xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision a96705020bd7e362116d3e2c8daa1efc28dedc1e)
1 /*
2   Defines matrix-matrix product routines for pairs of SeqAIJ matrices
3           C = A * B
4 */
5 
6 #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
7 #include <../src/mat/utils/freespace.h>
8 #include <petscbt.h>
9 #include <petsc/private/isimpl.h>
10 #include <../src/mat/impls/dense/seq/dense.h>
11 
12 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
13 {
14   PetscFunctionBegin;
15   if (C->ops->matmultnumeric) PetscCall((*C->ops->matmultnumeric)(A, B, C));
16   else PetscCall(MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(A, B, C));
17   PetscFunctionReturn(PETSC_SUCCESS);
18 }
19 
20 /* Modified from MatCreateSeqAIJWithArrays() */
21 PETSC_INTERN PetscErrorCode MatSetSeqAIJWithArrays_private(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt i[], PetscInt j[], PetscScalar a[], MatType mtype, Mat mat)
22 {
23   PetscInt    ii;
24   Mat_SeqAIJ *aij;
25   PetscBool   isseqaij, osingle, ofree_a, ofree_ij;
26 
27   PetscFunctionBegin;
28   PetscCheck(m <= 0 || !i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
29   PetscCall(MatSetSizes(mat, m, n, m, n));
30 
31   if (!mtype) {
32     PetscCall(PetscObjectBaseTypeCompare((PetscObject)mat, MATSEQAIJ, &isseqaij));
33     if (!isseqaij) PetscCall(MatSetType(mat, MATSEQAIJ));
34   } else {
35     PetscCall(MatSetType(mat, mtype));
36   }
37 
38   aij      = (Mat_SeqAIJ *)(mat)->data;
39   osingle  = aij->singlemalloc;
40   ofree_a  = aij->free_a;
41   ofree_ij = aij->free_ij;
42   /* changes the free flags */
43   PetscCall(MatSeqAIJSetPreallocation_SeqAIJ(mat, MAT_SKIP_ALLOCATION, NULL));
44 
45   PetscCall(PetscFree(aij->ilen));
46   PetscCall(PetscFree(aij->imax));
47   PetscCall(PetscMalloc1(m, &aij->imax));
48   PetscCall(PetscMalloc1(m, &aij->ilen));
49   for (ii = 0, aij->nonzerorowcnt = 0, aij->rmax = 0; ii < m; ii++) {
50     const PetscInt rnz = i[ii + 1] - i[ii];
51     aij->nonzerorowcnt += !!rnz;
52     aij->rmax     = PetscMax(aij->rmax, rnz);
53     aij->ilen[ii] = aij->imax[ii] = i[ii + 1] - i[ii];
54   }
55   aij->maxnz = i[m];
56   aij->nz    = i[m];
57 
58   if (osingle) {
59     PetscCall(PetscFree3(aij->a, aij->j, aij->i));
60   } else {
61     if (ofree_a) PetscCall(PetscFree(aij->a));
62     if (ofree_ij) PetscCall(PetscFree(aij->j));
63     if (ofree_ij) PetscCall(PetscFree(aij->i));
64   }
65   aij->i     = i;
66   aij->j     = j;
67   aij->a     = a;
68   aij->nonew = -1; /* this indicates that inserting a new value in the matrix that generates a new nonzero is an error */
69   /* default to not retain ownership */
70   aij->singlemalloc = PETSC_FALSE;
71   aij->free_a       = PETSC_FALSE;
72   aij->free_ij      = PETSC_FALSE;
73   PetscCall(MatCheckCompressedRow(mat, aij->nonzerorowcnt, &aij->compressedrow, aij->i, m, 0.6));
74   PetscFunctionReturn(PETSC_SUCCESS);
75 }
76 
77 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
78 {
79   Mat_Product        *product = C->product;
80   MatProductAlgorithm alg;
81   PetscBool           flg;
82 
83   PetscFunctionBegin;
84   if (product) {
85     alg = product->alg;
86   } else {
87     alg = "sorted";
88   }
89   /* sorted */
90   PetscCall(PetscStrcmp(alg, "sorted", &flg));
91   if (flg) {
92     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(A, B, fill, C));
93     PetscFunctionReturn(PETSC_SUCCESS);
94   }
95 
96   /* scalable */
97   PetscCall(PetscStrcmp(alg, "scalable", &flg));
98   if (flg) {
99     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A, B, fill, C));
100     PetscFunctionReturn(PETSC_SUCCESS);
101   }
102 
103   /* scalable_fast */
104   PetscCall(PetscStrcmp(alg, "scalable_fast", &flg));
105   if (flg) {
106     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A, B, fill, C));
107     PetscFunctionReturn(PETSC_SUCCESS);
108   }
109 
110   /* heap */
111   PetscCall(PetscStrcmp(alg, "heap", &flg));
112   if (flg) {
113     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A, B, fill, C));
114     PetscFunctionReturn(PETSC_SUCCESS);
115   }
116 
117   /* btheap */
118   PetscCall(PetscStrcmp(alg, "btheap", &flg));
119   if (flg) {
120     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A, B, fill, C));
121     PetscFunctionReturn(PETSC_SUCCESS);
122   }
123 
124   /* llcondensed */
125   PetscCall(PetscStrcmp(alg, "llcondensed", &flg));
126   if (flg) {
127     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A, B, fill, C));
128     PetscFunctionReturn(PETSC_SUCCESS);
129   }
130 
131   /* rowmerge */
132   PetscCall(PetscStrcmp(alg, "rowmerge", &flg));
133   if (flg) {
134     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(A, B, fill, C));
135     PetscFunctionReturn(PETSC_SUCCESS);
136   }
137 
138 #if defined(PETSC_HAVE_HYPRE)
139   PetscCall(PetscStrcmp(alg, "hypre", &flg));
140   if (flg) {
141     PetscCall(MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A, B, fill, C));
142     PetscFunctionReturn(PETSC_SUCCESS);
143   }
144 #endif
145 
146   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
147 }
148 
149 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A, Mat B, PetscReal fill, Mat C)
150 {
151   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
152   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
153   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
154   PetscReal          afill;
155   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
156   PetscHMapI         ta;
157   PetscBT            lnkbt;
158   PetscFreeSpaceList free_space = NULL, current_space = NULL;
159 
160   PetscFunctionBegin;
161   /* Get ci and cj */
162   /* Allocate ci array, arrays for fill computation and */
163   /* free space for accumulating nonzero column info */
164   PetscCall(PetscMalloc1(am + 2, &ci));
165   ci[0] = 0;
166 
167   /* create and initialize a linked list */
168   PetscCall(PetscHMapICreateWithSize(bn, &ta));
169   MatRowMergeMax_SeqAIJ(b, bm, ta);
170   PetscCall(PetscHMapIGetSize(ta, &Crmax));
171   PetscCall(PetscHMapIDestroy(&ta));
172 
173   PetscCall(PetscLLCondensedCreate(Crmax, bn, &lnk, &lnkbt));
174 
175   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
176   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
177 
178   current_space = free_space;
179 
180   /* Determine ci and cj */
181   for (i = 0; i < am; i++) {
182     anzi = ai[i + 1] - ai[i];
183     aj   = a->j + ai[i];
184     for (j = 0; j < anzi; j++) {
185       brow = aj[j];
186       bnzj = bi[brow + 1] - bi[brow];
187       bj   = b->j + bi[brow];
188       /* add non-zero cols of B into the sorted linked list lnk */
189       PetscCall(PetscLLCondensedAddSorted(bnzj, bj, lnk, lnkbt));
190     }
191     /* add possible missing diagonal entry */
192     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted(1, &i, lnk, lnkbt));
193     cnzi = lnk[0];
194 
195     /* If free space is not available, make more free space */
196     /* Double the amount of total space in the list */
197     if (current_space->local_remaining < cnzi) {
198       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
199       ndouble++;
200     }
201 
202     /* Copy data into free space, then initialize lnk */
203     PetscCall(PetscLLCondensedClean(bn, cnzi, current_space->array, lnk, lnkbt));
204 
205     current_space->array += cnzi;
206     current_space->local_used += cnzi;
207     current_space->local_remaining -= cnzi;
208 
209     ci[i + 1] = ci[i] + cnzi;
210   }
211 
212   /* Column indices are in the list of free space */
213   /* Allocate space for cj, initialize cj, and */
214   /* destroy list of free space and other temporary array(s) */
215   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
216   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
217   PetscCall(PetscLLCondensedDestroy(lnk, lnkbt));
218 
219   /* put together the new symbolic matrix */
220   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
221   PetscCall(MatSetBlockSizesFromMats(C, A, B));
222 
223   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
224   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
225   c          = (Mat_SeqAIJ *)(C->data);
226   c->free_a  = PETSC_FALSE;
227   c->free_ij = PETSC_TRUE;
228   c->nonew   = 0;
229 
230   /* fast, needs non-scalable O(bn) array 'abdense' */
231   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
232 
233   /* set MatInfo */
234   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
235   if (afill < 1.0) afill = 1.0;
236   C->info.mallocs           = ndouble;
237   C->info.fill_ratio_given  = fill;
238   C->info.fill_ratio_needed = afill;
239 
240 #if defined(PETSC_USE_INFO)
241   if (ci[am]) {
242     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
243     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
244   } else {
245     PetscCall(PetscInfo(C, "Empty matrix product\n"));
246   }
247 #endif
248   PetscFunctionReturn(PETSC_SUCCESS);
249 }
250 
251 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat A, Mat B, Mat C)
252 {
253   PetscLogDouble     flops = 0.0;
254   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
255   Mat_SeqAIJ        *b     = (Mat_SeqAIJ *)B->data;
256   Mat_SeqAIJ        *c     = (Mat_SeqAIJ *)C->data;
257   PetscInt          *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bjj, *ci = c->i, *cj = c->j;
258   PetscInt           am = A->rmap->n, cm = C->rmap->n;
259   PetscInt           i, j, k, anzi, bnzi, cnzi, brow;
260   PetscScalar       *ca, valtmp;
261   PetscScalar       *ab_dense;
262   PetscContainer     cab_dense;
263   const PetscScalar *aa, *ba, *baj;
264 
265   PetscFunctionBegin;
266   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
267   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
268   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
269     PetscCall(PetscMalloc1(ci[cm] + 1, &ca));
270     c->a      = ca;
271     c->free_a = PETSC_TRUE;
272   } else ca = c->a;
273 
274   /* TODO this should be done in the symbolic phase */
275   /* However, this function is so heavily used (sometimes in an hidden way through multnumeric function pointers
276      that is hard to eradicate) */
277   PetscCall(PetscObjectQuery((PetscObject)C, "__PETSc__ab_dense", (PetscObject *)&cab_dense));
278   if (!cab_dense) {
279     PetscCall(PetscMalloc1(B->cmap->N, &ab_dense));
280     PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &cab_dense));
281     PetscCall(PetscContainerSetPointer(cab_dense, ab_dense));
282     PetscCall(PetscContainerSetUserDestroy(cab_dense, PetscContainerUserDestroyDefault));
283     PetscCall(PetscObjectCompose((PetscObject)C, "__PETSc__ab_dense", (PetscObject)cab_dense));
284     PetscCall(PetscObjectDereference((PetscObject)cab_dense));
285   }
286   PetscCall(PetscContainerGetPointer(cab_dense, (void **)&ab_dense));
287   PetscCall(PetscArrayzero(ab_dense, B->cmap->N));
288 
289   /* clean old values in C */
290   PetscCall(PetscArrayzero(ca, ci[cm]));
291   /* Traverse A row-wise. */
292   /* Build the ith row in C by summing over nonzero columns in A, */
293   /* the rows of B corresponding to nonzeros of A. */
294   for (i = 0; i < am; i++) {
295     anzi = ai[i + 1] - ai[i];
296     for (j = 0; j < anzi; j++) {
297       brow = aj[j];
298       bnzi = bi[brow + 1] - bi[brow];
299       bjj  = bj + bi[brow];
300       baj  = ba + bi[brow];
301       /* perform dense axpy */
302       valtmp = aa[j];
303       for (k = 0; k < bnzi; k++) ab_dense[bjj[k]] += valtmp * baj[k];
304       flops += 2 * bnzi;
305     }
306     aj += anzi;
307     aa += anzi;
308 
309     cnzi = ci[i + 1] - ci[i];
310     for (k = 0; k < cnzi; k++) {
311       ca[k] += ab_dense[cj[k]];
312       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
313     }
314     flops += cnzi;
315     cj += cnzi;
316     ca += cnzi;
317   }
318 #if defined(PETSC_HAVE_DEVICE)
319   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
320 #endif
321   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
322   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
323   PetscCall(PetscLogFlops(flops));
324   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
325   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
326   PetscFunctionReturn(PETSC_SUCCESS);
327 }
328 
329 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A, Mat B, Mat C)
330 {
331   PetscLogDouble     flops = 0.0;
332   Mat_SeqAIJ        *a     = (Mat_SeqAIJ *)A->data;
333   Mat_SeqAIJ        *b     = (Mat_SeqAIJ *)B->data;
334   Mat_SeqAIJ        *c     = (Mat_SeqAIJ *)C->data;
335   PetscInt          *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, *bjj, *ci = c->i, *cj = c->j;
336   PetscInt           am = A->rmap->N, cm = C->rmap->N;
337   PetscInt           i, j, k, anzi, bnzi, cnzi, brow;
338   PetscScalar       *ca = c->a, valtmp;
339   const PetscScalar *aa, *ba, *baj;
340   PetscInt           nextb;
341 
342   PetscFunctionBegin;
343   PetscCall(MatSeqAIJGetArrayRead(A, &aa));
344   PetscCall(MatSeqAIJGetArrayRead(B, &ba));
345   if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
346     PetscCall(PetscMalloc1(ci[cm] + 1, &ca));
347     c->a      = ca;
348     c->free_a = PETSC_TRUE;
349   }
350 
351   /* clean old values in C */
352   PetscCall(PetscArrayzero(ca, ci[cm]));
353   /* Traverse A row-wise. */
354   /* Build the ith row in C by summing over nonzero columns in A, */
355   /* the rows of B corresponding to nonzeros of A. */
356   for (i = 0; i < am; i++) {
357     anzi = ai[i + 1] - ai[i];
358     cnzi = ci[i + 1] - ci[i];
359     for (j = 0; j < anzi; j++) {
360       brow = aj[j];
361       bnzi = bi[brow + 1] - bi[brow];
362       bjj  = bj + bi[brow];
363       baj  = ba + bi[brow];
364       /* perform sparse axpy */
365       valtmp = aa[j];
366       nextb  = 0;
367       for (k = 0; nextb < bnzi; k++) {
368         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
369           ca[k] += valtmp * baj[nextb++];
370         }
371       }
372       flops += 2 * bnzi;
373     }
374     aj += anzi;
375     aa += anzi;
376     cj += cnzi;
377     ca += cnzi;
378   }
379 #if defined(PETSC_HAVE_DEVICE)
380   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
381 #endif
382   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
383   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
384   PetscCall(PetscLogFlops(flops));
385   PetscCall(MatSeqAIJRestoreArrayRead(A, &aa));
386   PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
387   PetscFunctionReturn(PETSC_SUCCESS);
388 }
389 
390 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A, Mat B, PetscReal fill, Mat C)
391 {
392   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
393   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
394   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
395   MatScalar         *ca;
396   PetscReal          afill;
397   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
398   PetscHMapI         ta;
399   PetscFreeSpaceList free_space = NULL, current_space = NULL;
400 
401   PetscFunctionBegin;
402   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
403   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
404   PetscCall(PetscMalloc1(am + 2, &ci));
405   ci[0] = 0;
406 
407   /* create and initialize a linked list */
408   PetscCall(PetscHMapICreateWithSize(bn, &ta));
409   MatRowMergeMax_SeqAIJ(b, bm, ta);
410   PetscCall(PetscHMapIGetSize(ta, &Crmax));
411   PetscCall(PetscHMapIDestroy(&ta));
412 
413   PetscCall(PetscLLCondensedCreate_fast(Crmax, &lnk));
414 
415   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
416   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
417   current_space = free_space;
418 
419   /* Determine ci and cj */
420   for (i = 0; i < am; i++) {
421     anzi = ai[i + 1] - ai[i];
422     aj   = a->j + ai[i];
423     for (j = 0; j < anzi; j++) {
424       brow = aj[j];
425       bnzj = bi[brow + 1] - bi[brow];
426       bj   = b->j + bi[brow];
427       /* add non-zero cols of B into the sorted linked list lnk */
428       PetscCall(PetscLLCondensedAddSorted_fast(bnzj, bj, lnk));
429     }
430     /* add possible missing diagonal entry */
431     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted_fast(1, &i, lnk));
432     cnzi = lnk[1];
433 
434     /* If free space is not available, make more free space */
435     /* Double the amount of total space in the list */
436     if (current_space->local_remaining < cnzi) {
437       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
438       ndouble++;
439     }
440 
441     /* Copy data into free space, then initialize lnk */
442     PetscCall(PetscLLCondensedClean_fast(cnzi, current_space->array, lnk));
443 
444     current_space->array += cnzi;
445     current_space->local_used += cnzi;
446     current_space->local_remaining -= cnzi;
447 
448     ci[i + 1] = ci[i] + cnzi;
449   }
450 
451   /* Column indices are in the list of free space */
452   /* Allocate space for cj, initialize cj, and */
453   /* destroy list of free space and other temporary array(s) */
454   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
455   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
456   PetscCall(PetscLLCondensedDestroy_fast(lnk));
457 
458   /* Allocate space for ca */
459   PetscCall(PetscCalloc1(ci[am] + 1, &ca));
460 
461   /* put together the new symbolic matrix */
462   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, ca, ((PetscObject)A)->type_name, C));
463   PetscCall(MatSetBlockSizesFromMats(C, A, B));
464 
465   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
466   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
467   c          = (Mat_SeqAIJ *)(C->data);
468   c->free_a  = PETSC_TRUE;
469   c->free_ij = PETSC_TRUE;
470   c->nonew   = 0;
471 
472   /* slower, less memory */
473   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;
474 
475   /* set MatInfo */
476   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
477   if (afill < 1.0) afill = 1.0;
478   C->info.mallocs           = ndouble;
479   C->info.fill_ratio_given  = fill;
480   C->info.fill_ratio_needed = afill;
481 
482 #if defined(PETSC_USE_INFO)
483   if (ci[am]) {
484     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
485     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
486   } else {
487     PetscCall(PetscInfo(C, "Empty matrix product\n"));
488   }
489 #endif
490   PetscFunctionReturn(PETSC_SUCCESS);
491 }
492 
493 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A, Mat B, PetscReal fill, Mat C)
494 {
495   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
496   PetscInt          *ai = a->i, *bi = b->i, *ci, *cj;
497   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
498   MatScalar         *ca;
499   PetscReal          afill;
500   PetscInt           i, j, anzi, brow, bnzj, cnzi, *bj, *aj, *lnk, ndouble = 0, Crmax;
501   PetscHMapI         ta;
502   PetscFreeSpaceList free_space = NULL, current_space = NULL;
503 
504   PetscFunctionBegin;
505   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
506   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
507   PetscCall(PetscMalloc1(am + 2, &ci));
508   ci[0] = 0;
509 
510   /* create and initialize a linked list */
511   PetscCall(PetscHMapICreateWithSize(bn, &ta));
512   MatRowMergeMax_SeqAIJ(b, bm, ta);
513   PetscCall(PetscHMapIGetSize(ta, &Crmax));
514   PetscCall(PetscHMapIDestroy(&ta));
515   PetscCall(PetscLLCondensedCreate_Scalable(Crmax, &lnk));
516 
517   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
518   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
519   current_space = free_space;
520 
521   /* Determine ci and cj */
522   for (i = 0; i < am; i++) {
523     anzi = ai[i + 1] - ai[i];
524     aj   = a->j + ai[i];
525     for (j = 0; j < anzi; j++) {
526       brow = aj[j];
527       bnzj = bi[brow + 1] - bi[brow];
528       bj   = b->j + bi[brow];
529       /* add non-zero cols of B into the sorted linked list lnk */
530       PetscCall(PetscLLCondensedAddSorted_Scalable(bnzj, bj, lnk));
531     }
532     /* add possible missing diagonal entry */
533     if (C->force_diagonals) PetscCall(PetscLLCondensedAddSorted_Scalable(1, &i, lnk));
534 
535     cnzi = lnk[0];
536 
537     /* If free space is not available, make more free space */
538     /* Double the amount of total space in the list */
539     if (current_space->local_remaining < cnzi) {
540       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(cnzi, current_space->total_array_size), &current_space));
541       ndouble++;
542     }
543 
544     /* Copy data into free space, then initialize lnk */
545     PetscCall(PetscLLCondensedClean_Scalable(cnzi, current_space->array, lnk));
546 
547     current_space->array += cnzi;
548     current_space->local_used += cnzi;
549     current_space->local_remaining -= cnzi;
550 
551     ci[i + 1] = ci[i] + cnzi;
552   }
553 
554   /* Column indices are in the list of free space */
555   /* Allocate space for cj, initialize cj, and */
556   /* destroy list of free space and other temporary array(s) */
557   PetscCall(PetscMalloc1(ci[am] + 1, &cj));
558   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
559   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
560 
561   /* Allocate space for ca */
562   PetscCall(PetscCalloc1(ci[am] + 1, &ca));
563 
564   /* put together the new symbolic matrix */
565   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, ca, ((PetscObject)A)->type_name, C));
566   PetscCall(MatSetBlockSizesFromMats(C, A, B));
567 
568   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
569   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
570   c          = (Mat_SeqAIJ *)(C->data);
571   c->free_a  = PETSC_TRUE;
572   c->free_ij = PETSC_TRUE;
573   c->nonew   = 0;
574 
575   /* slower, less memory */
576   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;
577 
578   /* set MatInfo */
579   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
580   if (afill < 1.0) afill = 1.0;
581   C->info.mallocs           = ndouble;
582   C->info.fill_ratio_given  = fill;
583   C->info.fill_ratio_needed = afill;
584 
585 #if defined(PETSC_USE_INFO)
586   if (ci[am]) {
587     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
588     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
589   } else {
590     PetscCall(PetscInfo(C, "Empty matrix product\n"));
591   }
592 #endif
593   PetscFunctionReturn(PETSC_SUCCESS);
594 }
595 
596 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A, Mat B, PetscReal fill, Mat C)
597 {
598   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
599   const PetscInt    *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
600   PetscInt          *ci, *cj, *bb;
601   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
602   PetscReal          afill;
603   PetscInt           i, j, col, ndouble = 0;
604   PetscFreeSpaceList free_space = NULL, current_space = NULL;
605   PetscHeap          h;
606 
607   PetscFunctionBegin;
608   /* Get ci and cj - by merging sorted rows using a heap */
609   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
610   PetscCall(PetscMalloc1(am + 2, &ci));
611   ci[0] = 0;
612 
613   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
614   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
615   current_space = free_space;
616 
617   PetscCall(PetscHeapCreate(a->rmax, &h));
618   PetscCall(PetscMalloc1(a->rmax, &bb));
619 
620   /* Determine ci and cj */
621   for (i = 0; i < am; i++) {
622     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 */
623     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
624     ci[i + 1]            = ci[i];
625     /* Populate the min heap */
626     for (j = 0; j < anzi; j++) {
627       bb[j] = bi[acol[j]];           /* bb points at the start of the row */
628       if (bb[j] < bi[acol[j] + 1]) { /* Add if row is nonempty */
629         PetscCall(PetscHeapAdd(h, j, bj[bb[j]++]));
630       }
631     }
632     /* Pick off the min element, adding it to free space */
633     PetscCall(PetscHeapPop(h, &j, &col));
634     while (j >= 0) {
635       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
636         PetscCall(PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2, current_space->total_array_size), 16 << 20), &current_space));
637         ndouble++;
638       }
639       *(current_space->array++) = col;
640       current_space->local_used++;
641       current_space->local_remaining--;
642       ci[i + 1]++;
643 
644       /* stash if anything else remains in this row of B */
645       if (bb[j] < bi[acol[j] + 1]) PetscCall(PetscHeapStash(h, j, bj[bb[j]++]));
646       while (1) { /* pop and stash any other rows of B that also had an entry in this column */
647         PetscInt j2, col2;
648         PetscCall(PetscHeapPeek(h, &j2, &col2));
649         if (col2 != col) break;
650         PetscCall(PetscHeapPop(h, &j2, &col2));
651         if (bb[j2] < bi[acol[j2] + 1]) PetscCall(PetscHeapStash(h, j2, bj[bb[j2]++]));
652       }
653       /* Put any stashed elements back into the min heap */
654       PetscCall(PetscHeapUnstash(h));
655       PetscCall(PetscHeapPop(h, &j, &col));
656     }
657   }
658   PetscCall(PetscFree(bb));
659   PetscCall(PetscHeapDestroy(&h));
660 
661   /* Column indices are in the list of free space */
662   /* Allocate space for cj, initialize cj, and */
663   /* destroy list of free space and other temporary array(s) */
664   PetscCall(PetscMalloc1(ci[am], &cj));
665   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
666 
667   /* put together the new symbolic matrix */
668   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
669   PetscCall(MatSetBlockSizesFromMats(C, A, B));
670 
671   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
672   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
673   c          = (Mat_SeqAIJ *)(C->data);
674   c->free_a  = PETSC_TRUE;
675   c->free_ij = PETSC_TRUE;
676   c->nonew   = 0;
677 
678   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
679 
680   /* set MatInfo */
681   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
682   if (afill < 1.0) afill = 1.0;
683   C->info.mallocs           = ndouble;
684   C->info.fill_ratio_given  = fill;
685   C->info.fill_ratio_needed = afill;
686 
687 #if defined(PETSC_USE_INFO)
688   if (ci[am]) {
689     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
690     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
691   } else {
692     PetscCall(PetscInfo(C, "Empty matrix product\n"));
693   }
694 #endif
695   PetscFunctionReturn(PETSC_SUCCESS);
696 }
697 
698 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A, Mat B, PetscReal fill, Mat C)
699 {
700   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
701   const PetscInt    *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
702   PetscInt          *ci, *cj, *bb;
703   PetscInt           am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
704   PetscReal          afill;
705   PetscInt           i, j, col, ndouble = 0;
706   PetscFreeSpaceList free_space = NULL, current_space = NULL;
707   PetscHeap          h;
708   PetscBT            bt;
709 
710   PetscFunctionBegin;
711   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
712   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
713   PetscCall(PetscMalloc1(am + 2, &ci));
714   ci[0] = 0;
715 
716   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
717   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(ai[am], bi[bm])), &free_space));
718 
719   current_space = free_space;
720 
721   PetscCall(PetscHeapCreate(a->rmax, &h));
722   PetscCall(PetscMalloc1(a->rmax, &bb));
723   PetscCall(PetscBTCreate(bn, &bt));
724 
725   /* Determine ci and cj */
726   for (i = 0; i < am; i++) {
727     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 */
728     const PetscInt *acol = aj + ai[i];           /* column indices of nonzero entries in this row */
729     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
730     ci[i + 1]            = ci[i];
731     /* Populate the min heap */
732     for (j = 0; j < anzi; j++) {
733       PetscInt brow = acol[j];
734       for (bb[j] = bi[brow]; bb[j] < bi[brow + 1]; bb[j]++) {
735         PetscInt bcol = bj[bb[j]];
736         if (!PetscBTLookupSet(bt, bcol)) { /* new entry */
737           PetscCall(PetscHeapAdd(h, j, bcol));
738           bb[j]++;
739           break;
740         }
741       }
742     }
743     /* Pick off the min element, adding it to free space */
744     PetscCall(PetscHeapPop(h, &j, &col));
745     while (j >= 0) {
746       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
747         fptr = NULL;                            /* need PetscBTMemzero */
748         PetscCall(PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2, current_space->total_array_size), 16 << 20), &current_space));
749         ndouble++;
750       }
751       *(current_space->array++) = col;
752       current_space->local_used++;
753       current_space->local_remaining--;
754       ci[i + 1]++;
755 
756       /* stash if anything else remains in this row of B */
757       for (; bb[j] < bi[acol[j] + 1]; bb[j]++) {
758         PetscInt bcol = bj[bb[j]];
759         if (!PetscBTLookupSet(bt, bcol)) { /* new entry */
760           PetscCall(PetscHeapAdd(h, j, bcol));
761           bb[j]++;
762           break;
763         }
764       }
765       PetscCall(PetscHeapPop(h, &j, &col));
766     }
767     if (fptr) { /* Clear the bits for this row */
768       for (; fptr < current_space->array; fptr++) PetscCall(PetscBTClear(bt, *fptr));
769     } else { /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
770       PetscCall(PetscBTMemzero(bn, bt));
771     }
772   }
773   PetscCall(PetscFree(bb));
774   PetscCall(PetscHeapDestroy(&h));
775   PetscCall(PetscBTDestroy(&bt));
776 
777   /* Column indices are in the list of free space */
778   /* Allocate space for cj, initialize cj, and */
779   /* destroy list of free space and other temporary array(s) */
780   PetscCall(PetscMalloc1(ci[am], &cj));
781   PetscCall(PetscFreeSpaceContiguous(&free_space, cj));
782 
783   /* put together the new symbolic matrix */
784   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
785   PetscCall(MatSetBlockSizesFromMats(C, A, B));
786 
787   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
788   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
789   c          = (Mat_SeqAIJ *)(C->data);
790   c->free_a  = PETSC_TRUE;
791   c->free_ij = PETSC_TRUE;
792   c->nonew   = 0;
793 
794   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
795 
796   /* set MatInfo */
797   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
798   if (afill < 1.0) afill = 1.0;
799   C->info.mallocs           = ndouble;
800   C->info.fill_ratio_given  = fill;
801   C->info.fill_ratio_needed = afill;
802 
803 #if defined(PETSC_USE_INFO)
804   if (ci[am]) {
805     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
806     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
807   } else {
808     PetscCall(PetscInfo(C, "Empty matrix product\n"));
809   }
810 #endif
811   PetscFunctionReturn(PETSC_SUCCESS);
812 }
813 
814 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat A, Mat B, PetscReal fill, Mat C)
815 {
816   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
817   const PetscInt *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j, *inputi, *inputj, *inputcol, *inputcol_L1;
818   PetscInt       *ci, *cj, *outputj, worki_L1[9], worki_L2[9];
819   PetscInt        c_maxmem, a_maxrownnz = 0, a_rownnz;
820   const PetscInt  workcol[8] = {0, 1, 2, 3, 4, 5, 6, 7};
821   const PetscInt  am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
822   const PetscInt *brow_ptr[8], *brow_end[8];
823   PetscInt        window[8];
824   PetscInt        window_min, old_window_min, ci_nnz, outputi_nnz = 0, L1_nrows, L2_nrows;
825   PetscInt        i, k, ndouble = 0, L1_rowsleft, rowsleft;
826   PetscReal       afill;
827   PetscInt       *workj_L1, *workj_L2, *workj_L3;
828   PetscInt        L1_nnz, L2_nnz;
829 
830   /* Step 1: Get upper bound on memory required for allocation.
831              Because of the way virtual memory works,
832              only the memory pages that are actually needed will be physically allocated. */
833   PetscFunctionBegin;
834   PetscCall(PetscMalloc1(am + 1, &ci));
835   for (i = 0; i < am; i++) {
836     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 */
837     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
838     a_rownnz             = 0;
839     for (k = 0; k < anzi; ++k) {
840       a_rownnz += bi[acol[k] + 1] - bi[acol[k]];
841       if (a_rownnz > bn) {
842         a_rownnz = bn;
843         break;
844       }
845     }
846     a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz);
847   }
848   /* temporary work areas for merging rows */
849   PetscCall(PetscMalloc1(a_maxrownnz * 8, &workj_L1));
850   PetscCall(PetscMalloc1(a_maxrownnz * 8, &workj_L2));
851   PetscCall(PetscMalloc1(a_maxrownnz, &workj_L3));
852 
853   /* This should be enough for almost all matrices. If not, memory is reallocated later. */
854   c_maxmem = 8 * (ai[am] + bi[bm]);
855   /* Step 2: Populate pattern for C */
856   PetscCall(PetscMalloc1(c_maxmem, &cj));
857 
858   ci_nnz      = 0;
859   ci[0]       = 0;
860   worki_L1[0] = 0;
861   worki_L2[0] = 0;
862   for (i = 0; i < am; i++) {
863     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 */
864     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
865     rowsleft             = anzi;
866     inputcol_L1          = acol;
867     L2_nnz               = 0;
868     L2_nrows             = 1; /* Number of rows to be merged on Level 3. output of L3 already exists -> initial value 1   */
869     worki_L2[1]          = 0;
870     outputi_nnz          = 0;
871 
872     /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem  -> allocate more memory */
873     while (ci_nnz + a_maxrownnz > c_maxmem) {
874       c_maxmem *= 2;
875       ndouble++;
876       PetscCall(PetscRealloc(sizeof(PetscInt) * c_maxmem, &cj));
877     }
878 
879     while (rowsleft) {
880       L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */
881       L1_nrows    = 0;
882       L1_nnz      = 0;
883       inputcol    = inputcol_L1;
884       inputi      = bi;
885       inputj      = bj;
886 
887       /* The following macro is used to specialize for small rows in A.
888          This helps with compiler unrolling, improving performance substantially.
889           Input:  inputj   inputi  inputcol  bn
890           Output: outputj  outputi_nnz                       */
891 #define MatMatMultSymbolic_RowMergeMacro(ANNZ) \
892   do { \
893     window_min  = bn; \
894     outputi_nnz = 0; \
895     for (k = 0; k < ANNZ; ++k) { \
896       brow_ptr[k] = inputj + inputi[inputcol[k]]; \
897       brow_end[k] = inputj + inputi[inputcol[k] + 1]; \
898       window[k]   = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
899       window_min  = PetscMin(window[k], window_min); \
900     } \
901     while (window_min < bn) { \
902       outputj[outputi_nnz++] = window_min; \
903       /* advance front and compute new minimum */ \
904       old_window_min = window_min; \
905       window_min     = bn; \
906       for (k = 0; k < ANNZ; ++k) { \
907         if (window[k] == old_window_min) { \
908           brow_ptr[k]++; \
909           window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
910         } \
911         window_min = PetscMin(window[k], window_min); \
912       } \
913     } \
914   } while (0)
915 
916       /************** L E V E L  1 ***************/
917       /* Merge up to 8 rows of B to L1 work array*/
918       while (L1_rowsleft) {
919         outputi_nnz = 0;
920         if (anzi > 8) outputj = workj_L1 + L1_nnz; /* Level 1 rowmerge*/
921         else outputj = cj + ci_nnz;                /* Merge directly to C */
922 
923         switch (L1_rowsleft) {
924         case 1:
925           brow_ptr[0] = inputj + inputi[inputcol[0]];
926           brow_end[0] = inputj + inputi[inputcol[0] + 1];
927           for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
928           inputcol += L1_rowsleft;
929           rowsleft -= L1_rowsleft;
930           L1_rowsleft = 0;
931           break;
932         case 2:
933           MatMatMultSymbolic_RowMergeMacro(2);
934           inputcol += L1_rowsleft;
935           rowsleft -= L1_rowsleft;
936           L1_rowsleft = 0;
937           break;
938         case 3:
939           MatMatMultSymbolic_RowMergeMacro(3);
940           inputcol += L1_rowsleft;
941           rowsleft -= L1_rowsleft;
942           L1_rowsleft = 0;
943           break;
944         case 4:
945           MatMatMultSymbolic_RowMergeMacro(4);
946           inputcol += L1_rowsleft;
947           rowsleft -= L1_rowsleft;
948           L1_rowsleft = 0;
949           break;
950         case 5:
951           MatMatMultSymbolic_RowMergeMacro(5);
952           inputcol += L1_rowsleft;
953           rowsleft -= L1_rowsleft;
954           L1_rowsleft = 0;
955           break;
956         case 6:
957           MatMatMultSymbolic_RowMergeMacro(6);
958           inputcol += L1_rowsleft;
959           rowsleft -= L1_rowsleft;
960           L1_rowsleft = 0;
961           break;
962         case 7:
963           MatMatMultSymbolic_RowMergeMacro(7);
964           inputcol += L1_rowsleft;
965           rowsleft -= L1_rowsleft;
966           L1_rowsleft = 0;
967           break;
968         default:
969           MatMatMultSymbolic_RowMergeMacro(8);
970           inputcol += 8;
971           rowsleft -= 8;
972           L1_rowsleft -= 8;
973           break;
974         }
975         inputcol_L1 = inputcol;
976         L1_nnz += outputi_nnz;
977         worki_L1[++L1_nrows] = L1_nnz;
978       }
979 
980       /********************** L E V E L  2 ************************/
981       /* Merge from L1 work array to either C or to L2 work array */
982       if (anzi > 8) {
983         inputi      = worki_L1;
984         inputj      = workj_L1;
985         inputcol    = workcol;
986         outputi_nnz = 0;
987 
988         if (anzi <= 64) outputj = cj + ci_nnz; /* Merge from L1 work array to C */
989         else outputj = workj_L2 + L2_nnz;      /* Merge from L1 work array to L2 work array */
990 
991         switch (L1_nrows) {
992         case 1:
993           brow_ptr[0] = inputj + inputi[inputcol[0]];
994           brow_end[0] = inputj + inputi[inputcol[0] + 1];
995           for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
996           break;
997         case 2:
998           MatMatMultSymbolic_RowMergeMacro(2);
999           break;
1000         case 3:
1001           MatMatMultSymbolic_RowMergeMacro(3);
1002           break;
1003         case 4:
1004           MatMatMultSymbolic_RowMergeMacro(4);
1005           break;
1006         case 5:
1007           MatMatMultSymbolic_RowMergeMacro(5);
1008           break;
1009         case 6:
1010           MatMatMultSymbolic_RowMergeMacro(6);
1011           break;
1012         case 7:
1013           MatMatMultSymbolic_RowMergeMacro(7);
1014           break;
1015         case 8:
1016           MatMatMultSymbolic_RowMergeMacro(8);
1017           break;
1018         default:
1019           SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatMatMult logic error: Not merging 1-8 rows from L1 work array!");
1020         }
1021         L2_nnz += outputi_nnz;
1022         worki_L2[++L2_nrows] = L2_nnz;
1023 
1024         /************************ L E V E L  3 **********************/
1025         /* Merge from L2 work array to either C or to L2 work array */
1026         if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) {
1027           inputi      = worki_L2;
1028           inputj      = workj_L2;
1029           inputcol    = workcol;
1030           outputi_nnz = 0;
1031           if (rowsleft) outputj = workj_L3;
1032           else outputj = cj + ci_nnz;
1033           switch (L2_nrows) {
1034           case 1:
1035             brow_ptr[0] = inputj + inputi[inputcol[0]];
1036             brow_end[0] = inputj + inputi[inputcol[0] + 1];
1037             for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
1038             break;
1039           case 2:
1040             MatMatMultSymbolic_RowMergeMacro(2);
1041             break;
1042           case 3:
1043             MatMatMultSymbolic_RowMergeMacro(3);
1044             break;
1045           case 4:
1046             MatMatMultSymbolic_RowMergeMacro(4);
1047             break;
1048           case 5:
1049             MatMatMultSymbolic_RowMergeMacro(5);
1050             break;
1051           case 6:
1052             MatMatMultSymbolic_RowMergeMacro(6);
1053             break;
1054           case 7:
1055             MatMatMultSymbolic_RowMergeMacro(7);
1056             break;
1057           case 8:
1058             MatMatMultSymbolic_RowMergeMacro(8);
1059             break;
1060           default:
1061             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatMatMult logic error: Not merging 1-8 rows from L2 work array!");
1062           }
1063           L2_nrows    = 1;
1064           L2_nnz      = outputi_nnz;
1065           worki_L2[1] = outputi_nnz;
1066           /* Copy to workj_L2 */
1067           if (rowsleft) {
1068             for (k = 0; k < outputi_nnz; ++k) workj_L2[k] = outputj[k];
1069           }
1070         }
1071       }
1072     } /* while (rowsleft) */
1073 #undef MatMatMultSymbolic_RowMergeMacro
1074 
1075     /* terminate current row */
1076     ci_nnz += outputi_nnz;
1077     ci[i + 1] = ci_nnz;
1078   }
1079 
1080   /* Step 3: Create the new symbolic matrix */
1081   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
1082   PetscCall(MatSetBlockSizesFromMats(C, A, B));
1083 
1084   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1085   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1086   c          = (Mat_SeqAIJ *)(C->data);
1087   c->free_a  = PETSC_TRUE;
1088   c->free_ij = PETSC_TRUE;
1089   c->nonew   = 0;
1090 
1091   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
1092 
1093   /* set MatInfo */
1094   afill = (PetscReal)ci[am] / (ai[am] + bi[bm]) + 1.e-5;
1095   if (afill < 1.0) afill = 1.0;
1096   C->info.mallocs           = ndouble;
1097   C->info.fill_ratio_given  = fill;
1098   C->info.fill_ratio_needed = afill;
1099 
1100 #if defined(PETSC_USE_INFO)
1101   if (ci[am]) {
1102     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
1103     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1104   } else {
1105     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1106   }
1107 #endif
1108 
1109   /* Step 4: Free temporary work areas */
1110   PetscCall(PetscFree(workj_L1));
1111   PetscCall(PetscFree(workj_L2));
1112   PetscCall(PetscFree(workj_L3));
1113   PetscFunctionReturn(PETSC_SUCCESS);
1114 }
1115 
1116 /* concatenate unique entries and then sort */
1117 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat A, Mat B, PetscReal fill, Mat C)
1118 {
1119   Mat_SeqAIJ     *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c;
1120   const PetscInt *ai = a->i, *bi = b->i, *aj = a->j, *bj = b->j;
1121   PetscInt       *ci, *cj, bcol;
1122   PetscInt        am = A->rmap->N, bn = B->cmap->N, bm = B->rmap->N;
1123   PetscReal       afill;
1124   PetscInt        i, j, ndouble = 0;
1125   PetscSegBuffer  seg, segrow;
1126   char           *seen;
1127 
1128   PetscFunctionBegin;
1129   PetscCall(PetscMalloc1(am + 1, &ci));
1130   ci[0] = 0;
1131 
1132   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
1133   PetscCall(PetscSegBufferCreate(sizeof(PetscInt), (PetscInt)(fill * (ai[am] + bi[bm])), &seg));
1134   PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 100, &segrow));
1135   PetscCall(PetscCalloc1(bn, &seen));
1136 
1137   /* Determine ci and cj */
1138   for (i = 0; i < am; i++) {
1139     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 */
1140     const PetscInt *acol = aj + ai[i];        /* column indices of nonzero entries in this row */
1141     PetscInt packlen     = 0, *PETSC_RESTRICT crow;
1142 
1143     /* Pack segrow */
1144     for (j = 0; j < anzi; j++) {
1145       PetscInt brow = acol[j], bjstart = bi[brow], bjend = bi[brow + 1], k;
1146       for (k = bjstart; k < bjend; k++) {
1147         bcol = bj[k];
1148         if (!seen[bcol]) { /* new entry */
1149           PetscInt *PETSC_RESTRICT slot;
1150           PetscCall(PetscSegBufferGetInts(segrow, 1, &slot));
1151           *slot      = bcol;
1152           seen[bcol] = 1;
1153           packlen++;
1154         }
1155       }
1156     }
1157 
1158     /* Check i-th diagonal entry */
1159     if (C->force_diagonals && !seen[i]) {
1160       PetscInt *PETSC_RESTRICT slot;
1161       PetscCall(PetscSegBufferGetInts(segrow, 1, &slot));
1162       *slot   = i;
1163       seen[i] = 1;
1164       packlen++;
1165     }
1166 
1167     PetscCall(PetscSegBufferGetInts(seg, packlen, &crow));
1168     PetscCall(PetscSegBufferExtractTo(segrow, crow));
1169     PetscCall(PetscSortInt(packlen, crow));
1170     ci[i + 1] = ci[i] + packlen;
1171     for (j = 0; j < packlen; j++) seen[crow[j]] = 0;
1172   }
1173   PetscCall(PetscSegBufferDestroy(&segrow));
1174   PetscCall(PetscFree(seen));
1175 
1176   /* Column indices are in the segmented buffer */
1177   PetscCall(PetscSegBufferExtractAlloc(seg, &cj));
1178   PetscCall(PetscSegBufferDestroy(&seg));
1179 
1180   /* put together the new symbolic matrix */
1181   PetscCall(MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A), am, bn, ci, cj, NULL, ((PetscObject)A)->type_name, C));
1182   PetscCall(MatSetBlockSizesFromMats(C, A, B));
1183 
1184   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1185   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1186   c          = (Mat_SeqAIJ *)(C->data);
1187   c->free_a  = PETSC_TRUE;
1188   c->free_ij = PETSC_TRUE;
1189   c->nonew   = 0;
1190 
1191   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
1192 
1193   /* set MatInfo */
1194   afill = (PetscReal)ci[am] / PetscMax(ai[am] + bi[bm], 1) + 1.e-5;
1195   if (afill < 1.0) afill = 1.0;
1196   C->info.mallocs           = ndouble;
1197   C->info.fill_ratio_given  = fill;
1198   C->info.fill_ratio_needed = afill;
1199 
1200 #if defined(PETSC_USE_INFO)
1201   if (ci[am]) {
1202     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", ndouble, (double)fill, (double)afill));
1203     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1204   } else {
1205     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1206   }
1207 #endif
1208   PetscFunctionReturn(PETSC_SUCCESS);
1209 }
1210 
1211 static PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(void *data)
1212 {
1213   Mat_MatMatTransMult *abt = (Mat_MatMatTransMult *)data;
1214 
1215   PetscFunctionBegin;
1216   PetscCall(MatTransposeColoringDestroy(&abt->matcoloring));
1217   PetscCall(MatDestroy(&abt->Bt_den));
1218   PetscCall(MatDestroy(&abt->ABt_den));
1219   PetscCall(PetscFree(abt));
1220   PetscFunctionReturn(PETSC_SUCCESS);
1221 }
1222 
1223 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
1224 {
1225   Mat                  Bt;
1226   Mat_MatMatTransMult *abt;
1227   Mat_Product         *product = C->product;
1228   char                *alg;
1229 
1230   PetscFunctionBegin;
1231   PetscCheck(product, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1232   PetscCheck(!product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1233 
1234   /* create symbolic Bt */
1235   PetscCall(MatTransposeSymbolic(B, &Bt));
1236   PetscCall(MatSetBlockSizes(Bt, PetscAbs(A->cmap->bs), PetscAbs(B->cmap->bs)));
1237   PetscCall(MatSetType(Bt, ((PetscObject)A)->type_name));
1238 
1239   /* get symbolic C=A*Bt */
1240   PetscCall(PetscStrallocpy(product->alg, &alg));
1241   PetscCall(MatProductSetAlgorithm(C, "sorted")); /* set algorithm for C = A*Bt */
1242   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(A, Bt, fill, C));
1243   PetscCall(MatProductSetAlgorithm(C, alg)); /* resume original algorithm for ABt product */
1244   PetscCall(PetscFree(alg));
1245 
1246   /* create a supporting struct for reuse intermediate dense matrices with matcoloring */
1247   PetscCall(PetscNew(&abt));
1248 
1249   product->data    = abt;
1250   product->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
1251 
1252   C->ops->mattransposemultnumeric = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ;
1253 
1254   abt->usecoloring = PETSC_FALSE;
1255   PetscCall(PetscStrcmp(product->alg, "color", &abt->usecoloring));
1256   if (abt->usecoloring) {
1257     /* Create MatTransposeColoring from symbolic C=A*B^T */
1258     MatTransposeColoring matcoloring;
1259     MatColoring          coloring;
1260     ISColoring           iscoloring;
1261     Mat                  Bt_dense, C_dense;
1262 
1263     /* inode causes memory problem */
1264     PetscCall(MatSetOption(C, MAT_USE_INODES, PETSC_FALSE));
1265 
1266     PetscCall(MatColoringCreate(C, &coloring));
1267     PetscCall(MatColoringSetDistance(coloring, 2));
1268     PetscCall(MatColoringSetType(coloring, MATCOLORINGSL));
1269     PetscCall(MatColoringSetFromOptions(coloring));
1270     PetscCall(MatColoringApply(coloring, &iscoloring));
1271     PetscCall(MatColoringDestroy(&coloring));
1272     PetscCall(MatTransposeColoringCreate(C, iscoloring, &matcoloring));
1273 
1274     abt->matcoloring = matcoloring;
1275 
1276     PetscCall(ISColoringDestroy(&iscoloring));
1277 
1278     /* Create Bt_dense and C_dense = A*Bt_dense */
1279     PetscCall(MatCreate(PETSC_COMM_SELF, &Bt_dense));
1280     PetscCall(MatSetSizes(Bt_dense, A->cmap->n, matcoloring->ncolors, A->cmap->n, matcoloring->ncolors));
1281     PetscCall(MatSetType(Bt_dense, MATSEQDENSE));
1282     PetscCall(MatSeqDenseSetPreallocation(Bt_dense, NULL));
1283 
1284     Bt_dense->assembled = PETSC_TRUE;
1285     abt->Bt_den         = Bt_dense;
1286 
1287     PetscCall(MatCreate(PETSC_COMM_SELF, &C_dense));
1288     PetscCall(MatSetSizes(C_dense, A->rmap->n, matcoloring->ncolors, A->rmap->n, matcoloring->ncolors));
1289     PetscCall(MatSetType(C_dense, MATSEQDENSE));
1290     PetscCall(MatSeqDenseSetPreallocation(C_dense, NULL));
1291 
1292     Bt_dense->assembled = PETSC_TRUE;
1293     abt->ABt_den        = C_dense;
1294 
1295 #if defined(PETSC_USE_INFO)
1296     {
1297       Mat_SeqAIJ *c = (Mat_SeqAIJ *)C->data;
1298       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,
1299                           Bt_dense->cmap->n, c->nz, A->rmap->n * matcoloring->ncolors, (double)(((PetscReal)(c->nz)) / ((PetscReal)(A->rmap->n * matcoloring->ncolors)))));
1300     }
1301 #endif
1302   }
1303   /* clean up */
1304   PetscCall(MatDestroy(&Bt));
1305   PetscFunctionReturn(PETSC_SUCCESS);
1306 }
1307 
1308 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
1309 {
1310   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c = (Mat_SeqAIJ *)C->data;
1311   PetscInt            *ai = a->i, *aj = a->j, *bi = b->i, *bj = b->j, anzi, bnzj, nexta, nextb, *acol, *bcol, brow;
1312   PetscInt             cm = C->rmap->n, *ci = c->i, *cj = c->j, i, j, cnzi, *ccol;
1313   PetscLogDouble       flops = 0.0;
1314   MatScalar           *aa = a->a, *aval, *ba = b->a, *bval, *ca, *cval;
1315   Mat_MatMatTransMult *abt;
1316   Mat_Product         *product = C->product;
1317 
1318   PetscFunctionBegin;
1319   PetscCheck(product, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1320   abt = (Mat_MatMatTransMult *)product->data;
1321   PetscCheck(abt, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1322   /* clear old values in C */
1323   if (!c->a) {
1324     PetscCall(PetscCalloc1(ci[cm] + 1, &ca));
1325     c->a      = ca;
1326     c->free_a = PETSC_TRUE;
1327   } else {
1328     ca = c->a;
1329     PetscCall(PetscArrayzero(ca, ci[cm] + 1));
1330   }
1331 
1332   if (abt->usecoloring) {
1333     MatTransposeColoring matcoloring = abt->matcoloring;
1334     Mat                  Bt_dense, C_dense = abt->ABt_den;
1335 
1336     /* Get Bt_dense by Apply MatTransposeColoring to B */
1337     Bt_dense = abt->Bt_den;
1338     PetscCall(MatTransColoringApplySpToDen(matcoloring, B, Bt_dense));
1339 
1340     /* C_dense = A*Bt_dense */
1341     PetscCall(MatMatMultNumeric_SeqAIJ_SeqDense(A, Bt_dense, C_dense));
1342 
1343     /* Recover C from C_dense */
1344     PetscCall(MatTransColoringApplyDenToSp(matcoloring, C_dense, C));
1345     PetscFunctionReturn(PETSC_SUCCESS);
1346   }
1347 
1348   for (i = 0; i < cm; i++) {
1349     anzi = ai[i + 1] - ai[i];
1350     acol = aj + ai[i];
1351     aval = aa + ai[i];
1352     cnzi = ci[i + 1] - ci[i];
1353     ccol = cj + ci[i];
1354     cval = ca + ci[i];
1355     for (j = 0; j < cnzi; j++) {
1356       brow = ccol[j];
1357       bnzj = bi[brow + 1] - bi[brow];
1358       bcol = bj + bi[brow];
1359       bval = ba + bi[brow];
1360 
1361       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1362       nexta = 0;
1363       nextb = 0;
1364       while (nexta < anzi && nextb < bnzj) {
1365         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
1366         if (nexta == anzi) break;
1367         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
1368         if (nextb == bnzj) break;
1369         if (acol[nexta] == bcol[nextb]) {
1370           cval[j] += aval[nexta] * bval[nextb];
1371           nexta++;
1372           nextb++;
1373           flops += 2;
1374         }
1375       }
1376     }
1377   }
1378   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1379   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1380   PetscCall(PetscLogFlops(flops));
1381   PetscFunctionReturn(PETSC_SUCCESS);
1382 }
1383 
1384 PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(void *data)
1385 {
1386   Mat_MatTransMatMult *atb = (Mat_MatTransMatMult *)data;
1387 
1388   PetscFunctionBegin;
1389   PetscCall(MatDestroy(&atb->At));
1390   if (atb->destroy) PetscCall((*atb->destroy)(atb->data));
1391   PetscCall(PetscFree(atb));
1392   PetscFunctionReturn(PETSC_SUCCESS);
1393 }
1394 
1395 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A, Mat B, PetscReal fill, Mat C)
1396 {
1397   Mat          At      = NULL;
1398   Mat_Product *product = C->product;
1399   PetscBool    flg, def, square;
1400 
1401   PetscFunctionBegin;
1402   MatCheckProduct(C, 4);
1403   square = (PetscBool)(A == B && A->symmetric == PETSC_BOOL3_TRUE);
1404   /* outerproduct */
1405   PetscCall(PetscStrcmp(product->alg, "outerproduct", &flg));
1406   if (flg) {
1407     /* create symbolic At */
1408     if (!square) {
1409       PetscCall(MatTransposeSymbolic(A, &At));
1410       PetscCall(MatSetBlockSizes(At, PetscAbs(A->cmap->bs), PetscAbs(B->cmap->bs)));
1411       PetscCall(MatSetType(At, ((PetscObject)A)->type_name));
1412     }
1413     /* get symbolic C=At*B */
1414     PetscCall(MatProductSetAlgorithm(C, "sorted"));
1415     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At, B, fill, C));
1416 
1417     /* clean up */
1418     if (!square) PetscCall(MatDestroy(&At));
1419 
1420     C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ; /* outerproduct */
1421     PetscCall(MatProductSetAlgorithm(C, "outerproduct"));
1422     PetscFunctionReturn(PETSC_SUCCESS);
1423   }
1424 
1425   /* matmatmult */
1426   PetscCall(PetscStrcmp(product->alg, "default", &def));
1427   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
1428   if (flg || def) {
1429     Mat_MatTransMatMult *atb;
1430 
1431     PetscCheck(!product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1432     PetscCall(PetscNew(&atb));
1433     if (!square) PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
1434     PetscCall(MatProductSetAlgorithm(C, "sorted"));
1435     PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At, B, fill, C));
1436     PetscCall(MatProductSetAlgorithm(C, "at*b"));
1437     product->data    = atb;
1438     product->destroy = MatDestroy_SeqAIJ_MatTransMatMult;
1439     atb->At          = At;
1440 
1441     C->ops->mattransposemultnumeric = NULL; /* see MatProductNumeric_AtB_SeqAIJ_SeqAIJ */
1442     PetscFunctionReturn(PETSC_SUCCESS);
1443   }
1444 
1445   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
1446 }
1447 
1448 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A, Mat B, Mat C)
1449 {
1450   Mat_SeqAIJ    *a = (Mat_SeqAIJ *)A->data, *b = (Mat_SeqAIJ *)B->data, *c = (Mat_SeqAIJ *)C->data;
1451   PetscInt       am = A->rmap->n, anzi, *ai = a->i, *aj = a->j, *bi = b->i, *bj, bnzi, nextb;
1452   PetscInt       cm = C->rmap->n, *ci = c->i, *cj = c->j, crow, *cjj, i, j, k;
1453   PetscLogDouble flops = 0.0;
1454   MatScalar     *aa    = a->a, *ba, *ca, *caj;
1455 
1456   PetscFunctionBegin;
1457   if (!c->a) {
1458     PetscCall(PetscCalloc1(ci[cm] + 1, &ca));
1459 
1460     c->a      = ca;
1461     c->free_a = PETSC_TRUE;
1462   } else {
1463     ca = c->a;
1464     PetscCall(PetscArrayzero(ca, ci[cm]));
1465   }
1466 
1467   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1468   for (i = 0; i < am; i++) {
1469     bj   = b->j + bi[i];
1470     ba   = b->a + bi[i];
1471     bnzi = bi[i + 1] - bi[i];
1472     anzi = ai[i + 1] - ai[i];
1473     for (j = 0; j < anzi; j++) {
1474       nextb = 0;
1475       crow  = *aj++;
1476       cjj   = cj + ci[crow];
1477       caj   = ca + ci[crow];
1478       /* perform sparse axpy operation.  Note cjj includes bj. */
1479       for (k = 0; nextb < bnzi; k++) {
1480         if (cjj[k] == *(bj + nextb)) { /* ccol == bcol */
1481           caj[k] += (*aa) * (*(ba + nextb));
1482           nextb++;
1483         }
1484       }
1485       flops += 2 * bnzi;
1486       aa++;
1487     }
1488   }
1489 
1490   /* Assemble the final matrix and clean up */
1491   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1492   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1493   PetscCall(PetscLogFlops(flops));
1494   PetscFunctionReturn(PETSC_SUCCESS);
1495 }
1496 
1497 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A, Mat B, PetscReal fill, Mat C)
1498 {
1499   PetscFunctionBegin;
1500   PetscCall(MatMatMultSymbolic_SeqDense_SeqDense(A, B, 0.0, C));
1501   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1502   PetscFunctionReturn(PETSC_SUCCESS);
1503 }
1504 
1505 PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A, Mat B, Mat C, const PetscBool add)
1506 {
1507   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)A->data;
1508   PetscScalar       *c, r1, r2, r3, r4, *c1, *c2, *c3, *c4;
1509   const PetscScalar *aa, *b, *b1, *b2, *b3, *b4, *av;
1510   const PetscInt    *aj;
1511   PetscInt           cm = C->rmap->n, cn = B->cmap->n, bm, am = A->rmap->n;
1512   PetscInt           clda;
1513   PetscInt           am4, bm4, col, i, j, n;
1514 
1515   PetscFunctionBegin;
1516   if (!cm || !cn) PetscFunctionReturn(PETSC_SUCCESS);
1517   PetscCall(MatSeqAIJGetArrayRead(A, &av));
1518   if (add) {
1519     PetscCall(MatDenseGetArray(C, &c));
1520   } else {
1521     PetscCall(MatDenseGetArrayWrite(C, &c));
1522   }
1523   PetscCall(MatDenseGetArrayRead(B, &b));
1524   PetscCall(MatDenseGetLDA(B, &bm));
1525   PetscCall(MatDenseGetLDA(C, &clda));
1526   am4 = 4 * clda;
1527   bm4 = 4 * bm;
1528   if (b) {
1529     b1 = b;
1530     b2 = b1 + bm;
1531     b3 = b2 + bm;
1532     b4 = b3 + bm;
1533   } else b1 = b2 = b3 = b4 = NULL;
1534   c1 = c;
1535   c2 = c1 + clda;
1536   c3 = c2 + clda;
1537   c4 = c3 + clda;
1538   for (col = 0; col < (cn / 4) * 4; col += 4) { /* over columns of C */
1539     for (i = 0; i < am; i++) {                  /* over rows of A in those columns */
1540       r1 = r2 = r3 = r4 = 0.0;
1541       n                 = a->i[i + 1] - a->i[i];
1542       aj                = a->j ? a->j + a->i[i] : NULL;
1543       aa                = av ? av + a->i[i] : NULL;
1544       for (j = 0; j < n; j++) {
1545         const PetscScalar aatmp = aa[j];
1546         const PetscInt    ajtmp = aj[j];
1547         r1 += aatmp * b1[ajtmp];
1548         r2 += aatmp * b2[ajtmp];
1549         r3 += aatmp * b3[ajtmp];
1550         r4 += aatmp * b4[ajtmp];
1551       }
1552       if (add) {
1553         c1[i] += r1;
1554         c2[i] += r2;
1555         c3[i] += r3;
1556         c4[i] += r4;
1557       } else {
1558         c1[i] = r1;
1559         c2[i] = r2;
1560         c3[i] = r3;
1561         c4[i] = r4;
1562       }
1563     }
1564     if (b) {
1565       b1 += bm4;
1566       b2 += bm4;
1567       b3 += bm4;
1568       b4 += bm4;
1569     }
1570     c1 += am4;
1571     c2 += am4;
1572     c3 += am4;
1573     c4 += am4;
1574   }
1575   /* process remaining columns */
1576   if (col != cn) {
1577     PetscInt rc = cn - col;
1578 
1579     if (rc == 1) {
1580       for (i = 0; i < am; i++) {
1581         r1 = 0.0;
1582         n  = a->i[i + 1] - a->i[i];
1583         aj = a->j + a->i[i];
1584         aa = av + a->i[i];
1585         for (j = 0; j < n; j++) r1 += aa[j] * b1[aj[j]];
1586         if (add) c1[i] += r1;
1587         else c1[i] = r1;
1588       }
1589     } else if (rc == 2) {
1590       for (i = 0; i < am; i++) {
1591         r1 = r2 = 0.0;
1592         n       = a->i[i + 1] - a->i[i];
1593         aj      = a->j + a->i[i];
1594         aa      = av + a->i[i];
1595         for (j = 0; j < n; j++) {
1596           const PetscScalar aatmp = aa[j];
1597           const PetscInt    ajtmp = aj[j];
1598           r1 += aatmp * b1[ajtmp];
1599           r2 += aatmp * b2[ajtmp];
1600         }
1601         if (add) {
1602           c1[i] += r1;
1603           c2[i] += r2;
1604         } else {
1605           c1[i] = r1;
1606           c2[i] = r2;
1607         }
1608       }
1609     } else {
1610       for (i = 0; i < am; i++) {
1611         r1 = r2 = r3 = 0.0;
1612         n            = a->i[i + 1] - a->i[i];
1613         aj           = a->j ? a->j + a->i[i] : NULL;
1614         aa           = av ? av + a->i[i] : NULL;
1615         for (j = 0; j < n; j++) {
1616           const PetscScalar aatmp = aa[j];
1617           const PetscInt    ajtmp = aj[j];
1618           r1 += aatmp * b1[ajtmp];
1619           r2 += aatmp * b2[ajtmp];
1620           r3 += aatmp * b3[ajtmp];
1621         }
1622         if (add) {
1623           c1[i] += r1;
1624           c2[i] += r2;
1625           c3[i] += r3;
1626         } else {
1627           c1[i] = r1;
1628           c2[i] = r2;
1629           c3[i] = r3;
1630         }
1631       }
1632     }
1633   }
1634   PetscCall(PetscLogFlops(cn * (2.0 * a->nz)));
1635   if (add) {
1636     PetscCall(MatDenseRestoreArray(C, &c));
1637   } else {
1638     PetscCall(MatDenseRestoreArrayWrite(C, &c));
1639   }
1640   PetscCall(MatDenseRestoreArrayRead(B, &b));
1641   PetscCall(MatSeqAIJRestoreArrayRead(A, &av));
1642   PetscFunctionReturn(PETSC_SUCCESS);
1643 }
1644 
1645 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A, Mat B, Mat C)
1646 {
1647   PetscFunctionBegin;
1648   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);
1649   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);
1650   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);
1651 
1652   PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(A, B, C, PETSC_FALSE));
1653   PetscFunctionReturn(PETSC_SUCCESS);
1654 }
1655 
1656 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AB(Mat C)
1657 {
1658   PetscFunctionBegin;
1659   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqDense;
1660   C->ops->productsymbolic = MatProductSymbolic_AB;
1661   PetscFunctionReturn(PETSC_SUCCESS);
1662 }
1663 
1664 PETSC_INTERN PetscErrorCode MatTMatTMultSymbolic_SeqAIJ_SeqDense(Mat, Mat, PetscReal, Mat);
1665 
1666 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(Mat C)
1667 {
1668   PetscFunctionBegin;
1669   C->ops->transposematmultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1670   C->ops->productsymbolic          = MatProductSymbolic_AtB;
1671   PetscFunctionReturn(PETSC_SUCCESS);
1672 }
1673 
1674 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(Mat C)
1675 {
1676   PetscFunctionBegin;
1677   C->ops->mattransposemultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1678   C->ops->productsymbolic          = MatProductSymbolic_ABt;
1679   PetscFunctionReturn(PETSC_SUCCESS);
1680 }
1681 
1682 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat C)
1683 {
1684   Mat_Product *product = C->product;
1685 
1686   PetscFunctionBegin;
1687   switch (product->type) {
1688   case MATPRODUCT_AB:
1689     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_AB(C));
1690     break;
1691   case MATPRODUCT_AtB:
1692     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(C));
1693     break;
1694   case MATPRODUCT_ABt:
1695     PetscCall(MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(C));
1696     break;
1697   default:
1698     break;
1699   }
1700   PetscFunctionReturn(PETSC_SUCCESS);
1701 }
1702 
1703 static PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(Mat C)
1704 {
1705   Mat_Product *product = C->product;
1706   Mat          A       = product->A;
1707   PetscBool    baij;
1708 
1709   PetscFunctionBegin;
1710   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQBAIJ, &baij));
1711   if (!baij) { /* A is seqsbaij */
1712     PetscBool sbaij;
1713     PetscCall(PetscObjectTypeCompare((PetscObject)A, MATSEQSBAIJ, &sbaij));
1714     PetscCheck(sbaij, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "Mat must be either seqbaij or seqsbaij format");
1715 
1716     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqSBAIJ_SeqDense;
1717   } else { /* A is seqbaij */
1718     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqBAIJ_SeqDense;
1719   }
1720 
1721   C->ops->productsymbolic = MatProductSymbolic_AB;
1722   PetscFunctionReturn(PETSC_SUCCESS);
1723 }
1724 
1725 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense(Mat C)
1726 {
1727   Mat_Product *product = C->product;
1728 
1729   PetscFunctionBegin;
1730   MatCheckProduct(C, 1);
1731   PetscCheck(product->A, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing A");
1732   if (product->type == MATPRODUCT_AB || (product->type == MATPRODUCT_AtB && product->A->symmetric == PETSC_BOOL3_TRUE)) PetscCall(MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(C));
1733   PetscFunctionReturn(PETSC_SUCCESS);
1734 }
1735 
1736 static PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ_AB(Mat C)
1737 {
1738   PetscFunctionBegin;
1739   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqDense_SeqAIJ;
1740   C->ops->productsymbolic = MatProductSymbolic_AB;
1741   PetscFunctionReturn(PETSC_SUCCESS);
1742 }
1743 
1744 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ(Mat C)
1745 {
1746   Mat_Product *product = C->product;
1747 
1748   PetscFunctionBegin;
1749   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_SeqDense_SeqAIJ_AB(C));
1750   PetscFunctionReturn(PETSC_SUCCESS);
1751 }
1752 
1753 PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring, Mat B, Mat Btdense)
1754 {
1755   Mat_SeqAIJ   *b       = (Mat_SeqAIJ *)B->data;
1756   Mat_SeqDense *btdense = (Mat_SeqDense *)Btdense->data;
1757   PetscInt     *bi = b->i, *bj = b->j;
1758   PetscInt      m = Btdense->rmap->n, n = Btdense->cmap->n, j, k, l, col, anz, *btcol, brow, ncolumns;
1759   MatScalar    *btval, *btval_den, *ba = b->a;
1760   PetscInt     *columns = coloring->columns, *colorforcol = coloring->colorforcol, ncolors = coloring->ncolors;
1761 
1762   PetscFunctionBegin;
1763   btval_den = btdense->v;
1764   PetscCall(PetscArrayzero(btval_den, m * n));
1765   for (k = 0; k < ncolors; k++) {
1766     ncolumns = coloring->ncolumns[k];
1767     for (l = 0; l < ncolumns; l++) { /* insert a row of B to a column of Btdense */
1768       col   = *(columns + colorforcol[k] + l);
1769       btcol = bj + bi[col];
1770       btval = ba + bi[col];
1771       anz   = bi[col + 1] - bi[col];
1772       for (j = 0; j < anz; j++) {
1773         brow            = btcol[j];
1774         btval_den[brow] = btval[j];
1775       }
1776     }
1777     btval_den += m;
1778   }
1779   PetscFunctionReturn(PETSC_SUCCESS);
1780 }
1781 
1782 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring, Mat Cden, Mat Csp)
1783 {
1784   Mat_SeqAIJ        *csp = (Mat_SeqAIJ *)Csp->data;
1785   const PetscScalar *ca_den, *ca_den_ptr;
1786   PetscScalar       *ca = csp->a;
1787   PetscInt           k, l, m = Cden->rmap->n, ncolors = matcoloring->ncolors;
1788   PetscInt           brows = matcoloring->brows, *den2sp = matcoloring->den2sp;
1789   PetscInt           nrows, *row, *idx;
1790   PetscInt          *rows = matcoloring->rows, *colorforrow = matcoloring->colorforrow;
1791 
1792   PetscFunctionBegin;
1793   PetscCall(MatDenseGetArrayRead(Cden, &ca_den));
1794 
1795   if (brows > 0) {
1796     PetscInt *lstart, row_end, row_start;
1797     lstart = matcoloring->lstart;
1798     PetscCall(PetscArrayzero(lstart, ncolors));
1799 
1800     row_end = brows;
1801     if (row_end > m) row_end = m;
1802     for (row_start = 0; row_start < m; row_start += brows) { /* loop over row blocks of Csp */
1803       ca_den_ptr = ca_den;
1804       for (k = 0; k < ncolors; k++) { /* loop over colors (columns of Cden) */
1805         nrows = matcoloring->nrows[k];
1806         row   = rows + colorforrow[k];
1807         idx   = den2sp + colorforrow[k];
1808         for (l = lstart[k]; l < nrows; l++) {
1809           if (row[l] >= row_end) {
1810             lstart[k] = l;
1811             break;
1812           } else {
1813             ca[idx[l]] = ca_den_ptr[row[l]];
1814           }
1815         }
1816         ca_den_ptr += m;
1817       }
1818       row_end += brows;
1819       if (row_end > m) row_end = m;
1820     }
1821   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1822     ca_den_ptr = ca_den;
1823     for (k = 0; k < ncolors; k++) {
1824       nrows = matcoloring->nrows[k];
1825       row   = rows + colorforrow[k];
1826       idx   = den2sp + colorforrow[k];
1827       for (l = 0; l < nrows; l++) ca[idx[l]] = ca_den_ptr[row[l]];
1828       ca_den_ptr += m;
1829     }
1830   }
1831 
1832   PetscCall(MatDenseRestoreArrayRead(Cden, &ca_den));
1833 #if defined(PETSC_USE_INFO)
1834   if (matcoloring->brows > 0) {
1835     PetscCall(PetscInfo(Csp, "Loop over %" PetscInt_FMT " row blocks for den2sp\n", brows));
1836   } else {
1837     PetscCall(PetscInfo(Csp, "Loop over colors/columns of Cden, inefficient for large sparse matrix product \n"));
1838   }
1839 #endif
1840   PetscFunctionReturn(PETSC_SUCCESS);
1841 }
1842 
1843 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat, ISColoring iscoloring, MatTransposeColoring c)
1844 {
1845   PetscInt        i, n, nrows, Nbs, j, k, m, ncols, col, cm;
1846   const PetscInt *is, *ci, *cj, *row_idx;
1847   PetscInt        nis = iscoloring->n, *rowhit, bs = 1;
1848   IS             *isa;
1849   Mat_SeqAIJ     *csp = (Mat_SeqAIJ *)mat->data;
1850   PetscInt       *colorforrow, *rows, *rows_i, *idxhit, *spidx, *den2sp, *den2sp_i;
1851   PetscInt       *colorforcol, *columns, *columns_i, brows;
1852   PetscBool       flg;
1853 
1854   PetscFunctionBegin;
1855   PetscCall(ISColoringGetIS(iscoloring, PETSC_USE_POINTER, PETSC_IGNORE, &isa));
1856 
1857   /* bs >1 is not being tested yet! */
1858   Nbs       = mat->cmap->N / bs;
1859   c->M      = mat->rmap->N / bs; /* set total rows, columns and local rows */
1860   c->N      = Nbs;
1861   c->m      = c->M;
1862   c->rstart = 0;
1863   c->brows  = 100;
1864 
1865   c->ncolors = nis;
1866   PetscCall(PetscMalloc3(nis, &c->ncolumns, nis, &c->nrows, nis + 1, &colorforrow));
1867   PetscCall(PetscMalloc1(csp->nz + 1, &rows));
1868   PetscCall(PetscMalloc1(csp->nz + 1, &den2sp));
1869 
1870   brows = c->brows;
1871   PetscCall(PetscOptionsGetInt(NULL, NULL, "-matden2sp_brows", &brows, &flg));
1872   if (flg) c->brows = brows;
1873   if (brows > 0) PetscCall(PetscMalloc1(nis + 1, &c->lstart));
1874 
1875   colorforrow[0] = 0;
1876   rows_i         = rows;
1877   den2sp_i       = den2sp;
1878 
1879   PetscCall(PetscMalloc1(nis + 1, &colorforcol));
1880   PetscCall(PetscMalloc1(Nbs + 1, &columns));
1881 
1882   colorforcol[0] = 0;
1883   columns_i      = columns;
1884 
1885   /* get column-wise storage of mat */
1886   PetscCall(MatGetColumnIJ_SeqAIJ_Color(mat, 0, PETSC_FALSE, PETSC_FALSE, &ncols, &ci, &cj, &spidx, NULL));
1887 
1888   cm = c->m;
1889   PetscCall(PetscMalloc1(cm + 1, &rowhit));
1890   PetscCall(PetscMalloc1(cm + 1, &idxhit));
1891   for (i = 0; i < nis; i++) { /* loop over color */
1892     PetscCall(ISGetLocalSize(isa[i], &n));
1893     PetscCall(ISGetIndices(isa[i], &is));
1894 
1895     c->ncolumns[i] = n;
1896     if (n) PetscCall(PetscArraycpy(columns_i, is, n));
1897     colorforcol[i + 1] = colorforcol[i] + n;
1898     columns_i += n;
1899 
1900     /* fast, crude version requires O(N*N) work */
1901     PetscCall(PetscArrayzero(rowhit, cm));
1902 
1903     for (j = 0; j < n; j++) { /* loop over columns*/
1904       col     = is[j];
1905       row_idx = cj + ci[col];
1906       m       = ci[col + 1] - ci[col];
1907       for (k = 0; k < m; k++) { /* loop over columns marking them in rowhit */
1908         idxhit[*row_idx]   = spidx[ci[col] + k];
1909         rowhit[*row_idx++] = col + 1;
1910       }
1911     }
1912     /* count the number of hits */
1913     nrows = 0;
1914     for (j = 0; j < cm; j++) {
1915       if (rowhit[j]) nrows++;
1916     }
1917     c->nrows[i]        = nrows;
1918     colorforrow[i + 1] = colorforrow[i] + nrows;
1919 
1920     nrows = 0;
1921     for (j = 0; j < cm; j++) { /* loop over rows */
1922       if (rowhit[j]) {
1923         rows_i[nrows]   = j;
1924         den2sp_i[nrows] = idxhit[j];
1925         nrows++;
1926       }
1927     }
1928     den2sp_i += nrows;
1929 
1930     PetscCall(ISRestoreIndices(isa[i], &is));
1931     rows_i += nrows;
1932   }
1933   PetscCall(MatRestoreColumnIJ_SeqAIJ_Color(mat, 0, PETSC_FALSE, PETSC_FALSE, &ncols, &ci, &cj, &spidx, NULL));
1934   PetscCall(PetscFree(rowhit));
1935   PetscCall(ISColoringRestoreIS(iscoloring, PETSC_USE_POINTER, &isa));
1936   PetscCheck(csp->nz == colorforrow[nis], PETSC_COMM_SELF, PETSC_ERR_PLIB, "csp->nz %" PetscInt_FMT " != colorforrow[nis] %" PetscInt_FMT, csp->nz, colorforrow[nis]);
1937 
1938   c->colorforrow = colorforrow;
1939   c->rows        = rows;
1940   c->den2sp      = den2sp;
1941   c->colorforcol = colorforcol;
1942   c->columns     = columns;
1943 
1944   PetscCall(PetscFree(idxhit));
1945   PetscFunctionReturn(PETSC_SUCCESS);
1946 }
1947 
1948 static PetscErrorCode MatProductNumeric_AtB_SeqAIJ_SeqAIJ(Mat C)
1949 {
1950   Mat_Product *product = C->product;
1951   Mat          A = product->A, B = product->B;
1952 
1953   PetscFunctionBegin;
1954   if (C->ops->mattransposemultnumeric) {
1955     /* Alg: "outerproduct" */
1956     PetscCall((*C->ops->mattransposemultnumeric)(A, B, C));
1957   } else {
1958     /* Alg: "matmatmult" -- C = At*B */
1959     Mat_MatTransMatMult *atb = (Mat_MatTransMatMult *)product->data;
1960 
1961     PetscCheck(atb, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing product struct");
1962     if (atb->At) {
1963       /* At is computed in MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ();
1964          user may have called MatProductReplaceMats() to get this A=product->A */
1965       PetscCall(MatTransposeSetPrecursor(A, atb->At));
1966       PetscCall(MatTranspose(A, MAT_REUSE_MATRIX, &atb->At));
1967     }
1968     PetscCall(MatMatMultNumeric_SeqAIJ_SeqAIJ(atb->At ? atb->At : A, B, C));
1969   }
1970   PetscFunctionReturn(PETSC_SUCCESS);
1971 }
1972 
1973 static PetscErrorCode MatProductSymbolic_AtB_SeqAIJ_SeqAIJ(Mat C)
1974 {
1975   Mat_Product *product = C->product;
1976   Mat          A = product->A, B = product->B;
1977   PetscReal    fill = product->fill;
1978 
1979   PetscFunctionBegin;
1980   PetscCall(MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A, B, fill, C));
1981 
1982   C->ops->productnumeric = MatProductNumeric_AtB_SeqAIJ_SeqAIJ;
1983   PetscFunctionReturn(PETSC_SUCCESS);
1984 }
1985 
1986 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AB(Mat C)
1987 {
1988   Mat_Product *product = C->product;
1989   PetscInt     alg     = 0; /* default algorithm */
1990   PetscBool    flg     = PETSC_FALSE;
1991 #if !defined(PETSC_HAVE_HYPRE)
1992   const char *algTypes[7] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge"};
1993   PetscInt    nalg        = 7;
1994 #else
1995   const char *algTypes[8] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge", "hypre"};
1996   PetscInt    nalg        = 8;
1997 #endif
1998 
1999   PetscFunctionBegin;
2000   /* Set default algorithm */
2001   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2002   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2003 
2004   /* Get runtime option */
2005   if (product->api_user) {
2006     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2007     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[0], &alg, &flg));
2008     PetscOptionsEnd();
2009   } else {
2010     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2011     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AB", algTypes, nalg, algTypes[0], &alg, &flg));
2012     PetscOptionsEnd();
2013   }
2014   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2015 
2016   C->ops->productsymbolic = MatProductSymbolic_AB;
2017   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqAIJ;
2018   PetscFunctionReturn(PETSC_SUCCESS);
2019 }
2020 
2021 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AtB(Mat C)
2022 {
2023   Mat_Product *product     = C->product;
2024   PetscInt     alg         = 0; /* default algorithm */
2025   PetscBool    flg         = PETSC_FALSE;
2026   const char  *algTypes[3] = {"default", "at*b", "outerproduct"};
2027   PetscInt     nalg        = 3;
2028 
2029   PetscFunctionBegin;
2030   /* Get runtime option */
2031   if (product->api_user) {
2032     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2033     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2034     PetscOptionsEnd();
2035   } else {
2036     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2037     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_AtB", algTypes, nalg, algTypes[alg], &alg, &flg));
2038     PetscOptionsEnd();
2039   }
2040   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2041 
2042   C->ops->productsymbolic = MatProductSymbolic_AtB_SeqAIJ_SeqAIJ;
2043   PetscFunctionReturn(PETSC_SUCCESS);
2044 }
2045 
2046 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABt(Mat C)
2047 {
2048   Mat_Product *product     = C->product;
2049   PetscInt     alg         = 0; /* default algorithm */
2050   PetscBool    flg         = PETSC_FALSE;
2051   const char  *algTypes[2] = {"default", "color"};
2052   PetscInt     nalg        = 2;
2053 
2054   PetscFunctionBegin;
2055   /* Set default algorithm */
2056   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2057   if (!flg) {
2058     alg = 1;
2059     PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2060   }
2061 
2062   /* Get runtime option */
2063   if (product->api_user) {
2064     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatTransposeMult", "Mat");
2065     PetscCall(PetscOptionsEList("-matmattransmult_via", "Algorithmic approach", "MatMatTransposeMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2066     PetscOptionsEnd();
2067   } else {
2068     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABt", "Mat");
2069     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABt", algTypes, nalg, algTypes[alg], &alg, &flg));
2070     PetscOptionsEnd();
2071   }
2072   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2073 
2074   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ;
2075   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2076   PetscFunctionReturn(PETSC_SUCCESS);
2077 }
2078 
2079 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_PtAP(Mat C)
2080 {
2081   Mat_Product *product = C->product;
2082   PetscBool    flg     = PETSC_FALSE;
2083   PetscInt     alg     = 0; /* default algorithm -- alg=1 should be default!!! */
2084 #if !defined(PETSC_HAVE_HYPRE)
2085   const char *algTypes[2] = {"scalable", "rap"};
2086   PetscInt    nalg        = 2;
2087 #else
2088   const char *algTypes[3] = {"scalable", "rap", "hypre"};
2089   PetscInt    nalg        = 3;
2090 #endif
2091 
2092   PetscFunctionBegin;
2093   /* Set default algorithm */
2094   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2095   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2096 
2097   /* Get runtime option */
2098   if (product->api_user) {
2099     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2100     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[0], &alg, &flg));
2101     PetscOptionsEnd();
2102   } else {
2103     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2104     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_PtAP", algTypes, nalg, algTypes[0], &alg, &flg));
2105     PetscOptionsEnd();
2106   }
2107   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2108 
2109   C->ops->productsymbolic = MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ;
2110   PetscFunctionReturn(PETSC_SUCCESS);
2111 }
2112 
2113 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_RARt(Mat C)
2114 {
2115   Mat_Product *product     = C->product;
2116   PetscBool    flg         = PETSC_FALSE;
2117   PetscInt     alg         = 0; /* default algorithm */
2118   const char  *algTypes[3] = {"r*a*rt", "r*art", "coloring_rart"};
2119   PetscInt     nalg        = 3;
2120 
2121   PetscFunctionBegin;
2122   /* Set default algorithm */
2123   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2124   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2125 
2126   /* Get runtime option */
2127   if (product->api_user) {
2128     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatRARt", "Mat");
2129     PetscCall(PetscOptionsEList("-matrart_via", "Algorithmic approach", "MatRARt", algTypes, nalg, algTypes[0], &alg, &flg));
2130     PetscOptionsEnd();
2131   } else {
2132     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_RARt", "Mat");
2133     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_RARt", algTypes, nalg, algTypes[0], &alg, &flg));
2134     PetscOptionsEnd();
2135   }
2136   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2137 
2138   C->ops->productsymbolic = MatProductSymbolic_RARt_SeqAIJ_SeqAIJ;
2139   PetscFunctionReturn(PETSC_SUCCESS);
2140 }
2141 
2142 /* ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm */
2143 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABC(Mat C)
2144 {
2145   Mat_Product *product     = C->product;
2146   PetscInt     alg         = 0; /* default algorithm */
2147   PetscBool    flg         = PETSC_FALSE;
2148   const char  *algTypes[7] = {"sorted", "scalable", "scalable_fast", "heap", "btheap", "llcondensed", "rowmerge"};
2149   PetscInt     nalg        = 7;
2150 
2151   PetscFunctionBegin;
2152   /* Set default algorithm */
2153   PetscCall(PetscStrcmp(product->alg, "default", &flg));
2154   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2155 
2156   /* Get runtime option */
2157   if (product->api_user) {
2158     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2159     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2160     PetscOptionsEnd();
2161   } else {
2162     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2163     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2164     PetscOptionsEnd();
2165   }
2166   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2167 
2168   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ;
2169   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2170   PetscFunctionReturn(PETSC_SUCCESS);
2171 }
2172 
2173 PetscErrorCode MatProductSetFromOptions_SeqAIJ(Mat C)
2174 {
2175   Mat_Product *product = C->product;
2176 
2177   PetscFunctionBegin;
2178   switch (product->type) {
2179   case MATPRODUCT_AB:
2180     PetscCall(MatProductSetFromOptions_SeqAIJ_AB(C));
2181     break;
2182   case MATPRODUCT_AtB:
2183     PetscCall(MatProductSetFromOptions_SeqAIJ_AtB(C));
2184     break;
2185   case MATPRODUCT_ABt:
2186     PetscCall(MatProductSetFromOptions_SeqAIJ_ABt(C));
2187     break;
2188   case MATPRODUCT_PtAP:
2189     PetscCall(MatProductSetFromOptions_SeqAIJ_PtAP(C));
2190     break;
2191   case MATPRODUCT_RARt:
2192     PetscCall(MatProductSetFromOptions_SeqAIJ_RARt(C));
2193     break;
2194   case MATPRODUCT_ABC:
2195     PetscCall(MatProductSetFromOptions_SeqAIJ_ABC(C));
2196     break;
2197   default:
2198     break;
2199   }
2200   PetscFunctionReturn(PETSC_SUCCESS);
2201 }
2202