xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision dde8958d96c09bc677f093c6b71afab400f91c19)
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   PetscErrorCode ierr;
16 
17   PetscFunctionBegin;
18   if (C->ops->matmultnumeric) {
19     if (C->ops->matmultnumeric == MatMatMultNumeric_SeqAIJ_SeqAIJ) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Recursive call");
20     ierr = (*C->ops->matmultnumeric)(A,B,C);CHKERRQ(ierr);
21   } else {
22     ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(A,B,C);CHKERRQ(ierr);
23   }
24   PetscFunctionReturn(0);
25 }
26 
27 /* Modified from MatCreateSeqAIJWithArrays() */
28 PETSC_INTERN PetscErrorCode MatSetSeqAIJWithArrays_private(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt i[],PetscInt j[],PetscScalar a[],MatType mtype,Mat mat)
29 {
30   PetscErrorCode ierr;
31   PetscInt       ii;
32   Mat_SeqAIJ     *aij;
33   PetscBool      isseqaij;
34 
35   PetscFunctionBegin;
36   if (m > 0 && i[0]) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"i (row indices) must start with 0");
37   ierr = MatSetSizes(mat,m,n,m,n);CHKERRQ(ierr);
38 
39   if (!mtype) {
40     ierr = PetscObjectBaseTypeCompare((PetscObject)mat,MATSEQAIJ,&isseqaij);CHKERRQ(ierr);
41     if (!isseqaij) { ierr = MatSetType(mat,MATSEQAIJ);CHKERRQ(ierr); }
42   } else {
43     ierr = MatSetType(mat,mtype);CHKERRQ(ierr);
44   }
45   ierr = MatSeqAIJSetPreallocation_SeqAIJ(mat,MAT_SKIP_ALLOCATION,NULL);CHKERRQ(ierr);
46   aij  = (Mat_SeqAIJ*)(mat)->data;
47   ierr = PetscMalloc1(m,&aij->imax);CHKERRQ(ierr);
48   ierr = PetscMalloc1(m,&aij->ilen);CHKERRQ(ierr);
49 
50   aij->i            = i;
51   aij->j            = j;
52   aij->a            = a;
53   aij->singlemalloc = PETSC_FALSE;
54   aij->nonew        = -1; /*this indicates that inserting a new value in the matrix that generates a new nonzero is an error*/
55   aij->free_a       = PETSC_FALSE;
56   aij->free_ij      = PETSC_FALSE;
57 
58   for (ii=0; ii<m; ii++) {
59     aij->ilen[ii] = aij->imax[ii] = i[ii+1] - i[ii];
60   }
61   PetscFunctionReturn(0);
62 }
63 
64 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat C)
65 {
66   PetscErrorCode      ierr;
67   Mat_Product         *product = C->product;
68   MatProductAlgorithm alg;
69   PetscBool           flg;
70 
71   PetscFunctionBegin;
72   if (product) {
73     alg = product->alg;
74   } else {
75     alg = "sorted";
76   }
77   /* sorted */
78   ierr = PetscStrcmp(alg,"sorted",&flg);CHKERRQ(ierr);
79   if (flg) {
80     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(A,B,fill,C);CHKERRQ(ierr);
81     PetscFunctionReturn(0);
82   }
83 
84   /* scalable */
85   ierr = PetscStrcmp(alg,"scalable",&flg);CHKERRQ(ierr);
86   if (flg) {
87     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
88     PetscFunctionReturn(0);
89   }
90 
91   /* scalable_fast */
92   ierr = PetscStrcmp(alg,"scalable_fast",&flg);CHKERRQ(ierr);
93   if (flg) {
94     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
95     PetscFunctionReturn(0);
96   }
97 
98   /* heap */
99   ierr = PetscStrcmp(alg,"heap",&flg);CHKERRQ(ierr);
100   if (flg) {
101     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
102     PetscFunctionReturn(0);
103   }
104 
105   /* btheap */
106   ierr = PetscStrcmp(alg,"btheap",&flg);CHKERRQ(ierr);
107   if (flg) {
108     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
109     PetscFunctionReturn(0);
110   }
111 
112   /* llcondensed */
113   ierr = PetscStrcmp(alg,"llcondensed",&flg);CHKERRQ(ierr);
114   if (flg) {
115     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr);
116     PetscFunctionReturn(0);
117   }
118 
119   /* rowmerge */
120   ierr = PetscStrcmp(alg,"rowmerge",&flg);CHKERRQ(ierr);
121   if (flg) {
122     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(A,B,fill,C);CHKERRQ(ierr);
123     PetscFunctionReturn(0);
124   }
125 
126 #if defined(PETSC_HAVE_HYPRE)
127   ierr = PetscStrcmp(alg,"hypre",&flg);CHKERRQ(ierr);
128   if (flg) {
129     ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr);
130     PetscFunctionReturn(0);
131   }
132 #endif
133 
134   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
135 }
136 
137 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat C)
138 {
139   PetscErrorCode     ierr;
140   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
141   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
142   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
143   PetscReal          afill;
144   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
145   PetscTable         ta;
146   PetscBT            lnkbt;
147   PetscFreeSpaceList free_space=NULL,current_space=NULL;
148 
149   PetscFunctionBegin;
150   /* Get ci and cj */
151   /*---------------*/
152   /* Allocate ci array, arrays for fill computation and */
153   /* free space for accumulating nonzero column info */
154   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
155   ci[0] = 0;
156 
157   /* create and initialize a linked list */
158   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
159   MatRowMergeMax_SeqAIJ(b,bm,ta);
160   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
161   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
162 
163   ierr = PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);CHKERRQ(ierr);
164 
165   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
166   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
167 
168   current_space = free_space;
169 
170   /* Determine ci and cj */
171   for (i=0; i<am; i++) {
172     anzi = ai[i+1] - ai[i];
173     aj   = a->j + ai[i];
174     for (j=0; j<anzi; j++) {
175       brow = aj[j];
176       bnzj = bi[brow+1] - bi[brow];
177       bj   = b->j + bi[brow];
178       /* add non-zero cols of B into the sorted linked list lnk */
179       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
180     }
181     /* add possible missing diagonal entry */
182     if (C->force_diagonals) {
183       ierr = PetscLLCondensedAddSorted(1,&i,lnk,lnkbt);CHKERRQ(ierr);
184     }
185     cnzi = lnk[0];
186 
187     /* If free space is not available, make more free space */
188     /* Double the amount of total space in the list */
189     if (current_space->local_remaining<cnzi) {
190       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
191       ndouble++;
192     }
193 
194     /* Copy data into free space, then initialize lnk */
195     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
196 
197     current_space->array           += cnzi;
198     current_space->local_used      += cnzi;
199     current_space->local_remaining -= cnzi;
200 
201     ci[i+1] = ci[i] + cnzi;
202   }
203 
204   /* Column indices are in the list of free space */
205   /* Allocate space for cj, initialize cj, and */
206   /* destroy list of free space and other temporary array(s) */
207   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
208   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
209   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
210 
211   /* put together the new symbolic matrix */
212   ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,((PetscObject)A)->type_name,C);CHKERRQ(ierr);
213   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
214 
215   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
216   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
217   c          = (Mat_SeqAIJ*)(C->data);
218   c->free_a  = PETSC_FALSE;
219   c->free_ij = PETSC_TRUE;
220   c->nonew   = 0;
221 
222   /* fast, needs non-scalable O(bn) array 'abdense' */
223   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
224 
225   /* set MatInfo */
226   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
227   if (afill < 1.0) afill = 1.0;
228   c->maxnz                  = ci[am];
229   c->nz                     = ci[am];
230   C->info.mallocs           = ndouble;
231   C->info.fill_ratio_given  = fill;
232   C->info.fill_ratio_needed = afill;
233 
234 #if defined(PETSC_USE_INFO)
235   if (ci[am]) {
236     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
237     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
238   } else {
239     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
240   }
241 #endif
242   PetscFunctionReturn(0);
243 }
244 
245 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat A,Mat B,Mat C)
246 {
247   PetscErrorCode    ierr;
248   PetscLogDouble    flops=0.0;
249   Mat_SeqAIJ        *a   = (Mat_SeqAIJ*)A->data;
250   Mat_SeqAIJ        *b   = (Mat_SeqAIJ*)B->data;
251   Mat_SeqAIJ        *c   = (Mat_SeqAIJ*)C->data;
252   PetscInt          *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
253   PetscInt          am   =A->rmap->n,cm=C->rmap->n;
254   PetscInt          i,j,k,anzi,bnzi,cnzi,brow;
255   PetscScalar       *ca,valtmp;
256   PetscScalar       *ab_dense;
257   PetscContainer    cab_dense;
258   const PetscScalar *aa,*ba,*baj;
259 
260   PetscFunctionBegin;
261   ierr = MatSeqAIJGetArrayRead(A,&aa);CHKERRQ(ierr);
262   ierr = MatSeqAIJGetArrayRead(B,&ba);CHKERRQ(ierr);
263   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
264     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
265     c->a      = ca;
266     c->free_a = PETSC_TRUE;
267   } else ca = c->a;
268 
269   /* TODO this should be done in the symbolic phase */
270   /* However, this function is so heavily used (sometimes in an hidden way through multnumeric function pointers
271      that is hard to eradicate) */
272   ierr = PetscObjectQuery((PetscObject)C,"__PETSc__ab_dense",(PetscObject*)&cab_dense);CHKERRQ(ierr);
273   if (!cab_dense) {
274     ierr = PetscMalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr);
275     ierr = PetscContainerCreate(PETSC_COMM_SELF,&cab_dense);CHKERRQ(ierr);
276     ierr = PetscContainerSetPointer(cab_dense,ab_dense);CHKERRQ(ierr);
277     ierr = PetscContainerSetUserDestroy(cab_dense,PetscContainerUserDestroyDefault);CHKERRQ(ierr);
278     ierr = PetscObjectCompose((PetscObject)C,"__PETSc__ab_dense",(PetscObject)cab_dense);CHKERRQ(ierr);
279     ierr = PetscObjectDereference((PetscObject)cab_dense);CHKERRQ(ierr);
280   }
281   ierr = PetscContainerGetPointer(cab_dense,(void**)&ab_dense);CHKERRQ(ierr);
282   ierr = PetscArrayzero(ab_dense,B->cmap->N);CHKERRQ(ierr);
283 
284   /* clean old values in C */
285   ierr = PetscArrayzero(ca,ci[cm]);CHKERRQ(ierr);
286   /* Traverse A row-wise. */
287   /* Build the ith row in C by summing over nonzero columns in A, */
288   /* the rows of B corresponding to nonzeros of A. */
289   for (i=0; i<am; i++) {
290     anzi = ai[i+1] - ai[i];
291     for (j=0; j<anzi; j++) {
292       brow = aj[j];
293       bnzi = bi[brow+1] - bi[brow];
294       bjj  = bj + bi[brow];
295       baj  = ba + bi[brow];
296       /* perform dense axpy */
297       valtmp = aa[j];
298       for (k=0; k<bnzi; k++) {
299         ab_dense[bjj[k]] += valtmp*baj[k];
300       }
301       flops += 2*bnzi;
302     }
303     aj += anzi; aa += anzi;
304 
305     cnzi = ci[i+1] - ci[i];
306     for (k=0; k<cnzi; k++) {
307       ca[k]          += ab_dense[cj[k]];
308       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
309     }
310     flops += cnzi;
311     cj    += cnzi; ca += cnzi;
312   }
313 #if defined(PETSC_HAVE_DEVICE)
314   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
315 #endif
316   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
317   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
318   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
319   ierr = MatSeqAIJRestoreArrayRead(A,&aa);CHKERRQ(ierr);
320   ierr = MatSeqAIJRestoreArrayRead(B,&ba);CHKERRQ(ierr);
321   PetscFunctionReturn(0);
322 }
323 
324 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
325 {
326   PetscErrorCode    ierr;
327   PetscLogDouble    flops=0.0;
328   Mat_SeqAIJ        *a   = (Mat_SeqAIJ*)A->data;
329   Mat_SeqAIJ        *b   = (Mat_SeqAIJ*)B->data;
330   Mat_SeqAIJ        *c   = (Mat_SeqAIJ*)C->data;
331   PetscInt          *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
332   PetscInt          am   = A->rmap->N,cm=C->rmap->N;
333   PetscInt          i,j,k,anzi,bnzi,cnzi,brow;
334   PetscScalar       *ca=c->a,valtmp;
335   const PetscScalar *aa,*ba,*baj;
336   PetscInt          nextb;
337 
338   PetscFunctionBegin;
339   ierr = MatSeqAIJGetArrayRead(A,&aa);CHKERRQ(ierr);
340   ierr = MatSeqAIJGetArrayRead(B,&ba);CHKERRQ(ierr);
341   if (!ca) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
342     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
343     c->a      = ca;
344     c->free_a = PETSC_TRUE;
345   }
346 
347   /* clean old values in C */
348   ierr = PetscArrayzero(ca,ci[cm]);CHKERRQ(ierr);
349   /* Traverse A row-wise. */
350   /* Build the ith row in C by summing over nonzero columns in A, */
351   /* the rows of B corresponding to nonzeros of A. */
352   for (i=0; i<am; i++) {
353     anzi = ai[i+1] - ai[i];
354     cnzi = ci[i+1] - ci[i];
355     for (j=0; j<anzi; j++) {
356       brow = aj[j];
357       bnzi = bi[brow+1] - bi[brow];
358       bjj  = bj + bi[brow];
359       baj  = ba + bi[brow];
360       /* perform sparse axpy */
361       valtmp = aa[j];
362       nextb  = 0;
363       for (k=0; nextb<bnzi; k++) {
364         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
365           ca[k] += valtmp*baj[nextb++];
366         }
367       }
368       flops += 2*bnzi;
369     }
370     aj += anzi; aa += anzi;
371     cj += cnzi; ca += cnzi;
372   }
373 #if defined(PETSC_HAVE_DEVICE)
374   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
375 #endif
376   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
377   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
378   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
379   ierr = MatSeqAIJRestoreArrayRead(A,&aa);CHKERRQ(ierr);
380   ierr = MatSeqAIJRestoreArrayRead(B,&ba);CHKERRQ(ierr);
381   PetscFunctionReturn(0);
382 }
383 
384 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat C)
385 {
386   PetscErrorCode     ierr;
387   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
388   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
389   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
390   MatScalar          *ca;
391   PetscReal          afill;
392   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
393   PetscTable         ta;
394   PetscFreeSpaceList free_space=NULL,current_space=NULL;
395 
396   PetscFunctionBegin;
397   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
398   /*-----------------------------------------------------------------------------------------*/
399   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
400   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
401   ci[0] = 0;
402 
403   /* create and initialize a linked list */
404   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
405   MatRowMergeMax_SeqAIJ(b,bm,ta);
406   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
407   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
408 
409   ierr = PetscLLCondensedCreate_fast(Crmax,&lnk);CHKERRQ(ierr);
410 
411   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
412   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
413   current_space = free_space;
414 
415   /* Determine ci and cj */
416   for (i=0; i<am; i++) {
417     anzi = ai[i+1] - ai[i];
418     aj   = a->j + ai[i];
419     for (j=0; j<anzi; j++) {
420       brow = aj[j];
421       bnzj = bi[brow+1] - bi[brow];
422       bj   = b->j + bi[brow];
423       /* add non-zero cols of B into the sorted linked list lnk */
424       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
425     }
426     /* add possible missing diagonal entry */
427     if (C->force_diagonals) {
428       ierr = PetscLLCondensedAddSorted_fast(1,&i,lnk);CHKERRQ(ierr);
429     }
430     cnzi = lnk[1];
431 
432     /* If free space is not available, make more free space */
433     /* Double the amount of total space in the list */
434     if (current_space->local_remaining<cnzi) {
435       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
436       ndouble++;
437     }
438 
439     /* Copy data into free space, then initialize lnk */
440     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
441 
442     current_space->array           += cnzi;
443     current_space->local_used      += cnzi;
444     current_space->local_remaining -= cnzi;
445 
446     ci[i+1] = ci[i] + cnzi;
447   }
448 
449   /* Column indices are in the list of free space */
450   /* Allocate space for cj, initialize cj, and */
451   /* destroy list of free space and other temporary array(s) */
452   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
453   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
454   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
455 
456   /* Allocate space for ca */
457   ierr = PetscCalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
458 
459   /* put together the new symbolic matrix */
460   ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,((PetscObject)A)->type_name,C);CHKERRQ(ierr);
461   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
462 
463   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
464   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
465   c          = (Mat_SeqAIJ*)(C->data);
466   c->free_a  = PETSC_TRUE;
467   c->free_ij = PETSC_TRUE;
468   c->nonew   = 0;
469 
470   /* slower, less memory */
471   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable;
472 
473   /* set MatInfo */
474   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
475   if (afill < 1.0) afill = 1.0;
476   c->maxnz                     = ci[am];
477   c->nz                        = ci[am];
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     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
485     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
486   } else {
487     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
488   }
489 #endif
490   PetscFunctionReturn(0);
491 }
492 
493 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat C)
494 {
495   PetscErrorCode     ierr;
496   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
497   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
498   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
499   MatScalar          *ca;
500   PetscReal          afill;
501   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
502   PetscTable         ta;
503   PetscFreeSpaceList free_space=NULL,current_space=NULL;
504 
505   PetscFunctionBegin;
506   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
507   /*---------------------------------------------------------------------------------------------*/
508   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
509   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
510   ci[0] = 0;
511 
512   /* create and initialize a linked list */
513   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
514   MatRowMergeMax_SeqAIJ(b,bm,ta);
515   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
516   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
517   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
518 
519   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
520   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
521   current_space = free_space;
522 
523   /* Determine ci and cj */
524   for (i=0; i<am; i++) {
525     anzi = ai[i+1] - ai[i];
526     aj   = a->j + ai[i];
527     for (j=0; j<anzi; j++) {
528       brow = aj[j];
529       bnzj = bi[brow+1] - bi[brow];
530       bj   = b->j + bi[brow];
531       /* add non-zero cols of B into the sorted linked list lnk */
532       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
533     }
534     /* add possible missing diagonal entry */
535     if (C->force_diagonals) {
536       ierr = PetscLLCondensedAddSorted_Scalable(1,&i,lnk);CHKERRQ(ierr);
537     }
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       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
545       ndouble++;
546     }
547 
548     /* Copy data into free space, then initialize lnk */
549     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
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   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
562   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
563   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
564 
565   /* Allocate space for ca */
566   /*-----------------------*/
567   ierr = PetscCalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
568 
569   /* put together the new symbolic matrix */
570   ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,((PetscObject)A)->type_name,C);CHKERRQ(ierr);
571   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
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->maxnz                     = ci[am];
587   c->nz                        = ci[am];
588   C->info.mallocs           = ndouble;
589   C->info.fill_ratio_given  = fill;
590   C->info.fill_ratio_needed = afill;
591 
592 #if defined(PETSC_USE_INFO)
593   if (ci[am]) {
594     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
595     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
596   } else {
597     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
598   }
599 #endif
600   PetscFunctionReturn(0);
601 }
602 
603 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat C)
604 {
605   PetscErrorCode     ierr;
606   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
607   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
608   PetscInt           *ci,*cj,*bb;
609   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
610   PetscReal          afill;
611   PetscInt           i,j,col,ndouble = 0;
612   PetscFreeSpaceList free_space=NULL,current_space=NULL;
613   PetscHeap          h;
614 
615   PetscFunctionBegin;
616   /* Get ci and cj - by merging sorted rows using a heap */
617   /*---------------------------------------------------------------------------------------------*/
618   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
619   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
620   ci[0] = 0;
621 
622   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
623   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
624   current_space = free_space;
625 
626   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
627   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
628 
629   /* Determine ci and cj */
630   for (i=0; i<am; i++) {
631     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 */
632     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
633     ci[i+1] = ci[i];
634     /* Populate the min heap */
635     for (j=0; j<anzi; j++) {
636       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
637       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
638         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
639       }
640     }
641     /* Pick off the min element, adding it to free space */
642     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
643     while (j >= 0) {
644       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
645         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
646         ndouble++;
647       }
648       *(current_space->array++) = col;
649       current_space->local_used++;
650       current_space->local_remaining--;
651       ci[i+1]++;
652 
653       /* stash if anything else remains in this row of B */
654       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
655       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
656         PetscInt j2,col2;
657         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
658         if (col2 != col) break;
659         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
660         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
661       }
662       /* Put any stashed elements back into the min heap */
663       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
664       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
665     }
666   }
667   ierr = PetscFree(bb);CHKERRQ(ierr);
668   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
669 
670   /* Column indices are in the list of free space */
671   /* Allocate space for cj, initialize cj, and */
672   /* destroy list of free space and other temporary array(s) */
673   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
674   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
675 
676   /* put together the new symbolic matrix */
677   ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,((PetscObject)A)->type_name,C);CHKERRQ(ierr);
678   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
679 
680   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
681   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
682   c          = (Mat_SeqAIJ*)(C->data);
683   c->free_a  = PETSC_TRUE;
684   c->free_ij = PETSC_TRUE;
685   c->nonew   = 0;
686 
687   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
688 
689   /* set MatInfo */
690   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
691   if (afill < 1.0) afill = 1.0;
692   c->maxnz                     = ci[am];
693   c->nz                        = ci[am];
694   C->info.mallocs           = ndouble;
695   C->info.fill_ratio_given  = fill;
696   C->info.fill_ratio_needed = afill;
697 
698 #if defined(PETSC_USE_INFO)
699   if (ci[am]) {
700     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
701     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
702   } else {
703     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
704   }
705 #endif
706   PetscFunctionReturn(0);
707 }
708 
709 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat C)
710 {
711   PetscErrorCode     ierr;
712   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
713   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
714   PetscInt           *ci,*cj,*bb;
715   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
716   PetscReal          afill;
717   PetscInt           i,j,col,ndouble = 0;
718   PetscFreeSpaceList free_space=NULL,current_space=NULL;
719   PetscHeap          h;
720   PetscBT            bt;
721 
722   PetscFunctionBegin;
723   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
724   /*---------------------------------------------------------------------------------------------*/
725   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
726   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
727   ci[0] = 0;
728 
729   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
730   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
731 
732   current_space = free_space;
733 
734   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
735   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
736   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
737 
738   /* Determine ci and cj */
739   for (i=0; i<am; i++) {
740     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 */
741     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
742     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
743     ci[i+1] = ci[i];
744     /* Populate the min heap */
745     for (j=0; j<anzi; j++) {
746       PetscInt brow = acol[j];
747       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
748         PetscInt bcol = bj[bb[j]];
749         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
750           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
751           bb[j]++;
752           break;
753         }
754       }
755     }
756     /* Pick off the min element, adding it to free space */
757     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
758     while (j >= 0) {
759       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
760         fptr = NULL;                      /* need PetscBTMemzero */
761         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
762         ndouble++;
763       }
764       *(current_space->array++) = col;
765       current_space->local_used++;
766       current_space->local_remaining--;
767       ci[i+1]++;
768 
769       /* stash if anything else remains in this row of B */
770       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
771         PetscInt bcol = bj[bb[j]];
772         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
773           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
774           bb[j]++;
775           break;
776         }
777       }
778       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
779     }
780     if (fptr) {                 /* Clear the bits for this row */
781       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
782     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
783       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
784     }
785   }
786   ierr = PetscFree(bb);CHKERRQ(ierr);
787   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
788   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
789 
790   /* Column indices are in the list of free space */
791   /* Allocate space for cj, initialize cj, and */
792   /* destroy list of free space and other temporary array(s) */
793   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
794   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
795 
796   /* put together the new symbolic matrix */
797   ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,((PetscObject)A)->type_name,C);CHKERRQ(ierr);
798   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
799 
800   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
801   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
802   c          = (Mat_SeqAIJ*)(C->data);
803   c->free_a  = PETSC_TRUE;
804   c->free_ij = PETSC_TRUE;
805   c->nonew   = 0;
806 
807   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
808 
809   /* set MatInfo */
810   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
811   if (afill < 1.0) afill = 1.0;
812   c->maxnz                     = ci[am];
813   c->nz                        = ci[am];
814   C->info.mallocs           = ndouble;
815   C->info.fill_ratio_given  = fill;
816   C->info.fill_ratio_needed = afill;
817 
818 #if defined(PETSC_USE_INFO)
819   if (ci[am]) {
820     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
821     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
822   } else {
823     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
824   }
825 #endif
826   PetscFunctionReturn(0);
827 }
828 
829 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat A,Mat B,PetscReal fill,Mat C)
830 {
831   PetscErrorCode     ierr;
832   Mat_SeqAIJ         *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
833   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j,*inputi,*inputj,*inputcol,*inputcol_L1;
834   PetscInt           *ci,*cj,*outputj,worki_L1[9],worki_L2[9];
835   PetscInt           c_maxmem,a_maxrownnz=0,a_rownnz;
836   const PetscInt     workcol[8]={0,1,2,3,4,5,6,7};
837   const PetscInt     am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
838   const PetscInt     *brow_ptr[8],*brow_end[8];
839   PetscInt           window[8];
840   PetscInt           window_min,old_window_min,ci_nnz,outputi_nnz=0,L1_nrows,L2_nrows;
841   PetscInt           i,k,ndouble=0,L1_rowsleft,rowsleft;
842   PetscReal          afill;
843   PetscInt           *workj_L1,*workj_L2,*workj_L3;
844   PetscInt           L1_nnz,L2_nnz;
845 
846   /* Step 1: Get upper bound on memory required for allocation.
847              Because of the way virtual memory works,
848              only the memory pages that are actually needed will be physically allocated. */
849   PetscFunctionBegin;
850   ierr = PetscMalloc1(am+1,&ci);CHKERRQ(ierr);
851   for (i=0; i<am; i++) {
852     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 */
853     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
854     a_rownnz = 0;
855     for (k=0; k<anzi; ++k) {
856       a_rownnz += bi[acol[k]+1] - bi[acol[k]];
857       if (a_rownnz > bn) {
858         a_rownnz = bn;
859         break;
860       }
861     }
862     a_maxrownnz = PetscMax(a_maxrownnz, a_rownnz);
863   }
864   /* temporary work areas for merging rows */
865   ierr = PetscMalloc1(a_maxrownnz*8,&workj_L1);CHKERRQ(ierr);
866   ierr = PetscMalloc1(a_maxrownnz*8,&workj_L2);CHKERRQ(ierr);
867   ierr = PetscMalloc1(a_maxrownnz,&workj_L3);CHKERRQ(ierr);
868 
869   /* This should be enough for almost all matrices. If not, memory is reallocated later. */
870   c_maxmem = 8*(ai[am]+bi[bm]);
871   /* Step 2: Populate pattern for C */
872   ierr  = PetscMalloc1(c_maxmem,&cj);CHKERRQ(ierr);
873 
874   ci_nnz       = 0;
875   ci[0]        = 0;
876   worki_L1[0]  = 0;
877   worki_L2[0]  = 0;
878   for (i=0; i<am; i++) {
879     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 */
880     const PetscInt *acol = aj + ai[i];      /* column indices of nonzero entries in this row */
881     rowsleft             = anzi;
882     inputcol_L1          = acol;
883     L2_nnz               = 0;
884     L2_nrows             = 1;  /* Number of rows to be merged on Level 3. output of L3 already exists -> initial value 1   */
885     worki_L2[1]          = 0;
886     outputi_nnz          = 0;
887 
888     /* If the number of indices in C so far + the max number of columns in the next row > c_maxmem  -> allocate more memory */
889     while (ci_nnz+a_maxrownnz > c_maxmem) {
890       c_maxmem *= 2;
891       ndouble++;
892       ierr = PetscRealloc(sizeof(PetscInt)*c_maxmem,&cj);CHKERRQ(ierr);
893     }
894 
895     while (rowsleft) {
896       L1_rowsleft = PetscMin(64, rowsleft); /* In the inner loop max 64 rows of B can be merged */
897       L1_nrows    = 0;
898       L1_nnz      = 0;
899       inputcol    = inputcol_L1;
900       inputi      = bi;
901       inputj      = bj;
902 
903       /* The following macro is used to specialize for small rows in A.
904          This helps with compiler unrolling, improving performance substantially.
905           Input:  inputj   inputi  inputcol  bn
906           Output: outputj  outputi_nnz                       */
907        #define MatMatMultSymbolic_RowMergeMacro(ANNZ)                        \
908          window_min  = bn;                                                   \
909          outputi_nnz = 0;                                                    \
910          for (k=0; k<ANNZ; ++k) {                                            \
911            brow_ptr[k] = inputj + inputi[inputcol[k]];                       \
912            brow_end[k] = inputj + inputi[inputcol[k]+1];                     \
913            window[k]   = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn;   \
914            window_min  = PetscMin(window[k], window_min);                    \
915          }                                                                   \
916          while (window_min < bn) {                                           \
917            outputj[outputi_nnz++] = window_min;                              \
918            /* advance front and compute new minimum */                       \
919            old_window_min = window_min;                                      \
920            window_min = bn;                                                  \
921            for (k=0; k<ANNZ; ++k) {                                          \
922              if (window[k] == old_window_min) {                              \
923                brow_ptr[k]++;                                                \
924                window[k] = (brow_ptr[k] != brow_end[k]) ? *brow_ptr[k] : bn; \
925              }                                                               \
926              window_min = PetscMin(window[k], window_min);                   \
927            }                                                                 \
928          }
929 
930       /************** L E V E L  1 ***************/
931       /* Merge up to 8 rows of B to L1 work array*/
932       while (L1_rowsleft) {
933         outputi_nnz = 0;
934         if (anzi > 8)  outputj = workj_L1 + L1_nnz;     /* Level 1 rowmerge*/
935         else           outputj = cj + ci_nnz;           /* Merge directly to C */
936 
937         switch (L1_rowsleft) {
938         case 1:  brow_ptr[0] = inputj + inputi[inputcol[0]];
939                  brow_end[0] = inputj + inputi[inputcol[0]+1];
940                  for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
941                  inputcol    += L1_rowsleft;
942                  rowsleft    -= L1_rowsleft;
943                  L1_rowsleft  = 0;
944                  break;
945         case 2:  MatMatMultSymbolic_RowMergeMacro(2);
946                  inputcol    += L1_rowsleft;
947                  rowsleft    -= L1_rowsleft;
948                  L1_rowsleft  = 0;
949                  break;
950         case 3: MatMatMultSymbolic_RowMergeMacro(3);
951                  inputcol    += L1_rowsleft;
952                  rowsleft    -= L1_rowsleft;
953                  L1_rowsleft  = 0;
954                  break;
955         case 4:  MatMatMultSymbolic_RowMergeMacro(4);
956                  inputcol    += L1_rowsleft;
957                  rowsleft    -= L1_rowsleft;
958                  L1_rowsleft  = 0;
959                  break;
960         case 5:  MatMatMultSymbolic_RowMergeMacro(5);
961                  inputcol    += L1_rowsleft;
962                  rowsleft    -= L1_rowsleft;
963                  L1_rowsleft  = 0;
964                  break;
965         case 6:  MatMatMultSymbolic_RowMergeMacro(6);
966                  inputcol    += L1_rowsleft;
967                  rowsleft    -= L1_rowsleft;
968                  L1_rowsleft  = 0;
969                  break;
970         case 7:  MatMatMultSymbolic_RowMergeMacro(7);
971                  inputcol    += L1_rowsleft;
972                  rowsleft    -= L1_rowsleft;
973                  L1_rowsleft  = 0;
974                  break;
975         default: MatMatMultSymbolic_RowMergeMacro(8);
976                  inputcol    += 8;
977                  rowsleft    -= 8;
978                  L1_rowsleft -= 8;
979                  break;
980         }
981         inputcol_L1           = inputcol;
982         L1_nnz               += outputi_nnz;
983         worki_L1[++L1_nrows]  = L1_nnz;
984       }
985 
986       /********************** L E V E L  2 ************************/
987       /* Merge from L1 work array to either C or to L2 work array */
988       if (anzi > 8) {
989         inputi      = worki_L1;
990         inputj      = workj_L1;
991         inputcol    = workcol;
992         outputi_nnz = 0;
993 
994         if (anzi <= 64) outputj = cj + ci_nnz;        /* Merge from L1 work array to C */
995         else            outputj = workj_L2 + L2_nnz;  /* Merge from L1 work array to L2 work array */
996 
997         switch (L1_nrows) {
998         case 1:  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:  MatMatMultSymbolic_RowMergeMacro(2); break;
1003         case 3:  MatMatMultSymbolic_RowMergeMacro(3); break;
1004         case 4:  MatMatMultSymbolic_RowMergeMacro(4); break;
1005         case 5:  MatMatMultSymbolic_RowMergeMacro(5); break;
1006         case 6:  MatMatMultSymbolic_RowMergeMacro(6); break;
1007         case 7:  MatMatMultSymbolic_RowMergeMacro(7); break;
1008         case 8:  MatMatMultSymbolic_RowMergeMacro(8); break;
1009         default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L1 work array!");
1010         }
1011         L2_nnz               += outputi_nnz;
1012         worki_L2[++L2_nrows]  = L2_nnz;
1013 
1014         /************************ L E V E L  3 **********************/
1015         /* Merge from L2 work array to either C or to L2 work array */
1016         if (anzi > 64 && (L2_nrows == 8 || rowsleft == 0)) {
1017           inputi      = worki_L2;
1018           inputj      = workj_L2;
1019           inputcol    = workcol;
1020           outputi_nnz = 0;
1021           if (rowsleft) outputj = workj_L3;
1022           else          outputj = cj + ci_nnz;
1023           switch (L2_nrows) {
1024           case 1:  brow_ptr[0] = inputj + inputi[inputcol[0]];
1025                    brow_end[0] = inputj + inputi[inputcol[0]+1];
1026                    for (; brow_ptr[0] != brow_end[0]; ++brow_ptr[0]) outputj[outputi_nnz++] = *brow_ptr[0]; /* copy row in b over */
1027                    break;
1028           case 2:  MatMatMultSymbolic_RowMergeMacro(2); break;
1029           case 3:  MatMatMultSymbolic_RowMergeMacro(3); break;
1030           case 4:  MatMatMultSymbolic_RowMergeMacro(4); break;
1031           case 5:  MatMatMultSymbolic_RowMergeMacro(5); break;
1032           case 6:  MatMatMultSymbolic_RowMergeMacro(6); break;
1033           case 7:  MatMatMultSymbolic_RowMergeMacro(7); break;
1034           case 8:  MatMatMultSymbolic_RowMergeMacro(8); break;
1035           default: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatMatMult logic error: Not merging 1-8 rows from L2 work array!");
1036           }
1037           L2_nrows    = 1;
1038           L2_nnz      = outputi_nnz;
1039           worki_L2[1] = outputi_nnz;
1040           /* Copy to workj_L2 */
1041           if (rowsleft) {
1042             for (k=0; k<outputi_nnz; ++k)  workj_L2[k] = outputj[k];
1043           }
1044         }
1045       }
1046     }  /* while (rowsleft) */
1047 #undef MatMatMultSymbolic_RowMergeMacro
1048 
1049     /* terminate current row */
1050     ci_nnz += outputi_nnz;
1051     ci[i+1] = ci_nnz;
1052   }
1053 
1054   /* Step 3: Create the new symbolic matrix */
1055   ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,((PetscObject)A)->type_name,C);CHKERRQ(ierr);
1056   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
1057 
1058   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1059   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1060   c          = (Mat_SeqAIJ*)(C->data);
1061   c->free_a  = PETSC_TRUE;
1062   c->free_ij = PETSC_TRUE;
1063   c->nonew   = 0;
1064 
1065   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
1066 
1067   /* set MatInfo */
1068   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
1069   if (afill < 1.0) afill = 1.0;
1070   c->maxnz                  = ci[am];
1071   c->nz                     = ci[am];
1072   C->info.mallocs           = ndouble;
1073   C->info.fill_ratio_given  = fill;
1074   C->info.fill_ratio_needed = afill;
1075 
1076 #if defined(PETSC_USE_INFO)
1077   if (ci[am]) {
1078     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
1079     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1080   } else {
1081     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1082   }
1083 #endif
1084 
1085   /* Step 4: Free temporary work areas */
1086   ierr = PetscFree(workj_L1);CHKERRQ(ierr);
1087   ierr = PetscFree(workj_L2);CHKERRQ(ierr);
1088   ierr = PetscFree(workj_L3);CHKERRQ(ierr);
1089   PetscFunctionReturn(0);
1090 }
1091 
1092 /* concatenate unique entries and then sort */
1093 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat A,Mat B,PetscReal fill,Mat C)
1094 {
1095   PetscErrorCode ierr;
1096   Mat_SeqAIJ     *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
1097   const PetscInt *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
1098   PetscInt       *ci,*cj,bcol;
1099   PetscInt       am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
1100   PetscReal      afill;
1101   PetscInt       i,j,ndouble = 0;
1102   PetscSegBuffer seg,segrow;
1103   char           *seen;
1104 
1105   PetscFunctionBegin;
1106   ierr  = PetscMalloc1(am+1,&ci);CHKERRQ(ierr);
1107   ci[0] = 0;
1108 
1109   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
1110   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
1111   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
1112   ierr = PetscCalloc1(bn,&seen);CHKERRQ(ierr);
1113 
1114   /* Determine ci and cj */
1115   for (i=0; i<am; i++) {
1116     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 */
1117     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
1118     PetscInt packlen = 0,*PETSC_RESTRICT crow;
1119 
1120     /* Pack segrow */
1121     for (j=0; j<anzi; j++) {
1122       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
1123       for (k=bjstart; k<bjend; k++) {
1124         bcol = bj[k];
1125         if (!seen[bcol]) { /* new entry */
1126           PetscInt *PETSC_RESTRICT slot;
1127           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
1128           *slot = bcol;
1129           seen[bcol] = 1;
1130           packlen++;
1131         }
1132       }
1133     }
1134 
1135     /* Check i-th diagonal entry */
1136     if (C->force_diagonals && !seen[i]) {
1137       PetscInt *PETSC_RESTRICT slot;
1138       ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
1139       *slot   = i;
1140       seen[i] = 1;
1141       packlen++;
1142     }
1143 
1144     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
1145     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
1146     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
1147     ci[i+1] = ci[i] + packlen;
1148     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
1149   }
1150   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
1151   ierr = PetscFree(seen);CHKERRQ(ierr);
1152 
1153   /* Column indices are in the segmented buffer */
1154   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
1155   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
1156 
1157   /* put together the new symbolic matrix */
1158   ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,((PetscObject)A)->type_name,C);CHKERRQ(ierr);
1159   ierr = MatSetBlockSizesFromMats(C,A,B);CHKERRQ(ierr);
1160 
1161   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
1162   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
1163   c          = (Mat_SeqAIJ*)(C->data);
1164   c->free_a  = PETSC_TRUE;
1165   c->free_ij = PETSC_TRUE;
1166   c->nonew   = 0;
1167 
1168   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted;
1169 
1170   /* set MatInfo */
1171   afill = (PetscReal)ci[am]/PetscMax(ai[am]+bi[bm],1) + 1.e-5;
1172   if (afill < 1.0) afill = 1.0;
1173   c->maxnz                  = ci[am];
1174   c->nz                     = ci[am];
1175   C->info.mallocs           = ndouble;
1176   C->info.fill_ratio_given  = fill;
1177   C->info.fill_ratio_needed = afill;
1178 
1179 #if defined(PETSC_USE_INFO)
1180   if (ci[am]) {
1181     ierr = PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
1182     ierr = PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
1183   } else {
1184     ierr = PetscInfo(C,"Empty matrix product\n");CHKERRQ(ierr);
1185   }
1186 #endif
1187   PetscFunctionReturn(0);
1188 }
1189 
1190 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(void *data)
1191 {
1192   PetscErrorCode      ierr;
1193   Mat_MatMatTransMult *abt=(Mat_MatMatTransMult *)data;
1194 
1195   PetscFunctionBegin;
1196   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
1197   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
1198   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
1199   ierr = PetscFree(abt);CHKERRQ(ierr);
1200   PetscFunctionReturn(0);
1201 }
1202 
1203 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat C)
1204 {
1205   PetscErrorCode      ierr;
1206   Mat                 Bt;
1207   PetscInt            *bti,*btj;
1208   Mat_MatMatTransMult *abt;
1209   Mat_Product         *product = C->product;
1210   char                *alg;
1211 
1212   PetscFunctionBegin;
1213   if (!product) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing product struct");
1214   if (product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1215 
1216   /* create symbolic Bt */
1217   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
1218   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
1219   ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
1220   ierr = MatSetType(Bt,((PetscObject)A)->type_name);CHKERRQ(ierr);
1221 
1222   /* get symbolic C=A*Bt */
1223   ierr = PetscStrallocpy(product->alg,&alg);CHKERRQ(ierr);
1224   ierr = MatProductSetAlgorithm(C,"sorted");CHKERRQ(ierr); /* set algorithm for C = A*Bt */
1225   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
1226   ierr = MatProductSetAlgorithm(C,alg);CHKERRQ(ierr); /* resume original algorithm for ABt product */
1227   ierr = PetscFree(alg);CHKERRQ(ierr);
1228 
1229   /* create a supporting struct for reuse intermediate dense matrices with matcoloring */
1230   ierr = PetscNew(&abt);CHKERRQ(ierr);
1231 
1232   product->data    = abt;
1233   product->destroy = MatDestroy_SeqAIJ_MatMatMultTrans;
1234 
1235   C->ops->mattransposemultnumeric = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ;
1236 
1237   abt->usecoloring = PETSC_FALSE;
1238   ierr = PetscStrcmp(product->alg,"color",&abt->usecoloring);CHKERRQ(ierr);
1239   if (abt->usecoloring) {
1240     /* Create MatTransposeColoring from symbolic C=A*B^T */
1241     MatTransposeColoring matcoloring;
1242     MatColoring          coloring;
1243     ISColoring           iscoloring;
1244     Mat                  Bt_dense,C_dense;
1245 
1246     /* inode causes memory problem */
1247     ierr = MatSetOption(C,MAT_USE_INODES,PETSC_FALSE);CHKERRQ(ierr);
1248 
1249     ierr = MatColoringCreate(C,&coloring);CHKERRQ(ierr);
1250     ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
1251     ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
1252     ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
1253     ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
1254     ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
1255     ierr = MatTransposeColoringCreate(C,iscoloring,&matcoloring);CHKERRQ(ierr);
1256 
1257     abt->matcoloring = matcoloring;
1258 
1259     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
1260 
1261     /* Create Bt_dense and C_dense = A*Bt_dense */
1262     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
1263     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
1264     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
1265     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
1266 
1267     Bt_dense->assembled = PETSC_TRUE;
1268     abt->Bt_den         = Bt_dense;
1269 
1270     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
1271     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
1272     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
1273     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
1274 
1275     Bt_dense->assembled = PETSC_TRUE;
1276     abt->ABt_den  = C_dense;
1277 
1278 #if defined(PETSC_USE_INFO)
1279     {
1280       Mat_SeqAIJ *c = (Mat_SeqAIJ*)C->data;
1281       ierr = PetscInfo7(C,"Use coloring of C=A*B^T; B^T: %D %D, Bt_dense: %D,%D; Cnz %D / (cm*ncolors %D) = %g\n",B->cmap->n,B->rmap->n,Bt_dense->rmap->n,Bt_dense->cmap->n,c->nz,A->rmap->n*matcoloring->ncolors,(PetscReal)(c->nz)/(A->rmap->n*matcoloring->ncolors));CHKERRQ(ierr);
1282     }
1283 #endif
1284   }
1285   /* clean up */
1286   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
1287   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
1288   PetscFunctionReturn(0);
1289 }
1290 
1291 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1292 {
1293   PetscErrorCode      ierr;
1294   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1295   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
1296   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
1297   PetscLogDouble      flops=0.0;
1298   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
1299   Mat_MatMatTransMult *abt;
1300   Mat_Product         *product = C->product;
1301 
1302   PetscFunctionBegin;
1303   if (!product) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing product struct");
1304   abt = (Mat_MatMatTransMult *)product->data;
1305   if (!abt) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing product struct");
1306   /* clear old values in C */
1307   if (!c->a) {
1308     ierr      = PetscCalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
1309     c->a      = ca;
1310     c->free_a = PETSC_TRUE;
1311   } else {
1312     ca =  c->a;
1313     ierr = PetscArrayzero(ca,ci[cm]+1);CHKERRQ(ierr);
1314   }
1315 
1316   if (abt->usecoloring) {
1317     MatTransposeColoring matcoloring = abt->matcoloring;
1318     Mat                  Bt_dense,C_dense = abt->ABt_den;
1319 
1320     /* Get Bt_dense by Apply MatTransposeColoring to B */
1321     Bt_dense = abt->Bt_den;
1322     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
1323 
1324     /* C_dense = A*Bt_dense */
1325     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
1326 
1327     /* Recover C from C_dense */
1328     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
1329     PetscFunctionReturn(0);
1330   }
1331 
1332   for (i=0; i<cm; i++) {
1333     anzi = ai[i+1] - ai[i];
1334     acol = aj + ai[i];
1335     aval = aa + ai[i];
1336     cnzi = ci[i+1] - ci[i];
1337     ccol = cj + ci[i];
1338     cval = ca + ci[i];
1339     for (j=0; j<cnzi; j++) {
1340       brow = ccol[j];
1341       bnzj = bi[brow+1] - bi[brow];
1342       bcol = bj + bi[brow];
1343       bval = ba + bi[brow];
1344 
1345       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
1346       nexta = 0; nextb = 0;
1347       while (nexta<anzi && nextb<bnzj) {
1348         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
1349         if (nexta == anzi) break;
1350         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
1351         if (nextb == bnzj) break;
1352         if (acol[nexta] == bcol[nextb]) {
1353           cval[j] += aval[nexta]*bval[nextb];
1354           nexta++; nextb++;
1355           flops += 2;
1356         }
1357       }
1358     }
1359   }
1360   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1361   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1362   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1363   PetscFunctionReturn(0);
1364 }
1365 
1366 PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(void *data)
1367 {
1368   PetscErrorCode      ierr;
1369   Mat_MatTransMatMult *atb = (Mat_MatTransMatMult*)data;
1370 
1371   PetscFunctionBegin;
1372   ierr = MatDestroy(&atb->At);CHKERRQ(ierr);
1373   if (atb->destroy) {
1374     ierr = (*atb->destroy)(atb->data);CHKERRQ(ierr);
1375   }
1376   ierr = PetscFree(atb);CHKERRQ(ierr);
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat C)
1381 {
1382   PetscErrorCode ierr;
1383   Mat            At = NULL;
1384   PetscInt       *ati,*atj;
1385   Mat_Product    *product = C->product;
1386   PetscBool      flg,def,square;
1387 
1388   PetscFunctionBegin;
1389   MatCheckProduct(C,4);
1390   square = (PetscBool)(A == B && A->symmetric && A->symmetric_set);
1391   /* outerproduct */
1392   ierr = PetscStrcmp(product->alg,"outerproduct",&flg);CHKERRQ(ierr);
1393   if (flg) {
1394     /* create symbolic At */
1395     if (!square) {
1396       ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1397       ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1398       ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
1399       ierr = MatSetType(At,((PetscObject)A)->type_name);CHKERRQ(ierr);
1400     }
1401     /* get symbolic C=At*B */
1402     ierr = MatProductSetAlgorithm(C,"sorted");CHKERRQ(ierr);
1403     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At,B,fill,C);CHKERRQ(ierr);
1404 
1405     /* clean up */
1406     if (!square) {
1407       ierr = MatDestroy(&At);CHKERRQ(ierr);
1408       ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1409     }
1410 
1411     C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ; /* outerproduct */
1412     ierr = MatProductSetAlgorithm(C,"outerproduct");CHKERRQ(ierr);
1413     PetscFunctionReturn(0);
1414   }
1415 
1416   /* matmatmult */
1417   ierr = PetscStrcmp(product->alg,"default",&def);CHKERRQ(ierr);
1418   ierr = PetscStrcmp(product->alg,"at*b",&flg);CHKERRQ(ierr);
1419   if (flg || def) {
1420     Mat_MatTransMatMult *atb;
1421 
1422     if (product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1423     ierr = PetscNew(&atb);CHKERRQ(ierr);
1424     if (!square) {
1425       ierr = MatTranspose_SeqAIJ(A,MAT_INITIAL_MATRIX,&At);CHKERRQ(ierr);
1426     }
1427     ierr = MatProductSetAlgorithm(C,"sorted");CHKERRQ(ierr);
1428     ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(square ? A : At,B,fill,C);CHKERRQ(ierr);
1429     ierr = MatProductSetAlgorithm(C,"at*b");CHKERRQ(ierr);
1430     product->data    = atb;
1431     product->destroy = MatDestroy_SeqAIJ_MatTransMatMult;
1432     atb->At          = At;
1433     atb->updateAt    = PETSC_FALSE; /* because At is computed here */
1434 
1435     C->ops->mattransposemultnumeric = NULL; /* see MatProductNumeric_AtB_SeqAIJ_SeqAIJ */
1436     PetscFunctionReturn(0);
1437   }
1438 
1439   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
1440 }
1441 
1442 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1443 {
1444   PetscErrorCode ierr;
1445   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1446   PetscInt       am=A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1447   PetscInt       cm=C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1448   PetscLogDouble flops=0.0;
1449   MatScalar      *aa=a->a,*ba,*ca,*caj;
1450 
1451   PetscFunctionBegin;
1452   if (!c->a) {
1453     ierr = PetscCalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
1454 
1455     c->a      = ca;
1456     c->free_a = PETSC_TRUE;
1457   } else {
1458     ca   = c->a;
1459     ierr = PetscArrayzero(ca,ci[cm]);CHKERRQ(ierr);
1460   }
1461 
1462   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1463   for (i=0; i<am; i++) {
1464     bj   = b->j + bi[i];
1465     ba   = b->a + bi[i];
1466     bnzi = bi[i+1] - bi[i];
1467     anzi = ai[i+1] - ai[i];
1468     for (j=0; j<anzi; j++) {
1469       nextb = 0;
1470       crow  = *aj++;
1471       cjj   = cj + ci[crow];
1472       caj   = ca + ci[crow];
1473       /* perform sparse axpy operation.  Note cjj includes bj. */
1474       for (k=0; nextb<bnzi; k++) {
1475         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1476           caj[k] += (*aa)*(*(ba+nextb));
1477           nextb++;
1478         }
1479       }
1480       flops += 2*bnzi;
1481       aa++;
1482     }
1483   }
1484 
1485   /* Assemble the final matrix and clean up */
1486   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1487   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1488   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1489   PetscFunctionReturn(0);
1490 }
1491 
1492 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat C)
1493 {
1494   PetscErrorCode ierr;
1495 
1496   PetscFunctionBegin;
1497   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1498   C->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1499   PetscFunctionReturn(0);
1500 }
1501 
1502 PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C,const PetscBool add)
1503 {
1504   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1505   Mat_SeqDense      *bd=(Mat_SeqDense*)B->data;
1506   Mat_SeqDense      *cd=(Mat_SeqDense*)C->data;
1507   PetscErrorCode    ierr;
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=bd->lda,am=A->rmap->n;
1512   PetscInt          clda=cd->lda;
1513   PetscInt          am4=4*clda,bm4=4*bm,col,i,j,n;
1514 
1515   PetscFunctionBegin;
1516   if (!cm || !cn) PetscFunctionReturn(0);
1517   ierr = MatSeqAIJGetArrayRead(A,&av);CHKERRQ(ierr);
1518   if (add) {
1519     ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1520   } else {
1521     ierr = MatDenseGetArrayWrite(C,&c);CHKERRQ(ierr);
1522   }
1523   ierr = MatDenseGetArrayRead(B,&b);CHKERRQ(ierr);
1524   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1525   c1 = c; c2 = c1 + clda; c3 = c2 + clda; c4 = c3 + clda;
1526   for (col=0; col<(cn/4)*4; col += 4) {  /* over columns of C */
1527     for (i=0; i<am; i++) {        /* over rows of A in those columns */
1528       r1 = r2 = r3 = r4 = 0.0;
1529       n  = a->i[i+1] - a->i[i];
1530       aj = a->j + a->i[i];
1531       aa = av + a->i[i];
1532       for (j=0; j<n; j++) {
1533         const PetscScalar aatmp = aa[j];
1534         const PetscInt    ajtmp = aj[j];
1535         r1 += aatmp*b1[ajtmp];
1536         r2 += aatmp*b2[ajtmp];
1537         r3 += aatmp*b3[ajtmp];
1538         r4 += aatmp*b4[ajtmp];
1539       }
1540       if (add) {
1541         c1[i] += r1;
1542         c2[i] += r2;
1543         c3[i] += r3;
1544         c4[i] += r4;
1545       } else {
1546         c1[i] = r1;
1547         c2[i] = r2;
1548         c3[i] = r3;
1549         c4[i] = r4;
1550       }
1551     }
1552     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1553     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1554   }
1555   /* process remaining columns */
1556   if (col != cn) {
1557     PetscInt rc = cn-col;
1558 
1559     if (rc == 1) {
1560       for (i=0; i<am; i++) {
1561         r1 = 0.0;
1562         n  = a->i[i+1] - a->i[i];
1563         aj = a->j + a->i[i];
1564         aa = av + a->i[i];
1565         for (j=0; j<n; j++) r1 += aa[j]*b1[aj[j]];
1566         if (add) c1[i] += r1;
1567         else c1[i] = r1;
1568       }
1569     } else if (rc == 2) {
1570       for (i=0; i<am; i++) {
1571         r1 = r2 = 0.0;
1572         n  = a->i[i+1] - a->i[i];
1573         aj = a->j + a->i[i];
1574         aa = av + a->i[i];
1575         for (j=0; j<n; j++) {
1576           const PetscScalar aatmp = aa[j];
1577           const PetscInt    ajtmp = aj[j];
1578           r1 += aatmp*b1[ajtmp];
1579           r2 += aatmp*b2[ajtmp];
1580         }
1581         if (add) {
1582           c1[i] += r1;
1583           c2[i] += r2;
1584         } else {
1585           c1[i] = r1;
1586           c2[i] = r2;
1587         }
1588       }
1589     } else {
1590       for (i=0; i<am; i++) {
1591         r1 = r2 = r3 = 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           r3 += aatmp*b3[ajtmp];
1601         }
1602         if (add) {
1603           c1[i] += r1;
1604           c2[i] += r2;
1605           c3[i] += r3;
1606         } else {
1607           c1[i] = r1;
1608           c2[i] = r2;
1609           c3[i] = r3;
1610         }
1611       }
1612     }
1613   }
1614   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1615   if (add) {
1616     ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1617   } else {
1618     ierr = MatDenseRestoreArrayWrite(C,&c);CHKERRQ(ierr);
1619   }
1620   ierr = MatDenseRestoreArrayRead(B,&b);CHKERRQ(ierr);
1621   ierr = MatSeqAIJRestoreArrayRead(A,&av);CHKERRQ(ierr);
1622   PetscFunctionReturn(0);
1623 }
1624 
1625 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1626 {
1627   PetscErrorCode ierr;
1628 
1629   PetscFunctionBegin;
1630   if (B->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in A %D not equal rows in B %D\n",A->cmap->n,B->rmap->n);
1631   if (A->rmap->n != C->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number rows in C %D not equal rows in A %D\n",C->rmap->n,A->rmap->n);
1632   if (B->cmap->n != C->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Number columns in B %D not equal columns in C %D\n",B->cmap->n,C->cmap->n);
1633 
1634   ierr = MatMatMultNumericAdd_SeqAIJ_SeqDense(A,B,C,PETSC_FALSE);CHKERRQ(ierr);
1635   PetscFunctionReturn(0);
1636 }
1637 
1638 /* ------------------------------------------------------- */
1639 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AB(Mat C)
1640 {
1641   PetscFunctionBegin;
1642   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqDense;
1643   C->ops->productsymbolic = MatProductSymbolic_AB;
1644   PetscFunctionReturn(0);
1645 }
1646 
1647 PETSC_INTERN PetscErrorCode MatTMatTMultSymbolic_SeqAIJ_SeqDense(Mat,Mat,PetscReal,Mat);
1648 
1649 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(Mat C)
1650 {
1651   PetscFunctionBegin;
1652   C->ops->transposematmultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1653   C->ops->productsymbolic          = MatProductSymbolic_AtB;
1654   PetscFunctionReturn(0);
1655 }
1656 
1657 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(Mat C)
1658 {
1659   PetscFunctionBegin;
1660   C->ops->mattransposemultsymbolic = MatTMatTMultSymbolic_SeqAIJ_SeqDense;
1661   C->ops->productsymbolic          = MatProductSymbolic_ABt;
1662   PetscFunctionReturn(0);
1663 }
1664 
1665 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqDense(Mat C)
1666 {
1667   PetscErrorCode ierr;
1668   Mat_Product    *product = C->product;
1669 
1670   PetscFunctionBegin;
1671   switch (product->type) {
1672   case MATPRODUCT_AB:
1673     ierr = MatProductSetFromOptions_SeqAIJ_SeqDense_AB(C);CHKERRQ(ierr);
1674     break;
1675   case MATPRODUCT_AtB:
1676     ierr = MatProductSetFromOptions_SeqAIJ_SeqDense_AtB(C);CHKERRQ(ierr);
1677     break;
1678   case MATPRODUCT_ABt:
1679     ierr = MatProductSetFromOptions_SeqAIJ_SeqDense_ABt(C);CHKERRQ(ierr);
1680     break;
1681   default:
1682     break;
1683   }
1684   PetscFunctionReturn(0);
1685 }
1686 /* ------------------------------------------------------- */
1687 static PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(Mat C)
1688 {
1689   PetscErrorCode ierr;
1690   Mat_Product    *product = C->product;
1691   Mat            A = product->A;
1692   PetscBool      baij;
1693 
1694   PetscFunctionBegin;
1695   ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQBAIJ,&baij);CHKERRQ(ierr);
1696   if (!baij) { /* A is seqsbaij */
1697     PetscBool sbaij;
1698     ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQSBAIJ,&sbaij);CHKERRQ(ierr);
1699     if (!sbaij) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"Mat must be either seqbaij or seqsbaij format");
1700 
1701     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqSBAIJ_SeqDense;
1702   } else { /* A is seqbaij */
1703     C->ops->matmultsymbolic = MatMatMultSymbolic_SeqBAIJ_SeqDense;
1704   }
1705 
1706   C->ops->productsymbolic = MatProductSymbolic_AB;
1707   PetscFunctionReturn(0);
1708 }
1709 
1710 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqXBAIJ_SeqDense(Mat C)
1711 {
1712   PetscErrorCode ierr;
1713   Mat_Product    *product = C->product;
1714 
1715   PetscFunctionBegin;
1716   MatCheckProduct(C,1);
1717   if (!product->A) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing A");
1718   if (product->type == MATPRODUCT_AB || (product->type == MATPRODUCT_AtB && product->A->symmetric)) {
1719     ierr = MatProductSetFromOptions_SeqXBAIJ_SeqDense_AB(C);CHKERRQ(ierr);
1720   }
1721   PetscFunctionReturn(0);
1722 }
1723 
1724 /* ------------------------------------------------------- */
1725 static PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ_AB(Mat C)
1726 {
1727   PetscFunctionBegin;
1728   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqDense_SeqAIJ;
1729   C->ops->productsymbolic = MatProductSymbolic_AB;
1730   PetscFunctionReturn(0);
1731 }
1732 
1733 PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqDense_SeqAIJ(Mat C)
1734 {
1735   PetscErrorCode ierr;
1736   Mat_Product    *product = C->product;
1737 
1738   PetscFunctionBegin;
1739   if (product->type == MATPRODUCT_AB) {
1740     ierr = MatProductSetFromOptions_SeqDense_SeqAIJ_AB(C);CHKERRQ(ierr);
1741   }
1742   PetscFunctionReturn(0);
1743 }
1744 /* ------------------------------------------------------- */
1745 
1746 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1747 {
1748   PetscErrorCode ierr;
1749   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1750   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1751   PetscInt       *bi      = b->i,*bj=b->j;
1752   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1753   MatScalar      *btval,*btval_den,*ba=b->a;
1754   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1755 
1756   PetscFunctionBegin;
1757   btval_den=btdense->v;
1758   ierr     = PetscArrayzero(btval_den,m*n);CHKERRQ(ierr);
1759   for (k=0; k<ncolors; k++) {
1760     ncolumns = coloring->ncolumns[k];
1761     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1762       col   = *(columns + colorforcol[k] + l);
1763       btcol = bj + bi[col];
1764       btval = ba + bi[col];
1765       anz   = bi[col+1] - bi[col];
1766       for (j=0; j<anz; j++) {
1767         brow            = btcol[j];
1768         btval_den[brow] = btval[j];
1769       }
1770     }
1771     btval_den += m;
1772   }
1773   PetscFunctionReturn(0);
1774 }
1775 
1776 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1777 {
1778   PetscErrorCode    ierr;
1779   Mat_SeqAIJ        *csp = (Mat_SeqAIJ*)Csp->data;
1780   const PetscScalar *ca_den,*ca_den_ptr;
1781   PetscScalar       *ca=csp->a;
1782   PetscInt          k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1783   PetscInt          brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1784   PetscInt          nrows,*row,*idx;
1785   PetscInt          *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1786 
1787   PetscFunctionBegin;
1788   ierr   = MatDenseGetArrayRead(Cden,&ca_den);CHKERRQ(ierr);
1789 
1790   if (brows > 0) {
1791     PetscInt *lstart,row_end,row_start;
1792     lstart = matcoloring->lstart;
1793     ierr = PetscArrayzero(lstart,ncolors);CHKERRQ(ierr);
1794 
1795     row_end = brows;
1796     if (row_end > m) row_end = m;
1797     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1798       ca_den_ptr = ca_den;
1799       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1800         nrows = matcoloring->nrows[k];
1801         row   = rows  + colorforrow[k];
1802         idx   = den2sp + colorforrow[k];
1803         for (l=lstart[k]; l<nrows; l++) {
1804           if (row[l] >= row_end) {
1805             lstart[k] = l;
1806             break;
1807           } else {
1808             ca[idx[l]] = ca_den_ptr[row[l]];
1809           }
1810         }
1811         ca_den_ptr += m;
1812       }
1813       row_end += brows;
1814       if (row_end > m) row_end = m;
1815     }
1816   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1817     ca_den_ptr = ca_den;
1818     for (k=0; k<ncolors; k++) {
1819       nrows = matcoloring->nrows[k];
1820       row   = rows  + colorforrow[k];
1821       idx   = den2sp + colorforrow[k];
1822       for (l=0; l<nrows; l++) {
1823         ca[idx[l]] = ca_den_ptr[row[l]];
1824       }
1825       ca_den_ptr += m;
1826     }
1827   }
1828 
1829   ierr = MatDenseRestoreArrayRead(Cden,&ca_den);CHKERRQ(ierr);
1830 #if defined(PETSC_USE_INFO)
1831   if (matcoloring->brows > 0) {
1832     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1833   } else {
1834     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1835   }
1836 #endif
1837   PetscFunctionReturn(0);
1838 }
1839 
1840 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1841 {
1842   PetscErrorCode ierr;
1843   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1844   const PetscInt *is,*ci,*cj,*row_idx;
1845   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1846   IS             *isa;
1847   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1848   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1849   PetscInt       *colorforcol,*columns,*columns_i,brows;
1850   PetscBool      flg;
1851 
1852   PetscFunctionBegin;
1853   ierr = ISColoringGetIS(iscoloring,PETSC_USE_POINTER,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1854 
1855   /* bs >1 is not being tested yet! */
1856   Nbs       = mat->cmap->N/bs;
1857   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1858   c->N      = Nbs;
1859   c->m      = c->M;
1860   c->rstart = 0;
1861   c->brows  = 100;
1862 
1863   c->ncolors = nis;
1864   ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr);
1865   ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr);
1866   ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr);
1867 
1868   brows = c->brows;
1869   ierr = PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1870   if (flg) c->brows = brows;
1871   if (brows > 0) {
1872     ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr);
1873   }
1874 
1875   colorforrow[0] = 0;
1876   rows_i         = rows;
1877   den2sp_i       = den2sp;
1878 
1879   ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr);
1880   ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr);
1881 
1882   colorforcol[0] = 0;
1883   columns_i      = columns;
1884 
1885   /* get column-wise storage of mat */
1886   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1887 
1888   cm   = c->m;
1889   ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr);
1890   ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr);
1891   for (i=0; i<nis; i++) { /* loop over color */
1892     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1893     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1894 
1895     c->ncolumns[i] = n;
1896     if (n) {
1897       ierr = PetscArraycpy(columns_i,is,n);CHKERRQ(ierr);
1898     }
1899     colorforcol[i+1] = colorforcol[i] + n;
1900     columns_i       += n;
1901 
1902     /* fast, crude version requires O(N*N) work */
1903     ierr = PetscArrayzero(rowhit,cm);CHKERRQ(ierr);
1904 
1905     for (j=0; j<n; j++) { /* loop over columns*/
1906       col     = is[j];
1907       row_idx = cj + ci[col];
1908       m       = ci[col+1] - ci[col];
1909       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1910         idxhit[*row_idx]   = spidx[ci[col] + k];
1911         rowhit[*row_idx++] = col + 1;
1912       }
1913     }
1914     /* count the number of hits */
1915     nrows = 0;
1916     for (j=0; j<cm; j++) {
1917       if (rowhit[j]) nrows++;
1918     }
1919     c->nrows[i]      = nrows;
1920     colorforrow[i+1] = colorforrow[i] + nrows;
1921 
1922     nrows = 0;
1923     for (j=0; j<cm; j++) { /* loop over rows */
1924       if (rowhit[j]) {
1925         rows_i[nrows]   = j;
1926         den2sp_i[nrows] = idxhit[j];
1927         nrows++;
1928       }
1929     }
1930     den2sp_i += nrows;
1931 
1932     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1933     rows_i += nrows;
1934   }
1935   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1936   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1937   ierr = ISColoringRestoreIS(iscoloring,PETSC_USE_POINTER,&isa);CHKERRQ(ierr);
1938   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1939 
1940   c->colorforrow = colorforrow;
1941   c->rows        = rows;
1942   c->den2sp      = den2sp;
1943   c->colorforcol = colorforcol;
1944   c->columns     = columns;
1945 
1946   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1947   PetscFunctionReturn(0);
1948 }
1949 
1950 /* --------------------------------------------------------------- */
1951 static PetscErrorCode MatProductNumeric_AtB_SeqAIJ_SeqAIJ(Mat C)
1952 {
1953   PetscErrorCode ierr;
1954   Mat_Product    *product = C->product;
1955   Mat            A=product->A,B=product->B;
1956 
1957   PetscFunctionBegin;
1958   if (C->ops->mattransposemultnumeric) {
1959     /* Alg: "outerproduct" */
1960     ierr = (*C->ops->mattransposemultnumeric)(A,B,C);CHKERRQ(ierr);
1961   } else {
1962     /* Alg: "matmatmult" -- C = At*B */
1963     Mat_MatTransMatMult *atb = (Mat_MatTransMatMult *)product->data;
1964     Mat                 At;
1965 
1966     if (!atb) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Missing product struct");
1967     At = atb->At;
1968     if (atb->updateAt && At) { /* At is computed in MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ() */
1969       ierr = MatTranspose_SeqAIJ(A,MAT_REUSE_MATRIX,&At);CHKERRQ(ierr);
1970     }
1971     ierr = MatMatMultNumeric_SeqAIJ_SeqAIJ(At ? At : A,B,C);CHKERRQ(ierr);
1972     atb->updateAt = PETSC_TRUE;
1973   }
1974   PetscFunctionReturn(0);
1975 }
1976 
1977 static PetscErrorCode MatProductSymbolic_AtB_SeqAIJ_SeqAIJ(Mat C)
1978 {
1979   PetscErrorCode ierr;
1980   Mat_Product    *product = C->product;
1981   Mat            A=product->A,B=product->B;
1982   PetscReal      fill=product->fill;
1983 
1984   PetscFunctionBegin;
1985   ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1986 
1987   C->ops->productnumeric = MatProductNumeric_AtB_SeqAIJ_SeqAIJ;
1988   PetscFunctionReturn(0);
1989 }
1990 
1991 /* --------------------------------------------------------------- */
1992 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AB(Mat C)
1993 {
1994   PetscErrorCode ierr;
1995   Mat_Product    *product = C->product;
1996   PetscInt       alg = 0; /* default algorithm */
1997   PetscBool      flg = PETSC_FALSE;
1998 #if !defined(PETSC_HAVE_HYPRE)
1999   const char     *algTypes[7] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","rowmerge"};
2000   PetscInt       nalg = 7;
2001 #else
2002   const char     *algTypes[8] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","rowmerge","hypre"};
2003   PetscInt       nalg = 8;
2004 #endif
2005 
2006   PetscFunctionBegin;
2007   /* Set default algorithm */
2008   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2009   if (flg) {
2010     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2011   }
2012 
2013   /* Get runtime option */
2014   if (product->api_user) {
2015     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");CHKERRQ(ierr);
2016     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[0],&alg,&flg);CHKERRQ(ierr);
2017     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2018   } else {
2019     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");CHKERRQ(ierr);
2020     ierr = PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatProduct_AB",algTypes,nalg,algTypes[0],&alg,&flg);CHKERRQ(ierr);
2021     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2022   }
2023   if (flg) {
2024     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2025   }
2026 
2027   C->ops->productsymbolic = MatProductSymbolic_AB;
2028   C->ops->matmultsymbolic = MatMatMultSymbolic_SeqAIJ_SeqAIJ;
2029   PetscFunctionReturn(0);
2030 }
2031 
2032 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_AtB(Mat C)
2033 {
2034   PetscErrorCode ierr;
2035   Mat_Product    *product = C->product;
2036   PetscInt       alg = 0; /* default algorithm */
2037   PetscBool      flg = PETSC_FALSE;
2038   const char     *algTypes[3] = {"default","at*b","outerproduct"};
2039   PetscInt       nalg = 3;
2040 
2041   PetscFunctionBegin;
2042   /* Get runtime option */
2043   if (product->api_user) {
2044     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");CHKERRQ(ierr);
2045     ierr = PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2046     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2047   } else {
2048     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");CHKERRQ(ierr);
2049     ierr = PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatProduct_AtB",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2050     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2051   }
2052   if (flg) {
2053     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2054   }
2055 
2056   C->ops->productsymbolic = MatProductSymbolic_AtB_SeqAIJ_SeqAIJ;
2057   PetscFunctionReturn(0);
2058 }
2059 
2060 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABt(Mat C)
2061 {
2062   PetscErrorCode ierr;
2063   Mat_Product    *product = C->product;
2064   PetscInt       alg = 0; /* default algorithm */
2065   PetscBool      flg = PETSC_FALSE;
2066   const char     *algTypes[2] = {"default","color"};
2067   PetscInt       nalg = 2;
2068 
2069   PetscFunctionBegin;
2070   /* Set default algorithm */
2071   ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
2072   if (!flg) {
2073     alg = 1;
2074     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2075   }
2076 
2077   /* Get runtime option */
2078   if (product->api_user) {
2079     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatTransposeMult","Mat");CHKERRQ(ierr);
2080     ierr = PetscOptionsEList("-matmattransmult_via","Algorithmic approach","MatMatTransposeMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2081     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2082   } else {
2083     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABt","Mat");CHKERRQ(ierr);
2084     ierr = PetscOptionsEList("-matproduct_abt_via","Algorithmic approach","MatProduct_ABt",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2085     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2086   }
2087   if (flg) {
2088     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2089   }
2090 
2091   C->ops->mattransposemultsymbolic = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ;
2092   C->ops->productsymbolic          = MatProductSymbolic_ABt;
2093   PetscFunctionReturn(0);
2094 }
2095 
2096 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_PtAP(Mat C)
2097 {
2098   PetscErrorCode ierr;
2099   Mat_Product    *product = C->product;
2100   PetscBool      flg = PETSC_FALSE;
2101   PetscInt       alg = 0; /* default algorithm -- alg=1 should be default!!! */
2102 #if !defined(PETSC_HAVE_HYPRE)
2103   const char     *algTypes[2] = {"scalable","rap"};
2104   PetscInt       nalg = 2;
2105 #else
2106   const char     *algTypes[3] = {"scalable","rap","hypre"};
2107   PetscInt       nalg = 3;
2108 #endif
2109 
2110   PetscFunctionBegin;
2111   /* Set default algorithm */
2112   ierr = PetscStrcmp(product->alg,"default",&flg);CHKERRQ(ierr);
2113   if (flg) {
2114     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2115   }
2116 
2117   /* Get runtime option */
2118   if (product->api_user) {
2119     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");CHKERRQ(ierr);
2120     ierr = PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[0],&alg,&flg);CHKERRQ(ierr);
2121     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2122   } else {
2123     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");CHKERRQ(ierr);
2124     ierr = PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatProduct_PtAP",algTypes,nalg,algTypes[0],&alg,&flg);CHKERRQ(ierr);
2125     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2126   }
2127   if (flg) {
2128     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2129   }
2130 
2131   C->ops->productsymbolic = MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ;
2132   PetscFunctionReturn(0);
2133 }
2134 
2135 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_RARt(Mat C)
2136 {
2137   PetscErrorCode ierr;
2138   Mat_Product    *product = C->product;
2139   PetscBool      flg = PETSC_FALSE;
2140   PetscInt       alg = 0; /* default algorithm */
2141   const char     *algTypes[3] = {"r*a*rt","r*art","coloring_rart"};
2142   PetscInt        nalg = 3;
2143 
2144   PetscFunctionBegin;
2145   /* Set default algorithm */
2146   ierr = PetscStrcmp(product->alg,"default",&flg);CHKERRQ(ierr);
2147   if (flg) {
2148     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2149   }
2150 
2151   /* Get runtime option */
2152   if (product->api_user) {
2153     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatRARt","Mat");CHKERRQ(ierr);
2154     ierr = PetscOptionsEList("-matrart_via","Algorithmic approach","MatRARt",algTypes,nalg,algTypes[0],&alg,&flg);CHKERRQ(ierr);
2155     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2156   } else {
2157     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_RARt","Mat");CHKERRQ(ierr);
2158     ierr = PetscOptionsEList("-matproduct_rart_via","Algorithmic approach","MatProduct_RARt",algTypes,nalg,algTypes[0],&alg,&flg);CHKERRQ(ierr);
2159     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2160   }
2161   if (flg) {
2162     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2163   }
2164 
2165   C->ops->productsymbolic = MatProductSymbolic_RARt_SeqAIJ_SeqAIJ;
2166   PetscFunctionReturn(0);
2167 }
2168 
2169 /* ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm */
2170 static PetscErrorCode MatProductSetFromOptions_SeqAIJ_ABC(Mat C)
2171 {
2172   PetscErrorCode ierr;
2173   Mat_Product    *product = C->product;
2174   PetscInt       alg = 0; /* default algorithm */
2175   PetscBool      flg = PETSC_FALSE;
2176   const char     *algTypes[7] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","rowmerge"};
2177   PetscInt       nalg = 7;
2178 
2179   PetscFunctionBegin;
2180   /* Set default algorithm */
2181   ierr = PetscStrcmp(product->alg,"default",&flg);CHKERRQ(ierr);
2182   if (flg) {
2183     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2184   }
2185 
2186   /* Get runtime option */
2187   if (product->api_user) {
2188     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");CHKERRQ(ierr);
2189     ierr = PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2190     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2191   } else {
2192     ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");CHKERRQ(ierr);
2193     ierr = PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
2194     ierr = PetscOptionsEnd();CHKERRQ(ierr);
2195   }
2196   if (flg) {
2197     ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
2198   }
2199 
2200   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ;
2201   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2202   PetscFunctionReturn(0);
2203 }
2204 
2205 PetscErrorCode MatProductSetFromOptions_SeqAIJ(Mat C)
2206 {
2207   PetscErrorCode ierr;
2208   Mat_Product    *product = C->product;
2209 
2210   PetscFunctionBegin;
2211   switch (product->type) {
2212   case MATPRODUCT_AB:
2213     ierr = MatProductSetFromOptions_SeqAIJ_AB(C);CHKERRQ(ierr);
2214     break;
2215   case MATPRODUCT_AtB:
2216     ierr = MatProductSetFromOptions_SeqAIJ_AtB(C);CHKERRQ(ierr);
2217     break;
2218   case MATPRODUCT_ABt:
2219     ierr = MatProductSetFromOptions_SeqAIJ_ABt(C);CHKERRQ(ierr);
2220     break;
2221   case MATPRODUCT_PtAP:
2222     ierr = MatProductSetFromOptions_SeqAIJ_PtAP(C);CHKERRQ(ierr);
2223     break;
2224   case MATPRODUCT_RARt:
2225     ierr = MatProductSetFromOptions_SeqAIJ_RARt(C);CHKERRQ(ierr);
2226     break;
2227   case MATPRODUCT_ABC:
2228     ierr = MatProductSetFromOptions_SeqAIJ_ABC(C);CHKERRQ(ierr);
2229     break;
2230   default:
2231     break;
2232   }
2233   PetscFunctionReturn(0);
2234 }
2235