xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 16a9b8de2019c191953d52ed8be9fc0021dcda4c)
1 
2 /*
3   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
4           C = A * B
5 */
6 
7 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
8 #include <../src/mat/utils/freespace.h>
9 #include <petscbt.h>
10 #include <petsc/private/isimpl.h>
11 #include <../src/mat/impls/dense/seq/dense.h>
12 
13 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
14 {
15   PetscFunctionBegin;
16   if (C->ops->matmultnumeric) PetscCall((*C->ops->matmultnumeric)(A, B, C));
17   else PetscCall(MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(A, B, C));
18   PetscFunctionReturn(PETSC_SUCCESS);
19 }
20 
21 /* Modified from MatCreateSeqAIJWithArrays() */
22 PETSC_INTERN PetscErrorCode MatSetSeqAIJWithArrays_private(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt i[], PetscInt j[], PetscScalar a[], MatType mtype, Mat mat)
23 {
24   PetscInt    ii;
25   Mat_SeqAIJ *aij;
26   PetscBool   isseqaij, osingle, ofree_a, ofree_ij;
27 
28   PetscFunctionBegin;
29   PetscCheck(m <= 0 || !i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
30   PetscCall(MatSetSizes(mat, m, n, m, n));
31 
32   if (!mtype) {
33     PetscCall(PetscObjectBaseTypeCompare((PetscObject)mat, MATSEQAIJ, &isseqaij));
34     if (!isseqaij) PetscCall(MatSetType(mat, MATSEQAIJ));
35   } else {
36     PetscCall(MatSetType(mat, mtype));
37   }
38 
39   aij      = (Mat_SeqAIJ *)(mat)->data;
40   osingle  = aij->singlemalloc;
41   ofree_a  = aij->free_a;
42   ofree_ij = aij->free_ij;
43   /* changes the free flags */
44   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(mat, MAT_SKIP_ALLOCATION, NULL));
45 
46   PetscCall(PetscFree(aij->ilen));
47   PetscCall(PetscFree(aij->imax));
48   PetscCall(PetscMalloc1(m, &aij->imax));
49   PetscCall(PetscMalloc1(m, &aij->ilen));
50   for (ii = 0, aij->nonzerorowcnt = 0, aij->rmax = 0; ii < m; ii++) {
51     const PetscInt rnz = i[ii + 1] - i[ii];
52     aij->nonzerorowcnt += !!rnz;
53     aij->rmax     = PetscMax(aij->rmax, rnz);
54     aij->ilen[ii] = aij->imax[ii] = i[ii + 1] - i[ii];
55   }
56   aij->maxnz = i[m];
57   aij->nz    = i[m];
58 
59   if (osingle) {
60     PetscCall(PetscFree3(aij->a, aij->j, aij->i));
61   } else {
62     if (ofree_a) PetscCall(PetscFree(aij->a));
63     if (ofree_ij) PetscCall(PetscFree(aij->j));
64     if (ofree_ij) PetscCall(PetscFree(aij->i));
65   }
66   aij->i     = i;
67   aij->j     = j;
68   aij->a     = a;
69   aij->nonew = -1; /* this indicates that inserting a new value in the matrix that generates a new nonzero is an error */
70   /* default to not retain ownership */
71   aij->singlemalloc = PETSC_FALSE;
72   aij->free_a       = PETSC_FALSE;
73   aij->free_ij      = PETSC_FALSE;
74   PetscCall(MatCheckCompressedRow(mat, aij->nonzerorowcnt, &aij->compressedrow, aij->i, m, 0.6));
75   PetscFunctionReturn(PETSC_SUCCESS);
76 }
77 
78 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
79 {
80   Mat_Product        *product = C->product;
81   MatProductAlgorithm alg;
82   PetscBool           flg;
83 
84   PetscFunctionBegin;
85   if (product) {
86     alg = product->alg;
87   } else {
88     alg = "sorted";
89   }
90   /* sorted */
91   PetscCall(PetscStrcmp(alg, "sorted", &flg));
92   if (flg) {
93     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(A, B, fill, C));
94     PetscFunctionReturn(PETSC_SUCCESS);
95   }
96 
97   /* scalable */
98   PetscCall(PetscStrcmp(alg, "scalable", &flg));
99   if (flg) {
100     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A, B, fill, C));
101     PetscFunctionReturn(PETSC_SUCCESS);
102   }
103 
104   /* scalable_fast */
105   PetscCall(PetscStrcmp(alg, "scalable_fast", &flg));
106   if (flg) {
107     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A, B, fill, C));
108     PetscFunctionReturn(PETSC_SUCCESS);
109   }
110 
111   /* heap */
112   PetscCall(PetscStrcmp(alg, "heap", &flg));
113   if (flg) {
114     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A, B, fill, C));
115     PetscFunctionReturn(PETSC_SUCCESS);
116   }
117 
118   /* btheap */
119   PetscCall(PetscStrcmp(alg, "btheap", &flg));
120   if (flg) {
121     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A, B, fill, C));
122     PetscFunctionReturn(PETSC_SUCCESS);
123   }
124 
125   /* llcondensed */
126   PetscCall(PetscStrcmp(alg, "llcondensed", &flg));
127   if (flg) {
128     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A, B, fill, C));
129     PetscFunctionReturn(PETSC_SUCCESS);
130   }
131 
132   /* rowmerge */
133   PetscCall(PetscStrcmp(alg, "rowmerge", &flg));
134   if (flg) {
135     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(A, B, fill, C));
136     PetscFunctionReturn(PETSC_SUCCESS);
137   }
138 
139 #if defined(PETSC_HAVE_HYPRE)
140   PetscCall(PetscStrcmp(alg, "hypre", &flg));
141   if (flg) {
142     PetscCall(MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A, B, fill, C));
143     PetscFunctionReturn(PETSC_SUCCESS);
144   }
145 #endif
146 
147   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
148 }
149 
150 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A, Mat B, PetscReal fill, Mat C)
151 {
152   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
153   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
154   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
155   PetscReal          afill;
156   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
157   PetscHMapI         ta;
158   PetscBT            lnkbt;
159   PetscFreeSpaceList free_space = NULL, current_space = NULL;
160 
161   PetscFunctionBegin;
162   /* Get ci and cj */
163   /* Allocate ci array, arrays for fill computation and */
164   /* free space for accumulating nonzero column info */
165   PetscCall(PetscMalloc1(am + 2, &ci));
166   ci[0] = 0;
167 
168   /* create and initialize a linked list */
169   PetscCall(PetscHMapICreateWithSize(bn, &ta));
170   MatRowMergeMax_SeqAIJ(b, bm, ta);
171   PetscCall(PetscHMapIGetSize(ta, &Crmax));
172   PetscCall(PetscHMapIDestroy(&ta));
173 
174   PetscCall(PetscLLCondensedCreate(Crmax, bn, &lnk, &lnkbt));
175 
176   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
177   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
178 
179   current_space = free_space;
180 
181   /* Determine ci and cj */
182   for (i = 0; i < am; i++) {
183     anzi = ai[i + 1] - ai[i];
184     aj   = a->j + ai[i];
185     for (j = 0; j < anzi; j++) {
186       brow = aj[j];
187       bnzj = bi[brow + 1] - bi[brow];
188       bj   = b->j + bi[brow];
189       /* add non-zero cols of B into the sorted linked list lnk */
190       PetscCall(PetscLLCondensedAddSorted(bnzj, bj, lnk, lnkbt));
191     }
192     /* add possible missing diagonal entry */
193     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted(1, &i, lnk, lnkbt));
194     cnzi = lnk[0];
195 
196     /* If free space is not available, make more free space */
197     /* Double the amount of total space in the list */
198     if (current_space->local_remaining < cnzi) {
199       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
200       ndouble++;
201     }
202 
203     /* Copy data into free space, then initialize lnk */
204     PetscCall(PetscLLCondensedClean(bn, cnzi, current_space->array, lnk, lnkbt));
205 
206     current_space->array += cnzi;
207     current_space->local_used += cnzi;
208     current_space->local_remaining -= cnzi;
209 
210     ci[i + 1] = ci[i] + cnzi;
211   }
212 
213   /* Column indices are in the list of free space */
214   /* Allocate space for cj, initialize cj, and */
215   /* destroy list of free space and other temporary array(s) */
216   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
217   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
218   PetscCall(PetscLLCondensedDestroy(lnk, lnkbt));
219 
220   /* put together the new symbolic matrix */
221   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
222   PetscCall(MatSetBlockSizesFromMats(C, A, B));
223 
224   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
225   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
226   c          = (Mat_SeqAIJ *)(C->data);
227   c->free_a  = PETSC_FALSE;
228   c->free_ij = PETSC_TRUE;
229   c->nonew   = 0;
230 
231   /* fast, needs non-scalable O(bn) array 'abdense' */
232   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
233 
234   /* set MatInfo */
235   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
236   if (afill < 1.0) afill = 1.0;
237   C->info.mallocs           = ndouble;
238   C->info.fill_ratio_given  = fill;
239   C->info.fill_ratio_needed = afill;
240 
241 #if defined(PETSC_USE_INFO)
242   if (ci[am]) {
243     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
244     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
245   } else {
246     PetscCall(PetscInfo(C, "Empty matrix product\n"));
247   }
248 #endif
249   PetscFunctionReturn(PETSC_SUCCESS);
250 }
251 
252 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat A, Mat B, Mat C)
253 {
254   PetscLogDouble     flops = 0.0;
255   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
256   Mat_SeqAIJ        *b     = (Mat_SeqAIJ *)B->data;
257   Mat_SeqAIJ        *c     = (Mat_SeqAIJ *)C->data;
258   PetscInt          *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bjj, *ci = c->i, *cj = c->j;
259   PetscInt           am = A->rmap->n, cm = C->rmap->n;
260   PetscInt           i, j, k, anzi, bnzi, cnzi, brow;
261   PetscScalar       *ca, valtmp;
262   PetscScalar       *ab_dense;
263   PetscContainer     cab_dense;
264   const PetscScalar *aa, *ba, *baj;
265 
266   PetscFunctionBegin;
267   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
268   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
269   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
270     PetscCall(PetscMalloc1(ci[cm] + 1, &ca));
271     c->a      = ca;
272     c->free_a = PETSC_TRUE;
273   } else ca = c->a;
274 
275   /* TODO this should be done in the symbolic phase */
276   /* However, this function is so heavily used (sometimes in an hidden way through multnumeric function pointers
277      that is hard to eradicate) */
278   PetscCall(PetscObjectQuery((PetscObject)C, "__PETSc__ab_dense", (PetscObject *)&cab_dense));
279   if (!cab_dense) {
280     PetscCall(PetscMalloc1(B->cmap->N, &ab_dense));
281     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &cab_dense));
282     PetscCall(PetscContainerSetPointer(cab_dense, ab_dense));
283     PetscCall(PetscContainerSetUserDestroy(cab_dense, PetscContainerUserDestroyDefault));
284     PetscCall(PetscObjectCompose((PetscObject)C, "__PETSc__ab_dense", (PetscObject)cab_dense));
285     PetscCall(PetscObjectDereference((PetscObject)cab_dense));
286   }
287   PetscCall(PetscContainerGetPointer(cab_dense, (void **)&ab_dense));
288   PetscCall(PetscArrayzero(ab_dense, B->cmap->N));
289 
290   /* clean old values in C */
291   PetscCall(PetscArrayzero(ca, ci[cm]));
292   /* Traverse A row-wise. */
293   /* Build the ith row in C by summing over nonzero columns in A, */
294   /* the rows of B corresponding to nonzeros of A. */
295   for (i = 0; i < am; i++) {
296     anzi = ai[i + 1] - ai[i];
297     for (j = 0; j < anzi; j++) {
298       brow = aj[j];
299       bnzi = bi[brow + 1] - bi[brow];
300       bjj  = bj + bi[brow];
301       baj  = ba + bi[brow];
302       /* perform dense axpy */
303       valtmp = aa[j];
304       for (k = 0; k < bnzi; k++) ab_dense[bjj[k]] += valtmp * baj[k];
305       flops += 2 * bnzi;
306     }
307     aj += anzi;
308     aa += anzi;
309 
310     cnzi = ci[i + 1] - ci[i];
311     for (k = 0; k < cnzi; k++) {
312       ca[k] += ab_dense[cj[k]];
313       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
314     }
315     flops += cnzi;
316     cj += cnzi;
317     ca += cnzi;
318   }
319 #if defined(PETSC_HAVE_DEVICE)
320   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
321 #endif
322   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
323   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
324   PetscCall(PetscLogFlops(flops));
325   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
326   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
327   PetscFunctionReturn(PETSC_SUCCESS);
328 }
329 
330 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A, Mat B, Mat C)
331 {
332   PetscLogDouble     flops = 0.0;
333   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
334   Mat_SeqAIJ        *b     = (Mat_SeqAIJ *)B->data;
335   Mat_SeqAIJ        *c     = (Mat_SeqAIJ *)C->data;
336   PetscInt          *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bjj, *ci = c->i, *cj = c->j;
337   PetscInt           am = A->rmap->N, cm = C->rmap->N;
338   PetscInt           i, j, k, anzi, bnzi, cnzi, brow;
339   PetscScalar       *ca = c->a, valtmp;
340   const PetscScalar *aa, *ba, *baj;
341   PetscInt           nextb;
342 
343   PetscFunctionBegin;
344   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
345   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
346   if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
347     PetscCall(PetscMalloc1(ci[cm] + 1, &ca));
348     c->a      = ca;
349     c->free_a = PETSC_TRUE;
350   }
351 
352   /* clean old values in C */
353   PetscCall(PetscArrayzero(ca, ci[cm]));
354   /* Traverse A row-wise. */
355   /* Build the ith row in C by summing over nonzero columns in A, */
356   /* the rows of B corresponding to nonzeros of A. */
357   for (i = 0; i < am; i++) {
358     anzi = ai[i + 1] - ai[i];
359     cnzi = ci[i + 1] - ci[i];
360     for (j = 0; j < anzi; j++) {
361       brow = aj[j];
362       bnzi = bi[brow + 1] - bi[brow];
363       bjj  = bj + bi[brow];
364       baj  = ba + bi[brow];
365       /* perform sparse axpy */
366       valtmp = aa[j];
367       nextb  = 0;
368       for (k = 0; nextb < bnzi; k++) {
369         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
370           ca[k] += valtmp * baj[nextb++];
371         }
372       }
373       flops += 2 * bnzi;
374     }
375     aj += anzi;
376     aa += anzi;
377     cj += cnzi;
378     ca += cnzi;
379   }
380 #if defined(PETSC_HAVE_DEVICE)
381   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
382 #endif
383   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
384   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
385   PetscCall(PetscLogFlops(flops));
386   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
387   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
388   PetscFunctionReturn(PETSC_SUCCESS);
389 }
390 
391 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A, Mat B, PetscReal fill, Mat C)
392 {
393   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
394   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
395   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
396   MatScalar         *ca;
397   PetscReal          afill;
398   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
399   PetscHMapI         ta;
400   PetscFreeSpaceList free_space = NULL, current_space = NULL;
401 
402   PetscFunctionBegin;
403   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
404   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
405   PetscCall(PetscMalloc1(am + 2, &ci));
406   ci[0] = 0;
407 
408   /* create and initialize a linked list */
409   PetscCall(PetscHMapICreateWithSize(bn, &ta));
410   MatRowMergeMax_SeqAIJ(b, bm, ta);
411   PetscCall(PetscHMapIGetSize(ta, &Crmax));
412   PetscCall(PetscHMapIDestroy(&ta));
413 
414   PetscCall(PetscLLCondensedCreate_fast(Crmax, &lnk));
415 
416   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
417   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
418   current_space = free_space;
419 
420   /* Determine ci and cj */
421   for (i = 0; i < am; i++) {
422     anzi = ai[i + 1] - ai[i];
423     aj   = a->j + ai[i];
424     for (j = 0; j < anzi; j++) {
425       brow = aj[j];
426       bnzj = bi[brow + 1] - bi[brow];
427       bj   = b->j + bi[brow];
428       /* add non-zero cols of B into the sorted linked list lnk */
429       PetscCall(PetscLLCondensedAddSorted_fast(bnzj, bj, lnk));
430     }
431     /* add possible missing diagonal entry */
432     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted_fast(1, &i, lnk));
433     cnzi = lnk[1];
434 
435     /* If free space is not available, make more free space */
436     /* Double the amount of total space in the list */
437     if (current_space->local_remaining < cnzi) {
438       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
439       ndouble++;
440     }
441 
442     /* Copy data into free space, then initialize lnk */
443     PetscCall(PetscLLCondensedClean_fast(cnzi, current_space->array, lnk));
444 
445     current_space->array += cnzi;
446     current_space->local_used += cnzi;
447     current_space->local_remaining -= cnzi;
448 
449     ci[i + 1] = ci[i] + cnzi;
450   }
451 
452   /* Column indices are in the list of free space */
453   /* Allocate space for cj, initialize cj, and */
454   /* destroy list of free space and other temporary array(s) */
455   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
456   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
457   PetscCall(PetscLLCondensedDestroy_fast(lnk));
458 
459   /* Allocate space for ca */
460   PetscCall(PetscCalloc1(ci[am] + 1, &ca));
461 
462   /* put together the new symbolic matrix */
463   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, ca, ((PetscObject)A)->type_name, C));
464   PetscCall(MatSetBlockSizesFromMats(C, A, B));
465 
466   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
467   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
468   c          = (Mat_SeqAIJ *)(C->data);
469   c->free_a  = PETSC_TRUE;
470   c->free_ij = PETSC_TRUE;
471   c->nonew   = 0;
472 
473   /* slower, less memory */
474   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;
475 
476   /* set MatInfo */
477   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
478   if (afill < 1.0) afill = 1.0;
479   C->info.mallocs           = ndouble;
480   C->info.fill_ratio_given  = fill;
481   C->info.fill_ratio_needed = afill;
482 
483 #if defined(PETSC_USE_INFO)
484   if (ci[am]) {
485     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
486     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
487   } else {
488     PetscCall(PetscInfo(C, "Empty matrix product\n"));
489   }
490 #endif
491   PetscFunctionReturn(PETSC_SUCCESS);
492 }
493 
494 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A, Mat B, PetscReal fill, Mat C)
495 {
496   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
497   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
498   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
499   MatScalar         *ca;
500   PetscReal          afill;
501   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
502   PetscHMapI         ta;
503   PetscFreeSpaceList free_space = NULL, current_space = NULL;
504 
505   PetscFunctionBegin;
506   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
507   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
508   PetscCall(PetscMalloc1(am + 2, &ci));
509   ci[0] = 0;
510 
511   /* create and initialize a linked list */
512   PetscCall(PetscHMapICreateWithSize(bn, &ta));
513   MatRowMergeMax_SeqAIJ(b, bm, ta);
514   PetscCall(PetscHMapIGetSize(ta, &Crmax));
515   PetscCall(PetscHMapIDestroy(&ta));
516   PetscCall(PetscLLCondensedCreate_Scalable(Crmax, &lnk));
517 
518   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
519   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
520   current_space = free_space;
521 
522   /* Determine ci and cj */
523   for (i = 0; i < am; i++) {
524     anzi = ai[i + 1] - ai[i];
525     aj   = a->j + ai[i];
526     for (j = 0; j < anzi; j++) {
527       brow = aj[j];
528       bnzj = bi[brow + 1] - bi[brow];
529       bj   = b->j + bi[brow];
530       /* add non-zero cols of B into the sorted linked list lnk */
531       PetscCall(PetscLLCondensedAddSorted_Scalable(bnzj, bj, lnk));
532     }
533     /* add possible missing diagonal entry */
534     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted_Scalable(1, &i, lnk));
535 
536     cnzi = lnk[0];
537 
538     /* If free space is not available, make more free space */
539     /* Double the amount of total space in the list */
540     if (current_space->local_remaining < cnzi) {
541       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
542       ndouble++;
543     }
544 
545     /* Copy data into free space, then initialize lnk */
546     PetscCall(PetscLLCondensedClean_Scalable(cnzi, current_space->array, lnk));
547 
548     current_space->array += cnzi;
549     current_space->local_used += cnzi;
550     current_space->local_remaining -= cnzi;
551 
552     ci[i + 1] = ci[i] + cnzi;
553   }
554 
555   /* Column indices are in the list of free space */
556   /* Allocate space for cj, initialize cj, and */
557   /* destroy list of free space and other temporary array(s) */
558   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
559   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
560   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
561 
562   /* Allocate space for ca */
563   PetscCall(PetscCalloc1(ci[am] + 1, &ca));
564 
565   /* put together the new symbolic matrix */
566   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, ca, ((PetscObject)A)->type_name, C));
567   PetscCall(MatSetBlockSizesFromMats(C, A, B));
568 
569   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
570   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
571   c          = (Mat_SeqAIJ *)(C->data);
572   c->free_a  = PETSC_TRUE;
573   c->free_ij = PETSC_TRUE;
574   c->nonew   = 0;
575 
576   /* slower, less memory */
577   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;
578 
579   /* set MatInfo */
580   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
581   if (afill < 1.0) afill = 1.0;
582   C->info.mallocs           = ndouble;
583   C->info.fill_ratio_given  = fill;
584   C->info.fill_ratio_needed = afill;
585 
586 #if defined(PETSC_USE_INFO)
587   if (ci[am]) {
588     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
589     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
590   } else {
591     PetscCall(PetscInfo(C, "Empty matrix product\n"));
592   }
593 #endif
594   PetscFunctionReturn(PETSC_SUCCESS);
595 }
596 
597 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A, Mat B, PetscReal fill, Mat C)
598 {
599   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
600   const PetscInt    *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
601   PetscInt          *ci, *cj, *bb;
602   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
603   PetscReal          afill;
604   PetscInt           i, j, col, ndouble = 0;
605   PetscFreeSpaceList free_space = NULL, current_space = NULL;
606   PetscHeap          h;
607 
608   PetscFunctionBegin;
609   /* Get ci and cj - by merging sorted rows using a heap */
610   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
611   PetscCall(PetscMalloc1(am + 2, &ci));
612   ci[0] = 0;
613 
614   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
615   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
616   current_space = free_space;
617 
618   PetscCall(PetscHeapCreate(a->rmax, &h));
619   PetscCall(PetscMalloc1(a->rmax, &bb));
620 
621   /* Determine ci and cj */
622   for (i = 0; i < am; i++) {
623     const PetscInt  anzi = ai[i + 1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
624     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
625     ci[i + 1]            = ci[i];
626     /* Populate the min heap */
627     for (j = 0; j < anzi; j++) {
628       bb[j] = bi[acol[j]];           /* bb points at the start of the row */
629       if (bb[j] < bi[acol[j] + 1]) { /* Add if row is nonempty */
630         PetscCall(PetscHeapAdd(h, j, bj[bb[j]++]));
631       }
632     }
633     /* Pick off the min element, adding it to free space */
634     PetscCall(PetscHeapPop(h, &j, &col));
635     while (j >= 0) {
636       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
637         PetscCall(PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2, current_space->total_array_size), 16 << 20), &current_space));
638         ndouble++;
639       }
640       *(current_space->array++) = col;
641       current_space->local_used++;
642       current_space->local_remaining--;
643       ci[i + 1]++;
644 
645       /* stash if anything else remains in this row of B */
646       if (bb[j] < bi[acol[j] + 1]) PetscCall(PetscHeapStash(h, j, bj[bb[j]++]));
647       while (1) { /* pop and stash any other rows of B that also had an entry in this column */
648         PetscInt j2, col2;
649         PetscCall(PetscHeapPeek(h, &j2, &col2));
650         if (col2 != col) break;
651         PetscCall(PetscHeapPop(h, &j2, &col2));
652         if (bb[j2] < bi[acol[j2] + 1]) PetscCall(PetscHeapStash(h, j2, bj[bb[j2]++]));
653       }
654       /* Put any stashed elements back into the min heap */
655       PetscCall(PetscHeapUnstash(h));
656       PetscCall(PetscHeapPop(h, &j, &col));
657     }
658   }
659   PetscCall(PetscFree(bb));
660   PetscCall(PetscHeapDestroy(&h));
661 
662   /* Column indices are in the list of free space */
663   /* Allocate space for cj, initialize cj, and */
664   /* destroy list of free space and other temporary array(s) */
665   PetscCall(PetscMalloc1(ci[am], &cj));
666   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
667 
668   /* put together the new symbolic matrix */
669   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
670   PetscCall(MatSetBlockSizesFromMats(C, A, B));
671 
672   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
673   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
674   c          = (Mat_SeqAIJ *)(C->data);
675   c->free_a  = PETSC_TRUE;
676   c->free_ij = PETSC_TRUE;
677   c->nonew   = 0;
678 
679   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
680 
681   /* set MatInfo */
682   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
683   if (afill < 1.0) afill = 1.0;
684   C->info.mallocs           = ndouble;
685   C->info.fill_ratio_given  = fill;
686   C->info.fill_ratio_needed = afill;
687 
688 #if defined(PETSC_USE_INFO)
689   if (ci[am]) {
690     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
691     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
692   } else {
693     PetscCall(PetscInfo(C, "Empty matrix product\n"));
694   }
695 #endif
696   PetscFunctionReturn(PETSC_SUCCESS);
697 }
698 
699 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A, Mat B, PetscReal fill, Mat C)
700 {
701   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
702   const PetscInt    *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
703   PetscInt          *ci, *cj, *bb;
704   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
705   PetscReal          afill;
706   PetscInt           i, j, col, ndouble = 0;
707   PetscFreeSpaceList free_space = NULL, current_space = NULL;
708   PetscHeap          h;
709   PetscBT            bt;
710 
711   PetscFunctionBegin;
712   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
713   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
714   PetscCall(PetscMalloc1(am + 2, &ci));
715   ci[0] = 0;
716 
717   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
718   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
719 
720   current_space = free_space;
721 
722   PetscCall(PetscHeapCreate(a->rmax, &h));
723   PetscCall(PetscMalloc1(a->rmax, &bb));
724   PetscCall(PetscBTCreate(bn, &bt));
725 
726   /* Determine ci and cj */
727   for (i = 0; i < am; i++) {
728     const PetscInt  anzi = ai[i + 1] - ai[i];    /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
729     const PetscInt *acol = aj + ai[i];           /* column indices of nonzero entries in this row */
730     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
731     ci[i + 1]            = ci[i];
732     /* Populate the min heap */
733     for (j = 0; j < anzi; j++) {
734       PetscInt brow = acol[j];
735       for (bb[j] = bi[brow]; bb[j] < bi[brow + 1]; bb[j]++) {
736         PetscInt bcol = bj[bb[j]];
737         if (!PetscBTLookupSet(bt, bcol)) { /* new entry */
738           PetscCall(PetscHeapAdd(h, j, bcol));
739           bb[j]++;
740           break;
741         }
742       }
743     }
744     /* Pick off the min element, adding it to free space */
745     PetscCall(PetscHeapPop(h, &j, &col));
746     while (j >= 0) {
747       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
748         fptr = NULL;                            /* need PetscBTMemzero */
749         PetscCall(PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2, current_space->total_array_size), 16 << 20), &current_space));
750         ndouble++;
751       }
752       *(current_space->array++) = col;
753       current_space->local_used++;
754       current_space->local_remaining--;
755       ci[i + 1]++;
756 
757       /* stash if anything else remains in this row of B */
758       for (; bb[j] < bi[acol[j] + 1]; bb[j]++) {
759         PetscInt bcol = bj[bb[j]];
760         if (!PetscBTLookupSet(bt, bcol)) { /* new entry */
761           PetscCall(PetscHeapAdd(h, j, bcol));
762           bb[j]++;
763           break;
764         }
765       }
766       PetscCall(PetscHeapPop(h, &j, &col));
767     }
768     if (fptr) { /* Clear the bits for this row */
769       for (; fptr < current_space->array; fptr++) PetscCall(PetscBTClear(bt, *fptr));
770     } else { /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
771       PetscCall(PetscBTMemzero(bn, bt));
772     }
773   }
774   PetscCall(PetscFree(bb));
775   PetscCall(PetscHeapDestroy(&h));
776   PetscCall(PetscBTDestroy(&bt));
777 
778   /* Column indices are in the list of free space */
779   /* Allocate space for cj, initialize cj, and */
780   /* destroy list of free space and other temporary array(s) */
781   PetscCall(PetscMalloc1(ci[am], &cj));
782   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
783 
784   /* put together the new symbolic matrix */
785   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
786   PetscCall(MatSetBlockSizesFromMats(C, A, B));
787 
788   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
789   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
790   c          = (Mat_SeqAIJ *)(C->data);
791   c->free_a  = PETSC_TRUE;
792   c->free_ij = PETSC_TRUE;
793   c->nonew   = 0;
794 
795   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
796 
797   /* set MatInfo */
798   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
799   if (afill < 1.0) afill = 1.0;
800   C->info.mallocs           = ndouble;
801   C->info.fill_ratio_given  = fill;
802   C->info.fill_ratio_needed = afill;
803 
804 #if defined(PETSC_USE_INFO)
805   if (ci[am]) {
806     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
807     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
808   } else {
809     PetscCall(PetscInfo(C, "Empty matrix product\n"));
810   }
811 #endif
812   PetscFunctionReturn(PETSC_SUCCESS);
813 }
814 
815 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat A, Mat B, PetscReal fill, Mat C)
816 {
817   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
818   const PetscInt *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j, *inputi, *inputj, *inputcol, *inputcol_L1;
819   PetscInt       *ci, *cj, *outputj, worki_L1[9], worki_L2[9];
820   PetscInt        c_maxmem, a_maxrownnz = 0, a_rownnz;
821   const PetscInt  workcol[8] = {0, 1, 2, 3, 4, 5, 6, 7};
822   const PetscInt  am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
823   const PetscInt *brow_ptr[8], *brow_end[8];
824   PetscInt        window[8];
825   PetscInt        window_min, old_window_min, ci_nnz, outputi_nnz = 0, L1_nrows, L2_nrows;
826   PetscInt        i, k, ndouble = 0, L1_rowsleft, rowsleft;
827   PetscReal       afill;
828   PetscInt       *workj_L1, *workj_L2, *workj_L3;
829   PetscInt        L1_nnz, L2_nnz;
830 
831   /* Step 1: Get upper bound on memory required for allocation.
832              Because of the way virtual memory works,
833              only the memory pages that are actually needed will be physically allocated. */
834   PetscFunctionBegin;
835   PetscCall(PetscMalloc1(am + 1, &ci));
836   for (i = 0; i < am; i++) {
837     const PetscInt  anzi = ai[i + 1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
838     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
839     a_rownnz             = 0;
840     for (k = 0; k < anzi; ++k) {
841       a_rownnz += bi[acol[k] + 1] - bi[acol[k]];
842       if (a_rownnz > bn) {
843         a_rownnz = bn;
844         break;
845       }
846     }
847     a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz);
848   }
849   /* temporary work areas for merging rows */
850   PetscCall(PetscMalloc1(a_maxrownnz * 8, &workj_L1));
851   PetscCall(PetscMalloc1(a_maxrownnz * 8, &workj_L2));
852   PetscCall(PetscMalloc1(a_maxrownnz, &workj_L3));
853 
854   /* This should be enough for almost all matrices. If not, memory is reallocated later. */
855   c_maxmem = 8 * (ai[am] + bi[bm]);
856   /* Step 2: Populate pattern for C */
857   PetscCall(PetscMalloc1(c_maxmem, &cj));
858 
859   ci_nnz      = 0;
860   ci[0]       = 0;
861   worki_L1[0] = 0;
862   worki_L2[0] = 0;
863   for (i = 0; i < am; i++) {
864     const PetscInt  anzi = ai[i + 1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
865     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
866     rowsleft             = anzi;
867     inputcol_L1          = acol;
868     L2_nnz               = 0;
869     L2_nrows             = 1; /* Number of rows to be merged on Level 3. output of L3 already exists -> initial value 1   */
870     worki_L2[1]          = 0;
871     outputi_nnz          = 0;
872 
873     /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem  -> allocate more memory */
874     while (ci_nnz + a_maxrownnz > c_maxmem) {
875       c_maxmem *= 2;
876       ndouble++;
877       PetscCall(PetscRealloc(sizeof(PetscInt) * c_maxmem, &cj));
878     }
879 
880     while (rowsleft) {
881       L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */
882       L1_nrows    = 0;
883       L1_nnz      = 0;
884       inputcol    = inputcol_L1;
885       inputi      = bi;
886       inputj      = bj;
887 
888       /* The following macro is used to specialize for small rows in A.
889          This helps with compiler unrolling, improving performance substantially.
890           Input:  inputj   inputi  inputcol  bn
891           Output: outputj  outputi_nnz                       */
892 #define MatMatMultSymbolic_RowMergeMacro(ANNZ) \
893   do { \
894     window_min  = bn; \
895     outputi_nnz = 0; \
896     for (k = 0; k < ANNZ; ++k) { \
897       brow_ptr[k] = inputj + inputi[inputcol[k]]; \
898       brow_end[k] = inputj + inputi[inputcol[k] + 1]; \
899       window[k]   = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
900       window_min  = PetscMin(window[k], window_min); \
901     } \
902     while (window_min < bn) { \
903       outputj[outputi_nnz++] = window_min; \
904       /* advance front and compute new minimum */ \
905       old_window_min = window_min; \
906       window_min     = bn; \
907       for (k = 0; k < ANNZ; ++k) { \
908         if (window[k] == old_window_min) { \
909           brow_ptr[k]++; \
910           window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
911         } \
912         window_min = PetscMin(window[k], window_min); \
913       } \
914     } \
915   } while (0)
916 
917       /************** L E V E L  1 ***************/
918       /* Merge up to 8 rows of B to L1 work array*/
919       while (L1_rowsleft) {
920         outputi_nnz = 0;
921         if (anzi > 8) outputj = workj_L1 + L1_nnz; /* Level 1 rowmerge*/
922         else outputj = cj + ci_nnz;                /* Merge directly to C */
923 
924         switch (L1_rowsleft) {
925         case 1:
926           brow_ptr[0] = inputj + inputi[inputcol[0]];
927           brow_end[0] = inputj + inputi[inputcol[0] + 1];
928           for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
929           inputcol += L1_rowsleft;
930           rowsleft -= L1_rowsleft;
931           L1_rowsleft = 0;
932           break;
933         case 2:
934           MatMatMultSymbolic_RowMergeMacro(2);
935           inputcol += L1_rowsleft;
936           rowsleft -= L1_rowsleft;
937           L1_rowsleft = 0;
938           break;
939         case 3:
940           MatMatMultSymbolic_RowMergeMacro(3);
941           inputcol += L1_rowsleft;
942           rowsleft -= L1_rowsleft;
943           L1_rowsleft = 0;
944           break;
945         case 4:
946           MatMatMultSymbolic_RowMergeMacro(4);
947           inputcol += L1_rowsleft;
948           rowsleft -= L1_rowsleft;
949           L1_rowsleft = 0;
950           break;
951         case 5:
952           MatMatMultSymbolic_RowMergeMacro(5);
953           inputcol += L1_rowsleft;
954           rowsleft -= L1_rowsleft;
955           L1_rowsleft = 0;
956           break;
957         case 6:
958           MatMatMultSymbolic_RowMergeMacro(6);
959           inputcol += L1_rowsleft;
960           rowsleft -= L1_rowsleft;
961           L1_rowsleft = 0;
962           break;
963         case 7:
964           MatMatMultSymbolic_RowMergeMacro(7);
965           inputcol += L1_rowsleft;
966           rowsleft -= L1_rowsleft;
967           L1_rowsleft = 0;
968           break;
969         default:
970           MatMatMultSymbolic_RowMergeMacro(8);
971           inputcol += 8;
972           rowsleft -= 8;
973           L1_rowsleft -= 8;
974           break;
975         }
976         inputcol_L1 = inputcol;
977         L1_nnz += outputi_nnz;
978         worki_L1[++L1_nrows] = L1_nnz;
979       }
980 
981       /********************** L E V E L  2 ************************/
982       /* Merge from L1 work array to either C or to L2 work array */
983       if (anzi > 8) {
984         inputi      = worki_L1;
985         inputj      = workj_L1;
986         inputcol    = workcol;
987         outputi_nnz = 0;
988 
989         if (anzi <= 64) outputj = cj + ci_nnz; /* Merge from L1 work array to C */
990         else outputj = workj_L2 + L2_nnz;      /* Merge from L1 work array to L2 work array */
991 
992         switch (L1_nrows) {
993         case 1:
994           brow_ptr[0] = inputj + inputi[inputcol[0]];
995           brow_end[0] = inputj + inputi[inputcol[0] + 1];
996           for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
997           break;
998         case 2:
999           MatMatMultSymbolic_RowMergeMacro(2);
1000           break;
1001         case 3:
1002           MatMatMultSymbolic_RowMergeMacro(3);
1003           break;
1004         case 4:
1005           MatMatMultSymbolic_RowMergeMacro(4);
1006           break;
1007         case 5:
1008           MatMatMultSymbolic_RowMergeMacro(5);
1009           break;
1010         case 6:
1011           MatMatMultSymbolic_RowMergeMacro(6);
1012           break;
1013         case 7:
1014           MatMatMultSymbolic_RowMergeMacro(7);
1015           break;
1016         case 8:
1017           MatMatMultSymbolic_RowMergeMacro(8);
1018           break;
1019         default:
1020           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatMatMult logic error: Not merging 1-8 rows from L1 work array!");
1021         }
1022         L2_nnz += outputi_nnz;
1023         worki_L2[++L2_nrows] = L2_nnz;
1024 
1025         /************************ L E V E L  3 **********************/
1026         /* Merge from L2 work array to either C or to L2 work array */
1027         if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) {
1028           inputi      = worki_L2;
1029           inputj      = workj_L2;
1030           inputcol    = workcol;
1031           outputi_nnz = 0;
1032           if (rowsleft) outputj = workj_L3;
1033           else outputj = cj + ci_nnz;
1034           switch (L2_nrows) {
1035           case 1:
1036             brow_ptr[0] = inputj + inputi[inputcol[0]];
1037             brow_end[0] = inputj + inputi[inputcol[0] + 1];
1038             for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
1039             break;
1040           case 2:
1041             MatMatMultSymbolic_RowMergeMacro(2);
1042             break;
1043           case 3:
1044             MatMatMultSymbolic_RowMergeMacro(3);
1045             break;
1046           case 4:
1047             MatMatMultSymbolic_RowMergeMacro(4);
1048             break;
1049           case 5:
1050             MatMatMultSymbolic_RowMergeMacro(5);
1051             break;
1052           case 6:
1053             MatMatMultSymbolic_RowMergeMacro(6);
1054             break;
1055           case 7:
1056             MatMatMultSymbolic_RowMergeMacro(7);
1057             break;
1058           case 8:
1059             MatMatMultSymbolic_RowMergeMacro(8);
1060             break;
1061           default:
1062             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatMatMult logic error: Not merging 1-8 rows from L2 work array!");
1063           }
1064           L2_nrows    = 1;
1065           L2_nnz      = outputi_nnz;
1066           worki_L2[1] = outputi_nnz;
1067           /* Copy to workj_L2 */
1068           if (rowsleft) {
1069             for (k = 0; k < outputi_nnz; ++k) workj_L2[k] = outputj[k];
1070           }
1071         }
1072       }
1073     } /* while (rowsleft) */
1074 #undef MatMatMultSymbolic_RowMergeMacro
1075 
1076     /* terminate current row */
1077     ci_nnz += outputi_nnz;
1078     ci[i + 1] = ci_nnz;
1079   }
1080 
1081   /* Step 3: Create the new symbolic matrix */
1082   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
1083   PetscCall(MatSetBlockSizesFromMats(C, A, B));
1084 
1085   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1086   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1087   c          = (Mat_SeqAIJ *)(C->data);
1088   c->free_a  = PETSC_TRUE;
1089   c->free_ij = PETSC_TRUE;
1090   c->nonew   = 0;
1091 
1092   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
1093 
1094   /* set MatInfo */
1095   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
1096   if (afill < 1.0) afill = 1.0;
1097   C->info.mallocs           = ndouble;
1098   C->info.fill_ratio_given  = fill;
1099   C->info.fill_ratio_needed = afill;
1100 
1101 #if defined(PETSC_USE_INFO)
1102   if (ci[am]) {
1103     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
1104     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1105   } else {
1106     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1107   }
1108 #endif
1109 
1110   /* Step 4: Free temporary work areas */
1111   PetscCall(PetscFree(workj_L1));
1112   PetscCall(PetscFree(workj_L2));
1113   PetscCall(PetscFree(workj_L3));
1114   PetscFunctionReturn(PETSC_SUCCESS);
1115 }
1116 
1117 /* concatenate unique entries and then sort */
1118 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat A, Mat B, PetscReal fill, Mat C)
1119 {
1120   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
1121   const PetscInt *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
1122   PetscInt       *ci, *cj, bcol;
1123   PetscInt        am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
1124   PetscReal       afill;
1125   PetscInt        i, j, ndouble = 0;
1126   PetscSegBuffer  seg, segrow;
1127   char           *seen;
1128 
1129   PetscFunctionBegin;
1130   PetscCall(PetscMalloc1(am + 1, &ci));
1131   ci[0] = 0;
1132 
1133   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
1134   PetscCall(PetscSegBufferCreate(sizeof(PetscInt), (PetscInt)(fill * (ai[am] + bi[bm])), &seg));
1135   PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 100, &segrow));
1136   PetscCall(PetscCalloc1(bn, &seen));
1137 
1138   /* Determine ci and cj */
1139   for (i = 0; i < am; i++) {
1140     const PetscInt  anzi = ai[i + 1] - ai[i]; /* number of nonzeros in this row of A, this is the number of rows of B that we merge */
1141     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
1142     PetscInt packlen     = 0, *PETSC_RESTRICT crow;
1143 
1144     /* Pack segrow */
1145     for (j = 0; j < anzi; j++) {
1146       PetscInt brow = acol[j], bjstart = bi[brow], bjend = bi[brow + 1], k;
1147       for (k = bjstart; k < bjend; k++) {
1148         bcol = bj[k];
1149         if (!seen[bcol]) { /* new entry */
1150           PetscInt *PETSC_RESTRICT slot;
1151           PetscCall(PetscSegBufferGetInts(segrow, 1, &slot));
1152           *slot      = bcol;
1153           seen[bcol] = 1;
1154           packlen++;
1155         }
1156       }
1157     }
1158 
1159     /* Check i-th diagonal entry */
1160     if (C->force_diagonals && !seen[i]) {
1161       PetscInt *PETSC_RESTRICT slot;
1162       PetscCall(PetscSegBufferGetInts(segrow, 1, &slot));
1163       *slot   = i;
1164       seen[i] = 1;
1165       packlen++;
1166     }
1167 
1168     PetscCall(PetscSegBufferGetInts(seg, packlen, &crow));
1169     PetscCall(PetscSegBufferExtractTo(segrow, crow));
1170     PetscCall(PetscSortInt(packlen, crow));
1171     ci[i + 1] = ci[i] + packlen;
1172     for (j = 0; j < packlen; j++) seen[crow[j]] = 0;
1173   }
1174   PetscCall(PetscSegBufferDestroy(&segrow));
1175   PetscCall(PetscFree(seen));
1176 
1177   /* Column indices are in the segmented buffer */
1178   PetscCall(PetscSegBufferExtractAlloc(seg, &cj));
1179   PetscCall(PetscSegBufferDestroy(&seg));
1180 
1181   /* put together the new symbolic matrix */
1182   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
1183   PetscCall(MatSetBlockSizesFromMats(C, A, B));
1184 
1185   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1186   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1187   c          = (Mat_SeqAIJ *)(C->data);
1188   c->free_a  = PETSC_TRUE;
1189   c->free_ij = PETSC_TRUE;
1190   c->nonew   = 0;
1191 
1192   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
1193 
1194   /* set MatInfo */
1195   afill = (PetscReal)ci[am] / PetscMax(ai[am] + bi[bm], 1) + 1.e-5;
1196   if (afill < 1.0) afill = 1.0;
1197   C->info.mallocs           = ndouble;
1198   C->info.fill_ratio_given  = fill;
1199   C->info.fill_ratio_needed = afill;
1200 
1201 #if defined(PETSC_USE_INFO)
1202   if (ci[am]) {
1203     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
1204     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1205   } else {
1206     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1207   }
1208 #endif
1209   PetscFunctionReturn(PETSC_SUCCESS);
1210 }
1211 
1212 static PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(void *data)
1213 {
1214   Mat_MatMatTransMult *abt = (Mat_MatMatTransMult *)data;
1215 
1216   PetscFunctionBegin;
1217   PetscCall(MatTransposeColoringDestroy(&abt->matcoloring));
1218   PetscCall(MatDestroy(&abt->Bt_den));
1219   PetscCall(MatDestroy(&abt->ABt_den));
1220   PetscCall(PetscFree(abt));
1221   PetscFunctionReturn(PETSC_SUCCESS);
1222 }
1223 
1224 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
1225 {
1226   Mat                  Bt;
1227   Mat_MatMatTransMult *abt;
1228   Mat_Product         *product = C->product;
1229   char                *alg;
1230 
1231   PetscFunctionBegin;
1232   PetscCheck(product, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1233   PetscCheck(!product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1234 
1235   /* create symbolic Bt */
1236   PetscCall(MatTransposeSymbolic(B, &Bt));
1237   PetscCall(MatSetBlockSizes(Bt, PetscAbs(A->cmap->bs), PetscAbs(B->cmap->bs)));
1238   PetscCall(MatSetType(Bt, ((PetscObject)A)->type_name));
1239 
1240   /* get symbolic C=A*Bt */
1241   PetscCall(PetscStrallocpy(product->alg, &alg));
1242   PetscCall(MatProductSetAlgorithm(C, "sorted")); /* set algorithm for C = A*Bt */
1243   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(A, Bt, fill, C));
1244   PetscCall(MatProductSetAlgorithm(C, alg)); /* resume original algorithm for ABt product */
1245   PetscCall(PetscFree(alg));
1246 
1247   /* create a supporting struct for reuse intermediate dense matrices with matcoloring */
1248   PetscCall(PetscNew(&abt));
1249 
1250   product->data    = abt;
1251   product->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
1252 
1253   C->ops->mattransposemultnumeric = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ;
1254 
1255   abt->usecoloring = PETSC_FALSE;
1256   PetscCall(PetscStrcmp(product->alg, "color", &abt->usecoloring));
1257   if (abt->usecoloring) {
1258     /* Create MatTransposeColoring from symbolic C=A*B^T */
1259     MatTransposeColoring matcoloring;
1260     MatColoring          coloring;
1261     ISColoring           iscoloring;
1262     Mat                  Bt_dense, C_dense;
1263 
1264     /* inode causes memory problem */
1265     PetscCall(MatSetOption(C, MAT_USE_INODES, PETSC_FALSE));
1266 
1267     PetscCall(MatColoringCreate(C, &coloring));
1268     PetscCall(MatColoringSetDistance(coloring, 2));
1269     PetscCall(MatColoringSetType(coloring, MATCOLORINGSL));
1270     PetscCall(MatColoringSetFromOptions(coloring));
1271     PetscCall(MatColoringApply(coloring, &iscoloring));
1272     PetscCall(MatColoringDestroy(&coloring));
1273     PetscCall(MatTransposeColoringCreate(C, iscoloring, &matcoloring));
1274 
1275     abt->matcoloring = matcoloring;
1276 
1277     PetscCall(ISColoringDestroy(&iscoloring));
1278 
1279     /* Create Bt_dense and C_dense = A*Bt_dense */
1280     PetscCall(MatCreate(PETSC_COMM_SELF, &Bt_dense));
1281     PetscCall(MatSetSizes(Bt_dense, A->cmap->n, matcoloring->ncolors, A->cmap->n, matcoloring->ncolors));
1282     PetscCall(MatSetType(Bt_dense, MATSEQDENSE));
1283     PetscCall(MatSeqDenseSetPreallocation(Bt_dense, NULL));
1284 
1285     Bt_dense->assembled = PETSC_TRUE;
1286     abt->Bt_den         = Bt_dense;
1287 
1288     PetscCall(MatCreate(PETSC_COMM_SELF, &C_dense));
1289     PetscCall(MatSetSizes(C_dense, A->rmap->n, matcoloring->ncolors, A->rmap->n, matcoloring->ncolors));
1290     PetscCall(MatSetType(C_dense, MATSEQDENSE));
1291     PetscCall(MatSeqDenseSetPreallocation(C_dense, NULL));
1292 
1293     Bt_dense->assembled = PETSC_TRUE;
1294     abt->ABt_den        = C_dense;
1295 
1296 #if defined(PETSC_USE_INFO)
1297     {
1298       Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data;
1299       PetscCall(PetscInfo(C, "Use coloring of C=A*B^T; B^T: %" PetscInt_FMT " %" PetscInt_FMT ", Bt_dense: %" PetscInt_FMT ",%" PetscInt_FMT "; Cnz %" PetscInt_FMT " / (cm*ncolors %" PetscInt_FMT ") = %g\n", B->cmap->n, B->rmap->n, Bt_dense->rmap->n,
1300                           Bt_dense->cmap->n, c->nz, A->rmap->n * matcoloring->ncolors, (double)(((PetscReal)(c->nz)) / ((PetscReal)(A->rmap->n * matcoloring->ncolors)))));
1301     }
1302 #endif
1303   }
1304   /* clean up */
1305   PetscCall(MatDestroy(&Bt));
1306   PetscFunctionReturn(PETSC_SUCCESS);
1307 }
1308 
1309 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
1310 {
1311   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c = (Mat_SeqAIJ *)C->data;
1312   PetscInt            *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, anzi, bnzj, nexta, nextb, *acol, *bcol, brow;
1313   PetscInt             cm = C->rmap->n, *ci = c->i, *cj = c->j, i, j, cnzi, *ccol;
1314   PetscLogDouble       flops = 0.0;
1315   MatScalar           *aa = a->a, *aval, *ba = b->a, *bval, *ca, *cval;
1316   Mat_MatMatTransMult *abt;
1317   Mat_Product         *product = C->product;
1318 
1319   PetscFunctionBegin;
1320   PetscCheck(product, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1321   abt = (Mat_MatMatTransMult *)product->data;
1322   PetscCheck(abt, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1323   /* clear old values in C */
1324   if (!c->a) {
1325     PetscCall(PetscCalloc1(ci[cm] + 1, &ca));
1326     c->a      = ca;
1327     c->free_a = PETSC_TRUE;
1328   } else {
1329     ca = c->a;
1330     PetscCall(PetscArrayzero(ca, ci[cm] + 1));
1331   }
1332 
1333   if (abt->usecoloring) {
1334     MatTransposeColoring matcoloring = abt->matcoloring;
1335     Mat                  Bt_dense, C_dense = abt->ABt_den;
1336 
1337     /* Get Bt_dense by Apply MatTransposeColoring to B */
1338     Bt_dense = abt->Bt_den;
1339     PetscCall(MatTransColoringApplySpToDen(matcoloring, B, Bt_dense));
1340 
1341     /* C_dense = A*Bt_dense */
1342     PetscCall(MatMatMultNumeric_SeqAIJ_SeqDense(A, Bt_dense, C_dense));
1343 
1344     /* Recover C from C_dense */
1345     PetscCall(MatTransColoringApplyDenToSp(matcoloring, C_dense, C));
1346     PetscFunctionReturn(PETSC_SUCCESS);
1347   }
1348 
1349   for (i = 0; i < cm; i++) {
1350     anzi = ai[i + 1] - ai[i];
1351     acol = aj + ai[i];
1352     aval = aa + ai[i];
1353     cnzi = ci[i + 1] - ci[i];
1354     ccol = cj + ci[i];
1355     cval = ca + ci[i];
1356     for (j = 0; j < cnzi; j++) {
1357       brow = ccol[j];
1358       bnzj = bi[brow + 1] - bi[brow];
1359       bcol = bj + bi[brow];
1360       bval = ba + bi[brow];
1361 
1362       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1363       nexta = 0;
1364       nextb = 0;
1365       while (nexta < anzi && nextb < bnzj) {
1366         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
1367         if (nexta == anzi) break;
1368         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
1369         if (nextb == bnzj) break;
1370         if (acol[nexta] == bcol[nextb]) {
1371           cval[j] += aval[nexta] * bval[nextb];
1372           nexta++;
1373           nextb++;
1374           flops += 2;
1375         }
1376       }
1377     }
1378   }
1379   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1380   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1381   PetscCall(PetscLogFlops(flops));
1382   PetscFunctionReturn(PETSC_SUCCESS);
1383 }
1384 
1385 PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(void *data)
1386 {
1387   Mat_MatTransMatMult *atb = (Mat_MatTransMatMult *)data;
1388 
1389   PetscFunctionBegin;
1390   PetscCall(MatDestroy(&atb->At));
1391   if (atb->destroy) PetscCall((*atb->destroy)(atb->data));
1392   PetscCall(PetscFree(atb));
1393   PetscFunctionReturn(PETSC_SUCCESS);
1394 }
1395 
1396 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
1397 {
1398   Mat          At      = NULL;
1399   Mat_Product *product = C->product;
1400   PetscBool    flg, def, square;
1401 
1402   PetscFunctionBegin;
1403   MatCheckProduct(C, 4);
1404   square = (PetscBool)(A == B && A->symmetric == PETSC_BOOL3_TRUE);
1405   /* outerproduct */
1406   PetscCall(PetscStrcmp(product->alg, "outerproduct", &flg));
1407   if (flg) {
1408     /* create symbolic At */
1409     if (!square) {
1410       PetscCall(MatTransposeSymbolic(A, &At));
1411       PetscCall(MatSetBlockSizes(At, PetscAbs(A->cmap->bs), PetscAbs(B->cmap->bs)));
1412       PetscCall(MatSetType(At, ((PetscObject)A)->type_name));
1413     }
1414     /* get symbolic C=At*B */
1415     PetscCall(MatProductSetAlgorithm(C, "sorted"));
1416     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At, B, fill, C));
1417 
1418     /* clean up */
1419     if (!square) PetscCall(MatDestroy(&At));
1420 
1421     C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ; /* outerproduct */
1422     PetscCall(MatProductSetAlgorithm(C, "outerproduct"));
1423     PetscFunctionReturn(PETSC_SUCCESS);
1424   }
1425 
1426   /* matmatmult */
1427   PetscCall(PetscStrcmp(product->alg, "default", &def));
1428   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
1429   if (flg || def) {
1430     Mat_MatTransMatMult *atb;
1431 
1432     PetscCheck(!product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1433     PetscCall(PetscNew(&atb));
1434     if (!square) PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
1435     PetscCall(MatProductSetAlgorithm(C, "sorted"));
1436     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At, B, fill, C));
1437     PetscCall(MatProductSetAlgorithm(C, "at*b"));
1438     product->data    = atb;
1439     product->destroy = MatDestroy_SeqAIJ_MatTransMatMult;
1440     atb->At          = At;
1441 
1442     C->ops->mattransposemultnumeric = NULL; /* see MatProductNumeric_AtB_SeqAIJ_SeqAIJ */
1443     PetscFunctionReturn(PETSC_SUCCESS);
1444   }
1445 
1446   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
1447 }
1448 
1449 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
1450 {
1451   Mat_SeqAIJ    *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c = (Mat_SeqAIJ *)C->data;
1452   PetscInt       am = A->rmap->n, anzi, *ai = a->i, *aj = a->j, *bi = b->i, *bj, bnzi, nextb;
1453   PetscInt       cm = C->rmap->n, *ci = c->i, *cj = c->j, crow, *cjj, i, j, k;
1454   PetscLogDouble flops = 0.0;
1455   MatScalar     *aa    = a->a, *ba, *ca, *caj;
1456 
1457   PetscFunctionBegin;
1458   if (!c->a) {
1459     PetscCall(PetscCalloc1(ci[cm] + 1, &ca));
1460 
1461     c->a      = ca;
1462     c->free_a = PETSC_TRUE;
1463   } else {
1464     ca = c->a;
1465     PetscCall(PetscArrayzero(ca, ci[cm]));
1466   }
1467 
1468   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1469   for (i = 0; i < am; i++) {
1470     bj   = b->j + bi[i];
1471     ba   = b->a + bi[i];
1472     bnzi = bi[i + 1] - bi[i];
1473     anzi = ai[i + 1] - ai[i];
1474     for (j = 0; j < anzi; j++) {
1475       nextb = 0;
1476       crow  = *aj++;
1477       cjj   = cj + ci[crow];
1478       caj   = ca + ci[crow];
1479       /* perform sparse axpy operation.  Note cjj includes bj. */
1480       for (k = 0; nextb < bnzi; k++) {
1481         if (cjj[k] == *(bj + nextb)) { /* ccol == bcol */
1482           caj[k] += (*aa) * (*(ba + nextb));
1483           nextb++;
1484         }
1485       }
1486       flops += 2 * bnzi;
1487       aa++;
1488     }
1489   }
1490 
1491   /* Assemble the final matrix and clean up */
1492   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1493   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1494   PetscCall(PetscLogFlops(flops));
1495   PetscFunctionReturn(PETSC_SUCCESS);
1496 }
1497 
1498 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
1499 {
1500   PetscFunctionBegin;
1501   PetscCall(MatMatMultSymbolic_SeqDense_SeqDense(A, B, 0.0, C));
1502   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1503   PetscFunctionReturn(PETSC_SUCCESS);
1504 }
1505 
1506 PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A, Mat B, Mat C, const PetscBool add)
1507 {
1508   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1509   PetscScalar       *c, r1, r2, r3, r4, *c1, *c2, *c3, *c4;
1510   const PetscScalar *aa, *b, *b1, *b2, *b3, *b4, *av;
1511   const PetscInt    *aj;
1512   PetscInt           cm = C->rmap->n, cn = B->cmap->n, bm, am = A->rmap->n;
1513   PetscInt           clda;
1514   PetscInt           am4, bm4, col, i, j, n;
1515 
1516   PetscFunctionBegin;
1517   if (!cm || !cn) PetscFunctionReturn(PETSC_SUCCESS);
1518   PetscCall(MatSeqAIJGetArrayRead(A, &av));
1519   if (add) {
1520     PetscCall(MatDenseGetArray(C, &c));
1521   } else {
1522     PetscCall(MatDenseGetArrayWrite(C, &c));
1523   }
1524   PetscCall(MatDenseGetArrayRead(B, &b));
1525   PetscCall(MatDenseGetLDA(B, &bm));
1526   PetscCall(MatDenseGetLDA(C, &clda));
1527   am4 = 4 * clda;
1528   bm4 = 4 * bm;
1529   if (b) {
1530     b1 = b;
1531     b2 = b1 + bm;
1532     b3 = b2 + bm;
1533     b4 = b3 + bm;
1534   } else b1 = b2 = b3 = b4 = NULL;
1535   c1 = c;
1536   c2 = c1 + clda;
1537   c3 = c2 + clda;
1538   c4 = c3 + clda;
1539   for (col = 0; col < (cn / 4) * 4; col += 4) { /* over columns of C */
1540     for (i = 0; i < am; i++) {                  /* over rows of A in those columns */
1541       r1 = r2 = r3 = r4 = 0.0;
1542       n                 = a->i[i + 1] - a->i[i];
1543       aj                = a->j ? a->j + a->i[i] : NULL;
1544       aa                = av ? av + a->i[i] : NULL;
1545       for (j = 0; j < n; j++) {
1546         const PetscScalar aatmp = aa[j];
1547         const PetscInt    ajtmp = aj[j];
1548         r1 += aatmp * b1[ajtmp];
1549         r2 += aatmp * b2[ajtmp];
1550         r3 += aatmp * b3[ajtmp];
1551         r4 += aatmp * b4[ajtmp];
1552       }
1553       if (add) {
1554         c1[i] += r1;
1555         c2[i] += r2;
1556         c3[i] += r3;
1557         c4[i] += r4;
1558       } else {
1559         c1[i] = r1;
1560         c2[i] = r2;
1561         c3[i] = r3;
1562         c4[i] = r4;
1563       }
1564     }
1565     if (b) {
1566       b1 += bm4;
1567       b2 += bm4;
1568       b3 += bm4;
1569       b4 += bm4;
1570     }
1571     c1 += am4;
1572     c2 += am4;
1573     c3 += am4;
1574     c4 += am4;
1575   }
1576   /* process remaining columns */
1577   if (col != cn) {
1578     PetscInt rc = cn - col;
1579 
1580     if (rc == 1) {
1581       for (i = 0; i < am; i++) {
1582         r1 = 0.0;
1583         n  = a->i[i + 1] - a->i[i];
1584         aj = a->j + a->i[i];
1585         aa = av + a->i[i];
1586         for (j = 0; j < n; j++) r1 += aa[j] * b1[aj[j]];
1587         if (add) c1[i] += r1;
1588         else c1[i] = r1;
1589       }
1590     } else if (rc == 2) {
1591       for (i = 0; i < am; i++) {
1592         r1 = r2 = 0.0;
1593         n       = a->i[i + 1] - a->i[i];
1594         aj      = a->j + a->i[i];
1595         aa      = av + a->i[i];
1596         for (j = 0; j < n; j++) {
1597           const PetscScalar aatmp = aa[j];
1598           const PetscInt    ajtmp = aj[j];
1599           r1 += aatmp * b1[ajtmp];
1600           r2 += aatmp * b2[ajtmp];
1601         }
1602         if (add) {
1603           c1[i] += r1;
1604           c2[i] += r2;
1605         } else {
1606           c1[i] = r1;
1607           c2[i] = r2;
1608         }
1609       }
1610     } else {
1611       for (i = 0; i < am; i++) {
1612         r1 = r2 = r3 = 0.0;
1613         n            = a->i[i + 1] - a->i[i];
1614         aj           = a->j ? a->j + a->i[i] : NULL;
1615         aa           = av ? av + a->i[i] : NULL;
1616         for (j = 0; j < n; j++) {
1617           const PetscScalar aatmp = aa[j];
1618           const PetscInt    ajtmp = aj[j];
1619           r1 += aatmp * b1[ajtmp];
1620           r2 += aatmp * b2[ajtmp];
1621           r3 += aatmp * b3[ajtmp];
1622         }
1623         if (add) {
1624           c1[i] += r1;
1625           c2[i] += r2;
1626           c3[i] += r3;
1627         } else {
1628           c1[i] = r1;
1629           c2[i] = r2;
1630           c3[i] = r3;
1631         }
1632       }
1633     }
1634   }
1635   PetscCall(PetscLogFlops(cn * (2.0 * a->nz)));
1636   if (add) {
1637     PetscCall(MatDenseRestoreArray(C, &c));
1638   } else {
1639     PetscCall(MatDenseRestoreArrayWrite(C, &c));
1640   }
1641   PetscCall(MatDenseRestoreArrayRead(B, &b));
1642   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
1643   PetscFunctionReturn(PETSC_SUCCESS);
1644 }
1645 
1646 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A, Mat B, Mat C)
1647 {
1648   PetscFunctionBegin;
1649   PetscCheck(B->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in A %" PetscInt_FMT " not equal rows in B %" PetscInt_FMT, A->cmap->n, B->rmap->n);
1650   PetscCheck(A->rmap->n == C->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number rows in C %" PetscInt_FMT " not equal rows in A %" PetscInt_FMT, C->rmap->n, A->rmap->n);
1651   PetscCheck(B->cmap->n == C->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Number columns in B %" PetscInt_FMT " not equal columns in C %" PetscInt_FMT, B->cmap->n, C->cmap->n);
1652 
1653   PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(A, B, C, PETSC_FALSE));
1654   PetscFunctionReturn(PETSC_SUCCESS);
1655 }
1656 
1657 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AB(Mat C)
1658 {
1659   PetscFunctionBegin;
1660   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqDense;
1661   C->ops->productsymbolic = MatProductSymbolic_AB;
1662   PetscFunctionReturn(PETSC_SUCCESS);
1663 }
1664 
1665 PETSC_INTERN PetscErrorCode MatTMatTMultSymbolic_SeqAIJ_SeqDense(Mat, Mat, PetscReal, Mat);
1666 
1667 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(Mat C)
1668 {
1669   PetscFunctionBegin;
1670   C->ops->transposematmultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1671   C->ops->productsymbolic          = MatProductSymbolic_AtB;
1672   PetscFunctionReturn(PETSC_SUCCESS);
1673 }
1674 
1675 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(Mat C)
1676 {
1677   PetscFunctionBegin;
1678   C->ops->mattransposemultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1679   C->ops->productsymbolic          = MatProductSymbolic_ABt;
1680   PetscFunctionReturn(PETSC_SUCCESS);
1681 }
1682 
1683 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat C)
1684 {
1685   Mat_Product *product = C->product;
1686 
1687   PetscFunctionBegin;
1688   switch (product->type) {
1689   case MATPRODUCT_AB:
1690     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_AB(C));
1691     break;
1692   case MATPRODUCT_AtB:
1693     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(C));
1694     break;
1695   case MATPRODUCT_ABt:
1696     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(C));
1697     break;
1698   default:
1699     break;
1700   }
1701   PetscFunctionReturn(PETSC_SUCCESS);
1702 }
1703 
1704 static PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(Mat C)
1705 {
1706   Mat_Product *product = C->product;
1707   Mat          A       = product->A;
1708   PetscBool    baij;
1709 
1710   PetscFunctionBegin;
1711   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &baij));
1712   if (!baij) { /* A is seqsbaij */
1713     PetscBool sbaij;
1714     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &sbaij));
1715     PetscCheck(sbaij, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "Mat must be either seqbaij or seqsbaij format");
1716 
1717     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqSBAIJ_SeqDense;
1718   } else { /* A is seqbaij */
1719     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqBAIJ_SeqDense;
1720   }
1721 
1722   C->ops->productsymbolic = MatProductSymbolic_AB;
1723   PetscFunctionReturn(PETSC_SUCCESS);
1724 }
1725 
1726 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense(Mat C)
1727 {
1728   Mat_Product *product = C->product;
1729 
1730   PetscFunctionBegin;
1731   MatCheckProduct(C, 1);
1732   PetscCheck(product->A, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing A");
1733   if (product->type == MATPRODUCT_AB || (product->type == MATPRODUCT_AtB && product->A->symmetric == PETSC_BOOL3_TRUE)) PetscCall(MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(C));
1734   PetscFunctionReturn(PETSC_SUCCESS);
1735 }
1736 
1737 static PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ_AB(Mat C)
1738 {
1739   PetscFunctionBegin;
1740   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqDense_SeqAIJ;
1741   C->ops->productsymbolic = MatProductSymbolic_AB;
1742   PetscFunctionReturn(PETSC_SUCCESS);
1743 }
1744 
1745 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ(Mat C)
1746 {
1747   Mat_Product *product = C->product;
1748 
1749   PetscFunctionBegin;
1750   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_SeqDense_SeqAIJ_AB(C));
1751   PetscFunctionReturn(PETSC_SUCCESS);
1752 }
1753 
1754 PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring, Mat B, Mat Btdense)
1755 {
1756   Mat_SeqAIJ   *b       = (Mat_SeqAIJ *)B->data;
1757   Mat_SeqDense *btdense = (Mat_SeqDense *)Btdense->data;
1758   PetscInt     *bi = b->i, *bj = b->j;
1759   PetscInt      m = Btdense->rmap->n, n = Btdense->cmap->n, j, k, l, col, anz, *btcol, brow, ncolumns;
1760   MatScalar    *btval, *btval_den, *ba = b->a;
1761   PetscInt     *columns = coloring->columns, *colorforcol = coloring->colorforcol, ncolors = coloring->ncolors;
1762 
1763   PetscFunctionBegin;
1764   btval_den = btdense->v;
1765   PetscCall(PetscArrayzero(btval_den, m * n));
1766   for (k = 0; k < ncolors; k++) {
1767     ncolumns = coloring->ncolumns[k];
1768     for (l = 0; l < ncolumns; l++) { /* insert a row of B to a column of Btdense */
1769       col   = *(columns + colorforcol[k] + l);
1770       btcol = bj + bi[col];
1771       btval = ba + bi[col];
1772       anz   = bi[col + 1] - bi[col];
1773       for (j = 0; j < anz; j++) {
1774         brow            = btcol[j];
1775         btval_den[brow] = btval[j];
1776       }
1777     }
1778     btval_den += m;
1779   }
1780   PetscFunctionReturn(PETSC_SUCCESS);
1781 }
1782 
1783 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring, Mat Cden, Mat Csp)
1784 {
1785   Mat_SeqAIJ        *csp = (Mat_SeqAIJ *)Csp->data;
1786   const PetscScalar *ca_den, *ca_den_ptr;
1787   PetscScalar       *ca = csp->a;
1788   PetscInt           k, l, m = Cden->rmap->n, ncolors = matcoloring->ncolors;
1789   PetscInt           brows = matcoloring->brows, *den2sp = matcoloring->den2sp;
1790   PetscInt           nrows, *row, *idx;
1791   PetscInt          *rows = matcoloring->rows, *colorforrow = matcoloring->colorforrow;
1792 
1793   PetscFunctionBegin;
1794   PetscCall(MatDenseGetArrayRead(Cden, &ca_den));
1795 
1796   if (brows > 0) {
1797     PetscInt *lstart, row_end, row_start;
1798     lstart = matcoloring->lstart;
1799     PetscCall(PetscArrayzero(lstart, ncolors));
1800 
1801     row_end = brows;
1802     if (row_end > m) row_end = m;
1803     for (row_start = 0; row_start < m; row_start += brows) { /* loop over row blocks of Csp */
1804       ca_den_ptr = ca_den;
1805       for (k = 0; k < ncolors; k++) { /* loop over colors (columns of Cden) */
1806         nrows = matcoloring->nrows[k];
1807         row   = rows + colorforrow[k];
1808         idx   = den2sp + colorforrow[k];
1809         for (l = lstart[k]; l < nrows; l++) {
1810           if (row[l] >= row_end) {
1811             lstart[k] = l;
1812             break;
1813           } else {
1814             ca[idx[l]] = ca_den_ptr[row[l]];
1815           }
1816         }
1817         ca_den_ptr += m;
1818       }
1819       row_end += brows;
1820       if (row_end > m) row_end = m;
1821     }
1822   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1823     ca_den_ptr = ca_den;
1824     for (k = 0; k < ncolors; k++) {
1825       nrows = matcoloring->nrows[k];
1826       row   = rows + colorforrow[k];
1827       idx   = den2sp + colorforrow[k];
1828       for (l = 0; l < nrows; l++) ca[idx[l]] = ca_den_ptr[row[l]];
1829       ca_den_ptr += m;
1830     }
1831   }
1832 
1833   PetscCall(MatDenseRestoreArrayRead(Cden, &ca_den));
1834 #if defined(PETSC_USE_INFO)
1835   if (matcoloring->brows > 0) {
1836     PetscCall(PetscInfo(Csp, "Loop over %" PetscInt_FMT " row blocks for den2sp\n", brows));
1837   } else {
1838     PetscCall(PetscInfo(Csp, "Loop over colors/columns of Cden, inefficient for large sparse matrix product \n"));
1839   }
1840 #endif
1841   PetscFunctionReturn(PETSC_SUCCESS);
1842 }
1843 
1844 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat, ISColoring iscoloring, MatTransposeColoring c)
1845 {
1846   PetscInt        i, n, nrows, Nbs, j, k, m, ncols, col, cm;
1847   const PetscInt *is, *ci, *cj, *row_idx;
1848   PetscInt        nis = iscoloring->n, *rowhit, bs = 1;
1849   IS             *isa;
1850   Mat_SeqAIJ     *csp = (Mat_SeqAIJ *)mat->data;
1851   PetscInt       *colorforrow, *rows, *rows_i, *idxhit, *spidx, *den2sp, *den2sp_i;
1852   PetscInt       *colorforcol, *columns, *columns_i, brows;
1853   PetscBool       flg;
1854 
1855   PetscFunctionBegin;
1856   PetscCall(ISColoringGetIS(iscoloring, PETSC_USE_POINTER, PETSC_IGNORE, &isa));
1857 
1858   /* bs >1 is not being tested yet! */
1859   Nbs       = mat->cmap->N / bs;
1860   c->M      = mat->rmap->N / bs; /* set total rows, columns and local rows */
1861   c->N      = Nbs;
1862   c->m      = c->M;
1863   c->rstart = 0;
1864   c->brows  = 100;
1865 
1866   c->ncolors = nis;
1867   PetscCall(PetscMalloc3(nis, &c->ncolumns, nis, &c->nrows, nis + 1, &colorforrow));
1868   PetscCall(PetscMalloc1(csp->nz + 1, &rows));
1869   PetscCall(PetscMalloc1(csp->nz + 1, &den2sp));
1870 
1871   brows = c->brows;
1872   PetscCall(PetscOptionsGetInt(NULL, NULL, "-matden2sp_brows", &brows, &flg));
1873   if (flg) c->brows = brows;
1874   if (brows > 0) PetscCall(PetscMalloc1(nis + 1, &c->lstart));
1875 
1876   colorforrow[0] = 0;
1877   rows_i         = rows;
1878   den2sp_i       = den2sp;
1879 
1880   PetscCall(PetscMalloc1(nis + 1, &colorforcol));
1881   PetscCall(PetscMalloc1(Nbs + 1, &columns));
1882 
1883   colorforcol[0] = 0;
1884   columns_i      = columns;
1885 
1886   /* get column-wise storage of mat */
1887   PetscCall(MatGetColumnIJ_SeqAIJ_Color(mat, 0, PETSC_FALSE, PETSC_FALSE, &ncols, &ci, &cj, &spidx, NULL));
1888 
1889   cm = c->m;
1890   PetscCall(PetscMalloc1(cm + 1, &rowhit));
1891   PetscCall(PetscMalloc1(cm + 1, &idxhit));
1892   for (i = 0; i < nis; i++) { /* loop over color */
1893     PetscCall(ISGetLocalSize(isa[i], &n));
1894     PetscCall(ISGetIndices(isa[i], &is));
1895 
1896     c->ncolumns[i] = n;
1897     if (n) PetscCall(PetscArraycpy(columns_i, is, n));
1898     colorforcol[i + 1] = colorforcol[i] + n;
1899     columns_i += n;
1900 
1901     /* fast, crude version requires O(N*N) work */
1902     PetscCall(PetscArrayzero(rowhit, cm));
1903 
1904     for (j = 0; j < n; j++) { /* loop over columns*/
1905       col     = is[j];
1906       row_idx = cj + ci[col];
1907       m       = ci[col + 1] - ci[col];
1908       for (k = 0; k < m; k++) { /* loop over columns marking them in rowhit */
1909         idxhit[*row_idx]   = spidx[ci[col] + k];
1910         rowhit[*row_idx++] = col + 1;
1911       }
1912     }
1913     /* count the number of hits */
1914     nrows = 0;
1915     for (j = 0; j < cm; j++) {
1916       if (rowhit[j]) nrows++;
1917     }
1918     c->nrows[i]        = nrows;
1919     colorforrow[i + 1] = colorforrow[i] + nrows;
1920 
1921     nrows = 0;
1922     for (j = 0; j < cm; j++) { /* loop over rows */
1923       if (rowhit[j]) {
1924         rows_i[nrows]   = j;
1925         den2sp_i[nrows] = idxhit[j];
1926         nrows++;
1927       }
1928     }
1929     den2sp_i += nrows;
1930 
1931     PetscCall(ISRestoreIndices(isa[i], &is));
1932     rows_i += nrows;
1933   }
1934   PetscCall(MatRestoreColumnIJ_SeqAIJ_Color(mat, 0, PETSC_FALSE, PETSC_FALSE, &ncols, &ci, &cj, &spidx, NULL));
1935   PetscCall(PetscFree(rowhit));
1936   PetscCall(ISColoringRestoreIS(iscoloring, PETSC_USE_POINTER, &isa));
1937   PetscCheck(csp->nz == colorforrow[nis], PETSC_COMM_SELF, PETSC_ERR_PLIB, "csp->nz %" PetscInt_FMT " != colorforrow[nis] %" PetscInt_FMT, csp->nz, colorforrow[nis]);
1938 
1939   c->colorforrow = colorforrow;
1940   c->rows        = rows;
1941   c->den2sp      = den2sp;
1942   c->colorforcol = colorforcol;
1943   c->columns     = columns;
1944 
1945   PetscCall(PetscFree(idxhit));
1946   PetscFunctionReturn(PETSC_SUCCESS);
1947 }
1948 
1949 static PetscErrorCode MatProductNumeric_AtB_SeqAIJ_SeqAIJ(Mat C)
1950 {
1951   Mat_Product *product = C->product;
1952   Mat          A = product->A, B = product->B;
1953 
1954   PetscFunctionBegin;
1955   if (C->ops->mattransposemultnumeric) {
1956     /* Alg: "outerproduct" */
1957     PetscCall((*C->ops->mattransposemultnumeric)(A, B, C));
1958   } else {
1959     /* Alg: "matmatmult" -- C = At*B */
1960     Mat_MatTransMatMult *atb = (Mat_MatTransMatMult *)product->data;
1961 
1962     PetscCheck(atb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1963     if (atb->At) {
1964       /* At is computed in MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ();
1965          user may have called MatProductReplaceMats() to get this A=product->A */
1966       PetscCall(MatTransposeSetPrecursor(A, atb->At));
1967       PetscCall(MatTranspose(A, MAT_REUSE_MATRIX, &atb->At));
1968     }
1969     PetscCall(MatMatMultNumeric_SeqAIJ_SeqAIJ(atb->At ? atb->At : A, B, C));
1970   }
1971   PetscFunctionReturn(PETSC_SUCCESS);
1972 }
1973 
1974 static PetscErrorCode MatProductSymbolic_AtB_SeqAIJ_SeqAIJ(Mat C)
1975 {
1976   Mat_Product *product = C->product;
1977   Mat          A = product->A, B = product->B;
1978   PetscReal    fill = product->fill;
1979 
1980   PetscFunctionBegin;
1981   PetscCall(MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A, B, fill, C));
1982 
1983   C->ops->productnumeric = MatProductNumeric_AtB_SeqAIJ_SeqAIJ;
1984   PetscFunctionReturn(PETSC_SUCCESS);
1985 }
1986 
1987 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AB(Mat C)
1988 {
1989   Mat_Product *product = C->product;
1990   PetscInt     alg     = 0; /* default algorithm */
1991   PetscBool    flg     = PETSC_FALSE;
1992 #if !defined(PETSC_HAVE_HYPRE)
1993   const char *algTypes[7] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge"};
1994   PetscInt    nalg        = 7;
1995 #else
1996   const char *algTypes[8] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge", "hypre"};
1997   PetscInt    nalg        = 8;
1998 #endif
1999 
2000   PetscFunctionBegin;
2001   /* Set default algorithm */
2002   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2003   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2004 
2005   /* Get runtime option */
2006   if (product->api_user) {
2007     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2008     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[0], &alg, &flg));
2009     PetscOptionsEnd();
2010   } else {
2011     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2012     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AB", algTypes, nalg, algTypes[0], &alg, &flg));
2013     PetscOptionsEnd();
2014   }
2015   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2016 
2017   C->ops->productsymbolic = MatProductSymbolic_AB;
2018   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqAIJ;
2019   PetscFunctionReturn(PETSC_SUCCESS);
2020 }
2021 
2022 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AtB(Mat C)
2023 {
2024   Mat_Product *product     = C->product;
2025   PetscInt     alg         = 0; /* default algorithm */
2026   PetscBool    flg         = PETSC_FALSE;
2027   const char  *algTypes[3] = {"default", "at*b", "outerproduct"};
2028   PetscInt     nalg        = 3;
2029 
2030   PetscFunctionBegin;
2031   /* Get runtime option */
2032   if (product->api_user) {
2033     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2034     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2035     PetscOptionsEnd();
2036   } else {
2037     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2038     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AtB", algTypes, nalg, algTypes[alg], &alg, &flg));
2039     PetscOptionsEnd();
2040   }
2041   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2042 
2043   C->ops->productsymbolic = MatProductSymbolic_AtB_SeqAIJ_SeqAIJ;
2044   PetscFunctionReturn(PETSC_SUCCESS);
2045 }
2046 
2047 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABt(Mat C)
2048 {
2049   Mat_Product *product     = C->product;
2050   PetscInt     alg         = 0; /* default algorithm */
2051   PetscBool    flg         = PETSC_FALSE;
2052   const char  *algTypes[2] = {"default", "color"};
2053   PetscInt     nalg        = 2;
2054 
2055   PetscFunctionBegin;
2056   /* Set default algorithm */
2057   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2058   if (!flg) {
2059     alg = 1;
2060     PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2061   }
2062 
2063   /* Get runtime option */
2064   if (product->api_user) {
2065     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatTransposeMult", "Mat");
2066     PetscCall(PetscOptionsEList("-matmattransmult_via", "Algorithmic approach", "MatMatTransposeMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2067     PetscOptionsEnd();
2068   } else {
2069     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABt", "Mat");
2070     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABt", algTypes, nalg, algTypes[alg], &alg, &flg));
2071     PetscOptionsEnd();
2072   }
2073   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2074 
2075   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ;
2076   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2077   PetscFunctionReturn(PETSC_SUCCESS);
2078 }
2079 
2080 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_PtAP(Mat C)
2081 {
2082   Mat_Product *product = C->product;
2083   PetscBool    flg     = PETSC_FALSE;
2084   PetscInt     alg     = 0; /* default algorithm -- alg=1 should be default!!! */
2085 #if !defined(PETSC_HAVE_HYPRE)
2086   const char *algTypes[2] = {"scalable", "rap"};
2087   PetscInt    nalg        = 2;
2088 #else
2089   const char *algTypes[3] = {"scalable", "rap", "hypre"};
2090   PetscInt    nalg        = 3;
2091 #endif
2092 
2093   PetscFunctionBegin;
2094   /* Set default algorithm */
2095   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2096   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2097 
2098   /* Get runtime option */
2099   if (product->api_user) {
2100     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2101     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[0], &alg, &flg));
2102     PetscOptionsEnd();
2103   } else {
2104     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2105     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_PtAP", algTypes, nalg, algTypes[0], &alg, &flg));
2106     PetscOptionsEnd();
2107   }
2108   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2109 
2110   C->ops->productsymbolic = MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ;
2111   PetscFunctionReturn(PETSC_SUCCESS);
2112 }
2113 
2114 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_RARt(Mat C)
2115 {
2116   Mat_Product *product     = C->product;
2117   PetscBool    flg         = PETSC_FALSE;
2118   PetscInt     alg         = 0; /* default algorithm */
2119   const char  *algTypes[3] = {"r*a*rt", "r*art", "coloring_rart"};
2120   PetscInt     nalg        = 3;
2121 
2122   PetscFunctionBegin;
2123   /* Set default algorithm */
2124   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2125   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2126 
2127   /* Get runtime option */
2128   if (product->api_user) {
2129     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatRARt", "Mat");
2130     PetscCall(PetscOptionsEList("-matrart_via", "Algorithmic approach", "MatRARt", algTypes, nalg, algTypes[0], &alg, &flg));
2131     PetscOptionsEnd();
2132   } else {
2133     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_RARt", "Mat");
2134     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_RARt", algTypes, nalg, algTypes[0], &alg, &flg));
2135     PetscOptionsEnd();
2136   }
2137   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2138 
2139   C->ops->productsymbolic = MatProductSymbolic_RARt_SeqAIJ_SeqAIJ;
2140   PetscFunctionReturn(PETSC_SUCCESS);
2141 }
2142 
2143 /* ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm */
2144 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABC(Mat C)
2145 {
2146   Mat_Product *product     = C->product;
2147   PetscInt     alg         = 0; /* default algorithm */
2148   PetscBool    flg         = PETSC_FALSE;
2149   const char  *algTypes[7] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge"};
2150   PetscInt     nalg        = 7;
2151 
2152   PetscFunctionBegin;
2153   /* Set default algorithm */
2154   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2155   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2156 
2157   /* Get runtime option */
2158   if (product->api_user) {
2159     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2160     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2161     PetscOptionsEnd();
2162   } else {
2163     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2164     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2165     PetscOptionsEnd();
2166   }
2167   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2168 
2169   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ;
2170   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2171   PetscFunctionReturn(PETSC_SUCCESS);
2172 }
2173 
2174 PetscErrorCode MatProductSetFromOptions_SeqAIJ(Mat C)
2175 {
2176   Mat_Product *product = C->product;
2177 
2178   PetscFunctionBegin;
2179   switch (product->type) {
2180   case MATPRODUCT_AB:
2181     PetscCall(MatProductSetFromOptions_SeqAIJ_AB(C));
2182     break;
2183   case MATPRODUCT_AtB:
2184     PetscCall(MatProductSetFromOptions_SeqAIJ_AtB(C));
2185     break;
2186   case MATPRODUCT_ABt:
2187     PetscCall(MatProductSetFromOptions_SeqAIJ_ABt(C));
2188     break;
2189   case MATPRODUCT_PtAP:
2190     PetscCall(MatProductSetFromOptions_SeqAIJ_PtAP(C));
2191     break;
2192   case MATPRODUCT_RARt:
2193     PetscCall(MatProductSetFromOptions_SeqAIJ_RARt(C));
2194     break;
2195   case MATPRODUCT_ABC:
2196     PetscCall(MatProductSetFromOptions_SeqAIJ_ABC(C));
2197     break;
2198   default:
2199     break;
2200   }
2201   PetscFunctionReturn(PETSC_SUCCESS);
2202 }
2203