xref: /petsc/src/mat/impls/aij/seq/matmatmult.c (revision b48ab24ab3d10fe53e9be11bf7e4243edd5ad7ec)
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 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat,Mat,PetscReal,Mat*);
14 
15 #if defined(PETSC_HAVE_HYPRE)
16 PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat*);
17 #endif
18 
19 #undef __FUNCT__
20 #define __FUNCT__ "MatMatMult_SeqAIJ_SeqAIJ"
21 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
22 {
23   PetscErrorCode ierr;
24 #if !defined(PETSC_HAVE_HYPRE)
25   const char     *algTypes[6] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed"};
26   PetscInt       nalg = 6;
27 #else
28   const char     *algTypes[7] = {"sorted","scalable","scalable_fast","heap","btheap","llcondensed","hypre"};
29   PetscInt       nalg = 7;
30 #endif
31   PetscInt       alg = 0; /* set default algorithm */
32 
33   PetscFunctionBegin;
34   if (scall == MAT_INITIAL_MATRIX) {
35     ierr = PetscObjectOptionsBegin((PetscObject)A);CHKERRQ(ierr);
36     ierr = PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[0],&alg,NULL);CHKERRQ(ierr);
37     ierr = PetscOptionsEnd();CHKERRQ(ierr);
38     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
39     switch (alg) {
40     case 1:
41       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(A,B,fill,C);CHKERRQ(ierr);
42       break;
43     case 2:
44       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(A,B,fill,C);CHKERRQ(ierr);
45       break;
46     case 3:
47       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(A,B,fill,C);CHKERRQ(ierr);
48       break;
49     case 4:
50       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(A,B,fill,C);CHKERRQ(ierr);
51       break;
52     case 5:
53       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(A,B,fill,C);CHKERRQ(ierr);
54       break;
55 #if defined(PETSC_HAVE_HYPRE)
56     case 6:
57       ierr = MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);CHKERRQ(ierr);
58       break;
59 #endif
60     default:
61       ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
62      break;
63     }
64     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
65   }
66 
67   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
68   ierr = (*(*C)->ops->matmultnumeric)(A,B,*C);CHKERRQ(ierr);
69   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
70   PetscFunctionReturn(0);
71 }
72 
73 static PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat A,Mat B,PetscReal fill,Mat *C)
74 {
75   PetscErrorCode     ierr;
76   Mat_SeqAIJ         *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
77   PetscInt           *ai=a->i,*bi=b->i,*ci,*cj;
78   PetscInt           am =A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
79   PetscReal          afill;
80   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
81   PetscTable         ta;
82   PetscBT            lnkbt;
83   PetscFreeSpaceList free_space=NULL,current_space=NULL;
84 
85   PetscFunctionBegin;
86   /* Get ci and cj */
87   /*---------------*/
88   /* Allocate ci array, arrays for fill computation and */
89   /* free space for accumulating nonzero column info */
90   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
91   ci[0] = 0;
92 
93   /* create and initialize a linked list */
94   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
95   MatRowMergeMax_SeqAIJ(b,bm,ta);
96   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
97   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
98 
99   ierr = PetscLLCondensedCreate(Crmax,bn,&lnk,&lnkbt);CHKERRQ(ierr);
100 
101   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
102   ierr = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
103 
104   current_space = free_space;
105 
106   /* Determine ci and cj */
107   for (i=0; i<am; i++) {
108     anzi = ai[i+1] - ai[i];
109     aj   = a->j + ai[i];
110     for (j=0; j<anzi; j++) {
111       brow = aj[j];
112       bnzj = bi[brow+1] - bi[brow];
113       bj   = b->j + bi[brow];
114       /* add non-zero cols of B into the sorted linked list lnk */
115       ierr = PetscLLCondensedAddSorted(bnzj,bj,lnk,lnkbt);CHKERRQ(ierr);
116     }
117     cnzi = lnk[0];
118 
119     /* If free space is not available, make more free space */
120     /* Double the amount of total space in the list */
121     if (current_space->local_remaining<cnzi) {
122       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
123       ndouble++;
124     }
125 
126     /* Copy data into free space, then initialize lnk */
127     ierr = PetscLLCondensedClean(bn,cnzi,current_space->array,lnk,lnkbt);CHKERRQ(ierr);
128 
129     current_space->array           += cnzi;
130     current_space->local_used      += cnzi;
131     current_space->local_remaining -= cnzi;
132 
133     ci[i+1] = ci[i] + cnzi;
134   }
135 
136   /* Column indices are in the list of free space */
137   /* Allocate space for cj, initialize cj, and */
138   /* destroy list of free space and other temporary array(s) */
139   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
140   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
141   ierr = PetscLLCondensedDestroy(lnk,lnkbt);CHKERRQ(ierr);
142 
143   /* put together the new symbolic matrix */
144   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
145   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
146 
147   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
148   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
149   c                         = (Mat_SeqAIJ*)((*C)->data);
150   c->free_a                 = PETSC_FALSE;
151   c->free_ij                = PETSC_TRUE;
152   c->nonew                  = 0;
153   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ; /* fast, needs non-scalable O(bn) array 'abdense' */
154 
155   /* set MatInfo */
156   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
157   if (afill < 1.0) afill = 1.0;
158   c->maxnz                     = ci[am];
159   c->nz                        = ci[am];
160   (*C)->info.mallocs           = ndouble;
161   (*C)->info.fill_ratio_given  = fill;
162   (*C)->info.fill_ratio_needed = afill;
163 
164 #if defined(PETSC_USE_INFO)
165   if (ci[am]) {
166     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
167     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
168   } else {
169     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
170   }
171 #endif
172   PetscFunctionReturn(0);
173 }
174 
175 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
176 {
177   PetscErrorCode ierr;
178   PetscLogDouble flops=0.0;
179   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
180   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
181   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
182   PetscInt       *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
183   PetscInt       am   =A->rmap->n,cm=C->rmap->n;
184   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
185   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca,valtmp;
186   PetscScalar    *ab_dense;
187 
188   PetscFunctionBegin;
189   if (!c->a) { /* first call of MatMatMultNumeric_SeqAIJ_SeqAIJ, allocate ca and matmult_abdense */
190     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
191     c->a      = ca;
192     c->free_a = PETSC_TRUE;
193   } else {
194     ca        = c->a;
195   }
196   if (!c->matmult_abdense) {
197     ierr = PetscCalloc1(B->cmap->N,&ab_dense);CHKERRQ(ierr);
198     c->matmult_abdense = ab_dense;
199   } else {
200     ab_dense = c->matmult_abdense;
201   }
202 
203   /* clean old values in C */
204   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
205   /* Traverse A row-wise. */
206   /* Build the ith row in C by summing over nonzero columns in A, */
207   /* the rows of B corresponding to nonzeros of A. */
208   for (i=0; i<am; i++) {
209     anzi = ai[i+1] - ai[i];
210     for (j=0; j<anzi; j++) {
211       brow = aj[j];
212       bnzi = bi[brow+1] - bi[brow];
213       bjj  = bj + bi[brow];
214       baj  = ba + bi[brow];
215       /* perform dense axpy */
216       valtmp = aa[j];
217       for (k=0; k<bnzi; k++) {
218         ab_dense[bjj[k]] += valtmp*baj[k];
219       }
220       flops += 2*bnzi;
221     }
222     aj += anzi; aa += anzi;
223 
224     cnzi = ci[i+1] - ci[i];
225     for (k=0; k<cnzi; k++) {
226       ca[k]          += ab_dense[cj[k]];
227       ab_dense[cj[k]] = 0.0; /* zero ab_dense */
228     }
229     flops += cnzi;
230     cj    += cnzi; ca += cnzi;
231   }
232   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
233   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
234   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
235   PetscFunctionReturn(0);
236 }
237 
238 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,Mat C)
239 {
240   PetscErrorCode ierr;
241   PetscLogDouble flops=0.0;
242   Mat_SeqAIJ     *a   = (Mat_SeqAIJ*)A->data;
243   Mat_SeqAIJ     *b   = (Mat_SeqAIJ*)B->data;
244   Mat_SeqAIJ     *c   = (Mat_SeqAIJ*)C->data;
245   PetscInt       *ai  = a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bjj,*ci=c->i,*cj=c->j;
246   PetscInt       am   = A->rmap->N,cm=C->rmap->N;
247   PetscInt       i,j,k,anzi,bnzi,cnzi,brow;
248   PetscScalar    *aa=a->a,*ba=b->a,*baj,*ca=c->a,valtmp;
249   PetscInt       nextb;
250 
251   PetscFunctionBegin;
252   /* clean old values in C */
253   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
254   /* Traverse A row-wise. */
255   /* Build the ith row in C by summing over nonzero columns in A, */
256   /* the rows of B corresponding to nonzeros of A. */
257   for (i=0; i<am; i++) {
258     anzi = ai[i+1] - ai[i];
259     cnzi = ci[i+1] - ci[i];
260     for (j=0; j<anzi; j++) {
261       brow = aj[j];
262       bnzi = bi[brow+1] - bi[brow];
263       bjj  = bj + bi[brow];
264       baj  = ba + bi[brow];
265       /* perform sparse axpy */
266       valtmp = aa[j];
267       nextb  = 0;
268       for (k=0; nextb<bnzi; k++) {
269         if (cj[k] == bjj[nextb]) { /* ccol == bcol */
270           ca[k] += valtmp*baj[nextb++];
271         }
272       }
273       flops += 2*bnzi;
274     }
275     aj += anzi; aa += anzi;
276     cj += cnzi; ca += cnzi;
277   }
278 
279   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
280   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
281   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
282   PetscFunctionReturn(0);
283 }
284 
285 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat A,Mat B,PetscReal fill,Mat *C)
286 {
287   PetscErrorCode     ierr;
288   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
289   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
290   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
291   MatScalar          *ca;
292   PetscReal          afill;
293   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
294   PetscTable         ta;
295   PetscFreeSpaceList free_space=NULL,current_space=NULL;
296 
297   PetscFunctionBegin;
298   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_fast() */
299   /*-----------------------------------------------------------------------------------------*/
300   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
301   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
302   ci[0] = 0;
303 
304   /* create and initialize a linked list */
305   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
306   MatRowMergeMax_SeqAIJ(b,bm,ta);
307   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
308   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
309 
310   ierr = PetscLLCondensedCreate_fast(Crmax,&lnk);CHKERRQ(ierr);
311 
312   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
313   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
314   current_space = free_space;
315 
316   /* Determine ci and cj */
317   for (i=0; i<am; i++) {
318     anzi = ai[i+1] - ai[i];
319     aj   = a->j + ai[i];
320     for (j=0; j<anzi; j++) {
321       brow = aj[j];
322       bnzj = bi[brow+1] - bi[brow];
323       bj   = b->j + bi[brow];
324       /* add non-zero cols of B into the sorted linked list lnk */
325       ierr = PetscLLCondensedAddSorted_fast(bnzj,bj,lnk);CHKERRQ(ierr);
326     }
327     cnzi = lnk[1];
328 
329     /* If free space is not available, make more free space */
330     /* Double the amount of total space in the list */
331     if (current_space->local_remaining<cnzi) {
332       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
333       ndouble++;
334     }
335 
336     /* Copy data into free space, then initialize lnk */
337     ierr = PetscLLCondensedClean_fast(cnzi,current_space->array,lnk);CHKERRQ(ierr);
338 
339     current_space->array           += cnzi;
340     current_space->local_used      += cnzi;
341     current_space->local_remaining -= cnzi;
342 
343     ci[i+1] = ci[i] + cnzi;
344   }
345 
346   /* Column indices are in the list of free space */
347   /* Allocate space for cj, initialize cj, and */
348   /* destroy list of free space and other temporary array(s) */
349   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
350   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
351   ierr = PetscLLCondensedDestroy_fast(lnk);CHKERRQ(ierr);
352 
353   /* Allocate space for ca */
354   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
355   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
356 
357   /* put together the new symbolic matrix */
358   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
359   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
360 
361   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
362   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
363   c          = (Mat_SeqAIJ*)((*C)->data);
364   c->free_a  = PETSC_TRUE;
365   c->free_ij = PETSC_TRUE;
366   c->nonew   = 0;
367 
368   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
369 
370   /* set MatInfo */
371   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
372   if (afill < 1.0) afill = 1.0;
373   c->maxnz                     = ci[am];
374   c->nz                        = ci[am];
375   (*C)->info.mallocs           = ndouble;
376   (*C)->info.fill_ratio_given  = fill;
377   (*C)->info.fill_ratio_needed = afill;
378 
379 #if defined(PETSC_USE_INFO)
380   if (ci[am]) {
381     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
382     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
383   } else {
384     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
385   }
386 #endif
387   PetscFunctionReturn(0);
388 }
389 
390 
391 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat A,Mat B,PetscReal fill,Mat *C)
392 {
393   PetscErrorCode     ierr;
394   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
395   PetscInt           *ai = a->i,*bi=b->i,*ci,*cj;
396   PetscInt           am  = A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
397   MatScalar          *ca;
398   PetscReal          afill;
399   PetscInt           i,j,anzi,brow,bnzj,cnzi,*bj,*aj,*lnk,ndouble=0,Crmax;
400   PetscTable         ta;
401   PetscFreeSpaceList free_space=NULL,current_space=NULL;
402 
403   PetscFunctionBegin;
404   /* Get ci and cj - same as MatMatMultSymbolic_SeqAIJ_SeqAIJ except using PetscLLxxx_Scalalbe() */
405   /*---------------------------------------------------------------------------------------------*/
406   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
407   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
408   ci[0] = 0;
409 
410   /* create and initialize a linked list */
411   ierr = PetscTableCreate(bn,bn,&ta);CHKERRQ(ierr);
412   MatRowMergeMax_SeqAIJ(b,bm,ta);
413   ierr = PetscTableGetCount(ta,&Crmax);CHKERRQ(ierr);
414   ierr = PetscTableDestroy(&ta);CHKERRQ(ierr);
415   ierr = PetscLLCondensedCreate_Scalable(Crmax,&lnk);CHKERRQ(ierr);
416 
417   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
418   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
419   current_space = free_space;
420 
421   /* Determine ci and cj */
422   for (i=0; i<am; i++) {
423     anzi = ai[i+1] - ai[i];
424     aj   = a->j + ai[i];
425     for (j=0; j<anzi; j++) {
426       brow = aj[j];
427       bnzj = bi[brow+1] - bi[brow];
428       bj   = b->j + bi[brow];
429       /* add non-zero cols of B into the sorted linked list lnk */
430       ierr = PetscLLCondensedAddSorted_Scalable(bnzj,bj,lnk);CHKERRQ(ierr);
431     }
432     cnzi = lnk[0];
433 
434     /* If free space is not available, make more free space */
435     /* Double the amount of total space in the list */
436     if (current_space->local_remaining<cnzi) {
437       ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
438       ndouble++;
439     }
440 
441     /* Copy data into free space, then initialize lnk */
442     ierr = PetscLLCondensedClean_Scalable(cnzi,current_space->array,lnk);CHKERRQ(ierr);
443 
444     current_space->array           += cnzi;
445     current_space->local_used      += cnzi;
446     current_space->local_remaining -= cnzi;
447 
448     ci[i+1] = ci[i] + cnzi;
449   }
450 
451   /* Column indices are in the list of free space */
452   /* Allocate space for cj, initialize cj, and */
453   /* destroy list of free space and other temporary array(s) */
454   ierr = PetscMalloc1(ci[am]+1,&cj);CHKERRQ(ierr);
455   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
456   ierr = PetscLLCondensedDestroy_Scalable(lnk);CHKERRQ(ierr);
457 
458   /* Allocate space for ca */
459   /*-----------------------*/
460   ierr = PetscMalloc1(ci[am]+1,&ca);CHKERRQ(ierr);
461   ierr = PetscMemzero(ca,(ci[am]+1)*sizeof(MatScalar));CHKERRQ(ierr);
462 
463   /* put together the new symbolic matrix */
464   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,ca,C);CHKERRQ(ierr);
465   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
466 
467   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
468   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
469   c          = (Mat_SeqAIJ*)((*C)->data);
470   c->free_a  = PETSC_TRUE;
471   c->free_ij = PETSC_TRUE;
472   c->nonew   = 0;
473 
474   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable; /* slower, less memory */
475 
476   /* set MatInfo */
477   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
478   if (afill < 1.0) afill = 1.0;
479   c->maxnz                     = ci[am];
480   c->nz                        = ci[am];
481   (*C)->info.mallocs           = ndouble;
482   (*C)->info.fill_ratio_given  = fill;
483   (*C)->info.fill_ratio_needed = afill;
484 
485 #if defined(PETSC_USE_INFO)
486   if (ci[am]) {
487     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
488     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
489   } else {
490     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
491   }
492 #endif
493   PetscFunctionReturn(0);
494 }
495 
496 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat A,Mat B,PetscReal fill,Mat *C)
497 {
498   PetscErrorCode     ierr;
499   Mat_SeqAIJ         *a = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
500   const PetscInt     *ai=a->i,*bi=b->i,*aj=a->j,*bj=b->j;
501   PetscInt           *ci,*cj,*bb;
502   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
503   PetscReal          afill;
504   PetscInt           i,j,col,ndouble = 0;
505   PetscFreeSpaceList free_space=NULL,current_space=NULL;
506   PetscHeap          h;
507 
508   PetscFunctionBegin;
509   /* Get ci and cj - by merging sorted rows using a heap */
510   /*---------------------------------------------------------------------------------------------*/
511   /* Allocate arrays for fill computation and free space for accumulating nonzero column */
512   ierr  = PetscMalloc1(am+2,&ci);CHKERRQ(ierr);
513   ci[0] = 0;
514 
515   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
516   ierr          = PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(ai[am],bi[bm])),&free_space);CHKERRQ(ierr);
517   current_space = free_space;
518 
519   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
520   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
521 
522   /* Determine ci and cj */
523   for (i=0; i<am; i++) {
524     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 */
525     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
526     ci[i+1] = ci[i];
527     /* Populate the min heap */
528     for (j=0; j<anzi; j++) {
529       bb[j] = bi[acol[j]];         /* bb points at the start of the row */
530       if (bb[j] < bi[acol[j]+1]) { /* Add if row is nonempty */
531         ierr = PetscHeapAdd(h,j,bj[bb[j]++]);CHKERRQ(ierr);
532       }
533     }
534     /* Pick off the min element, adding it to free space */
535     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
536     while (j >= 0) {
537       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
538         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
539         ndouble++;
540       }
541       *(current_space->array++) = col;
542       current_space->local_used++;
543       current_space->local_remaining--;
544       ci[i+1]++;
545 
546       /* stash if anything else remains in this row of B */
547       if (bb[j] < bi[acol[j]+1]) {ierr = PetscHeapStash(h,j,bj[bb[j]++]);CHKERRQ(ierr);}
548       while (1) {               /* pop and stash any other rows of B that also had an entry in this column */
549         PetscInt j2,col2;
550         ierr = PetscHeapPeek(h,&j2,&col2);CHKERRQ(ierr);
551         if (col2 != col) break;
552         ierr = PetscHeapPop(h,&j2,&col2);CHKERRQ(ierr);
553         if (bb[j2] < bi[acol[j2]+1]) {ierr = PetscHeapStash(h,j2,bj[bb[j2]++]);CHKERRQ(ierr);}
554       }
555       /* Put any stashed elements back into the min heap */
556       ierr = PetscHeapUnstash(h);CHKERRQ(ierr);
557       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
558     }
559   }
560   ierr = PetscFree(bb);CHKERRQ(ierr);
561   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
562 
563   /* Column indices are in the list of free space */
564   /* Allocate space for cj, initialize cj, and */
565   /* destroy list of free space and other temporary array(s) */
566   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
567   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
568 
569   /* put together the new symbolic matrix */
570   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,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   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
581 
582   /* set MatInfo */
583   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
584   if (afill < 1.0) afill = 1.0;
585   c->maxnz                     = ci[am];
586   c->nz                        = ci[am];
587   (*C)->info.mallocs           = ndouble;
588   (*C)->info.fill_ratio_given  = fill;
589   (*C)->info.fill_ratio_needed = afill;
590 
591 #if defined(PETSC_USE_INFO)
592   if (ci[am]) {
593     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
594     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
595   } else {
596     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
597   }
598 #endif
599   PetscFunctionReturn(0);
600 }
601 
602 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat A,Mat B,PetscReal fill,Mat *C)
603 {
604   PetscErrorCode     ierr;
605   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
606   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
607   PetscInt           *ci,*cj,*bb;
608   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
609   PetscReal          afill;
610   PetscInt           i,j,col,ndouble = 0;
611   PetscFreeSpaceList free_space=NULL,current_space=NULL;
612   PetscHeap          h;
613   PetscBT            bt;
614 
615   PetscFunctionBegin;
616   /* Get ci and cj - using a heap for the sorted rows, but use BT so that each index is only added once */
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 
625   current_space = free_space;
626 
627   ierr = PetscHeapCreate(a->rmax,&h);CHKERRQ(ierr);
628   ierr = PetscMalloc1(a->rmax,&bb);CHKERRQ(ierr);
629   ierr = PetscBTCreate(bn,&bt);CHKERRQ(ierr);
630 
631   /* Determine ci and cj */
632   for (i=0; i<am; i++) {
633     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 */
634     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
635     const PetscInt *fptr = current_space->array; /* Save beginning of the row so we can clear the BT later */
636     ci[i+1] = ci[i];
637     /* Populate the min heap */
638     for (j=0; j<anzi; j++) {
639       PetscInt brow = acol[j];
640       for (bb[j] = bi[brow]; bb[j] < bi[brow+1]; bb[j]++) {
641         PetscInt bcol = bj[bb[j]];
642         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
643           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
644           bb[j]++;
645           break;
646         }
647       }
648     }
649     /* Pick off the min element, adding it to free space */
650     ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
651     while (j >= 0) {
652       if (current_space->local_remaining < 1) { /* double the size, but don't exceed 16 MiB */
653         fptr = NULL;                      /* need PetscBTMemzero */
654         ierr = PetscFreeSpaceGet(PetscMin(PetscIntMultTruncate(2,current_space->total_array_size),16 << 20),&current_space);CHKERRQ(ierr);
655         ndouble++;
656       }
657       *(current_space->array++) = col;
658       current_space->local_used++;
659       current_space->local_remaining--;
660       ci[i+1]++;
661 
662       /* stash if anything else remains in this row of B */
663       for (; bb[j] < bi[acol[j]+1]; bb[j]++) {
664         PetscInt bcol = bj[bb[j]];
665         if (!PetscBTLookupSet(bt,bcol)) { /* new entry */
666           ierr = PetscHeapAdd(h,j,bcol);CHKERRQ(ierr);
667           bb[j]++;
668           break;
669         }
670       }
671       ierr = PetscHeapPop(h,&j,&col);CHKERRQ(ierr);
672     }
673     if (fptr) {                 /* Clear the bits for this row */
674       for (; fptr<current_space->array; fptr++) {ierr = PetscBTClear(bt,*fptr);CHKERRQ(ierr);}
675     } else {                    /* We reallocated so we don't remember (easily) how to clear only the bits we changed */
676       ierr = PetscBTMemzero(bn,bt);CHKERRQ(ierr);
677     }
678   }
679   ierr = PetscFree(bb);CHKERRQ(ierr);
680   ierr = PetscHeapDestroy(&h);CHKERRQ(ierr);
681   ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
682 
683   /* Column indices are in the list of free space */
684   /* Allocate space for cj, initialize cj, and */
685   /* destroy list of free space and other temporary array(s) */
686   ierr = PetscMalloc1(ci[am],&cj);CHKERRQ(ierr);
687   ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
688 
689   /* put together the new symbolic matrix */
690   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
691   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
692 
693   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
694   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
695   c          = (Mat_SeqAIJ*)((*C)->data);
696   c->free_a  = PETSC_TRUE;
697   c->free_ij = PETSC_TRUE;
698   c->nonew   = 0;
699 
700   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
701 
702   /* set MatInfo */
703   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
704   if (afill < 1.0) afill = 1.0;
705   c->maxnz                     = ci[am];
706   c->nz                        = ci[am];
707   (*C)->info.mallocs           = ndouble;
708   (*C)->info.fill_ratio_given  = fill;
709   (*C)->info.fill_ratio_needed = afill;
710 
711 #if defined(PETSC_USE_INFO)
712   if (ci[am]) {
713     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
714     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
715   } else {
716     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
717   }
718 #endif
719   PetscFunctionReturn(0);
720 }
721 
722 /* concatenate unique entries and then sort */
723 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
724 {
725   PetscErrorCode     ierr;
726   Mat_SeqAIJ         *a  = (Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c;
727   const PetscInt     *ai = a->i,*bi=b->i,*aj=a->j,*bj=b->j;
728   PetscInt           *ci,*cj;
729   PetscInt           am=A->rmap->N,bn=B->cmap->N,bm=B->rmap->N;
730   PetscReal          afill;
731   PetscInt           i,j,ndouble = 0;
732   PetscSegBuffer     seg,segrow;
733   char               *seen;
734 
735   PetscFunctionBegin;
736   ierr  = PetscMalloc1(am+1,&ci);CHKERRQ(ierr);
737   ci[0] = 0;
738 
739   /* Initial FreeSpace size is fill*(nnz(A)+nnz(B)) */
740   ierr = PetscSegBufferCreate(sizeof(PetscInt),(PetscInt)(fill*(ai[am]+bi[bm])),&seg);CHKERRQ(ierr);
741   ierr = PetscSegBufferCreate(sizeof(PetscInt),100,&segrow);CHKERRQ(ierr);
742   ierr = PetscMalloc1(bn,&seen);CHKERRQ(ierr);
743   ierr = PetscMemzero(seen,bn*sizeof(char));CHKERRQ(ierr);
744 
745   /* Determine ci and cj */
746   for (i=0; i<am; i++) {
747     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 */
748     const PetscInt *acol = aj + ai[i]; /* column indices of nonzero entries in this row */
749     PetscInt packlen = 0,*PETSC_RESTRICT crow;
750     /* Pack segrow */
751     for (j=0; j<anzi; j++) {
752       PetscInt brow = acol[j],bjstart = bi[brow],bjend = bi[brow+1],k;
753       for (k=bjstart; k<bjend; k++) {
754         PetscInt bcol = bj[k];
755         if (!seen[bcol]) { /* new entry */
756           PetscInt *PETSC_RESTRICT slot;
757           ierr = PetscSegBufferGetInts(segrow,1,&slot);CHKERRQ(ierr);
758           *slot = bcol;
759           seen[bcol] = 1;
760           packlen++;
761         }
762       }
763     }
764     ierr = PetscSegBufferGetInts(seg,packlen,&crow);CHKERRQ(ierr);
765     ierr = PetscSegBufferExtractTo(segrow,crow);CHKERRQ(ierr);
766     ierr = PetscSortInt(packlen,crow);CHKERRQ(ierr);
767     ci[i+1] = ci[i] + packlen;
768     for (j=0; j<packlen; j++) seen[crow[j]] = 0;
769   }
770   ierr = PetscSegBufferDestroy(&segrow);CHKERRQ(ierr);
771   ierr = PetscFree(seen);CHKERRQ(ierr);
772 
773   /* Column indices are in the segmented buffer */
774   ierr = PetscSegBufferExtractAlloc(seg,&cj);CHKERRQ(ierr);
775   ierr = PetscSegBufferDestroy(&seg);CHKERRQ(ierr);
776 
777   /* put together the new symbolic matrix */
778   ierr = MatCreateSeqAIJWithArrays(PetscObjectComm((PetscObject)A),am,bn,ci,cj,NULL,C);CHKERRQ(ierr);
779   ierr = MatSetBlockSizesFromMats(*C,A,B);CHKERRQ(ierr);
780 
781   /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
782   /* These are PETSc arrays, so change flags so arrays can be deleted by PETSc */
783   c          = (Mat_SeqAIJ*)((*C)->data);
784   c->free_a  = PETSC_TRUE;
785   c->free_ij = PETSC_TRUE;
786   c->nonew   = 0;
787 
788   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqAIJ;
789 
790   /* set MatInfo */
791   afill = (PetscReal)ci[am]/(ai[am]+bi[bm]) + 1.e-5;
792   if (afill < 1.0) afill = 1.0;
793   c->maxnz                     = ci[am];
794   c->nz                        = ci[am];
795   (*C)->info.mallocs           = ndouble;
796   (*C)->info.fill_ratio_given  = fill;
797   (*C)->info.fill_ratio_needed = afill;
798 
799 #if defined(PETSC_USE_INFO)
800   if (ci[am]) {
801     ierr = PetscInfo3((*C),"Reallocs %D; Fill ratio: given %g needed %g.\n",ndouble,(double)fill,(double)afill);CHKERRQ(ierr);
802     ierr = PetscInfo1((*C),"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);CHKERRQ(ierr);
803   } else {
804     ierr = PetscInfo((*C),"Empty matrix product\n");CHKERRQ(ierr);
805   }
806 #endif
807   PetscFunctionReturn(0);
808 }
809 
810 /* This routine is not used. Should be removed! */
811 PetscErrorCode MatMatTransposeMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
812 {
813   PetscErrorCode ierr;
814 
815   PetscFunctionBegin;
816   if (scall == MAT_INITIAL_MATRIX) {
817     ierr = PetscLogEventBegin(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
818     ierr = MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
819     ierr = PetscLogEventEnd(MAT_MatTransposeMultSymbolic,A,B,0,0);CHKERRQ(ierr);
820   }
821   ierr = PetscLogEventBegin(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
822   ierr = MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
823   ierr = PetscLogEventEnd(MAT_MatTransposeMultNumeric,A,B,0,0);CHKERRQ(ierr);
824   PetscFunctionReturn(0);
825 }
826 
827 PetscErrorCode MatDestroy_SeqAIJ_MatMatMultTrans(Mat A)
828 {
829   PetscErrorCode      ierr;
830   Mat_SeqAIJ          *a=(Mat_SeqAIJ*)A->data;
831   Mat_MatMatTransMult *abt=a->abt;
832 
833   PetscFunctionBegin;
834   ierr = (abt->destroy)(A);CHKERRQ(ierr);
835   ierr = MatTransposeColoringDestroy(&abt->matcoloring);CHKERRQ(ierr);
836   ierr = MatDestroy(&abt->Bt_den);CHKERRQ(ierr);
837   ierr = MatDestroy(&abt->ABt_den);CHKERRQ(ierr);
838   ierr = PetscFree(abt);CHKERRQ(ierr);
839   PetscFunctionReturn(0);
840 }
841 
842 PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
843 {
844   PetscErrorCode      ierr;
845   Mat                 Bt;
846   PetscInt            *bti,*btj;
847   Mat_MatMatTransMult *abt;
848   Mat_SeqAIJ          *c;
849 
850   PetscFunctionBegin;
851   /* create symbolic Bt */
852   ierr = MatGetSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
853   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,B->cmap->n,B->rmap->n,bti,btj,NULL,&Bt);CHKERRQ(ierr);
854   ierr = MatSetBlockSizes(Bt,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
855 
856   /* get symbolic C=A*Bt */
857   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(A,Bt,fill,C);CHKERRQ(ierr);
858 
859   /* create a supporting struct for reuse intermidiate dense matrices with matcoloring */
860   ierr   = PetscNew(&abt);CHKERRQ(ierr);
861   c      = (Mat_SeqAIJ*)(*C)->data;
862   c->abt = abt;
863 
864   abt->usecoloring = PETSC_FALSE;
865   abt->destroy     = (*C)->ops->destroy;
866   (*C)->ops->destroy     = MatDestroy_SeqAIJ_MatMatMultTrans;
867 
868   ierr = PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-matmattransmult_color",&abt->usecoloring,NULL);CHKERRQ(ierr);
869   if (abt->usecoloring) {
870     /* Create MatTransposeColoring from symbolic C=A*B^T */
871     MatTransposeColoring matcoloring;
872     MatColoring          coloring;
873     ISColoring           iscoloring;
874     Mat                  Bt_dense,C_dense;
875     Mat_SeqAIJ           *c=(Mat_SeqAIJ*)(*C)->data;
876     /* inode causes memory problem, don't know why */
877     if (c->inode.use) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MAT_USE_INODES is not supported. Use '-mat_no_inode'");
878 
879     ierr = MatColoringCreate(*C,&coloring);CHKERRQ(ierr);
880     ierr = MatColoringSetDistance(coloring,2);CHKERRQ(ierr);
881     ierr = MatColoringSetType(coloring,MATCOLORINGSL);CHKERRQ(ierr);
882     ierr = MatColoringSetFromOptions(coloring);CHKERRQ(ierr);
883     ierr = MatColoringApply(coloring,&iscoloring);CHKERRQ(ierr);
884     ierr = MatColoringDestroy(&coloring);CHKERRQ(ierr);
885     ierr = MatTransposeColoringCreate(*C,iscoloring,&matcoloring);CHKERRQ(ierr);
886 
887     abt->matcoloring = matcoloring;
888 
889     ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
890 
891     /* Create Bt_dense and C_dense = A*Bt_dense */
892     ierr = MatCreate(PETSC_COMM_SELF,&Bt_dense);CHKERRQ(ierr);
893     ierr = MatSetSizes(Bt_dense,A->cmap->n,matcoloring->ncolors,A->cmap->n,matcoloring->ncolors);CHKERRQ(ierr);
894     ierr = MatSetType(Bt_dense,MATSEQDENSE);CHKERRQ(ierr);
895     ierr = MatSeqDenseSetPreallocation(Bt_dense,NULL);CHKERRQ(ierr);
896 
897     Bt_dense->assembled = PETSC_TRUE;
898     abt->Bt_den   = Bt_dense;
899 
900     ierr = MatCreate(PETSC_COMM_SELF,&C_dense);CHKERRQ(ierr);
901     ierr = MatSetSizes(C_dense,A->rmap->n,matcoloring->ncolors,A->rmap->n,matcoloring->ncolors);CHKERRQ(ierr);
902     ierr = MatSetType(C_dense,MATSEQDENSE);CHKERRQ(ierr);
903     ierr = MatSeqDenseSetPreallocation(C_dense,NULL);CHKERRQ(ierr);
904 
905     Bt_dense->assembled = PETSC_TRUE;
906     abt->ABt_den  = C_dense;
907 
908 #if defined(PETSC_USE_INFO)
909     {
910       Mat_SeqAIJ *c = (Mat_SeqAIJ*)(*C)->data;
911       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);
912     }
913 #endif
914   }
915   /* clean up */
916   ierr = MatDestroy(&Bt);CHKERRQ(ierr);
917   ierr = MatRestoreSymbolicTranspose_SeqAIJ(B,&bti,&btj);CHKERRQ(ierr);
918   PetscFunctionReturn(0);
919 }
920 
921 PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
922 {
923   PetscErrorCode      ierr;
924   Mat_SeqAIJ          *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
925   PetscInt            *ai  =a->i,*aj=a->j,*bi=b->i,*bj=b->j,anzi,bnzj,nexta,nextb,*acol,*bcol,brow;
926   PetscInt            cm   =C->rmap->n,*ci=c->i,*cj=c->j,i,j,cnzi,*ccol;
927   PetscLogDouble      flops=0.0;
928   MatScalar           *aa  =a->a,*aval,*ba=b->a,*bval,*ca,*cval;
929   Mat_MatMatTransMult *abt = c->abt;
930 
931   PetscFunctionBegin;
932   /* clear old values in C */
933   if (!c->a) {
934     ierr      = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
935     c->a      = ca;
936     c->free_a = PETSC_TRUE;
937   } else {
938     ca =  c->a;
939   }
940   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
941 
942   if (abt->usecoloring) {
943     MatTransposeColoring matcoloring = abt->matcoloring;
944     Mat                  Bt_dense,C_dense = abt->ABt_den;
945 
946     /* Get Bt_dense by Apply MatTransposeColoring to B */
947     Bt_dense = abt->Bt_den;
948     ierr = MatTransColoringApplySpToDen(matcoloring,B,Bt_dense);CHKERRQ(ierr);
949 
950     /* C_dense = A*Bt_dense */
951     ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,Bt_dense,C_dense);CHKERRQ(ierr);
952 
953     /* Recover C from C_dense */
954     ierr = MatTransColoringApplyDenToSp(matcoloring,C_dense,C);CHKERRQ(ierr);
955     PetscFunctionReturn(0);
956   }
957 
958   for (i=0; i<cm; i++) {
959     anzi = ai[i+1] - ai[i];
960     acol = aj + ai[i];
961     aval = aa + ai[i];
962     cnzi = ci[i+1] - ci[i];
963     ccol = cj + ci[i];
964     cval = ca + ci[i];
965     for (j=0; j<cnzi; j++) {
966       brow = ccol[j];
967       bnzj = bi[brow+1] - bi[brow];
968       bcol = bj + bi[brow];
969       bval = ba + bi[brow];
970 
971       /* perform sparse inner-product c(i,j)=A[i,:]*B[j,:]^T */
972       nexta = 0; nextb = 0;
973       while (nexta<anzi && nextb<bnzj) {
974         while (nexta < anzi && acol[nexta] < bcol[nextb]) nexta++;
975         if (nexta == anzi) break;
976         while (nextb < bnzj && acol[nexta] > bcol[nextb]) nextb++;
977         if (nextb == bnzj) break;
978         if (acol[nexta] == bcol[nextb]) {
979           cval[j] += aval[nexta]*bval[nextb];
980           nexta++; nextb++;
981           flops += 2;
982         }
983       }
984     }
985   }
986   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
987   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
988   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
989   PetscFunctionReturn(0);
990 }
991 
992 PetscErrorCode MatTransposeMatMult_SeqAIJ_SeqAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
993 {
994   PetscErrorCode ierr;
995 
996   PetscFunctionBegin;
997   if (scall == MAT_INITIAL_MATRIX) {
998     ierr = PetscLogEventBegin(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
999     ierr = MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(A,B,fill,C);CHKERRQ(ierr);
1000     ierr = PetscLogEventEnd(MAT_TransposeMatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1001   }
1002   ierr = PetscLogEventBegin(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1003   ierr = MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(A,B,*C);CHKERRQ(ierr);
1004   ierr = PetscLogEventEnd(MAT_TransposeMatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1005   PetscFunctionReturn(0);
1006 }
1007 
1008 PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat A,Mat B,PetscReal fill,Mat *C)
1009 {
1010   PetscErrorCode ierr;
1011   Mat            At;
1012   PetscInt       *ati,*atj;
1013 
1014   PetscFunctionBegin;
1015   /* create symbolic At */
1016   ierr = MatGetSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1017   ierr = MatCreateSeqAIJWithArrays(PETSC_COMM_SELF,A->cmap->n,A->rmap->n,ati,atj,NULL,&At);CHKERRQ(ierr);
1018   ierr = MatSetBlockSizes(At,PetscAbs(A->cmap->bs),PetscAbs(B->cmap->bs));CHKERRQ(ierr);
1019 
1020   /* get symbolic C=At*B */
1021   ierr = MatMatMultSymbolic_SeqAIJ_SeqAIJ(At,B,fill,C);CHKERRQ(ierr);
1022 
1023   /* clean up */
1024   ierr = MatDestroy(&At);CHKERRQ(ierr);
1025   ierr = MatRestoreSymbolicTranspose_SeqAIJ(A,&ati,&atj);CHKERRQ(ierr);
1026   PetscFunctionReturn(0);
1027 }
1028 
1029 PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat A,Mat B,Mat C)
1030 {
1031   PetscErrorCode ierr;
1032   Mat_SeqAIJ     *a   =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)B->data,*c=(Mat_SeqAIJ*)C->data;
1033   PetscInt       am   =A->rmap->n,anzi,*ai=a->i,*aj=a->j,*bi=b->i,*bj,bnzi,nextb;
1034   PetscInt       cm   =C->rmap->n,*ci=c->i,*cj=c->j,crow,*cjj,i,j,k;
1035   PetscLogDouble flops=0.0;
1036   MatScalar      *aa  =a->a,*ba,*ca,*caj;
1037 
1038   PetscFunctionBegin;
1039   if (!c->a) {
1040     ierr = PetscMalloc1(ci[cm]+1,&ca);CHKERRQ(ierr);
1041 
1042     c->a      = ca;
1043     c->free_a = PETSC_TRUE;
1044   } else {
1045     ca = c->a;
1046   }
1047   /* clear old values in C */
1048   ierr = PetscMemzero(ca,ci[cm]*sizeof(MatScalar));CHKERRQ(ierr);
1049 
1050   /* compute A^T*B using outer product (A^T)[:,i]*B[i,:] */
1051   for (i=0; i<am; i++) {
1052     bj   = b->j + bi[i];
1053     ba   = b->a + bi[i];
1054     bnzi = bi[i+1] - bi[i];
1055     anzi = ai[i+1] - ai[i];
1056     for (j=0; j<anzi; j++) {
1057       nextb = 0;
1058       crow  = *aj++;
1059       cjj   = cj + ci[crow];
1060       caj   = ca + ci[crow];
1061       /* perform sparse axpy operation.  Note cjj includes bj. */
1062       for (k=0; nextb<bnzi; k++) {
1063         if (cjj[k] == *(bj+nextb)) { /* ccol == bcol */
1064           caj[k] += (*aa)*(*(ba+nextb));
1065           nextb++;
1066         }
1067       }
1068       flops += 2*bnzi;
1069       aa++;
1070     }
1071   }
1072 
1073   /* Assemble the final matrix and clean up */
1074   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1075   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1076   ierr = PetscLogFlops(flops);CHKERRQ(ierr);
1077   PetscFunctionReturn(0);
1078 }
1079 
1080 PETSC_INTERN PetscErrorCode MatMatMult_SeqAIJ_SeqDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
1081 {
1082   PetscErrorCode ierr;
1083 
1084   PetscFunctionBegin;
1085   if (scall == MAT_INITIAL_MATRIX) {
1086     ierr = PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1087     ierr = MatMatMultSymbolic_SeqAIJ_SeqDense(A,B,fill,C);CHKERRQ(ierr);
1088     ierr = PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);CHKERRQ(ierr);
1089   }
1090   ierr = PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1091   ierr = MatMatMultNumeric_SeqAIJ_SeqDense(A,B,*C);CHKERRQ(ierr);
1092   ierr = PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);CHKERRQ(ierr);
1093   PetscFunctionReturn(0);
1094 }
1095 
1096 PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqDense(Mat A,Mat B,PetscReal fill,Mat *C)
1097 {
1098   PetscErrorCode ierr;
1099 
1100   PetscFunctionBegin;
1101   ierr = MatMatMultSymbolic_SeqDense_SeqDense(A,B,0.0,C);CHKERRQ(ierr);
1102 
1103   (*C)->ops->matmultnumeric = MatMatMultNumeric_SeqAIJ_SeqDense;
1104   PetscFunctionReturn(0);
1105 }
1106 
1107 PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1108 {
1109   Mat_SeqAIJ        *a=(Mat_SeqAIJ*)A->data;
1110   Mat_SeqDense      *bd = (Mat_SeqDense*)B->data;
1111   PetscErrorCode    ierr;
1112   PetscScalar       *c,*b,r1,r2,r3,r4,*c1,*c2,*c3,*c4,aatmp;
1113   const PetscScalar *aa,*b1,*b2,*b3,*b4;
1114   const PetscInt    *aj;
1115   PetscInt          cm=C->rmap->n,cn=B->cmap->n,bm=bd->lda,am=A->rmap->n;
1116   PetscInt          am4=4*am,bm4=4*bm,col,i,j,n,ajtmp;
1117 
1118   PetscFunctionBegin;
1119   if (!cm || !cn) PetscFunctionReturn(0);
1120   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);
1121   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);
1122   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);
1123   b = bd->v;
1124   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1125   b1 = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1126   c1 = c; c2 = c1 + am; c3 = c2 + am; c4 = c3 + am;
1127   for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1128     for (i=0; i<am; i++) {        /* over rows of C in those columns */
1129       r1 = r2 = r3 = r4 = 0.0;
1130       n  = a->i[i+1] - a->i[i];
1131       aj = a->j + a->i[i];
1132       aa = a->a + a->i[i];
1133       for (j=0; j<n; j++) {
1134         aatmp = aa[j]; ajtmp = aj[j];
1135         r1 += aatmp*b1[ajtmp];
1136         r2 += aatmp*b2[ajtmp];
1137         r3 += aatmp*b3[ajtmp];
1138         r4 += aatmp*b4[ajtmp];
1139       }
1140       c1[i] = r1;
1141       c2[i] = r2;
1142       c3[i] = r3;
1143       c4[i] = r4;
1144     }
1145     b1 += bm4; b2 += bm4; b3 += bm4; b4 += bm4;
1146     c1 += am4; c2 += am4; c3 += am4; c4 += am4;
1147   }
1148   for (; col<cn; col++) {   /* over extra columns of C */
1149     for (i=0; i<am; i++) {  /* over rows of C in those columns */
1150       r1 = 0.0;
1151       n  = a->i[i+1] - a->i[i];
1152       aj = a->j + a->i[i];
1153       aa = a->a + a->i[i];
1154       for (j=0; j<n; j++) {
1155         r1 += aa[j]*b1[aj[j]];
1156       }
1157       c1[i] = r1;
1158     }
1159     b1 += bm;
1160     c1 += am;
1161   }
1162   ierr = PetscLogFlops(cn*(2.0*a->nz));CHKERRQ(ierr);
1163   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1164   ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1165   ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1166   PetscFunctionReturn(0);
1167 }
1168 
1169 /*
1170    Note very similar to MatMult_SeqAIJ(), should generate both codes from same base
1171 */
1172 PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat A,Mat B,Mat C)
1173 {
1174   Mat_SeqAIJ     *a=(Mat_SeqAIJ*)A->data;
1175   Mat_SeqDense   *bd = (Mat_SeqDense*)B->data;
1176   PetscErrorCode ierr;
1177   PetscScalar    *b,*c,r1,r2,r3,r4,*b1,*b2,*b3,*b4;
1178   MatScalar      *aa;
1179   PetscInt       cm  = C->rmap->n, cn=B->cmap->n, bm=bd->lda, col, i,j,n,*aj, am = A->rmap->n,*ii,arm;
1180   PetscInt       am2 = 2*am, am3 = 3*am,  bm4 = 4*bm,colam,*ridx;
1181 
1182   PetscFunctionBegin;
1183   if (!cm || !cn) PetscFunctionReturn(0);
1184   b = bd->v;
1185   ierr = MatDenseGetArray(C,&c);CHKERRQ(ierr);
1186   b1   = b; b2 = b1 + bm; b3 = b2 + bm; b4 = b3 + bm;
1187 
1188   if (a->compressedrow.use) { /* use compressed row format */
1189     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1190       colam = col*am;
1191       arm   = a->compressedrow.nrows;
1192       ii    = a->compressedrow.i;
1193       ridx  = a->compressedrow.rindex;
1194       for (i=0; i<arm; i++) {        /* over rows of C in those columns */
1195         r1 = r2 = r3 = r4 = 0.0;
1196         n  = ii[i+1] - ii[i];
1197         aj = a->j + ii[i];
1198         aa = a->a + ii[i];
1199         for (j=0; j<n; j++) {
1200           r1 += (*aa)*b1[*aj];
1201           r2 += (*aa)*b2[*aj];
1202           r3 += (*aa)*b3[*aj];
1203           r4 += (*aa++)*b4[*aj++];
1204         }
1205         c[colam       + ridx[i]] += r1;
1206         c[colam + am  + ridx[i]] += r2;
1207         c[colam + am2 + ridx[i]] += r3;
1208         c[colam + am3 + ridx[i]] += r4;
1209       }
1210       b1 += bm4;
1211       b2 += bm4;
1212       b3 += bm4;
1213       b4 += bm4;
1214     }
1215     for (; col<cn; col++) {     /* over extra columns of C */
1216       colam = col*am;
1217       arm   = a->compressedrow.nrows;
1218       ii    = a->compressedrow.i;
1219       ridx  = a->compressedrow.rindex;
1220       for (i=0; i<arm; i++) {  /* over rows of C in those columns */
1221         r1 = 0.0;
1222         n  = ii[i+1] - ii[i];
1223         aj = a->j + ii[i];
1224         aa = a->a + ii[i];
1225 
1226         for (j=0; j<n; j++) {
1227           r1 += (*aa++)*b1[*aj++];
1228         }
1229         c[colam + ridx[i]] += r1;
1230       }
1231       b1 += bm;
1232     }
1233   } else {
1234     for (col=0; col<cn-4; col += 4) {  /* over columns of C */
1235       colam = col*am;
1236       for (i=0; i<am; i++) {        /* over rows of C in those columns */
1237         r1 = r2 = r3 = r4 = 0.0;
1238         n  = a->i[i+1] - a->i[i];
1239         aj = a->j + a->i[i];
1240         aa = a->a + a->i[i];
1241         for (j=0; j<n; j++) {
1242           r1 += (*aa)*b1[*aj];
1243           r2 += (*aa)*b2[*aj];
1244           r3 += (*aa)*b3[*aj];
1245           r4 += (*aa++)*b4[*aj++];
1246         }
1247         c[colam + i]       += r1;
1248         c[colam + am + i]  += r2;
1249         c[colam + am2 + i] += r3;
1250         c[colam + am3 + i] += r4;
1251       }
1252       b1 += bm4;
1253       b2 += bm4;
1254       b3 += bm4;
1255       b4 += bm4;
1256     }
1257     for (; col<cn; col++) {     /* over extra columns of C */
1258       colam = col*am;
1259       for (i=0; i<am; i++) {  /* over rows of C in those columns */
1260         r1 = 0.0;
1261         n  = a->i[i+1] - a->i[i];
1262         aj = a->j + a->i[i];
1263         aa = a->a + a->i[i];
1264 
1265         for (j=0; j<n; j++) {
1266           r1 += (*aa++)*b1[*aj++];
1267         }
1268         c[colam + i] += r1;
1269       }
1270       b1 += bm;
1271     }
1272   }
1273   ierr = PetscLogFlops(cn*2.0*a->nz);CHKERRQ(ierr);
1274   ierr = MatDenseRestoreArray(C,&c);CHKERRQ(ierr);
1275   PetscFunctionReturn(0);
1276 }
1277 
1278 PetscErrorCode  MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring coloring,Mat B,Mat Btdense)
1279 {
1280   PetscErrorCode ierr;
1281   Mat_SeqAIJ     *b       = (Mat_SeqAIJ*)B->data;
1282   Mat_SeqDense   *btdense = (Mat_SeqDense*)Btdense->data;
1283   PetscInt       *bi      = b->i,*bj=b->j;
1284   PetscInt       m        = Btdense->rmap->n,n=Btdense->cmap->n,j,k,l,col,anz,*btcol,brow,ncolumns;
1285   MatScalar      *btval,*btval_den,*ba=b->a;
1286   PetscInt       *columns=coloring->columns,*colorforcol=coloring->colorforcol,ncolors=coloring->ncolors;
1287 
1288   PetscFunctionBegin;
1289   btval_den=btdense->v;
1290   ierr     = PetscMemzero(btval_den,(m*n)*sizeof(MatScalar));CHKERRQ(ierr);
1291   for (k=0; k<ncolors; k++) {
1292     ncolumns = coloring->ncolumns[k];
1293     for (l=0; l<ncolumns; l++) { /* insert a row of B to a column of Btdense */
1294       col   = *(columns + colorforcol[k] + l);
1295       btcol = bj + bi[col];
1296       btval = ba + bi[col];
1297       anz   = bi[col+1] - bi[col];
1298       for (j=0; j<anz; j++) {
1299         brow            = btcol[j];
1300         btval_den[brow] = btval[j];
1301       }
1302     }
1303     btval_den += m;
1304   }
1305   PetscFunctionReturn(0);
1306 }
1307 
1308 PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring matcoloring,Mat Cden,Mat Csp)
1309 {
1310   PetscErrorCode ierr;
1311   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)Csp->data;
1312   PetscScalar    *ca_den,*ca_den_ptr,*ca=csp->a;
1313   PetscInt       k,l,m=Cden->rmap->n,ncolors=matcoloring->ncolors;
1314   PetscInt       brows=matcoloring->brows,*den2sp=matcoloring->den2sp;
1315   PetscInt       nrows,*row,*idx;
1316   PetscInt       *rows=matcoloring->rows,*colorforrow=matcoloring->colorforrow;
1317 
1318   PetscFunctionBegin;
1319   ierr   = MatDenseGetArray(Cden,&ca_den);CHKERRQ(ierr);
1320 
1321   if (brows > 0) {
1322     PetscInt *lstart,row_end,row_start;
1323     lstart = matcoloring->lstart;
1324     ierr = PetscMemzero(lstart,ncolors*sizeof(PetscInt));CHKERRQ(ierr);
1325 
1326     row_end = brows;
1327     if (row_end > m) row_end = m;
1328     for (row_start=0; row_start<m; row_start+=brows) { /* loop over row blocks of Csp */
1329       ca_den_ptr = ca_den;
1330       for (k=0; k<ncolors; k++) { /* loop over colors (columns of Cden) */
1331         nrows = matcoloring->nrows[k];
1332         row   = rows  + colorforrow[k];
1333         idx   = den2sp + colorforrow[k];
1334         for (l=lstart[k]; l<nrows; l++) {
1335           if (row[l] >= row_end) {
1336             lstart[k] = l;
1337             break;
1338           } else {
1339             ca[idx[l]] = ca_den_ptr[row[l]];
1340           }
1341         }
1342         ca_den_ptr += m;
1343       }
1344       row_end += brows;
1345       if (row_end > m) row_end = m;
1346     }
1347   } else { /* non-blocked impl: loop over columns of Csp - slow if Csp is large */
1348     ca_den_ptr = ca_den;
1349     for (k=0; k<ncolors; k++) {
1350       nrows = matcoloring->nrows[k];
1351       row   = rows  + colorforrow[k];
1352       idx   = den2sp + colorforrow[k];
1353       for (l=0; l<nrows; l++) {
1354         ca[idx[l]] = ca_den_ptr[row[l]];
1355       }
1356       ca_den_ptr += m;
1357     }
1358   }
1359 
1360   ierr = MatDenseRestoreArray(Cden,&ca_den);CHKERRQ(ierr);
1361 #if defined(PETSC_USE_INFO)
1362   if (matcoloring->brows > 0) {
1363     ierr = PetscInfo1(Csp,"Loop over %D row blocks for den2sp\n",brows);CHKERRQ(ierr);
1364   } else {
1365     ierr = PetscInfo(Csp,"Loop over colors/columns of Cden, inefficient for large sparse matrix product \n");CHKERRQ(ierr);
1366   }
1367 #endif
1368   PetscFunctionReturn(0);
1369 }
1370 
1371 PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat mat,ISColoring iscoloring,MatTransposeColoring c)
1372 {
1373   PetscErrorCode ierr;
1374   PetscInt       i,n,nrows,Nbs,j,k,m,ncols,col,cm;
1375   const PetscInt *is,*ci,*cj,*row_idx;
1376   PetscInt       nis = iscoloring->n,*rowhit,bs = 1;
1377   IS             *isa;
1378   Mat_SeqAIJ     *csp = (Mat_SeqAIJ*)mat->data;
1379   PetscInt       *colorforrow,*rows,*rows_i,*idxhit,*spidx,*den2sp,*den2sp_i;
1380   PetscInt       *colorforcol,*columns,*columns_i,brows;
1381   PetscBool      flg;
1382 
1383   PetscFunctionBegin;
1384   ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
1385 
1386   /* bs >1 is not being tested yet! */
1387   Nbs       = mat->cmap->N/bs;
1388   c->M      = mat->rmap->N/bs;  /* set total rows, columns and local rows */
1389   c->N      = Nbs;
1390   c->m      = c->M;
1391   c->rstart = 0;
1392   c->brows  = 100;
1393 
1394   c->ncolors = nis;
1395   ierr = PetscMalloc3(nis,&c->ncolumns,nis,&c->nrows,nis+1,&colorforrow);CHKERRQ(ierr);
1396   ierr = PetscMalloc1(csp->nz+1,&rows);CHKERRQ(ierr);
1397   ierr = PetscMalloc1(csp->nz+1,&den2sp);CHKERRQ(ierr);
1398 
1399   brows = c->brows;
1400   ierr = PetscOptionsGetInt(NULL,NULL,"-matden2sp_brows",&brows,&flg);CHKERRQ(ierr);
1401   if (flg) c->brows = brows;
1402   if (brows > 0) {
1403     ierr = PetscMalloc1(nis+1,&c->lstart);CHKERRQ(ierr);
1404   }
1405 
1406   colorforrow[0] = 0;
1407   rows_i         = rows;
1408   den2sp_i       = den2sp;
1409 
1410   ierr = PetscMalloc1(nis+1,&colorforcol);CHKERRQ(ierr);
1411   ierr = PetscMalloc1(Nbs+1,&columns);CHKERRQ(ierr);
1412 
1413   colorforcol[0] = 0;
1414   columns_i      = columns;
1415 
1416   /* get column-wise storage of mat */
1417   ierr = MatGetColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1418 
1419   cm   = c->m;
1420   ierr = PetscMalloc1(cm+1,&rowhit);CHKERRQ(ierr);
1421   ierr = PetscMalloc1(cm+1,&idxhit);CHKERRQ(ierr);
1422   for (i=0; i<nis; i++) { /* loop over color */
1423     ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
1424     ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);
1425 
1426     c->ncolumns[i] = n;
1427     if (n) {
1428       ierr = PetscMemcpy(columns_i,is,n*sizeof(PetscInt));CHKERRQ(ierr);
1429     }
1430     colorforcol[i+1] = colorforcol[i] + n;
1431     columns_i       += n;
1432 
1433     /* fast, crude version requires O(N*N) work */
1434     ierr = PetscMemzero(rowhit,cm*sizeof(PetscInt));CHKERRQ(ierr);
1435 
1436     for (j=0; j<n; j++) { /* loop over columns*/
1437       col     = is[j];
1438       row_idx = cj + ci[col];
1439       m       = ci[col+1] - ci[col];
1440       for (k=0; k<m; k++) { /* loop over columns marking them in rowhit */
1441         idxhit[*row_idx]   = spidx[ci[col] + k];
1442         rowhit[*row_idx++] = col + 1;
1443       }
1444     }
1445     /* count the number of hits */
1446     nrows = 0;
1447     for (j=0; j<cm; j++) {
1448       if (rowhit[j]) nrows++;
1449     }
1450     c->nrows[i]      = nrows;
1451     colorforrow[i+1] = colorforrow[i] + nrows;
1452 
1453     nrows = 0;
1454     for (j=0; j<cm; j++) { /* loop over rows */
1455       if (rowhit[j]) {
1456         rows_i[nrows]   = j;
1457         den2sp_i[nrows] = idxhit[j];
1458         nrows++;
1459       }
1460     }
1461     den2sp_i += nrows;
1462 
1463     ierr    = ISRestoreIndices(isa[i],&is);CHKERRQ(ierr);
1464     rows_i += nrows;
1465   }
1466   ierr = MatRestoreColumnIJ_SeqAIJ_Color(mat,0,PETSC_FALSE,PETSC_FALSE,&ncols,&ci,&cj,&spidx,NULL);CHKERRQ(ierr);
1467   ierr = PetscFree(rowhit);CHKERRQ(ierr);
1468   ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);
1469   if (csp->nz != colorforrow[nis]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csp->nz %d != colorforrow[nis] %d",csp->nz,colorforrow[nis]);
1470 
1471   c->colorforrow = colorforrow;
1472   c->rows        = rows;
1473   c->den2sp      = den2sp;
1474   c->colorforcol = colorforcol;
1475   c->columns     = columns;
1476 
1477   ierr = PetscFree(idxhit);CHKERRQ(ierr);
1478   PetscFunctionReturn(0);
1479 }
1480