xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision 21e3ffae2f3b73c0bd738cf6d0a809700fc04bb0) !
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   /*---------------*/
164   /* Allocate ci array, arrays for fill computation and */
165   /* free space for accumulating nonzero column info */
166   PetscCall(PetscMalloc1(am + 2, &ci));
167   ci[0] = 0;
168 
169   /* create and initialize a linked list */
170   PetscCall(PetscHMapICreateWithSize(bn, &ta));
171   MatRowMergeMax_SeqAIJ(b, bm, ta);
172   PetscCall(PetscHMapIGetSize(ta, &Crmax));
173   PetscCall(PetscHMapIDestroy(&ta));
174 
175   PetscCall(PetscLLCondensedCreate(Crmax, bn, &lnk, &lnkbt));
176 
177   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
178   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
179 
180   current_space = free_space;
181 
182   /* Determine ci and cj */
183   for (i = 0; i < am; i++) {
184     anzi = ai[i + 1] - ai[i];
185     aj   = a->j + ai[i];
186     for (j = 0; j < anzi; j++) {
187       brow = aj[j];
188       bnzj = bi[brow + 1] - bi[brow];
189       bj   = b->j + bi[brow];
190       /* add non-zero cols of B into the sorted linked list lnk */
191       PetscCall(PetscLLCondensedAddSorted(bnzj, bj, lnk, lnkbt));
192     }
193     /* add possible missing diagonal entry */
194     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted(1, &i, lnk, lnkbt));
195     cnzi = lnk[0];
196 
197     /* If free space is not available, make more free space */
198     /* Double the amount of total space in the list */
199     if (current_space->local_remaining < cnzi) {
200       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
201       ndouble++;
202     }
203 
204     /* Copy data into free space, then initialize lnk */
205     PetscCall(PetscLLCondensedClean(bn, cnzi, current_space->array, lnk, lnkbt));
206 
207     current_space->array += cnzi;
208     current_space->local_used += cnzi;
209     current_space->local_remaining -= cnzi;
210 
211     ci[i + 1] = ci[i] + cnzi;
212   }
213 
214   /* Column indices are in the list of free space */
215   /* Allocate space for cj, initialize cj, and */
216   /* destroy list of free space and other temporary array(s) */
217   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
218   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
219   PetscCall(PetscLLCondensedDestroy(lnk, lnkbt));
220 
221   /* put together the new symbolic matrix */
222   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
223   PetscCall(MatSetBlockSizesFromMats(C, A, B));
224 
225   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
226   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
227   c          = (Mat_SeqAIJ *)(C->data);
228   c->free_a  = PETSC_FALSE;
229   c->free_ij = PETSC_TRUE;
230   c->nonew   = 0;
231 
232   /* fast, needs non-scalable O(bn) array 'abdense' */
233   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
234 
235   /* set MatInfo */
236   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
237   if (afill < 1.0) afill = 1.0;
238   C->info.mallocs           = ndouble;
239   C->info.fill_ratio_given  = fill;
240   C->info.fill_ratio_needed = afill;
241 
242 #if defined(PETSC_USE_INFO)
243   if (ci[am]) {
244     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
245     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
246   } else {
247     PetscCall(PetscInfo(C, "Empty matrix product\n"));
248   }
249 #endif
250   PetscFunctionReturn(PETSC_SUCCESS);
251 }
252 
253 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat A, Mat B, Mat C)
254 {
255   PetscLogDouble     flops = 0.0;
256   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
257   Mat_SeqAIJ        *b     = (Mat_SeqAIJ *)B->data;
258   Mat_SeqAIJ        *c     = (Mat_SeqAIJ *)C->data;
259   PetscInt          *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bjj, *ci = c->i, *cj = c->j;
260   PetscInt           am = A->rmap->n, cm = C->rmap->n;
261   PetscInt           i, j, k, anzi, bnzi, cnzi, brow;
262   PetscScalar       *ca, valtmp;
263   PetscScalar       *ab_dense;
264   PetscContainer     cab_dense;
265   const PetscScalar *aa, *ba, *baj;
266 
267   PetscFunctionBegin;
268   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
269   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
270   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
271     PetscCall(PetscMalloc1(ci[cm] + 1, &ca));
272     c->a      = ca;
273     c->free_a = PETSC_TRUE;
274   } else ca = c->a;
275 
276   /* TODO this should be done in the symbolic phase */
277   /* However, this function is so heavily used (sometimes in an hidden way through multnumeric function pointers
278      that is hard to eradicate) */
279   PetscCall(PetscObjectQuery((PetscObject)C, "__PETSc__ab_dense", (PetscObject *)&cab_dense));
280   if (!cab_dense) {
281     PetscCall(PetscMalloc1(B->cmap->N, &ab_dense));
282     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &cab_dense));
283     PetscCall(PetscContainerSetPointer(cab_dense, ab_dense));
284     PetscCall(PetscContainerSetUserDestroy(cab_dense, PetscContainerUserDestroyDefault));
285     PetscCall(PetscObjectCompose((PetscObject)C, "__PETSc__ab_dense", (PetscObject)cab_dense));
286     PetscCall(PetscObjectDereference((PetscObject)cab_dense));
287   }
288   PetscCall(PetscContainerGetPointer(cab_dense, (void **)&ab_dense));
289   PetscCall(PetscArrayzero(ab_dense, B->cmap->N));
290 
291   /* clean old values in C */
292   PetscCall(PetscArrayzero(ca, ci[cm]));
293   /* Traverse A row-wise. */
294   /* Build the ith row in C by summing over nonzero columns in A, */
295   /* the rows of B corresponding to nonzeros of A. */
296   for (i = 0; i < am; i++) {
297     anzi = ai[i + 1] - ai[i];
298     for (j = 0; j < anzi; j++) {
299       brow = aj[j];
300       bnzi = bi[brow + 1] - bi[brow];
301       bjj  = bj + bi[brow];
302       baj  = ba + bi[brow];
303       /* perform dense axpy */
304       valtmp = aa[j];
305       for (k = 0; k < bnzi; k++) ab_dense[bjj[k]] += valtmp * baj[k];
306       flops += 2 * bnzi;
307     }
308     aj += anzi;
309     aa += anzi;
310 
311     cnzi = ci[i + 1] - ci[i];
312     for (k = 0; k < cnzi; k++) {
313       ca[k] += ab_dense[cj[k]];
314       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
315     }
316     flops += cnzi;
317     cj += cnzi;
318     ca += cnzi;
319   }
320 #if defined(PETSC_HAVE_DEVICE)
321   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
322 #endif
323   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
324   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
325   PetscCall(PetscLogFlops(flops));
326   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
327   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
328   PetscFunctionReturn(PETSC_SUCCESS);
329 }
330 
331 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A, Mat B, Mat C)
332 {
333   PetscLogDouble     flops = 0.0;
334   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
335   Mat_SeqAIJ        *b     = (Mat_SeqAIJ *)B->data;
336   Mat_SeqAIJ        *c     = (Mat_SeqAIJ *)C->data;
337   PetscInt          *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bjj, *ci = c->i, *cj = c->j;
338   PetscInt           am = A->rmap->N, cm = C->rmap->N;
339   PetscInt           i, j, k, anzi, bnzi, cnzi, brow;
340   PetscScalar       *ca = c->a, valtmp;
341   const PetscScalar *aa, *ba, *baj;
342   PetscInt           nextb;
343 
344   PetscFunctionBegin;
345   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
346   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
347   if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
348     PetscCall(PetscMalloc1(ci[cm] + 1, &ca));
349     c->a      = ca;
350     c->free_a = PETSC_TRUE;
351   }
352 
353   /* clean old values in C */
354   PetscCall(PetscArrayzero(ca, ci[cm]));
355   /* Traverse A row-wise. */
356   /* Build the ith row in C by summing over nonzero columns in A, */
357   /* the rows of B corresponding to nonzeros of A. */
358   for (i = 0; i < am; i++) {
359     anzi = ai[i + 1] - ai[i];
360     cnzi = ci[i + 1] - ci[i];
361     for (j = 0; j < anzi; j++) {
362       brow = aj[j];
363       bnzi = bi[brow + 1] - bi[brow];
364       bjj  = bj + bi[brow];
365       baj  = ba + bi[brow];
366       /* perform sparse axpy */
367       valtmp = aa[j];
368       nextb  = 0;
369       for (k = 0; nextb < bnzi; k++) {
370         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
371           ca[k] += valtmp * baj[nextb++];
372         }
373       }
374       flops += 2 * bnzi;
375     }
376     aj += anzi;
377     aa += anzi;
378     cj += cnzi;
379     ca += cnzi;
380   }
381 #if defined(PETSC_HAVE_DEVICE)
382   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
383 #endif
384   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
385   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
386   PetscCall(PetscLogFlops(flops));
387   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
388   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
389   PetscFunctionReturn(PETSC_SUCCESS);
390 }
391 
392 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A, Mat B, PetscReal fill, Mat C)
393 {
394   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
395   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
396   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
397   MatScalar         *ca;
398   PetscReal          afill;
399   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
400   PetscHMapI         ta;
401   PetscFreeSpaceList free_space = NULL, current_space = NULL;
402 
403   PetscFunctionBegin;
404   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
405   /*-----------------------------------------------------------------------------------------*/
406   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
407   PetscCall(PetscMalloc1(am + 2, &ci));
408   ci[0] = 0;
409 
410   /* create and initialize a linked list */
411   PetscCall(PetscHMapICreateWithSize(bn, &ta));
412   MatRowMergeMax_SeqAIJ(b, bm, ta);
413   PetscCall(PetscHMapIGetSize(ta, &Crmax));
414   PetscCall(PetscHMapIDestroy(&ta));
415 
416   PetscCall(PetscLLCondensedCreate_fast(Crmax, &lnk));
417 
418   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
419   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
420   current_space = free_space;
421 
422   /* Determine ci and cj */
423   for (i = 0; i < am; i++) {
424     anzi = ai[i + 1] - ai[i];
425     aj   = a->j + ai[i];
426     for (j = 0; j < anzi; j++) {
427       brow = aj[j];
428       bnzj = bi[brow + 1] - bi[brow];
429       bj   = b->j + bi[brow];
430       /* add non-zero cols of B into the sorted linked list lnk */
431       PetscCall(PetscLLCondensedAddSorted_fast(bnzj, bj, lnk));
432     }
433     /* add possible missing diagonal entry */
434     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted_fast(1, &i, lnk));
435     cnzi = lnk[1];
436 
437     /* If free space is not available, make more free space */
438     /* Double the amount of total space in the list */
439     if (current_space->local_remaining < cnzi) {
440       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
441       ndouble++;
442     }
443 
444     /* Copy data into free space, then initialize lnk */
445     PetscCall(PetscLLCondensedClean_fast(cnzi, current_space->array, lnk));
446 
447     current_space->array += cnzi;
448     current_space->local_used += cnzi;
449     current_space->local_remaining -= cnzi;
450 
451     ci[i + 1] = ci[i] + cnzi;
452   }
453 
454   /* Column indices are in the list of free space */
455   /* Allocate space for cj, initialize cj, and */
456   /* destroy list of free space and other temporary array(s) */
457   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
458   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
459   PetscCall(PetscLLCondensedDestroy_fast(lnk));
460 
461   /* Allocate space for ca */
462   PetscCall(PetscCalloc1(ci[am] + 1, &ca));
463 
464   /* put together the new symbolic matrix */
465   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, ca, ((PetscObject)A)->type_name, C));
466   PetscCall(MatSetBlockSizesFromMats(C, A, B));
467 
468   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
469   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
470   c          = (Mat_SeqAIJ *)(C->data);
471   c->free_a  = PETSC_TRUE;
472   c->free_ij = PETSC_TRUE;
473   c->nonew   = 0;
474 
475   /* slower, less memory */
476   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;
477 
478   /* set MatInfo */
479   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
480   if (afill < 1.0) afill = 1.0;
481   C->info.mallocs           = ndouble;
482   C->info.fill_ratio_given  = fill;
483   C->info.fill_ratio_needed = afill;
484 
485 #if defined(PETSC_USE_INFO)
486   if (ci[am]) {
487     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
488     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
489   } else {
490     PetscCall(PetscInfo(C, "Empty matrix product\n"));
491   }
492 #endif
493   PetscFunctionReturn(PETSC_SUCCESS);
494 }
495 
496 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A, Mat B, PetscReal fill, Mat C)
497 {
498   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
499   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
500   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
501   MatScalar         *ca;
502   PetscReal          afill;
503   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
504   PetscHMapI         ta;
505   PetscFreeSpaceList free_space = NULL, current_space = NULL;
506 
507   PetscFunctionBegin;
508   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
509   /*---------------------------------------------------------------------------------------------*/
510   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
511   PetscCall(PetscMalloc1(am + 2, &ci));
512   ci[0] = 0;
513 
514   /* create and initialize a linked list */
515   PetscCall(PetscHMapICreateWithSize(bn, &ta));
516   MatRowMergeMax_SeqAIJ(b, bm, ta);
517   PetscCall(PetscHMapIGetSize(ta, &Crmax));
518   PetscCall(PetscHMapIDestroy(&ta));
519   PetscCall(PetscLLCondensedCreate_Scalable(Crmax, &lnk));
520 
521   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
522   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
523   current_space = free_space;
524 
525   /* Determine ci and cj */
526   for (i = 0; i < am; i++) {
527     anzi = ai[i + 1] - ai[i];
528     aj   = a->j + ai[i];
529     for (j = 0; j < anzi; j++) {
530       brow = aj[j];
531       bnzj = bi[brow + 1] - bi[brow];
532       bj   = b->j + bi[brow];
533       /* add non-zero cols of B into the sorted linked list lnk */
534       PetscCall(PetscLLCondensedAddSorted_Scalable(bnzj, bj, lnk));
535     }
536     /* add possible missing diagonal entry */
537     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted_Scalable(1, &i, lnk));
538 
539     cnzi = lnk[0];
540 
541     /* If free space is not available, make more free space */
542     /* Double the amount of total space in the list */
543     if (current_space->local_remaining < cnzi) {
544       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
545       ndouble++;
546     }
547 
548     /* Copy data into free space, then initialize lnk */
549     PetscCall(PetscLLCondensedClean_Scalable(cnzi, current_space->array, lnk));
550 
551     current_space->array += cnzi;
552     current_space->local_used += cnzi;
553     current_space->local_remaining -= cnzi;
554 
555     ci[i + 1] = ci[i] + cnzi;
556   }
557 
558   /* Column indices are in the list of free space */
559   /* Allocate space for cj, initialize cj, and */
560   /* destroy list of free space and other temporary array(s) */
561   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
562   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
563   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
564 
565   /* Allocate space for ca */
566   /*-----------------------*/
567   PetscCall(PetscCalloc1(ci[am] + 1, &ca));
568 
569   /* put together the new symbolic matrix */
570   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, ca, ((PetscObject)A)->type_name, C));
571   PetscCall(MatSetBlockSizesFromMats(C, A, B));
572 
573   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
574   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
575   c          = (Mat_SeqAIJ *)(C->data);
576   c->free_a  = PETSC_TRUE;
577   c->free_ij = PETSC_TRUE;
578   c->nonew   = 0;
579 
580   /* slower, less memory */
581   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;
582 
583   /* set MatInfo */
584   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
585   if (afill < 1.0) afill = 1.0;
586   C->info.mallocs           = ndouble;
587   C->info.fill_ratio_given  = fill;
588   C->info.fill_ratio_needed = afill;
589 
590 #if defined(PETSC_USE_INFO)
591   if (ci[am]) {
592     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
593     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
594   } else {
595     PetscCall(PetscInfo(C, "Empty matrix product\n"));
596   }
597 #endif
598   PetscFunctionReturn(PETSC_SUCCESS);
599 }
600 
601 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A, Mat B, PetscReal fill, Mat C)
602 {
603   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
604   const PetscInt    *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
605   PetscInt          *ci, *cj, *bb;
606   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
607   PetscReal          afill;
608   PetscInt           i, j, col, ndouble = 0;
609   PetscFreeSpaceList free_space = NULL, current_space = NULL;
610   PetscHeap          h;
611 
612   PetscFunctionBegin;
613   /* Get ci and cj - by merging sorted rows using a heap */
614   /*---------------------------------------------------------------------------------------------*/
615   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
616   PetscCall(PetscMalloc1(am + 2, &ci));
617   ci[0] = 0;
618 
619   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
620   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
621   current_space = free_space;
622 
623   PetscCall(PetscHeapCreate(a->rmax, &h));
624   PetscCall(PetscMalloc1(a->rmax, &bb));
625 
626   /* Determine ci and cj */
627   for (i = 0; i < am; i++) {
628     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 */
629     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
630     ci[i + 1]            = ci[i];
631     /* Populate the min heap */
632     for (j = 0; j < anzi; j++) {
633       bb[j] = bi[acol[j]];           /* bb points at the start of the row */
634       if (bb[j] < bi[acol[j] + 1]) { /* Add if row is nonempty */
635         PetscCall(PetscHeapAdd(h, j, bj[bb[j]++]));
636       }
637     }
638     /* Pick off the min element, adding it to free space */
639     PetscCall(PetscHeapPop(h, &j, &col));
640     while (j >= 0) {
641       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
642         PetscCall(PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2, current_space->total_array_size), 16 << 20), &current_space));
643         ndouble++;
644       }
645       *(current_space->array++) = col;
646       current_space->local_used++;
647       current_space->local_remaining--;
648       ci[i + 1]++;
649 
650       /* stash if anything else remains in this row of B */
651       if (bb[j] < bi[acol[j] + 1]) PetscCall(PetscHeapStash(h, j, bj[bb[j]++]));
652       while (1) { /* pop and stash any other rows of B that also had an entry in this column */
653         PetscInt j2, col2;
654         PetscCall(PetscHeapPeek(h, &j2, &col2));
655         if (col2 != col) break;
656         PetscCall(PetscHeapPop(h, &j2, &col2));
657         if (bb[j2] < bi[acol[j2] + 1]) PetscCall(PetscHeapStash(h, j2, bj[bb[j2]++]));
658       }
659       /* Put any stashed elements back into the min heap */
660       PetscCall(PetscHeapUnstash(h));
661       PetscCall(PetscHeapPop(h, &j, &col));
662     }
663   }
664   PetscCall(PetscFree(bb));
665   PetscCall(PetscHeapDestroy(&h));
666 
667   /* Column indices are in the list of free space */
668   /* Allocate space for cj, initialize cj, and */
669   /* destroy list of free space and other temporary array(s) */
670   PetscCall(PetscMalloc1(ci[am], &cj));
671   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
672 
673   /* put together the new symbolic matrix */
674   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
675   PetscCall(MatSetBlockSizesFromMats(C, A, B));
676 
677   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
678   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
679   c          = (Mat_SeqAIJ *)(C->data);
680   c->free_a  = PETSC_TRUE;
681   c->free_ij = PETSC_TRUE;
682   c->nonew   = 0;
683 
684   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
685 
686   /* set MatInfo */
687   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
688   if (afill < 1.0) afill = 1.0;
689   C->info.mallocs           = ndouble;
690   C->info.fill_ratio_given  = fill;
691   C->info.fill_ratio_needed = afill;
692 
693 #if defined(PETSC_USE_INFO)
694   if (ci[am]) {
695     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
696     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
697   } else {
698     PetscCall(PetscInfo(C, "Empty matrix product\n"));
699   }
700 #endif
701   PetscFunctionReturn(PETSC_SUCCESS);
702 }
703 
704 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A, Mat B, PetscReal fill, Mat C)
705 {
706   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
707   const PetscInt    *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
708   PetscInt          *ci, *cj, *bb;
709   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
710   PetscReal          afill;
711   PetscInt           i, j, col, ndouble = 0;
712   PetscFreeSpaceList free_space = NULL, current_space = NULL;
713   PetscHeap          h;
714   PetscBT            bt;
715 
716   PetscFunctionBegin;
717   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
718   /*---------------------------------------------------------------------------------------------*/
719   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
720   PetscCall(PetscMalloc1(am + 2, &ci));
721   ci[0] = 0;
722 
723   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
724   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
725 
726   current_space = free_space;
727 
728   PetscCall(PetscHeapCreate(a->rmax, &h));
729   PetscCall(PetscMalloc1(a->rmax, &bb));
730   PetscCall(PetscBTCreate(bn, &bt));
731 
732   /* Determine ci and cj */
733   for (i = 0; i < am; i++) {
734     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 */
735     const PetscInt *acol = aj + ai[i];           /* column indices of nonzero entries in this row */
736     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
737     ci[i + 1]            = ci[i];
738     /* Populate the min heap */
739     for (j = 0; j < anzi; j++) {
740       PetscInt brow = acol[j];
741       for (bb[j] = bi[brow]; bb[j] < bi[brow + 1]; bb[j]++) {
742         PetscInt bcol = bj[bb[j]];
743         if (!PetscBTLookupSet(bt, bcol)) { /* new entry */
744           PetscCall(PetscHeapAdd(h, j, bcol));
745           bb[j]++;
746           break;
747         }
748       }
749     }
750     /* Pick off the min element, adding it to free space */
751     PetscCall(PetscHeapPop(h, &j, &col));
752     while (j >= 0) {
753       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
754         fptr = NULL;                            /* need PetscBTMemzero */
755         PetscCall(PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2, current_space->total_array_size), 16 << 20), &current_space));
756         ndouble++;
757       }
758       *(current_space->array++) = col;
759       current_space->local_used++;
760       current_space->local_remaining--;
761       ci[i + 1]++;
762 
763       /* stash if anything else remains in this row of B */
764       for (; bb[j] < bi[acol[j] + 1]; bb[j]++) {
765         PetscInt bcol = bj[bb[j]];
766         if (!PetscBTLookupSet(bt, bcol)) { /* new entry */
767           PetscCall(PetscHeapAdd(h, j, bcol));
768           bb[j]++;
769           break;
770         }
771       }
772       PetscCall(PetscHeapPop(h, &j, &col));
773     }
774     if (fptr) { /* Clear the bits for this row */
775       for (; fptr < current_space->array; fptr++) PetscCall(PetscBTClear(bt, *fptr));
776     } else { /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
777       PetscCall(PetscBTMemzero(bn, bt));
778     }
779   }
780   PetscCall(PetscFree(bb));
781   PetscCall(PetscHeapDestroy(&h));
782   PetscCall(PetscBTDestroy(&bt));
783 
784   /* Column indices are in the list of free space */
785   /* Allocate space for cj, initialize cj, and */
786   /* destroy list of free space and other temporary array(s) */
787   PetscCall(PetscMalloc1(ci[am], &cj));
788   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
789 
790   /* put together the new symbolic matrix */
791   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
792   PetscCall(MatSetBlockSizesFromMats(C, A, B));
793 
794   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
795   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
796   c          = (Mat_SeqAIJ *)(C->data);
797   c->free_a  = PETSC_TRUE;
798   c->free_ij = PETSC_TRUE;
799   c->nonew   = 0;
800 
801   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
802 
803   /* set MatInfo */
804   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
805   if (afill < 1.0) afill = 1.0;
806   C->info.mallocs           = ndouble;
807   C->info.fill_ratio_given  = fill;
808   C->info.fill_ratio_needed = afill;
809 
810 #if defined(PETSC_USE_INFO)
811   if (ci[am]) {
812     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
813     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
814   } else {
815     PetscCall(PetscInfo(C, "Empty matrix product\n"));
816   }
817 #endif
818   PetscFunctionReturn(PETSC_SUCCESS);
819 }
820 
821 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat A, Mat B, PetscReal fill, Mat C)
822 {
823   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
824   const PetscInt *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j, *inputi, *inputj, *inputcol, *inputcol_L1;
825   PetscInt       *ci, *cj, *outputj, worki_L1[9], worki_L2[9];
826   PetscInt        c_maxmem, a_maxrownnz = 0, a_rownnz;
827   const PetscInt  workcol[8] = {0, 1, 2, 3, 4, 5, 6, 7};
828   const PetscInt  am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
829   const PetscInt *brow_ptr[8], *brow_end[8];
830   PetscInt        window[8];
831   PetscInt        window_min, old_window_min, ci_nnz, outputi_nnz = 0, L1_nrows, L2_nrows;
832   PetscInt        i, k, ndouble = 0, L1_rowsleft, rowsleft;
833   PetscReal       afill;
834   PetscInt       *workj_L1, *workj_L2, *workj_L3;
835   PetscInt        L1_nnz, L2_nnz;
836 
837   /* Step 1: Get upper bound on memory required for allocation.
838              Because of the way virtual memory works,
839              only the memory pages that are actually needed will be physically allocated. */
840   PetscFunctionBegin;
841   PetscCall(PetscMalloc1(am + 1, &ci));
842   for (i = 0; i < am; i++) {
843     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 */
844     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
845     a_rownnz             = 0;
846     for (k = 0; k < anzi; ++k) {
847       a_rownnz += bi[acol[k] + 1] - bi[acol[k]];
848       if (a_rownnz > bn) {
849         a_rownnz = bn;
850         break;
851       }
852     }
853     a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz);
854   }
855   /* temporary work areas for merging rows */
856   PetscCall(PetscMalloc1(a_maxrownnz * 8, &workj_L1));
857   PetscCall(PetscMalloc1(a_maxrownnz * 8, &workj_L2));
858   PetscCall(PetscMalloc1(a_maxrownnz, &workj_L3));
859 
860   /* This should be enough for almost all matrices. If not, memory is reallocated later. */
861   c_maxmem = 8 * (ai[am] + bi[bm]);
862   /* Step 2: Populate pattern for C */
863   PetscCall(PetscMalloc1(c_maxmem, &cj));
864 
865   ci_nnz      = 0;
866   ci[0]       = 0;
867   worki_L1[0] = 0;
868   worki_L2[0] = 0;
869   for (i = 0; i < am; i++) {
870     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 */
871     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
872     rowsleft             = anzi;
873     inputcol_L1          = acol;
874     L2_nnz               = 0;
875     L2_nrows             = 1; /* Number of rows to be merged on Level 3. output of L3 already exists -> initial value 1   */
876     worki_L2[1]          = 0;
877     outputi_nnz          = 0;
878 
879     /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem  -> allocate more memory */
880     while (ci_nnz + a_maxrownnz > c_maxmem) {
881       c_maxmem *= 2;
882       ndouble++;
883       PetscCall(PetscRealloc(sizeof(PetscInt) * c_maxmem, &cj));
884     }
885 
886     while (rowsleft) {
887       L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */
888       L1_nrows    = 0;
889       L1_nnz      = 0;
890       inputcol    = inputcol_L1;
891       inputi      = bi;
892       inputj      = bj;
893 
894       /* The following macro is used to specialize for small rows in A.
895          This helps with compiler unrolling, improving performance substantially.
896           Input:  inputj   inputi  inputcol  bn
897           Output: outputj  outputi_nnz                       */
898 #define MatMatMultSymbolic_RowMergeMacro(ANNZ) \
899   window_min  = bn; \
900   outputi_nnz = 0; \
901   for (k = 0; k < ANNZ; ++k) { \
902     brow_ptr[k] = inputj + inputi[inputcol[k]]; \
903     brow_end[k] = inputj + inputi[inputcol[k] + 1]; \
904     window[k]   = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
905     window_min  = PetscMin(window[k], window_min); \
906   } \
907   while (window_min < bn) { \
908     outputj[outputi_nnz++] = window_min; \
909     /* advance front and compute new minimum */ \
910     old_window_min = window_min; \
911     window_min     = bn; \
912     for (k = 0; k < ANNZ; ++k) { \
913       if (window[k] == old_window_min) { \
914         brow_ptr[k]++; \
915         window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
916       } \
917       window_min = PetscMin(window[k], window_min); \
918     } \
919   }
920 
921       /************** L E V E L  1 ***************/
922       /* Merge up to 8 rows of B to L1 work array*/
923       while (L1_rowsleft) {
924         outputi_nnz = 0;
925         if (anzi > 8) outputj = workj_L1 + L1_nnz; /* Level 1 rowmerge*/
926         else outputj = cj + ci_nnz;                /* Merge directly to C */
927 
928         switch (L1_rowsleft) {
929         case 1:
930           brow_ptr[0] = inputj + inputi[inputcol[0]];
931           brow_end[0] = inputj + inputi[inputcol[0] + 1];
932           for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
933           inputcol += L1_rowsleft;
934           rowsleft -= L1_rowsleft;
935           L1_rowsleft = 0;
936           break;
937         case 2:
938           MatMatMultSymbolic_RowMergeMacro(2);
939           inputcol += L1_rowsleft;
940           rowsleft -= L1_rowsleft;
941           L1_rowsleft = 0;
942           break;
943         case 3:
944           MatMatMultSymbolic_RowMergeMacro(3);
945           inputcol += L1_rowsleft;
946           rowsleft -= L1_rowsleft;
947           L1_rowsleft = 0;
948           break;
949         case 4:
950           MatMatMultSymbolic_RowMergeMacro(4);
951           inputcol += L1_rowsleft;
952           rowsleft -= L1_rowsleft;
953           L1_rowsleft = 0;
954           break;
955         case 5:
956           MatMatMultSymbolic_RowMergeMacro(5);
957           inputcol += L1_rowsleft;
958           rowsleft -= L1_rowsleft;
959           L1_rowsleft = 0;
960           break;
961         case 6:
962           MatMatMultSymbolic_RowMergeMacro(6);
963           inputcol += L1_rowsleft;
964           rowsleft -= L1_rowsleft;
965           L1_rowsleft = 0;
966           break;
967         case 7:
968           MatMatMultSymbolic_RowMergeMacro(7);
969           inputcol += L1_rowsleft;
970           rowsleft -= L1_rowsleft;
971           L1_rowsleft = 0;
972           break;
973         default:
974           MatMatMultSymbolic_RowMergeMacro(8);
975           inputcol += 8;
976           rowsleft -= 8;
977           L1_rowsleft -= 8;
978           break;
979         }
980         inputcol_L1 = inputcol;
981         L1_nnz += outputi_nnz;
982         worki_L1[++L1_nrows] = L1_nnz;
983       }
984 
985       /********************** L E V E L  2 ************************/
986       /* Merge from L1 work array to either C or to L2 work array */
987       if (anzi > 8) {
988         inputi      = worki_L1;
989         inputj      = workj_L1;
990         inputcol    = workcol;
991         outputi_nnz = 0;
992 
993         if (anzi <= 64) outputj = cj + ci_nnz; /* Merge from L1 work array to C */
994         else outputj = workj_L2 + L2_nnz;      /* Merge from L1 work array to L2 work array */
995 
996         switch (L1_nrows) {
997         case 1:
998           brow_ptr[0] = inputj + inputi[inputcol[0]];
999           brow_end[0] = inputj + inputi[inputcol[0] + 1];
1000           for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
1001           break;
1002         case 2:
1003           MatMatMultSymbolic_RowMergeMacro(2);
1004           break;
1005         case 3:
1006           MatMatMultSymbolic_RowMergeMacro(3);
1007           break;
1008         case 4:
1009           MatMatMultSymbolic_RowMergeMacro(4);
1010           break;
1011         case 5:
1012           MatMatMultSymbolic_RowMergeMacro(5);
1013           break;
1014         case 6:
1015           MatMatMultSymbolic_RowMergeMacro(6);
1016           break;
1017         case 7:
1018           MatMatMultSymbolic_RowMergeMacro(7);
1019           break;
1020         case 8:
1021           MatMatMultSymbolic_RowMergeMacro(8);
1022           break;
1023         default:
1024           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatMatMult logic error: Not merging 1-8 rows from L1 work array!");
1025         }
1026         L2_nnz += outputi_nnz;
1027         worki_L2[++L2_nrows] = L2_nnz;
1028 
1029         /************************ L E V E L  3 **********************/
1030         /* Merge from L2 work array to either C or to L2 work array */
1031         if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) {
1032           inputi      = worki_L2;
1033           inputj      = workj_L2;
1034           inputcol    = workcol;
1035           outputi_nnz = 0;
1036           if (rowsleft) outputj = workj_L3;
1037           else outputj = cj + ci_nnz;
1038           switch (L2_nrows) {
1039           case 1:
1040             brow_ptr[0] = inputj + inputi[inputcol[0]];
1041             brow_end[0] = inputj + inputi[inputcol[0] + 1];
1042             for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
1043             break;
1044           case 2:
1045             MatMatMultSymbolic_RowMergeMacro(2);
1046             break;
1047           case 3:
1048             MatMatMultSymbolic_RowMergeMacro(3);
1049             break;
1050           case 4:
1051             MatMatMultSymbolic_RowMergeMacro(4);
1052             break;
1053           case 5:
1054             MatMatMultSymbolic_RowMergeMacro(5);
1055             break;
1056           case 6:
1057             MatMatMultSymbolic_RowMergeMacro(6);
1058             break;
1059           case 7:
1060             MatMatMultSymbolic_RowMergeMacro(7);
1061             break;
1062           case 8:
1063             MatMatMultSymbolic_RowMergeMacro(8);
1064             break;
1065           default:
1066             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatMatMult logic error: Not merging 1-8 rows from L2 work array!");
1067           }
1068           L2_nrows    = 1;
1069           L2_nnz      = outputi_nnz;
1070           worki_L2[1] = outputi_nnz;
1071           /* Copy to workj_L2 */
1072           if (rowsleft) {
1073             for (k = 0; k < outputi_nnz; ++k) workj_L2[k] = outputj[k];
1074           }
1075         }
1076       }
1077     } /* while (rowsleft) */
1078 #undef MatMatMultSymbolic_RowMergeMacro
1079 
1080     /* terminate current row */
1081     ci_nnz += outputi_nnz;
1082     ci[i + 1] = ci_nnz;
1083   }
1084 
1085   /* Step 3: Create the new symbolic matrix */
1086   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
1087   PetscCall(MatSetBlockSizesFromMats(C, A, B));
1088 
1089   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1090   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1091   c          = (Mat_SeqAIJ *)(C->data);
1092   c->free_a  = PETSC_TRUE;
1093   c->free_ij = PETSC_TRUE;
1094   c->nonew   = 0;
1095 
1096   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
1097 
1098   /* set MatInfo */
1099   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
1100   if (afill < 1.0) afill = 1.0;
1101   C->info.mallocs           = ndouble;
1102   C->info.fill_ratio_given  = fill;
1103   C->info.fill_ratio_needed = afill;
1104 
1105 #if defined(PETSC_USE_INFO)
1106   if (ci[am]) {
1107     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
1108     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1109   } else {
1110     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1111   }
1112 #endif
1113 
1114   /* Step 4: Free temporary work areas */
1115   PetscCall(PetscFree(workj_L1));
1116   PetscCall(PetscFree(workj_L2));
1117   PetscCall(PetscFree(workj_L3));
1118   PetscFunctionReturn(PETSC_SUCCESS);
1119 }
1120 
1121 /* concatenate unique entries and then sort */
1122 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat A, Mat B, PetscReal fill, Mat C)
1123 {
1124   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
1125   const PetscInt *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
1126   PetscInt       *ci, *cj, bcol;
1127   PetscInt        am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
1128   PetscReal       afill;
1129   PetscInt        i, j, ndouble = 0;
1130   PetscSegBuffer  seg, segrow;
1131   char           *seen;
1132 
1133   PetscFunctionBegin;
1134   PetscCall(PetscMalloc1(am + 1, &ci));
1135   ci[0] = 0;
1136 
1137   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
1138   PetscCall(PetscSegBufferCreate(sizeof(PetscInt), (PetscInt)(fill * (ai[am] + bi[bm])), &seg));
1139   PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 100, &segrow));
1140   PetscCall(PetscCalloc1(bn, &seen));
1141 
1142   /* Determine ci and cj */
1143   for (i = 0; i < am; i++) {
1144     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 */
1145     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
1146     PetscInt packlen     = 0, *PETSC_RESTRICT crow;
1147 
1148     /* Pack segrow */
1149     for (j = 0; j < anzi; j++) {
1150       PetscInt brow = acol[j], bjstart = bi[brow], bjend = bi[brow + 1], k;
1151       for (k = bjstart; k < bjend; k++) {
1152         bcol = bj[k];
1153         if (!seen[bcol]) { /* new entry */
1154           PetscInt *PETSC_RESTRICT slot;
1155           PetscCall(PetscSegBufferGetInts(segrow, 1, &slot));
1156           *slot      = bcol;
1157           seen[bcol] = 1;
1158           packlen++;
1159         }
1160       }
1161     }
1162 
1163     /* Check i-th diagonal entry */
1164     if (C->force_diagonals && !seen[i]) {
1165       PetscInt *PETSC_RESTRICT slot;
1166       PetscCall(PetscSegBufferGetInts(segrow, 1, &slot));
1167       *slot   = i;
1168       seen[i] = 1;
1169       packlen++;
1170     }
1171 
1172     PetscCall(PetscSegBufferGetInts(seg, packlen, &crow));
1173     PetscCall(PetscSegBufferExtractTo(segrow, crow));
1174     PetscCall(PetscSortInt(packlen, crow));
1175     ci[i + 1] = ci[i] + packlen;
1176     for (j = 0; j < packlen; j++) seen[crow[j]] = 0;
1177   }
1178   PetscCall(PetscSegBufferDestroy(&segrow));
1179   PetscCall(PetscFree(seen));
1180 
1181   /* Column indices are in the segmented buffer */
1182   PetscCall(PetscSegBufferExtractAlloc(seg, &cj));
1183   PetscCall(PetscSegBufferDestroy(&seg));
1184 
1185   /* put together the new symbolic matrix */
1186   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
1187   PetscCall(MatSetBlockSizesFromMats(C, A, B));
1188 
1189   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1190   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1191   c          = (Mat_SeqAIJ *)(C->data);
1192   c->free_a  = PETSC_TRUE;
1193   c->free_ij = PETSC_TRUE;
1194   c->nonew   = 0;
1195 
1196   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
1197 
1198   /* set MatInfo */
1199   afill = (PetscReal)ci[am] / PetscMax(ai[am] + bi[bm], 1) + 1.e-5;
1200   if (afill < 1.0) afill = 1.0;
1201   C->info.mallocs           = ndouble;
1202   C->info.fill_ratio_given  = fill;
1203   C->info.fill_ratio_needed = afill;
1204 
1205 #if defined(PETSC_USE_INFO)
1206   if (ci[am]) {
1207     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
1208     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1209   } else {
1210     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1211   }
1212 #endif
1213   PetscFunctionReturn(PETSC_SUCCESS);
1214 }
1215 
1216 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(void *data)
1217 {
1218   Mat_MatMatTransMult *abt = (Mat_MatMatTransMult *)data;
1219 
1220   PetscFunctionBegin;
1221   PetscCall(MatTransposeColoringDestroy(&abt->matcoloring));
1222   PetscCall(MatDestroy(&abt->Bt_den));
1223   PetscCall(MatDestroy(&abt->ABt_den));
1224   PetscCall(PetscFree(abt));
1225   PetscFunctionReturn(PETSC_SUCCESS);
1226 }
1227 
1228 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
1229 {
1230   Mat                  Bt;
1231   Mat_MatMatTransMult *abt;
1232   Mat_Product         *product = C->product;
1233   char                *alg;
1234 
1235   PetscFunctionBegin;
1236   PetscCheck(product, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1237   PetscCheck(!product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1238 
1239   /* create symbolic Bt */
1240   PetscCall(MatTransposeSymbolic(B, &Bt));
1241   PetscCall(MatSetBlockSizes(Bt, PetscAbs(A->cmap->bs), PetscAbs(B->cmap->bs)));
1242   PetscCall(MatSetType(Bt, ((PetscObject)A)->type_name));
1243 
1244   /* get symbolic C=A*Bt */
1245   PetscCall(PetscStrallocpy(product->alg, &alg));
1246   PetscCall(MatProductSetAlgorithm(C, "sorted")); /* set algorithm for C = A*Bt */
1247   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(A, Bt, fill, C));
1248   PetscCall(MatProductSetAlgorithm(C, alg)); /* resume original algorithm for ABt product */
1249   PetscCall(PetscFree(alg));
1250 
1251   /* create a supporting struct for reuse intermediate dense matrices with matcoloring */
1252   PetscCall(PetscNew(&abt));
1253 
1254   product->data    = abt;
1255   product->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
1256 
1257   C->ops->mattransposemultnumeric = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ;
1258 
1259   abt->usecoloring = PETSC_FALSE;
1260   PetscCall(PetscStrcmp(product->alg, "color", &abt->usecoloring));
1261   if (abt->usecoloring) {
1262     /* Create MatTransposeColoring from symbolic C=A*B^T */
1263     MatTransposeColoring matcoloring;
1264     MatColoring          coloring;
1265     ISColoring           iscoloring;
1266     Mat                  Bt_dense, C_dense;
1267 
1268     /* inode causes memory problem */
1269     PetscCall(MatSetOption(C, MAT_USE_INODES, PETSC_FALSE));
1270 
1271     PetscCall(MatColoringCreate(C, &coloring));
1272     PetscCall(MatColoringSetDistance(coloring, 2));
1273     PetscCall(MatColoringSetType(coloring, MATCOLORINGSL));
1274     PetscCall(MatColoringSetFromOptions(coloring));
1275     PetscCall(MatColoringApply(coloring, &iscoloring));
1276     PetscCall(MatColoringDestroy(&coloring));
1277     PetscCall(MatTransposeColoringCreate(C, iscoloring, &matcoloring));
1278 
1279     abt->matcoloring = matcoloring;
1280 
1281     PetscCall(ISColoringDestroy(&iscoloring));
1282 
1283     /* Create Bt_dense and C_dense = A*Bt_dense */
1284     PetscCall(MatCreate(PETSC_COMM_SELF, &Bt_dense));
1285     PetscCall(MatSetSizes(Bt_dense, A->cmap->n, matcoloring->ncolors, A->cmap->n, matcoloring->ncolors));
1286     PetscCall(MatSetType(Bt_dense, MATSEQDENSE));
1287     PetscCall(MatSeqDenseSetPreallocation(Bt_dense, NULL));
1288 
1289     Bt_dense->assembled = PETSC_TRUE;
1290     abt->Bt_den         = Bt_dense;
1291 
1292     PetscCall(MatCreate(PETSC_COMM_SELF, &C_dense));
1293     PetscCall(MatSetSizes(C_dense, A->rmap->n, matcoloring->ncolors, A->rmap->n, matcoloring->ncolors));
1294     PetscCall(MatSetType(C_dense, MATSEQDENSE));
1295     PetscCall(MatSeqDenseSetPreallocation(C_dense, NULL));
1296 
1297     Bt_dense->assembled = PETSC_TRUE;
1298     abt->ABt_den        = C_dense;
1299 
1300 #if defined(PETSC_USE_INFO)
1301     {
1302       Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data;
1303       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,
1304                           Bt_dense->cmap->n, c->nz, A->rmap->n * matcoloring->ncolors, (double)(((PetscReal)(c->nz)) / ((PetscReal)(A->rmap->n * matcoloring->ncolors)))));
1305     }
1306 #endif
1307   }
1308   /* clean up */
1309   PetscCall(MatDestroy(&Bt));
1310   PetscFunctionReturn(PETSC_SUCCESS);
1311 }
1312 
1313 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
1314 {
1315   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c = (Mat_SeqAIJ *)C->data;
1316   PetscInt            *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, anzi, bnzj, nexta, nextb, *acol, *bcol, brow;
1317   PetscInt             cm = C->rmap->n, *ci = c->i, *cj = c->j, i, j, cnzi, *ccol;
1318   PetscLogDouble       flops = 0.0;
1319   MatScalar           *aa = a->a, *aval, *ba = b->a, *bval, *ca, *cval;
1320   Mat_MatMatTransMult *abt;
1321   Mat_Product         *product = C->product;
1322 
1323   PetscFunctionBegin;
1324   PetscCheck(product, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1325   abt = (Mat_MatMatTransMult *)product->data;
1326   PetscCheck(abt, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1327   /* clear old values in C */
1328   if (!c->a) {
1329     PetscCall(PetscCalloc1(ci[cm] + 1, &ca));
1330     c->a      = ca;
1331     c->free_a = PETSC_TRUE;
1332   } else {
1333     ca = c->a;
1334     PetscCall(PetscArrayzero(ca, ci[cm] + 1));
1335   }
1336 
1337   if (abt->usecoloring) {
1338     MatTransposeColoring matcoloring = abt->matcoloring;
1339     Mat                  Bt_dense, C_dense = abt->ABt_den;
1340 
1341     /* Get Bt_dense by Apply MatTransposeColoring to B */
1342     Bt_dense = abt->Bt_den;
1343     PetscCall(MatTransColoringApplySpToDen(matcoloring, B, Bt_dense));
1344 
1345     /* C_dense = A*Bt_dense */
1346     PetscCall(MatMatMultNumeric_SeqAIJ_SeqDense(A, Bt_dense, C_dense));
1347 
1348     /* Recover C from C_dense */
1349     PetscCall(MatTransColoringApplyDenToSp(matcoloring, C_dense, C));
1350     PetscFunctionReturn(PETSC_SUCCESS);
1351   }
1352 
1353   for (i = 0; i < cm; i++) {
1354     anzi = ai[i + 1] - ai[i];
1355     acol = aj + ai[i];
1356     aval = aa + ai[i];
1357     cnzi = ci[i + 1] - ci[i];
1358     ccol = cj + ci[i];
1359     cval = ca + ci[i];
1360     for (j = 0; j < cnzi; j++) {
1361       brow = ccol[j];
1362       bnzj = bi[brow + 1] - bi[brow];
1363       bcol = bj + bi[brow];
1364       bval = ba + bi[brow];
1365 
1366       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1367       nexta = 0;
1368       nextb = 0;
1369       while (nexta < anzi && nextb < bnzj) {
1370         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
1371         if (nexta == anzi) break;
1372         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
1373         if (nextb == bnzj) break;
1374         if (acol[nexta] == bcol[nextb]) {
1375           cval[j] += aval[nexta] * bval[nextb];
1376           nexta++;
1377           nextb++;
1378           flops += 2;
1379         }
1380       }
1381     }
1382   }
1383   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1384   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1385   PetscCall(PetscLogFlops(flops));
1386   PetscFunctionReturn(PETSC_SUCCESS);
1387 }
1388 
1389 PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(void *data)
1390 {
1391   Mat_MatTransMatMult *atb = (Mat_MatTransMatMult *)data;
1392 
1393   PetscFunctionBegin;
1394   PetscCall(MatDestroy(&atb->At));
1395   if (atb->destroy) PetscCall((*atb->destroy)(atb->data));
1396   PetscCall(PetscFree(atb));
1397   PetscFunctionReturn(PETSC_SUCCESS);
1398 }
1399 
1400 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
1401 {
1402   Mat          At      = NULL;
1403   Mat_Product *product = C->product;
1404   PetscBool    flg, def, square;
1405 
1406   PetscFunctionBegin;
1407   MatCheckProduct(C, 4);
1408   square = (PetscBool)(A == B && A->symmetric == PETSC_BOOL3_TRUE);
1409   /* outerproduct */
1410   PetscCall(PetscStrcmp(product->alg, "outerproduct", &flg));
1411   if (flg) {
1412     /* create symbolic At */
1413     if (!square) {
1414       PetscCall(MatTransposeSymbolic(A, &At));
1415       PetscCall(MatSetBlockSizes(At, PetscAbs(A->cmap->bs), PetscAbs(B->cmap->bs)));
1416       PetscCall(MatSetType(At, ((PetscObject)A)->type_name));
1417     }
1418     /* get symbolic C=At*B */
1419     PetscCall(MatProductSetAlgorithm(C, "sorted"));
1420     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At, B, fill, C));
1421 
1422     /* clean up */
1423     if (!square) PetscCall(MatDestroy(&At));
1424 
1425     C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ; /* outerproduct */
1426     PetscCall(MatProductSetAlgorithm(C, "outerproduct"));
1427     PetscFunctionReturn(PETSC_SUCCESS);
1428   }
1429 
1430   /* matmatmult */
1431   PetscCall(PetscStrcmp(product->alg, "default", &def));
1432   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
1433   if (flg || def) {
1434     Mat_MatTransMatMult *atb;
1435 
1436     PetscCheck(!product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1437     PetscCall(PetscNew(&atb));
1438     if (!square) PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
1439     PetscCall(MatProductSetAlgorithm(C, "sorted"));
1440     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At, B, fill, C));
1441     PetscCall(MatProductSetAlgorithm(C, "at*b"));
1442     product->data    = atb;
1443     product->destroy = MatDestroy_SeqAIJ_MatTransMatMult;
1444     atb->At          = At;
1445 
1446     C->ops->mattransposemultnumeric = NULL; /* see MatProductNumeric_AtB_SeqAIJ_SeqAIJ */
1447     PetscFunctionReturn(PETSC_SUCCESS);
1448   }
1449 
1450   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
1451 }
1452 
1453 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
1454 {
1455   Mat_SeqAIJ    *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c = (Mat_SeqAIJ *)C->data;
1456   PetscInt       am = A->rmap->n, anzi, *ai = a->i, *aj = a->j, *bi = b->i, *bj, bnzi, nextb;
1457   PetscInt       cm = C->rmap->n, *ci = c->i, *cj = c->j, crow, *cjj, i, j, k;
1458   PetscLogDouble flops = 0.0;
1459   MatScalar     *aa    = a->a, *ba, *ca, *caj;
1460 
1461   PetscFunctionBegin;
1462   if (!c->a) {
1463     PetscCall(PetscCalloc1(ci[cm] + 1, &ca));
1464 
1465     c->a      = ca;
1466     c->free_a = PETSC_TRUE;
1467   } else {
1468     ca = c->a;
1469     PetscCall(PetscArrayzero(ca, ci[cm]));
1470   }
1471 
1472   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1473   for (i = 0; i < am; i++) {
1474     bj   = b->j + bi[i];
1475     ba   = b->a + bi[i];
1476     bnzi = bi[i + 1] - bi[i];
1477     anzi = ai[i + 1] - ai[i];
1478     for (j = 0; j < anzi; j++) {
1479       nextb = 0;
1480       crow  = *aj++;
1481       cjj   = cj + ci[crow];
1482       caj   = ca + ci[crow];
1483       /* perform sparse axpy operation.  Note cjj includes bj. */
1484       for (k = 0; nextb < bnzi; k++) {
1485         if (cjj[k] == *(bj + nextb)) { /* ccol == bcol */
1486           caj[k] += (*aa) * (*(ba + nextb));
1487           nextb++;
1488         }
1489       }
1490       flops += 2 * bnzi;
1491       aa++;
1492     }
1493   }
1494 
1495   /* Assemble the final matrix and clean up */
1496   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1497   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1498   PetscCall(PetscLogFlops(flops));
1499   PetscFunctionReturn(PETSC_SUCCESS);
1500 }
1501 
1502 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
1503 {
1504   PetscFunctionBegin;
1505   PetscCall(MatMatMultSymbolic_SeqDense_SeqDense(A, B, 0.0, C));
1506   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1507   PetscFunctionReturn(PETSC_SUCCESS);
1508 }
1509 
1510 PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A, Mat B, Mat C, const PetscBool add)
1511 {
1512   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1513   PetscScalar       *c, r1, r2, r3, r4, *c1, *c2, *c3, *c4;
1514   const PetscScalar *aa, *b, *b1, *b2, *b3, *b4, *av;
1515   const PetscInt    *aj;
1516   PetscInt           cm = C->rmap->n, cn = B->cmap->n, bm, am = A->rmap->n;
1517   PetscInt           clda;
1518   PetscInt           am4, bm4, col, i, j, n;
1519 
1520   PetscFunctionBegin;
1521   if (!cm || !cn) PetscFunctionReturn(PETSC_SUCCESS);
1522   PetscCall(MatSeqAIJGetArrayRead(A, &av));
1523   if (add) {
1524     PetscCall(MatDenseGetArray(C, &c));
1525   } else {
1526     PetscCall(MatDenseGetArrayWrite(C, &c));
1527   }
1528   PetscCall(MatDenseGetArrayRead(B, &b));
1529   PetscCall(MatDenseGetLDA(B, &bm));
1530   PetscCall(MatDenseGetLDA(C, &clda));
1531   am4 = 4 * clda;
1532   bm4 = 4 * bm;
1533   b1  = b;
1534   b2  = b1 + bm;
1535   b3  = b2 + bm;
1536   b4  = b3 + bm;
1537   c1  = c;
1538   c2  = c1 + clda;
1539   c3  = c2 + clda;
1540   c4  = c3 + clda;
1541   for (col = 0; col < (cn / 4) * 4; col += 4) { /* over columns of C */
1542     for (i = 0; i < am; i++) {                  /* over rows of A in those columns */
1543       r1 = r2 = r3 = r4 = 0.0;
1544       n                 = a->i[i + 1] - a->i[i];
1545       aj                = a->j + a->i[i];
1546       aa                = av + a->i[i];
1547       for (j = 0; j < n; j++) {
1548         const PetscScalar aatmp = aa[j];
1549         const PetscInt    ajtmp = aj[j];
1550         r1 += aatmp * b1[ajtmp];
1551         r2 += aatmp * b2[ajtmp];
1552         r3 += aatmp * b3[ajtmp];
1553         r4 += aatmp * b4[ajtmp];
1554       }
1555       if (add) {
1556         c1[i] += r1;
1557         c2[i] += r2;
1558         c3[i] += r3;
1559         c4[i] += r4;
1560       } else {
1561         c1[i] = r1;
1562         c2[i] = r2;
1563         c3[i] = r3;
1564         c4[i] = r4;
1565       }
1566     }
1567     b1 += bm4;
1568     b2 += bm4;
1569     b3 += bm4;
1570     b4 += bm4;
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->i[i];
1615         aa           = av + a->i[i];
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 /* ------------------------------------------------------- */
1658 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AB(Mat C)
1659 {
1660   PetscFunctionBegin;
1661   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqDense;
1662   C->ops->productsymbolic = MatProductSymbolic_AB;
1663   PetscFunctionReturn(PETSC_SUCCESS);
1664 }
1665 
1666 PETSC_INTERN PetscErrorCode MatTMatTMultSymbolic_SeqAIJ_SeqDense(Mat, Mat, PetscReal, Mat);
1667 
1668 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(Mat C)
1669 {
1670   PetscFunctionBegin;
1671   C->ops->transposematmultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1672   C->ops->productsymbolic          = MatProductSymbolic_AtB;
1673   PetscFunctionReturn(PETSC_SUCCESS);
1674 }
1675 
1676 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(Mat C)
1677 {
1678   PetscFunctionBegin;
1679   C->ops->mattransposemultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1680   C->ops->productsymbolic          = MatProductSymbolic_ABt;
1681   PetscFunctionReturn(PETSC_SUCCESS);
1682 }
1683 
1684 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat C)
1685 {
1686   Mat_Product *product = C->product;
1687 
1688   PetscFunctionBegin;
1689   switch (product->type) {
1690   case MATPRODUCT_AB:
1691     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_AB(C));
1692     break;
1693   case MATPRODUCT_AtB:
1694     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(C));
1695     break;
1696   case MATPRODUCT_ABt:
1697     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(C));
1698     break;
1699   default:
1700     break;
1701   }
1702   PetscFunctionReturn(PETSC_SUCCESS);
1703 }
1704 /* ------------------------------------------------------- */
1705 static PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(Mat C)
1706 {
1707   Mat_Product *product = C->product;
1708   Mat          A       = product->A;
1709   PetscBool    baij;
1710 
1711   PetscFunctionBegin;
1712   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &baij));
1713   if (!baij) { /* A is seqsbaij */
1714     PetscBool sbaij;
1715     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &sbaij));
1716     PetscCheck(sbaij, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "Mat must be either seqbaij or seqsbaij format");
1717 
1718     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqSBAIJ_SeqDense;
1719   } else { /* A is seqbaij */
1720     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqBAIJ_SeqDense;
1721   }
1722 
1723   C->ops->productsymbolic = MatProductSymbolic_AB;
1724   PetscFunctionReturn(PETSC_SUCCESS);
1725 }
1726 
1727 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense(Mat C)
1728 {
1729   Mat_Product *product = C->product;
1730 
1731   PetscFunctionBegin;
1732   MatCheckProduct(C, 1);
1733   PetscCheck(product->A, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing A");
1734   if (product->type == MATPRODUCT_AB || (product->type == MATPRODUCT_AtB && product->A->symmetric == PETSC_BOOL3_TRUE)) PetscCall(MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(C));
1735   PetscFunctionReturn(PETSC_SUCCESS);
1736 }
1737 
1738 /* ------------------------------------------------------- */
1739 static PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ_AB(Mat C)
1740 {
1741   PetscFunctionBegin;
1742   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqDense_SeqAIJ;
1743   C->ops->productsymbolic = MatProductSymbolic_AB;
1744   PetscFunctionReturn(PETSC_SUCCESS);
1745 }
1746 
1747 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ(Mat C)
1748 {
1749   Mat_Product *product = C->product;
1750 
1751   PetscFunctionBegin;
1752   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_SeqDense_SeqAIJ_AB(C));
1753   PetscFunctionReturn(PETSC_SUCCESS);
1754 }
1755 /* ------------------------------------------------------- */
1756 
1757 PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring, Mat B, Mat Btdense)
1758 {
1759   Mat_SeqAIJ   *b       = (Mat_SeqAIJ *)B->data;
1760   Mat_SeqDense *btdense = (Mat_SeqDense *)Btdense->data;
1761   PetscInt     *bi = b->i, *bj = b->j;
1762   PetscInt      m = Btdense->rmap->n, n = Btdense->cmap->n, j, k, l, col, anz, *btcol, brow, ncolumns;
1763   MatScalar    *btval, *btval_den, *ba = b->a;
1764   PetscInt     *columns = coloring->columns, *colorforcol = coloring->colorforcol, ncolors = coloring->ncolors;
1765 
1766   PetscFunctionBegin;
1767   btval_den = btdense->v;
1768   PetscCall(PetscArrayzero(btval_den, m * n));
1769   for (k = 0; k < ncolors; k++) {
1770     ncolumns = coloring->ncolumns[k];
1771     for (l = 0; l < ncolumns; l++) { /* insert a row of B to a column of Btdense */
1772       col   = *(columns + colorforcol[k] + l);
1773       btcol = bj + bi[col];
1774       btval = ba + bi[col];
1775       anz   = bi[col + 1] - bi[col];
1776       for (j = 0; j < anz; j++) {
1777         brow            = btcol[j];
1778         btval_den[brow] = btval[j];
1779       }
1780     }
1781     btval_den += m;
1782   }
1783   PetscFunctionReturn(PETSC_SUCCESS);
1784 }
1785 
1786 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring, Mat Cden, Mat Csp)
1787 {
1788   Mat_SeqAIJ        *csp = (Mat_SeqAIJ *)Csp->data;
1789   const PetscScalar *ca_den, *ca_den_ptr;
1790   PetscScalar       *ca = csp->a;
1791   PetscInt           k, l, m = Cden->rmap->n, ncolors = matcoloring->ncolors;
1792   PetscInt           brows = matcoloring->brows, *den2sp = matcoloring->den2sp;
1793   PetscInt           nrows, *row, *idx;
1794   PetscInt          *rows = matcoloring->rows, *colorforrow = matcoloring->colorforrow;
1795 
1796   PetscFunctionBegin;
1797   PetscCall(MatDenseGetArrayRead(Cden, &ca_den));
1798 
1799   if (brows > 0) {
1800     PetscInt *lstart, row_end, row_start;
1801     lstart = matcoloring->lstart;
1802     PetscCall(PetscArrayzero(lstart, ncolors));
1803 
1804     row_end = brows;
1805     if (row_end > m) row_end = m;
1806     for (row_start = 0; row_start < m; row_start += brows) { /* loop over row blocks of Csp */
1807       ca_den_ptr = ca_den;
1808       for (k = 0; k < ncolors; k++) { /* loop over colors (columns of Cden) */
1809         nrows = matcoloring->nrows[k];
1810         row   = rows + colorforrow[k];
1811         idx   = den2sp + colorforrow[k];
1812         for (l = lstart[k]; l < nrows; l++) {
1813           if (row[l] >= row_end) {
1814             lstart[k] = l;
1815             break;
1816           } else {
1817             ca[idx[l]] = ca_den_ptr[row[l]];
1818           }
1819         }
1820         ca_den_ptr += m;
1821       }
1822       row_end += brows;
1823       if (row_end > m) row_end = m;
1824     }
1825   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1826     ca_den_ptr = ca_den;
1827     for (k = 0; k < ncolors; k++) {
1828       nrows = matcoloring->nrows[k];
1829       row   = rows + colorforrow[k];
1830       idx   = den2sp + colorforrow[k];
1831       for (l = 0; l < nrows; l++) ca[idx[l]] = ca_den_ptr[row[l]];
1832       ca_den_ptr += m;
1833     }
1834   }
1835 
1836   PetscCall(MatDenseRestoreArrayRead(Cden, &ca_den));
1837 #if defined(PETSC_USE_INFO)
1838   if (matcoloring->brows > 0) {
1839     PetscCall(PetscInfo(Csp, "Loop over %" PetscInt_FMT " row blocks for den2sp\n", brows));
1840   } else {
1841     PetscCall(PetscInfo(Csp, "Loop over colors/columns of Cden, inefficient for large sparse matrix product \n"));
1842   }
1843 #endif
1844   PetscFunctionReturn(PETSC_SUCCESS);
1845 }
1846 
1847 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat, ISColoring iscoloring, MatTransposeColoring c)
1848 {
1849   PetscInt        i, n, nrows, Nbs, j, k, m, ncols, col, cm;
1850   const PetscInt *is, *ci, *cj, *row_idx;
1851   PetscInt        nis = iscoloring->n, *rowhit, bs = 1;
1852   IS             *isa;
1853   Mat_SeqAIJ     *csp = (Mat_SeqAIJ *)mat->data;
1854   PetscInt       *colorforrow, *rows, *rows_i, *idxhit, *spidx, *den2sp, *den2sp_i;
1855   PetscInt       *colorforcol, *columns, *columns_i, brows;
1856   PetscBool       flg;
1857 
1858   PetscFunctionBegin;
1859   PetscCall(ISColoringGetIS(iscoloring, PETSC_USE_POINTER, PETSC_IGNORE, &isa));
1860 
1861   /* bs >1 is not being tested yet! */
1862   Nbs       = mat->cmap->N / bs;
1863   c->M      = mat->rmap->N / bs; /* set total rows, columns and local rows */
1864   c->N      = Nbs;
1865   c->m      = c->M;
1866   c->rstart = 0;
1867   c->brows  = 100;
1868 
1869   c->ncolors = nis;
1870   PetscCall(PetscMalloc3(nis, &c->ncolumns, nis, &c->nrows, nis + 1, &colorforrow));
1871   PetscCall(PetscMalloc1(csp->nz + 1, &rows));
1872   PetscCall(PetscMalloc1(csp->nz + 1, &den2sp));
1873 
1874   brows = c->brows;
1875   PetscCall(PetscOptionsGetInt(NULL, NULL, "-matden2sp_brows", &brows, &flg));
1876   if (flg) c->brows = brows;
1877   if (brows > 0) PetscCall(PetscMalloc1(nis + 1, &c->lstart));
1878 
1879   colorforrow[0] = 0;
1880   rows_i         = rows;
1881   den2sp_i       = den2sp;
1882 
1883   PetscCall(PetscMalloc1(nis + 1, &colorforcol));
1884   PetscCall(PetscMalloc1(Nbs + 1, &columns));
1885 
1886   colorforcol[0] = 0;
1887   columns_i      = columns;
1888 
1889   /* get column-wise storage of mat */
1890   PetscCall(MatGetColumnIJ_SeqAIJ_Color(mat, 0, PETSC_FALSE, PETSC_FALSE, &ncols, &ci, &cj, &spidx, NULL));
1891 
1892   cm = c->m;
1893   PetscCall(PetscMalloc1(cm + 1, &rowhit));
1894   PetscCall(PetscMalloc1(cm + 1, &idxhit));
1895   for (i = 0; i < nis; i++) { /* loop over color */
1896     PetscCall(ISGetLocalSize(isa[i], &n));
1897     PetscCall(ISGetIndices(isa[i], &is));
1898 
1899     c->ncolumns[i] = n;
1900     if (n) PetscCall(PetscArraycpy(columns_i, is, n));
1901     colorforcol[i + 1] = colorforcol[i] + n;
1902     columns_i += n;
1903 
1904     /* fast, crude version requires O(N*N) work */
1905     PetscCall(PetscArrayzero(rowhit, cm));
1906 
1907     for (j = 0; j < n; j++) { /* loop over columns*/
1908       col     = is[j];
1909       row_idx = cj + ci[col];
1910       m       = ci[col + 1] - ci[col];
1911       for (k = 0; k < m; k++) { /* loop over columns marking them in rowhit */
1912         idxhit[*row_idx]   = spidx[ci[col] + k];
1913         rowhit[*row_idx++] = col + 1;
1914       }
1915     }
1916     /* count the number of hits */
1917     nrows = 0;
1918     for (j = 0; j < cm; j++) {
1919       if (rowhit[j]) nrows++;
1920     }
1921     c->nrows[i]        = nrows;
1922     colorforrow[i + 1] = colorforrow[i] + nrows;
1923 
1924     nrows = 0;
1925     for (j = 0; j < cm; j++) { /* loop over rows */
1926       if (rowhit[j]) {
1927         rows_i[nrows]   = j;
1928         den2sp_i[nrows] = idxhit[j];
1929         nrows++;
1930       }
1931     }
1932     den2sp_i += nrows;
1933 
1934     PetscCall(ISRestoreIndices(isa[i], &is));
1935     rows_i += nrows;
1936   }
1937   PetscCall(MatRestoreColumnIJ_SeqAIJ_Color(mat, 0, PETSC_FALSE, PETSC_FALSE, &ncols, &ci, &cj, &spidx, NULL));
1938   PetscCall(PetscFree(rowhit));
1939   PetscCall(ISColoringRestoreIS(iscoloring, PETSC_USE_POINTER, &isa));
1940   PetscCheck(csp->nz == colorforrow[nis], PETSC_COMM_SELF, PETSC_ERR_PLIB, "csp->nz %" PetscInt_FMT " != colorforrow[nis] %" PetscInt_FMT, csp->nz, colorforrow[nis]);
1941 
1942   c->colorforrow = colorforrow;
1943   c->rows        = rows;
1944   c->den2sp      = den2sp;
1945   c->colorforcol = colorforcol;
1946   c->columns     = columns;
1947 
1948   PetscCall(PetscFree(idxhit));
1949   PetscFunctionReturn(PETSC_SUCCESS);
1950 }
1951 
1952 /* --------------------------------------------------------------- */
1953 static PetscErrorCode MatProductNumeric_AtB_SeqAIJ_SeqAIJ(Mat C)
1954 {
1955   Mat_Product *product = C->product;
1956   Mat          A = product->A, B = product->B;
1957 
1958   PetscFunctionBegin;
1959   if (C->ops->mattransposemultnumeric) {
1960     /* Alg: "outerproduct" */
1961     PetscCall((*C->ops->mattransposemultnumeric)(A, B, C));
1962   } else {
1963     /* Alg: "matmatmult" -- C = At*B */
1964     Mat_MatTransMatMult *atb = (Mat_MatTransMatMult *)product->data;
1965 
1966     PetscCheck(atb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1967     if (atb->At) {
1968       /* At is computed in MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ();
1969          user may have called MatProductReplaceMats() to get this A=product->A */
1970       PetscCall(MatTransposeSetPrecursor(A, atb->At));
1971       PetscCall(MatTranspose(A, MAT_REUSE_MATRIX, &atb->At));
1972     }
1973     PetscCall(MatMatMultNumeric_SeqAIJ_SeqAIJ(atb->At ? atb->At : A, B, C));
1974   }
1975   PetscFunctionReturn(PETSC_SUCCESS);
1976 }
1977 
1978 static PetscErrorCode MatProductSymbolic_AtB_SeqAIJ_SeqAIJ(Mat C)
1979 {
1980   Mat_Product *product = C->product;
1981   Mat          A = product->A, B = product->B;
1982   PetscReal    fill = product->fill;
1983 
1984   PetscFunctionBegin;
1985   PetscCall(MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A, B, fill, C));
1986 
1987   C->ops->productnumeric = MatProductNumeric_AtB_SeqAIJ_SeqAIJ;
1988   PetscFunctionReturn(PETSC_SUCCESS);
1989 }
1990 
1991 /* --------------------------------------------------------------- */
1992 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AB(Mat C)
1993 {
1994   Mat_Product *product = C->product;
1995   PetscInt     alg     = 0; /* default algorithm */
1996   PetscBool    flg     = PETSC_FALSE;
1997 #if !defined(PETSC_HAVE_HYPRE)
1998   const char *algTypes[7] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge"};
1999   PetscInt    nalg        = 7;
2000 #else
2001   const char *algTypes[8] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge", "hypre"};
2002   PetscInt    nalg        = 8;
2003 #endif
2004 
2005   PetscFunctionBegin;
2006   /* Set default algorithm */
2007   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2008   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2009 
2010   /* Get runtime option */
2011   if (product->api_user) {
2012     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2013     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[0], &alg, &flg));
2014     PetscOptionsEnd();
2015   } else {
2016     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2017     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AB", algTypes, nalg, algTypes[0], &alg, &flg));
2018     PetscOptionsEnd();
2019   }
2020   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2021 
2022   C->ops->productsymbolic = MatProductSymbolic_AB;
2023   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqAIJ;
2024   PetscFunctionReturn(PETSC_SUCCESS);
2025 }
2026 
2027 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AtB(Mat C)
2028 {
2029   Mat_Product *product     = C->product;
2030   PetscInt     alg         = 0; /* default algorithm */
2031   PetscBool    flg         = PETSC_FALSE;
2032   const char  *algTypes[3] = {"default", "at*b", "outerproduct"};
2033   PetscInt     nalg        = 3;
2034 
2035   PetscFunctionBegin;
2036   /* Get runtime option */
2037   if (product->api_user) {
2038     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2039     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2040     PetscOptionsEnd();
2041   } else {
2042     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2043     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AtB", algTypes, nalg, algTypes[alg], &alg, &flg));
2044     PetscOptionsEnd();
2045   }
2046   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2047 
2048   C->ops->productsymbolic = MatProductSymbolic_AtB_SeqAIJ_SeqAIJ;
2049   PetscFunctionReturn(PETSC_SUCCESS);
2050 }
2051 
2052 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABt(Mat C)
2053 {
2054   Mat_Product *product     = C->product;
2055   PetscInt     alg         = 0; /* default algorithm */
2056   PetscBool    flg         = PETSC_FALSE;
2057   const char  *algTypes[2] = {"default", "color"};
2058   PetscInt     nalg        = 2;
2059 
2060   PetscFunctionBegin;
2061   /* Set default algorithm */
2062   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2063   if (!flg) {
2064     alg = 1;
2065     PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2066   }
2067 
2068   /* Get runtime option */
2069   if (product->api_user) {
2070     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatTransposeMult", "Mat");
2071     PetscCall(PetscOptionsEList("-matmattransmult_via", "Algorithmic approach", "MatMatTransposeMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2072     PetscOptionsEnd();
2073   } else {
2074     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABt", "Mat");
2075     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABt", algTypes, nalg, algTypes[alg], &alg, &flg));
2076     PetscOptionsEnd();
2077   }
2078   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2079 
2080   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ;
2081   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2082   PetscFunctionReturn(PETSC_SUCCESS);
2083 }
2084 
2085 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_PtAP(Mat C)
2086 {
2087   Mat_Product *product = C->product;
2088   PetscBool    flg     = PETSC_FALSE;
2089   PetscInt     alg     = 0; /* default algorithm -- alg=1 should be default!!! */
2090 #if !defined(PETSC_HAVE_HYPRE)
2091   const char *algTypes[2] = {"scalable", "rap"};
2092   PetscInt    nalg        = 2;
2093 #else
2094   const char *algTypes[3] = {"scalable", "rap", "hypre"};
2095   PetscInt    nalg        = 3;
2096 #endif
2097 
2098   PetscFunctionBegin;
2099   /* Set default algorithm */
2100   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2101   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2102 
2103   /* Get runtime option */
2104   if (product->api_user) {
2105     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2106     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[0], &alg, &flg));
2107     PetscOptionsEnd();
2108   } else {
2109     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2110     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_PtAP", algTypes, nalg, algTypes[0], &alg, &flg));
2111     PetscOptionsEnd();
2112   }
2113   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2114 
2115   C->ops->productsymbolic = MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ;
2116   PetscFunctionReturn(PETSC_SUCCESS);
2117 }
2118 
2119 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_RARt(Mat C)
2120 {
2121   Mat_Product *product     = C->product;
2122   PetscBool    flg         = PETSC_FALSE;
2123   PetscInt     alg         = 0; /* default algorithm */
2124   const char  *algTypes[3] = {"r*a*rt", "r*art", "coloring_rart"};
2125   PetscInt     nalg        = 3;
2126 
2127   PetscFunctionBegin;
2128   /* Set default algorithm */
2129   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2130   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2131 
2132   /* Get runtime option */
2133   if (product->api_user) {
2134     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatRARt", "Mat");
2135     PetscCall(PetscOptionsEList("-matrart_via", "Algorithmic approach", "MatRARt", algTypes, nalg, algTypes[0], &alg, &flg));
2136     PetscOptionsEnd();
2137   } else {
2138     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_RARt", "Mat");
2139     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_RARt", algTypes, nalg, algTypes[0], &alg, &flg));
2140     PetscOptionsEnd();
2141   }
2142   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2143 
2144   C->ops->productsymbolic = MatProductSymbolic_RARt_SeqAIJ_SeqAIJ;
2145   PetscFunctionReturn(PETSC_SUCCESS);
2146 }
2147 
2148 /* ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm */
2149 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABC(Mat C)
2150 {
2151   Mat_Product *product     = C->product;
2152   PetscInt     alg         = 0; /* default algorithm */
2153   PetscBool    flg         = PETSC_FALSE;
2154   const char  *algTypes[7] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge"};
2155   PetscInt     nalg        = 7;
2156 
2157   PetscFunctionBegin;
2158   /* Set default algorithm */
2159   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2160   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2161 
2162   /* Get runtime option */
2163   if (product->api_user) {
2164     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2165     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2166     PetscOptionsEnd();
2167   } else {
2168     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2169     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2170     PetscOptionsEnd();
2171   }
2172   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2173 
2174   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ;
2175   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2176   PetscFunctionReturn(PETSC_SUCCESS);
2177 }
2178 
2179 PetscErrorCode MatProductSetFromOptions_SeqAIJ(Mat C)
2180 {
2181   Mat_Product *product = C->product;
2182 
2183   PetscFunctionBegin;
2184   switch (product->type) {
2185   case MATPRODUCT_AB:
2186     PetscCall(MatProductSetFromOptions_SeqAIJ_AB(C));
2187     break;
2188   case MATPRODUCT_AtB:
2189     PetscCall(MatProductSetFromOptions_SeqAIJ_AtB(C));
2190     break;
2191   case MATPRODUCT_ABt:
2192     PetscCall(MatProductSetFromOptions_SeqAIJ_ABt(C));
2193     break;
2194   case MATPRODUCT_PtAP:
2195     PetscCall(MatProductSetFromOptions_SeqAIJ_PtAP(C));
2196     break;
2197   case MATPRODUCT_RARt:
2198     PetscCall(MatProductSetFromOptions_SeqAIJ_RARt(C));
2199     break;
2200   case MATPRODUCT_ABC:
2201     PetscCall(MatProductSetFromOptions_SeqAIJ_ABC(C));
2202     break;
2203   default:
2204     break;
2205   }
2206   PetscFunctionReturn(PETSC_SUCCESS);
2207 }
2208