size, &merge->len_s));
4842 
4843   m      = merge->rowmap->n;
4844   owners = merge->rowmap->range;
4845 
4846   /* determine the number of messages to send, their lengths */
4847   len_s = merge->len_s;
4848 
4849   len          = 0; /* length of buf_si[] */
4850   merge->nsend = 0;
4851   for (proc = 0; proc < size; proc++) {
4852     len_si[proc] = 0;
4853     if (proc == rank) {
4854       len_s[proc] = 0;
4855     } else {
4856       len_si[proc] = owners[proc + 1] - owners[proc] + 1;
4857       len_s[proc]  = ai[owners[proc + 1]] - ai[owners[proc]]; /* num of rows to be sent to [proc] */
4858     }
4859     if (len_s[proc]) {
4860       merge->nsend++;
4861       nrows = 0;
4862       for (i = owners[proc]; i < owners[proc + 1]; i++) {
4863         if (ai[i + 1] > ai[i]) nrows++;
4864       }
4865       len_si[proc] = 2 * (nrows + 1);
4866       len += len_si[proc];
4867     }
4868   }
4869 
4870   /* determine the number and length of messages to receive for ij-structure */
4871   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
4872   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));
4873 
4874   /* post the Irecv of j-structure */
4875   PetscCall(PetscCommGetNewTag(comm, &tagj));
4876   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rj_waits));
4877 
4878   /* post the Isend of j-structure */
4879   PetscCall(PetscMalloc2(merge->nsend, &si_waits, merge->nsend, &sj_waits));
4880 
4881   for (proc = 0, k = 0; proc < size; proc++) {
4882     if (!len_s[proc]) continue;
4883     i = owners[proc];
4884     PetscCallMPI(MPI_Isend(aj + ai[i], len_s[proc], MPIU_INT, proc, tagj, comm, sj_waits + k));
4885     k++;
4886   }
4887 
4888   /* receives and sends of j-structure are complete */
4889   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, rj_waits, status));
4890   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, sj_waits, status));
4891 
4892   /* send and recv i-structure */
4893   PetscCall(PetscCommGetNewTag(comm, &tagi));
4894   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &ri_waits));
4895 
4896   PetscCall(PetscMalloc1(len + 1, &buf_s));
4897   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
4898   for (proc = 0, k = 0; proc < size; proc++) {
4899     if (!len_s[proc]) continue;
4900     /* form outgoing message for i-structure:
4901          buf_si[0]:                 nrows to be sent
4902                [1:nrows]:           row index (global)
4903                [nrows+1:2*nrows+1]: i-structure index
4904     */
4905     nrows       = len_si[proc] / 2 - 1;
4906     buf_si_i    = buf_si + nrows + 1;
4907     buf_si[0]   = nrows;
4908     buf_si_i[0] = 0;
4909     nrows       = 0;
4910     for (i = owners[proc]; i < owners[proc + 1]; i++) {
4911       anzi = ai[i + 1] - ai[i];
4912       if (anzi) {
4913         buf_si_i[nrows + 1] = buf_si_i[nrows] + anzi; /* i-structure */
4914         buf_si[nrows + 1]   = i - owners[proc];       /* local row index */
4915         nrows++;
4916       }
4917     }
4918     PetscCallMPI(MPI_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, si_waits + k));
4919     k++;
4920     buf_si += len_si[proc];
4921   }
4922 
4923   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, ri_waits, status));
4924   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, si_waits, status));
4925 
4926   PetscCall(PetscInfo(seqmat, "nsend: %d, nrecv: %d\n", merge->nsend, merge->nrecv));
4927   for (i = 0; i < merge->nrecv; i++) PetscCall(PetscInfo(seqmat, "recv len_ri=%d, len_rj=%d from [%d]\n", len_ri[i], merge->len_r[i], merge->id_r[i]));
4928 
4929   PetscCall(PetscFree(len_si));
4930   PetscCall(PetscFree(len_ri));
4931   PetscCall(PetscFree(rj_waits));
4932   PetscCall(PetscFree2(si_waits, sj_waits));
4933   PetscCall(PetscFree(ri_waits));
4934   PetscCall(PetscFree(buf_s));
4935   PetscCall(PetscFree(status));
4936 
4937   /* compute a local seq matrix in each processor */
4938   /* allocate bi array and free space for accumulating nonzero column info */
4939   PetscCall(PetscMalloc1(m + 1, &bi));
4940   bi[0] = 0;
4941 
4942   /* create and initialize a linked list */
4943   nlnk = N + 1;
4944   PetscCall(PetscLLCreate(N, N, nlnk, lnk, lnkbt));
4945 
4946   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
4947   len = ai[owners[rank + 1]] - ai[owners[rank]];
4948   PetscCall(PetscFreeSpaceGet(PetscIntMultTruncate(2, len) + 1, &free_space));
4949 
4950   current_space = free_space;
4951 
4952   /* determine symbolic info for each local row */
4953   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));
4954 
4955   for (k = 0; k < merge->nrecv; k++) {
4956     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
4957     nrows       = *buf_ri_k[k];
4958     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
4959     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
4960   }
4961 
4962   MatPreallocateBegin(comm, m, n, dnz, onz);
4963   len = 0;
4964   for (i = 0; i < m; i++) {
4965     bnzi = 0;
4966     /* add local non-zero cols of this proc's seqmat into lnk */
4967     arow = owners[rank] + i;
4968     anzi = ai[arow + 1] - ai[arow];
4969     aj   = a->j + ai[arow];
4970     PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
4971     bnzi += nlnk;
4972     /* add received col data into lnk */
4973     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
4974       if (i == *nextrow[k]) {            /* i-th row */
4975         anzi = *(nextai[k] + 1) - *nextai[k];
4976         aj   = buf_rj[k] + *nextai[k];
4977         PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
4978         bnzi += nlnk;
4979         nextrow[k]++;
4980         nextai[k]++;
4981       }
4982     }
4983     if (len < bnzi) len = bnzi; /* =max(bnzi) */
4984 
4985     /* if free space is not available, make more free space */
4986     if (current_space->local_remaining < bnzi) PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(bnzi, current_space->total_array_size), &current_space));
4987     /* copy data into free space, then initialize lnk */
4988     PetscCall(PetscLLClean(N, N, bnzi, lnk, current_space->array, lnkbt));
4989     PetscCall(MatPreallocateSet(i + owners[rank], bnzi, current_space->array, dnz, onz));
4990 
4991     current_space->array += bnzi;
4992     current_space->local_used += bnzi;
4993     current_space->local_remaining -= bnzi;
4994 
4995     bi[i + 1] = bi[i] + bnzi;
4996   }
4997 
4998   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));
4999 
5000   PetscCall(PetscMalloc1(bi[m] + 1, &bj));
5001   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
5002   PetscCall(PetscLLDestroy(lnk, lnkbt));
5003 
5004   /* create symbolic parallel matrix B_mpi */
5005   PetscCall(MatGetBlockSizes(seqmat, &bs, &cbs));
5006   PetscCall(MatCreate(comm, &B_mpi));
5007   if (n == PETSC_DECIDE) {
5008     PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, N));
5009   } else {
5010     PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
5011   }
5012   PetscCall(MatSetBlockSizes(B_mpi, bs, cbs));
5013   PetscCall(MatSetType(B_mpi, MATMPIAIJ));
5014   PetscCall(MatMPIAIJSetPreallocation(B_mpi, 0, dnz, 0, onz));
5015   MatPreallocateEnd(dnz, onz);
5016   PetscCall(MatSetOption(B_mpi, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));
5017 
5018   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
5019   B_mpi->assembled = PETSC_FALSE;
5020   merge->bi        = bi;
5021   merge->bj        = bj;
5022   merge->buf_ri    = buf_ri;
5023   merge->buf_rj    = buf_rj;
5024   merge->coi       = NULL;
5025   merge->coj       = NULL;
5026   merge->owners_co = NULL;
5027 
5028   PetscCall(PetscCommDestroy(&comm));
5029 
5030   /* attach the supporting struct to B_mpi for reuse */
5031   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
5032   PetscCall(PetscContainerSetPointer(container, merge));
5033   PetscCall(PetscContainerSetUserDestroy(container, MatDestroy_MPIAIJ_SeqsToMPI));
5034   PetscCall(PetscObjectCompose((PetscObject)B_mpi, "MatMergeSeqsToMPI", (PetscObject)container));
5035   PetscCall(PetscContainerDestroy(&container));
5036   *mpimat = B_mpi;
5037 
5038   PetscCall(PetscLogEventEnd(MAT_Seqstompisym, seqmat, 0, 0, 0));
5039   PetscFunctionReturn(PETSC_SUCCESS);
5040 }
5041 
5042 /*@C
5043   MatCreateMPIAIJSumSeqAIJ - Creates a `MATMPIAIJ` matrix by adding sequential
5044   matrices from each processor
5045 
5046   Collective
5047 
5048   Input Parameters:
5049 + comm   - the communicators the parallel matrix will live on
5050 . seqmat - the input sequential matrices
5051 . m      - number of local rows (or `PETSC_DECIDE`)
5052 . n      - number of local columns (or `PETSC_DECIDE`)
5053 - scall  - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
5054 
5055   Output Parameter:
5056 . mpimat - the parallel matrix generated
5057 
5058   Level: advanced
5059 
5060   Note:
5061   The dimensions of the sequential matrix in each processor MUST be the same.
5062   The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
5063   destroyed when mpimat is destroyed. Call `PetscObjectQuery()` to access seqmat.
5064 
5065 .seealso: [](ch_matrices), `Mat`, `MatCreateAIJ()`
5066 @*/
5067 PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, MatReuse scall, Mat *mpimat)
5068 {
5069   PetscMPIInt size;
5070 
5071   PetscFunctionBegin;
5072   PetscCallMPI(MPI_Comm_size(comm, &size));
5073   if (size == 1) {
5074     PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
5075     if (scall == MAT_INITIAL_MATRIX) {
5076       PetscCall(MatDuplicate(seqmat, MAT_COPY_VALUES, mpimat));
5077     } else {
5078       PetscCall(MatCopy(seqmat, *mpimat, SAME_NONZERO_PATTERN));
5079     }
5080     PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
5081     PetscFunctionReturn(PETSC_SUCCESS);
5082   }
5083   PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
5084   if (scall == MAT_INITIAL_MATRIX) PetscCall(MatCreateMPIAIJSumSeqAIJSymbolic(comm, seqmat, m, n, mpimat));
5085   PetscCall(MatCreateMPIAIJSumSeqAIJNumeric(seqmat, *mpimat));
5086   PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
5087   PetscFunctionReturn(PETSC_SUCCESS);
5088 }
5089 
5090 /*@
5091   MatAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATAIJ` matrix.
5092 
5093   Not Collective
5094 
5095   Input Parameter:
5096 . A - the matrix
5097 
5098   Output Parameter:
5099 . A_loc - the local sequential matrix generated
5100 
5101   Level: developer
5102 
5103   Notes:
5104   The matrix is created by taking `A`'s local rows and putting them into a sequential matrix
5105   with `mlocal` rows and `n` columns. Where `mlocal` is obtained with `MatGetLocalSize()` and
5106   `n` is the global column count obtained with `MatGetSize()`
5107 
5108   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.
5109 
5110   For parallel matrices this creates an entirely new matrix. If the matrix is sequential it merely increases the reference count.
5111 
5112   Destroy the matrix with `MatDestroy()`
5113 
5114 .seealso: [](ch_matrices), `Mat`, `MatMPIAIJGetLocalMat()`
5115 @*/
5116 PetscErrorCode MatAIJGetLocalMat(Mat A, Mat *A_loc)
5117 {
5118   PetscBool mpi;
5119 
5120   PetscFunctionBegin;
5121   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &mpi));
5122   if (mpi) {
5123     PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, A_loc));
5124   } else {
5125     *A_loc = A;
5126     PetscCall(PetscObjectReference((PetscObject)*A_loc));
5127   }
5128   PetscFunctionReturn(PETSC_SUCCESS);
5129 }
5130 
5131 /*@
5132   MatMPIAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix.
5133 
5134   Not Collective
5135 
5136   Input Parameters:
5137 + A     - the matrix
5138 - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
5139 
5140   Output Parameter:
5141 . A_loc - the local sequential matrix generated
5142 
5143   Level: developer
5144 
5145   Notes:
5146   The matrix is created by taking all `A`'s local rows and putting them into a sequential
5147   matrix with `mlocal` rows and `n` columns.`mlocal` is the row count obtained with
5148   `MatGetLocalSize()` and `n` is the global column count obtained with `MatGetSize()`.
5149 
5150   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.
5151 
5152   When `A` is sequential and `MAT_INITIAL_MATRIX` is requested, the matrix returned is the diagonal part of `A` (which contains the entire matrix),
5153   with its reference count increased by one. Hence changing values of `A_loc` changes `A`. If `MAT_REUSE_MATRIX` is requested on a sequential matrix
5154   then `MatCopy`(Adiag,*`A_loc`,`SAME_NONZERO_PATTERN`) is called to fill `A_loc`. Thus one can preallocate the appropriate sequential matrix `A_loc`
5155   and then call this routine with `MAT_REUSE_MATRIX`. In this case, one can modify the values of `A_loc` without affecting the original sequential matrix.
5156 
5157 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMatCondensed()`, `MatMPIAIJGetLocalMatMerge()`
5158 @*/
5159 PetscErrorCode MatMPIAIJGetLocalMat(Mat A, MatReuse scall, Mat *A_loc)
5160 {
5161   Mat_MPIAIJ        *mpimat = (Mat_MPIAIJ *)A->data;
5162   Mat_SeqAIJ        *mat, *a, *b;
5163   PetscInt          *ai, *aj, *bi, *bj, *cmap = mpimat->garray;
5164   const PetscScalar *aa, *ba, *aav, *bav;
5165   PetscScalar       *ca, *cam;
5166   PetscMPIInt        size;
5167   PetscInt           am = A->rmap->n, i, j, k, cstart = A->cmap->rstart;
5168   PetscInt          *ci, *cj, col, ncols_d, ncols_o, jo;
5169   PetscBool          match;
5170 
5171   PetscFunctionBegin;
5172   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &match));
5173   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
5174   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
5175   if (size == 1) {
5176     if (scall == MAT_INITIAL_MATRIX) {
5177       PetscCall(PetscObjectReference((PetscObject)mpimat->A));
5178       *A_loc = mpimat->A;
5179     } else if (scall == MAT_REUSE_MATRIX) {
5180       PetscCall(MatCopy(mpimat->A, *A_loc, SAME_NONZERO_PATTERN));
5181     }
5182     PetscFunctionReturn(PETSC_SUCCESS);
5183   }
5184 
5185   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
5186   a  = (Mat_SeqAIJ *)(mpimat->A)->data;
5187   b  = (Mat_SeqAIJ *)(mpimat->B)->data;
5188   ai = a->i;
5189   aj = a->j;
5190   bi = b->i;
5191   bj = b->j;
5192   PetscCall(MatSeqAIJGetArrayRead(mpimat->A, &aav));
5193   PetscCall(MatSeqAIJGetArrayRead(mpimat->B, &bav));
5194   aa = aav;
5195   ba = bav;
5196   if (scall == MAT_INITIAL_MATRIX) {
5197     PetscCall(PetscMalloc1(1 + am, &ci));
5198     ci[0] = 0;
5199     for (i = 0; i < am; i++) ci[i + 1] = ci[i] + (ai[i + 1] - ai[i]) + (bi[i + 1] - bi[i]);
5200     PetscCall(PetscMalloc1(1 + ci[am], &cj));
5201     PetscCall(PetscMalloc1(1 + ci[am], &ca));
5202     k = 0;
5203     for (i = 0; i < am; i++) {
5204       ncols_o = bi[i + 1] - bi[i];
5205       ncols_d = ai[i + 1] - ai[i];
5206       /* off-diagonal portion of A */
5207       for (jo = 0; jo < ncols_o; jo++) {
5208         col = cmap[*bj];
5209         if (col >= cstart) break;
5210         cj[k] = col;
5211         bj++;
5212         ca[k++] = *ba++;
5213       }
5214       /* diagonal portion of A */
5215       for (j = 0; j < ncols_d; j++) {
5216         cj[k]   = cstart + *aj++;
5217         ca[k++] = *aa++;
5218       }
5219       /* off-diagonal portion of A */
5220       for (j = jo; j < ncols_o; j++) {
5221         cj[k]   = cmap[*bj++];
5222         ca[k++] = *ba++;
5223       }
5224     }
5225     /* put together the new matrix */
5226     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, A->cmap->N, ci, cj, ca, A_loc));
5227     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5228     /* Since these are PETSc arrays, change flags to free them as necessary. */
5229     mat          = (Mat_SeqAIJ *)(*A_loc)->data;
5230     mat->free_a  = PETSC_TRUE;
5231     mat->free_ij = PETSC_TRUE;
5232     mat->nonew   = 0;
5233   } else if (scall == MAT_REUSE_MATRIX) {
5234     mat = (Mat_SeqAIJ *)(*A_loc)->data;
5235     ci  = mat->i;
5236     cj  = mat->j;
5237     PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &cam));
5238     for (i = 0; i < am; i++) {
5239       /* off-diagonal portion of A */
5240       ncols_o = bi[i + 1] - bi[i];
5241       for (jo = 0; jo < ncols_o; jo++) {
5242         col = cmap[*bj];
5243         if (col >= cstart) break;
5244         *cam++ = *ba++;
5245         bj++;
5246       }
5247       /* diagonal portion of A */
5248       ncols_d = ai[i + 1] - ai[i];
5249       for (j = 0; j < ncols_d; j++) *cam++ = *aa++;
5250       /* off-diagonal portion of A */
5251       for (j = jo; j < ncols_o; j++) {
5252         *cam++ = *ba++;
5253         bj++;
5254       }
5255     }
5256     PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &cam));
5257   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
5258   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->A, &aav));
5259   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->B, &bav));
5260   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
5261   PetscFunctionReturn(PETSC_SUCCESS);
5262 }
5263 
5264 /*@
5265   MatMPIAIJGetLocalMatMerge - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix by taking all its local rows and putting them into a sequential matrix with
5266   mlocal rows and n columns. Where n is the sum of the number of columns of the diagonal and off-diagonal part
5267 
5268   Not Collective
5269 
5270   Input Parameters:
5271 + A     - the matrix
5272 - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
5273 
5274   Output Parameters:
5275 + glob  - sequential `IS` with global indices associated with the columns of the local sequential matrix generated (can be `NULL`)
5276 - A_loc - the local sequential matrix generated
5277 
5278   Level: developer
5279 
5280   Note:
5281   This is different from `MatMPIAIJGetLocalMat()` since the first columns in the returning matrix are those associated with the diagonal
5282   part, then those associated with the off-diagonal part (in its local ordering)
5283 
5284 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`
5285 @*/
5286 PetscErrorCode MatMPIAIJGetLocalMatMerge(Mat A, MatReuse scall, IS *glob, Mat *A_loc)
5287 {
5288   Mat             Ao, Ad;
5289   const PetscInt *cmap;
5290   PetscMPIInt     size;
5291   PetscErrorCode (*f)(Mat, MatReuse, IS *, Mat *);
5292 
5293   PetscFunctionBegin;
5294   PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &cmap));
5295   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
5296   if (size == 1) {
5297     if (scall == MAT_INITIAL_MATRIX) {
5298       PetscCall(PetscObjectReference((PetscObject)Ad));
5299       *A_loc = Ad;
5300     } else if (scall == MAT_REUSE_MATRIX) {
5301       PetscCall(MatCopy(Ad, *A_loc, SAME_NONZERO_PATTERN));
5302     }
5303     if (glob) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)Ad), Ad->cmap->n, Ad->cmap->rstart, 1, glob));
5304     PetscFunctionReturn(PETSC_SUCCESS);
5305   }
5306   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatMPIAIJGetLocalMatMerge_C", &f));
5307   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
5308   if (f) {
5309     PetscCall((*f)(A, scall, glob, A_loc));
5310   } else {
5311     Mat_SeqAIJ        *a = (Mat_SeqAIJ *)Ad->data;
5312     Mat_SeqAIJ        *b = (Mat_SeqAIJ *)Ao->data;
5313     Mat_SeqAIJ        *c;
5314     PetscInt          *ai = a->i, *aj = a->j;
5315     PetscInt          *bi = b->i, *bj = b->j;
5316     PetscInt          *ci, *cj;
5317     const PetscScalar *aa, *ba;
5318     PetscScalar       *ca;
5319     PetscInt           i, j, am, dn, on;
5320 
5321     PetscCall(MatGetLocalSize(Ad, &am, &dn));
5322     PetscCall(MatGetLocalSize(Ao, NULL, &on));
5323     PetscCall(MatSeqAIJGetArrayRead(Ad, &aa));
5324     PetscCall(MatSeqAIJGetArrayRead(Ao, &ba));
5325     if (scall == MAT_INITIAL_MATRIX) {
5326       PetscInt k;
5327       PetscCall(PetscMalloc1(1 + am, &ci));
5328       PetscCall(PetscMalloc1(ai[am] + bi[am], &cj));
5329       PetscCall(PetscMalloc1(ai[am] + bi[am], &ca));
5330       ci[0] = 0;
5331       for (i = 0, k = 0; i < am; i++) {
5332         const PetscInt ncols_o = bi[i + 1] - bi[i];
5333         const PetscInt ncols_d = ai[i + 1] - ai[i];
5334         ci[i + 1]              = ci[i] + ncols_o + ncols_d;
5335         /* diagonal portion of A */
5336         for (j = 0; j < ncols_d; j++, k++) {
5337           cj[k] = *aj++;
5338           ca[k] = *aa++;
5339         }
5340         /* off-diagonal portion of A */
5341         for (j = 0; j < ncols_o; j++, k++) {
5342           cj[k] = dn + *bj++;
5343           ca[k] = *ba++;
5344         }
5345       }
5346       /* put together the new matrix */
5347       PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, dn + on, ci, cj, ca, A_loc));
5348       /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5349       /* Since these are PETSc arrays, change flags to free them as necessary. */
5350       c          = (Mat_SeqAIJ *)(*A_loc)->data;
5351       c->free_a  = PETSC_TRUE;
5352       c->free_ij = PETSC_TRUE;
5353       c->nonew   = 0;
5354       PetscCall(MatSetType(*A_loc, ((PetscObject)Ad)->type_name));
5355     } else if (scall == MAT_REUSE_MATRIX) {
5356       PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &ca));
5357       for (i = 0; i < am; i++) {
5358         const PetscInt ncols_d = ai[i + 1] - ai[i];
5359         const PetscInt ncols_o = bi[i + 1] - bi[i];
5360         /* diagonal portion of A */
5361         for (j = 0; j < ncols_d; j++) *ca++ = *aa++;
5362         /* off-diagonal portion of A */
5363         for (j = 0; j < ncols_o; j++) *ca++ = *ba++;
5364       }
5365       PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &ca));
5366     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
5367     PetscCall(MatSeqAIJRestoreArrayRead(Ad, &aa));
5368     PetscCall(MatSeqAIJRestoreArrayRead(Ao, &aa));
5369     if (glob) {
5370       PetscInt cst, *gidx;
5371 
5372       PetscCall(MatGetOwnershipRangeColumn(A, &cst, NULL));
5373       PetscCall(PetscMalloc1(dn + on, &gidx));
5374       for (i = 0; i < dn; i++) gidx[i] = cst + i;
5375       for (i = 0; i < on; i++) gidx[i + dn] = cmap[i];
5376       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)Ad), dn + on, gidx, PETSC_OWN_POINTER, glob));
5377     }
5378   }
5379   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
5380   PetscFunctionReturn(PETSC_SUCCESS);
5381 }
5382 
5383 /*@C
5384   MatMPIAIJGetLocalMatCondensed - Creates a `MATSEQAIJ` matrix from an `MATMPIAIJ` matrix by taking all its local rows and NON-ZERO columns
5385 
5386   Not Collective
5387 
5388   Input Parameters:
5389 + A     - the matrix
5390 . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
5391 . row   - index set of rows to extract (or `NULL`)
5392 - col   - index set of columns to extract (or `NULL`)
5393 
5394   Output Parameter:
5395 . A_loc - the local sequential matrix generated
5396 
5397   Level: developer
5398 
5399 .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`
5400 @*/
5401 PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A, MatReuse scall, IS *row, IS *col, Mat *A_loc)
5402 {
5403   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
5404   PetscInt    i, start, end, ncols, nzA, nzB, *cmap, imark, *idx;
5405   IS          isrowa, iscola;
5406   Mat        *aloc;
5407   PetscBool   match;
5408 
5409   PetscFunctionBegin;
5410   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &match));
5411   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
5412   PetscCall(PetscLogEventBegin(MAT_Getlocalmatcondensed, A, 0, 0, 0));
5413   if (!row) {
5414     start = A->rmap->rstart;
5415     end   = A->rmap->rend;
5416     PetscCall(ISCreateStride(PETSC_COMM_SELF, end - start, start, 1, &isrowa));
5417   } else {
5418     isrowa = *row;
5419   }
5420   if (!col) {
5421     start = A->cmap->rstart;
5422     cmap  = a->garray;
5423     nzA   = a->A->cmap->n;
5424     nzB   = a->B->cmap->n;
5425     PetscCall(PetscMalloc1(nzA + nzB, &idx));
5426     ncols = 0;
5427     for (i = 0; i < nzB; i++) {
5428       if (cmap[i] < start) idx[ncols++] = cmap[i];
5429       else break;
5430     }
5431     imark = i;
5432     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;
5433     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i];
5434     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &iscola));
5435   } else {
5436     iscola = *col;
5437   }
5438   if (scall != MAT_INITIAL_MATRIX) {
5439     PetscCall(PetscMalloc1(1, &aloc));
5440     aloc[0] = *A_loc;
5441   }
5442   PetscCall(MatCreateSubMatrices(A, 1, &isrowa, &iscola, scall, &aloc));
5443   if (!col) { /* attach global id of condensed columns */
5444     PetscCall(PetscObjectCompose((PetscObject)aloc[0], "_petsc_GetLocalMatCondensed_iscol", (PetscObject)iscola));
5445   }
5446   *A_loc = aloc[0];
5447   PetscCall(PetscFree(aloc));
5448   if (!row) PetscCall(ISDestroy(&isrowa));
5449   if (!col) PetscCall(ISDestroy(&iscola));
5450   PetscCall(PetscLogEventEnd(MAT_Getlocalmatcondensed, A, 0, 0, 0));
5451   PetscFunctionReturn(PETSC_SUCCESS);
5452 }
5453 
5454 /*
5455  * Create a sequential AIJ matrix based on row indices. a whole column is extracted once a row is matched.
5456  * Row could be local or remote.The routine is designed to be scalable in memory so that nothing is based
5457  * on a global size.
5458  * */
5459 static PetscErrorCode MatCreateSeqSubMatrixWithRows_Private(Mat P, IS rows, Mat *P_oth)
5460 {
5461   Mat_MPIAIJ            *p  = (Mat_MPIAIJ *)P->data;
5462   Mat_SeqAIJ            *pd = (Mat_SeqAIJ *)(p->A)->data, *po = (Mat_SeqAIJ *)(p->B)->data, *p_oth;
5463   PetscInt               plocalsize, nrows, *ilocal, *oilocal, i, lidx, *nrcols, *nlcols, ncol;
5464   PetscMPIInt            owner;
5465   PetscSFNode           *iremote, *oiremote;
5466   const PetscInt        *lrowindices;
5467   PetscSF                sf, osf;
5468   PetscInt               pcstart, *roffsets, *loffsets, *pnnz, j;
5469   PetscInt               ontotalcols, dntotalcols, ntotalcols, nout;
5470   MPI_Comm               comm;
5471   ISLocalToGlobalMapping mapping;
5472   const PetscScalar     *pd_a, *po_a;
5473 
5474   PetscFunctionBegin;
5475   PetscCall(PetscObjectGetComm((PetscObject)P, &comm));
5476   /* plocalsize is the number of roots
5477    * nrows is the number of leaves
5478    * */
5479   PetscCall(MatGetLocalSize(P, &plocalsize, NULL));
5480   PetscCall(ISGetLocalSize(rows, &nrows));
5481   PetscCall(PetscCalloc1(nrows, &iremote));
5482   PetscCall(ISGetIndices(rows, &lrowindices));
5483   for (i = 0; i < nrows; i++) {
5484     /* Find a remote index and an owner for a row
5485      * The row could be local or remote
5486      * */
5487     owner = 0;
5488     lidx  = 0;
5489     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, &lidx));
5490     iremote[i].index = lidx;
5491     iremote[i].rank  = owner;
5492   }
5493   /* Create SF to communicate how many nonzero columns for each row */
5494   PetscCall(PetscSFCreate(comm, &sf));
5495   /* SF will figure out the number of nonzero columns for each row, and their
5496    * offsets
5497    * */
5498   PetscCall(PetscSFSetGraph(sf, plocalsize, nrows, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
5499   PetscCall(PetscSFSetFromOptions(sf));
5500   PetscCall(PetscSFSetUp(sf));
5501 
5502   PetscCall(PetscCalloc1(2 * (plocalsize + 1), &roffsets));
5503   PetscCall(PetscCalloc1(2 * plocalsize, &nrcols));
5504   PetscCall(PetscCalloc1(nrows, &pnnz));
5505   roffsets[0] = 0;
5506   roffsets[1] = 0;
5507   for (i = 0; i < plocalsize; i++) {
5508     /* diagonal */
5509     nrcols[i * 2 + 0] = pd->i[i + 1] - pd->i[i];
5510     /* off-diagonal */
5511     nrcols[i * 2 + 1] = po->i[i + 1] - po->i[i];
5512     /* compute offsets so that we relative location for each row */
5513     roffsets[(i + 1) * 2 + 0] = roffsets[i * 2 + 0] + nrcols[i * 2 + 0];
5514     roffsets[(i + 1) * 2 + 1] = roffsets[i * 2 + 1] + nrcols[i * 2 + 1];
5515   }
5516   PetscCall(PetscCalloc1(2 * nrows, &nlcols));
5517   PetscCall(PetscCalloc1(2 * nrows, &loffsets));
5518   /* 'r' means root, and 'l' means leaf */
5519   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
5520   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
5521   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
5522   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
5523   PetscCall(PetscSFDestroy(&sf));
5524   PetscCall(PetscFree(roffsets));
5525   PetscCall(PetscFree(nrcols));
5526   dntotalcols = 0;
5527   ontotalcols = 0;
5528   ncol        = 0;
5529   for (i = 0; i < nrows; i++) {
5530     pnnz[i] = nlcols[i * 2 + 0] + nlcols[i * 2 + 1];
5531     ncol    = PetscMax(pnnz[i], ncol);
5532     /* diagonal */
5533     dntotalcols += nlcols[i * 2 + 0];
5534     /* off-diagonal */
5535     ontotalcols += nlcols[i * 2 + 1];
5536   }
5537   /* We do not need to figure the right number of columns
5538    * since all the calculations will be done by going through the raw data
5539    * */
5540   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nrows, ncol, 0, pnnz, P_oth));
5541   PetscCall(MatSetUp(*P_oth));
5542   PetscCall(PetscFree(pnnz));
5543   p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
5544   /* diagonal */
5545   PetscCall(PetscCalloc1(dntotalcols, &iremote));
5546   /* off-diagonal */
5547   PetscCall(PetscCalloc1(ontotalcols, &oiremote));
5548   /* diagonal */
5549   PetscCall(PetscCalloc1(dntotalcols, &ilocal));
5550   /* off-diagonal */
5551   PetscCall(PetscCalloc1(ontotalcols, &oilocal));
5552   dntotalcols = 0;
5553   ontotalcols = 0;
5554   ntotalcols  = 0;
5555   for (i = 0; i < nrows; i++) {
5556     owner = 0;
5557     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, NULL));
5558     /* Set iremote for diag matrix */
5559     for (j = 0; j < nlcols[i * 2 + 0]; j++) {
5560       iremote[dntotalcols].index = loffsets[i * 2 + 0] + j;
5561       iremote[dntotalcols].rank  = owner;
5562       /* P_oth is seqAIJ so that ilocal need to point to the first part of memory */
5563       ilocal[dntotalcols++] = ntotalcols++;
5564     }
5565     /* off-diagonal */
5566     for (j = 0; j < nlcols[i * 2 + 1]; j++) {
5567       oiremote[ontotalcols].index = loffsets[i * 2 + 1] + j;
5568       oiremote[ontotalcols].rank  = owner;
5569       oilocal[ontotalcols++]      = ntotalcols++;
5570     }
5571   }
5572   PetscCall(ISRestoreIndices(rows, &lrowindices));
5573   PetscCall(PetscFree(loffsets));
5574   PetscCall(PetscFree(nlcols));
5575   PetscCall(PetscSFCreate(comm, &sf));
5576   /* P serves as roots and P_oth is leaves
5577    * Diag matrix
5578    * */
5579   PetscCall(PetscSFSetGraph(sf, pd->i[plocalsize], dntotalcols, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
5580   PetscCall(PetscSFSetFromOptions(sf));
5581   PetscCall(PetscSFSetUp(sf));
5582 
5583   PetscCall(PetscSFCreate(comm, &osf));
5584   /* off-diagonal */
5585   PetscCall(PetscSFSetGraph(osf, po->i[plocalsize], ontotalcols, oilocal, PETSC_OWN_POINTER, oiremote, PETSC_OWN_POINTER));
5586   PetscCall(PetscSFSetFromOptions(osf));
5587   PetscCall(PetscSFSetUp(osf));
5588   PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
5589   PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
5590   /* operate on the matrix internal data to save memory */
5591   PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
5592   PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
5593   PetscCall(MatGetOwnershipRangeColumn(P, &pcstart, NULL));
5594   /* Convert to global indices for diag matrix */
5595   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] += pcstart;
5596   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
5597   /* We want P_oth store global indices */
5598   PetscCall(ISLocalToGlobalMappingCreate(comm, 1, p->B->cmap->n, p->garray, PETSC_COPY_VALUES, &mapping));
5599   /* Use memory scalable approach */
5600   PetscCall(ISLocalToGlobalMappingSetType(mapping, ISLOCALTOGLOBALMAPPINGHASH));
5601   PetscCall(ISLocalToGlobalMappingApply(mapping, po->i[plocalsize], po->j, po->j));
5602   PetscCall(PetscSFBcastBegin(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
5603   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
5604   /* Convert back to local indices */
5605   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] -= pcstart;
5606   PetscCall(PetscSFBcastEnd(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
5607   nout = 0;
5608   PetscCall(ISGlobalToLocalMappingApply(mapping, IS_GTOLM_DROP, po->i[plocalsize], po->j, &nout, po->j));
5609   PetscCheck(nout == po->i[plocalsize], comm, PETSC_ERR_ARG_INCOMP, "n %" PetscInt_FMT " does not equal to nout %" PetscInt_FMT " ", po->i[plocalsize], nout);
5610   PetscCall(ISLocalToGlobalMappingDestroy(&mapping));
5611   /* Exchange values */
5612   PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
5613   PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
5614   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
5615   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
5616   /* Stop PETSc from shrinking memory */
5617   for (i = 0; i < nrows; i++) p_oth->ilen[i] = p_oth->imax[i];
5618   PetscCall(MatAssemblyBegin(*P_oth, MAT_FINAL_ASSEMBLY));
5619   PetscCall(MatAssemblyEnd(*P_oth, MAT_FINAL_ASSEMBLY));
5620   /* Attach PetscSF objects to P_oth so that we can reuse it later */
5621   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "diagsf", (PetscObject)sf));
5622   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "offdiagsf", (PetscObject)osf));
5623   PetscCall(PetscSFDestroy(&sf));
5624   PetscCall(PetscSFDestroy(&osf));
5625   PetscFunctionReturn(PETSC_SUCCESS);
5626 }
5627 
5628 /*
5629  * Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
5630  * This supports MPIAIJ and MAIJ
5631  * */
5632 PetscErrorCode MatGetBrowsOfAcols_MPIXAIJ(Mat A, Mat P, PetscInt dof, MatReuse reuse, Mat *P_oth)
5633 {
5634   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data, *p = (Mat_MPIAIJ *)P->data;
5635   Mat_SeqAIJ *p_oth;
5636   IS          rows, map;
5637   PetscHMapI  hamp;
5638   PetscInt    i, htsize, *rowindices, off, *mapping, key, count;
5639   MPI_Comm    comm;
5640   PetscSF     sf, osf;
5641   PetscBool   has;
5642 
5643   PetscFunctionBegin;
5644   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
5645   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, P, 0, 0));
5646   /* If it is the first time, create an index set of off-diag nonzero columns of A,
5647    *  and then create a submatrix (that often is an overlapping matrix)
5648    * */
5649   if (reuse == MAT_INITIAL_MATRIX) {
5650     /* Use a hash table to figure out unique keys */
5651     PetscCall(PetscHMapICreateWithSize(a->B->cmap->n, &hamp));
5652     PetscCall(PetscCalloc1(a->B->cmap->n, &mapping));
5653     count = 0;
5654     /* Assume that  a->g is sorted, otherwise the following does not make sense */
5655     for (i = 0; i < a->B->cmap->n; i++) {
5656       key = a->garray[i] / dof;
5657       PetscCall(PetscHMapIHas(hamp, key, &has));
5658       if (!has) {
5659         mapping[i] = count;
5660         PetscCall(PetscHMapISet(hamp, key, count++));
5661       } else {
5662         /* Current 'i' has the same value the previous step */
5663         mapping[i] = count - 1;
5664       }
5665     }
5666     PetscCall(ISCreateGeneral(comm, a->B->cmap->n, mapping, PETSC_OWN_POINTER, &map));
5667     PetscCall(PetscHMapIGetSize(hamp, &htsize));
5668     PetscCheck(htsize == count, comm, PETSC_ERR_ARG_INCOMP, " Size of hash map %" PetscInt_FMT " is inconsistent with count %" PetscInt_FMT, htsize, count);
5669     PetscCall(PetscCalloc1(htsize, &rowindices));
5670     off = 0;
5671     PetscCall(PetscHMapIGetKeys(hamp, &off, rowindices));
5672     PetscCall(PetscHMapIDestroy(&hamp));
5673     PetscCall(PetscSortInt(htsize, rowindices));
5674     PetscCall(ISCreateGeneral(comm, htsize, rowindices, PETSC_OWN_POINTER, &rows));
5675     /* In case, the matrix was already created but users want to recreate the matrix */
5676     PetscCall(MatDestroy(P_oth));
5677     PetscCall(MatCreateSeqSubMatrixWithRows_Private(P, rows, P_oth));
5678     PetscCall(PetscObjectCompose((PetscObject)*P_oth, "aoffdiagtopothmapping", (PetscObject)map));
5679     PetscCall(ISDestroy(&map));
5680     PetscCall(ISDestroy(&rows));
5681   } else if (reuse == MAT_REUSE_MATRIX) {
5682     /* If matrix was already created, we simply update values using SF objects
5683      * that as attached to the matrix earlier.
5684      */
5685     const PetscScalar *pd_a, *po_a;
5686 
5687     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "diagsf", (PetscObject *)&sf));
5688     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "offdiagsf", (PetscObject *)&osf));
5689     PetscCheck(sf && osf, comm, PETSC_ERR_ARG_NULL, "Matrix is not initialized yet");
5690     p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
5691     /* Update values in place */
5692     PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
5693     PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
5694     PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
5695     PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
5696     PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
5697     PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
5698     PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
5699     PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
5700   } else SETERRQ(comm, PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown reuse type");
5701   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, P, 0, 0));
5702   PetscFunctionReturn(PETSC_SUCCESS);
5703 }
5704 
5705 /*@C
5706   MatGetBrowsOfAcols - Returns `IS` that contain rows of `B` that equal to nonzero columns of local `A`
5707 
5708   Collective
5709 
5710   Input Parameters:
5711 + A     - the first matrix in `MATMPIAIJ` format
5712 . B     - the second matrix in `MATMPIAIJ` format
5713 - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
5714 
5715   Output Parameters:
5716 + rowb  - On input index sets of rows of B to extract (or `NULL`), modified on output
5717 . colb  - On input index sets of columns of B to extract (or `NULL`), modified on output
5718 - B_seq - the sequential matrix generated
5719 
5720   Level: developer
5721 
5722 .seealso: `Mat`, `MATMPIAIJ`, `IS`, `MatReuse`
5723 @*/
5724 PetscErrorCode MatGetBrowsOfAcols(Mat A, Mat B, MatReuse scall, IS *rowb, IS *colb, Mat *B_seq)
5725 {
5726   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
5727   PetscInt   *idx, i, start, ncols, nzA, nzB, *cmap, imark;
5728   IS          isrowb, iscolb;
5729   Mat        *bseq = NULL;
5730 
5731   PetscFunctionBegin;
5732   PetscCheck(A->cmap->rstart == B->rmap->rstart && A->cmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",
5733              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
5734   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAcols, A, B, 0, 0));
5735 
5736   if (scall == MAT_INITIAL_MATRIX) {
5737     start = A->cmap->rstart;
5738     cmap  = a->garray;
5739     nzA   = a->A->cmap->n;
5740     nzB   = a->B->cmap->n;
5741     PetscCall(PetscMalloc1(nzA + nzB, &idx));
5742     ncols = 0;
5743     for (i = 0; i < nzB; i++) { /* row < local row index */
5744       if (cmap[i] < start) idx[ncols++] = cmap[i];
5745       else break;
5746     }
5747     imark = i;
5748     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;   /* local rows */
5749     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
5750     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &isrowb));
5751     PetscCall(ISCreateStride(PETSC_COMM_SELF, B->cmap->N, 0, 1, &iscolb));
5752   } else {
5753     PetscCheck(rowb && colb, PETSC_COMM_SELF, PETSC_ERR_SUP, "IS rowb and colb must be provided for MAT_REUSE_MATRIX");
5754     isrowb = *rowb;
5755     iscolb = *colb;
5756     PetscCall(PetscMalloc1(1, &bseq));
5757     bseq[0] = *B_seq;
5758   }
5759   PetscCall(MatCreateSubMatrices(B, 1, &isrowb, &iscolb, scall, &bseq));
5760   *B_seq = bseq[0];
5761   PetscCall(PetscFree(bseq));
5762   if (!rowb) {
5763     PetscCall(ISDestroy(&isrowb));
5764   } else {
5765     *rowb = isrowb;
5766   }
5767   if (!colb) {
5768     PetscCall(ISDestroy(&iscolb));
5769   } else {
5770     *colb = iscolb;
5771   }
5772   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAcols, A, B, 0, 0));
5773   PetscFunctionReturn(PETSC_SUCCESS);
5774 }
5775 
5776 /*
5777     MatGetBrowsOfAoCols_MPIAIJ - Creates a `MATSEQAIJ` matrix by taking rows of B that equal to nonzero columns
5778     of the OFF-DIAGONAL portion of local A
5779 
5780     Collective
5781 
5782    Input Parameters:
5783 +    A,B - the matrices in `MATMPIAIJ` format
5784 -    scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
5785 
5786    Output Parameter:
5787 +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
5788 .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
5789 .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
5790 -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N
5791 
5792     Developer Note:
5793     This directly accesses information inside the VecScatter associated with the matrix-vector product
5794      for this matrix. This is not desirable..
5795 
5796     Level: developer
5797 
5798 */
5799 PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A, Mat B, MatReuse scall, PetscInt **startsj_s, PetscInt **startsj_r, MatScalar **bufa_ptr, Mat *B_oth)
5800 {
5801   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
5802   Mat_SeqAIJ        *b_oth;
5803   VecScatter         ctx;
5804   MPI_Comm           comm;
5805   const PetscMPIInt *rprocs, *sprocs;
5806   const PetscInt    *srow, *rstarts, *sstarts;
5807   PetscInt          *rowlen, *bufj, *bufJ, ncols = 0, aBn = a->B->cmap->n, row, *b_othi, *b_othj, *rvalues = NULL, *svalues = NULL, *cols, sbs, rbs;
5808   PetscInt           i, j, k = 0, l, ll, nrecvs, nsends, nrows, *rstartsj = NULL, *sstartsj, len;
5809   PetscScalar       *b_otha, *bufa, *bufA, *vals = NULL;
5810   MPI_Request       *reqs = NULL, *rwaits = NULL, *swaits = NULL;
5811   PetscMPIInt        size, tag, rank, nreqs;
5812 
5813   PetscFunctionBegin;
5814   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
5815   PetscCallMPI(MPI_Comm_size(comm, &size));
5816 
5817   PetscCheck(A->cmap->rstart == B->rmap->rstart && A->cmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",
5818              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
5819   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, B, 0, 0));
5820   PetscCallMPI(MPI_Comm_rank(comm, &rank));
5821 
5822   if (size == 1) {
5823     startsj_s = NULL;
5824     bufa_ptr  = NULL;
5825     *B_oth    = NULL;
5826     PetscFunctionReturn(PETSC_SUCCESS);
5827   }
5828 
5829   ctx = a->Mvctx;
5830   tag = ((PetscObject)ctx)->tag;
5831 
5832   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &srow, &sprocs, &sbs));
5833   /* rprocs[] must be ordered so that indices received from them are ordered in rvalues[], which is key to algorithms used in this subroutine */
5834   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL /*indices not needed*/, &rprocs, &rbs));
5835   PetscCall(PetscMPIIntCast(nsends + nrecvs, &nreqs));
5836   PetscCall(PetscMalloc1(nreqs, &reqs));
5837   rwaits = reqs;
5838   swaits = reqs + nrecvs;
5839 
5840   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
5841   if (scall == MAT_INITIAL_MATRIX) {
5842     /* i-array */
5843     /*  post receives */
5844     if (nrecvs) PetscCall(PetscMalloc1(rbs * (rstarts[nrecvs] - rstarts[0]), &rvalues)); /* rstarts can be NULL when nrecvs=0 */
5845     for (i = 0; i < nrecvs; i++) {
5846       rowlen = rvalues + rstarts[i] * rbs;
5847       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of indices to be received */
5848       PetscCallMPI(MPI_Irecv(rowlen, nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
5849     }
5850 
5851     /* pack the outgoing message */
5852     PetscCall(PetscMalloc2(nsends + 1, &sstartsj, nrecvs + 1, &rstartsj));
5853 
5854     sstartsj[0] = 0;
5855     rstartsj[0] = 0;
5856     len         = 0; /* total length of j or a array to be sent */
5857     if (nsends) {
5858       k = sstarts[0]; /* ATTENTION: sstarts[0] and rstarts[0] are not necessarily zero */
5859       PetscCall(PetscMalloc1(sbs * (sstarts[nsends] - sstarts[0]), &svalues));
5860     }
5861     for (i = 0; i < nsends; i++) {
5862       rowlen = svalues + (sstarts[i] - sstarts[0]) * sbs;
5863       nrows  = sstarts[i + 1] - sstarts[i]; /* num of block rows */
5864       for (j = 0; j < nrows; j++) {
5865         row = srow[k] + B->rmap->range[rank]; /* global row idx */
5866         for (l = 0; l < sbs; l++) {
5867           PetscCall(MatGetRow_MPIAIJ(B, row + l, &ncols, NULL, NULL)); /* rowlength */
5868 
5869           rowlen[j * sbs + l] = ncols;
5870 
5871           len += ncols;
5872           PetscCall(MatRestoreRow_MPIAIJ(B, row + l, &ncols, NULL, NULL));
5873         }
5874         k++;
5875       }
5876       PetscCallMPI(MPI_Isend(rowlen, nrows * sbs, MPIU_INT, sprocs[i], tag, comm, swaits + i));
5877 
5878       sstartsj[i + 1] = len; /* starting point of (i+1)-th outgoing msg in bufj and bufa */
5879     }
5880     /* recvs and sends of i-array are completed */
5881     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
5882     PetscCall(PetscFree(svalues));
5883 
5884     /* allocate buffers for sending j and a arrays */
5885     PetscCall(PetscMalloc1(len + 1, &bufj));
5886     PetscCall(PetscMalloc1(len + 1, &bufa));
5887 
5888     /* create i-array of B_oth */
5889     PetscCall(PetscMalloc1(aBn + 2, &b_othi));
5890 
5891     b_othi[0] = 0;
5892     len       = 0; /* total length of j or a array to be received */
5893     k         = 0;
5894     for (i = 0; i < nrecvs; i++) {
5895       rowlen = rvalues + (rstarts[i] - rstarts[0]) * rbs;
5896       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of rows to be received */
5897       for (j = 0; j < nrows; j++) {
5898         b_othi[k + 1] = b_othi[k] + rowlen[j];
5899         PetscCall(PetscIntSumError(rowlen[j], len, &len));
5900         k++;
5901       }
5902       rstartsj[i + 1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
5903     }
5904     PetscCall(PetscFree(rvalues));
5905 
5906     /* allocate space for j and a arrays of B_oth */
5907     PetscCall(PetscMalloc1(b_othi[aBn] + 1, &b_othj));
5908     PetscCall(PetscMalloc1(b_othi[aBn] + 1, &b_otha));
5909 
5910     /* j-array */
5911     /*  post receives of j-array */
5912     for (i = 0; i < nrecvs; i++) {
5913       nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
5914       PetscCallMPI(MPI_Irecv(b_othj + rstartsj[i], nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
5915     }
5916 
5917     /* pack the outgoing message j-array */
5918     if (nsends) k = sstarts[0];
5919     for (i = 0; i < nsends; i++) {
5920       nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
5921       bufJ  = bufj + sstartsj[i];
5922       for (j = 0; j < nrows; j++) {
5923         row = srow[k++] + B->rmap->range[rank]; /* global row idx */
5924         for (ll = 0; ll < sbs; ll++) {
5925           PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
5926           for (l = 0; l < ncols; l++) *bufJ++ = cols[l];
5927           PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
5928         }
5929       }
5930       PetscCallMPI(MPI_Isend(bufj + sstartsj[i], sstartsj[i + 1] - sstartsj[i], MPIU_INT, sprocs[i], tag, comm, swaits + i));
5931     }
5932 
5933     /* recvs and sends of j-array are completed */
5934     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
5935   } else if (scall == MAT_REUSE_MATRIX) {
5936     sstartsj = *startsj_s;
5937     rstartsj = *startsj_r;
5938     bufa     = *bufa_ptr;
5939     b_oth    = (Mat_SeqAIJ *)(*B_oth)->data;
5940     PetscCall(MatSeqAIJGetArrayWrite(*B_oth, &b_otha));
5941   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not possess an object container");
5942 
5943   /* a-array */
5944   /*  post receives of a-array */
5945   for (i = 0; i < nrecvs; i++) {
5946     nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
5947     PetscCallMPI(MPI_Irecv(b_otha + rstartsj[i], nrows, MPIU_SCALAR, rprocs[i], tag, comm, rwaits + i));
5948   }
5949 
5950   /* pack the outgoing message a-array */
5951   if (nsends) k = sstarts[0];
5952   for (i = 0; i < nsends; i++) {
5953     nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
5954     bufA  = bufa + sstartsj[i];
5955     for (j = 0; j < nrows; j++) {
5956       row = srow[k++] + B->rmap->range[rank]; /* global row idx */
5957       for (ll = 0; ll < sbs; ll++) {
5958         PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
5959         for (l = 0; l < ncols; l++) *bufA++ = vals[l];
5960         PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
5961       }
5962     }
5963     PetscCallMPI(MPI_Isend(bufa + sstartsj[i], sstartsj[i + 1] - sstartsj[i], MPIU_SCALAR, sprocs[i], tag, comm, swaits + i));
5964   }
5965   /* recvs and sends of a-array are completed */
5966   if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
5967   PetscCall(PetscFree(reqs));
5968 
5969   if (scall == MAT_INITIAL_MATRIX) {
5970     /* put together the new matrix */
5971     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, aBn, B->cmap->N, b_othi, b_othj, b_otha, B_oth));
5972 
5973     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
5974     /* Since these are PETSc arrays, change flags to free them as necessary. */
5975     b_oth          = (Mat_SeqAIJ *)(*B_oth)->data;
5976     b_oth->free_a  = PETSC_TRUE;
5977     b_oth->free_ij = PETSC_TRUE;
5978     b_oth->nonew   = 0;
5979 
5980     PetscCall(PetscFree(bufj));
5981     if (!startsj_s || !bufa_ptr) {
5982       PetscCall(PetscFree2(sstartsj, rstartsj));
5983       PetscCall(PetscFree(bufa_ptr));
5984     } else {
5985       *startsj_s = sstartsj;
5986       *startsj_r = rstartsj;
5987       *bufa_ptr  = bufa;
5988     }
5989   } else if (scall == MAT_REUSE_MATRIX) {
5990     PetscCall(MatSeqAIJRestoreArrayWrite(*B_oth, &b_otha));
5991   }
5992 
5993   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE, &nsends, &sstarts, &srow, &sprocs, &sbs));
5994   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE, &nrecvs, &rstarts, NULL, &rprocs, &rbs));
5995   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, B, 0, 0));
5996   PetscFunctionReturn(PETSC_SUCCESS);
5997 }
5998 
5999 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat, MatType, MatReuse, Mat *);
6000 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat, MatType, MatReuse, Mat *);
6001 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJSELL(Mat, MatType, MatReuse, Mat *);
6002 #if defined(PETSC_HAVE_MKL_SPARSE)
6003 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJMKL(Mat, MatType, MatReuse, Mat *);
6004 #endif
6005 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIBAIJ(Mat, MatType, MatReuse, Mat *);
6006 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat, MatType, MatReuse, Mat *);
6007 #if defined(PETSC_HAVE_ELEMENTAL)
6008 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
6009 #endif
6010 #if defined(PETSC_HAVE_SCALAPACK)
6011 PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
6012 #endif
6013 #if defined(PETSC_HAVE_HYPRE)
6014 PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat, MatType, MatReuse, Mat *);
6015 #endif
6016 #if defined(PETSC_HAVE_CUDA)
6017 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
6018 #endif
6019 #if defined(PETSC_HAVE_HIP)
6020 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJHIPSPARSE(Mat, MatType, MatReuse, Mat *);
6021 #endif
6022 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
6023 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJKokkos(Mat, MatType, MatReuse, Mat *);
6024 #endif
6025 PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISELL(Mat, MatType, MatReuse, Mat *);
6026 PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);
6027 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);
6028 
6029 /*
6030     Computes (B'*A')' since computing B*A directly is untenable
6031 
6032                n                       p                          p
6033         [             ]       [             ]         [                 ]
6034       m [      A      ]  *  n [       B     ]   =   m [         C       ]
6035         [             ]       [             ]         [                 ]
6036 
6037 */
6038 static PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A, Mat B, Mat C)
6039 {
6040   Mat At, Bt, Ct;
6041 
6042   PetscFunctionBegin;
6043   PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
6044   PetscCall(MatTranspose(B, MAT_INITIAL_MATRIX, &Bt));
6045   PetscCall(MatMatMult(Bt, At, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Ct));
6046   PetscCall(MatDestroy(&At));
6047   PetscCall(MatDestroy(&Bt));
6048   PetscCall(MatTransposeSetPrecursor(Ct, C));
6049   PetscCall(MatTranspose(Ct, MAT_REUSE_MATRIX, &C));
6050   PetscCall(MatDestroy(&Ct));
6051   PetscFunctionReturn(PETSC_SUCCESS);
6052 }
6053 
6054 static PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A, Mat B, PetscReal fill, Mat C)
6055 {
6056   PetscBool cisdense;
6057 
6058   PetscFunctionBegin;
6059   PetscCheck(A->cmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "A->cmap->n %" PetscInt_FMT " != B->rmap->n %" PetscInt_FMT, A->cmap->n, B->rmap->n);
6060   PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
6061   PetscCall(MatSetBlockSizesFromMats(C, A, B));
6062   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATMPIDENSE, MATMPIDENSECUDA, MATMPIDENSEHIP, ""));
6063   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
6064   PetscCall(MatSetUp(C));
6065 
6066   C->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
6067   PetscFunctionReturn(PETSC_SUCCESS);
6068 }
6069 
6070 static PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ_AB(Mat C)
6071 {
6072   Mat_Product *product = C->product;
6073   Mat          A = product->A, B = product->B;
6074 
6075   PetscFunctionBegin;
6076   PetscCheck(A->cmap->rstart == B->rmap->rstart && A->cmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",
6077              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
6078   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIDense_MPIAIJ;
6079   C->ops->productsymbolic = MatProductSymbolic_AB;
6080   PetscFunctionReturn(PETSC_SUCCESS);
6081 }
6082 
6083 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ(Mat C)
6084 {
6085   Mat_Product *product = C->product;
6086 
6087   PetscFunctionBegin;
6088   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_MPIDense_MPIAIJ_AB(C));
6089   PetscFunctionReturn(PETSC_SUCCESS);
6090 }
6091 
6092 /*
6093    Merge two sets of sorted nonzeros and return a CSR for the merged (sequential) matrix
6094 
6095   Input Parameters:
6096 
6097     j1,rowBegin1,rowEnd1,jmap1: describe the first set of nonzeros (Set1)
6098     j2,rowBegin2,rowEnd2,jmap2: describe the second set of nonzeros (Set2)
6099 
6100     mat: both sets' nonzeros are on m rows, where m is the number of local rows of the matrix mat
6101 
6102     For Set1, j1[] contains column indices of the nonzeros.
6103     For the k-th row (0<=k<m), [rowBegin1[k],rowEnd1[k]) index into j1[] and point to the begin/end nonzero in row k
6104     respectively (note rowEnd1[k] is not necessarily equal to rwoBegin1[k+1]). Indices in this range of j1[] are sorted,
6105     but might have repeats. jmap1[t+1] - jmap1[t] is the number of repeats for the t-th unique nonzero in Set1.
6106 
6107     Similar for Set2.
6108 
6109     This routine merges the two sets of nonzeros row by row and removes repeats.
6110 
6111   Output Parameters: (memory is allocated by the caller)
6112 
6113     i[],j[]: the CSR of the merged matrix, which has m rows.
6114     imap1[]: the k-th unique nonzero in Set1 (k=0,1,...) corresponds to imap1[k]-th unique nonzero in the merged matrix.
6115     imap2[]: similar to imap1[], but for Set2.
6116     Note we order nonzeros row-by-row and from left to right.
6117 */
6118 static PetscErrorCode MatMergeEntries_Internal(Mat mat, const PetscInt j1[], const PetscInt j2[], const PetscCount rowBegin1[], const PetscCount rowEnd1[], const PetscCount rowBegin2[], const PetscCount rowEnd2[], const PetscCount jmap1[], const PetscCount jmap2[], PetscCount imap1[], PetscCount imap2[], PetscInt i[], PetscInt j[])
6119 {
6120   PetscInt   r, m; /* Row index of mat */
6121   PetscCount t, t1, t2, b1, e1, b2, e2;
6122 
6123   PetscFunctionBegin;
6124   PetscCall(MatGetLocalSize(mat, &m, NULL));
6125   t1 = t2 = t = 0; /* Count unique nonzeros of in Set1, Set1 and the merged respectively */
6126   i[0]        = 0;
6127   for (r = 0; r < m; r++) { /* Do row by row merging */
6128     b1 = rowBegin1[r];
6129     e1 = rowEnd1[r];
6130     b2 = rowBegin2[r];
6131     e2 = rowEnd2[r];
6132     while (b1 < e1 && b2 < e2) {
6133       if (j1[b1] == j2[b2]) { /* Same column index and hence same nonzero */
6134         j[t]      = j1[b1];
6135         imap1[t1] = t;
6136         imap2[t2] = t;
6137         b1 += jmap1[t1 + 1] - jmap1[t1]; /* Jump to next unique local nonzero */
6138         b2 += jmap2[t2 + 1] - jmap2[t2]; /* Jump to next unique remote nonzero */
6139         t1++;
6140         t2++;
6141         t++;
6142       } else if (j1[b1] < j2[b2]) {
6143         j[t]      = j1[b1];
6144         imap1[t1] = t;
6145         b1 += jmap1[t1 + 1] - jmap1[t1];
6146         t1++;
6147         t++;
6148       } else {
6149         j[t]      = j2[b2];
6150         imap2[t2] = t;
6151         b2 += jmap2[t2 + 1] - jmap2[t2];
6152         t2++;
6153         t++;
6154       }
6155     }
6156     /* Merge the remaining in either j1[] or j2[] */
6157     while (b1 < e1) {
6158       j[t]      = j1[b1];
6159       imap1[t1] = t;
6160       b1 += jmap1[t1 + 1] - jmap1[t1];
6161       t1++;
6162       t++;
6163     }
6164     while (b2 < e2) {
6165       j[t]      = j2[b2];
6166       imap2[t2] = t;
6167       b2 += jmap2[t2 + 1] - jmap2[t2];
6168       t2++;
6169       t++;
6170     }
6171     i[r + 1] = t;
6172   }
6173   PetscFunctionReturn(PETSC_SUCCESS);
6174 }
6175 
6176 /*
6177   Split nonzeros in a block of local rows into two subsets: those in the diagonal block and those in the off-diagonal block
6178 
6179   Input Parameters:
6180     mat: an MPI matrix that provides row and column layout information for splitting. Let's say its number of local rows is m.
6181     n,i[],j[],perm[]: there are n input entries, belonging to m rows. Row/col indices of the entries are stored in i[] and j[]
6182       respectively, along with a permutation array perm[]. Length of the i[],j[],perm[] arrays is n.
6183 
6184       i[] is already sorted, but within a row, j[] is not sorted and might have repeats.
6185       i[] might contain negative indices at the beginning, which means the corresponding entries should be ignored in the splitting.
6186 
6187   Output Parameters:
6188     j[],perm[]: the routine needs to sort j[] within each row along with perm[].
6189     rowBegin[],rowMid[],rowEnd[]: of length m, and the memory is preallocated and zeroed by the caller.
6190       They contain indices pointing to j[]. For 0<=r<m, [rowBegin[r],rowMid[r]) point to begin/end entries of row r of the diagonal block,
6191       and [rowMid[r],rowEnd[r]) point to begin/end entries of row r of the off-diagonal block.
6192 
6193     Aperm[],Ajmap[],Atot,Annz: Arrays are allocated by this routine.
6194       Atot: number of entries belonging to the diagonal block.
6195       Annz: number of unique nonzeros belonging to the diagonal block.
6196       Aperm[Atot] stores values from perm[] for entries belonging to the diagonal block. Length of Aperm[] is Atot, though it may also count
6197         repeats (i.e., same 'i,j' pair).
6198       Ajmap[Annz+1] stores the number of repeats of each unique entry belonging to the diagonal block. More precisely, Ajmap[t+1] - Ajmap[t]
6199         is the number of repeats for the t-th unique entry in the diagonal block. Ajmap[0] is always 0.
6200 
6201       Atot: number of entries belonging to the diagonal block
6202       Annz: number of unique nonzeros belonging to the diagonal block.
6203 
6204     Bperm[], Bjmap[], Btot, Bnnz are similar but for the off-diagonal block.
6205 
6206     Aperm[],Bperm[],Ajmap[] and Bjmap[] are allocated separately by this routine with PetscMalloc1().
6207 */
6208 static PetscErrorCode MatSplitEntries_Internal(Mat mat, PetscCount n, const PetscInt i[], PetscInt j[], PetscCount perm[], PetscCount rowBegin[], PetscCount rowMid[], PetscCount rowEnd[], PetscCount *Atot_, PetscCount **Aperm_, PetscCount *Annz_, PetscCount **Ajmap_, PetscCount *Btot_, PetscCount **Bperm_, PetscCount *Bnnz_, PetscCount **Bjmap_)
6209 {
6210   PetscInt    cstart, cend, rstart, rend, row, col;
6211   PetscCount  Atot = 0, Btot = 0; /* Total number of nonzeros in the diagonal and off-diagonal blocks */
6212   PetscCount  Annz = 0, Bnnz = 0; /* Number of unique nonzeros in the diagonal and off-diagonal blocks */
6213   PetscCount  k, m, p, q, r, s, mid;
6214   PetscCount *Aperm, *Bperm, *Ajmap, *Bjmap;
6215 
6216   PetscFunctionBegin;
6217   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
6218   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
6219   m = rend - rstart;
6220 
6221   /* Skip negative rows */
6222   for (k = 0; k < n; k++)
6223     if (i[k] >= 0) break;
6224 
6225   /* Process [k,n): sort and partition each local row into diag and offdiag portions,
6226      fill rowBegin[], rowMid[], rowEnd[], and count Atot, Btot, Annz, Bnnz.
6227   */
6228   while (k < n) {
6229     row = i[k];
6230     /* Entries in [k,s) are in one row. Shift diagonal block col indices so that diag is ahead of offdiag after sorting the row */
6231     for (s = k; s < n; s++)
6232       if (i[s] != row) break;
6233 
6234     /* Shift diag columns to range of [-PETSC_MAX_INT, -1] */
6235     for (p = k; p < s; p++) {
6236       if (j[p] >= cstart && j[p] < cend) j[p] -= PETSC_MAX_INT;
6237       else PetscAssert((j[p] >= 0) && (j[p] <= mat->cmap->N), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column index %" PetscInt_FMT " is out of range", j[p]);
6238     }
6239     PetscCall(PetscSortIntWithCountArray(s - k, j + k, perm + k));
6240     PetscCall(PetscSortedIntUpperBound(j, k, s, -1, &mid)); /* Separate [k,s) into [k,mid) for diag and [mid,s) for offdiag */
6241     rowBegin[row - rstart] = k;
6242     rowMid[row - rstart]   = mid;
6243     rowEnd[row - rstart]   = s;
6244 
6245     /* Count nonzeros of this diag/offdiag row, which might have repeats */
6246     Atot += mid - k;
6247     Btot += s - mid;
6248 
6249     /* Count unique nonzeros of this diag row */
6250     for (p = k; p < mid;) {
6251       col = j[p];
6252       do {
6253         j[p] += PETSC_MAX_INT; /* Revert the modified diagonal indices */
6254         p++;
6255       } while (p < mid && j[p] == col);
6256       Annz++;
6257     }
6258 
6259     /* Count unique nonzeros of this offdiag row */
6260     for (p = mid; p < s;) {
6261       col = j[p];
6262       do {
6263         p++;
6264       } while (p < s && j[p] == col);
6265       Bnnz++;
6266     }
6267     k = s;
6268   }
6269 
6270   /* Allocation according to Atot, Btot, Annz, Bnnz */
6271   PetscCall(PetscMalloc1(Atot, &Aperm));
6272   PetscCall(PetscMalloc1(Btot, &Bperm));
6273   PetscCall(PetscMalloc1(Annz + 1, &Ajmap));
6274   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap));
6275 
6276   /* Re-scan indices and copy diag/offdiag permutation indices to Aperm, Bperm and also fill Ajmap and Bjmap */
6277   Ajmap[0] = Bjmap[0] = Atot = Btot = Annz = Bnnz = 0;
6278   for (r = 0; r < m; r++) {
6279     k   = rowBegin[r];
6280     mid = rowMid[r];
6281     s   = rowEnd[r];
6282     PetscCall(PetscArraycpy(Aperm + Atot, perm + k, mid - k));
6283     PetscCall(PetscArraycpy(Bperm + Btot, perm + mid, s - mid));
6284     Atot += mid - k;
6285     Btot += s - mid;
6286 
6287     /* Scan column indices in this row and find out how many repeats each unique nonzero has */
6288     for (p = k; p < mid;) {
6289       col = j[p];
6290       q   = p;
6291       do {
6292         p++;
6293       } while (p < mid && j[p] == col);
6294       Ajmap[Annz + 1] = Ajmap[Annz] + (p - q);
6295       Annz++;
6296     }
6297 
6298     for (p = mid; p < s;) {
6299       col = j[p];
6300       q   = p;
6301       do {
6302         p++;
6303       } while (p < s && j[p] == col);
6304       Bjmap[Bnnz + 1] = Bjmap[Bnnz] + (p - q);
6305       Bnnz++;
6306     }
6307   }
6308   /* Output */
6309   *Aperm_ = Aperm;
6310   *Annz_  = Annz;
6311   *Atot_  = Atot;
6312   *Ajmap_ = Ajmap;
6313   *Bperm_ = Bperm;
6314   *Bnnz_  = Bnnz;
6315   *Btot_  = Btot;
6316   *Bjmap_ = Bjmap;
6317   PetscFunctionReturn(PETSC_SUCCESS);
6318 }
6319 
6320 /*
6321   Expand the jmap[] array to make a new one in view of nonzeros in the merged matrix
6322 
6323   Input Parameters:
6324     nnz1: number of unique nonzeros in a set that was used to produce imap[], jmap[]
6325     nnz:  number of unique nonzeros in the merged matrix
6326     imap[nnz1]: i-th nonzero in the set is the imap[i]-th nonzero in the merged matrix
6327     jmap[nnz1+1]: i-th nonzero in the set has jmap[i+1] - jmap[i] repeats in the set
6328 
6329   Output Parameter: (memory is allocated by the caller)
6330     jmap_new[nnz+1]: i-th nonzero in the merged matrix has jmap_new[i+1] - jmap_new[i] repeats in the set
6331 
6332   Example:
6333     nnz1 = 4
6334     nnz  = 6
6335     imap = [1,3,4,5]
6336     jmap = [0,3,5,6,7]
6337    then,
6338     jmap_new = [0,0,3,3,5,6,7]
6339 */
6340 static PetscErrorCode ExpandJmap_Internal(PetscCount nnz1, PetscCount nnz, const PetscCount imap[], const PetscCount jmap[], PetscCount jmap_new[])
6341 {
6342   PetscCount k, p;
6343 
6344   PetscFunctionBegin;
6345   jmap_new[0] = 0;
6346   p           = nnz;                /* p loops over jmap_new[] backwards */
6347   for (k = nnz1 - 1; k >= 0; k--) { /* k loops over imap[] */
6348     for (; p > imap[k]; p--) jmap_new[p] = jmap[k + 1];
6349   }
6350   for (; p >= 0; p--) jmap_new[p] = jmap[0];
6351   PetscFunctionReturn(PETSC_SUCCESS);
6352 }
6353 
6354 static PetscErrorCode MatCOOStructDestroy_MPIAIJ(void *data)
6355 {
6356   MatCOOStruct_MPIAIJ *coo = (MatCOOStruct_MPIAIJ *)data;
6357 
6358   PetscFunctionBegin;
6359   PetscCall(PetscSFDestroy(&coo->sf));
6360   PetscCall(PetscFree(coo->Aperm1));
6361   PetscCall(PetscFree(coo->Bperm1));
6362   PetscCall(PetscFree(coo->Ajmap1));
6363   PetscCall(PetscFree(coo->Bjmap1));
6364   PetscCall(PetscFree(coo->Aimap2));
6365   PetscCall(PetscFree(coo->Bimap2));
6366   PetscCall(PetscFree(coo->Aperm2));
6367   PetscCall(PetscFree(coo->Bperm2));
6368   PetscCall(PetscFree(coo->Ajmap2));
6369   PetscCall(PetscFree(coo->Bjmap2));
6370   PetscCall(PetscFree(coo->Cperm1));
6371   PetscCall(PetscFree2(coo->sendbuf, coo->recvbuf));
6372   PetscCall(PetscFree(coo));
6373   PetscFunctionReturn(PETSC_SUCCESS);
6374 }
6375 
6376 PetscErrorCode MatSetPreallocationCOO_MPIAIJ(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
6377 {
6378   MPI_Comm             comm;
6379   PetscMPIInt          rank, size;
6380   PetscInt             m, n, M, N, rstart, rend, cstart, cend; /* Sizes, indices of row/col, therefore with type PetscInt */
6381   PetscCount           k, p, q, rem;                           /* Loop variables over coo arrays */
6382   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
6383   PetscContainer       container;
6384   MatCOOStruct_MPIAIJ *coo;
6385 
6386   PetscFunctionBegin;
6387   PetscCall(PetscFree(mpiaij->garray));
6388   PetscCall(VecDestroy(&mpiaij->lvec));
6389 #if defined(PETSC_USE_CTABLE)
6390   PetscCall(PetscHMapIDestroy(&mpiaij->colmap));
6391 #else
6392   PetscCall(PetscFree(mpiaij->colmap));
6393 #endif
6394   PetscCall(VecScatterDestroy(&mpiaij->Mvctx));
6395   mat->assembled     = PETSC_FALSE;
6396   mat->was_assembled = PETSC_FALSE;
6397 
6398   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
6399   PetscCallMPI(MPI_Comm_size(comm, &size));
6400   PetscCallMPI(MPI_Comm_rank(comm, &rank));
6401   PetscCall(PetscLayoutSetUp(mat->rmap));
6402   PetscCall(PetscLayoutSetUp(mat->cmap));
6403   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
6404   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
6405   PetscCall(MatGetLocalSize(mat, &m, &n));
6406   PetscCall(MatGetSize(mat, &M, &N));
6407 
6408   /* Sort (i,j) by row along with a permutation array, so that the to-be-ignored */
6409   /* entries come first, then local rows, then remote rows.                     */
6410   PetscCount n1 = coo_n, *perm1;
6411   PetscInt  *i1 = coo_i, *j1 = coo_j;
6412 
6413   PetscCall(PetscMalloc1(n1, &perm1));
6414   for (k = 0; k < n1; k++) perm1[k] = k;
6415 
6416   /* Manipulate indices so that entries with negative row or col indices will have smallest
6417      row indices, local entries will have greater but negative row indices, and remote entries
6418      will have positive row indices.
6419   */
6420   for (k = 0; k < n1; k++) {
6421     if (i1[k] < 0 || j1[k] < 0) i1[k] = PETSC_MIN_INT;                /* e.g., -2^31, minimal to move them ahead */
6422     else if (i1[k] >= rstart && i1[k] < rend) i1[k] -= PETSC_MAX_INT; /* e.g., minus 2^31-1 to shift local rows to range of [-PETSC_MAX_INT, -1] */
6423     else {
6424       PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "MAT_NO_OFF_PROC_ENTRIES is set but insert to remote rows");
6425       if (mpiaij->donotstash) i1[k] = PETSC_MIN_INT; /* Ignore offproc entries as if they had negative indices */
6426     }
6427   }
6428 
6429   /* Sort by row; after that, [0,k) have ignored entries, [k,rem) have local rows and [rem,n1) have remote rows */
6430   PetscCall(PetscSortIntWithIntCountArrayPair(n1, i1, j1, perm1));
6431 
6432   /* Advance k to the first entry we need to take care of */
6433   for (k = 0; k < n1; k++)
6434     if (i1[k] > PETSC_MIN_INT) break;
6435   PetscInt i1start = k;
6436 
6437   PetscCall(PetscSortedIntUpperBound(i1, k, n1, rend - 1 - PETSC_MAX_INT, &rem)); /* rem is upper bound of the last local row */
6438   for (; k < rem; k++) i1[k] += PETSC_MAX_INT;                                    /* Revert row indices of local rows*/
6439 
6440   /*           Send remote rows to their owner                                  */
6441   /* Find which rows should be sent to which remote ranks*/
6442   PetscInt        nsend = 0; /* Number of MPI ranks to send data to */
6443   PetscMPIInt    *sendto;    /* [nsend], storing remote ranks */
6444   PetscInt       *nentries;  /* [nsend], storing number of entries sent to remote ranks; Assume PetscInt is big enough for this count, and error if not */
6445   const PetscInt *ranges;
6446   PetscInt        maxNsend = size >= 128 ? 128 : size; /* Assume max 128 neighbors; realloc when needed */
6447 
6448   PetscCall(PetscLayoutGetRanges(mat->rmap, &ranges));
6449   PetscCall(PetscMalloc2(maxNsend, &sendto, maxNsend, &nentries));
6450   for (k = rem; k < n1;) {
6451     PetscMPIInt owner;
6452     PetscInt    firstRow, lastRow;
6453 
6454     /* Locate a row range */
6455     firstRow = i1[k]; /* first row of this owner */
6456     PetscCall(PetscLayoutFindOwner(mat->rmap, firstRow, &owner));
6457     lastRow = ranges[owner + 1] - 1; /* last row of this owner */
6458 
6459     /* Find the first index 'p' in [k,n) with i[p] belonging to next owner */
6460     PetscCall(PetscSortedIntUpperBound(i1, k, n1, lastRow, &p));
6461 
6462     /* All entries in [k,p) belong to this remote owner */
6463     if (nsend >= maxNsend) { /* Double the remote ranks arrays if not long enough */
6464       PetscMPIInt *sendto2;
6465       PetscInt    *nentries2;
6466       PetscInt     maxNsend2 = (maxNsend <= size / 2) ? maxNsend * 2 : size;
6467 
6468       PetscCall(PetscMalloc2(maxNsend2, &sendto2, maxNsend2, &nentries2));
6469       PetscCall(PetscArraycpy(sendto2, sendto, maxNsend));
6470       PetscCall(PetscArraycpy(nentries2, nentries2, maxNsend + 1));
6471       PetscCall(PetscFree2(sendto, nentries2));
6472       sendto   = sendto2;
6473       nentries = nentries2;
6474       maxNsend = maxNsend2;
6475     }
6476     sendto[nsend]   = owner;
6477     nentries[nsend] = p - k;
6478     PetscCall(PetscCountCast(p - k, &nentries[nsend]));
6479     nsend++;
6480     k = p;
6481   }
6482 
6483   /* Build 1st SF to know offsets on remote to send data */
6484   PetscSF      sf1;
6485   PetscInt     nroots = 1, nroots2 = 0;
6486   PetscInt     nleaves = nsend, nleaves2 = 0;
6487   PetscInt    *offsets;
6488   PetscSFNode *iremote;
6489 
6490   PetscCall(PetscSFCreate(comm, &sf1));
6491   PetscCall(PetscMalloc1(nsend, &iremote));
6492   PetscCall(PetscMalloc1(nsend, &offsets));
6493   for (k = 0; k < nsend; k++) {
6494     iremote[k].rank  = sendto[k];
6495     iremote[k].index = 0;
6496     nleaves2 += nentries[k];
6497     PetscCheck(nleaves2 >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF leaves is too large for PetscInt");
6498   }
6499   PetscCall(PetscSFSetGraph(sf1, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
6500   PetscCall(PetscSFFetchAndOpWithMemTypeBegin(sf1, MPIU_INT, PETSC_MEMTYPE_HOST, &nroots2 /*rootdata*/, PETSC_MEMTYPE_HOST, nentries /*leafdata*/, PETSC_MEMTYPE_HOST, offsets /*leafupdate*/, MPI_SUM));
6501   PetscCall(PetscSFFetchAndOpEnd(sf1, MPIU_INT, &nroots2, nentries, offsets, MPI_SUM)); /* Would nroots2 overflow, we check offsets[] below */
6502   PetscCall(PetscSFDestroy(&sf1));
6503   PetscAssert(nleaves2 == n1 - rem, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nleaves2 %" PetscInt_FMT " != number of remote entries %" PetscCount_FMT "", nleaves2, n1 - rem);
6504 
6505   /* Build 2nd SF to send remote COOs to their owner */
6506   PetscSF sf2;
6507   nroots  = nroots2;
6508   nleaves = nleaves2;
6509   PetscCall(PetscSFCreate(comm, &sf2));
6510   PetscCall(PetscSFSetFromOptions(sf2));
6511   PetscCall(PetscMalloc1(nleaves, &iremote));
6512   p = 0;
6513   for (k = 0; k < nsend; k++) {
6514     PetscCheck(offsets[k] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF roots is too large for PetscInt");
6515     for (q = 0; q < nentries[k]; q++, p++) {
6516       iremote[p].rank  = sendto[k];
6517       iremote[p].index = offsets[k] + q;
6518     }
6519   }
6520   PetscCall(PetscSFSetGraph(sf2, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
6521 
6522   /* Send the remote COOs to their owner */
6523   PetscInt    n2 = nroots, *i2, *j2; /* Buffers for received COOs from other ranks, along with a permutation array */
6524   PetscCount *perm2;                 /* Though PetscInt is enough for remote entries, we use PetscCount here as we want to reuse MatSplitEntries_Internal() */
6525   PetscCall(PetscMalloc3(n2, &i2, n2, &j2, n2, &perm2));
6526   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, i1 + rem, PETSC_MEMTYPE_HOST, i2, MPI_REPLACE));
6527   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, i1 + rem, i2, MPI_REPLACE));
6528   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, j1 + rem, PETSC_MEMTYPE_HOST, j2, MPI_REPLACE));
6529   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, j1 + rem, j2, MPI_REPLACE));
6530 
6531   PetscCall(PetscFree(offsets));
6532   PetscCall(PetscFree2(sendto, nentries));
6533 
6534   /* Sort received COOs by row along with the permutation array     */
6535   for (k = 0; k < n2; k++) perm2[k] = k;
6536   PetscCall(PetscSortIntWithIntCountArrayPair(n2, i2, j2, perm2));
6537 
6538   /* sf2 only sends contiguous leafdata to contiguous rootdata. We record the permutation which will be used to fill leafdata */
6539   PetscCount *Cperm1;
6540   PetscCall(PetscMalloc1(nleaves, &Cperm1));
6541   PetscCall(PetscArraycpy(Cperm1, perm1 + rem, nleaves));
6542 
6543   /* Support for HYPRE matrices, kind of a hack.
6544      Swap min column with diagonal so that diagonal values will go first */
6545   PetscBool   hypre;
6546   const char *name;
6547   PetscCall(PetscObjectGetName((PetscObject)mat, &name));
6548   PetscCall(PetscStrcmp("_internal_COO_mat_for_hypre", name, &hypre));
6549   if (hypre) {
6550     PetscInt *minj;
6551     PetscBT   hasdiag;
6552 
6553     PetscCall(PetscBTCreate(m, &hasdiag));
6554     PetscCall(PetscMalloc1(m, &minj));
6555     for (k = 0; k < m; k++) minj[k] = PETSC_MAX_INT;
6556     for (k = i1start; k < rem; k++) {
6557       if (j1[k] < cstart || j1[k] >= cend) continue;
6558       const PetscInt rindex = i1[k] - rstart;
6559       if ((j1[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
6560       minj[rindex] = PetscMin(minj[rindex], j1[k]);
6561     }
6562     for (k = 0; k < n2; k++) {
6563       if (j2[k] < cstart || j2[k] >= cend) continue;
6564       const PetscInt rindex = i2[k] - rstart;
6565       if ((j2[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
6566       minj[rindex] = PetscMin(minj[rindex], j2[k]);
6567     }
6568     for (k = i1start; k < rem; k++) {
6569       const PetscInt rindex = i1[k] - rstart;
6570       if (j1[k] < cstart || j1[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
6571       if (j1[k] == minj[rindex]) j1[k] = i1[k] + (cstart - rstart);
6572       else if ((j1[k] - cstart) == rindex) j1[k] = minj[rindex];
6573     }
6574     for (k = 0; k < n2; k++) {
6575       const PetscInt rindex = i2[k] - rstart;
6576       if (j2[k] < cstart || j2[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
6577       if (j2[k] == minj[rindex]) j2[k] = i2[k] + (cstart - rstart);
6578       else if ((j2[k] - cstart) == rindex) j2[k] = minj[rindex];
6579     }
6580     PetscCall(PetscBTDestroy(&hasdiag));
6581     PetscCall(PetscFree(minj));
6582   }
6583 
6584   /* Split local COOs and received COOs into diag/offdiag portions */
6585   PetscCount *rowBegin1, *rowMid1, *rowEnd1;
6586   PetscCount *Ajmap1, *Aperm1, *Bjmap1, *Bperm1;
6587   PetscCount  Annz1, Bnnz1, Atot1, Btot1;
6588   PetscCount *rowBegin2, *rowMid2, *rowEnd2;
6589   PetscCount *Ajmap2, *Aperm2, *Bjmap2, *Bperm2;
6590   PetscCount  Annz2, Bnnz2, Atot2, Btot2;
6591 
6592   PetscCall(PetscCalloc3(m, &rowBegin1, m, &rowMid1, m, &rowEnd1));
6593   PetscCall(PetscCalloc3(m, &rowBegin2, m, &rowMid2, m, &rowEnd2));
6594   PetscCall(MatSplitEntries_Internal(mat, rem, i1, j1, perm1, rowBegin1, rowMid1, rowEnd1, &Atot1, &Aperm1, &Annz1, &Ajmap1, &Btot1, &Bperm1, &Bnnz1, &Bjmap1));
6595   PetscCall(MatSplitEntries_Internal(mat, n2, i2, j2, perm2, rowBegin2, rowMid2, rowEnd2, &Atot2, &Aperm2, &Annz2, &Ajmap2, &Btot2, &Bperm2, &Bnnz2, &Bjmap2));
6596 
6597   /* Merge local COOs with received COOs: diag with diag, offdiag with offdiag */
6598   PetscInt *Ai, *Bi;
6599   PetscInt *Aj, *Bj;
6600 
6601   PetscCall(PetscMalloc1(m + 1, &Ai));
6602   PetscCall(PetscMalloc1(m + 1, &Bi));
6603   PetscCall(PetscMalloc1(Annz1 + Annz2, &Aj)); /* Since local and remote entries might have dups, we might allocate excess memory */
6604   PetscCall(PetscMalloc1(Bnnz1 + Bnnz2, &Bj));
6605 
6606   PetscCount *Aimap1, *Bimap1, *Aimap2, *Bimap2;
6607   PetscCall(PetscMalloc1(Annz1, &Aimap1));
6608   PetscCall(PetscMalloc1(Bnnz1, &Bimap1));
6609   PetscCall(PetscMalloc1(Annz2, &Aimap2));
6610   PetscCall(PetscMalloc1(Bnnz2, &Bimap2));
6611 
6612   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowBegin1, rowMid1, rowBegin2, rowMid2, Ajmap1, Ajmap2, Aimap1, Aimap2, Ai, Aj));
6613   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowMid1, rowEnd1, rowMid2, rowEnd2, Bjmap1, Bjmap2, Bimap1, Bimap2, Bi, Bj));
6614 
6615   /* Expand Ajmap1/Bjmap1 to make them based off nonzeros in A/B, since we     */
6616   /* expect nonzeros in A/B most likely have local contributing entries        */
6617   PetscInt    Annz = Ai[m];
6618   PetscInt    Bnnz = Bi[m];
6619   PetscCount *Ajmap1_new, *Bjmap1_new;
6620 
6621   PetscCall(PetscMalloc1(Annz + 1, &Ajmap1_new));
6622   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap1_new));
6623 
6624   PetscCall(ExpandJmap_Internal(Annz1, Annz, Aimap1, Ajmap1, Ajmap1_new));
6625   PetscCall(ExpandJmap_Internal(Bnnz1, Bnnz, Bimap1, Bjmap1, Bjmap1_new));
6626 
6627   PetscCall(PetscFree(Aimap1));
6628   PetscCall(PetscFree(Ajmap1));
6629   PetscCall(PetscFree(Bimap1));
6630   PetscCall(PetscFree(Bjmap1));
6631   PetscCall(PetscFree3(rowBegin1, rowMid1, rowEnd1));
6632   PetscCall(PetscFree3(rowBegin2, rowMid2, rowEnd2));
6633   PetscCall(PetscFree(perm1));
6634   PetscCall(PetscFree3(i2, j2, perm2));
6635 
6636   Ajmap1 = Ajmap1_new;
6637   Bjmap1 = Bjmap1_new;
6638 
6639   /* Reallocate Aj, Bj once we know actual numbers of unique nonzeros in A and B */
6640   if (Annz < Annz1 + Annz2) {
6641     PetscInt *Aj_new;
6642     PetscCall(PetscMalloc1(Annz, &Aj_new));
6643     PetscCall(PetscArraycpy(Aj_new, Aj, Annz));
6644     PetscCall(PetscFree(Aj));
6645     Aj = Aj_new;
6646   }
6647 
6648   if (Bnnz < Bnnz1 + Bnnz2) {
6649     PetscInt *Bj_new;
6650     PetscCall(PetscMalloc1(Bnnz, &Bj_new));
6651     PetscCall(PetscArraycpy(Bj_new, Bj, Bnnz));
6652     PetscCall(PetscFree(Bj));
6653     Bj = Bj_new;
6654   }
6655 
6656   /* Create new submatrices for on-process and off-process coupling                  */
6657   PetscScalar     *Aa, *Ba;
6658   MatType          rtype;
6659   Mat_SeqAIJ      *a, *b;
6660   PetscObjectState state;
6661   PetscCall(PetscCalloc1(Annz, &Aa)); /* Zero matrix on device */
6662   PetscCall(PetscCalloc1(Bnnz, &Ba));
6663   /* make Aj[] local, i.e, based off the start column of the diagonal portion */
6664   if (cstart) {
6665     for (k = 0; k < Annz; k++) Aj[k] -= cstart;
6666   }
6667   PetscCall(MatDestroy(&mpiaij->A));
6668   PetscCall(MatDestroy(&mpiaij->B));
6669   PetscCall(MatGetRootType_Private(mat, &rtype));
6670   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, Ai, Aj, Aa, &mpiaij->A));
6671   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, mat->cmap->N, Bi, Bj, Ba, &mpiaij->B));
6672   PetscCall(MatSetUpMultiply_MPIAIJ(mat));
6673   mat->was_assembled = PETSC_TRUE; // was_assembled in effect means the Mvctx is built; doing so avoids redundant MatSetUpMultiply_MPIAIJ
6674   state              = mpiaij->A->nonzerostate + mpiaij->B->nonzerostate;
6675   PetscCall(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));
6676 
6677   a               = (Mat_SeqAIJ *)mpiaij->A->data;
6678   b               = (Mat_SeqAIJ *)mpiaij->B->data;
6679   a->singlemalloc = b->singlemalloc = PETSC_FALSE; /* Let newmat own Ai,Aj,Aa,Bi,Bj,Ba */
6680   a->free_a = b->free_a = PETSC_TRUE;
6681   a->free_ij = b->free_ij = PETSC_TRUE;
6682 
6683   /* conversion must happen AFTER multiply setup */
6684   PetscCall(MatConvert(mpiaij->A, rtype, MAT_INPLACE_MATRIX, &mpiaij->A));
6685   PetscCall(MatConvert(mpiaij->B, rtype, MAT_INPLACE_MATRIX, &mpiaij->B));
6686   PetscCall(VecDestroy(&mpiaij->lvec));
6687   PetscCall(MatCreateVecs(mpiaij->B, &mpiaij->lvec, NULL));
6688 
6689   // Put the COO struct in a container and then attach that to the matrix
6690   PetscCall(PetscMalloc1(1, &coo));
6691   coo->n       = coo_n;
6692   coo->sf      = sf2;
6693   coo->sendlen = nleaves;
6694   coo->recvlen = nroots;
6695   coo->Annz    = Annz;
6696   coo->Bnnz    = Bnnz;
6697   coo->Annz2   = Annz2;
6698   coo->Bnnz2   = Bnnz2;
6699   coo->Atot1   = Atot1;
6700   coo->Atot2   = Atot2;
6701   coo->Btot1   = Btot1;
6702   coo->Btot2   = Btot2;
6703   coo->Ajmap1  = Ajmap1;
6704   coo->Aperm1  = Aperm1;
6705   coo->Bjmap1  = Bjmap1;
6706   coo->Bperm1  = Bperm1;
6707   coo->Aimap2  = Aimap2;
6708   coo->Ajmap2  = Ajmap2;
6709   coo->Aperm2  = Aperm2;
6710   coo->Bimap2  = Bimap2;
6711   coo->Bjmap2  = Bjmap2;
6712   coo->Bperm2  = Bperm2;
6713   coo->Cperm1  = Cperm1;
6714   // Allocate in preallocation. If not used, it has zero cost on host
6715   PetscCall(PetscMalloc2(coo->sendlen, &coo->sendbuf, coo->recvlen, &coo->recvbuf));
6716   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
6717   PetscCall(PetscContainerSetPointer(container, coo));
6718   PetscCall(PetscContainerSetUserDestroy(container, MatCOOStructDestroy_MPIAIJ));
6719   PetscCall(PetscObjectCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject)container));
6720   PetscCall(PetscContainerDestroy(&container));
6721   PetscFunctionReturn(PETSC_SUCCESS);
6722 }
6723 
6724 static PetscErrorCode MatSetValuesCOO_MPIAIJ(Mat mat, const PetscScalar v[], InsertMode imode)
6725 {
6726   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
6727   Mat                  A = mpiaij->A, B = mpiaij->B;
6728   PetscScalar         *Aa, *Ba;
6729   PetscScalar         *sendbuf, *recvbuf;
6730   const PetscCount    *Ajmap1, *Ajmap2, *Aimap2;
6731   const PetscCount    *Bjmap1, *Bjmap2, *Bimap2;
6732   const PetscCount    *Aperm1, *Aperm2, *Bperm1, *Bperm2;
6733   const PetscCount    *Cperm1;
6734   PetscContainer       container;
6735   MatCOOStruct_MPIAIJ *coo;
6736 
6737   PetscFunctionBegin;
6738   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container));
6739   PetscCheck(container, PetscObjectComm((PetscObject)mat), PETSC_ERR_PLIB, "Not found MatCOOStruct on this matrix");
6740   PetscCall(PetscContainerGetPointer(container, (void **)&coo));
6741   sendbuf = coo->sendbuf;
6742   recvbuf = coo->recvbuf;
6743   Ajmap1  = coo->Ajmap1;
6744   Ajmap2  = coo->Ajmap2;
6745   Aimap2  = coo->Aimap2;
6746   Bjmap1  = coo->Bjmap1;
6747   Bjmap2  = coo->Bjmap2;
6748   Bimap2  = coo->Bimap2;
6749   Aperm1  = coo->Aperm1;
6750   Aperm2  = coo->Aperm2;
6751   Bperm1  = coo->Bperm1;
6752   Bperm2  = coo->Bperm2;
6753   Cperm1  = coo->Cperm1;
6754 
6755   PetscCall(MatSeqAIJGetArray(A, &Aa)); /* Might read and write matrix values */
6756   PetscCall(MatSeqAIJGetArray(B, &Ba));
6757 
6758   /* Pack entries to be sent to remote */
6759   for (PetscCount i = 0; i < coo->sendlen; i++) sendbuf[i] = v[Cperm1[i]];
6760 
6761   /* Send remote entries to their owner and overlap the communication with local computation */
6762   PetscCall(PetscSFReduceWithMemTypeBegin(coo->sf, MPIU_SCALAR, PETSC_MEMTYPE_HOST, sendbuf, PETSC_MEMTYPE_HOST, recvbuf, MPI_REPLACE));
6763   /* Add local entries to A and B */
6764   for (PetscCount i = 0; i < coo->Annz; i++) { /* All nonzeros in A are either zero'ed or added with a value (i.e., initialized) */
6765     PetscScalar sum = 0.0;                     /* Do partial summation first to improve numerical stability */
6766     for (PetscCount k = Ajmap1[i]; k < Ajmap1[i + 1]; k++) sum += v[Aperm1[k]];
6767     Aa[i] = (imode == INSERT_VALUES ? 0.0 : Aa[i]) + sum;
6768   }
6769   for (PetscCount i = 0; i < coo->Bnnz; i++) {
6770     PetscScalar sum = 0.0;
6771     for (PetscCount k = Bjmap1[i]; k < Bjmap1[i + 1]; k++) sum += v[Bperm1[k]];
6772     Ba[i] = (imode == INSERT_VALUES ? 0.0 : Ba[i]) + sum;
6773   }
6774   PetscCall(PetscSFReduceEnd(coo->sf, MPIU_SCALAR, sendbuf, recvbuf, MPI_REPLACE));
6775 
6776   /* Add received remote entries to A and B */
6777   for (PetscCount i = 0; i < coo->Annz2; i++) {
6778     for (PetscCount k = Ajmap2[i]; k < Ajmap2[i + 1]; k++) Aa[Aimap2[i]] += recvbuf[Aperm2[k]];
6779   }
6780   for (PetscCount i = 0; i < coo->Bnnz2; i++) {
6781     for (PetscCount k = Bjmap2[i]; k < Bjmap2[i + 1]; k++) Ba[Bimap2[i]] += recvbuf[Bperm2[k]];
6782   }
6783   PetscCall(MatSeqAIJRestoreArray(A, &Aa));
6784   PetscCall(MatSeqAIJRestoreArray(B, &Ba));
6785   PetscFunctionReturn(PETSC_SUCCESS);
6786 }
6787 
6788 /*MC
6789    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.
6790 
6791    Options Database Keys:
6792 . -mat_type mpiaij - sets the matrix type to `MATMPIAIJ` during a call to `MatSetFromOptions()`
6793 
6794    Level: beginner
6795 
6796    Notes:
6797    `MatSetValues()` may be called for this matrix type with a `NULL` argument for the numerical values,
6798     in this case the values associated with the rows and columns one passes in are set to zero
6799     in the matrix
6800 
6801     `MatSetOptions`(,`MAT_STRUCTURE_ONLY`,`PETSC_TRUE`) may be called for this matrix type. In this no
6802     space is allocated for the nonzero entries and any entries passed with `MatSetValues()` are ignored
6803 
6804 .seealso: [](ch_matrices), `Mat`, `MATSEQAIJ`, `MATAIJ`, `MatCreateAIJ()`
6805 M*/
6806 PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
6807 {
6808   Mat_MPIAIJ *b;
6809   PetscMPIInt size;
6810 
6811   PetscFunctionBegin;
6812   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));
6813 
6814   PetscCall(PetscNew(&b));
6815   B->data       = (void *)b;
6816   B->ops[0]     = MatOps_Values;
6817   B->assembled  = PETSC_FALSE;
6818   B->insertmode = NOT_SET_VALUES;
6819   b->size       = size;
6820 
6821   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)B), &b->rank));
6822 
6823   /* build cache for off array entries formed */
6824   PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)B), 1, &B->stash));
6825 
6826   b->donotstash  = PETSC_FALSE;
6827   b->colmap      = NULL;
6828   b->garray      = NULL;
6829   b->roworiented = PETSC_TRUE;
6830 
6831   /* stuff used for matrix vector multiply */
6832   b->lvec  = NULL;
6833   b->Mvctx = NULL;
6834 
6835   /* stuff for MatGetRow() */
6836   b->rowindices   = NULL;
6837   b->rowvalues    = NULL;
6838   b->getrowactive = PETSC_FALSE;
6839 
6840   /* flexible pointer used in CUSPARSE classes */
6841   b->spptr = NULL;
6842 
6843   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetUseScalableIncreaseOverlap_C", MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ));
6844   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_MPIAIJ));
6845   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_MPIAIJ));
6846   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsTranspose_C", MatIsTranspose_MPIAIJ));
6847   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocation_C", MatMPIAIJSetPreallocation_MPIAIJ));
6848   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetPreallocation_C", MatResetPreallocation_MPIAIJ));
6849   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocationCSR_C", MatMPIAIJSetPreallocationCSR_MPIAIJ));
6850   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDiagonalScaleLocal_C", MatDiagonalScaleLocal_MPIAIJ));
6851   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijperm_C", MatConvert_MPIAIJ_MPIAIJPERM));
6852   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijsell_C", MatConvert_MPIAIJ_MPIAIJSELL));
6853 #if defined(PETSC_HAVE_CUDA)
6854   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcusparse_C", MatConvert_MPIAIJ_MPIAIJCUSPARSE));
6855 #endif
6856 #if defined(PETSC_HAVE_HIP)
6857   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijhipsparse_C", MatConvert_MPIAIJ_MPIAIJHIPSPARSE));
6858 #endif
6859 #if defined(PETSC_HAVE_KOKKOS_KERNELS)
6860   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijkokkos_C", MatConvert_MPIAIJ_MPIAIJKokkos));
6861 #endif
6862 #if defined(PETSC_HAVE_MKL_SPARSE)
6863   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijmkl_C", MatConvert_MPIAIJ_MPIAIJMKL));
6864 #endif
6865   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcrl_C", MatConvert_MPIAIJ_MPIAIJCRL));
6866   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpibaij_C", MatConvert_MPIAIJ_MPIBAIJ));
6867   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisbaij_C", MatConvert_MPIAIJ_MPISBAIJ));
6868   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpidense_C", MatConvert_MPIAIJ_MPIDense));
6869 #if defined(PETSC_HAVE_ELEMENTAL)
6870   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_elemental_C", MatConvert_MPIAIJ_Elemental));
6871 #endif
6872 #if defined(PETSC_HAVE_SCALAPACK)
6873   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_scalapack_C", MatConvert_AIJ_ScaLAPACK));
6874 #endif
6875   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_is_C", MatConvert_XAIJ_IS));
6876   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisell_C", MatConvert_MPIAIJ_MPISELL));
6877 #if defined(PETSC_HAVE_HYPRE)
6878   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_hypre_C", MatConvert_AIJ_HYPRE));
6879   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", MatProductSetFromOptions_Transpose_AIJ_AIJ));
6880 #endif
6881   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_is_mpiaij_C", MatProductSetFromOptions_IS_XAIJ));
6882   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_mpiaij_mpiaij_C", MatProductSetFromOptions_MPIAIJ));
6883   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_MPIAIJ));
6884   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetValuesCOO_C", MatSetValuesCOO_MPIAIJ));
6885   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATMPIAIJ));
6886   PetscFunctionReturn(PETSC_SUCCESS);
6887 }
6888 
6889 /*@C
6890   MatCreateMPIAIJWithSplitArrays - creates a `MATMPIAIJ` matrix using arrays that contain the "diagonal"
6891   and "off-diagonal" part of the matrix in CSR format.
6892 
6893   Collective
6894 
6895   Input Parameters:
6896 + comm - MPI communicator
6897 . m    - number of local rows (Cannot be `PETSC_DECIDE`)
6898 . n    - This value should be the same as the local size used in creating the
6899        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
6900        calculated if `N` is given) For square matrices `n` is almost always `m`.
6901 . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
6902 . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
6903 . i    - row indices for "diagonal" portion of matrix; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
6904 . j    - column indices, which must be local, i.e., based off the start column of the diagonal portion
6905 . a    - matrix values
6906 . oi   - row indices for "off-diagonal" portion of matrix; that is oi[0] = 0, oi[row] = oi[row-1] + number of elements in that row of the matrix
6907 . oj   - column indices, which must be global, representing global columns in the `MATMPIAIJ` matrix
6908 - oa   - matrix values
6909 
6910   Output Parameter:
6911 . mat - the matrix
6912 
6913   Level: advanced
6914 
6915   Notes:
6916   The `i`, `j`, and `a` arrays ARE NOT copied by this routine into the internal format used by PETSc. The user
6917   must free the arrays once the matrix has been destroyed and not before.
6918 
6919   The `i` and `j` indices are 0 based
6920 
6921   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix
6922 
6923   This sets local rows and cannot be used to set off-processor values.
6924 
6925   Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
6926   legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
6927   not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
6928   the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
6929   keep track of the underlying array. Use `MatSetOption`(A,`MAT_NO_OFF_PROC_ENTRIES`,`PETSC_TRUE`) to disable all
6930   communication if it is known that only local entries will be set.
6931 
6932 .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
6933           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithArrays()`
6934 @*/
6935 PetscErrorCode MatCreateMPIAIJWithSplitArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, PetscInt i[], PetscInt j[], PetscScalar a[], PetscInt oi[], PetscInt oj[], PetscScalar oa[], Mat *mat)
6936 {
6937   Mat_MPIAIJ *maij;
6938 
6939   PetscFunctionBegin;
6940   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
6941   PetscCheck(i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
6942   PetscCheck(oi[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "oi (row indices) must start with 0");
6943   PetscCall(MatCreate(comm, mat));
6944   PetscCall(MatSetSizes(*mat, m, n, M, N));
6945   PetscCall(MatSetType(*mat, MATMPIAIJ));
6946   maij = (Mat_MPIAIJ *)(*mat)->data;
6947 
6948   (*mat)->preallocated = PETSC_TRUE;
6949 
6950   PetscCall(PetscLayoutSetUp((*mat)->rmap));
6951   PetscCall(PetscLayoutSetUp((*mat)->cmap));
6952 
6953   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, i, j, a, &maij->A));
6954   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, (*mat)->cmap->N, oi, oj, oa, &maij->B));
6955 
6956   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
6957   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
6958   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
6959   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
6960   PetscCall(MatSetOption(*mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
6961   PetscFunctionReturn(PETSC_SUCCESS);
6962 }
6963 
6964 typedef struct {
6965   Mat       *mp;    /* intermediate products */
6966   PetscBool *mptmp; /* is the intermediate product temporary ? */
6967   PetscInt   cp;    /* number of intermediate products */
6968 
6969   /* support for MatGetBrowsOfAoCols_MPIAIJ for P_oth */
6970   PetscInt    *startsj_s, *startsj_r;
6971   PetscScalar *bufa;
6972   Mat          P_oth;
6973 
6974   /* may take advantage of merging product->B */
6975   Mat Bloc; /* B-local by merging diag and off-diag */
6976 
6977   /* cusparse does not have support to split between symbolic and numeric phases.
6978      When api_user is true, we don't need to update the numerical values
6979      of the temporary storage */
6980   PetscBool reusesym;
6981 
6982   /* support for COO values insertion */
6983   PetscScalar *coo_v, *coo_w; /* store on-process and off-process COO scalars, and used as MPI recv/send buffers respectively */
6984   PetscInt   **own;           /* own[i] points to address of on-process COO indices for Mat mp[i] */
6985   PetscInt   **off;           /* off[i] points to address of off-process COO indices for Mat mp[i] */
6986   PetscBool    hasoffproc;    /* if true, have off-process values insertion (i.e. AtB or PtAP) */
6987   PetscSF      sf;            /* used for non-local values insertion and memory malloc */
6988   PetscMemType mtype;
6989 
6990   /* customization */
6991   PetscBool abmerge;
6992   PetscBool P_oth_bind;
6993 } MatMatMPIAIJBACKEND;
6994 
6995 static PetscErrorCode MatDestroy_MatMatMPIAIJBACKEND(void *data)
6996 {
6997   MatMatMPIAIJBACKEND *mmdata = (MatMatMPIAIJBACKEND *)data;
6998   PetscInt             i;
6999 
7000   PetscFunctionBegin;
7001   PetscCall(PetscFree2(mmdata->startsj_s, mmdata->startsj_r));
7002   PetscCall(PetscFree(mmdata->bufa));
7003   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_v));
7004   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_w));
7005   PetscCall(MatDestroy(&mmdata->P_oth));
7006   PetscCall(MatDestroy(&mmdata->Bloc));
7007   PetscCall(PetscSFDestroy(&mmdata->sf));
7008   for (i = 0; i < mmdata->cp; i++) PetscCall(MatDestroy(&mmdata->mp[i]));
7009   PetscCall(PetscFree2(mmdata->mp, mmdata->mptmp));
7010   PetscCall(PetscFree(mmdata->own[0]));
7011   PetscCall(PetscFree(mmdata->own));
7012   PetscCall(PetscFree(mmdata->off[0]));
7013   PetscCall(PetscFree(mmdata->off));
7014   PetscCall(PetscFree(mmdata));
7015   PetscFunctionReturn(PETSC_SUCCESS);
7016 }
7017 
7018 /* Copy selected n entries with indices in idx[] of A to v[].
7019    If idx is NULL, copy the whole data array of A to v[]
7020  */
7021 static PetscErrorCode MatSeqAIJCopySubArray(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
7022 {
7023   PetscErrorCode (*f)(Mat, PetscInt, const PetscInt[], PetscScalar[]);
7024 
7025   PetscFunctionBegin;
7026   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", &f));
7027   if (f) {
7028     PetscCall((*f)(A, n, idx, v));
7029   } else {
7030     const PetscScalar *vv;
7031 
7032     PetscCall(MatSeqAIJGetArrayRead(A, &vv));
7033     if (n && idx) {
7034       PetscScalar    *w  = v;
7035       const PetscInt *oi = idx;
7036       PetscInt        j;
7037 
7038       for (j = 0; j < n; j++) *w++ = vv[*oi++];
7039     } else {
7040       PetscCall(PetscArraycpy(v, vv, n));
7041     }
7042     PetscCall(MatSeqAIJRestoreArrayRead(A, &vv));
7043   }
7044   PetscFunctionReturn(PETSC_SUCCESS);
7045 }
7046 
7047 static PetscErrorCode MatProductNumeric_MPIAIJBACKEND(Mat C)
7048 {
7049   MatMatMPIAIJBACKEND *mmdata;
7050   PetscInt             i, n_d, n_o;
7051 
7052   PetscFunctionBegin;
7053   MatCheckProduct(C, 1);
7054   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
7055   mmdata = (MatMatMPIAIJBACKEND *)C->product->data;
7056   if (!mmdata->reusesym) { /* update temporary matrices */
7057     if (mmdata->P_oth) PetscCall(MatGetBrowsOfAoCols_MPIAIJ(C->product->A, C->product->B, MAT_REUSE_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));
7058     if (mmdata->Bloc) PetscCall(MatMPIAIJGetLocalMatMerge(C->product->B, MAT_REUSE_MATRIX, NULL, &mmdata->Bloc));
7059   }
7060   mmdata->reusesym = PETSC_FALSE;
7061 
7062   for (i = 0; i < mmdata->cp; i++) {
7063     PetscCheck(mmdata->mp[i]->ops->productnumeric, PetscObjectComm((PetscObject)mmdata->mp[i]), PETSC_ERR_PLIB, "Missing numeric op for %s", MatProductTypes[mmdata->mp[i]->product->type]);
7064     PetscCall((*mmdata->mp[i]->ops->productnumeric)(mmdata->mp[i]));
7065   }
7066   for (i = 0, n_d = 0, n_o = 0; i < mmdata->cp; i++) {
7067     PetscInt noff = mmdata->off[i + 1] - mmdata->off[i];
7068 
7069     if (mmdata->mptmp[i]) continue;
7070     if (noff) {
7071       PetscInt nown = mmdata->own[i + 1] - mmdata->own[i];
7072 
7073       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], noff, mmdata->off[i], mmdata->coo_w + n_o));
7074       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], nown, mmdata->own[i], mmdata->coo_v + n_d));
7075       n_o += noff;
7076       n_d += nown;
7077     } else {
7078       Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mmdata->mp[i]->data;
7079 
7080       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], mm->nz, NULL, mmdata->coo_v + n_d));
7081       n_d += mm->nz;
7082     }
7083   }
7084   if (mmdata->hasoffproc) { /* offprocess insertion */
7085     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
7086     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
7087   }
7088   PetscCall(MatSetValuesCOO(C, mmdata->coo_v, INSERT_VALUES));
7089   PetscFunctionReturn(PETSC_SUCCESS);
7090 }
7091 
7092 /* Support for Pt * A, A * P, or Pt * A * P */
7093 #define MAX_NUMBER_INTERMEDIATE 4
7094 PetscErrorCode MatProductSymbolic_MPIAIJBACKEND(Mat C)
7095 {
7096   Mat_Product           *product = C->product;
7097   Mat                    A, P, mp[MAX_NUMBER_INTERMEDIATE]; /* A, P and a series of intermediate matrices */
7098   Mat_MPIAIJ            *a, *p;
7099   MatMatMPIAIJBACKEND   *mmdata;
7100   ISLocalToGlobalMapping P_oth_l2g = NULL;
7101   IS                     glob      = NULL;
7102   const char            *prefix;
7103   char                   pprefix[256];
7104   const PetscInt        *globidx, *P_oth_idx;
7105   PetscInt               i, j, cp, m, n, M, N, *coo_i, *coo_j;
7106   PetscCount             ncoo, ncoo_d, ncoo_o, ncoo_oown;
7107   PetscInt               cmapt[MAX_NUMBER_INTERMEDIATE], rmapt[MAX_NUMBER_INTERMEDIATE]; /* col/row map type for each Mat in mp[]. */
7108                                                                                          /* type-0: consecutive, start from 0; type-1: consecutive with */
7109                                                                                          /* a base offset; type-2: sparse with a local to global map table */
7110   const PetscInt *cmapa[MAX_NUMBER_INTERMEDIATE], *rmapa[MAX_NUMBER_INTERMEDIATE];       /* col/row local to global map array (table) for type-2 map type */
7111 
7112   MatProductType ptype;
7113   PetscBool      mptmp[MAX_NUMBER_INTERMEDIATE], hasoffproc = PETSC_FALSE, iscuda, iship, iskokk;
7114   PetscMPIInt    size;
7115 
7116   PetscFunctionBegin;
7117   MatCheckProduct(C, 1);
7118   PetscCheck(!product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
7119   ptype = product->type;
7120   if (product->A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
7121     ptype                                          = MATPRODUCT_AB;
7122     product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
7123   }
7124   switch (ptype) {
7125   case MATPRODUCT_AB:
7126     A          = product->A;
7127     P          = product->B;
7128     m          = A->rmap->n;
7129     n          = P->cmap->n;
7130     M          = A->rmap->N;
7131     N          = P->cmap->N;
7132     hasoffproc = PETSC_FALSE; /* will not scatter mat product values to other processes */
7133     break;
7134   case MATPRODUCT_AtB:
7135     P          = product->A;
7136     A          = product->B;
7137     m          = P->cmap->n;
7138     n          = A->cmap->n;
7139     M          = P->cmap->N;
7140     N          = A->cmap->N;
7141     hasoffproc = PETSC_TRUE;
7142     break;
7143   case MATPRODUCT_PtAP:
7144     A          = product->A;
7145     P          = product->B;
7146     m          = P->cmap->n;
7147     n          = P->cmap->n;
7148     M          = P->cmap->N;
7149     N          = P->cmap->N;
7150     hasoffproc = PETSC_TRUE;
7151     break;
7152   default:
7153     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
7154   }
7155   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)C), &size));
7156   if (size == 1) hasoffproc = PETSC_FALSE;
7157 
7158   /* defaults */
7159   for (i = 0; i < MAX_NUMBER_INTERMEDIATE; i++) {
7160     mp[i]    = NULL;
7161     mptmp[i] = PETSC_FALSE;
7162     rmapt[i] = -1;
7163     cmapt[i] = -1;
7164     rmapa[i] = NULL;
7165     cmapa[i] = NULL;
7166   }
7167 
7168   /* customization */
7169   PetscCall(PetscNew(&mmdata));
7170   mmdata->reusesym = product->api_user;
7171   if (ptype == MATPRODUCT_AB) {
7172     if (product->api_user) {
7173       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
7174       PetscCall(PetscOptionsBool("-matmatmult_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
7175       PetscCall(PetscOptionsBool("-matmatmult_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
7176       PetscOptionsEnd();
7177     } else {
7178       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
7179       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
7180       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
7181       PetscOptionsEnd();
7182     }
7183   } else if (ptype == MATPRODUCT_PtAP) {
7184     if (product->api_user) {
7185       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
7186       PetscCall(PetscOptionsBool("-matptap_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
7187       PetscOptionsEnd();
7188     } else {
7189       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
7190       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
7191       PetscOptionsEnd();
7192     }
7193   }
7194   a = (Mat_MPIAIJ *)A->data;
7195   p = (Mat_MPIAIJ *)P->data;
7196   PetscCall(MatSetSizes(C, m, n, M, N));
7197   PetscCall(PetscLayoutSetUp(C->rmap));
7198   PetscCall(PetscLayoutSetUp(C->cmap));
7199   PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
7200   PetscCall(MatGetOptionsPrefix(C, &prefix));
7201 
7202   cp = 0;
7203   switch (ptype) {
7204   case MATPRODUCT_AB: /* A * P */
7205     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));
7206 
7207     /* A_diag * P_local (merged or not) */
7208     if (mmdata->abmerge) { /* P's diagonal and off-diag blocks are merged to one matrix, then multiplied by A_diag */
7209       /* P is product->B */
7210       PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
7211       PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
7212       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
7213       PetscCall(MatProductSetFill(mp[cp], product->fill));
7214       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7215       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7216       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7217       mp[cp]->product->api_user = product->api_user;
7218       PetscCall(MatProductSetFromOptions(mp[cp]));
7219       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7220       PetscCall(ISGetIndices(glob, &globidx));
7221       rmapt[cp] = 1;
7222       cmapt[cp] = 2;
7223       cmapa[cp] = globidx;
7224       mptmp[cp] = PETSC_FALSE;
7225       cp++;
7226     } else { /* A_diag * P_diag and A_diag * P_off */
7227       PetscCall(MatProductCreate(a->A, p->A, NULL, &mp[cp]));
7228       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
7229       PetscCall(MatProductSetFill(mp[cp], product->fill));
7230       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7231       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7232       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7233       mp[cp]->product->api_user = product->api_user;
7234       PetscCall(MatProductSetFromOptions(mp[cp]));
7235       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7236       rmapt[cp] = 1;
7237       cmapt[cp] = 1;
7238       mptmp[cp] = PETSC_FALSE;
7239       cp++;
7240       PetscCall(MatProductCreate(a->A, p->B, NULL, &mp[cp]));
7241       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
7242       PetscCall(MatProductSetFill(mp[cp], product->fill));
7243       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7244       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7245       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7246       mp[cp]->product->api_user = product->api_user;
7247       PetscCall(MatProductSetFromOptions(mp[cp]));
7248       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7249       rmapt[cp] = 1;
7250       cmapt[cp] = 2;
7251       cmapa[cp] = p->garray;
7252       mptmp[cp] = PETSC_FALSE;
7253       cp++;
7254     }
7255 
7256     /* A_off * P_other */
7257     if (mmdata->P_oth) {
7258       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g)); /* make P_oth use local col ids */
7259       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
7260       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)(a->B))->type_name));
7261       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
7262       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
7263       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
7264       PetscCall(MatProductSetFill(mp[cp], product->fill));
7265       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7266       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7267       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7268       mp[cp]->product->api_user = product->api_user;
7269       PetscCall(MatProductSetFromOptions(mp[cp]));
7270       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7271       rmapt[cp] = 1;
7272       cmapt[cp] = 2;
7273       cmapa[cp] = P_oth_idx;
7274       mptmp[cp] = PETSC_FALSE;
7275       cp++;
7276     }
7277     break;
7278 
7279   case MATPRODUCT_AtB: /* (P^t * A): P_diag * A_loc + P_off * A_loc */
7280     /* A is product->B */
7281     PetscCall(MatMPIAIJGetLocalMatMerge(A, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
7282     if (A == P) { /* when A==P, we can take advantage of the already merged mmdata->Bloc */
7283       PetscCall(MatProductCreate(mmdata->Bloc, mmdata->Bloc, NULL, &mp[cp]));
7284       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
7285       PetscCall(MatProductSetFill(mp[cp], product->fill));
7286       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7287       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7288       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7289       mp[cp]->product->api_user = product->api_user;
7290       PetscCall(MatProductSetFromOptions(mp[cp]));
7291       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7292       PetscCall(ISGetIndices(glob, &globidx));
7293       rmapt[cp] = 2;
7294       rmapa[cp] = globidx;
7295       cmapt[cp] = 2;
7296       cmapa[cp] = globidx;
7297       mptmp[cp] = PETSC_FALSE;
7298       cp++;
7299     } else {
7300       PetscCall(MatProductCreate(p->A, mmdata->Bloc, NULL, &mp[cp]));
7301       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
7302       PetscCall(MatProductSetFill(mp[cp], product->fill));
7303       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7304       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7305       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7306       mp[cp]->product->api_user = product->api_user;
7307       PetscCall(MatProductSetFromOptions(mp[cp]));
7308       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7309       PetscCall(ISGetIndices(glob, &globidx));
7310       rmapt[cp] = 1;
7311       cmapt[cp] = 2;
7312       cmapa[cp] = globidx;
7313       mptmp[cp] = PETSC_FALSE;
7314       cp++;
7315       PetscCall(MatProductCreate(p->B, mmdata->Bloc, NULL, &mp[cp]));
7316       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
7317       PetscCall(MatProductSetFill(mp[cp], product->fill));
7318       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7319       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7320       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7321       mp[cp]->product->api_user = product->api_user;
7322       PetscCall(MatProductSetFromOptions(mp[cp]));
7323       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7324       rmapt[cp] = 2;
7325       rmapa[cp] = p->garray;
7326       cmapt[cp] = 2;
7327       cmapa[cp] = globidx;
7328       mptmp[cp] = PETSC_FALSE;
7329       cp++;
7330     }
7331     break;
7332   case MATPRODUCT_PtAP:
7333     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));
7334     /* P is product->B */
7335     PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
7336     PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
7337     PetscCall(MatProductSetType(mp[cp], MATPRODUCT_PtAP));
7338     PetscCall(MatProductSetFill(mp[cp], product->fill));
7339     PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7340     PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7341     PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7342     mp[cp]->product->api_user = product->api_user;
7343     PetscCall(MatProductSetFromOptions(mp[cp]));
7344     PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7345     PetscCall(ISGetIndices(glob, &globidx));
7346     rmapt[cp] = 2;
7347     rmapa[cp] = globidx;
7348     cmapt[cp] = 2;
7349     cmapa[cp] = globidx;
7350     mptmp[cp] = PETSC_FALSE;
7351     cp++;
7352     if (mmdata->P_oth) {
7353       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g));
7354       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
7355       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)(a->B))->type_name));
7356       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
7357       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
7358       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
7359       PetscCall(MatProductSetFill(mp[cp], product->fill));
7360       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7361       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7362       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7363       mp[cp]->product->api_user = product->api_user;
7364       PetscCall(MatProductSetFromOptions(mp[cp]));
7365       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7366       mptmp[cp] = PETSC_TRUE;
7367       cp++;
7368       PetscCall(MatProductCreate(mmdata->Bloc, mp[1], NULL, &mp[cp]));
7369       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
7370       PetscCall(MatProductSetFill(mp[cp], product->fill));
7371       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
7372       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
7373       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
7374       mp[cp]->product->api_user = product->api_user;
7375       PetscCall(MatProductSetFromOptions(mp[cp]));
7376       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
7377       rmapt[cp] = 2;
7378       rmapa[cp] = globidx;
7379       cmapt[cp] = 2;
7380       cmapa[cp] = P_oth_idx;
7381       mptmp[cp] = PETSC_FALSE;
7382       cp++;
7383     }
7384     break;
7385   default:
7386     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
7387   }
7388   /* sanity check */
7389   if (size > 1)
7390     for (i = 0; i < cp; i++) PetscCheck(rmapt[i] != 2 || hasoffproc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected offproc map type for product %" PetscInt_FMT, i);
7391 
7392   PetscCall(PetscMalloc2(cp, &mmdata->mp, cp, &mmdata->mptmp));
7393   for (i = 0; i < cp; i++) {
7394     mmdata->mp[i]    = mp[i];
7395     mmdata->mptmp[i] = mptmp[i];
7396   }
7397   mmdata->cp             = cp;
7398   C->product->data       = mmdata;
7399   C->product->destroy    = MatDestroy_MatMatMPIAIJBACKEND;
7400   C->ops->productnumeric = MatProductNumeric_MPIAIJBACKEND;
7401 
7402   /* memory type */
7403   mmdata->mtype = PETSC_MEMTYPE_HOST;
7404   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iscuda, MATSEQAIJCUSPARSE, MATMPIAIJCUSPARSE, ""));
7405   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iship, MATSEQAIJHIPSPARSE, MATMPIAIJHIPSPARSE, ""));
7406   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iskokk, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, ""));
7407   if (iscuda) mmdata->mtype = PETSC_MEMTYPE_CUDA;
7408   else if (iship) mmdata->mtype = PETSC_MEMTYPE_HIP;
7409   else if (iskokk) mmdata->mtype = PETSC_MEMTYPE_KOKKOS;
7410 
7411   /* prepare coo coordinates for values insertion */
7412 
7413   /* count total nonzeros of those intermediate seqaij Mats
7414     ncoo_d:    # of nonzeros of matrices that do not have offproc entries
7415     ncoo_o:    # of nonzeros (of matrices that might have offproc entries) that will be inserted to remote procs
7416     ncoo_oown: # of nonzeros (of matrices that might have offproc entries) that will be inserted locally
7417   */
7418   for (cp = 0, ncoo_d = 0, ncoo_o = 0, ncoo_oown = 0; cp < mmdata->cp; cp++) {
7419     Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mp[cp]->data;
7420     if (mptmp[cp]) continue;
7421     if (rmapt[cp] == 2 && hasoffproc) { /* the rows need to be scatter to all processes (might include self) */
7422       const PetscInt *rmap = rmapa[cp];
7423       const PetscInt  mr   = mp[cp]->rmap->n;
7424       const PetscInt  rs   = C->rmap->rstart;
7425       const PetscInt  re   = C->rmap->rend;
7426       const PetscInt *ii   = mm->i;
7427       for (i = 0; i < mr; i++) {
7428         const PetscInt gr = rmap[i];
7429         const PetscInt nz = ii[i + 1] - ii[i];
7430         if (gr < rs || gr >= re) ncoo_o += nz; /* this row is offproc */
7431         else ncoo_oown += nz;                  /* this row is local */
7432       }
7433     } else ncoo_d += mm->nz;
7434   }
7435 
7436   /*
7437     ncoo: total number of nonzeros (including those inserted by remote procs) belonging to this proc
7438 
7439     ncoo = ncoo_d + ncoo_oown + ncoo2, which ncoo2 is number of nonzeros inserted to me by other procs.
7440 
7441     off[0] points to a big index array, which is shared by off[1,2,...]. Similarly, for own[0].
7442 
7443     off[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert to others
7444     own[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert locally
7445     so, off[p+1]-off[p] is the number of nonzeros that mp[p] will send to others.
7446 
7447     coo_i/j/v[]: [ncoo] row/col/val of nonzeros belonging to this proc.
7448     Ex. coo_i[]: the beginning part (of size ncoo_d + ncoo_oown) stores i of local nonzeros, and the remaining part stores i of nonzeros I will receive.
7449   */
7450   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->off)); /* +1 to make a csr-like data structure */
7451   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->own));
7452 
7453   /* gather (i,j) of nonzeros inserted by remote procs */
7454   if (hasoffproc) {
7455     PetscSF  msf;
7456     PetscInt ncoo2, *coo_i2, *coo_j2;
7457 
7458     PetscCall(PetscMalloc1(ncoo_o, &mmdata->off[0]));
7459     PetscCall(PetscMalloc1(ncoo_oown, &mmdata->own[0]));
7460     PetscCall(PetscMalloc2(ncoo_o, &coo_i, ncoo_o, &coo_j)); /* to collect (i,j) of entries to be sent to others */
7461 
7462     for (cp = 0, ncoo_o = 0; cp < mmdata->cp; cp++) {
7463       Mat_SeqAIJ *mm     = (Mat_SeqAIJ *)mp[cp]->data;
7464       PetscInt   *idxoff = mmdata->off[cp];
7465       PetscInt   *idxown = mmdata->own[cp];
7466       if (!mptmp[cp] && rmapt[cp] == 2) { /* row map is sparse */
7467         const PetscInt *rmap = rmapa[cp];
7468         const PetscInt *cmap = cmapa[cp];
7469         const PetscInt *ii   = mm->i;
7470         PetscInt       *coi  = coo_i + ncoo_o;
7471         PetscInt       *coj  = coo_j + ncoo_o;
7472         const PetscInt  mr   = mp[cp]->rmap->n;
7473         const PetscInt  rs   = C->rmap->rstart;
7474         const PetscInt  re   = C->rmap->rend;
7475         const PetscInt  cs   = C->cmap->rstart;
7476         for (i = 0; i < mr; i++) {
7477           const PetscInt *jj = mm->j + ii[i];
7478           const PetscInt  gr = rmap[i];
7479           const PetscInt  nz = ii[i + 1] - ii[i];
7480           if (gr < rs || gr >= re) { /* this is an offproc row */
7481             for (j = ii[i]; j < ii[i + 1]; j++) {
7482               *coi++    = gr;
7483               *idxoff++ = j;
7484             }
7485             if (!cmapt[cp]) { /* already global */
7486               for (j = 0; j < nz; j++) *coj++ = jj[j];
7487             } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
7488               for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
7489             } else { /* offdiag */
7490               for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
7491             }
7492             ncoo_o += nz;
7493           } else { /* this is a local row */
7494             for (j = ii[i]; j < ii[i + 1]; j++) *idxown++ = j;
7495           }
7496         }
7497       }
7498       mmdata->off[cp + 1] = idxoff;
7499       mmdata->own[cp + 1] = idxown;
7500     }
7501 
7502     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
7503     PetscCall(PetscSFSetGraphLayout(mmdata->sf, C->rmap, ncoo_o /*nleaves*/, NULL /*ilocal*/, PETSC_OWN_POINTER, coo_i));
7504     PetscCall(PetscSFGetMultiSF(mmdata->sf, &msf));
7505     PetscCall(PetscSFGetGraph(msf, &ncoo2 /*nroots*/, NULL, NULL, NULL));
7506     ncoo = ncoo_d + ncoo_oown + ncoo2;
7507     PetscCall(PetscMalloc2(ncoo, &coo_i2, ncoo, &coo_j2));
7508     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown)); /* put (i,j) of remote nonzeros at back */
7509     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown));
7510     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
7511     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
7512     PetscCall(PetscFree2(coo_i, coo_j));
7513     /* allocate MPI send buffer to collect nonzero values to be sent to remote procs */
7514     PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo_o * sizeof(PetscScalar), (void **)&mmdata->coo_w));
7515     coo_i = coo_i2;
7516     coo_j = coo_j2;
7517   } else { /* no offproc values insertion */
7518     ncoo = ncoo_d;
7519     PetscCall(PetscMalloc2(ncoo, &coo_i, ncoo, &coo_j));
7520 
7521     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
7522     PetscCall(PetscSFSetGraph(mmdata->sf, 0, 0, NULL, PETSC_OWN_POINTER, NULL, PETSC_OWN_POINTER));
7523     PetscCall(PetscSFSetUp(mmdata->sf));
7524   }
7525   mmdata->hasoffproc = hasoffproc;
7526 
7527   /* gather (i,j) of nonzeros inserted locally */
7528   for (cp = 0, ncoo_d = 0; cp < mmdata->cp; cp++) {
7529     Mat_SeqAIJ     *mm   = (Mat_SeqAIJ *)mp[cp]->data;
7530     PetscInt       *coi  = coo_i + ncoo_d;
7531     PetscInt       *coj  = coo_j + ncoo_d;
7532     const PetscInt *jj   = mm->j;
7533     const PetscInt *ii   = mm->i;
7534     const PetscInt *cmap = cmapa[cp];
7535     const PetscInt *rmap = rmapa[cp];
7536     const PetscInt  mr   = mp[cp]->rmap->n;
7537     const PetscInt  rs   = C->rmap->rstart;
7538     const PetscInt  re   = C->rmap->rend;
7539     const PetscInt  cs   = C->cmap->rstart;
7540 
7541     if (mptmp[cp]) continue;
7542     if (rmapt[cp] == 1) { /* consecutive rows */
7543       /* fill coo_i */
7544       for (i = 0; i < mr; i++) {
7545         const PetscInt gr = i + rs;
7546         for (j = ii[i]; j < ii[i + 1]; j++) coi[j] = gr;
7547       }
7548       /* fill coo_j */
7549       if (!cmapt[cp]) { /* type-0, already global */
7550         PetscCall(PetscArraycpy(coj, jj, mm->nz));
7551       } else if (cmapt[cp] == 1) {                        /* type-1, local to global for consecutive columns of C */
7552         for (j = 0; j < mm->nz; j++) coj[j] = jj[j] + cs; /* lid + col start */
7553       } else {                                            /* type-2, local to global for sparse columns */
7554         for (j = 0; j < mm->nz; j++) coj[j] = cmap[jj[j]];
7555       }
7556       ncoo_d += mm->nz;
7557     } else if (rmapt[cp] == 2) { /* sparse rows */
7558       for (i = 0; i < mr; i++) {
7559         const PetscInt *jj = mm->j + ii[i];
7560         const PetscInt  gr = rmap[i];
7561         const PetscInt  nz = ii[i + 1] - ii[i];
7562         if (gr >= rs && gr < re) { /* local rows */
7563           for (j = ii[i]; j < ii[i + 1]; j++) *coi++ = gr;
7564           if (!cmapt[cp]) { /* type-0, already global */
7565             for (j = 0; j < nz; j++) *coj++ = jj[j];
7566           } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
7567             for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
7568           } else { /* type-2, local to global for sparse columns */
7569             for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
7570           }
7571           ncoo_d += nz;
7572         }
7573       }
7574     }
7575   }
7576   if (glob) PetscCall(ISRestoreIndices(glob, &globidx));
7577   PetscCall(ISDestroy(&glob));
7578   if (P_oth_l2g) PetscCall(ISLocalToGlobalMappingRestoreIndices(P_oth_l2g, &P_oth_idx));
7579   PetscCall(ISLocalToGlobalMappingDestroy(&P_oth_l2g));
7580   /* allocate an array to store all nonzeros (inserted locally or remotely) belonging to this proc */
7581   PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo * sizeof(PetscScalar), (void **)&mmdata->coo_v));
7582 
7583   /* preallocate with COO data */
7584   PetscCall(MatSetPreallocationCOO(C, ncoo, coo_i, coo_j));
7585   PetscCall(PetscFree2(coo_i, coo_j));
7586   PetscFunctionReturn(PETSC_SUCCESS);
7587 }
7588 
7589 PetscErrorCode MatProductSetFromOptions_MPIAIJBACKEND(Mat mat)
7590 {
7591   Mat_Product *product = mat->product;
7592 #if defined(PETSC_HAVE_DEVICE)
7593   PetscBool match  = PETSC_FALSE;
7594   PetscBool usecpu = PETSC_FALSE;
7595 #else
7596   PetscBool match = PETSC_TRUE;
7597 #endif
7598 
7599   PetscFunctionBegin;
7600   MatCheckProduct(mat, 1);
7601 #if defined(PETSC_HAVE_DEVICE)
7602   if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, ((PetscObject)product->A)->type_name, &match));
7603   if (match) { /* we can always fallback to the CPU if requested */
7604     switch (product->type) {
7605     case MATPRODUCT_AB:
7606       if (product->api_user) {
7607         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
7608         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
7609         PetscOptionsEnd();
7610       } else {
7611         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
7612         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
7613         PetscOptionsEnd();
7614       }
7615       break;
7616     case MATPRODUCT_AtB:
7617       if (product->api_user) {
7618         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
7619         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
7620         PetscOptionsEnd();
7621       } else {
7622         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
7623         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
7624         PetscOptionsEnd();
7625       }
7626       break;
7627     case MATPRODUCT_PtAP:
7628       if (product->api_user) {
7629         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
7630         PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
7631         PetscOptionsEnd();
7632       } else {
7633         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
7634         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
7635         PetscOptionsEnd();
7636       }
7637       break;
7638     default:
7639       break;
7640     }
7641     match = (PetscBool)!usecpu;
7642   }
7643 #endif
7644   if (match) {
7645     switch (product->type) {
7646     case MATPRODUCT_AB:
7647     case MATPRODUCT_AtB:
7648     case MATPRODUCT_PtAP:
7649       mat->ops->productsymbolic = MatProductSymbolic_MPIAIJBACKEND;
7650       break;
7651     default:
7652       break;
7653     }
7654   }
7655   /* fallback to MPIAIJ ops */
7656   if (!mat->ops->productsymbolic) PetscCall(MatProductSetFromOptions_MPIAIJ(mat));
7657   PetscFunctionReturn(PETSC_SUCCESS);
7658 }
7659 
7660 /*
7661    Produces a set of block column indices of the matrix row, one for each block represented in the original row
7662 
7663    n - the number of block indices in cc[]
7664    cc - the block indices (must be large enough to contain the indices)
7665 */
7666 static inline PetscErrorCode MatCollapseRow(Mat Amat, PetscInt row, PetscInt bs, PetscInt *n, PetscInt *cc)
7667 {
7668   PetscInt        cnt = -1, nidx, j;
7669   const PetscInt *idx;
7670 
7671   PetscFunctionBegin;
7672   PetscCall(MatGetRow(Amat, row, &nidx, &idx, NULL));
7673   if (nidx) {
7674     cnt     = 0;
7675     cc[cnt] = idx[0] / bs;
7676     for (j = 1; j < nidx; j++) {
7677       if (cc[cnt] < idx[j] / bs) cc[++cnt] = idx[j] / bs;
7678     }
7679   }
7680   PetscCall(MatRestoreRow(Amat, row, &nidx, &idx, NULL));
7681   *n = cnt + 1;
7682   PetscFunctionReturn(PETSC_SUCCESS);
7683 }
7684 
7685 /*
7686     Produces a set of block column indices of the matrix block row, one for each block represented in the original set of rows
7687 
7688     ncollapsed - the number of block indices
7689     collapsed - the block indices (must be large enough to contain the indices)
7690 */
7691 static inline PetscErrorCode MatCollapseRows(Mat Amat, PetscInt start, PetscInt bs, PetscInt *w0, PetscInt *w1, PetscInt *w2, PetscInt *ncollapsed, PetscInt **collapsed)
7692 {
7693   PetscInt i, nprev, *cprev = w0, ncur = 0, *ccur = w1, *merged = w2, *cprevtmp;
7694 
7695   PetscFunctionBegin;
7696   PetscCall(MatCollapseRow(Amat, start, bs, &nprev, cprev));
7697   for (i = start + 1; i < start + bs; i++) {
7698     PetscCall(MatCollapseRow(Amat, i, bs, &ncur, ccur));
7699     PetscCall(PetscMergeIntArray(nprev, cprev, ncur, ccur, &nprev, &merged));
7700     cprevtmp = cprev;
7701     cprev    = merged;
7702     merged   = cprevtmp;
7703   }
7704   *ncollapsed = nprev;
7705   if (collapsed) *collapsed = cprev;
7706   PetscFunctionReturn(PETSC_SUCCESS);
7707 }
7708 
7709 /*
7710  MatCreateGraph_Simple_AIJ - create simple scalar matrix (graph) from potentially blocked matrix
7711 
7712  Input Parameter:
7713  . Amat - matrix
7714  - symmetrize - make the result symmetric
7715  + scale - scale with diagonal
7716 
7717  Output Parameter:
7718  . a_Gmat - output scalar graph >= 0
7719 
7720 */
7721 PETSC_INTERN PetscErrorCode MatCreateGraph_Simple_AIJ(Mat Amat, PetscBool symmetrize, PetscBool scale, PetscReal filter, Mat *a_Gmat)
7722 {
7723   PetscInt  Istart, Iend, Ii, jj, kk, ncols, nloc, NN, MM, bs;
7724   MPI_Comm  comm;
7725   Mat       Gmat;
7726   PetscBool ismpiaij, isseqaij;
7727   Mat       a, b, c;
7728   MatType   jtype;
7729 
7730   PetscFunctionBegin;
7731   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
7732   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
7733   PetscCall(MatGetSize(Amat, &MM, &NN));
7734   PetscCall(MatGetBlockSize(Amat, &bs));
7735   nloc = (Iend - Istart) / bs;
7736 
7737   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATSEQAIJ, &isseqaij));
7738   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATMPIAIJ, &ismpiaij));
7739   PetscCheck(isseqaij || ismpiaij, comm, PETSC_ERR_USER, "Require (MPI)AIJ matrix type");
7740 
7741   /* TODO GPU: these calls are potentially expensive if matrices are large and we want to use the GPU */
7742   /* A solution consists in providing a new API, MatAIJGetCollapsedAIJ, and each class can provide a fast
7743      implementation */
7744   if (bs > 1) {
7745     PetscCall(MatGetType(Amat, &jtype));
7746     PetscCall(MatCreate(comm, &Gmat));
7747     PetscCall(MatSetType(Gmat, jtype));
7748     PetscCall(MatSetSizes(Gmat, nloc, nloc, PETSC_DETERMINE, PETSC_DETERMINE));
7749     PetscCall(MatSetBlockSizes(Gmat, 1, 1));
7750     if (isseqaij || ((Mat_MPIAIJ *)Amat->data)->garray) {
7751       PetscInt  *d_nnz, *o_nnz;
7752       MatScalar *aa, val, *AA;
7753       PetscInt  *aj, *ai, *AJ, nc, nmax = 0;
7754       if (isseqaij) {
7755         a = Amat;
7756         b = NULL;
7757       } else {
7758         Mat_MPIAIJ *d = (Mat_MPIAIJ *)Amat->data;
7759         a             = d->A;
7760         b             = d->B;
7761       }
7762       PetscCall(PetscInfo(Amat, "New bs>1 Graph. nloc=%" PetscInt_FMT "\n", nloc));
7763       PetscCall(PetscMalloc2(nloc, &d_nnz, isseqaij ? 0 : nloc, &o_nnz));
7764       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
7765         PetscInt       *nnz = (c == a) ? d_nnz : o_nnz;
7766         const PetscInt *cols1, *cols2;
7767         for (PetscInt brow = 0, nc1, nc2, ok = 1; brow < nloc * bs; brow += bs) { // block rows
7768           PetscCall(MatGetRow(c, brow, &nc2, &cols2, NULL));
7769           nnz[brow / bs] = nc2 / bs;
7770           if (nc2 % bs) ok = 0;
7771           if (nnz[brow / bs] > nmax) nmax = nnz[brow / bs];
7772           for (PetscInt ii = 1; ii < bs; ii++) { // check for non-dense blocks
7773             PetscCall(MatGetRow(c, brow + ii, &nc1, &cols1, NULL));
7774             if (nc1 != nc2) ok = 0;
7775             else {
7776               for (PetscInt jj = 0; jj < nc1 && ok == 1; jj++) {
7777                 if (cols1[jj] != cols2[jj]) ok = 0;
7778                 if (cols1[jj] % bs != jj % bs) ok = 0;
7779               }
7780             }
7781             PetscCall(MatRestoreRow(c, brow + ii, &nc1, &cols1, NULL));
7782           }
7783           PetscCall(MatRestoreRow(c, brow, &nc2, &cols2, NULL));
7784           if (!ok) {
7785             PetscCall(PetscFree2(d_nnz, o_nnz));
7786             PetscCall(PetscInfo(Amat, "Found sparse blocks - revert to slow method\n"));
7787             goto old_bs;
7788           }
7789         }
7790       }
7791       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
7792       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
7793       PetscCall(PetscFree2(d_nnz, o_nnz));
7794       PetscCall(PetscMalloc2(nmax, &AA, nmax, &AJ));
7795       // diag
7796       for (PetscInt brow = 0, n, grow; brow < nloc * bs; brow += bs) { // block rows
7797         Mat_SeqAIJ *aseq = (Mat_SeqAIJ *)a->data;
7798         ai               = aseq->i;
7799         n                = ai[brow + 1] - ai[brow];
7800         aj               = aseq->j + ai[brow];
7801         for (int k = 0; k < n; k += bs) {        // block columns
7802           AJ[k / bs] = aj[k] / bs + Istart / bs; // diag starts at (Istart,Istart)
7803           val        = 0;
7804           for (int ii = 0; ii < bs; ii++) { // rows in block
7805             aa = aseq->a + ai[brow + ii] + k;
7806             for (int jj = 0; jj < bs; jj++) {         // columns in block
7807               val += PetscAbs(PetscRealPart(aa[jj])); // a sort of norm
7808             }
7809           }
7810           PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%d) >= nmax (%d)", (int)(k / bs), (int)nmax);
7811           AA[k / bs] = val;
7812         }
7813         grow = Istart / bs + brow / bs;
7814         PetscCall(MatSetValues(Gmat, 1, &grow, n / bs, AJ, AA, INSERT_VALUES));
7815       }
7816       // off-diag
7817       if (ismpiaij) {
7818         Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)Amat->data;
7819         const PetscScalar *vals;
7820         const PetscInt    *cols, *garray = aij->garray;
7821         PetscCheck(garray, PETSC_COMM_SELF, PETSC_ERR_USER, "No garray ?");
7822         for (PetscInt brow = 0, grow; brow < nloc * bs; brow += bs) { // block rows
7823           PetscCall(MatGetRow(b, brow, &ncols, &cols, NULL));
7824           for (int k = 0, cidx = 0; k < ncols; k += bs, cidx++) {
7825             PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs >= nmax");
7826             AA[k / bs] = 0;
7827             AJ[cidx]   = garray[cols[k]] / bs;
7828           }
7829           nc = ncols / bs;
7830           PetscCall(MatRestoreRow(b, brow, &ncols, &cols, NULL));
7831           for (int ii = 0; ii < bs; ii++) { // rows in block
7832             PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
7833             for (int k = 0; k < ncols; k += bs) {
7834               for (int jj = 0; jj < bs; jj++) { // cols in block
7835                 PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%d) >= nmax (%d)", (int)(k / bs), (int)nmax);
7836                 AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
7837               }
7838             }
7839             PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
7840           }
7841           grow = Istart / bs + brow / bs;
7842           PetscCall(MatSetValues(Gmat, 1, &grow, nc, AJ, AA, INSERT_VALUES));
7843         }
7844       }
7845       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
7846       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
7847       PetscCall(PetscFree2(AA, AJ));
7848     } else {
7849       const PetscScalar *vals;
7850       const PetscInt    *idx;
7851       PetscInt          *d_nnz, *o_nnz, *w0, *w1, *w2;
7852     old_bs:
7853       /*
7854        Determine the preallocation needed for the scalar matrix derived from the vector matrix.
7855        */
7856       PetscCall(PetscInfo(Amat, "OLD bs>1 CreateGraph\n"));
7857       PetscCall(PetscMalloc2(nloc, &d_nnz, isseqaij ? 0 : nloc, &o_nnz));
7858       if (isseqaij) {
7859         PetscInt max_d_nnz;
7860         /*
7861          Determine exact preallocation count for (sequential) scalar matrix
7862          */
7863         PetscCall(MatSeqAIJGetMaxRowNonzeros(Amat, &max_d_nnz));
7864         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
7865         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
7866         for (Ii = 0, jj = 0; Ii < Iend; Ii += bs, jj++) PetscCall(MatCollapseRows(Amat, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
7867         PetscCall(PetscFree3(w0, w1, w2));
7868       } else if (ismpiaij) {
7869         Mat             Daij, Oaij;
7870         const PetscInt *garray;
7871         PetscInt        max_d_nnz;
7872         PetscCall(MatMPIAIJGetSeqAIJ(Amat, &Daij, &Oaij, &garray));
7873         /*
7874          Determine exact preallocation count for diagonal block portion of scalar matrix
7875          */
7876         PetscCall(MatSeqAIJGetMaxRowNonzeros(Daij, &max_d_nnz));
7877         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
7878         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
7879         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) PetscCall(MatCollapseRows(Daij, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
7880         PetscCall(PetscFree3(w0, w1, w2));
7881         /*
7882          Over estimate (usually grossly over), preallocation count for off-diagonal portion of scalar matrix
7883          */
7884         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
7885           o_nnz[jj] = 0;
7886           for (kk = 0; kk < bs; kk++) { /* rows that get collapsed to a single row */
7887             PetscCall(MatGetRow(Oaij, Ii + kk, &ncols, NULL, NULL));
7888             o_nnz[jj] += ncols;
7889             PetscCall(MatRestoreRow(Oaij, Ii + kk, &ncols, NULL, NULL));
7890           }
7891           if (o_nnz[jj] > (NN / bs - nloc)) o_nnz[jj] = NN / bs - nloc;
7892         }
7893       } else SETERRQ(comm, PETSC_ERR_USER, "Require AIJ matrix type");
7894       /* get scalar copy (norms) of matrix */
7895       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
7896       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
7897       PetscCall(PetscFree2(d_nnz, o_nnz));
7898       for (Ii = Istart; Ii < Iend; Ii++) {
7899         PetscInt dest_row = Ii / bs;
7900         PetscCall(MatGetRow(Amat, Ii, &ncols, &idx, &vals));
7901         for (jj = 0; jj < ncols; jj++) {
7902           PetscInt    dest_col = idx[jj] / bs;
7903           PetscScalar sv       = PetscAbs(PetscRealPart(vals[jj]));
7904           PetscCall(MatSetValues(Gmat, 1, &dest_row, 1, &dest_col, &sv, ADD_VALUES));
7905         }
7906         PetscCall(MatRestoreRow(Amat, Ii, &ncols, &idx, &vals));
7907       }
7908       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
7909       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
7910     }
7911   } else {
7912     if (symmetrize || filter >= 0 || scale) PetscCall(MatDuplicate(Amat, MAT_COPY_VALUES, &Gmat));
7913     else {
7914       Gmat = Amat;
7915       PetscCall(PetscObjectReference((PetscObject)Gmat));
7916     }
7917     if (isseqaij) {
7918       a = Gmat;
7919       b = NULL;
7920     } else {
7921       Mat_MPIAIJ *d = (Mat_MPIAIJ *)Gmat->data;
7922       a             = d->A;
7923       b             = d->B;
7924     }
7925     if (filter >= 0 || scale) {
7926       /* take absolute value of each entry */
7927       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
7928         MatInfo      info;
7929         PetscScalar *avals;
7930         PetscCall(MatGetInfo(c, MAT_LOCAL, &info));
7931         PetscCall(MatSeqAIJGetArray(c, &avals));
7932         for (int jj = 0; jj < info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
7933         PetscCall(MatSeqAIJRestoreArray(c, &avals));
7934       }
7935     }
7936   }
7937   if (symmetrize) {
7938     PetscBool isset, issym;
7939     PetscCall(MatIsSymmetricKnown(Amat, &isset, &issym));
7940     if (!isset || !issym) {
7941       Mat matTrans;
7942       PetscCall(MatTranspose(Gmat, MAT_INITIAL_MATRIX, &matTrans));
7943       PetscCall(MatAXPY(Gmat, 1.0, matTrans, Gmat->structurally_symmetric == PETSC_BOOL3_TRUE ? SAME_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN));
7944       PetscCall(MatDestroy(&matTrans));
7945     }
7946     PetscCall(MatSetOption(Gmat, MAT_SYMMETRIC, PETSC_TRUE));
7947   } else if (Amat != Gmat) PetscCall(MatPropagateSymmetryOptions(Amat, Gmat));
7948   if (scale) {
7949     /* scale c for all diagonal values = 1 or -1 */
7950     Vec diag;
7951     PetscCall(MatCreateVecs(Gmat, &diag, NULL));
7952     PetscCall(MatGetDiagonal(Gmat, diag));
7953     PetscCall(VecReciprocal(diag));
7954     PetscCall(VecSqrtAbs(diag));
7955     PetscCall(MatDiagonalScale(Gmat, diag, diag));
7956     PetscCall(VecDestroy(&diag));
7957   }
7958   PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_graph_view"));
7959 
7960   if (filter >= 0) {
7961     PetscCall(MatFilter(Gmat, filter, PETSC_TRUE, PETSC_TRUE));
7962     PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_filter_graph_view"));
7963   }
7964   *a_Gmat = Gmat;
7965   PetscFunctionReturn(PETSC_SUCCESS);
7966 }
7967 
7968 /*
7969     Special version for direct calls from Fortran
7970 */
7971 #include <petsc/private/fortranimpl.h>
7972 
7973 /* Change these macros so can be used in void function */
7974 /* Identical to PetscCallVoid, except it assigns to *_ierr */
7975 #undef PetscCall
7976 #define PetscCall(...) \
7977   do { \
7978     PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__; \
7979     if (PetscUnlikely(ierr_msv_mpiaij)) { \
7980       *_ierr = PetscError(PETSC_COMM_SELF, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr_msv_mpiaij, PETSC_ERROR_REPEAT, " "); \
7981       return; \
7982     } \
7983   } while (0)
7984 
7985 #undef SETERRQ
7986 #define SETERRQ(comm, ierr, ...) \
7987   do { \
7988     *_ierr = PetscError(comm, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr, PETSC_ERROR_INITIAL, __VA_ARGS__); \
7989     return; \
7990   } while (0)
7991 
7992 #if defined(PETSC_HAVE_FORTRAN_CAPS)
7993   #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
7994 #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
7995   #define matsetvaluesmpiaij_ matsetvaluesmpiaij
7996 #else
7997 #endif
7998 PETSC_EXTERN void matsetvaluesmpiaij_(Mat *mmat, PetscInt *mm, const PetscInt im[], PetscInt *mn, const PetscInt in[], const PetscScalar v[], InsertMode *maddv, PetscErrorCode *_ierr)
7999 {
8000   Mat         mat = *mmat;
8001   PetscInt    m = *mm, n = *mn;
8002   InsertMode  addv = *maddv;
8003   Mat_MPIAIJ *aij  = (Mat_MPIAIJ *)mat->data;
8004   PetscScalar value;
8005 
8006   MatCheckPreallocated(mat, 1);
8007   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
8008   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
8009   {
8010     PetscInt  i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
8011     PetscInt  cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
8012     PetscBool roworiented = aij->roworiented;
8013 
8014     /* Some Variables required in the macro */
8015     Mat         A     = aij->A;
8016     Mat_SeqAIJ *a     = (Mat_SeqAIJ *)A->data;
8017     PetscInt   *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
8018     MatScalar  *aa;
8019     PetscBool   ignorezeroentries = (((a->ignorezeroentries) && (addv == ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
8020     Mat         B                 = aij->B;
8021     Mat_SeqAIJ *b                 = (Mat_SeqAIJ *)B->data;
8022     PetscInt   *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j, bm = aij->B->rmap->n, am = aij->A->rmap->n;
8023     MatScalar  *ba;
8024     /* This variable below is only for the PETSC_HAVE_VIENNACL or PETSC_HAVE_CUDA cases, but we define it in all cases because we
8025      * cannot use "#if defined" inside a macro. */
8026     PETSC_UNUSED PetscBool inserted = PETSC_FALSE;
8027 
8028     PetscInt  *rp1, *rp2, ii, nrow1, nrow2, _i, rmax1, rmax2, N, low1, high1, low2, high2, t, lastcol1, lastcol2;
8029     PetscInt   nonew = a->nonew;
8030     MatScalar *ap1, *ap2;
8031 
8032     PetscFunctionBegin;
8033     PetscCall(MatSeqAIJGetArray(A, &aa));
8034     PetscCall(MatSeqAIJGetArray(B, &ba));
8035     for (i = 0; i < m; i++) {
8036       if (im[i] < 0) continue;
8037       PetscCheck(im[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, im[i], mat->rmap->N - 1);
8038       if (im[i] >= rstart && im[i] < rend) {
8039         row      = im[i] - rstart;
8040         lastcol1 = -1;
8041         rp1      = aj + ai[row];
8042         ap1      = aa + ai[row];
8043         rmax1    = aimax[row];
8044         nrow1    = ailen[row];
8045         low1     = 0;
8046         high1    = nrow1;
8047         lastcol2 = -1;
8048         rp2      = bj + bi[row];
8049         ap2      = ba + bi[row];
8050         rmax2    = bimax[row];
8051         nrow2    = bilen[row];
8052         low2     = 0;
8053         high2    = nrow2;
8054 
8055         for (j = 0; j < n; j++) {
8056           if (roworiented) value = v[i * n + j];
8057           else value = v[i + j * m];
8058           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
8059           if (in[j] >= cstart && in[j] < cend) {
8060             col = in[j] - cstart;
8061             MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
8062           } else if (in[j] < 0) continue;
8063           else if (PetscUnlikelyDebug(in[j] >= mat->cmap->N)) {
8064             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
8065           } else {
8066             if (mat->was_assembled) {
8067               if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
8068 #if defined(PETSC_USE_CTABLE)
8069               PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col));
8070               col--;
8071 #else
8072               col = aij->colmap[in[j]] - 1;
8073 #endif
8074               if (col < 0 && !((Mat_SeqAIJ *)(aij->A->data))->nonew) {
8075                 PetscCall(MatDisAssemble_MPIAIJ(mat));
8076                 col = in[j];
8077                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
8078                 B        = aij->B;
8079                 b        = (Mat_SeqAIJ *)B->data;
8080                 bimax    = b->imax;
8081                 bi       = b->i;
8082                 bilen    = b->ilen;
8083                 bj       = b->j;
8084                 rp2      = bj + bi[row];
8085                 ap2      = ba + bi[row];
8086                 rmax2    = bimax[row];
8087                 nrow2    = bilen[row];
8088                 low2     = 0;
8089                 high2    = nrow2;
8090                 bm       = aij->B->rmap->n;
8091                 ba       = b->a;
8092                 inserted = PETSC_FALSE;
8093               }
8094             } else col = in[j];
8095             MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
8096           }
8097         }
8098       } else if (!aij->donotstash) {
8099         if (roworiented) {
8100           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, v + i * n, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
8101         } else {
8102           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, v + i, m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
8103         }
8104       }
8105     }
8106     PetscCall(MatSeqAIJRestoreArray(A, &aa));
8107     PetscCall(MatSeqAIJRestoreArray(B, &ba));
8108   }
8109   PetscFunctionReturnVoid();
8110 }
8111 
8112 /* Undefining these here since they were redefined from their original definition above! No
8113  * other PETSc functions should be defined past this point, as it is impossible to recover the
8114  * original definitions */
8115 #undef PetscCall
8116 #undef SETERRQ
8117